Characterizing the Impacts of Significant
Wind Generation Facilities on Bulk Power
System Operations Planning
Xcel Energy – North Case Study
Final Report
Prepared for
The Utility Wind Interest Group
In Cooperation with:
Xcel Energy
NRECA Cooperative Research Network
American Public Power Association DEED
Western Area Power Administration
Electric Power Research Institute
By
2111 Wilson Boulevard, Suite 323
Arlington, VA 22201
Telephone: 703-351-4492
Facsimile: 703-351-4495
May 2003
i
Characterizing the Impacts of Significant
Wind Generation Facilities on Bulk Power
System Operations Planning
Xcel Energy – North Case Study
Final Report
Authors:
Daniel Brooks, Project Manager
Edward Lo, Principal Investigator
Robert Zavadil, Senior Consultant
Surya Santoso, Project Engineer
Jeff Smith, Senior Engineer
Prepared for:
Utility Wind Interest Group
2111 Wilson Blvd., Suite 323
Arlington, Virginia 22201
703.351.4492 x121
www.uwig.org
J. Charles Smith, Senior Technical Advisor
Karen Lane, Project Coordinator
ii
~ Table of Contents ~
PREFACE....................................................................................................................................... I
ACKNOWLEDGMENTS ..........................................................................................................III
EXECUTIVE SUMMARY ..........................................................................................................V
1
INTRODUCTION................................................................................................................ 1-1
1.1 PROBLEM DEFINITION ........................................................................................................ 1-2
1.2 ANALYTICAL APPROACH AND RELATED WORK ............................................................... 1-3
2
ANALYTICAL APPROACH ............................................................................................. 2-1
2.1 NEED FOR A NOVEL APPROACH AND METHODOLOGY ....................................................... 2-1
2.2 OVERVIEW OF POWER SYSTEMS OPERATIONS AND PLANNING ....................................... 2-2
2.2.1 AGC AND ECONOMIC DISPATCH ...................................................................................... 2-2
2.2.2 UNIT COMMITMENT .......................................................................................................... 2-3
2.2.3 LOAD FORECASTING ......................................................................................................... 2-3
2.3 WIND MODEL REQUIREMENTS .......................................................................................... 2-4
2.4 NSP CASE STUDY ANALYTICAL FRAMEWORK ................................................................. 2-4
2.4.1 COST OF WIND GENERATION FORECAST INACCURACY..................................................... 2-7
2.4.2 COST IMPACT OF WIND ON FOLLOWING INTRA-HOUR CHANGES IN LOAD ....................... 2-8
2.4.3 IMPACT OF WIND ON REGULATING MINUTE-TO-MINUTE FLUCTUATIONS IN LOAD ........ 2-10
3
SYSTEM DESCRIPTION .................................................................................................. 3-1
3.1 EXISTING NSP WIND PLANT ............................................................................................. 3-1
3.2 NSP CONTROL AREA CHARACTERISTICS ......................................................................... 3-3
3.2.1 NSP GENERATION RESOURCES......................................................................................... 3-4
3.2.2 LOAD ................................................................................................................................ 3-7
3.2.3 NSP OPERATIONAL PROCEDURES..................................................................................... 3-9
3.2.3.1 Contingency reserve requirement ................................................................................. 3-9
3.2.3.2 Day-ahead planning ...................................................................................................... 3-9
3.2.3.3 Real-time operation..................................................................................................... 3-10
iii
3.2.3.4
3.2.3.5
4
Energy Transactions.................................................................................................... 3-11
Integration of wind plant............................................................................................. 3-11
WIND MODELING RESULTS ......................................................................................... 4-1
4.1 WIND GENERATION TIME SERIES SYNTHESIS MODEL ..................................................... 4-1
4.1.1 USE OF THE MODEL .......................................................................................................... 4-1
4.1.2 TIME SCALES OF THE MODEL ............................................................................................ 4-1
4.1.3 MARKOV PROBABILITY IN STATE TRANSITION ................................................................. 4-2
4.2 DATA SOURCES FOR PROBABILISTIC MODEL DEVELOPMENT ......................................... 4-3
4.3 SAMPLE OUTPUT OF THE SYNTHESIS MODEL ................................................................... 4-4
4.3.1 TRANSITION MATRIX ........................................................................................................ 4-4
4.4 SAMPLE GENERATED TIME SERIES ................................................................................... 4-6
4.5 TIME-DEPENDENCE CONSIDERATION OF THE MARKOV PROBABILISTIC MODEL
FOR CASE STUDY UTILITY .......................................................................................................... 4-9
4.5.1 HOURLY PROBABILISTIC MODEL ...................................................................................... 4-9
4.6 5-MINUTE AND 4-SECOND PROBABILISTIC MODEL ........................................................ 4-10
4.7 PROBABILISTIC MODEL VALIDATION ............................................................................. 4-11
4.8 WIND PLANT OPERATION RESERVE REQUIREMENT ASSESSMENT ................................ 4-12
4.8.1 RESERVE REQUIRED FOR WIND PLANT OPERATION........................................................ 4-12
4.9 STATISTICS OF WIND GENERATION FLUCTUATION ........................................................ 4-13
4.9.1 REGULATING RESERVE ................................................................................................... 4-14
4.9.2 LOAD FOLLOWING RESERVE ........................................................................................... 4-15
4.10 RESULTS ANALYSIS .......................................................................................................... 4-15
5
UNIT COMMITMENT OPERATION SCHEDULING STUDY ................................... 5-1
5.1 STUDY OBJECTIVES ............................................................................................................ 5-1
5.2 UNIT COMMITMENT STUDY FRAMEWORK ........................................................................ 5-2
5.2.1 SEASONAL SCENARIOS ...................................................................................................... 5-2
5.2.2 GENERAL APPROACH AND ASSUMPTIONS ......................................................................... 5-4
5.2.3 SPECIFIC APPROACH FOR DETERMINING WIND ENERGY VALUE ...................................... 5-6
5.2.4 SPECIFIC APPROACH FOR DETERMINING SYSTEM OPERATIONS COST IMPACT OF
INACCURATE WIND FORECAST ..................................................................................................... 5-6
5.3 COMPUTATIONAL ASPECTS ............................................................................................. 5-10
5.4 SIMULATION RESULTS ..................................................................................................... 5-11
5.4.1 NO WIND AND PERFECTLY FORECASTED WIND CASES .................................................. 5-11
5.4.2 INACCURATE WIND FORECAST CASES ............................................................................ 5-16
5.4.2.1 Impact of Inaccurate Forecast on Forward Energy Purchases -- Winter Scenario ..... 5-16
5.4.2.2 Impact of Inaccurate Forecast on Total Production Cost -- Winter Scenario............. 5-18
5.4.2.3 Impact of Inaccurate Forecast on Forward Energy Purchases -- Summer
Scenario 5-21
5.4.2.4 Impact of Inaccurate Forecast on Total Production Cost -- Summer Scenario .......... 5-23
5.5 STRATEGY IN OPERATION PLANNING FOR WIND GENERATION FORECAST WITH
RANDOM ERROR........................................................................................................................ 5-27
iv
5.5.1 COST OF INACCURACY FUNCTION AND LINEARITY ASSUMPTION ................................... 5-27
5.5.2 PROBABILITY DENSITY OF FORECAST ERROR ................................................................. 5-29
5.5.3 EXPECTED EXTRA OPERATING COST FOR DIFFERENT SCALING STRATEGIES.................. 5-30
5.5.3.1 Strategy A – No Scaling ............................................................................................. 5-30
5.5.3.2 Strategy B – Scale Forecasts by 50% ......................................................................... 5-31
5.5.3.3 Strategy C – Scale Forecasts by 200% ....................................................................... 5-32
5.5.3.4 Strategy D – Scale Forecasts so Upper Error Distribution Range Equals Actual
Generation.................................................................................................................................. 5-34
5.5.3.5 Determination of Optimal Scaling Strategy................................................................ 5-35
5.5.4 EXPECTED EXTRA COST INCURRED BY NSP DUE TO WIND GENERATION FORECAST
INACCURACY IN DAY-AHEAD UC SCHEDULING ......................................................................... 5-36
5.5.4.1 Winter Scenario .......................................................................................................... 5-36
5.5.4.2 Summer Scenario ........................................................................................................ 5-37
5.5.4.3 Annualized Cost Value ............................................................................................... 5-37
6
INTRA-HOUR LOAD FOLLOWING STUDY................................................................ 6-1
6.1 LOAD FOLLOWING COST DEFINITION ............................................................................... 6-1
6.1.1 RESERVE COMPONENT OF LOAD FOLLOWING COST ......................................................... 6-2
6.1.2 ENERGY COMPONENT OF LOAD FOLLOWING COST ........................................................... 6-3
6.2 HISTORICAL DATA ANALYSIS ............................................................................................ 6-4
6.3 LOAD FOLLOWING ASSESSMENT APPROACH.................................................................... 6-4
6.3.1 COMPLETE APPROACH ...................................................................................................... 6-4
6.3.1.1 Reserve Component Calculation Details ...................................................................... 6-5
6.3.1.2 Energy Component Calculation Details........................................................................ 6-6
6.3.2 IMPLEMENTATION FOR NSP CASE STUDY ........................................................................ 6-7
6.3.2.1 Reserve Component ...................................................................................................... 6-8
6.3.2.2 Energy Component ..................................................................................................... 6-10
6.4 SIMULATION RESULTS ..................................................................................................... 6-14
6.4.1 COMPUTATIONAL ASPECTS ............................................................................................. 6-14
6.4.2 LF ENERGY COMPONENT SIMULATION RESULTS ........................................................... 6-15
7
REGULATION STUDY- LOAD FREQUENCY CONTROL ........................................ 7-1
7.1 STUDY OBJECTIVE.............................................................................................................. 7-2
7.2 REGULATION STUDY APPROACH ....................................................................................... 7-3
7.2.1 SCENARIO ......................................................................................................................... 7-3
7.2.2 SIMULATION TOOL............................................................................................................ 7-4
7.2.3 COMPUTATIONAL ASPECTS ............................................................................................... 7-4
7.3 LFC SIMULATION RESULTS .............................................................................................. 7-5
8
CONCLUSIONS AND RECOMMENDATIONS............................................................. 8-1
8.1 WORK ACCOMPLISHED ...................................................................................................... 8-1
8.2 SUMMARY OF ANALYSIS RESULTS ..................................................................................... 8-2
v
8.3
9
RECOMMENDED FUTURE WORK ....................................................................................... 8-5
REFERENCES..................................................................................................................... 9-1
APPENDIX A:
SUMMARY OF RELATED WORKS ...................................................... A-1
APPENDIX B:
UNIT COMMITMENT PRIMER..............................................................B-1
B.1 BACKGROUND .................................................................................................................... B-1
B.1.1 SPINNING RESERVE REQUIREMENT IN REAL TIME ........................................................... B-2
B.1.2 NSP UC RESERVE REQUIREMENTS ................................................................................. B-2
B.2 UNIT COMMITMENT IN HOURLY RESOLUTION ................................................................ B-3
B.3 EXAMPLE #1 -- UNIT COMMITMENT SCHEDULE AND INTRA-HOUR REAL-TIME
OPERATION ................................................................................................................................. B-4
B.4 EXAMPLE #2 -- LOAD FOLLOWING RESERVE FOR UNIT COMMITMENT ........................ B-8
APPENDIX C:
Y2000 NSP HOURLY WIND GENERATION DATA............................ C-1
C.1 JANUARY 2000- APRIL 2000 ............................................................................................. C-1
C.2 MAY 2000- AUGUST 2000 ................................................................................................. C-2
C.3 SEPTEMBER 2000 – DECEMBER 2000 ............................................................................... C-3
APPENDIX D:
SUMMARY OF RELATED WORKS ...................................................... D-1
APPENDIX E:
SAMPLE COUGERPLUS SOLUTION OUTPUT...................................E-1
APPENDIX F:
DESCRIPTION OF ECONOMIC DISPATCH TOOL............................F-1
F.1
F.2
F.3
F.4
ECONOMIC DISPATCH FORMULATION ..............................................................................F-1
SOME IMPLEMENTATION DETAILS ....................................................................................F-3
IMPLEMENTATION EXAMPLE .............................................................................................F-4
EXAMPLE ............................................................................................................................F-4
vi
~ List of Figures ~
Figure 2-1. Flowchart representing the analytical framework utilized for the NSP wind impacts case study.
........................................................................................................................................................... 2-6
Figure 3-1 Geographical Location of Lake Benton Wind Farm.................................................................. 3-2
Figure 3-2 One-Line Diagram of Buffalo Ridge Substation ....................................................................... 3-3
Figure 3-3 Control Area Map of NSP.......................................................................................................... 3-4
Figure 3-4. NSP January 2001 hourly load profile and categorized generation plotted against the NDC
capacity of NSP’s 57 thermal generating units that are included in the NSP AGC generating unit
database.............................................................................................................................................. 3-5
Figure 3-5. NSP July 2001 hourly load profile and categorized generation plotted against the NDC capacity
of NSP’s 57 thermal generating units that are included in the NSP AGC generating unit database.. 3-6
Figure 3-6. NSP 72-hour summer load profile plotted against the NDC capacity of NSP’s 57 thermal
generating units that are included in the NSP AGC generating unit database. .................................. 3-7
Figure 3-7 Xcel Energy Hourly Load Profile of Jan 2-4, 2001 ................................................................... 3-8
Figure 3-8 Xcel Energy Hourly Load Profile of July 18-20, 2001 .............................................................. 3-8
Figure 3-9. Comparison of NSP hourly load and total generation for January 2-4, 2001. ....................... 3-10
Figure 4-1 Sample Transition Matrix-View 1 (Hourly Resolution) ............................................................ 4-5
Figure 4-2 Sample Transition Matrix-View 2 (Hourly Resolution) ............................................................ 4-5
Figure 4-3. Sample 72-hour Synthetic Series .............................................................................................. 4-6
Figure 4-4 Sample 1-hour-horizon synthesized series................................................................................. 4-8
Figure 4-5 Sample 5-minute, 4-second resolution synthesized series ......................................................... 4-9
Figure 4-6 Hourly Average Wind Farm Output for Each Season (Year 2000) ......................................... 4-10
Figure 4-7. Monthly MWh Value for Each Month.................................................................................... 4-10
Figure 4-8. Probability Distribution Function for Hourly Measured Data and Synthetic Series............... 4-11
Figure 4-9. Probability Distribution Function for 5-Minute Measured Data and Synthetic Series ........... 4-12
Figure 4-10 Regulation Time Scale Wind Generation Variability Plots (Month of Year Basis) .............. 4-16
Figure 4-11 Load Following Time Scale Wind Generation Variability Plots (Month of Year Basis) ...... 4-17
Figure 4-12 Load Following Time Scale Wind Generation Variability Plots (MW Range) ..................... 4-18
Figure 5-1 Load, Generation and Interchange Profile of NSP Jan 2-4, 2001 .............................................. 5-3
Figure 5-2 Load, Generation and Interchange Profile of NSP July 18-20, 2001......................................... 5-4
Figure 5-3 Hourly Generation of all Peaking Units during January 2001 ................................................... 5-7
Figure 5-4 Hourly Generation of all NSP Peaking Units during July 2001................................................. 5-8
Figure 5-5. Flow chart summarizing process for assessing cost impact of imperfect wind forecasting on
day-ahead scheduling....................................................................................................................... 5-10
Figure 5-6 Distribution of Total Cost with Wind Generation, Winter Case.............................................. 5-11
Figure 5-7 Distribution of Total Cost with Wind Generation, Summer Case ........................................... 5-12
Figure 5-8 Comparison of the simulated and measured load, generation and interchange profiles for the
winter scenario, no wind generation case. ....................................................................................... 5-13
Figure 5-9 Comparison of the simulated and measured generation profiles of the 3 Sherco units for the
winter scenario, no wind generation case. ....................................................................................... 5-14
Figure 5-10 Comparison of the simulated and measured load, generation and interchange profiles for the
summer scenario, no wind generation case...................................................................................... 5-15
Figure 5-11. Comparison of the simulated and measured generation profiles of the 3 Sherco units for the
summer scenario, no wind generation case...................................................................................... 5-15
Figure 5-12 Distribution of Energy Purchase for +/- 10% Forecast Inaccuracy, Winter Case.................. 5-17
Figure 5-13 Distribution of Energy Purchase for +/- 20% Forecast Inaccuracy, Winter Case.................. 5-17
Figure 5-14 Distribution of Energy Purchase for +/- 50% Forecast Inaccuracy, Winter Case.................. 5-18
Figure 5-15 Distribution of Cost for +/- 10% Forecast Inaccuracy, Winter Case ..................................... 5-19
Figure 5-16 Distribution of Cost for +/- 20% Forecast Inaccuracy, Winter Case ..................................... 5-19
Figure 5-17 Distribution of Cost for +/- 50% Forecast Inaccuracy, Winter Case ..................................... 5-20
Figure 5-18 Plots of Expected Cost versus Forecast Inaccuracy - Winter Case ........................................ 5-21
vii
Figure 5-19 Distribution of Energy Purchase for +/- 10% Forecast Inaccuracy, Summer Case ............... 5-22
Figure 5-20 Distribution of Energy Purchase for +/- 20% Forecast Inaccuracy, Summer Case ............... 5-22
Figure 5-21 Distribution of Energy Purchase for +/- 50% Forecast Inaccuracy, Summer Case ............... 5-23
Figure 5-22 Distribution of Cost for +/- 10% Forecast Inaccuracy, Summer Case ................................... 5-24
Figure 5-23 Distribution of Cost for +/- 20% Forecast Inaccuracy, Summer Case ................................... 5-24
Figure 5-24 Distribution of Cost for +/- 50% Forecast Inaccuracy, Summer Case ................................... 5-25
Figure 5-25 Plot of Expected Cost versus Forecast Inaccuracy, Summer Case ........................................ 5-26
Figure 5-26 Linearized Inaccuracy Cost Functions for Winter Case......................................................... 5-28
Figure 5-27 Linearized Inaccuracy Cost Functions for Summer Case ...................................................... 5-28
Figure 5-28. Assumed uniformly distributed forecast error probability density function. ........................ 5-30
Figure 5-29. Change in forecast error distribution in UC day-ahead planning using scaling Strategy B. . 5-32
Figure 5-30. Change in forecast error distribution in UC day-ahead planning using scaling Strategy C. . 5-33
Figure 5-31. Change in forecast error distribution in UC day-ahead planning using scaling Strategy D.. 5-35
Figure 6-1 Comparison of LFRR for load only and for load and wind generation based on January 2001
data..................................................................................................................................................... 6-9
Figure 6-2 Comparison of LFRR for load only and for load and wind generation based on July 2001 data. 610
Figure 6-3. Load profiles for selected hours that are used in ED simulations. .......................................... 6-11
Figure 6-4. Flowchart of approach implemented for determining NSP load following energy component
cost attributable to wind generation. ................................................................................................ 6-13
viii
~ List of Tables ~
Table 3-1. NSP Control Area Load Max and Min for January, April and July 2001 .................................. 3-7
Table 3-2 Peak Hourly Import of January, April and July 2001................................................................ 3-10
Table 4-1. Hourly Standard Deviation and Mean Calculated from Real Measurements and Synthetic Series
......................................................................................................................................................... 4-11
Table 4-2. 5-Minute Standard Deviation and Mean Calculated from Real Measurements and Synthetic
Series................................................................................................................................................ 4-12
Table 4-3 Wind Generation and System Load Variation Statistics in Regulation Time Scale.................. 4-16
Table 4-4 Load Following Time Scale Wind Generation Statistics, Based on Month of Year ................. 4-18
Table 4-5 Load Following Time Scale Wind Generation Statistics, Based on Hourly Energy Level ....... 4-18
Table 5-1 Statistics of Wind Generation Time Series ................................................................................. 5-4
Table 5-2 Hypothetical Transaction Price Schedule for Simulation Winter Case....................................... 5-5
Table 5-3 Hypothetical Transaction Price Schedule for Simulation Summer Case .................................... 5-5
Table 5-4 Winter Scenario Simulation Results for “No Wind” and “Perfectly Forecasted Wind Generation”
Cases ................................................................................................................................................ 5-11
Table 5-5. Summer Scenario Simulation Results for no Wind and with Wind Generation Cases ............ 5-12
Table 5-6. Operating Cost for Different Percentages of Forecast Error, Winter Case .............................. 5-20
Table 5-7. Extra Operating Cost for Different Percentages of Forecast Error, Winter Case..................... 5-20
Table 5-8. Operating Cost for Different Percentages of Forecast Error, Summer Case ............................ 5-25
Table 5-9. Extra Operating Cost for Different Percentages of Forecast Error, Summer Case .................. 5-25
Table 5-10. Summary of performance for identified scaling strategies..................................................... 5-35
Table 5-11. Scaling Factors and Expected Extra Costs for Different Distribution Ranges - Strategy D... 5-36
Table 5-12. NSP’s Expected Ancillary Costs for Different Forecast Error Distribution Ranges -- Winter
Scenario ........................................................................................................................................... 5-36
Table 5-13. NSP’s Expected Ancillary Costs for Different Forecast Error Distribution Ranges -- Summer
Scenario ........................................................................................................................................... 5-37
Table 5-14. NSP’s Expected Ancillary Costs for Different Forecast Error Distribution Ranges -Annualized ....................................................................................................................................... 5-37
Table 6-1. Differential LFRR with wind generation and system load considered relative to load only.... 6-10
Table 6-2. Wind Generation Hourly MW and Hourly Ramp Rate in Simulation Study ........................... 6-12
Table 6-3. Incremental load following energy component cost for supporting wind generation. ............. 6-15
Table 7-1. ACE Average from without and with Wind Simulation ............................................................ 7-5
Table 7-2. Standard Deviation of 4-second ACE from without and with Wind Simulation ....................... 7-5
Table 7-3. Standard Deviation of 1-minute-average ACE from without and with Wind Simulation.......... 7-5
Table 8-1. Cost of wind forecast inaccuracy as a function of the distribution range of forecast error. ....... 8-3
ix
x
Preface
The Utility Wind Interest Group (UWIG) was formed in 1989 by a group of eight utility
companies, with leadership and financial support from wind energy programs at the U.S.
Department of Energy (DOE) and the Electric Power Research Institute (EPRI). UWIG
was formed to provide a forum for utility-to-utility education on wind power issues and
experience, and to conduct outreach on progress with wind power for electric utility
applications. In 1994, UWIG incorporated as a non-profit organization. Since that time,
membership has expanded to some 55 organizations in the electric-utility, winddeveloper and technical-support sectors. Many in the utility and wind-power
communities have become familiar with a series of topical brochures UWIG has
produced over the years on key wind and utility issues.
The work described in this report represents a major departure from the traditional
functions of UWIG. Several years ago, the group decided to address key technical issues
associated with wind power and utility integration through focused projects conducted by
qualified contractors and supported with supplemental funds. The impact of wind
power’s variability on utility system operating costs was identified through a survey of
members as the highest priority technical issue. Subsequently, UWIG staff and its Board
of Directors obtained some $350,000 of funding for a project to address this issue. Funds
were provided by the case-study utility (Xcel Energy in Minneapolis, MN), the Western
Area Power Administration, EPRI, the National Rural Electric Cooperative Association
and the American Public Power Association. In addition, wind plant operating data and
technical support were provided by the DOE Wind Energy Program through the National
Wind Technology Center at the National Renewable Energy Laboratory. A substantial
in-kind contribution was also made by the contractor for the work, Electrotek Concepts,
Inc.
This project has provided a first estimate of wind power’s impacts on utility operating
costs in a traditional vertically integrated environment through the use of planning tools
well known in the electric-utility sector. The work focuses on differential operating costs
arising from the variability of wind power over time periods ranging from seconds to
days. The results apply to the case-study utility, and would be expected to vary for
different utilities. Nonetheless, these results very likely provide a reasonable indication
of wind power’s operating-cost impacts for a wide range of utility situations where wind
penetrations are less than 5% of total system generation. As explained in detail in the
report body, a number of conservative assumptions have been made in the course of the
work with the result that wind’s impacts have likely been overstated.
I
UWIG aims to conduct additional work in this important area to gain additional insights
into wind power’s impacts on utility-system operation, and to work closely with others
who are addressing similar issues. Through these collective efforts, an accurate and
authoritative perspective on these issues is expected to emerge in the near future.
Brad Reeve
President
Utility Wind Interest Group
II
Acknowledgments
The authors of this report would like to acknowledge the support provided by a number
of organizations with the foresight and leadership necessary to undertake this
investigation. Once the topic of this report had been identified by the Utility Wind
Interest Group (UWIG) as the most critical issue facing the successful integration of large
windplants into utility systems, the UWIG committed $25,000 of its member dues to
launch this project, and sought additional funding commitments from other interested
parties to perform the work. This effort was led by Mr. Brad Reeve, Chairman of the
Board of UWIG, and General Manager of the Kotzebue Electric Association in Kotzebue,
Alaska.
Xcel Energy (Northern States Power) was interested at the time in performing such an
investigation of the impact of the Buffalo Ridge projects on its system operation. NSP
made a substantial funding commitment to the work, and offered the use of their system
as a case study. The National Rural Electric Cooperative Association (NRECA) provided
a significant contribution to the work. Additional contributions were provided by the
American Public Power Association and the Western Area Power Administration
(WAPA). The NSP and WAPA contributions received cofunding from the Electric
Power Research Institute (EPRI).
Once the project was initiated, the UWIG created a Technical Review Committee (TRC)
to provide industry overview of the work. The TRC was chaired by Dr. Ed DeMeo of
Renewable Energy Consulting Services. The membership of the TRC included:
Ed DeMeo (Chairman)
Dan Belk
Jim Caldwell
George Darr
Les Evans
Rick Halet
Mike Hasenkamp
Jim Hill
Brendan Kirby
Paul Koehler
Chuck McGowin
Mark McGree
Brenner Munger
Brian Parsons
John Pease
Rob Sims
Tom Wind
UWIG (NREL, RECS)
Western Area Power Administration
Izaak Walton League Representative / AWEA
Bonneville Power Administration
Western Resources
Xcel Energy
Nebraska Public Power District
Xcel Energy
Oak Ridge National Laboratory
PacifiCorp Representative
EPRI
Xcel Energy
Hawaiian Electric Industries
National Renewable Energy Laboratory
Bonneville Power Administration
SeaWest WindPower
Wind Utility Consulting
The TRC held several review meetings during the course of the work, asked thoughtprovoking questions, and provided valuable critique of the methodology and interim
III
results of the work. The authors would like to particularly recognize the contribution
provided by Mr. Brendan Kirby of the Oak Ridge National Laboratory (ORNL) under the
support of the USDOE. His stimulating discussions with members of the project team
based on his knowledge and experience in the industry provided valuable assistance in
formulating the load following analysis methodology. In addition, the authors gratefully
acknowledge the contributions provided through the National Renewable Energy
Laboratory (NREL) of the United States Department of Energy (USDOE) by Michael
Milligan in the area of wind modeling methodology. Although the authors appreciate the
guidance and assistance of the many parties who contributed to the work, Electrotek
Concepts accepts full responsibility for the accuracy and completeness of the report.
IV
Executive Summary
Electric generating resources that are part of the interconnected power system must be
controlled so that their aggregate output matches the electric load at any given time.
Reliable and economic operation of interconnected power systems relies on multiple
layers of automatic control systems to insure that generator output follows the changes in
load. The continually fluctuating and mostly uncontrollable nature of wind generation
impacts the control systems in all time frames. Consequently, the operational and
scheduling systems must adjust generating patterns to accommodate the variability in the
wind in order to maintain the same level of system reliability.
In a 1999 survey of its members, the Utility Wind Interest Group (UWIG) identified the
impact to system operations as the most important issue affecting the large-scale
integration of wind generation into electric utility systems. In the past, the penetration
level of wind generation was insignificant relative to the total utility generation capacity
such that the associated costs to accommodate the wind were considered negligible. In
recent years, however, wind generation technologies and development have progressed to
the point that individual projects have reached sizes comparable to that of typical
conventional plants. As a result, identifying the impacts of wind generation on utility
operations has become a significant issue. Quantifying the costs associated with these
impacts is increasingly important as utilities evaluate competing capital expansion or allsource energy purchase alternatives.
UWIG contracted Electrotek Concepts, Inc. to conduct an operation impacts study using
actual utility data. Xcel Energy – North, formerly Northern States Power Co. (NSP)
offered to serve as the host utility and provide data for the study. The objectives of the
study included the following:
•
•
•
Conduct a quantitative investigation of large wind plant operating impacts on
utility operation planning
Identify operating cost impacts for the host utility system
Evaluate value of reduced wind forecast uncertainty
The analytical framework developed for evaluating the operational impacts of wind
generation integration is a simulation-based approach designed to determine the ancillary
service costs incurred by NSP to accommodate their existing 280 MW windplant. The
NSP operations impact study is conducted for 3 different time scales consistent with
NSP’s scheduling and real-time control operating procedures:
•
•
3-day (72-hour) study horizon of hourly resolution for performing unit
commitment simulations using operating costs as evaluation criteria
1-hour study horizon of 5-minute resolution for performing intra-hour load
following simulations using operating costs as evaluation criteria
V
•
1-hour study horizon of 4-second resolution for performing load frequency
control (LFC) simulations using statistics of Area Control Error (ACE) as
evaluation criteria
Traditional utility scheduling and operation tools are used in the evaluation.
These tools allow for time series simulations of the relevant scheduling and control
functions. Due to the variable and somewhat random nature of wind, the results of any
single time series simulation may not accurately represent the impacts of wind on the
scheduling and control functions. Consequently, a Monte Carlo approach is utilized,
whereby many realizations of wind generation time series are used in the simulations to
provide a distribution of results that are statistically representative of the impacts of the
NSP wind regime and not a single realization of the wind. A probabilistic wind plant
model and tool were developed using 1-second high-resolution wind data supplied by the
National Renewable Laboratory (NREL) and using 5-minute and hourly resolution wind
generation data supplied by NSP. The developed wind models were used to synthesize
multiple wind generation time series for each scenario evaluated for each of the
simulation time scales. As is often the case, however, utility system data was more
limited at the higher resolution time scales. Nonetheless, the impacts of each wind
generation time series were evaluated in a deterministic manner with the available system
data. The distribution of the impact values were compiled and used to provide a more
representative assessment.
A statistical assessment of the additional regulating reserve required for NSP to integrate
its current wind plant was performed based on the methodology published by the Oak
Ridge National Laboratory (ORNL). This assessment revealed that for the current NSP
wind generation penetration level, the additional regulating reserve required to maintain
the same level of control performance is less than 5% of what is required in the no wind
case.
The following cost impacts were assessed using the developed simulation framework:
•
•
•
•
Cost of wind generation forecast inaccuracy for day-ahead scheduling
Cost of additional load following reserves
Cost of intra-hour load following “energy component”
Cost of additional regulation reserves
Cost of wind generation forecast inaccuracy for day-ahead scheduling. Unit commitment
simulations were performed to assess the cost incurred by NSP to re-schedule units
because of unavoidable inaccuracy associated with the wind generation forecasts used in
the day-ahead scheduling. Several assumptions were utilized in the problem formulation,
partly to simplify the evaluation model and partly to account for unavailable data. The
methodology utilized provided a cost impact based on the assumed distribution range of
forecast error, all of which are shown in Table ES - 1. The results of the study also
enabled the derivation of a specific operational planning strategy, similar to a loosely
defined procedure already used by NSP, to hedge against the adverse effect of wind
generation forecast uncertainty. The results shown in Table ES - 1 are based on this
VI
hedging strategy. As demonstrated in the results, the cost impacts decrease as the
forecast accuracy increases.
Table ES - 1. Cost of wind forecast inaccuracy as a function of the distribution range of forecast
error.
Distribution Range %
Extra Cost ($/MWh)
10
0.391
20
0.716
30
0.995
40
1.231
50
1.436
As noted, many assumptions were made in modeling NSP’s system operations, many of
which the investigators believe provide a conservative estimate of the cost impacts.
Perhaps the most notable of these conservative assumptions was the assumption of
perfect load forecasting, such that no diversity was achieved in modeling the wind
forecasting uncertainty. Evaluation of the impacts of the wind uncertainty in isolation
yields a “worst-case” analysis of the forecast uncertainty impact cost component. It
should also be noted that the forecast uncertainty results obtained are strongly correlated
to the vertically-integrated operations environment modeled for NSP. The availability of
a fluid hour-ahead market or a regional imbalance energy market would likely reduce the
calculated cost impacts.
Cost of additional load following reserves. Calculation of the load following reserve
requirement (LFRR) of the NSP hourly resolution control area load and aggregate wind
generation data for January and July of 2000 indicated that the addition of wind does not
significantly increase the LFRR. Consequently, the reserve component of the load
following cost is assumed to be zero without performing the unit commitment
simulations that would be required to obtain a specific cost impact value. It should be
noted that this determination is for the existing NSP wind penetration level. Assuming a
reserve component cost of zero for wind means that the energy component assessed using
intra-hour economic dispatch simulation will be higher than the energy component cost
that would be calculated if additional load following reserves were added to support the
wind.
Cost of intra-hour load following “energy component”. Economic dispatch simulations
were performed to evaluate the cost of following the intra-hour ramping and fluctuation
of wind generation. This cost is referred to as the intra-hour load following “energy
component” because it is the cost of deploying the available load following reserve to
meet the intra-hour slow variation of load changes. Economic dispatch simulations were
performed for four hours of the day selected to represent the different load ramping and
wind variation characteristics associated with NSP’s typical daily load curve. The
average cost for a day was extrapolated from the simulations for these four hours by
dividing a day into 4 different periods based on the load ramping characteristic with each
period including a simulated hour. Additional assumptions and extrapolations were made
to obtain an annualized intra-hour load following “energy component” cost of
approximately 41¢/MWh.
VII
Cost of additional regulation reserves. Load frequency control (LFC) simulations were
performed for 4 representative hours of the day to calculate the impact of minute-byminute system load and wind generation fluctuation on NSP’s area control error (ACE)
statistics. Simulations were performed for no wind generation versus NSP’s current wind
generation penetration level without extra regulating reserve. Results show almost no
change in the ACE standard deviation between the without and with wind generation
scenarios. This suggests that NSP’s current wind penetration of 280 MW on an 8000 MW
peak system has no impact on the control performance. This means that for NSP’s current
wind penetration level and regulating capacity and for the reserves allocated in the
simulations, the variability of the wind on the 4-second time frame didn't significantly
affect the capability of the system to follow these variations. Accordingly, the cost impact
of additional regulating reserves to accommodate wind is assumed negligible. It should
be noted that the regulating burden does increase, however, by approximately 4%. The
existing system is able to absorb this increase such that the increase does not impact the
performance criteria.
Summing the cost impact results for the four components assessed using the distribution
forecast error range of ±50%, the impact of integrating NSP’s existing 280 MW
windplant is found to be approximately $1.85/MWh of wind generation. It should be
noted that it is very difficult to exactly model all of the operational scheduling and realtime operation procedures for a given utility and to obtain all of the necessary data, so
assumptions and extrapolations were made for the developed models. The investigators
attempted to select these simplifying measures such that the effect was to produce a more
conservative (more significant) impact. The results are, however, specific to the NSP
system, as it currently exists.
Much was learned from conducting this pioneering effort to calculate the cost of
integrating wind for a specific control area. The sensitivity of the results to many critical
modeling assumptions and parameter values should be studied further, including the
following specific sensitivities:
•
•
•
•
Market structure and imbalance pricing versus the modeled vertically-integrated
environment, which is scheduled to change significantly by the end of 2003.
Forecast uncertainty impacts considering load forecasting error versus the
evaluation of wind forecasting uncertainty in isolation.
Varying wind generation penetration levels.
Varying generation portfolio mix.
These additional analyses will provide a fuller understanding of the impacts of integrating
bulk wind generation into the NSP system and insights to extrapolate the results to other
systems. A very powerful simulation tool that can be used to examine the operating
impacts of integrating large amounts of wind generation into utility systems has been
developed. It can be used to examine a large variety of utility system characteristics and
operating scenarios to gain a much better understanding of the cost of wind integration
and the cost sensitivity to critical parameters. Additional sensitivity study and scenario
VIII
analysis are required to realize the full value of the tools and methodology that have been
developed.
IX
X
1 Introduction
Sometime during the mid to late 1990’s, wind generation in the United States crossed the
threshold to commercial reality. In times prior, wind generation was still a novelty and
mostly an unknown to all but a few domestic electric utility companies. Most thought of
it as just a “California thing.” Out of view of the electric power industry mainstream,
wind energy researchers, developers, and manufacturers were continuing the steady
progress of the late 1980’s and early 1990’s towards improving the hardware of wind
energy conversion. Lessons learned from previous generations of turbines were being
applied to improve the following generations, which resulted in increases in energy
production and availability as well as declines in capital costs and annualized cost of
energy. At the same time, others were working to create the first “markets” for wind
energy through the promotion and implementation of green energy programs and other
federal and state incentives for production of electric energy from renewable fuels and
resources.
Construction of large windplants outside of California is an obvious marker for this
important milestone in the industry. When developers moved to take advantage of the
vast wind resources of the Great Plains and Texas, installed wind generation capacity in
this region increased from tens of MW to over 1500 MW in a span of less than five years.
As a result, a number of utility companies received their first exposure to significant wind
generation, all the while noting the short lead times to plant commissioning and
commercial operation.
That the speed of the wind fluctuates is apparent to everyone. For electric utility
operators facing a utility-scale generating resource powered by the wind for the first time
– i.e. a windplant with an order of magnitude nameplate rating comparable to a more
conventional utility power plant with only a single interconnection to the transmission
network - the more precise nature of the variability became the question of the day.
Reliable and low-cost operation of the interconnected electric utility system is not a
“natural” state, but rather one that requires the uninterrupted vigilance, cooperation, and
coordination of a multitude of electric utility control centers and even more operations
personnel. How can a generating resource with a fuel source as capricious as the wind be
fit into the elaborate scheduling and operating routines designed to keep the lights on at
the lowest cost?
Utility control areas are where electric supply is kept in delicate balance with electric
demand. Control areas contain load, electric generating resources, and tie lines or
transmission interconnections with other, usually adjacent, control areas. Within these
areas, system operators schedule generating capacity to meet forecast demand over
periods ranging from ten minutes to two weeks. Adequate reserves must be kept on to
cover contingencies like the forced outage of a unit or the loss of a major transmission
network element. Some capacity must be allocated to respond to short-term changes in
the control area load that cannot be forecast accurately. Scheduled exchanges of capacity
and energy with other control areas must be executed. Finally, given all of these
1-1
constraints, the supply system should be scheduled and operated in a manner that will
minimize production costs.
Wind generation differs from the other uncertainties with which system operators
routinely deal mostly because it is new, and partly because the uncertainty in how fast the
wind will be blowing a few minutes, hours, or days from now is higher than, say, how
much water a reservoir powering a hydroelectric generating station might contain over
the same time frames. Wind speed and rainfall in a watershed are both stochastic
variables, but the latter is certainly better understood by utility system operators and
planners due to history and experience.
Actions taken by control area operators to maintain system voltage, frequency, and
security are categorized as ancillary services. To provide these services, operators
dispatch certain generating units assigned to the various regulating functions and deploy
other transmission network equipment such as capacitor banks. Ancillary services, vital
to the reliable operation of the power system, cost money to provide. In the days of
vertically integrated monopoly utilities, ancillary services were simply a part of the cost
of doing business. In this new era of competition in the bulk power industry, ancillary
services are to be bought and sold in auctions, with prices fluctuating according to the
needs of the system - ancillary services demand - and the ability and willingness of
generator owners to provide them.
Competition in bulk power markets is a relatively new thing, and implementation of
market competition in electric generation across the U.S. is not uniform. Some regions of
the country have well-functioning competitive markets for energy, capacity, and certain
ancillary services. In others, the transition to increased competition and deregulation is
slow such that control areas are operated much as they were under the vertically
integrated utility monopoly. Flaws in market structure, as so dramatically highlighted in
the California power crisis of 2000 and 2001, may have further slowed this transition,
such that in the near term, many utilities may continue to operate as vertically-integrated
monopolies responsible for providing their own ancillary services.
1.1 Problem definition
All users of the bulk power system – generators and users alike – contribute to the
amount of ancillary services that must be procured and delivered by the control area
operators. For wind generation, the major question is by what amount they require more
of these services on a per MW basis than conventional generators or loads.
The Utility Wind Interest Group (UWIG) membership had also identified the impact of
large wind plants on utility system operations as a high priority research topic. A case
study involving Xcel Energy -- North -- formerly Northern States Power Company (NSP)
of Minneapolis, Minnesota-- was commissioned to address the question in the context of
an actual utility system with existing wind generation resources of significant size. The
objectives of the study were to determine the actual incremental costs incurred in the
scheduling and real-time operations functions due to uncertainty about the output of the
1-2
wind plant on these time frames for the specific utility system under consideration. The
results of that study are documented in this report.
1.2 Analytical Approach and Related Work
Utility system integration issues related to wind generation have been studied for years.
Much of the early work was devoted to quantifying the value of wind energy in terms of
energy and capacity over some longer-term planning horizon. In the generation
expansion planning framework, analytical techniques employing production cost
calculations and reliability modeling were utilized to calculate various indices to
determine the energy and capacity value of wind generation. Conventional tools for
expansion planning were modified and adapted so that the variability and uncertainty of
wind generation could be quantitatively considered. Effective load carrying capability
(ELCC) or incremental improvements in system reliability were typical measures used to
compare the value of wind energy to more conventional resources.
Technical and economic impacts on a much shorter time frame are the subject of this
study. Given the state of the bulk power industry in the U.S., this problem could be
approached in two ways. The first would employ the framework of competitive and
deregulated markets for bulk power. Wind plants would play by the same “rules” as
conventional generators, bidding into next-day, hour-ahead, and possibly even real-time
markets for energy. In well-functioning markets, ancillary service charges would be a
combination of those explicit charges levied via tariff – such as a regulation or scheduling
charge based on nameplate rating of the facility – and any “penalties” incurred for not
meeting scheduled deliveries of energy in the real-time and forward markets.
A more conventional utility cost-based methodology provides another way to approach
the problem. Traditional utility operations utilize tools for committing, scheduling, and
operating generating units that simultaneously consider technical constraints necessary
for meeting system performance targets and maintaining security and economic
parameters for minimizing overall production cost. With this framework, cases can be
defined to elicit the incremental costs related to accommodating wind generation.
Statistical techniques used in combination with such an analytical method can account for
the variability and uncertainty of wind plant production.
The market-based analysis is likely the way of the future, although recent events in
California have definitely slowed the transition to this new structure in some regions. For
this case study, however, operations procedures of the system more closely paralleled
conventional utility operations, with some consideration of market-based mechanisms for
power purchases from adjacent control areas. Additionally, at the time this study was
commissioned, most ancillary service markets around the country were in their infancy,
and in a state of flux. For these reasons, a conventional cost-based methodology was
adopted for the case study.
Quantifying the impacts of bulk wind generation on system operation and control for a
specific utility is obviously a complex problem, but is necessary for wind energy to
maintain the momentum developed in the last two decades. As wind penetration levels
1-3
increase to the point that system operations are impacted, or at least perceived to be
impacted, utilities must understand any associated cost or reliability impacts. Otherwise,
unnecessary barriers will develop. Section 2 explains the general framework
implemented to assess these impacts for the NSP control area. Sections 3 through 7
provide detailed explanations of the methods used to determine the various potential
impacts, as well as the quantitative results obtained with the methods. Section 8
summarizes the aggregate findings of the study and provides recommendations for future
work.
1-4
2 Analytical Approach
The objective of this study was to quantitatively investigate the impacts on power system
operations and scheduling of integrating bulk wind generation. Given the sensitivity of
these impacts to specific operational procedures and system generating resource
characteristics, the study was performed as a specific case study using actual utility
system data. The specific case study objective was to determine the cost and control
performance impacts of integrating the existing 280 MW wind plant from Buffalo Ridge
into the Xcel Energy – North (NSP) control area. This section provides an overview of
the analytical framework utilized to estimate these impacts. The source of the various
impact components is identified, as well as an overview of the tools used to quantify
them. Detailed explanations of the complete approach utilized to determine the various
cost components are provided in subsequent sections of the report.
2.1 Need for a novel approach and methodology
Electric generating resources that are part of the interconnected power system must be
controlled so that their aggregate output matches the electric load at any given time.
Frequency deviations and unscheduled tie-line transfers between control areas are
indicators of a mismatch between load and generation. Reliable and economic operation
of interconnected power systems relies on operational planning and multiple layers of
automatic control systems to insure that generator output follows the changes in load. At
the same time, these systems must keep the operation of individual system components
within safe limits and maintain adequate security margins for likely contingencies.
The variable and mostly uncontrollable nature of wind generation introduces additional
considerations into the power system scheduling and control problem. Integration of a
continually fluctuating, uncontrolled generation resource such as wind impacts system
operations in all time frames. Consequently, the operational and scheduling systems
adjust the generating patterns to accommodate the variability in the wind in order to
maintain the same level of system reliability. These adjustments ensure that sufficient
generation is available to meet the control area load and interchange schedules in various
operational/control time frames. These adjustments also result in a higher cost of
operation as compared with the hypothetical situation of wind generation being perfectly
dispatchable. In a vertically integrated environment, each individual utility implements
these operational and control adjustments based on available resources and bears the
associated costs. In a deregulated electric power market environment, competitive
markets may exist to provide these additional services required to support wind [Hirst
1995-1]. These markets are referred to as “ancillary service” markets.
Valuation of the additional cost required to support the integration of bulk wind
generation is obviously a complex task. The extent of the cost impacts is very sensitive
to specific system characteristics such as generation resource mix, wind penetration level,
and system regulatory environment. There have been many research and development
efforts to address the range of technical and economic questions that together make up
this general issue. A summary of a collection of relevant work is included in Appendix
A. This study represents a significant effort to develop a systematic methodology to
2-1
quantify the ancillary services cost of wind generation in the operation time frame.
Although conventional utility analyses and software tools have been available to
investigate power systems operation and control issues for many years, these tools have
mainly been used to study deterministic scenarios. As result, these tools have yet to be
applied to the study of the impacts of wind generation, a variable and relatively
uncontrollable generation resource.
With limited resources for the project, the work that has been performed represented the
basic, but key, steps on the use of the operations tools to estimate the impacts of wind
generation. It was not possible for all the modeling details to be implemented or for
exhaustive simulations to be performed to provide the most accurate results.
Nevertheless, this report will identify improvements, scenarios and sensitivities to the
basic formulation that could provide additional insights.
2.2 Overview of Power Systems Operations and Planning
The primary objective in power system operations and scheduling is to continuously
provide sufficient generation to match load at the lowest possible cost to the utility. This
objective must be accomplished while maintaining system voltage and frequency within
specified tolerances, and providing for system security. Time frames of interest range
from seconds to weeks, months, and even years. As installed wind plant capacity
approaches and possibly surpasses that of other single units within a given power system,
integrating the performance characteristics of wind plants into the various algorithms and
programs used for planning and monitoring system operation will become more
important. Since these software tools provide a basis for determining costs associated
with the additional control actions associated with wind generation, this section is
included to provide a basic overview of how these scheduling and control systems
interact.
2.2.1 AGC and Economic Dispatch
Stable operation of the interconnected power system is dependent on an instantaneous
match between load and generation. System frequency is a primary indicator of this
balance. When electric load on a synchronous generator exceeds mechanical input, the
generator will begin to slow down as kinetic energy is extracted from the machine's
rotational inertia and is converted to electric power. The decrease in shaft speed
corresponds to a decrease in frequency in a synchronous generator. Conversely, when
power supplied by a generator prime mover exceeds electric demand, the generator
mechanical system will accelerate as the excess input is stored as rotational energy, with
a corresponding frequency increase.
Speed governors on individual generating units maintain constant generator speed by
adjusting the mechanical input from the prime mover (steam turbine, penstock, diesel
engine, etc.) in response to a speed error signal. These systems provide the fastest
response to speed deviations caused by mismatch between generator input and output.
Automatic generation control, or AGC, is the principle mechanism for coordinating the
output of all system generators to match aggregate electrical demand. In a given control
area, governor setpoints of generating units assigned responsibility for system regulation
2-2
are coordinated by AGC to maintain system frequency at 60 Hz. AGC involves two
interrelated functions: 1) Load/frequency control; and 2) Economic dispatch. Response
of load/frequency control is on the order of seconds. Variations that occur more quickly
are handled by the individual units’ speed governors.
The economic dispatch function in AGC attempts to minimize the cost of meeting the
load demand by adjusting individual generating units' participation in load/frequency
control. While load/frequency control acts to adjust generation every few seconds, the
economic dispatch adjusts participation every few minutes to minimize generating cost.
Inputs to economic dispatch algorithms include incremental generating costs for
participating units, transmission penalty factors, and scheduled interchanges with other
control areas.
2.2.2 Unit Commitment
Unit commitment is part of a set of programs for scheduling thermal generation on an
hourly to weekly basis. Using forecasts of system load and long-term power purchases or
sales to other utilities, unit commitment programs determine which units are to be put online, when they are to be online, and when they are to be taken off-line. The program also
determines any additional short-term transactions. The objective is to minimize total
operating costs over a time period of one to 10 days, taking into account unit start-up and
shut-down costs, maintenance schedules, unit operating costs, transaction prices and
other constraints. A general explanation of how unit commitment works is provided in
Appendix B.
Unit commitment programs use dynamic programming techniques to schedule units of a
fixed size to meet the predicted demand for each hour. It is sometimes necessary to
coordinate the use of these programs with other specialized routines, like those used for
scheduling hydroelectric production.
2.2.3 Load Forecasting
Forecasts of load for the next hour, day, season, or year drive the utility scheduling
process. Load forecasting is often subdivided into "long-term", where seasonal load
peaks and energy requirements are predicted on a long-range basis, and "short-term",
where hour-by-hour predictions are made for a particular day. Accurate forecasting of
system load is critical for minimizing operating costs. Load forecasts are the primary
inputs to the power system scheduling and operations process. When load forecasts are
inaccurate, adjustments to the generation schedule result in additional fuel expenses and
wear and tear on generating equipment. New and improved methods for load forecasting
are continually being developed because of the critical importance of accurate forecasts
for minimizing operating costs.
Short-term load forecasts rely on historical data and various other inputs such as weather
conditions, daily and seasonal patterns, and industrial demand, to predict the hourly load
for the next day. Short-term forecasting is a complex problem, and even if it were
possible to accurately predict the load based on known factors, random occurrences such
as storms, strikes, etc. can upset the prediction.
2-3
2.3 Wind Model Requirements
As noted, representation of the wind plant for studying its impact on system operations
requires a non-conventional approach. The intermittent, non-deterministic nature of wind
and the limited control of the wind plant generation result in cost and system control
performance impacts that vary with each specific realization of the wind generation over
time. Therefore, a reasonable approach for evaluating wind plant operation is to perform
a Monte Carlo (MC) type simulation, where a large number of wind generation time
series are synthesized with the impact of each time series being evaluated in a
deterministic manner. Then, the statistics of the evaluation indices for the study are
compiled over all the sampling time series.
The NSP case study was significantly enhanced by the availability of high-resolution
wind generation data for the Buffalo Ridge wind plant. This wind generation data was
collected as part of a National Renewable Energy Laboratory (NREL) research project
and was made available for this wind impact case study. As Section 2.4 explains, the
basic evaluation horizons utilized for this study were a 3-day (72-hour) period for the unit
commitment (UC) simulations and a 1-hour period for the economic dispatch (ED) and
load frequency control (LFC) simulations. At the time the analysis portion of the study
began, the NREL data set contained approximately 7-8 months of 1-second resolution
data. This data set obviously contained a large number of continuous, 72-hour wind
generation series that could be selected for simulation, and significantly more series of 5minute and 4-second resolution. In fact, the problem with selecting actual discrete length
time series from the actual data was how to select specific time series and ensure that the
set of sample series selected is representative of the entire data set. Consequently, it was
determined that a probabilistic model was needed to synthesize a limited set of wind
generation time series that were statistically representative of the actual data.
The wind plant model that was developed to synthesize the wind generation time series is
based on a probabilistic model quantifying the probability distribution of wind generation
for a time period given its past history. Following the modeling approach adopted by
NREL, [Milligan 1996-1], [Milligan 1997-2], the model assumes that a Markov chain can
represent the random process of wind generation. This means that only the most recent
observation is relevant in the probability distribution of future wind generation. The
details of the developed model are provided in Section 4 of this report.
2.4 NSP Case Study Analytical Framework
Quantifying the cost impacts of integrating wind is a complex problem. Vertically
integrated utilities have traditionally valued these services on a cost-of-service basis.
More recently, the unbundling of transmission and generation services has given rise to
deregulated environments characterized by competitive markets, including markets for
ancillary services such as those required to accommodate the NSP wind plant. NSP,
however, still operates in a regulated environment as a vertically integrated utility. NSP
is a member of the Mid-continent Area Power Pool (MAPP), which does provide a
reserve sharing pool to its members. MAPP does not currently provide a centralized
competitive market for electricity or for ancillary services. NSP is also a member of the
Midwest Independent Transmission System Operator (MISO), which began operation
2-4
February 2002. MISO is responsible for scheduling transmission services for members
engaging in bilateral transactions. However, NSP operates within its own control area as
a vertically integrated utility, utilizing bilateral contracts to purchase and sell electricity
as needed. NSP performs forward scheduling of generation and energy transactions to
meet forecasted system load while maintaining sufficient reserves for normal load
variation. In real time, NSP dispatches and controls its unit generation levels to meet
minute-by-minute load changes. In other words, NSP provides its own ancillary services
excluding the contingency reserves, which are shared among the MAPP members.
Given the vertically integrated environment in which NSP operates, the methodologies
developed to assess the impact of integrating NSP’s wind plant are based on a valuation
of NSP’s cost to provide the additional services required to accommodate the wind
energy. The assessments are made by simulating NSP’s generation scheduling and realtime operations using traditional utility scheduling and dispatch tools to evaluate the
various services on the appropriate time scales. The availability of energy and capacity
through forward bilateral contracts is considered in the developed models. The
availability of near real-time purchases and sales is not considered in the models. Thus,
the developed model is considered to be an approximation to NSP’s current operating
procedures. Although the various cost components incurred for supporting wind plant
operation that are identified for the case study may differ slightly from the standard
ancillary service offerings in a deregulated market, the case study costs can be indirectly
mapped to these standard ancillary service costs. It should also be noted that the
investigators expect that the developed approach of mimicking NSP’s current operational
procedures will provide a conservative (i.e., more significant) estimate of the wind
integration costs relative to the value of the equivalent services obtained from a
competitive market or relative to NSP’s minimal cost to provide these services under an
optimized operational strategy, which considers the inclusion of wind generation.
The cost and control performance impacts for integrating the NSP wind plant that are
evaluated in this case study are as follows:
1. Cost of Wind Generation Forecast Inaccuracy
2. Impact of Wind Generation on Cost of Following Intra-Hour Changes in Load
3. Impact of Wind Generation on Control Performance of Regulating Minute-toMinute Fluctuations in Load
Figure 2-1 provides a graphical overview of the processes utilized to evaluate the impacts
of wind on NSP system operations in terms of the cost components enumerated above
and identified in the 3 distinct component boxes overlying the flow chart. For each of the
cost components evaluated, this flow chart defines the tools utilized and the basic
inputs/outputs for these tools. Additionally, the common links between the components
are also identified. The following sub-sections explain the basic process depicted in the
flow chart for each of the cost impact categories identified. Detailed explanations of each
cost component valuations are contained in Sections 5, 6, and 7.
2-5
NSP Hist. Hr.
Avg. Wind Gen.
Data
STM Wind
Generation
Tool
NSP Unit
Characteristic and
Transaction Data
100 3-day, hr
res. MC Wind
Generation
Time Series
3-day, hr res.
NSP Hist.
Load Time
Series
Hr res. NSP Hist.
Load and Wind
Time Series
Annualize costs
from 2 seasonal
scenarios
Cost of Incremental
Load-Following
Reserve for Wind
Generation
Annualize costs
from 2 seasonal
scenarios
Economic
Dispatch
Simulation Tool
Distribution of Cost
of LF Energy
Component
Annualize costs
from 2 seasonal
scenarios
Load Frequency
Control
Simulation Tool
Distribution of ACE
Statistics
Unit Commitment
Simulation Tool
Calc. LFRR
from hourly
change in load
and wind gen
Commitment and
Transaction Schedule
for Selected Hours
(H3, H8, H14, H23)
NREL Hist. 5min Avg. Wind
Gen. Data
STM Wind
Generation
Tool
Distribution of Cost
of Inaccurate Wind
Gen. Forecast
(±10%, 20%, 50%)
100 1-hr, 5-min
res. MC Wind
Generation
Time Series
per selected hr
1-hr, 5-min res. NSP Load Series w/
load hour shape per selected hr
NREL Hist.
4-sec Avg.
Wind Gen.
Data
Select 2, 1-hr, 4sec res. wind gen.
series for each of
4 hrs per season
4 1-hr, 4-sec res. NSP Load Series for
each of 4 hrs per season
Figure 2-1. Flowchart representing the analytical framework utilized for the NSP wind impacts case
study.
NSP uses their unit commitment (UC) and automatic generation control (AGC, which
comprises the economic dispatch and load frequency control algorithms) to schedule and
control system operations in a hierarchical process. UC produces hourly generating
schedules each day, which are in turn used to provide schedules to the AGC program.
The interface between the different operations programs can be automated, as is the case
in the NSP control center where one software program receives all of the necessary inputs
and sends all of the necessary outputs. Manual intervention is allowed for operators to
overwrite the system inputs and outputs. This is demanded by the very nature of the
tools, not to mention that many real-time operating decisions are made based on intuition
and familiarity with the system. Developing a model that incorporates the interaction
2-6
between control layers and the manual intervention of operators in an automated
simulation would be very difficult. The method adopted for this study was to use tools
very similar to those used by NSP in an operational mode as representative as possible of
that used by NSP. As such, it was not possible to perform the iterative simulation process
for long periods. Instead, representative scenarios were selected for periods of the year
similar in regards to wind and load profiles.
As discussed in detail in Section 4, NSP’s Year 2000 hourly wind generation data
indicated that wind generation could be grouped into high-wind and low-wind seasons,
which are also referred to as winter (high-wind) and summer (low-wind) throughout the
report. For each of these wind “seasons,” the cost impacts are performed for selected 3day load profiles. These three-day periods were selected for the high demands relative to
the period of year such that the system operations cost numbers provide a somewhat
conservative assessment.
Because of the varying nature of wind, a Monte Carlo approach was utilized to generate a
distribution of cost impact values for each scenario to ensure that a representative cost
value was obtained. A probabilistic STM-based (state transition matrix) wind plant
model tool was developed to synthesize multiple wind generation time series as discussed
in detail in Section 4. These multiple wind series represent various realizations of the
wind for the simulated scenarios, thereby allowing a more representative assessment of
the cost impacts. The manner in which this Monte Carlo approach was utilized for each
of the cost components is represented in Figure 2-1 and discussed in the following subsections describing the more specific process used for each component.
2.4.1 Cost of Wind Generation Forecast Inaccuracy
NSP performs unit commitment each day for a 3-day horizon to obtain optimal
generation and transaction schedules to meet the hourly forecasted load and existing
transaction schedule profiles. Forecasted wind generation is included in this scheduling
process. The differential in the forecasted wind generation value used in scheduling and
the actual hourly wind generation realized requires that in real-time and near real-time
operations, other generators be re-dispatched from the levels determined in the original
schedule. In actuality, the differential will be covered in real-time operation by either
deploying operating reserves (for deficient wind generation) or by backing down
economic units (for excess wind generation). Additionally, for a deficiency in wind
generation, the operating reserves that are deployed in real-time operation must be
replaced for subsequent hours, i.e., the unrealized wind energy must be replaced from
other generating options. Immediate replacement of this generation can only be achieved
from more costly options (fast starting peaking units, real-time markets, etc.) until the
real-time operators have time to obtain more economic options (startup additional
economic units, purchase forward contracts, etc.).
Consequently, the generating schedules actually implemented in real-time operation are
more costly than the schedule determined by the unit commitment based on perfect
forecasting. This cost difference is assessed by running unit commitment simulations for
perfectly forecasted wind and inaccurate forecasts. The cost difference between the
2-7
imperfect and perfect forecast runs represents the cost due to forecast inaccuracy. Since
NSP uses a unit commitment tool for its operation planning, it is natural to use a similar
unit commitment tool to simulate the generation adjustment for discrepancies between
actual and forecast wind generation. In this simulation, all variables are in hourly
resolution.
The upper-layer of the flow chart of Figure 2-1 shows the use of unit commitment to
determine the wind generation forecast inaccuracy cost. A three-day period was selected
for each of the winter and summer seasons where winter is characterized by high-wind
and medium load level and summer by low wind and high load level. Unit commitment
simulations were performed for 100 corresponding wind generation time series
synthesized from the wind STM tool to represent the actual wind generation. Additional
sets of simulations were performed to determine the cost of actual generation when the
wind generation forecast is off by ±10%, ±20%, and ±50% of the actual wind generation.
Comparison of the cost distributions for the original set of simulations relative to the cost
distributions for the various sets of inaccuracy simulations provide the basis for
determining this cost component. The detailed process utilized for determining these
costs is discussed in Section 5.
2.4.2 Cost Impact of Wind on Following Intra-Hour Changes in Load
The generation schedule obtained from the unit commitment solution is determined such
that the hourly average generation level is sufficient to meet the expected hourly average
load. However, the control area load is varying continuously in real-time. The utility must
ensure that sufficient generation is available to cover the sub-hourly changes in load. The
load following component of these sub-hourly variations is the slow variation associated
with the general correlation in different customer loads that define the daily load cycle.
This variation is on the time scale of several minutes, corresponding to the cycle time of
economic dispatch execution in utility operation. For example, the typical weekday load
cycle for NSP is characterized by a steep ramp-up in the morning from approximately 410 a.m. and a steep ramp-down in the evening from 8 p.m.-12 midnight, with relatively
flat load levels throughout the midday and midnight hours. During an hour when the load
is ramping throughout the hour, the hourly generation level scheduled from the unit
commitment will exceed the actual intra-hour load value for approximately half of the
hour, but will be deficient to meet the intra-hour load value for the other half of the hour.
Consequently, reserves must be available to deploy within the hour to ensure that
sufficient generation is available to meet the ramping of the load. In general, the amount
of reserve required depends on how steeply the load ramps during the hour. The
variability of the hourly wind generation will affect the amount of reserves that must be
available to follow such load trends. If the system wind generation follows a daily cycle
that is similar to the load cycle, the total load following reserves required should be
reduced. If, however, the wind follows a pattern that is adversely related to the load
cycle, as is often the case for strong diurnal wind patterns, the wind would increase the
intra-hour load following reserve requirement (LFRR).
Load following reserve represents the extra generation capability to meet the intra-hour
load changes. This is an addition to the capacity required to meet the hourly average load.
2-8
Making such reserve available usually requires bringing more units online or scheduling
unit generation levels in a less economic manner in the operation planning stage. This
results in extra cost.
The deployment of the available load following reserve to meet the intra-hour slow
variation of load changes also results in extra cost. We refer to this cost as the energy
component of the load following cost. An economic dispatch program is used to simulate
the intra-hour deployment of generation every 5 minutes for 1 hour. The unit on/off
statuses are fixed according to the solution of the unit commitment run. The economic
dispatch simulation models the contingency reserve requirement and regulating reserve
requirement. It models the load following reserve requirement dynamically in the sense
that at a given time step, the amount of reserve is reduced to match the increase in load or
reduction in wind generation. The economic dispatch is in essence deploying the reserve
and converting it into generation. The economic dispatch program used for this study also
models an artificial unit that is dispatched when load and reserve requirements are not
met by the actual units currently online. A penalty charge commensurate with the
peaking unit average generation $/MWh cost at full load is assessed for the dispatch of
this artificial unit, representing an equivalent use of peaking energy or purchase of spot
market energy to meet the load requirement.
The middle-layer of the flow-chart in Figure 2-1 shows the process for assessing both the
reserve and energy components of the cost impact of wind on intra-hour load following.
Load following reserve requirements with and without wind generation are estimated
from historical data on the basis of the hourly load and wind generation changes. Unit
commitment is then used to determine the cost differential under different reserve
requirements between with- and without-wind generation scenarios.
The simulation process for calculating the energy component of load following cost is
shown in the lower half of the middle layer. The economic dispatch tool is used to
simulate the intra-hour effects of re-dispatching generator set points every 5 minutes.
Rather than simulate all 24 hours for each of the 3-day UC periods, the economic
dispatch is performed for 4 representative hours from the NSP daily load cycle – hours 3
(nightly flat), 8 (morning ramp-up), 14 (afternoon flat), and 23 (night ramp-down). The
commitment schedule for these hours is taken from the median wind generation
simulation for each of the 2 wind “season” scenarios. NSP provided 5-minute resolution
load data for 5 days during summer 2000. This data provided hourly load shapes that
were scaled for the hourly average load values for the selected hours from the 3-day
simulation windows. For each of the selected hours for each wind season, 100 wind
series of 5-minute resolution and 1-hour horizon were synthesized using the STM wind
tool. The economic dispatch was performed for each of these combinations of load and
wind series for the selected hours for the 2 wind seasons to provide distributions of the
energy component cost for the selected hours. These cost distributions were then used to
determine an annualized energy cost component.
2-9
2.4.3 Impact of Wind on Regulating Minute-to-Minute Fluctuations in
Load
In addition to providing generation to meet the slow intra-hour variations associated with
the ramping of the load through the load cycle, the minute-to-minute variations in load
must also be accommodated. This regulation service requires that fast-responding
generation be reserved to respond to these fast fluctuations. The minute-to-minute
variability of the wind production will impact the regulating reserve amount required to
meet these changes. Following the analytical methodology as proposed in [Hudson 20011], it is determined as described in Section 4 that the additional amount of regulating
reserve required to support the currently existing wind generation penetration of NSP is
very minimal. Therefore, it is assumed that no additional regulating reserve is required.
Simulations of the real-time regulation process with wind and without wind were
performed, however, and the control performances determined by the simulations were
compared.
The bottom layer of the flow chart in Figure 2-1 shows the simulation process for
assessing the impact of wind on regulating minute-to-minute fluctuations in load. To
perform this assessment, two high-resolution (4-second) wind generation series of 1-hour
duration were selected from the NREL wind generation data set for each of the selected
hours for the relevant wind season. NSP provided 4-second resolution load data for the
same 5 summer days for which the 5-minute resolution data was provided. For each of
the selected hours, four high-resolution load series were selected from the NSP historical
data. The LFC simulations determined the ACE statistics for each combination of load
and wind, which provided 8 distributions of 900 calculated ACE values. These ACE
statistics were also averaged up to 1-minute ACE values to correspond to the NERC
performance metric period. These statistics were compared to the ACE statistics
calculated for the load series without wind generation. The results showed that the
addition of wind had very little negative impact on system ACE. Consequently, it was
assumed that the cost impact was minimal as well.
2-10
3 System Description
This section provides an overview of the NSP system characteristics and system control
operational procedures, as they were understood by the investigators for this case study.
Although there was a significant exchange of raw data and NSP-specific operational
information between NSP and the investigators, several critical pieces were not obtained.
These missing data and information are noted, as well as the assumed data that were used
in their stead. In terms of raw data received, NSP provided all of the data except for the
high-resolution wind generation data from Lake Benton that was provided by NREL for
the development of the wind plant model. The following archived data were provided by
NSP to the investigators for the study:
1) hourly historical EMS archives for January, April, and July of 2001 for the following
quantities:
a) control area load
b) control area total generation
c) control area generation per generating unit
d) interchange
e) dynamic schedule
f) wind generation
g) portion of Sherco generation not owned by NSP
2) hourly historical EMS archives for wind generation for January - December of 2000
3) snapshot of unit commitment database
4) snapshot of AGC database
5) 5-minute historical EMS archives for 5 days (1 in June, 2 in July, 2 in August); data
included
6) 4-second historical EMS archives for 5 days (1 in June, 2 in July, 2 in August); data
included
3.1 Existing NSP Wind Plant
NSP has approximately 280 MW of installed wind generation capacity at the Lake
Benton wind site. The site is located in southwestern Minnesota, northwest of the town of
Lake Benton (Figure 3-1), along a topographic feature known as Buffalo Ridge. This site
is the premier wind resource area in the state of Minnesota due to the storm-driven winds,
which occur as a result of the passage of low-pressure systems throughout the year.
During winter and early spring, this wind resource is even higher as low-pressure centers
are even more intense and numerous.
3-1
Minnesota
Lake Benton
Wind Farm
South Dakota
Iowa
Nebraska
Figure 3-1 Geographical Location of Lake Benton Wind Farm
There are several wind plants in this region, with most of this energy being collected at
Xcel Energy’s Buffalo Ridge substation. Of NSP’s 280 MW total wind generation
capacity (nameplate rating), 230 MW is connected to the Buffalo Ridge substation, with
an additional 50 MW connected to another local substation. Wind generation data
collected at the Buffalo Ridge substation provides an aggregate of multiple smaller wind
farms that is indicative of the characteristics of a single, large, and geographically or
topographically diverse wind plant.
The majority of the wind generation connected to the Buffalo Ridge substation consists
of the Zond Z-750 wind turbines. Each turbine sits atop a 51.2 m (168 ft) tubular tower,
with each blade spanning approximately 24 m (79 ft). The actual rotor diameter is 50 m
(164 ft), giving a swept area of 1,966 sq. m (21,124 sq. ft).
A single-line diagram of the Buffalo Ridge substation is shown in Figure 3-2. Note that
the Fox and Golf projects as shown in the figure are no longer fed into the Buffalo Ridge
substation, but into the Chanarambie substation.
3-2
N.C.
To Pipestone
To Lake Yankton
115 kV
120 MVA
120 MVA
Metering
Points
N.C.
34.5 kV
Charlie
Bravo
322
313
323
311
LG&E
Delta
Echo
Alpha
Lakoto Ridge
321
N.O.
Foxtrot
312
Shaokaton Hills
Small projects 1
Alpha - 27.75 MW, Zond
Bravo - 36.75 MW, Zond
Charlie - 42.75 MW, Zond
Delta - 22.5 MW, Zond
Echo - 29.25 MW, Zond
Foxtrot - 10.5 MW, Zond
Golf - 41.25 MW, Zond
LG&E - 25 MW, Kenetech
Lakota Ridge 11.25 MW, ?
Shaokatan Hills, 11.88 MW, ?
Small Projects 1, 11.88 MW, ?
Small Project 2, 15.84, ?
Golf
Small projects 2
Figure 3-2 One-Line Diagram of Buffalo Ridge Substation
3.2 NSP Control Area Characteristics
The control area of NSP includes three-quarters of the power consumption of Minnesota
and parts of Michigan, Wisconsin and South Dakota. Figure 3-3 shows a map of the
utility’s geographic service area copied from Xcel Energy’s website. Note that the
service areas in North Dakota and northwestern Minnesota are not contained in the NSP
control area.
3-3
Figure 3-3 Control Area Map of NSP
3.2.1 NSP Generation Resources
The vast majority of NSP’s generating resources are thermal. NSP’s database of
generating units includes 57 units, all of which are thermal. NSP specifies two capacity
ratings for their units, the Normal Dependable Capability (NDC)1 and the Maximum
Dependable Capability (MDC)2. The total NDC of NSP’s 57 units is 7222 MW, and the
total MDC is 7912 MW. These units comprise an array of fuel types, production costs,
start-up costs, start-up times, ramp rates, and minimum operation times that determine
how these units are utilized to meet NSP’s control area load. As a generalization, the 57
units are categorized based on the following 3 applications:
•
•
Must-Run Units. 22 of the 57 units are run whenever available (not on
maintenance or forced outage) due to the relatively low operating costs and
minimum operation time constraints. Fuel types include coal, wood, gas and
nuclear. The 22 units have a total NDC capacity of 5275 MW and a total MDC
capacity of 5651 MW. These units are used as base load units with the exception
that three of these units are the primary source for providing operating reserves.
Discretionary Units. 4 of the 57 units are mid-range cost units that are used only
when economical based on the demand profile, unit characteristics, transaction
1
Normal dependable capability (NDC) of a generating unit was defined by NSP as : “The monthly value
representing a unit's high load operating limit used on normal system operating days. This high load limit
shall be maintainable during system peak hours (06:00 to 22:00) for five consecutive weekdays (Monday
through Friday) on a continuous basis. Under these conditions, there is typically no secondary fuel
consumption taking place.”
2
Maximum dependable capability (MDC) of a generating unit was defined by NSP as: “The monthly value
representing a unit's high operating limit when the system must burn oil to meet demand. During these
conditions, plant personnel may take steps to achieve additional output which may be equal to or less than
the unit's URGE rating. Such steps may include using secondary fuel, gas topping or curtailment of
nonessential auxiliary load. This high load limit shall be maintainable during system peak hours (06:00 to
22:00) Monday through Friday.” MDC is greater than NDC.
3-4
•
prices, etc. Fuel types include gas and coal. These 4 units have a total NDC
capacity of 444 MW and a total MDC capacity of 485 MW.
Peaking Units. 31 of the 57 are high-cost peaking units having a total NDC
capacity of 1503 MW and a total MDC capacity of 1776 MW. Fuel types are
natural gas and oil.
Figure 3-4 and Figure 3-5 show the NSP January and July 2001 hourly load profiles
plotted against a stack-up of the NDC capacity of the 57 thermal units grouped as noted
previously. Also included in the plots is the actual hourly generation per category for the
respective time periods. These plots show that the “Must-Run” units are operated at a
level near the bottom of the daily load cycle. This is due to several factors including the
minimum operating time and ramp rates of these units and the designation of some of
these units for operating reserves. The load following responsibility of these units is also
evident from the cyclic following of the load profile. Other general observations from
these plots are:
•
•
•
NSP depends on large energy imports to meet its control area load for both winter
and summer
NSP utilizes its peaking units during the daily load cycle for the summer demand
Assuming moderately valued energy is available through bilateral contracts, NSP
finds it economical to import energy to meet its demand profile for both summer
and winter.
January 2001
MW
Must Run
Disc.
Peak
Load
Must Run
Disc.
Peak
7000
7000
6000
6000
5000
5000
4000
4000
3000
3000
2000
2000
1000
1000
0
0
1/31/2001
00:00
1/28/2001
00:00
1/25/2001
00:00
1/22/2001
00:00
1/19/2001
00:00
1/16/2001
00:00
1/13/2001
00:00
1/10/2001
00:00
1/7/2001
00:00
1/4/2001
00:00
1/1/2001
00:00
time
Figure 3-4. NSP January 2001 hourly load profile and categorized generation plotted against the
NDC capacity of NSP’s 57 thermal generating units that are included in the NSP AGC generating
unit database.
3-5
July 2001
MW
Must Run
Disc.
Peak
Load
Must Run
Disc.
Peak
9000
9000
8000
8000
7000
7000
6000
6000
5000
5000
4000
4000
3000
3000
2000
2000
1000
1000
0
0
7/31/2001
00:00
7/28/2001
00:00
7/25/2001
00:00
7/22/2001
00:00
7/19/2001
00:00
7/16/2001
00:00
7/13/2001
00:00
7/10/2001
00:00
7/7/2001
00:00
7/4/2001
00:00
7/1/2001
00:00
time
Figure 3-5. NSP July 2001 hourly load profile and categorized generation plotted against the NDC
capacity of NSP’s 57 thermal generating units that are included in the NSP AGC generating unit
database.
In addition to the 57 units discussed above, NSP’s control area also comprises
approximately 500 MW of generation that is not controlled by NSP. There is no MW
telemetry for these units and only the hourly energy value is being archived. NSP does
not own some of these units. This generation is categorized as follows:
•
•
280 MW nameplate capacity of wind generation at Lake Benton site
About 220 MW of generation from approximately 10 thermal or hydro plants
Figure 3-6 shows a typical NSP 3-day summer load profile plotted against a stack-up of
the actual realized generation for the time period grouped as noted previously. Note that
the “Other” category comprises the 10 thermal and hydro units not on NSP AGC. This
graph emphasizes NSP’s use of energy purchases to meet summer demand.
3-6
2001 July 18-20
MW
Must Run
Disc.
Peak
Wind
Other
9000
Load
9000
8000
8000
7000
7000
6000
6000
5000
5000
4000
4000
3000
3000
2000
2000
1000
1000
0
0
7/20/2001
12:00
7/20/2001
00:00
7/19/2001
12:00
7/19/2001
00:00
7/18/2001
12:00
7/18/2001
00:00
time
Figure 3-6. NSP 72-hour summer load profile plotted against the NDC capacity of NSP’s 57 thermal
generating units that are included in the NSP AGC generating unit database.
3.2.2 Load
NSP’s hourly average load data for January, April, and July show that on a seasonal
basis, NSP’s load demand is highest in summer, medium in winter, and lowest in spring
and fall. The assumption that the spring and fall load profiles are similar is based on
communication with NSP personnel. The maximum and minimum control area loads of
each of these three months are shown in Table 3-1.
Table 3-1. NSP Control Area Load Max and Min for January, April and July 2001
Month
January
April
July
Max MW
6264
5733
8391
Min MW
3638
3089
3455
It is interesting to note that the daily load profile for winter has two peaks. Figure 3-7
shows the hourly average control area load for January 2-4, 2001. The figure shows that
system load starts ramping up rapidly at 5 a.m. in the morning and levels off at 9 a.m.
The load decreases slowly from noon until 4 p.m. and then picks up again. It peaks for
the second time around 8 p.m. and then drops off rapidly after 11 p.m.
3-7
2001 Jan 2-4
Must Run
Disc.
Peak
Load
8000
7000
6000
MW
5000
4000
3000
2000
1000
0
1/4/2001
12:00
1/4/2001
00:00
1/3/2001
12:00
1/3/2001
00:00
1/2/2001
12:00
1/2/2001
00:00
hour
Figure 3-7 Xcel Energy Hourly Load Profile of Jan 2-4, 2001
Figure 3-8 shows the hourly average control area load for July 18-20, 2001. This plot
does not exhibit such a noticeable double peak for the daily load profile, but rather ramps
throughout the morning, finally leveling out around noon.
2001 July 18-20
MW
Must Run
Disc.
Peak
Load
9000
9000
8000
8000
7000
7000
6000
6000
5000
5000
4000
4000
3000
3000
2000
2000
1000
1000
0
0
3-8
7/20/2001
12:00
Figure 3-8 Xcel Energy Hourly Load Profile of July 18-20, 2001
7/20/2001
00:00
7/19/2001
12:00
7/19/2001
00:00
7/18/2001
12:00
7/18/2001
00:00
time
3.2.3 NSP Operational Procedures
A critical component to this study was the development of an understanding of NSP’s
operational procedures and the issues that they’ve identified regarding their existing wind
plant. This knowledge base within NSP spans many departments and individuals within
the various relevant groups. Additionally, there were differences in the nomenclature
utilized by NSP personnel and the investigators. Consequently, obtaining the necessary
information was not a simple process. Instead, this information gathering was an
ongoing process, involving several iterations over the course of the project through the
following methods:
•
•
•
•
On site visit with NSP personnel from various departments during early April of
2001.
Email communication with NSP managers and engineers.
Phone conversation with NSP real-time trader.
Historical data analysis by the investigators
The information gathered is summarized in the following subsections. It should be noted
that not all of the information was obtained in time to be fully utilized in the simulations
performed. In such cases, assumptions had to be made. Such instances are also noted.
3.2.3.1 Contingency reserve requirement
NSP belongs to the Mid-Continent Area Power Pool (MAPP), with contingency reserves
being shared among all pool members. The reserve criteria used by MAPP are based on
the loss of the 500 kV ac transmission line between the MAPP region and Manitoba,
Canada. The transmission capacity of this line is 1200 MW. NSP’s share of this
contingency reserve requirement is 161 MW of 10-minute spinning and 160 MW of 10minute non-spinning. In the event this 1200 MW transmission line is out of service, the
reserve criteria is based on the loss of the largest generating unit of the region, which is
NSP’s Sherco 3 unit.
3.2.3.2 Day-ahead planning
Prior to 6 a.m. each morning, NSP runs its unit commitment program to schedule its
hourly generation for a three-day period beginning at 6 a.m. of the current day.
(Appendix B contains a general description of UC operation.) In obtaining each day’s
generation schedule, NSP sets the following generating unit parameters within its UC
program:
• Generating unit high limits are set to the unit normal dependable capabilities.
• The only reserve requirement modeled within the UC is the 161 MW of 10minute spinning and 160 MW of 10-minute non-spinning contingency reserve
requirement.
• All of NSP’s inexpensive cycling units (“Must-Run” units noted previously) are
scheduled to be online all the time except on scheduled or forced outage.
Figure 3-5 showed that NSP does not own enough generation to meet its annual peak
demand. Also evident from Figure 3-4 and Figure 3-5 is that NSP would have to run
3-9
expensive units to meet its daily peaks for most periods of the year. Consequently, NSP
purchases energy to make up for any capacity shortages and to obtain a more economical
generation mix. NSP purchases more energy during the higher load demand season and
during major unit outages. During the day, NSP’s purchasing period coincides with its
peak load periods, and is usually from 6 a.m. to 10 p.m. Table 3-2 shows the MW values
of the peak imports for the months of January, April, and July of 2001. NSP also sells
energy during its off-peak seasons. This typically occurs from 10 p.m. to 6 a.m. each day
as represented in Figure 3-9 by the excess of total generation above the NSP load for
January 2-4, 2001. In recent years, NSP has had to commit more coal-fired units to meet
the increase in daily peak load. With these units committed, however, the minimum
generation is higher than the load during minimum daily load period. The minimum
down time requirement of these coal units prohibits shutting them down for the short
low-load period, so NSP runs them and sells the energy.
Table 3-2 Peak Hourly Import of January, April and July 2001
Peak Import (MW)
2631
1768
1286
Month Year
July 2001
January 2001
April 2001
2001 Jan 2-4
Must Run
Disc.
Peak
Load
Tot. Generation
8000
7000
6000
MW
5000
4000
3000
2000
1000
0
1/4/2001
12:00
1/4/2001
00:00
1/3/2001
12:00
1/3/2001
00:00
1/2/2001
12:00
1/2/2001
00:00
hour
Figure 3-9. Comparison of NSP hourly load and total generation for January 2-4, 2001.
3.2.3.3 Real-time operation
NSP uses some or all of the 3 Sherco units (Sherco 1, 2 and 3) almost exclusively on
AGC to perform both regulation and load following. These units can ramp very fast with
3-10
ramp rates 12, 12, and 15 MW/min, respectively. These units also have large NDC
capacities with 654, 660, and 807 MW. In NSP’s AGC, the outputs of these units are set
to their respective NDC capacities, such that the units can be controlled up to the NDC
while still participating in AGC.
Based on the current generation and load pattern and the amount of reserves scheduled
for following load, each hour the NSP real-time operators determine any actions to be
taken in order to meet the changes in system load in the next 60 minutes. When needed,
the NSP real-time operators can request generation plant operators to raise the generating
limit of a unit above the unit’s NDC, up to the unit’s MDC limit. Operating above its
NDC, however, prohibits a unit from participating in AGC control. By allowing one or
two of the Sherco units to generate above the NDC, the generation level of the other
Sherco unit(s) remaining under AGC could be off-loaded, thus creating more loadfollowing capability from these units.
When NSP needs more generation and/or more load-following capability, the real-time
operator can take one of the following courses of actions:
•
•
•
Increase the generation of the Sherco units, or other units, up to MDC.
Start up the peaking units
Purchase energy at spot market
Analysis of NSP’s historical unit generation data shows that when all three Sherco units
generate above their NDC, such that they are not available on AGC for load following,
NSP’s peaking units and/or a more expensive cycling unit are used for load following.
During the peak and minimum load period of the day where ramping in load is very little,
only one of the Sherco units is on AGC for regulation and load following.
3.2.3.4 Energy Transactions
As mentioned, NSP imports and exports significant amounts of energy as part of their
regular operational strategy. These energy transactions are conducted on an hourly basis.
Also mentioned previously, NSP sells a large quantity of off-peak energy as non-firm
energy.
3.2.3.5 Integration of wind plant
The NSP personnel responsible for generation scheduling assume that the annual capacity
factor of the wind plant is about 30%, with a seasonal high of 40% for spring and a low
of 15% for summer. NSP personnel also indicated that the wind plant generation varies
between 0 to 150 MW, despite the 280 MW nameplate capacity. For performing the
hourly generation scheduling with the unit commitment, the day-ahead operators use a
wind generation value that is discounted a certain amount from the forecasted value. By
doing so, the NSP day-ahead operators in essence provide hedging against the uncertainty
in wind generation forecasting. The amount used for wind generation in unit commitment
varies from 0 to 50 MW. They have more confidence in the forecasting for steady wind
patterns, for which they discount less. They have less confidence in the forecasting for
3-11
volatile wind conditions, for which they discount more. The real-time operators receive
no information on how the wind plant is to be operated. They can only take the wind
generation on an as-given basis. AGC, therefore, must react to the wind generation
variation in real time through regulating the ACE.
3-12
4 Wind Modeling Results
In supporting the UWIG case study of wind generation with Xcel Energy – North as the
case study utility, two models related to wind-plant operation were developed. The first
model was developed for synthesizing the wind generation time series over a time
horizon with a given time resolution. The second model was developed to provide the
wind generation fluctuation statistics that determine the reserve requirements used in
electric utility operations planning.
4.1 Wind Generation Time Series Synthesis Model
4.1.1 Use of the Model
The goal of the UWIG case study, with Xcel Energy as host utility, is to evaluate the cost
impact and control performance impact with the integration of wind generation operation
over a study horizon. Due to the intermittent nature of wind and the limited control of the
wind plant generation, the cost and control performance impact varies with each specific
realization of the wind generation over time. Therefore, a reasonable approach for
evaluating wind plant operation is to perform a Monte Carlo type simulation, where a
large number of wind generation time series are synthesized with the impact of each time
series being evaluated in a deterministic manner. Then, the statistics of the evaluation
indices for the study are compiled over all the sampling time series. In this task, we
develop the model for synthesizing the wind generation time series that are statistically
representative of the actual Xcel Energy wind generation of Lake Benton wind plant.
This statistical model is developed from historical wind generation data collected from
the host utility as well as high-resolution wind generation data collected as part of a
National Renewable Energy Laboratory (NREL) research project.
4.1.2 Time Scales of the Model
Based on the discussion in Section 2 of this report, the system operational impacts of
integrating significant wind generation are evaluated on three different time scales as
follows:
3-day (72-hour) study horizon of hourly resolution for performing unit
commitment study using operating cost as evaluation criteria
1-hour study horizon of 5-minute resolution for performing intra-hour load
following study using operating cost as evaluation criteria
5-minute study horizon3 of 4-second resolution for performing load frequency
control (LFC) simulation using statistics of ACE (Area Control Error) as
evaluation criteria
The model that was developed synthesizes the time series of the three time scales as
listed above. For convenience, in this report the sub models for each time scale
3
5-minute study horizon for LFC simulation was proposed in the early stage of the project. However, 1hour study horizon is used for actual implementation. Reasons for this change are provided in Section 8.
4-1
(resolution for a time step) are referred to as separate models -- the hourly model, the 5minute model and the 4-second model.
4.1.3 Markov Probability in State Transition
The mechanism of synthesizing the wind generation time series is based on a
probabilistic model quantifying the probability distribution of wind generation for a time
period given its past history. Based on the modeling approach adopted by NREL,
[Milligan 1996], [Milligan 1997], we further assume that the random process model of
wind generation can be represented by a Markov chain. This means that only the most
recent observation is relevant in the probability distribution of future wind generation.
A random process {Xt, t ∈ T} is a family of random variables indexed by t over a set T of
time points or time periods. The set T can be a set of discrete units of time such as {0, 1,
2, 3…} or a continuous set of values such as [0, ∞). For a given t, the random variable Xt
can assume a value from a discrete set or a point from multi-dimensional state space,
which we call the state in either case.
Consider wind generation over time as a random process with t as any given time period
within the study horizon. We partition the wind generation space with a given step size
from 0 MW up to the wind plant capacity. We enumerate each partition by an integer
value that the random variable Xt can assume. A 1 MW step size was selected for
discretization for the 1-hour and 5-minute resolution models. For example, for these
models, Xt = 0 represents a wind generation value between 0 and 1 MW; and Xt = i
represents a wind generation value between i and (i+1) MW, and so on. For the 4-second
resolution model, a step size of 0.1 MW is used.
A Markov chain is a random process with a property that, given the value of Xt, the
probabilistic characteristics of Xt+1 does not depend on the value of Xu, where u < t. That
is to say that the probabilistic behavior of the random process at the next time period as
well as any time period further in the future when its present state is known exactly, is not
altered by additional knowledge concerning its past behavior.
The decision to use the Markov chain in describing the inter-temporal probabilistic
behavior of wind generation is based primarily on the simplicity of the model. This
method has been used by NREL, and as indicated in some of their publications, when
compared with other detailed models, Markov modeling provides a reasonable degree of
accuracy in synthesizing wind generation time series for case study simulation.
The probability of Xt+1 being in state j, given that Xt is in state i (called one-step
transition probability) is denoted by pijt , t +1 . When the one-step transition probabilities are
independent of the time period t, we say the Markov process has stationary transition
probabilities. This is the case for the Xcel case study because the wind does not exhibit
any strongly noticeable daily patterns, diurnal or otherwise. If the wind data for the Xcel
Energy – North case study did exhibit a particular daily pattern such as a diurnal pattern,
two separate probability models would be required to maintain the assumption of
stationary transition probabilities.
4-2
We define the state transition probability matrix Pt, t+1 as
t , t +1
 p00
 t , t +1
p
t , t +1
=  10t ,t +1
P
 p20

 Μ
t , t +1
p01
p11t ,t +1
t , t +1
p21
Μ
t , t +1
p02
Λ

t , t +1
p12
Λ
t , t +1
p22
Λ

Μ Ο 
Each row of the matrix corresponds to a state at time period t, and the row elements are
the probabilities of different states at t+1 reached from the state at t. Hence the row sum
of each row is equal to 1.
∑p
t , t +1
ij
=1
∀i
j
Consider that we have the state transition probability matrix for all time periods. Time
sequences of the random process governed by the state transition probability matrix can
be generated. In synthesizing the wind generation time series for system operations
simulations, consider a present generation level corresponding to state i’ at time period t.
The row of the state transition probability matrix for time period t corresponding to the
current state gives the conditional probability distribution of generation at t+1; that is
p it',tj +1 j = 0,1,2... We then use a random number generator of uniform distribution to
generate a point between 0 and 1. For convenience, we denote this number as y. We then
map this number y through the use of conditional probability distribution to obtain the
state j’ for time period t+1. To be precise, the state j’ at time period t+1 being mapped to
j ' −1
is such that
∑ pit',tj +1 ≤ y <
j =0
j'
∑p
j =0
t ,t +1
i' j
Repeating the same process with generation at t+1, we
obtain the generation level at t+2 and then up to end of the study horizon for one sample
time series.
4.2 Data Sources for Probabilistic Model Development
Two separate data sources were utilized as a basis for developing the Markov
probabilistic model of the Lake Benton wind farm located within the Xcel Energy service
territory.
Historical data collected by the host utility (Xcel Energy) was used for development of
the hourly wind generation model. This data consisted of average hourly MW output
values of the wind farm for all months of year 2000. Appendix C provides a graphical
view of the NSP Year 2000 hourly resolution data.
High-resolution data collected by Electrotek for the NREL Wind Farm Monitoring
Project was used to develop both the 5-minute and 4-second resolution wind generation
models. This data has been collected at the Lake Benton wind farm since January 2001,
4-3
and a total of approximately 7 months of data is used for developing the higher resolution
models (the data set ranges from January 31, 2001 to August 13, 2001).
Ideally, high-resolution data from the same period of time as the hourly data would be
preferred for developing the 5-minute and 4-second models for consistency reasons, but
this data was unfortunately not available from the host utility.
Note that the models developed for the wind farm are based upon year 2000 hourly
generation levels and partial year 2001 high-resolution data. Therefore the model is only
representative to the extent that this data represents wind farm operation.
High-resolution (4-second) wind generation data was used to develop the model for the
regulation reserve and load-following reserve requirement calculations. Additionally,
high-resolution system load data provided by Xcel was utilized. Xcel provided highresolution load data for 5 separate days -- June 29, July 2, August 25, 27 and 28, all in
year 2001.
4.3 Sample Output of the Synthesis Model
4.3.1 Transition Matrix
Using the process described in Section 4.1.3, a state transition probability matrix is
developed for each of the resolutions of interest: 1 hour, 5 minutes, and 4 seconds. Each
model has a resolution of 1 MW, with the exception of the 4-second model which uses a
0.1 MW resolution), with the maximum bin value of 250 MW.
Considering the development of the state transition probability matrix of a given
resolution, we count the number of occurrences from state i to state j for all possible state
transitions from a given set of historical data and we call it Nij. Then for each state i, we
count the total number of occurrences of the transition from state i to all possible states
and call it Ni. Hence ∑ N ij = N i . Dividing Nij by Ni, we obtain the conditional
j
probability of state j for the next time period given state i for the current period.
A 3-D graph of a sample transition matrix for hourly transition developed by using the
entire year 2000 hourly data set is shown in both Figure 4-1 and Figure 4-2 for two
separate views. Note the peaks that occur at the minimum and maximum levels. The
peaks toward the maximum MW range (approximately 230 MW) are a result of very few
data points present at that level, while the peaks occurring at the minimum MW range (<
1 MW) represent the high probability that if the generation is below 1 MW it will stay at
that level.
4-4
Figure 4-1 Sample Transition Matrix-View 1 (Hourly Resolution)
Figure 4-2 Sample Transition Matrix-View 2 (Hourly Resolution)
4-5
4.4 Sample Generated Time Series
Each type of time series, regardless of resolution, is synthesized using the same basic
methodology. Consider the time series starting at t = 0. Using a seed value Xt, t = 0, as a
starting point, the respective conditional probability distribution from the state transition
matrix corresponding to Xt is converted to a cumulative distribution function. A random
number, between 0 and 1, is mapped to the cumulative distribution and a new state Xt+1
for time period t+1 is derived as described in Section 4.1.3. This value is then used as a
new seed value and the process is repeated.
The hourly transition probability matrix is used to synthesize a set of 72-hour time series
of wind generation data to be used for unit commitment simulations. Each 72-hour time
series begins with a seed value that is derived from the unconditional probability
distribution function derived from the entire historical hourly data set of interest. This
seed value, Xt, is then used as input to the state transition probability matrix to calculate
the next value, Xt+1.
Five samples of synthesized 72-hour wind generation data series are shown in Figure 4-3.
Appendix C provides a graphical view of the NSP Year 2000 hourly resolution data for
comparison. The transition matrix used to generate the sample series for this figure is
based upon hourly, year 2000 high-wind-season data.4
Series 1
Series 2
Series 3
Series 4
Series 5
250
200
MW
150
100
50
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
Time (hour)
Figure 4-3. Sample 72-hour Synthetic Series
Using a similar process, the 1-hour-horizon, 5-minute resolution wind generation time
series are synthesized using the 5-minute transition matrix. However, there are additional
requirements on the synthesized time series. As this type of time series is used for intra-
4
High wind season for Xcel Energy – North based on year 2000 hourly data includes January, February,
April, November and December.
4-6
hour load following study, it should exhibit fluctuating behavior about a given hourly
average generation level. Specifically, the requirements are:
•
•
The total energy of the time series should match the energy of the given hourly
generation level.
The generation level of the initial time period should be in the neighborhood of
the given hourly generation level.
The following procedure describes the steps of generating such time series.
1. With the given hourly MWh value as the generation level of the initial 5-minute
period, generate a temporary time series for the remaining 11 time steps of an
hour using the 5-minute transition matrix.
2. Use the minimum and maximum values from this temporary series to set the
range for selecting the initial MW generation of the time series to be generated
next.
3. Assuming that the MW generation of the initial 5-minute period is uniformly
distributed between the minimum and maximum of step 2, use the random
number generator to select a value for such quantity.
4. With the MW value of the initial 5-minute period as determined in step 3, use the
5-minute transition matrix to generate the time series for the remaining 11 time
steps of an hour.
5. The resulting 12 5-minute data points are then scaled such that the total energy for
the hour matches the energy of the hourly MWh value in step 1.
6. Repeat step 1 to 5 for generating additional time series.
By developing a temporary series for finding the maximum and minimum values that could be
found within the hour, one is able to get an estimated range of possible values that could be
found within the hour. In addition, by modeling the MW level of the initial time period as a
uniformly distributed random variable, one is able to create a fluctuation effect for the quantity
between different time series.
Five samples of synthesized 1-hour, 5-minute resolution wind generation series are
shown in Figure 4-4. The 5-minute transition matrix used to develop these series is based
upon 5-minute averaged data derived from the 4-second high-resolution data. The five
series shown in Figure 4-4 were randomly selected and included for informational
purposes only. No conclusions regarding the percent fluctuation can be drawn from this
graph. If more series were included, one would begin to see wider fluctuations in output.
4-7
Series 1
Series 2
Series 3
Series 4
Series 5
120
110
MW
100
90
80
70
60
0
5
10
15
20
25
30
35
40
45
50
55
Tim e (Min)
Figure 4-4 Sample 1-hour-horizon synthesized series
The 5-minute-horizon, 4-second resolution time series to be synthesized for load frequency
control simulations have requirements similar to the synthesized 5-minute resolution time
series. Therefore, a similar procedure is used for synthesizing the 4-second resolution time
series.
Five samples of synthesized 5-minute, 4-second resolution wind generation time series
are shown in Figure 4-5. The 4-second transition matrix used to develop these series is
based upon 4-second averaged high-resolution data.
4-8
Series 1
Series 2
Series 3
Series 4
Series 5
57
56
55
MW
54
53
52
51
50
49
48
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
Time (seconds)
Figure 4-5 Sample 5-minute, 4-second resolution synthesized series
4.5 Time-Dependence Consideration of the Markov Probabilistic
Model for Case Study Utility
4.5.1 Hourly Probabilistic Model
Analysis of the year 2000 hourly wind generation data set has shown that the wind farm
output has a very weak diurnal pattern (see Figure 4-6), with the only noticeable change
in generation production levels being found from season to season. During the winter
season, the energy level is noticeably higher than the rest of the year. With the exception
of the month of April, the months from November through February have significantly
higher production levels, greater than 60,000 MWh (see Figure 4-7.). Due to the absence
of a noticeable diurnal pattern within any given season, one single probability matrix for
state transition for all hours of the day was implemented. However, significant
differences in energy production among seasons required the development of two
probability matrices based on season. A high-wind transition matrix was developed
using data from November, December, January, February and April. A low-wind
transition matrix for the remaining portions of the year was also developed. It should be
noted that the month of July is grouped with the other months designated as low wind
even though the July energy production is at least 25% less than the next lowest month in
the year 2000. This decision was made based on communications with the Xcel Energy
staff which indicated that the typical July energy production is only about 10% less than
its adjacent months. Therefore, it was concluded that development of a separate
probability for this particular month was not warranted.
4-9
Spring (Mar-May)
Summer (Jun-Aug)
Fall (Sept-Nov)
Winter (Dec-Feb)
120
Output (MW)
100
80
60
40
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Hour
Figure 4-6 Hourly Average Wind Farm Output for Each Season (Year 2000)
Total MWH
70,000
60,000
Total MWh
50,000
40,000
30,000
20,000
10,000
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Month
Figure 4-7. Monthly MWh Value for Each Month
4.6 5-Minute and 4-Second Probabilistic Model
The 5-minute and 4-second transition matrix was based upon the entire data set of highresolution data (January 31, 2001 – August 13, 2001). The time series developed only
needed to exhibit the fluctuation around the average MW generation level; therefore the
different seasons were merged into one single model. In addition, insufficient data was
available to determine whether the intra-hour fluctuations from season to season warrant
a separate 5-minute, and possibly 4-second, probability matrix.
4-10
4.7 Probabilistic Model Validation
In order to validate the probabilistic model, distributions and statistical quantities (mean
and standard deviation) were derived for both measured and synthetic data and compared.
Figure 4-8 shows the probability distributions for 8,760-point measured and 60,000
point-synthesized hourly time series (Note: Increased number of synthetic samples have
to be produced to simulate all possible combinations of state transitions found in the
measured data). Table 4-1 provides the summary statistics for the probability-distribution
functions shown in Figure 4-8. Table 4-1 and Figure 4-8 indicate that the developed
model produces synthesized hourly wind generation time series that are representative of
the measured data.
Synthetic
2
Measured
1.8
% Probability
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
239
225
211
197
183
169
155
141
127
113
99
85
71
57
43
29
15
1
0
MW
Figure 4-8. Probability Distribution Function for Hourly Measured Data and Synthetic Series
Table 4-1. Hourly Standard Deviation and Mean Calculated from Real Measurements and Synthetic
Series
Standard Deviation (MW)
Mean (MW)
Synthetic
64.0
71.5
Measured
63.7
71.6
The same verification process was performed for the intra-hour wind models and the
results are shown in Figure 4-9 and Table 4-2. Figure 4-9 illustrates the probability
distributions for 53,251-point measured and 1,000,000-point synthesized 5-minute
resolution time series. Table 4-2 shows the summary statistics for the PDFs shown in
Figure 4-9. These comparisons indicate that the developed model produces synthesized
intra-hour wind generation time series that are representative of the measured data.
4-11
Measured
Synthetic
2
1.8
1.6
% Probability
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
16
31
46
61
76
91 106 121 136 151 166 181 196 211 226 241
MW
Figure 4-9. Probability Distribution Function for 5-Minute Measured Data and Synthetic Series
Table 4-2. 5-Minute Standard Deviation and Mean Calculated from Real Measurements and
Synthetic Series
Standard Deviation (MW)
Mean (MW)
Measured
61.0
69.2
Synthetic
61.3
72.9
Additional validation of the 4-second probabilistic model is not warranted due to the
previously illustrated validation of the hourly and 5-minute probabilistic models, which
utilize the same technique as that used in development of the 4-second model.
4.8 Wind Plant Operation Reserve Requirement Assessment
4.8.1 Reserve Required for Wind Plant Operation
In general, during normal operation, utilities carry a certain amount of reserve for various
reasons including the following:
4-12
•
•
•
For reliability: This is the contingency reserve that can be deployed within 10-15
minutes in order to replace any MW loss following line or generator outage. Half
of the reserve must be spinning.
For regulation: This reserve is being provided by fast responding on-line units.
The reserve is deployed to meet the minute-by-minute fluctuation in system load.
North American Electric Reliability Council, NERC, has set the guidelines on
control performance in load regulation.
For intra-hour load following: This reserve is being deployed to follow the withinthe-hour load change in the frequency consistent with the economic dispatch
cycle, i.e. 5 to 10 minutes per cycle. Utilities may not model this requirement
explicitly in running their unit commitment model.
Due to the nature of limited control and variability for wind generation, the operation of wind
generation within the utility grid means that additional reserve is required in order to
•
•
Maintain the same level of control performance in minute-by-minute regulation
with respect to no wind plant scenario
Minimize any additional operating cost due to the balancing of intra-hour slow
variation of wind generation.
In this case study, the trip rate of the wind plant is not available for system reliability
evaluation. Therefore, no change was made in the contingency reserve requirement based on
the outage rate of the wind plant. In the following, we consider the regulation reserve and load
following reserve. We investigate the implication of the wind plant operation to the
requirements of these types of reserve.
Xcel Energy North’s automatic generation control operation explicitly enforces
regulation reserve through imposing regulating margins on the regulating units. For the
units designated as regulating units, a regulating margin is applied. The operating high
limit of a unit less its regulating margin and the operating low limit plus its margin are
respectively the MW amounts used to define the unit economic high and low limits, to be
observed by the economic dispatch calculation. This guarantees that the regulating unit
will always have at least the additional capacity of the regulating margin to ramp up and
down to perform regulation. Our investigation on this type of reserve is the assessment of
the additional amount of reserve required for wind plant operation as compared to the
reserve required with no wind plant operation. Although the case study utility does not
explicitly model load following reserve in the economic dispatch calculation, utility data
indicates that sufficient ramping capability between hours is ensured by the UC
simulation. We will assess the reserve requirement for supporting wind plant operation.
4.9 Statistics of Wind Generation Fluctuation
The methodology utilized to characterize the wind generation fluctuation for the Xcel
Energy case study is based on the approach presented in the report [Hudson 2001] by R.
Hudson and B. Kirby of Oak Ridge National Laboratory (ORNL). In the ORNL report,
only regulating reserve is considered. For this case study, the methodology is extended to
apply to the load following reserve also.
4-13
The approach is based on using the wind generation and system load historical data to
form the distribution of fluctuation with respect to some form of average. Reserve
requirement is then derived on the basis of the standard deviation of the distribution. This
report will not describe the theoretical background of the approach as it is well explained
in the referenced report.
4.9.1 Regulating Reserve
The following steps are taken in applying the ORNL methodology for reserve calculation
to the determination of regulating reserve for the Xcel Energy case study.
1. Use the high-resolution wind generation time series data to form a 1-minute
average time series.
2. Use the 1-minute time series to form the 30-minute moving average time series.
At each time step, the value of the moving average is the average value of all the
1-minute values that falls within the 15-minute window on either side of the
current time step.
3. From the 1-minute time series, subtract the moving average time series to obtain
the time series of fluctuation of wind generation in the regulation time scale.
4. Form the distribution of the fluctuation in the form of MW amount of fluctuation
versus the number of occurrences. Calculate the mean, median and standard
deviation of the distribution.
As the degree of fluctuation could vary from month to month, we apply the procedure above
separately on a monthly basis.
The same procedure was applied to Xcel Energy high-resolution system load time series
data to obtain the distribution of the system load fluctuation in the regulation time scale.
Since the amount of high-resolution historical data for system load available for analysis
was very limited, only a single distribution was developed for system load.
The standard deviation of the distribution provides a good measure of the degree of
variability of a quantity; regulating reserve requirement should be chosen in proportion to
the standard deviation of the quantity that requires regulation.
In the regulation time scale, the load fluctuations among individual customers are
generally not correlated to each other. This is also the case between load and wind
generation.
Let σload and σwind denote the standard deviation of fluctuation of system load and wind
generation, respectively, on separate bases. Without any wind plant operation, the
regulation reserve requirement is proportional to σload. With wind plant operation and
assuming statistical independence between the system load and wind generation
fluctuation, the standard deviation σtotal of the fluctuation of the two quantities in total is
σ2total = σ2load + σ2wind
4-14
The fractional increase in regulation reserve requirement from no wind generation to with
wind generation is (σtotal / σload) –1. According to [Hudson 2001], regulating reserve
chosen to be 3 times the total standard deviation will insure that 99% of the time, the
reserve will be able to cover the minute-by-minute fluctuation of the system load and
wind generation in total.
The statistical results for wind generation and system load fluctuation in the regulation
time scale are given in Section 4.10.
4.9.2 Load Following Reserve
Determining the degree of the wind generation fluctuation in the intra-hour load
following time scale is similar to the procedure for the regulation time scale. The
difference here is that we consider the fluctuation to be the deviation of the 30-minute
moving time series with respect to the hourly average MW level. For completeness, we
present the procedure as follows:
1. From the 30-minute moving average time series, subtract the hourly average MW
level to obtain the wind generation fluctuation time series for the intra-hour load
following time scale.
2. Form the distribution of the fluctuation in the form of MW amount of fluctuation
versus the number of occurrences. Calculate the mean, median and standard
deviation of the distribution.
We calculate distributions on a month of the year basis as well as on the average hourly
generation falling within certain MW range basis. Results are presented in Section 4.10.
The degree of variation in the load following time scale is a good indicator on the level of
load following requirement for the system. Similar to the regulating reserve requirement,
we have to consider both system load and wind generation in total to determine the load
following requirement. Given the degree of variation for these quantities, especially
system load variations from one hour to the next during the day, the load following
requirement is highly time-of-day dependent; for example, there is a large variation for
load during the ramp-up and ramp-down periods, and a small variation during the peak
and off-peak periods. In general, the optimal amount of load following reserve will
minimize the cost of intra-hour following of the change in system load and wind
generation in total. The calculation of such cost requires the knowledge of intra-hour load
ramping rate, amount of wind fluctuation, and generating unit operating limits and
operating costs. Detailed discussion of this subject will be presented in the subsequent
section.
4.10 Results Analysis
Statistical results of the wind generation variability in the regulation time scale are shown
in Figure 4-10 and Table 4-3. April is the month with the highest standard deviation
among all months for which data was available for the calculation. This is not surprising,
4-15
as April is the month with highest energy production. From Table 4-3, the wind
generation standard deviation is 6.34 MW; hence the variance is 40.2 MW2. The standard
deviation for load is 20.03 MW; hence the variance is 401.2 MW. The variance of the
wind generation and load in total is 441.4 MW2. Using the formula provided in Section
4.9.1, the increase in regulation reserve requirement due to wind generation is about
4.8%, which is very minimal.
Additional wind generation installations in the future will definitely require more
regulation reserve for supporting their operation. Consider a total of 10 wind farms
identical to the one at Lake Benton with a total nameplate capacity of about 2700 MW.
Assume that the wind generation fluctuations in the regulation time scale are statistically
independent among all these wind farms. Then the variance of fluctuation of the
aggregate wind generation is 10 times the variance of an individual wind farm which
amounts to 10*40.2 = 402 MW2. This is almost equal to the variance of system load. The
aggregation affect of the load, however, results in a regulating reserve requirement that is
41.5% higher with respect to the reserve requirement under no wind generation operation.
Apr
Feb
Mar
May
Jun
Jul
Aug
0.08
0.07
Frequency
0.06
0.05
0.04
0.03
0.02
0.01
Watts
Figure 4-10 Regulation Time Scale Wind Generation Variability Plots (Month of Year Basis)
Table 4-3 Wind Generation and System Load Variation Statistics in Regulation Time Scale
4-16
8.20E+06
7.20E+06
6.20E+06
5.20E+06
4.20E+06
3.20E+06
2.20E+06
1.20E+06
2.00E+05
-8.00E+05
-1.80E+06
-2.80E+06
-3.80E+06
-4.80E+06
-5.80E+06
-6.80E+06
0
Month
Mean (kW)
Median (kW)
Standard Deviation (kW)
Feb
-2.0
-12.6
3044
Mar
2.0
-3.5
3008
Apr
6.4
6.0
6340
May
2.1
-9.9
3575
Jun
4.8
-8.9
4031
Jul
4.2
-13.9
2763
Aug
4.4
-5.5
1921
Load
53.2
-74.2
20026
Results of the analysis of the wind generation variability in the load following time scale
are presented in
Figure 4-11 and Figure 4-12. The mean, median, and standard deviation for the wind
generation variation in load following time scale are presented in Table 4-4 and Table
4-5. Results of
Figure 4-11 and Table 4-4 are on a month of year basis, while Figure 4-12 and Table 4-5
are on a MW range basis. Table 4-4 shows that April, the month with highest energy
production, has the highest standard deviation. Table 4-5 shows that the 100 to 150 MW
range, the mid range of the wind plant capacity, has the highest standard deviation.
Apr
Feb
Mar
May
Jun
Jul
Aug
0.14
0.12
Frequency
0.1
0.08
0.06
0.04
0.02
2.95E+07
2.45E+07
1.95E+07
1.45E+07
9.50E+06
4.50E+06
-5.00E+05
-5.50E+06
-1.05E+07
-1.55E+07
-2.05E+07
-2.55E+07
-3.05E+07
0
Watts
Figure 4-11 Load Following Time Scale Wind Generation Variability Plots (Month of Year Basis)
4-17
0-25 MW
100-150 MW
25-50 MW
150-200 MW
50-100 MW
200-250 MW
0.14
0.12
Frequency
0.1
0.08
0.06
0.04
0.02
2.40E+07
1.90E+07
1.40E+07
9.00E+06
4.00E+06
-1.00E+06
-6.00E+06
-1.10E+07
-1.60E+07
-2.10E+07
-2.60E+07
0
Watts
Figure 4-12 Load Following Time Scale Wind Generation Variability Plots (MW Range)
Table 4-4 Load Following Time Scale Wind Generation Statistics, Based on Month of Year
Month
Mean (kW)
Median (kW)
Standard Deviation (kW)
Feb
21.7
-3.8
7505
Mar
-5.2
-3.3
6407
Apr
1.0
6.4
9178
May
-3.6
-7.8
6839
Jun
-1.6
0.9
7938
Jul
-8.8
-2.8
6079
Aug
7.1
-10.1
5486
Table 4-5 Load Following Time Scale Wind Generation Statistics, Based on Hourly Energy Level
MWh Range
Mean (kW)
Median (kW)
Standard Deviation
0-25 MW
103
-56
4248
25-50 MW
87
-46
6723
50-100 MW
17
-32
8806
4-18
100-150 MW
-112
49
10532
150-200 MW
-165
111
7104
200-250 MW
-117
56
3276
5 Unit Commitment Operation Scheduling Study
The overview of the project analytical framework described in Section 2 identified the
unit commitment (UC) software as the tools to be used to determine the impact of wind
on NSP’s day-ahead generation scheduling. This section provides a detailed explanation
of the methodologies developed for using the UC software to study the impact of bulk
wind generation on these scheduling functions, as well as the results obtained using the
developed methods. Appendix B provides a general description of how a typical UC
program functions. The analyses described in this section assess only the impacts on the
hourly-resolution time frame, and consequently, use hourly resolution for all study
quantities. All intra-hour impacts are discussed in subsequent sections. The cost of
carrying additional LF reserves to accommodate wind is discussed in Section 6 as part of
the LF cost impacts discussion, despite the fact that the additional LF reserve costs would
be evaluated as part of the day-ahead planning using the hourly resolution UC
simulations.
5.1 Study Objectives
The objectives of the analyses discussed in this section were three-fold:
1. Use UC simulations to evaluate the value of wind generation in terms of the
savings in fuel cost, assuming 100% day-ahead forecasting accuracy. NSP
typically assesses independent proposals for provision of energy from various
generating technologies. As such, the fuel cost savings associated with wind is
not NSP’s primary concern, as they are predominantly interested in the additional
cost to their system operations for incorporating the new generation resource.
Nonetheless, understanding the value of the wind energy is valuable when
considering the total cost to all stakeholders for each alternative. Furthermore, the
simulations required to make this assessment were prerequisite for the other
analyses performed to assess the impact on system operations. Consequently, the
first assessment provides the cost benefit of wind energy assuming the ideal
situation that wind generation is predicted perfectly in the day-ahead planning.
2. Use UC simulations to evaluate the extra operating cost due to the use of
inaccurate wind generation estimates in the operation planning stage. With a
sufficient amount of lead-time in day-ahead scheduling, utility operation planners
are able to consider all of the inexpensive resources and purchase/sell accordingly
to arrive with a minimum cost schedule to meet the system load and reserve
requirements. Wind generation cannot be forecasted perfectly for day-ahead
planning, however, and the NSP real-time operators have to adjust the day-ahead
schedule. They have to make hour-ahead re-scheduling decisions and real-time
re-dispatching decisions with respect to the day-ahead schedule. Since the leadtime for these adjustments is limited, operators must utilize more expensive
generating resources such as peaking units or unfavorably priced energy
transactions. Therefore, the overall operating cost is higher than had the wind
generation been predicted perfectly. The second objective is to evaluate the extra
cost incurred for different degrees of forecast inaccuracy resulting from the
5-1
variability of wind, assuming that the day-ahead scheduling is based on exactly
the forecasted wind generation amount.
3. Given the amount of wind generation forecasting uncertainty, determine the
optimal strategy in operation planning to minimize the extra operating cost due
to forecasting inaccuracy. Objective 2 considers the extra cost for a given
amount of forecast inaccuracy though the operation planner does not know this
amount when he conducts his scheduling. The study of Objective 3 models the
forecast error as a random variable with a given probability density function.
Using the simulation results as obtained in Objective 2 a strategy is developed for
scaling the wind generation forecast amount to be used in day-ahead scheduling.
The strategy will minimize the expected extra cost for the given probability
density of forecast error.
It should be noted that the cost associated with wind forecast inaccuracy in day-ahead
planning results from the inherent variability associated with wind and not operational
negligence. The fact that wind cannot be perfectly forecast in day-ahead planning results
in an unavoidable cost impact of integrating wind. The objectives associated with #2 and
#3 above are to evaluate these cost impacts.
5.2 Unit Commitment Study Framework
5.2.1 Seasonal Scenarios
All of the UC simulations performed for this study are based on a 3-day horizon with
hourly resolution, to be consistent with NSP’s operational planning approach. Two 72hour load profiles were selected from the NSP hourly data to represent two “seasonal”
study scenarios:
1. Winter Case. Characterized by a high wind and medium load scenario using the
load profile of January 2 – 4, 2001.
2. Summer Case. Characterized by a low wind and high load scenario using the load
profile of July 18 – 20, 2001.
These periods were selected based on the following criteria:
1. Relatively high load demand as compared to the remainder of the month.
2. No major generating units on forced outage during the 3-day period.
Note that one of the critical sensitivities not investigated in the current study is the impact
of load uncertainty on the hourly resolution UC simulations. It is expected that including
the variability in the hourly load profile will provide some diversity with the variable
hourly wind generation, decreasing the impact of wind forecast inaccuracy in the dayahead planning. This hypothesis is based on the documented diversity obtained from the
varying load and wind generation profiles at higher resolutions.
5-2
Figure 5-1 and Figure 5-2 show the hourly load, total generation, and interchange profiles
from NSP’s archived data for each of the two 3-day periods chosen for the simulation
study. The sign convention for interchange is a positive value for imports and a negative
value for exports. Note that the NSP generation levels for both 3-day periods are similar
in magnitude, despite the summer demand significantly exceeding the winter demand.
This is the reason that the import for summer is much higher, up to 2000 MW during the
daytime due to the high load demand. Also note that the “Residual” trace is a calculated
value equal to Load – (Generation + Interchange). This value should resolve to zero as it
does for the winter scenario. The investigators were unable to confirm the source of the
small positive “Residual” at the load peaks for summer, but it is assumed that the
associated data discrepancy is negligible.
During the load ramp-up period from 5 a.m. until late morning, both NSP generation and
energy imports increase to meet the increase in system load. During mid-day, imports
remain relatively flat, and generation moves up and down to follow any change in load
usually within a 500 MW range. During the load ramp-down period from very late
evening until 2 a.m., both generation and imports are reduced to follow the load
reduction.
2001 Jan 2-4
Load
Generation
Interchange
Residual
7000
6000
5000
MW
4000
3000
2000
1000
0
-1000
-2000
Figure 5-1 Load, Generation and Interchange Profile of NSP Jan 2-4, 2001
5-3
1/4/2001
12:00
1/4/2001
00:00
1/3/2001
12:00
1/3/2001
00:00
1/2/2001
12:00
1/2/2001
00:00
time
9000
Load
2001 July 18-20
Generation
Interchange
Residual
8000
7000
MW
6000
5000
4000
3000
2000
1000
0
7/20/2001
12:00
7/20/2001
00:00
7/19/2001
12:00
7/19/2001
00:00
7/18/2001
12:00
7/18/2001
00:00
time
Figure 5-2 Load, Generation and Interchange Profile of NSP July 18-20, 2001
5.2.2 General Approach and Assumptions
To account for the variable and non-dispatchable nature of wind generation, a Monte
Carlo approach is utilized. One hundred wind generation hourly-resolution time series of
72 hours (3 days) are generated for each scenario using the wind plant model described in
Section 4. For each wind generation time series, the control area load profile is netted
against wind generation in pre-processing. The UC is then executed with the net load as
an input to be served by non-wind generation. For each wind generation time series, one
unit commitment is performed. Execution is then looped over all wind generation time
series. The results are then obtained from the distribution of simulation outcomes.
As described in Section 4, two different hourly resolution wind models were built for the
study: a high-wind model and a low-wind model. These models synthesize wind
generation time series for the winter case and summer case, respectively. The statistics of
the wind generation time series used for the UC study are shown in Table 5-1. Note that
the “Average MWh” referred to in Table 5-1 is the average total energy of the 100 Monte
Carlo wind series over their respective 72-hour periods.
Table 5-1 Statistics of Wind Generation Time Series
Winter
5913.73
82.14
3183.55
44.22
Average MWh
Average MWh / 72hr
Standard Deviation
Standard Deviation / 72hr
5-4
Summer
4093.83
56.86
2480.72
34.45
The following modeling assumptions were made for the UC simulation setup:
•
•
•
•
•
•
Fuel cost used in the unit commitment simulation for both winter and summer
cases are from the AGC database snapshot of September 2001 provided by NSP.
Only 161 MW for 10-minute spinning reserve requirement and 160 MW for 10minute non-spinning reserve requirement are modeled for all cases, per NSP
personnel.
Consistent with the historical data, most of the inexpensive cycling units are fixed
at generation levels very close to their generating capability. Only four units are
set as dispatchable in the unit commitment setup. Three of the units, Sherco 1, 2
and 3, are from the least expensive “Must-Run” group discussed previously. The
fourth unit, LCG, is from the “Discretionary” group and is about twice as
expensive as the other 3 units. Nonetheless, LCG has an NDC capacity of
262MW and a ramp rate sufficient to meet the hourly load-following requirement
when the Sherco units are removed from AGC to reach their high MDC limits.
The generating unit high limits for Sherco 1, 2 and 35 are set to their respective
MDC capacities, while the high limit for all other units is set to their respective
NDC capacities.
No outage of major units is modeled.
Transaction pricing data is hypothesized, as they were not made available to the
investigators. The criteria for hypothesizing this data was that the transaction
schedule determined by simulation should be close to the historical data and that
the forward transaction price never exceeds $50/MWh. The Table 5-2 and Table
5-3 list the hypothesized transaction prices used for the UC simulations.
Table 5-2 Hypothetical Transaction Price Schedule for Simulation Winter Case
MW block
0-400
401-800
801-1200
Winter
Purchase
$/MWh
15
25
35
Sale
$/MWh
10
10
10
Table 5-3 Hypothetical Transaction Price Schedule for Simulation Summer Case
MW block
0-600
Summer
Purchase
$/MWh
10
5
Sale
$/MWh
8
This is in contrast to the modeling scheme used by NSP in their unit commitment run where normal
dependable capabilities are used as high limits for all Sherco units. This discrepancy was discovered after
the completion of all simulation tasks. Though this discrepancy will affect the absolute value of the
operating cost as determined by the simulation, the investigators believe that it has only a minimal effect on
the relative cost impact of wind generation, which is calculated by taking the operating cost difference
between the no wind generation and with wind generation scenarios.
5-5
601-1000
1001-1400
1401-1800
1801-2200
25
35
45
55
8
8
8
8
5.2.3 Specific Approach for Determining Wind Energy Value
As mentioned previously, the NSP wind energy is valued with a simple 2-step process for
each seasonal scenario:
Step 1
Step 2
Run unit commitment without any wind generation.
Run unit commitment with Monte Carlo loop over all wind generation time
series.
The cost saving of Step 2 with respect to Step 1 is the value of the wind generation. As
mentioned previously, this savings represents only the fuel cost savings compared to
providing this energy through NSP’s existing generation and transaction resources. The
reduced cost does not reflect the energy cost NSP would pay to the wind developer nor
does it include the additional integration costs discussed in the remainder of the study.
The results of this assessment are presented in Section 5.4.1.
5.2.4 Specific Approach for Determining System Operations Cost
Impact of Inaccurate Wind Forecast
In evaluating the cost impacts associated with inaccurate day-ahead wind generation
forecasting, the following assumptions are made regarding NSP’s hour-ahead and realtime re-scheduling strategies:
•
•
Optimistic forecasting of wind generation results in purchasing less energy than
necessary in the day-ahead planning. Thus, the interchange is fixed at the forward
schedule with no further transaction being arranged. Peaking units are dispatched
to compensate for the unrealized wind generation at real-time.
Pessimistic forecasting of wind generation results in purchasing more energy than
necessary in the day-ahead planning. Generation levels of low-cost units are
lowered to accommodate the unexpected increase in wind generation at real-time.
A member of the project Technical Review Committee noted that these two assumptions
may be too conservative and unrealistic, resulting in significantly higher cost impacts for
wind. The primary concern noted was the lack of modeling a real-time (or near real-time)
energy market where NSP can purchase and sell energy for the respective generation
deficits and surpluses resulting from the actual wind generation compared to the estimate
used in planning. Assuming that the real-time energy price should be similar to the
forward market price, the cost increase due to forecast inaccuracy should be much lower
than the results obtained based on the assumptions used in this study.
Having noted this concern, an examination of the historical hourly generation data shows
that NSP has deployed their peaking units routinely for meeting the daily peaks during
the high load summer season. Figure 5-3 and Figure 5-4 show the hourly total generation
5-6
of all NSP peaking units for January and July 2001. Note that NSP also used their
peaking generation on a somewhat regular basis during the lower demand winter daily
peaks. These plots provide a certain degree of validity to the assumptions made for the
UC simulations in this study.
NSP Peaker Generation -- January 2001
800
700
600
MW
500
400
300
200
100
0
1/31/2001
00:00
5-7
1/28/2001
00:00
Figure 5-3 Hourly Generation of all Peaking Units during January 2001
1/25/2001
00:00
1/22/2001
00:00
1/19/2001
00:00
1/16/2001
00:00
1/13/2001
00:00
1/10/2001
00:00
1/7/2001
00:00
1/4/2001
00:00
1/1/2001
00:00
time
NSP Peaker Generation -- July 2001
1200
1000
MW
800
600
400
200
0
7/31/2001
00:00
7/28/2001
00:00
7/25/2001
00:00
7/22/2001
00:00
7/19/2001
00:00
7/16/2001
00:00
7/13/2001
00:00
7/10/2001
00:00
7/7/2001
00:00
7/4/2001
00:00
7/1/2001
00:00
time
Figure 5-4 Hourly Generation of all NSP Peaking Units during July 2001
Based on the identified modeling assumptions of NSP’s re-scheduling scheme in
response to wind generation forecasting inaccuracy, the UC tool is used to evaluate the
increase in operating cost as follows:
Step 1
Use the synthesized wind generation time series as the actual wind
generation. Scale the entire wind generation time series up or down by
certain percentage to represent the error in over optimistic or pessimistic
forecasting.
Step 2 Run UC using Monte Carlo loop with forecasted wind generation time series
(scaled series) to determine the generating unit and transaction schedule as
determined in the day-ahead operation planning stage.
Step 3 Re-run UC using a Monte Carlo loop with the un-scaled wind generation series
and the corresponding transaction levels and cycling units on/off status fixed
according to the associated solution of Step 2 to determine the utility
operating cost under actual wind generation.
Step 4 The cost increase from the Step 3 solution relative to the cost of perfect
wind generation forecasting (Step 2 from Section 5.2.3) is the extra cost due
to forecasting inaccuracy.
The flow chart shown in Figure 5-5 illustrates the basic cost assessment procedure
described in steps 1-4. The STM wind synthesis tool at the left of the flow chart
generates 100 time series representing actual, realized wind generation series for the
seasonal scenario being studied. Through the multiplication operation, these time series
are scaled up and down to provide time series representing inaccurate wind generation
forecast series. Both actual and forecasted wind generation time series are subtracted
5-8
from the system load to obtain the net load as an input to the unit commitment program.
The UC execution shown on the upper path of the flow chart represents the scheduling of
operation planning under a perfect forecast in wind generation. This set of UC
simulations is based on the load series net of the actual wind generation series with no
restrictions on the unit on/off schedule or transaction schedule. The results of this UC
execution comprise the distribution of production cost for perfect wind forecasting, which
serves as the base cost against which the inaccurate forecast costs are compared (Step 2
from Section 5.2.3).
The lower path of the flow chart shows 2 UC executions in series. The first UC
execution (left-most UC box) represents the operation planning scheduling based on a
forecasted wind generation level with different degrees of inaccuracy. The net load series
for which these UC simulations are run is determined by scaling the actual wind
generation time series by a fixed percentage. The generation schedule produced by this
UC execution is used to fix the on/off schedule for the generating units and the
transaction schedule for the second set of UC simulations. The second set of UC
simulations on the lower path represent the generation adjustments made in real-time to
meet the net load based on the actual wind generation. These UC simulations are
performed for the net load associated with that actual wind generation series, but the
on/off schedule of the economic units and the forward transaction schedule is fixed from
the scheduling output for the inaccurate series. The difference in cost of this unit
commitment simulation and the one from perfect forecast is the cost due to forecast
inaccuracy. This cost is determined for both the winter and summer scenarios. These
costs are then annualized to provide an annual estimated cost impact. The results of this
assessment are presented in Section 5.4.2.
5-9
CougarPlus
Unit
Commitment
Tool
NSP Hist. Hr.
Avg. Wind
Gen. Data
100 72-hour
MC Wind
Generation
Time Series
STM Wind
Synthesis
Tool
Inaccuracy
factor
(±10%,
20%, 50%)
X
-
Σ
Σ
2 72-hr NSP
Hist. Load Time
Series
-
-
+
+
Σ
+
Flexible unit on/
off schedule &
transactions
allow ed
CougarPlus
Unit
Commitment
Tool
Fixed unit On/Off
sched. for all units
except peakers.
Fixed transaction
schedule.
CougarPlus
Unit
Commitment
Tool
NSP Unit
Characteristic and
Transaction Data.
Figure 5-5. Flow chart summarizing process for assessing cost impact of imperfect wind forecasting
on day-ahead scheduling.
5.3 Computational Aspects
ABB’s CougerPlusCougerPlus unit commitment software package was utilized for all
of the UC simulations. Upon signing a non-disclosure agreement with ABB, the
investigators were provided a copy of the CougerPlusCougerPlus package and a
temporary license from NSP to perform the simulations for this study. Appendix D
provides a description of the CougerPlusCougerPlus package.
Based on the flow chart, one can ascertain that more than 3600 72-hour UC simulations
were run to obtain the inaccurate wind forecast impacts. For such a large number of
simulations, it was not feasible to operate the UC program interactively through the
CougerPlus Graphical User Interface. Instead, the investigators were able to automate
the process by making use of the text file input/output functionality of the program.
The computer workstation used for the simulation was a Pentium III, 1GHz machine with
512 Mbytes of RAM. On this machine, one deterministic 72-hour horizon UC simulation
required approximately 30 seconds. One Monte Carlo loop consisting of 100
deterministic simulation runs required approximately 50 minutes.
5-10
5.4 Simulation Results
This section provides the results obtained by performing the procedures identified in
Section 5.2 to determine the impacts of wind generation on the hourly scheduling
determined by UC.
5.4.1 No Wind and Perfectly Forecasted Wind Cases
This section provides the simulation results for the no wind generation cases and perfect
forecast wind generation cases. These two results are the components that were
identified for determining the value of wind energy (Objective 1 from Section 5.1). The
perfect forecast wind generation case results are also used in determining the inaccurate
forecasting cost impacts as discussed in Section 5.2.4.
Winter Scenario
Table 5-4 summarizes the total cost for no wind generation and perfectly forecasted wind
generation cases as well as the cost saving in dollars and percentage. Note that the cost
included in Table 5-4 for the perfectly forecasted wind generation scenario is an expected
value over the entire MC set of 100 synthesized wind generation time series. Figure 5-6
shows the cost distribution for the 100 MC simulation solutions.
Table 5-4 Winter Scenario Simulation Results for “No Wind” and “Perfectly Forecasted Wind
Generation” Cases
Cost (k$)
No Wind Generation
Wind Generation assuming
Perfect Forecasting
Inc(+) / Dec(-)
Cost (k$)
Inc(+) / Dec(-)
Cost (%)
3235.70
3156.08
-79.62
-2.46
Figure 5-6 Distribution of Total Cost with Wind Generation, Winter Case
Dividing the expected value of cost saving which is 79.62 k$ by the expected total energy
of the wind generation which is 5913.73 MWh, the value of the wind energy is $13.46/
MWh. It should be noted that the reduced cost does not reflect the energy cost NSP
would pay to the wind developer nor does it include the additional integration costs
discussed in the remainder of the study.
Summer Scenario
5-11
Table 5-5 summarizes the total cost for no wind generation and perfectly forecasted wind
generation scenarios as well as the cost savings in dollars and percentage. Again the
perfectly forecasted wind generation cost in this table is an expected value. Figure 5-7
shows the cost distribution for 100 MC solutions.
Table 5-5. Summer Scenario Simulation Results for no Wind and with Wind Generation Cases
Cost (k$)
No Wind Generation
Wind Generation assuming
Perfect Forecasting
Inc(+) / Dec(-)
Cost (k$)
Inc(+) / Dec(-)
Cost (%)
5765.60
5630.31
-135.29
-2.30
Dividing the expected value of cost savings which is 135.29 k$ by the expected total
energy of the wind generation which is 4093.83 MWh, the value of the wind energy is
$33.05/ MWh.
Note that wind generation has a higher value in summer than in winter because the
energy purchase that wind generation displaces has a much higher marginal cost. Based
on our simulation with hypothetical transaction price data, the marginal cost for energy
purchases during the winter simulations is primarily 15 $/MWh compared to the energy
purchase cost for the mid-day summer hours where it could be as high as 55 $/MWh.
Again, the results should be considered along with the fact that the reduced cost does not
reflect the energy cost NSP would pay to the wind developer nor does it include the
additional integration costs discussed in the remainder of the study.
Figure 5-7 Distribution of Total Cost with Wind Generation, Summer Case
Annualized Value
Simulations were not performed for spring or fall. For determining an annualized value, it
is assumed that the value of the wind generation is equal to the value determined for the
winter scenarios as the load demand of these two seasons are less than for the winter
season. By taking the average over all four seasons of the year, the annualized value of
the wind generation is:
Wind Generation Annualized Value = 18.36 $ / MWh
Validation of Simulation Results
5-12
Figure 5-8 compares the simulation results for the no wind generation winter scenario
with the actual NSP measured data for the same 3-day period. Figure 5-8 shows that from
late morning to about 9 p.m. each day, the simulated interchange value tends to follow
the load shape slightly more than the measured interchange, which is flatter during this
period. This small discrepancy may be attributable to the fact that in the UC simulations,
transactions are determined independently on an hour-by-hour basis. The UC
optimization algorithm will seek the lowest cost solution by varying the transaction
amount for each hour. In actuality, NSP may get a better price by arranging energy
purchasing on a multiple-hour block basis.
2001 Jan 2-4
Meas. Load
Meas. Gen
Meas. Int
Sim. Int
Sim. Gen
7000
6000
5000
MW
4000
3000
2000
1000
0
-1000
1/4/2001
12:00
1/4/2001
00:00
1/3/2001
12:00
1/3/2001
00:00
1/2/2001
12:00
1/2/2001
00:00
time
Figure 5-8 Comparison of the simulated and measured load, generation and interchange profiles for
the winter scenario, no wind generation case.
Figure 5-9 compares the simulated and measured hourly generation levels of the 3 Sherco
units for the winter scenario “no wind” case. The associated plots show a similar
generating range for all 3 units. The measured data shows a much higher degree of
fluctuation in the generation levels of these units, whereas the simulated generation levels
are very steady during in the on-peak daytime hours and off-peak hours after midnight.
The relatively constant simulated generation levels are partly due to the hourly
transaction modeling described previously.
Inspection of the measured data suggests a considerable amount of real-time intervention
by the NSP operators, including the following:
•
Use of peaking units for increased generation as evidenced by the sharp
reductions of the Sherco units during peak hours
5-13
•
Increase of generation levels of some or all of the Sherco units from their NDC
capacity to their MDC capacity to obtain additional generation.
The UC simulations are intended to mimic the NSP operations planning mechanism for
developing hourly generating schedules. The decision to utilize the expensive peaker
units is a real-time operating decision. Consequently, none of the peaking units are
started in the results of this simulation run.
The complete hourly generation schedule obtained from the winter scenario, no wind
case is presented in Appendix E for reference.
2001 Jan 2-4
Meas. SHC1
Sim. SHC1
Meas. SHC2
Sim. SHC2
Meas. SHC3
Sim. SHC3
900
850
800
750
MW
700
650
600
550
500
450
400
1/4/2001
12:00
1/4/2001
00:00
1/3/2001
12:00
1/3/2001
00:00
1/2/2001
12:00
1/2/2001
00:00
time
Figure 5-9 Comparison of the simulated and measured generation profiles of the 3 Sherco units for
the winter scenario, no wind generation case.
Figure 5-10 compares the simulation results of the no wind generation summer case
scenario with the actual NSP measured data for the same 3-day period. Figure 5-11
compares the simulation results and the measured hourly generation levels of the 3
Sherco units for the summer scenario “no wind” case. These plots show similar results to
the winter case. Note that the zero generation level of Sherco 2 for the first several hours
of the study horizon suggests that the unit was on outage during that time.
5-14
9000
Meas. Load
2001 July 18-20
Meas. Gen
Meas. Int
Sim. Gen
Sim. Int
8000
7000
MW
6000
5000
4000
3000
2000
1000
0
7/20/2001
12:00
7/20/2001
00:00
7/19/2001
12:00
7/19/2001
00:00
7/18/2001
12:00
7/18/2001
00:00
time
Figure 5-10 Comparison of the simulated and measured load, generation and interchange profiles for
the summer scenario, no wind generation case.
1000
Meas. SHC1
Sim. SHC1
2001 July 18-20
Meas. SHC2
Sim. SHC2
Meas. SHC3
Sim. SHC3
900
800
700
MW
600
500
400
300
200
100
0
7/20/2001
12:00
7/20/2001
00:00
7/19/2001
12:00
7/19/2001
00:00
7/18/2001
12:00
7/18/2001
00:00
time
Figure 5-11. Comparison of the simulated and measured generation profiles of the 3 Sherco units for
the summer scenario, no wind generation case.
5-15
5.4.2 Inaccurate Wind Forecast Cases
This section provides the simulation results for the inaccurate wind generation cases.
These results along with the perfect forecast wind generation case results from the
previous section are the components that were identified for determining the cost impact
of inaccurate forecasting in the day-ahead scheduling (Objective 2 from section 5.1). As
noted in Section 5.2.4, the 100 wind generation time series synthesized by the wind
model for each season scenario represent the set of actual realized wind generation time
series. These wind generation series are scaled up and down to represent both overoptimistic and over-pessimistic wind generation forecasts to be used in the day-ahead
scheduling phase. Simulations were performed for forecast errors of ±10%, ±20% and
±50% with respect to the actual wind generation time series. The complete simulation
procedure is described in Section 5.2.4.
5.4.2.1 Impact of Inaccurate Forecast on Forward Energy Purchases -Winter Scenario
Figure 5-12 shows the distribution of energy purchase costs obtained from the UC MC
simulations for the ±10% forecast error cases for the winter scenario. The distribution of
energy purchase costs obtained from the perfect wind generation forecast MC simulations
are also shown for reference. Figure 5-12b shows that the distribution for the 10% overpessimistic forecast cases is shifted to the right indicating that more energy is purchased
in the day-ahead. Conversely, Figure 5-12b shows that the distribution of purchase costs
for the 10% over-optimistic forecast cases is shifted to the left indicating that less energy
is purchased forward when operators plan for more wind generation than is realized.
Figure 5-13 and Figure 5-14 show the simulated purchase cost distributions for the ±20%
and ±50% forecast inaccuracy MC sets, respectively. When viewed in sequence, these
three figures show that as the percentage of error for the over-pessimistic forecast
increases, the distribution shifts further to the right representing the fact that more energy
is purchased via forward contracts in the day-ahead market. These figures also show the
opposite trend towards fewer forward purchases for the over-optimistic case.
Another interesting observation is that as the forecasting inaccuracy for the overpessimistic cases increases, the spread of the distribution decreases. Conversely, the
distribution tends to spread out more as the level of over-optimistic forecasting increases.
The reason is mainly due to the way the time series representing the inaccurate wind
forecasts are manufactured. By scaling up the original, or realized, wind time series set,
the over-optimistic forecast set of time series clearly has a larger spread in total energy.
By scaling down, the spread is definitely smaller.
5-16
Costs (k$)
Figure 5-12 Distribution of Energy Purchase for +/- 10% Forecast Inaccuracy, Winter Case
Costs (k$)
Figure 5-13 Distribution of Energy Purchase for +/- 20% Forecast Inaccuracy, Winter Case
5-17
Costs (k$)
Figure 5-14 Distribution of Energy Purchase for +/- 50% Forecast Inaccuracy, Winter Case
5.4.2.2 Impact of Inaccurate Forecast on Total Production Cost -Winter Scenario
Figure 5-15, Figure 5-16 and Figure 5-17 show the total production cost distributions for
the ±10%, ±20% and ±50% forecast inaccuracy MC simulation sets, respectively. The
cost distribution for the perfect forecast MC simulation set is included in each figure for
reference.
5-18
Costs (k$)
Figure 5-15 Distribution of Cost for +/- 10% Forecast Inaccuracy, Winter Case
Costs (k$)
Figure 5-16 Distribution of Cost for +/- 20% Forecast Inaccuracy, Winter Case
5-19
Costs (k$)
Figure 5-17 Distribution of Cost for +/- 50% Forecast Inaccuracy, Winter Case
Table 5-6 provides the expected values for the total production cost distributions for the
various forecast inaccuracy MC simulation sets. Table 5-7 summarizes this expected cost
data in terms of the incremental cost above the perfect wind forecast distribution
expected value. Figure 5-18 summarizes these numbers graphically, showing the
expected cost versus the different percentages of forecast inaccuracy investigated. Note
that although a negative percentage value is used to indicate the pessimistic forecast
error, the cost of pessimistic forecasting error is plotted against the error percentage in
absolute value so that the cost of both optimistic and pessimistic inaccuracy can be
compared in one single figure.
Table 5-6. Operating Cost for Different Percentages of Forecast Error, Winter Case
Forecast Error %
Pessimistic case cost (k$)
Optimistic case cost (k$)
0
3160.23
3160.23
10
3160.04
3160.78
20
3160.12
3162.10
50
3162.91
3164.84
Table 5-7. Extra Operating Cost for Different Percentages of Forecast Error, Winter Case
Forecast Error %
Pessimistic case extra cost (k$)
Optimistic case extra cost (k$)
0
0.00
0.00
5-20
10
-0.19
0.55
20
-.11
1.87
50
2.68
4.61
Figure 5-18 Plots of Expected Cost versus Forecast Inaccuracy - Winter Case
In principle, given that exactly the inaccurate forecast amount is used in the unit
commitment for operation planning, it is expected that the total production cost should
not decrease, but rather will usually increase for any amount of forecast error,
irrespective of whether the error is optimistic or pessimistic. Figure 5-18, however, shows
that for the pessimistic case, the total cost for errors of 10% and 20% are very slightly
less than the perfect forecast production cost. This discrepancy can be attributed to the
sub-optimal nature of the unit commitment algorithm, which finds a solution within 3 to
4% of the true optimal cost solution.
5.4.2.3 Impact of Inaccurate Forecast on Forward Energy Purchases -Summer Scenario
Figure 5-19, Figure 5-20 and Figure 5-21 show the distribution of energy purchase costs
obtained from the UC MC simulations for the ±10%, ±20% and ±50% forecast error
cases, respectively, for the summer scenario. The distribution of energy purchase costs
obtained from the perfect wind generation forecast MC simulations are also shown for
reference. The same trends in distribution skew and spread as a function of the
percentage of forecast error that were noted for the winter scenario cases are also evident
in the summer scenario distributions.
5-21
Costs (k$)
Figure 5-19 Distribution of Energy Purchase for +/- 10% Forecast Inaccuracy, Summer Case
Costs (k$)
Figure 5-20 Distribution of Energy Purchase for +/- 20% Forecast Inaccuracy, Summer Case
5-22
Costs (k$)
Figure 5-21 Distribution of Energy Purchase for +/- 50% Forecast Inaccuracy, Summer Case
5.4.2.4 Impact of Inaccurate Forecast on Total Production Cost -Summer Scenario
Figure 5-22, Figure 5-23 and Figure 5-24 show the total production cost distributions for
the ±10%, ±20% and ±50% forecast inaccuracy MC simulation sets, respectively, for the
summer scenario. The cost distribution for the perfect forecast MC simulation set is
included in each figure for reference.
5-23
Costs (k$)
Figure 5-22 Distribution of Cost for +/- 10% Forecast Inaccuracy, Summer Case
Costs (k$)
Figure 5-23 Distribution of Cost for +/- 20% Forecast Inaccuracy, Summer Case
5-24
Costs (k$)
Figure 5-24 Distribution of Cost for +/- 50% Forecast Inaccuracy, Summer Case
Table 5-8 provides the expected values for the total production cost distributions for the
various summer scenario forecast inaccuracy MC simulation sets. Table 5-9 summarizes
this expected cost data in terms of the incremental cost above the perfect wind forecast
distribution expected value. Figure 5-25 summarizes these numbers graphically, showing
the expected cost versus the different percentages of forecast inaccuracy investigated.
Note that although a negative percentage value is used to indicate the pessimistic forecast
error, the cost of pessimistic forecasting error is plotted against the error percentage in
absolute value so that the cost of both optimistic and pessimistic inaccuracy can be
compared in one single figure.
Table 5-8. Operating Cost for Different Percentages of Forecast Error, Summer Case
Forecast Error %
Pessimistic case cost (k$)
Optimistic case cost (k$)
0
5670.27
5670.27
10
5677.98
5765.06
20
5683.85
5784.04
50
5699.99
5816.69
Table 5-9. Extra Operating Cost for Different Percentages of Forecast Error, Summer Case
Forecast Error %
Pessimistic case extra cost (k$)
Optimistic case extra cost (k$)
0
0.00
0.00
5-25
10
7.71
94.79
20
13.58
113.77
50
29.72
146.42
Figure 5-25 Plot of Expected Cost versus Forecast Inaccuracy, Summer Case
The cost increase due to forecast inaccuracy for the summer scenario is much more
pronounced than for winter. In the summer scenario, the marginal cost of energy
transactions is much higher because of the higher load demand. Furthermore, all NSP’s
coal-fired and oil-fired generating units that are capable of providing inexpensive
generation are scheduled up to their high limit. Consequently, for an over-optimistic
forecast error as small as 10%, an expensive peaking unit has to be dispatched for
additional generation during re-scheduling because there are no more inexpensive
generating resources available. The summer scenario simulations dispatched the FEN3
peaking unit, which is NSP’s least expensive peaking unit. The sharp increase in total
production cost for the 10% over-optimistic case relative to the perfect forecast case
shown in Figure 5-25 is due to the high peaking unit startup cost and no load cost.
The cost impacts of inaccurate wind forecasts presented in this section assume a constant
forecast error and are based on an operational strategy of including the exact wind
generation forecast in the day-ahead UC planning. This is not the strategy utilized by
NSP operators. As noted in Section 3.2, in the UC simulations used for day-ahead
scheduling, NSP Operators scale the forecasted wind generation based on an intuitionbased method. This is done to hedge against the uncertainty of the wind generation.
Consequently, the absolute forecast inaccuracy costs presented in this section might not
accurately represent the cost impact to NSP since the hedging strategy is not considered.
Such a strategy is considered in Section 5.5.
5-26
5.5 Strategy in Operation Planning for Wind Generation
Forecast with Random Error
In reality, forecasting error is random, fluctuating between positive and negative values
of varying magnitude. The error associated with a given forecast is unknown until after
the actual wind generation is observed. In evaluating the effect of randomness in
forecasting, the forecast error was modeled as a random variable with a given probability
distribution. Furthermore, the extra operating cost due to error in forecasting was treated
as a random variable for which its expected value can be evaluated. For simplicity in
calculation, a highly idealized uniform distribution with equal range for positive and
negative error values was considered. The simulation results presented in the previous
section assessed the extra operating costs for inaccurate wind forecasts based on an
operational strategy of including the exact wind generation forecast in the day-ahead UC
planning. As noted, this does not include the somewhat arbitrary hedging strategy utilized
by NSP operators. The section presents several operation planning strategies whereby
the wind generation forecast is scaled before inclusion in the unit commitment
scheduling. Implementation of these different strategies or scaling factors result in
different distributions of the extra operating cost and the associated expected values The
various strategies are evaluated relative to the reduction in the expected extra cost that
was determined for using exactly the forecasted generation value.
5.5.1 Cost of Inaccuracy Function and Linearity Assumption
Section 5.4.2 presented the additional costs associated with inclusion of both overoptimistic and over-pessimistic forecasts in NSP’s day-ahead planning. For either case,
the extra cost is a continuous function of the forecast error percentage. Consider these
two continuous functions, which shall be referred to as the extra cost of pessimistic
inaccuracy and extra cost of optimistic inaccuracy and denoted as ∆dn ( ⋅ ) and ∆up ( ⋅ ) ,
respectively, where the function argument is the absolute value of the error percentage.
The argument of these functions can only assume the positive range. Both functions start
at the origin because by definition, a zero percent results in no extra cost. As the error
percentage increases, the value of both functions increases, or at least does not decrease.
For illustration purposes, it is assumed that both functions are linear. The methodology
presented, however, is valid for any cost function, linear or not. It is further assumed that
the linear approximation is derived from the straight line going through the origin and the
point associated with extra cost of 50% error. For the remainder of this section, the
inaccuracy cost function is considered to be this line. Figure 5-26 shows the original cost
functions (broken lines) compared to the linear approximations (solid line) for the winter
scenario. Figure 5-27 shows the corresponding plots for the summer scenario.
5-27
Figure 5-26 Linearized Inaccuracy Cost Functions for Winter Case
Figure 5-27 Linearized Inaccuracy Cost Functions for Summer Case
The mathematical expressions for the linearized cost of inaccuracy functions with y
denoting the error percentage are:
Winter
Over Pessimistic: ∆dn ( y ) = 0.0536 y
5-28
Over Optimistic: ∆up ( y ) = 0.0922 y
Summer
Over Pessimistic: ∆dn ( y ) = 0.5944 y
Over Optimistic: ∆up ( y ) = 2.9284 y
5.5.2 Probability Density of Forecast Error
The key to this scaling methodology is understanding the statistical nature of the wind
generation forecast error. Since very little forecasting statistical data was available from
NSP, the following assumptions were made:
•
•
Wind generation forecast is unbiased in the sense that the expected value of the
forecast is equal to the actual generation or the expected value of the forecast error is
equal to zero.
The forecast error is a uniformly distributed random variable between –x% and x%,
where x is a non-negative number representing the reliability of the forecast. A
narrow distribution range means that the forecasting is reliable and accurate. As the
width of the distribution range increases, the implied accuracy of the forecast
decreases. This assumption is made to simplify the calculation of the expected extra
cost associated with the wind forecast inaccuracy using the scaling strategy. Without
this assumption, the expected value of the extra cost will not have a closed-form
solution, but rather will have to be evaluated numerically.
Mathematically, the uniformly distributed probability density function of the random
variable with a given range x is
p( y ) = 1 / (2 x )
= 0
for − x ≤ y ≤ x
otherwise
Figure 5-28 shows the assumed uniformly distributed forecast error probability density
function.
5-29
P (y)
-X%
+X%
0%
% Forecast Error
Figure 5-28. Assumed uniformly distributed forecast error probability density function.
5.5.3 Expected Extra Operating Cost for Different Scaling Strategies
In this section, several wind generation forecast scaling strategies for operations planning
are considered. The scaled forecasts are to be used as an input to the daily unit
commitment scheduling for operations planning. In this section, we calculate the
expected value of the extra cost due to forecast inaccuracy for a forecast error distribution
range of 50% (i.e. x = 50) of the actual wind generation. Other distribution ranges are
considered in the next section.
5.5.3.1 Strategy A – No Scaling
Strategy A serves as the base case whereby the wind generation forecast is not scaled, or
stated another way, whereby the forecast is scaled by 1, i.e. use the original forecast time
series for unit commitment simulation. For any positive forecast error of y% with 0 ≤ y ≤
50, the extra cost is determined from the cost function ∆up ( ⋅ ) evaluated at y. For any
negative forecast error of y%, the extra cost is determined from the cost function
∆dn ( ⋅ ) evaluated at y. As a random variable, the extra cost can assume values along
∆up ( ⋅ ) with argument y ranging from 0 to 50 and assume values from ∆dn ( ⋅ ) with the
same argument range. The expected value of the extra cost for Strategy A is evaluated as
follows:
50
E (extra cos t ) =
up
∫ p( y) ⋅ ∆ ( y) ⋅ dy +
0
50
50
∫ p(− y ) ⋅ ∆
dn
( y ) ⋅ dy
0
50
= ∫ (1 / 100) ⋅∆ ( y ) ⋅ dy + ∫ (1 / 100) ⋅ ∆dn ( y ) ⋅ dy
up
0
0
= 0.5 ⋅ (∆ (25) + ∆ (25))
up
dn
5-30
The second equality results from the uniformly distributed characteristic of the
probability density and the last equality results from the assumed linearity of the cost
functions.
Using the formula above, the expected extra cost due to wind forecast inaccuracy in dayahead scheduling using a scaling factor of 1 and an assumed forecast error distribution
range of ± 50% is
Winter: Expected extra cost = 1.82 k$
Summer: Expected extra cost = 44.04 k$
Note that by accounting for the fact that the forecast error is equally likely to be a value
in the range of ± 50%, the expected value of extra costs drops from the constant 50%
error values determined by simulation to be 4.61k$ and 146.62k$ (sections 5.4.2.2 and
5.4.2.4) for winter and summer, respectively.
5.5.3.2 Strategy B – Scale Forecasts by 50%
In strategy A, for any positive forecasting error, the extra cost incurred is determined
from ∆up ( ⋅ ) , which is characterized by much larger values than ∆dn ( ⋅ ) for summer
because the inclusion of over-optimistic wind generation forecast in day-ahead planning
requires peakers or other expensive adjustments. Here we use a different strategy, which
prohibits over-optimistic estimates and thereby avoids incurring the higher costs
associated with ∆up ( ⋅ ) . For Strategy B, the forecast is scaled by 0.5 prior to inclusion in
the unit commitment day-ahead scheduling. The result is the following:
•
•
For a positive forecast error of y% with 0 ≤ y ≤ 50, unit commitment actually sees a
negative forecast error of 100-0.5(100+y) or (50 – 0.5y)%. Therefore, for positive
forecast error ranging from 0 to 50%, unit commitment sees a negative error ranging
from 50 to 25%, moving the upper end of the forecast error distribution range to 75%
of the actual generation as shown in Figure 5-29.
For any negative error, the scaling by 0.5 actually increases the amount of negative
error seen by unit commitment. For negative forecast error of y% with 0 ≤ y ≤ 50,
unit commitment actually sees a negative error of 100-0.5(100-y) or (50+0.5y)%.
Therefore, for negative error ranging from 0 to 50%, unit commitment sees a negative
error ranging from 50 to 75%, moving the lower end of the forecast error distribution
range to 25% of the actual generation as shown in Figure 5-29.
5-31
P (y)
P (y)
50%
150%
25%
50%
75%
150%
100%
100%
Actual
Generation
Actual
Generation
Figure 5-29. Change in forecast error distribution in UC day-ahead planning using scaling Strategy
B.
The expected extra cost for strategy B is evaluated as follows:
50
E (extra cos t ) =
∫
50
p( y ) ⋅ ∆dn (50 − 0.5 y ) ⋅ dy +
0
∫ p(− y ) ⋅ ∆
dn
(50 + 0.5 y ) ⋅ dy
0
50
50
= ∫ (1 / 100) ⋅∆dn (50 − 0.5 y ) ⋅ dy + ∫ (1 / 100) ⋅ ∆dn (50 + 0.5 y ) ⋅ dy
0
0
= ∆ (50)
dn
Using the formula above, the expected extra cost due to wind forecast inaccuracy in dayahead scheduling using a scaling factor of 0.5 and an assumed forecast error distribution
range of ± 50% is
Winter: Expected extra cost = 2.68 k$
Summer: Expected extra cost = 29.72 k$
It is interesting to note that in summer, strategy B results in a lower expected extra cost
for the summer scenario than obtained for strategy A (no scaling). This is because ∆up ( ⋅ )
is much larger in value than ∆dn ( ⋅ ) for the same % error value for the summer scenario,
and strategy B moves all forecast errors to the over-pessimistic function. Conversely,
the spread between the two cost functions is much less for winter, such that strategy A is
slightly better for the winter scenario. This is because the expected value of strategy A is
evaluated using the low portion of both functions and it is evaluated in strategy B using
the middle portion of ∆dn ( ⋅ ) .
5.5.3.3 Strategy C – Scale Forecasts by 200%
To demonstrate the impact on the expected extra cost of exclusively using ∆up ( ⋅ ) ,
Strategy C is based on scaling the wind generation forecast by 2 for inclusion in the unit
commitment day-ahead planning. The result is the following:
5-32
•
•
For any positive error, the scaling by 2 actually increases the amount of positive error
seen by unit commitment. For a positive forecast error of y% with 0 ≤ y ≤ 50, unit
commitment actually sees a larger forecast error of 2(100+y) - 100 or (100 + 2y)%.
Therefore, for a positive forecast error ranging from 0 to 50%, unit commitment sees
a positive error ranging from 100 to 200%, moving the upper end of the forecast error
distribution range to 300% of the actual generation as shown in Figure 5-30.
For negative forecast error of y% with 0 ≤ y ≤ 50, unit commitment actually sees a
positive error of 2(100-y) – 100 or (100-2y)%. Therefore, for a negative error ranging
from 0 to 50%, unit commitment sees a positive error ranging from 100% to 0%,
moving the lower end of the forecast error distribution range to 100% of the actual
generation as shown in Figure 5-30.
P (y)
50%
150%
P (y)
100%
Actual
Generation
25%
50%
150%
75%
300%
100%
Actual
Generation
Figure 5-30. Change in forecast error distribution in UC day-ahead planning using scaling Strategy
C.
The expected extra cost for strategy C is evaluated as follows:
50
E (extra cos t ) =
∫ p( y) ⋅ ∆
up
0
50
(100 + 2 y ) ⋅ dy +
∫ p(− y ) ⋅ ∆
up
(100 − 2 y ) ⋅ dy
0
50
50
0
0
= ∫ (1 / 100) ⋅∆up (100 + 2 y ) ⋅ dy + ∫ (1 / 100) ⋅ ∆up (100 − 2 y ) ⋅ dy
= ∆ (100)
up
Using the formula above, the expected extra cost due to wind forecast inaccuracy in dayahead scheduling using a scaling factor of 2 and an assumed forecast error distribution
range of ± 50% is
5-33
Winter: Expected extra cost = 9.22 k$
Summer: Expected extra cost = 292.84 k$
As expected, the expected cost impact of wind forecast inaccuracy in day-ahead planning
increases significantly for both winter and summer scenarios using Strategy C. This is
because the over-optimistic cost inaccuracy functions produce higher expected cost
values than the over-pessimistic inaccuracy functions. By scaling the wind generation
forecast up, Strategy C basically transforms all of the forecast errors into over-optimistic
errors in the day-ahead UC scheduling. This is definitely not a good strategy.
5.5.3.4 Strategy D – Scale Forecasts so Upper Error Distribution Range
Equals Actual Generation
Using 0.5 as a scaling factor in strategy B, the expected extra cost is evaluated using the
25 to 75% range of the over-pessimistic inaccuracy function, ∆dn ( ⋅ ) , resulting in a lower
expected cost than the base case. The expected extra cost can be reduced further by
modifying the value of the scaling factor so that the lowest possible portion of ∆dn ( ⋅ ) is
used in the evaluation. Strategy D uses a wind generation forecast scaling factor that
transfers the upper end of the forecast error distribution range to 100% of the actual
generation. As shown in Figure 5-31, for a distribution error range of ± 50%, the
appropriate scaling factor is 2/3, or 0.667 prior to inclusion in the unit commitment dayahead scheduling. The result is as follows:
•
•
For a positive forecast error of y% with 0 ≤ y ≤ 50, unit commitment actually sees a
negative forecast error of 100-0.667(100+y) or (33.33 – 0.667y)%. Therefore, for
positive forecast error ranging from 0 to 50%, unit commitment sees a negative error
ranging from 33.33% to 0%, moving the upper end of the forecast error distribution
range to 100% of the actual generation as shown in Figure 5-31.
For any negative error, the scaling by 0.667 increases the amount of negative error
seen by unit commitment. For negative forecast error of y% with 0 ≤ y ≤ 50, unit
commitment actually sees a negative error of 100-0.667(100-y) or (33.33+0.667y)%.
Therefore, for a negative error ranging from 0 to 50%, unit commitment sees a
negative error ranging from 33.33% to 66.67%, moving the lower end of the forecast
error distribution range to 33% of the actual generation as shown in Figure 5-31.
P (y)
50%
P (y)
150%
33.33%
150%
100%
100%
Actual
Generation
Actual
Generation
5-34
Figure 5-31. Change in forecast error distribution in UC day-ahead planning using scaling Strategy
D.
The expected extra cost for strategy C is evaluated as follows:
50
dn
∫ p( y) ⋅ ∆ (33.33 − 0.667 y) ⋅ dy +
E (extra cos t ) =
0
50
50
∫ p(− y) ⋅ ∆
dn
(33.33 + 0.667 y ) ⋅ dy
0
50
= ∫ (1 / 100) ⋅∆ (33.33 − 0.667 y ) ⋅ dy + ∫ (1 / 100) ⋅ ∆dn (33.33 + 0.667 y ) ⋅ dy
dn
0
0
= ∆ (33.33)
dn
Using the formula above, the expected extra cost due to wind forecast inaccuracy in dayahead scheduling using a scaling factor of 0.667 and an assumed forecast error
distribution range of ± 50% is as follows
Winter: Expected extra cost = 1.77 k$
Summer: Expected extra cost = 19.83 k$
By avoiding the higher costs of over-optimistic forecasts, and moving the range of overpessimistic forecast errors to a less expensive range of the associated forecast inaccuracy
function, Strategy D reduces the expected cost impacted for both winter and summer
scenarios. It is clear from the summary of the investigated strategies shown in Table
5-10, Strategy D is the best strategy for both seasons by far.
Table 5-10. Summary of performance for identified scaling strategies.
Strategy
Scaling
Factor
A
B
C
D
1.000
0.500
2.000
0.667
Winter -- Expected
Cost Impact (k$)
Summer -- Expected
Cost Impact (k$)
1.82
2.68
9.22
1.77
44.04
29.72
292.84
19.83
5.5.3.5 Determination of Optimal Scaling Strategy
Using the two cost functions and the probability density function of the forecast error, we
can formulate a mathematical optimization problem to minimize the expected extra cost.
The detailed formulation is not presented here. For the summer scenario, the optimal
scaling factor is 0.723, which yields an expected extra cost of 18.98 k$. With this scaling
factor, a very small segment at the low end of ∆up ( ⋅ ) and a larger segment at the low end
∆dn ( ⋅ ) are used in the expected cost calculation. Of course, for the probability density
with different distribution ranges, the optimal scaling factor value is going to be different.
A similar calculation was not performed for the winter case.
In general, using a scaling factor less than 1 is consistent with the operation planning
strategy of NSP. The implication of using a scaling factor less than 1 when performing
operation planning is that the NSP operators are hedging against the situation where less
5-35
wind energy is realized than the forecasted amount. This strategy is equivalent to using
the actual forecast in operation planning, but setting aside extra reserve to hedge against
the forecasted wind energy not being realized in real time.
5.5.4 Expected Extra Cost Incurred by NSP due to Wind Generation
Forecast Inaccuracy in Day-Ahead UC Scheduling
Section 5.5.3 presents several different strategies for trying to minimize the cost of
forecast inaccuracy in day-ahead scheduling by scaling the wind generation forecast used
in performing unit commitment. These strategies were assessed using only the probability
density of the forecast error with a range from -50% to +50%. As mentioned previously,
the expected cost impact calculated for a particular strategy varies with the forecast error
range. In this section, Strategy D is used to determine scaling factors and inaccuracy cost
functions for different forecast error distribution ranges, which are then used to calculate
additional cost incurred by NSP due to the inclusion of inaccurate wind generation
forecast in the their day-ahead unit commitment scheduling. As mentioned previously,
NSP uses a scaling strategy that is less well defined. Although not identical to NSP’s
operational strategy, Strategy D is selected to determine this cost impact component for
the NSP case study due to its simplicity and effectiveness in minimizing the cost impact.
Note that the results presented in this section are all determined using the assumptions
described for Strategy D in Section 5.5.3.4, including the linearity of the cost function
and the uniform distribution of forecast error.
Using the same Strategy D approach presented for the 50% distribution range in the
previous section, the Strategy D scaling factors and inaccuracy cost expressions were
determined for error distribution ranges of ± 10%, ±20%, ± 30%, and ± 40. These results
are listed in Table 5-11.
Table 5-11. Scaling Factors and Expected Extra Costs for Different Distribution Ranges - Strategy D
Distribution Range %
10
Scaling Factor
0.909
Expected Extra Cost
∆dn ( 9.09 )
20
0.833
∆dn ( 16.67 )
30
0.769
∆dn ( 23.08 )
40
0.714
∆dn ( 28.58 )
50
0.667
∆dn ( 33.33 )
x
100/(100+x)
∆dn ( 100 x /(100 + x) )
5.5.4.1 Winter Scenario
Using the cost expressions shown in Table 5-11, the expected extra cost in k$ and in
$/MWh for different distribution ranges in winter are calculated and provided in Table
5-12. The calculation of $/MWh value is based on the average energy of all wind
generation time series of winter which is 5913.73 MWh.
Table 5-12. NSP’s Expected Ancillary Costs for Different Forecast Error Distribution Ranges -Winter Scenario
5-36
Distribution Range %
Extra Cost (k$)
Extra Cost ($/MWh)
10
0.487
0.082
20
0.894
0.151
30
1.24
0.209
40
1.53
0.259
50
1.79
0.302
5.5.4.2 Summer Scenario
The expected extra cost in k$ and in $/MWh for different distribution ranges in winter is
presented in Table 5-13. The calculation of $/MWh value is based on the average energy
of all wind generation time series of summer which is 4093.83 MWh
Table 5-13. NSP’s Expected Ancillary Costs for Different Forecast Error Distribution Ranges -Summer Scenario
Distribution Range %
Extra Cost (k$)
Extra Cost ($/MWh)
10
5.40
1.319
20
9.91
2.421
30
13.72
3.351
40
16.98
4.148
50
19.81
4.838
5.5.4.3 Annualized Cost Value
No simulations or cost calculations were performed for NSP’s spring and fall seasons. It
is expected, however, that the $/MWh expected extra cost due to forecast inaccuracy for
these two seasons are no worse than the cost for winter since the system load of these two
seasons is less than the load in winter. Conservatively assuming the worst case by using
the $/MWh extra cost of winter for the spring and fall seasons, the extra costs of all four
seasons are averaged to obtain the annualized extra costs in $/MWh for different
distribution ranges, which are shown in Table 5-14.
Table 5-14. NSP’s Expected Ancillary Costs for Different Forecast Error Distribution Ranges -Annualized
Distribution Range %
Extra Cost ($/MWh)
10
0.391
20
0.716
5-37
30
0.995
40
1.231
50
1.436
5-38
6 Intra-Hour Load Following Study
The overview of the project analytical framework described in Section 2 identified two
cost impact components associated with following the intra-hour changes in load – a
reserve component and an “energy” component. The hourly-resolution scheduling cost
impacts presented in Section 5 are associated with the use of inaccurate wind forecasts in
NSP’s day-ahead generation scheduling using their unit commitment software. The
generation schedule obtained from the unit commitment solution is determined such that
the hourly average generation level is sufficient to meet the expected hourly average load.
The control area load is varying continuously in real-time, however. NSP must ensure
that sufficient generation is available to cover the sub-hourly changes in load. This
increases the operating cost above the production cost obtained from the UC, which is
based on the load remaining fixed at the hourly average throughout each hour. The two
primary reasons for this increase are:
1. Additional generating resources may need to be started up for more generation
ramping capability to follow intra-hour load changes.
2. Online units might be dispatched in a less economic pattern for more generation
ramping capability to follow load changes.
This section provides a detailed explanation of the methodologies developed for
assessing the impact of bulk wind generation on the load following component of NSP’s
intra-hour operation and control functions, as well as the results obtained using the
developed methods. The load following component of these intra-hour variations is the
slow variation associated with the general correlation in different customer loads that
define the daily load cycle. This variation is on the time scale of several minutes,
corresponding to the cycle time of the execution of a typical utility economic dispatch
operation. Minute-to-minute fluctuations in system load, which belong to a much faster
time scale than load following is classified as a regulation problem and is discussed in
Section 7.
6.1 Load Following Cost Definition
For the NSP case study, the load following cost over a given study horizon is defined as
the increase in cost between the following two cost calculations:
1. The lowest operating cost associated with dispatching NSP’s generating units and
conducting energy transactions to meet the hourly system load while maintaining
the required contingency reserve and regulating reserve requirements.
2. The lowest operating cost associated with dispatching NSP’s generating units and
conducting energy transactions to meet the 5-minute system load while
maintaining the same contingency and regulating reserve requirements.
Cost #1 can be determined from a standard unit commitment simulation. Determination
of Cost #2, however, is more complicated in that the two cost drivers for this operating
cost are not easily simulated in a single utility operational software tool. On one hand,
the need for committing additional resources must be assessed, which implies the use of
6-1
the unit commitment simulation. On the other hand, the need to assess the cost impacts of
the sub-hourly generation dispatch to follow the system load in 5-minute resolution
requires the use of an economic dispatch program. In order to resolve this dilemma, the
load following cost is decomposed into two components with the first component being
assessed using unit commitment and the second component using economic dispatch.
It is important to note that the defined load following cost does not include any
component associated with inaccurate forecast of system load and wind generation. In
the framework used for this study, however, this cost component is isolated and assessed
in the hourly UC simulations presented in Section 5.
6.1.1 Reserve Component of Load Following Cost
As noted previously, the generation schedule obtained from the day-ahead unit
commitment solution is determined such that the hourly average generation level is
sufficient to meet the expected hourly average load. Because the load is continuously
deviating from the hourly average within the hour, however, these hourly unit generation
schedules may not be able to meet the load for all 5-minute intervals within the hour. For
example, during an hour when the load is ramping throughout the hour, the hourly
generation level scheduled from the unit commitment will exceed the actual intra-hour
load value for approximately half of the hour, but will be deficient to meet the intra-hour
load value for the other half of the hour. Consequently, reserves must be available to
deploy within the hour to ensure that sufficient generation is available to meet the
ramping of the load. In general, the amount of reserve required depends on how steeply
the load ramps during the hour. The variability of the hourly wind generation will affect
the amount of reserves that must be available to follow such load trends. If the system
wind generation follows a daily cycle that is similar to the load cycle, the total load
following reserves required should be reduced. If, however, the wind follows a pattern
that is adversely related to the load cycle, as is often the case for strong diurnal wind
patterns, the wind would increase the intra-hour load following reserve requirement
(LFRR).
Load following reserve represents the extra generation capability required to meet the
intra-hour load changes. This is an addition to the capacity required to meet the hourly
average load. Making such reserve available usually requires bringing more units online
or scheduling unit generation levels in a less economic manner in the operation planning
stage. This results in extra cost. To model this additional reserve requirement constraint
in a UC simulation, the following assumptions are made:
•
•
•
System load ramps up or down smoothly throughout the hour.
At 5-minute resolution, the system load at the mid-point of the hour is about equal
to the hourly average load.
Hourly average load plus one-half of the hourly load change is approximately the
maximum 5-minute resolution load value during the hour.
Based on these assumptions, to insure sufficient generating capability to meet the subhourly load variation, the LFRR for a given hour is modeled as half of the hourly load
6-2
change. This load following reserve is spinning and is in addition to the contingency
reserve and regulating reserve requirements. It is a 30-minute reserve because it
corresponds to the load change for half an hour. The cost of carrying additional load
following reserve to accommodate wind is assessed as the difference in operating cost
determined by a unit commitment simulation with and without the additional LFRR. This
reserve component of the load following cost captures the startup cost for additional units
to be online over the study horizon.
It is interesting to note that the hourly load following reserve requirement varies
throughout the day as the hourly load changes from hour to hour differ. There are several
ways to calculate the hourly load change. Consider hour 8. The hourly load change can
be calculated as a) the absolute difference between hourly load of hour 8 and 7, b) the
absolute difference between hourly load of hour 9 and 8, or c) the average of the two
absolute differences. Method (a) is used in this study.
6.1.2 Energy Component of Load Following Cost
The LF reserve cost component represents the capacity cost of extra generating capability
that must be online. It does not, however, include any consideration of actually
dispatching units to meet the 5-minute resolution load changes. The deployment of the
available load following reserve to meet the intra-hour slow variation of load changes
also results in extra cost. Consider that during any hour system load varies above and
below the hourly average value. Although the total energy consumption for the hour is
the same whether the load ramps throughout the hour or is constant at the hourly average
value, due to the nonlinear nature of the unit heat rate characteristic, the 5-minute
resolution dispatch for the load-ramping scenario results in a higher cost. For this study,
the difference in the dispatch cost between the fixed and varying load scenarios is
referred to as the energy component of the load following cost. An economic dispatch
program, which simulates the intra-hour deployment of generation every 5 to 10 minutes,
is used to assess this cost component.
For both the varying load and fixed load scenarios, the unit on/off status is fixed
according to the solution of the unit commitment run. The economic dispatch simulation
models the load following reserve requirement dynamically in the sense that at a given
time step, the amount of reserve is reduced to match the increase in load or reduction in
wind generation. The economic dispatch is in essence deploying the reserve and
converting it into generation. The contingency reserve requirement and regulating reserve
requirement are also modeled in the ED simulations.
The economic dispatch program used for this study was developed by the Electrotek
Concepts project team so that it could be altered to the needs of this study. See Appendix
F for a detailed description of the program. One interesting note is that the ED program
models an artificial unit that is dispatched when load and reserve requirements are not
met by the actual units currently online. A penalty charge commensurate with the
peaking unit average generation $/MWh cost at full load is assessed for the dispatch of
this artificial unit, representing an equivalent use of peaking energy or purchase of spot
market energy to meet the load requirement.
6-3
6.2 Historical Data Analysis
As noted previously, NSP provided hourly EMS archives for 3 months from 2001 and 4second and 5-minute archives for 5 days in the summer of 2001. These data sets included
control area load, control area total generation, scheduled and measured interchange, and
control area generation per generating unit (hourly and 5-minute data only). This data
was analyzed to better understand NSP’s generation dispatch operation to follow the
continuous load changes both within and between hours. Some of the observations made
through this process are as follows:
•
•
•
•
As observed from the 4-second historical data, actual interchange and its schedule
ramps from one hourly value to the next only during the 10-minute window from 5
minutes before to 5 minutes after the hour. The interchange schedule remains
relatively constant during the 50 minutes from 5 minutes after the hour to 5 minutes
before the next hour.
Hourly historical data shows that for most hours, the total ramping capability of
NSP’s online units is sufficient to meet the load change within the hour.
During load up-ramp periods, including early morning and early evening, part of the
ramping capability to follow the load is provided through either NSP’s peaking units
and/or more expensive coal fire units, while some of the Sherco units are operating at
fixed generation levels beyond their normal dependable capabilities (NDC). This was
evident from the generation plots shown in Figure 3-4 and Figure 3-5.
It appears that NSP does not model the load following reserve requirement into the
unit commitment formulation in day-ahead planning, but rather starts up peaking
units in real time to follow load when the overall ramping capability becomes low.
This may not be solely due to the normal load following requirement, but also to the
incorrect forecast in system load resulting in an unfavorable unit commitment
schedule for the actual load. It is also possible that the patterns observed in the limited
data available are not typical and do not reflect NSP’s normal operating strategy.
6.3 Load Following Assessment Approach
Section 6.1 suggests a basic approach for assessing the NSP system load following cost
by using unit commitment and economic dispatch to assess the reserve and energy cost
components, respectively.
This section describes the details of the approach used to assess the additional load
following cost associated with integrating bulk wind generation. A complete general
approach is described first. The implementation of this approach for the NSP case study
and simplifying assumptions are presented next.
6.3.1 Complete Approach
Section 6.1 identifies two load following cost components – the reserve component and
the energy component. The incremental cost for each of these components due to wind is
assessed separately according to the following basic algorithm.
6-4
Step 1
Calculate the load following reserve component cost attributable to the system
load alone.
Step 2
Calculate the load following reserve component cost attributable to the
combination of system load and wind generation. The difference between this
cost and the “load only” reserve cost of Step #1 is the incremental load
following reserve component cost for supporting wind generation.
Step 3
Calculate the load following energy component cost attributable to the system
load alone.
Step 4
Calculate the load following energy component cost attributable to the
combination of system load and wind generation. The difference between this
cost and the “load only” energy cost of Step #3 is the incremental load
following energy component cost for supporting wind generation.
Step 5
Sum the incremental reserve and energy component costs to obtain the total
incremental load following cost attributable to wind generation.
6.3.1.1 Reserve Component Calculation Details
The first two basic algorithm steps listed above are used to calculate the incremental
reserve component cost. Unit commitment is employed for the calculations for both steps.
The UC simulations could be performed for any time horizon, but for consistency with
NSP’s operational procedures, a 3-day study horizon and associated load profile is
specified for the cost assessment. A Monte Carlo approach could be utilized by
performing the simulations with multiple wind generation profiles obtained from the
probabilistic wind model. All of the unit commitment simulations are modeled with the
contingency reserve and regulating reserve requirements.
Basic Algorithm Step 1: Calculation of the load following reserve component cost
attributable to the system load alone.
A. Run unit commitment for the selected 3-day study horizon with wind generation.
The load following reserve requirement is set to zero for the entire study horizon.
Transaction scheduling is determined as part of the unit commitment optimization
process.
B. Run unit commitment for the selected 3-day study horizon with wind generation.
The load following reserve requirement is enforced with the LFRR value for each
hour equal to one-half of the absolute hourly load change. Note that the reserve
requirement for this step does not include the hourly change in wind generation.
Transaction scheduling is determined as part of the unit commitment optimization
process.
C. The cost difference of steps B and A of this Basic Algorithm Step 1 is the load
following reserve component cost attributable to the system load alone.
Basic Algorithm Step 2: Calculation of the load following reserve component cost
attributable to the combination of system load and wind generation.
6-5
A. Same as Step A of Basic Algorithm Step 1.
B. Run unit commitment for the selected 3-day study horizon with wind generation.
The load following reserve requirement is enforced with the LFRR value for each
hour equal to one-half of the absolute hourly change in load minus wind
generation. Transaction scheduling is determined as part of the unit commitment
optimization process.
C. The cost difference of steps B and A of this Basic Algorithm Step 2 is the load
following reserve component cost attributable to the combination of system load
and wind generation.
D. The cost difference of Step C of Basic Algorithm steps 1 and 2 is the incremental
load following reserve component cost for supporting wind generation.
It is interesting to note that the change in LFRR with wind generation included could be
either more than or less than the LFRR for system load only. If system load and wind
generation ramp in opposite directions for a given hour, including wind generation will
increase the reserve requirement. If, however, wind and load ramp in the same direction
for the hour, the reserve requirement is reduced, which means a cost savings for
integrating wind for that particular hour.
6.3.1.2 Energy Component Calculation Details
The last two steps of the basic algorithm require the use of economic dispatch, simulating
the generation dispatch for intra-hour load following in 5-minute resolution. The most
complete approach to calculating the LF energy component cost using the economic
dispatch program would be to simulate the entire unit commitment study horizon in 5minute resolution. To reduce simulation times, an alternative method was used whereby
certain representative hours of the day were selected. Economic dispatch was then
performed for these selected hours separately, and the resulting operating costs for these
hours used to project the costs of the remaining hours of the study horizon.
To perform the load following simulation for a given hour, time series system load and
wind generation of 5-minute resolution over that hour are used as inputs. The system load
time series are obtained from the NSP high-resolution historical data with total energy of
the time series scaled to the hourly load value of the corresponding hour in the unit
commitment run.
To account for the random and variable nature of wind generation, the Monte Carlo
approach is adopted in the simulation. Multiple wind generation time series are
synthesized for each hour to be used in the economic dispatch program simulations. For
each wind generation time series, the total energy is scaled to the hourly wind energy of
the corresponding hour in the unit commitment run. Furthermore, the trending of the
wind generation time series averaged over all time series is scaled to the hourly trend
value of the corresponding hour in the unit commitment run.
All of the economic dispatch simulations model the contingency reserve requirement and
regulating reserve requirement.
6-6
Basic Algorithm Step 3: For each selected hour, calculate the load following energy
component cost attributable to the system load alone
A. Run economic dispatch simulation with system load and wind generation fixed
throughout the hour at the hourly average values. The LFRR value is based on
system load only. Unit on/off status and transaction schedules are set as
determined by the unit commitment solution of Basic Algorithm Step 1-B.
B. Run economic dispatch simulation with system load ramping throughout the hour
and wind generation fixed at the hourly average value. The LFRR value is based
on system load only. Unit on/off status and transaction schedules are the same as
for Step A.
C. The cost difference of steps B and A is the load following energy component cost
attributable to the system load alone.
Basic Algorithm Step 4: For each selected hour, calculate the load following energy
component cost attributable to the combination of system load and wind generation
A. Run economic dispatch simulation with system load and wind generation fixed
throughout the hour at the hourly average values. The LFRR value is based on the
combination of system load and wind generation. Unit on/off status and
transaction schedules are set as determined by the unit commitment solution of
Basic Algorithm Step 2-B.
B. Run economic dispatch simulation with system load ramping and wind generation
varying throughout the hour. Monte Carlo approach is applied with hourly
simulation looping over all the synthesized wind generation time series. Hence the
cost of this step is an expected value. The LFRR value is based on the
combination of system load and wind generation. Unit on/off status and
transaction schedules are the same as for Step A.
C. The cost difference of steps B and A of this Basic Algorithm Step 4 is the load
following energy component cost attributable to the combination of system load
and wind generation.
D. The cost difference of C of Basic Algorithm Step 4 and Step 3 is the incremental
load following energy component cost for supporting wind generation.
Basic Algorithm Step 5: Calculate total incremental load following cost due to wind
generation.
A. Sum the reserve and the energy components of the load following cost for wind
generation that are calculated in Basic Algorithm Step 2-D and 4-D, respectively.
6.3.2 Implementation for NSP Case Study
The complete load following cost impact assessment presented in Section 6.3.1 was not
implemented exactly as stated. A significant simplification was made for the
determination of the reserve component. Additionally, lack of a complete understanding
of NSP’s operating procedures resulted in some modeling inaccuracies that are noted and
explained in this section.
6-7
6.3.2.1 Reserve Component
The complete approach for determining the load following reserve component cost
includes performing Monte Carlo 72-hour UC simulations with the LFRR time series
being altered for each simulation according to the associated wind generation time series.
In an attempt to most efficiently utilize remaining project funds, a preliminary analysis of
the impact of wind on the hourly LFRR was performed to determine if these simulations
were necessary. This analysis consisted of the following steps:
1. For both January 2001 and July 2001, the average hourly change in NSP system
load for each of the 24 hours of the day was calculated from the archived EMS
data provided by NSP.
2. For both January 2001 and July 2001, the average hourly change in NSP wind
generation for each of the 24 hours of the day was calculated from the archived
EMS data provided by NSP.
3. For each month, the average hourly load and wind generation differentials were
used to calculate the average hourly LFRR attributable to load only and to the
combination load and wind generation. LFRR values are both calculated as onehalf the absolute hourly change as explained in the complete approach.
4. For each month, the change in LFRR with and without consideration of the wind
generation was analyzed to qualitatively determine the impact of wind on the LF
reserve component.
Figure 6-1 and Figure 6-2 compare the average hourly LFRR attributable to load only and
attributable to the combination of load and wind generation based on the NSP archived
EMS data for January 2001 and July 2001, respectively. The data for both January and
July indicate that the inclusion of wind generation only slightly changes the reserve
requirement, with the largest increase in LFRR being 6 MW. Approximately 90% of all
hourly changes are below 3 MW as shown in Table 6-1. This small impact is because
NSP’s present wind penetration is small relative to the NSP system load. Furthermore,
Figure 6-1 and Figure 6-2 show that wind reduces the LFRR for some hours, in addition
to increasing the LFRR for some hours. As a matter of fact, there are an equal number of
hours of increase and decrease in reserve requirement due to the wind generation for both
months. Additionally, the sum of the increases and decreases for each month are
approximately 0 MW.
Based on this analysis, it was assumed that the reserve component cost impact due to
wind is negligible. This is due to the relatively low wind penetration level of 280 MW on
an 8000 MW system. Consequently, the cost impact is assumed to be zero without
actually performing the simulations as stated in the complete approach of Section 6.3.1.
This analysis is an approximation and should be considered with the following caveats:
•
Only two months of hourly historical data were used for the analysis due to the
limited amount of historical system load data available. A more representative data
set would obviously be preferred. The data utilized contains some patterns that are
considered unusual. For example, hour 8 of January 2001 exhibits a slight increase in
6-8
•
wind generation. As a result, including wind generation reduces the LFRR for this
hour, which is within the morning load ramp-up period. An examination of the Year
2000 hourly wind generation data indicates that wind generation tends to decrease
slightly for hour 8, which would slightly increase the reserve requirement.
Nonetheless, the relative magnitude of the changes is still small due to the existing
wind penetration level.
The LFRR is estimated simply on the basis of the hourly trending of the quantity for
load following, which is an average over the entire season per hour. While this
method of estimating LFRR provides a reasonable estimate, the LFRR does not
account for the variable and random nature of wind generation. A more complete
analysis would include the MC simulations of many different wind time series for
each month as indicated in the complete approach.
Comparison of LFRR - January 2001
300
LFRR_Ld
250
LFRR_Ld&Wg
MW
200
150
100
50
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
hour of day
Figure 6-1 Comparison of LFRR for load only and for load and wind generation based on January
2001 data.
6-9
Comparison of LFRR - July 2001
300
LFRR_Ld
250
LFRR_Ld&Wg
MW
200
150
100
50
23
21
19
hour of day
17
15
13
11
9
7
5
3
1
0
Figure 6-2 Comparison of LFRR for load only and for load and wind generation based on July 2001
data.
Table 6-1. Differential LFRR with wind generation and system load considered relative to load only.
Hour
Jan-01
Jul-01
1
2
1
4
3
2
4
4
-2
1
5
-1
-1
6
0
0
7
-1
-4
8
0
-2
9
4
-2
0
0
10 11 12
-3
-3
-2
3
2
0
Hour
13 14 15 16 17 18 19 20 21 22 23 24
0
0
-2
-2
-2
5
2
2
-1
0
2
2
Jan-01
0
-2
-1
1
-1
-1
-4
-4
-1
2
6
2
Jul-01
6.3.2.2 Energy Component
The approach implemented to determine NSP’s load following energy component cost
for integrating wind follows the complete approach identified in Section 6.3.1.2. As
noted in the complete approach, representative hours are selected for each seasonal
scenario to be simulated and the resulting costs used to extrapolate to daily, seasonal, and
annual values. For the NSP case study, the following 4 representative hours were
selected to characterize the NSP daily load shape, for both the winter and summer season
scenarios:
•
•
•
•
Hour 03 – representative of relatively flat minimum load night period
Hour 08 -- representative of rapid morning load ramp-up period
Hour 14 – representative of relatively flat peak load period through the middle of
the day
Hour 23 – representative of rapid evening load ramp-down period
6-10
Figure 6-3 shows the load profiles for the selected hours, which are used in the ED
simulations. Note that the hour designations are such that Hour 03 represents the hour
ending at 3 a.m.
Selected Hour Load Profiles
6000
5500
MW
5000
4500
Hour 3
Hour 8
Hour14
4000
Hour23
3500
3000
1
3
5
7
9
11
5-min resolution points
Figure 6-3. Load profiles for selected hours that are used in ED simulations.
For each of these hours, the complete approach described in Section 6.3.1.2 for
determining the LF energy component cost attributable to wind is applied as shown in the
flow chart of Figure 6-4. This flow chart shows the following basic steps:
1. As shown in the box in the upper left hand corner of Figure 6-4, the solutions
from the 100 MC unit commitment simulations are used to set the starting point
for each ED simulation. For each of the 4 hours for both summer and winter, the
UC simulation associated with the median wind generation level for the
respective hour is selected. The solution for the respective UC simulation sets the
unit on/off status, initial generation schedule and transaction schedule for the 5minute resolution economic dispatch simulation. Additionally, the hourly load
value and wind generation value for the particular hour of the UC simulation are
used to obtain the 5-minute resolution load and wind generation time series. The
load series is obtained by scaling the appropriate load shape of Figure 6-3 by the
hourly load value as shown in the middle left portion of Figure 6-4. The 5-minute
resolution wind series is synthesized from the STM wind synthesis tool so that the
total hourly energy matches the hourly value for the hour from the UC simulation
as shown in the lower left portion of Figure 6-4. The trending of the time series
averaged over the entire set is equal to the hourly trend as given in Table 6-2.
6-11
Table 6-2. Wind Generation Hourly MW and Hourly Ramp Rate in Simulation Study
Hour of Day
3
8
14
23
MW
65
61
52
65
Winter
Ramp Rate
0.0
2.5 (dn)
0.0
2.5 (up)
MW
34
52
30
27
Summer
Ramp Rate
0.0
2.0 (dn)
0.0
2.0 (up)
2. Using the varying 5-minute resolution load series from #1 and a constant wind
generation series at the hourly average value, ED is performed to determine the
load following energy component cost attributable to system load only as
represented by the upper right ED block in Figure 6-4. Note that the LFRR is
modeled the same as in the associated unit commitment run.
3. Using the varying 5-minute resolution load series from #1 and the varying 5minute wind generation series from #1, Monte Carlo ED is performed to
determine the load following energy component cost attributable to the
combination of system load and wind generation as represented by the lower right
ED block in Figure 6-4. Deterministic ED simulations are performed for 100
synthesized 5-minute resolution wind generation series. The expected value of
the distribution of results is used to calculate the energy component cost. For all
of the simulations, the LFRR is the same as in the previous step.
4. The incremental load following energy component cost for supporting wind
generation is the increase in the expected cost for the combination of load and
wind from Step #3, relative to the cost for load only from Step #2. This value
obtained for each of the 4 hours is then extrapolated to a daily, seasonal, and
annual value.
6-12
Commitment and
Transaction Schedule
for Selected Hours
(H3, H8, H14, H23)
Select median wind gen. case results for selected
hrs UC simulations for the 100 hourly resolution 3day periods selected per wind season
Hourly avg.
load for
selected hrs
Median
hourly avg.
wind gen.
NSP historical
5-min res. load
data (5 Sum.
2000 days)
-
5-min res.
load shape
for selected
hrs
NREL Hist.
5-min Avg.
Wind Gen.
Data
STM Wind
Synthesis
Tool
Scale 5min res.
load curve
100 1-hr, 5-min
res. MC Wind
Gen, Series
per selected hr
Σ
+
1-hr, 5-min res.
load series per
selected hr
-
+
Σ
Economic
Dispatch
Tool
LF Energy
Cost
(Load only)
-
Σ
NSP AGC Unit
Characteristic Data
+
Economic
Dispatch
Tool
Dist. of LF
Energy Cost
(Load &
Wind)
Figure 6-4. Flowchart of approach implemented for determining NSP load following energy
component cost attributable to wind generation.
This approach that was implemented for determining the NSP incremental load following
energy component cost for supporting wind generation is based on several assumptions.
As noted previously, the development of a solid understanding of NSP’s operational
procedures occurred over a lengthy period as data and insights were made available by
NSP personnel. As a result, some assumptions made for this study did not completely
match NSP’s operational procedures. The following modeling assumptions for this
analysis should be noted:
•
The model assumes that NSP models intra-hour LFRR in their operation planning,
allowing economic energy to be purchased in the forward planning stage to make
sufficient capability available for intra-hour load following. As such, the UC
simulations used to set the initial generation and transaction schedules for the ED
simulations explicitly model the LFRR. More recent conversations with NSP
personnel indicate that NSP does not explicitly model this requirement in their
day-ahead planning. Instead, NSP operators model 161 MW of contingency
reserve and obtain any additional LF reserves that might be needed by acting in
the hour-ahead time frame primarily through raising the generating capability of
various units from their normal dependable capability (NDC) to their maximum
dependable capability (MDC) and by starting up peaking units. The impact of this
modeling inconsistency on the determination of the LF energy component cost is
twofold: (1) the initial generation schedule obtained from the UC may not be
6-13
•
•
•
optimal due to consideration of the LFRR, and (2) the cost drivers for following
load in this model may not match the actual costs for NSP (see next bullet)
The model assumes that the Sherco 1 and 2 generating units exclusively provide
the load following reserve and their high limits are set to their MDC capacity.
The marginal production costs for these units and the impact on the other
generation schedules to reserve room for following load from these units drive the
costs in the model used for this study. As noted in the previous bullet, although
NSP definitely uses Sherco 1 and 2 for load following (with their high limits set
to their NDC capacity), when needed, they obtain additional LF capacity by
moving certain units above their NDC capacity. This is discussed in more detail
in the “Real-time operation” subsection of Section 3.2.3.3. The model will match
the actual NSP operation well for situations where the Sherco units are providing
the LF reserve. The discrepancy may also be small when significant additional
LF is needed. The model will charge a penalty representative of the startup cost
of the average NSP peaking unit. In reality, NSP may start a peaking unit, or they
may move a unit above its NDC capacity to provide additional LF headroom for
one of the Sherco units. Since there is a one-time cost associated with moving a
unit above the NDC, the discrepancy may be small.
The LFRR modeled in the UC simulations is fixed for all hours of the study
horizon, rather than varying the LFRR per hour based on the expected ramping of
the load. Consequently, the modeled LFRR may be too large for hours 3 and 14
during which the load is relatively steady and too small for hours 8 and 23 during
which the load ramps significantly. As a result, the LF energy component cost
calculated for hours 8 and 23 would be higher than if a more appropriate LFRR
had been used. On the other hand, however, the LF energy component cost
calculated for hours 3 and 14 would be lower than if a more appropriate LFRR
had been used.
The LFRR modeled in the UC simulations used the same amount of load
following reserve requirement for both with wind and without wind generation
scenarios for all hours. As noted previously, the hourly LFRR should reflect the
combined ramping of the load and wind. The impact of this discrepancy is
considered minor, however, as the impact of the wind on the LFRR was shown to
be negligible (Table 6-1).
6.4 Simulation Results
6.4.1 Computational Aspects
The economic dispatch program used for this study was developed by the Electrotek
Concepts project team so that it could be altered to meet the needs of this study. The
program is run under the MATLAB environment. The engine of the program is a linear
programming solution package provided within the environment. Microsoft Access is
used as database for data storage. See Appendix F for a detailed description of the
program.
6-14
The computer workstation used for the simulation was a Pentium III, 1GHz machine with
512 Mbytes of RAM. On this machine, one Monte Carlo economic dispatch loop
consisting of 100 deterministic simulation runs required approximately 60 minutes.
6.4.2 LF Energy Component Simulation Results
Using a LFRR of 90 MW for all simulated hours the calculated incremental load
following energy component cost for supporting wind generation in ¢/MWh for each of
the simulated hours for winter and for summer are presented in Table 6-3.
Table 6-3. Incremental load following energy component cost for supporting wind generation.
Hour of Day
3
8
14
23
Load Following Cost (¢/MWh)
Winter
Summer
0.100
0.090
78.953
32.988
0.074
0.000
52.289
136.105
In order to extrapolate the results for these 4 hours, each hour of a day is categorized into
one of 4 different periods based on the load ramping characteristic of the hour, with each
ramping category containing one of the simulated hours as follows:
•
•
•
•
Minimum-load hours –H03 – H04
Ramp-up hours – H05 – H12, including H8
Peak-load hours – H13 – H20, including H14
Ramp-down hours – H21 – H02, including H23
Using this grouping of hours, the seasonal incremental load following energy component
cost for supporting wind generation is calculated by weighted averaging as follows.
Winter
Load Following Cost = (2*0.1 + 8*78.953 + 8*0.074 + 6*52.289) / 24
= 39.38 ¢/MWh
Summer
Load Following Cost = (2*0.09 + 8*32.988 + 6*136.105) / 24
= 45.03 ¢/MWh
Assuming that load following cost for spring and fall is no worse than winter, the
annualized cost is calculated.
Annualized
Load Following Cost = (3*39.38 + 45.03) / 4
= 40.785 ¢/MWh
6-15
6-16
7 Regulation Study- Load Frequency Control
Regulation is the use of online generating units that are equipped with automatic
generation control and are able to change output quickly, to track the minute-to-minute
variations in customer loads and correct unintended variations in generation. In so doing,
regulation helps to maintain the scheduled system frequency, maintain scheduled tie-line
power flows among control areas, and match generation to load within the control area.
Regulation differs from load following as described in previous sections in the sense that:
•
•
Regulation concerns a much shorter time scale, on the order of one to several
minutes, while load following occurs over an interval of 10 minutes, or even
longer.
Regulation patterns among individual customers are essentially uncorrelated,
while load following patterns among customers are highly correlated as defined
by the daily load profile.
In general, utilities perform real-time regulation by issuing commands to their own
generating units from the control center using a function commonly known as Load
Frequency Control (LFC), which is part of the overall AGC function. Any mismatch
between the generation and obligation of a control area is determined through the
calculation of ACE. ACE is defined based on the measurements of control area net
interchange and system frequency as follows:
ACE = Ta − Ts − 10 B ( Fa − Fs )
where subscripts ‘a’ and ‘s’ respectively refer to actual (measured) and scheduled values,
T denotes the control area net interchange, and F denotes the system frequency. The
area’s share of support for interconnection frequency is 10 B ( Fa − Fs ) , where B is the
area’s defined frequency bias in MW per tenth Hz (a negative value).
The primary objective of LFC for all utilities is the regulation of ACE. The actual LFC
algorithm used by specific utilities may differ somewhat, however, as these algorithms
must also be tailored to other secondary area’s specific control requirements as well as
unit specific characteristics. The ability to adequately regulate a control area is based on
two attributes:
1. Amount of regulating reserve in both the raise and lower directions
2. Deployment time of the reserve
Section 4.9.1 describes one method of allocating the regulating reserve requirement as 3
times the standard deviation of the minute-by-minute fluctuation of system load. Another
rule of thumb is to allocate approximately 1 to 1.5 percent of the peak load. The minuteto-minute variability of the wind production can obviously impact the regulating reserve
requirement as well. As for the deployment time constraint, the units allocated for
7-1
regulating reserve must also be able to respond within the regulating time frame of 10 to
15 minutes. Consequently, only the fast responding units are usually used for providing
the regulation service.
In order to ensure that regulating reserve is available from the generating units assigned
for performing regulation, utilities typically define a band around the generating high
limit, which is reserved for regulation. Economic dispatch will avoid dispatching into
these regions to ensure the load frequency control has room for generation increase and
decrease. The MW range for the two regions is normally the same. It is called the
regulating margin of a generating unit.
7.1 Study Objective
The North American Electric Reliability Council (NERC) currently uses two criteria for
measuring the regulation control performance of a utility. These two criteria are called
Control Performance Standard 1 (CPS1) and 2 (CPS2). For precise definitions and indepth discussion of these metrics, refer to the NERC Operating Manual and Training
Documents at its website www.nerc.com.
CPS1 is a quantity calculated using the clock-minute averages of ACE and system
frequency over a rolling 12-month period. CPS2 is a quantity calculated using 10-minute
averages of ACE over each calendar month. Utilities are required to maintain these two
standards within certain bounds. Utilities that regulate their systems poorly as indicated
by their inability to comply with CPS1 and CPS2 are subjected to penalties. NSP realtime operators indicated that NSP meets the requirements with a comfortable margin.
At the project onset, the goal of the LFC study was to determine NSP’s compliance with
CPS1 and CPS2 under wind generation operation. As the project progressed, however, it
was realized that this goal was not achievable due to the inability to obtain realistic
estimates for the two performance standards through simulations. NSP’s real-time values
of ACE, CPS1 and CPS2 are very sensitive to the specific control operations performed
in real-time and the specific system conditions. The available data would not allow for
the development of a model to so closely mimic NSP’s real-time control that near-actual
control performance data could be simulated. Consequently, the decision was made to
select a single control performance metric, and using the available system data and LFC
control algorithm information, to evaluate the performance impact of including wind
generation relative to the performance without wind. As such, only the relative change in
the criteria is analyzed. To accomplish this objective, ACE time series data was collected
for simulations of both with and without wind generation cases. The ACE statistics for
these simulation cases were compiled and comparisons made to determine the effect of
wind generation.
The compiled ACE statistics include the ACE average and the standard deviation of the
1-minute average ACE. One minute is used as the averaging period of ACE in the
standard deviation calculation because this is the finest resolution time for which
generation controlled by load frequency control is able to track load. Generators are not
expected to respond to any load fluctuation below the minute level.
7-2
7.2 Regulation Study Approach
7.2.1 Scenario
LFC simulations were performed to compare the control performance with and without
wind generation. As with the load following study, simulations are performed for 4
different hours of the day for various load and wind generation patterns. The same 4
hours of the day simulated in the LF study are also used for the regulation study – H03,
H08, H14 and H23. In order to collect meaningful results from the simulation, a full hour
of operation for the 4 chosen hours of the day was simulated with a 4-second time step,
which corresponds to NSP’s AGC cycle length.
As with the UC and LF studies, a Monte Carlo approach is used to assess the impact of
wind on regulating minute-to-minute fluctuations in load. Unlike the previous studies,
however, multiple load series are combined with multiple wind generation series for the
regulation simulations. NSP provided 4-second resolution load data for the same 5
summer days for which the 5-minute resolution data was provided. Unfortunately, the
load data for one of the days appeared corrupted. For each of the selected hours, the four
high-resolution load series were selected from the four days of NSP historical data. LFC
simulations were conducted for the 4 load series associated with each of the 4 selected
hours of the day, without considering wind generation.
To study the impact of the wind generation fluctuations, two typical high-resolution (4second) wind generation series of 1-hour duration were selected from the NREL wind
generation data set for each of the selected hours for the relevant wind season. For each
hour of the day, LFC simulations were performed for each combination of wind
generation and load time series. There are eight cases in total for each hour. Wind
generation is treated as a negative load. The resulting net load is used as the input to the
simulation software for each of the 8 cases for each of the selected 4 hours.
Thus for each of the 4 selected hours, 4 “load only” cases were simulated and 8 “load &
wind” cases were simulated. The LFC simulations determined the ACE statistics for
each combination of load and wind, which provided 4 distributions of 900 ACE values
for the “load only” cases and 8 distributions of 900 calculated ACE values for the “with
wind” cases. These ACE statistics were also averaged up to 1-minute ACE values to
correspond to the NERC performance metric period. The following modeling
assumptions were made for the LFC simulations:
•
•
All 3 Sherco units, SHC 1, SHC 2 and SHC 3, are used for regulation in both
directions. Ramp rate limits for these three units are 12, 12 and 15 MW/minute
respectively. The total ramping capability of the three units is sufficient to track
the minute-by-minute fluctuation of the system load. Generation high limits for
these three units are 712 MW, 712 MW, and 871 MW, respectively.
At the initialization stage of each 1-hour operation simulation, Sherco units are
initialized to such MW levels that they will collectively have sufficient capacity to
meet the load change for the next 60 minutes.
7-3
•
•
•
NSP typically performs an economic dispatch once every 5 to 10 minutes to
determine unit base points. In the LFC simulations for this study, the ED is not
executed within each of the 1-hour simulation runs. Rather, to simplify the
simulation process, generation setpoints are adjusted by equally distributing any
load changes among the three Sherco units as the most economic way of
operation for load following.
Regulating reserve is 60 MW for each of the generation raise and lower
directions. This amount is consistent with the results from the wind model.
Regulating margin for each Sherco unit is 20 MW.
External areas always maintain their ACE at zero values.
7.2.2 Simulation Tool
The LFC simulation software tool used for this study is a modified version of a
commercial AGC software package currently used by a large utility within the WSCC
region. The original AGC software package was written in the C programming language.
The Electrotek Concepts project team converted the original software into a MATLAB
application to facilitate the modifications necessary for the simulation study.
The software tool used for the LFC simulation study consists of the following two main
modules, which interact with each other:
LFC module -- mimics the functionalities of the utility control center in controlling its
unit generation through regulating the area control error (ACE). Key features of the LFC
module are:
•
•
•
ACE calculation with user specified value for frequency bias.
Filters of measurement quantities, system frequency and raw ACE.
Observes the unit ramping rate limit and high and low generating limits in
determining unit control signal.
Power System Simulator module -- simulates the control area unit generation, external
area aggregate generation, MW flows at inter-ties and system frequency. Key features of
the Power System Simulator module are:
•
•
•
•
•
Receives unit control signals from the LFC module.
Models individual generating unit within the control area
Uses lower order model for unit dynamics.
Calculates external area generation through the specified external area frequency
bias.
Passes the calculated values for system frequency, tie-flows and unit generation to
LFC module as measurements.
7.2.3 Computational Aspects
As noted the LFC simulations are run under the MATLAB environment. Microsoft
Access is used as database for data storage. The computer workstation used for the
7-4
simulation was an Intel Celeron, 1.3GHz machine with 512 Mbytes of RAM. On this
machine, one Monte Carlo loop consisting of 12 deterministic LFC simulation runs
required approximately 100 minutes.
7.3 LFC Simulation Results
Table 7-1 shows the average ACE values calculated for the “without wind” and “with
wind generation” simulations for the 4 selected hours of the day. Note that for hours 8
and 23, ACE is noticeably biased towards the negative and positive values. Recall that
ACE is roughly the area generation minus area load and that the load ramps significantly
up and down for hours 8 and 23, respectively. Because the load leads the generation in a
more prominent way for these hours, the ACE values are biased to higher value
accordingly. On the other hand, the average ACE is relatively small for hours 3 and 14,
as system load remains quite steady over those hours. Comparing the “without wind” and
“with wind generation” simulation results, both hours 8 and 23 show a slight increase in
the absolute value of ACE average because wind generation ramps in the opposite
direction of system load for those hours, which increases the burden of load following.
Table 7-1. ACE Average from without and with Wind Simulation
Hour of Day
3
8
14
23
Average ACE
Without Wind Gen
With Wind Gen
2.1369
2.2171
-6.2329
-6.4640
-1.8293
-1.7989
7.4587
7.5975
Table 7-2 and Table 7-3 show the simulation results of standard deviations of ACE,
which reflect the random fluctuation of the variables being controlled. For all four hours
studied, the standard deviations are of the same order, though somewhat larger for hour 8.
The standard deviations are almost unchanged between the without and with wind
generation scenarios for each hour. This suggests that NSP’s current wind penetration of
280 MW on an 8000 MW peak system has no impact on the control performance. This
means that for NSP’s current wind penetration level and regulating capacity and for the
reserves allocated in the simulations, the variability of the wind on the 4-second time
frame didn't significantly affect the capability of the system to follow these variations.
Accordingly, the cost impact of additional regulating reserves to accommodate wind is
assumed negligible.
Table 7-2. Standard Deviation of 4-second ACE from without and with Wind Simulation
Hour of Day
3
8
14
23
Standard Deviation of 4-second ACE
Without Wind Gen
With Wind Gen
14.1622
14.1745
16.8842
16.8972
12.8812
12.8885
14.9126
14.9497
Table 7-3. Standard Deviation of 1-minute-average ACE from without and with Wind Simulation
7-5
Hour of Day
3
8
14
23
Standard Deviation of 1-minute-average ACE
Without Wind Gen
With Wind Gen
12.3548
12.3369
15.3375
15.3297
10.9075
10.9025
13.3211
13.3477
7-6
8 Conclusions and Recommendations
8.1 Work Accomplished
A simulation framework for evaluating the impacts of large wind generation resources on
power system operations and scheduling functions has been developed. The functions
incorporated into the framework include unit commitment, economic dispatch and load
frequency control. The framework was developed specifically to perform a case study of
the impacts of NSP’s existing 280 MW windplant on their system operations. As such,
NSP provided actual system data to be used for the case study. The developed framework
encompasses time scales of 3 different orders, consistent with the time scales that NSP
uses in operation planning, dispatching and real-time control. The three time scales of the
framework include:
•
•
•
Unit commitment time scale – hourly resolution with study horizon from several
days to several weeks.
Intra-hour load following time scale – 5- to 10-minute resolution with study
horizon of 1 hour.
Load frequency control time scale – 2- to 4- second resolution with study horizon
from several minutes to 1 hour.
In order to quantify the impacts of the variable and mostly uncontrollable nature of wind
generation, a wind plant model was developed to support the simulation study by
providing many wind generation time sequences of the required resolutions that are
representative of the NSP wind plant. The NREL high-resolution wind generation data
from Buffalo Ridge and hourly-resolution and 5-minute resolution EMS data from NSP
were used to develop the probabilistic wind model. Work accomplished for wind plant
model development includes:
•
•
Developing, for different time scales, the State Transition Matrix models, which
characterize the probability distribution of the one step state transition. Models are
used, if appropriate, to synthesize multiple numbers of wind generation time
series for Monte Carlo type simulation study.
Statistically determining the additional regulating reserve requirement (MW) for
integrating wind generation into the power grid.
The following analyses were performed for the unit commitment time scale study:
•
•
Use of unit commitment simulations to determine the value of the wind
generation. Cost comparison is made between the simulations with and without
wind generation.
Use of unit commitment simulations to determine the cost of wind generation
forecast inaccuracy. Cost comparison is made between perfect forecast and
inaccurate forecast scenarios. An operation planning strategy for reducing the
8-1
•
adverse effects of wind generation on the cost resulting from forecast uncertainty
is described.
Use of unit commitment simulations to determine the reserve component of the
load following cost for supporting wind generation integration. Although the
approach has been described in the report, it was not implemented because
analysis of historical load and wind data led to the assumption that no extra load
following reserve was required to accommodate wind.
The following analyses were performed for the intra-hour load following time scale
study:
•
Use of economic dispatch simulations to determine the energy component of the
load following cost for supporting wind generation integration. Cost comparison
is made between the simulations for scenarios of varying and fixed wind
generation.
The following analyses were performed for the load frequency control time scale study:
•
•
Use of the wind plant model to determine the additional regulating reserve
requirement for wind generation integration. Cost associated with the additional
reserve could be calculated using either unit commitment or economic dispatch
but calculation has not been performed.
Use of load frequency control simulations to calculate the area control error
(ACE) over the study horizon. Comparison is made on ACE statistics between
simulations with and without wind generation.
8.2 Summary of Analysis Results
The following cost impacts were assessed using the developed simulation framework:
•
•
•
•
Cost of wind generation forecast inaccuracy for day-ahead scheduling.
Cost of additional load following reserves.
Cost of intra-hour load following “energy component”
Cost of additional regulation reserves
Cost of wind generation forecast inaccuracy for day-ahead scheduling. Unit commitment
simulations were performed to assess the cost incurred by NSP to re-schedule units
because of inaccurate wind generation forecasts used in the day-ahead scheduling.
Several assumptions were utilized in the problem formulation, partly to simplify the
evaluation model and partly to account for unavailable data. The investigators believe
that the assumptions made provide a conservative estimate of the cost impacts. The
methodology utilized provided a cost impact based on the assumed distribution range of
forecast error, which is shown in Table 8-1. The results of the study also enabled the
derivation of a specific operational planning strategy, similar to a more intuitive
procedure already used by NSP, to hedge against the adverse effect of wind generation
forecast uncertainty. The results shown in Table 8-1 are based on this hedging strategy.
8-2
Table 8-1. Cost of wind forecast inaccuracy as a function of the distribution range of forecast error.
Distribution Range %
Extra Cost ($/MWh)
10
0.391
20
0.716
30
0.995
40
1.231
50
1.436
Cost of additional load following reserves. Calculation of the load following reserve
requirement (LFRR) from the NSP hourly resolution control area load and aggregate
wind generation data for January and July of 2000 indicated that the addition of wind
does not significantly increase the LFRR. Consequently, the reserve component of the
load following cost is assumed to be zero without performing the UC simulations that
would be required to obtain a specific cost impact value. It should be noted that this
determination is for the existing NSP wind penetration level. Assuming a reserve
component cost of zero for wind means that the energy component assessed using intrahour economic dispatch simulation will be higher than the energy component cost that
would be calculated if additional load following reserves were added to support the wind.
Cost of intra-hour load following “energy component”. Economic dispatch simulations
were performed to evaluate the cost of following the intra-hour ramping and fluctuation
of wind generation. This cost is referred to as the intra-hour load following “energy
component” because it is the cost of deploying the available load following reserve to
meet the intra-hour slow variation of load changes. ED simulations were performed for
four hours of the day selected to represent the different load ramping and wind variation
characteristics associated with NSP’s typical daily load curve. The average cost for a day
was extrapolated from the simulations for these four hours by dividing a day into 4
different periods based on the load ramping characteristic with each period including a
simulated hour. Additional assumptions and extrapolations were made to obtain an
annualized intra-hour load following “energy component” cost of approximately
41¢/MWh.
Cost of additional regulation reserves. Load frequency control (LFC) simulations were
performed for 4 representative hours of the day to determine the impact of minute-byminute system load and wind generation fluctuation on NSP’s area control error (ACE)
statistics. Simulations were performed for no wind generation versus NSP’s current wind
generation penetration level without extra regulating reserve. Results show almost no
change in the ACE standard deviation between the without and with wind generation
scenarios. This suggests that NSP’s current wind penetration of 280 MW on an 8000 MW
peak system has no impact on the control performance. This means that for NSP’s current
wind penetration level and regulating capacity and for the reserves allocated in the
simulations, the variability of the wind on the 4-second time frame didn't significantly
affect the capability of the system to follow these variations. Accordingly, the cost impact
of additional regulating reserves to accommodate wind is assumed negligible.
Summing the cost impact results for the four components assessed using the distribution
forecast error range of ±50%, the impact of integrating NSP’s existing 280 MW
windplant is found to be approximately $1.85/MWh of wind generation. It should be
noted that it is very difficult to exactly model all of the operational scheduling and realtime operation procedures for a given utility and to obtain all of the necessary data, so
8-3
assumptions and extrapolations were made for the developed models. The investigators
attempted to select these simplifying measures such that the effect was to produce a more
conservative (more significant) impact. Specific assumptions or model characteristics
that are believed to result in conservative estimates for the analyses performed are listed
as follows:
The cost of wind generation forecast inaccuracy is calculated in the unit commitment
time scale simulations:
•
•
•
Not modeling the energy spot market in the simulations causes a reduction of
generation from economic units for unexpected excessive amount of wind
generation, and the use of peaking units to cover the unexpected loss of wind
energy. The availability of a real-time energy market or regional imbalance
energy market would likely reduce the forecast inaccuracy cost. It should be
noted, however, that the developed model appears to closely represent NSP’s
current operating procedures based on the available historical data.
System load is modeled deterministically to reduce the computational effort.
Consequently, wind generation is the only random variable in the simulation. It’s
likely that some degree of diversity would be obtained by including the variability
of system load, reducing the impact of wind generation forecast uncertainty.
Wind generation forecast error is modeled as a uniformly distributed random
variable to simplify the calculation. A more realistic normal distribution will
make the error more concentrated around the zero mean, which will result in
lowering the inaccuracy cost.
The cost for following continuous but slow intra-hour variation (energy component cost)
is calculated in the intra-hour load following time scale simulations:
•
The load following cost consists of two components: reserve and energy
components. A simplified approach is adopted for the simulation where no extra
load following reserve is considered. This simplification results in the load
following cost only having the energy component, which could be much larger
than the total of the two components when the reserve amount is chosen
appropriately.
The general analysis approach developed for the NSP case study uses tools similar to
those utilized by NSP to simulate their operational procedures to determine the cost
impacts of integrating their existing wind plant. Accordingly, it should be noted that the
results presented in this report for the NSP impact study are specific to the system studied
as it currently exists. The sensitivity of the results to many critical parameters such as
wind penetration level, generation mix, and energy transaction pricing and market
structure should be investigated to more fully understand the impacts of integrating bulk
wind generation into the NSP system. Although the investigators believe that many of
the modeling assumptions lead to conservative results, it should not be understated that
the results obtained are for the existing NSP wind penetration level. The assessment of
the impact on both the load following and regulation reserve requirements resulted in
8-4
negligible costs impacts for the existing 280 MW of wind on NSP’s 8000 MW system.
At some penetration level, the windplant will impact these reserve requirements,
increasing the cost impacts of accommodating the wind. The sensitivity of the results to
penetration level should be studied further.
8.3 Recommended Future Work
The NSP case study was specifically focused on determining the cost of ancillary
services to accommodate NSP’s 280 MW wind plant on the existing NSP system. A
methodology for determining the cost impacts on the NSP system has been developed,
and simulations have been performed to calculate an annual cost of ancillary services
required for integrating the 280 MW windplant. As noted, the results presented in this
UWIG NSP Case Study final report are very specific to the base case scenario and
associated NSP operating strategy assumptions utilized in the case study simulations.
Although there were significant discussions with NSP systems operations personnel
throughout the project, there was difficulty in obtaining firm definitions of some
operating strategies prior to performing some of the simulation studies. The most
significant unresolved issues included the reserve allocations strategies for load following
and regulation, specification of the generating units from which the reserves are obtained,
and typical energy market seasonal transaction data. Additional uncertainty was
introduced in the intra-hour simulations due to the limited high-resolution load data that
was available for the study. Only 4 days of high-resolution data, all for the summer
season, were available for developing the intra-hour load models used in the study.
The schedule and budget of the project did not permit several important sensitivity
studies to be performed. Although this initial case study was not able to address several
important considerations, it did provide for the development of a very powerful
simulation based methodology and tool set for determining the cost of ancillary services.
This existing infrastructure provides the opportunity to investigate any number of
scenarios and operating procedures including the following:
•
Sensitivity Analyses. Understanding how the cost impacts of integrating wind
change with variations in operating strategy and system characteristics will be
critical to evaluating future generation alternatives. Among the more significant
analyses that are not included in the initial study are the impact of increasing
wind penetration, the impact of various reserve strategies, the impact of various
operating strategies related to treatment of the existing windplant, and the impact
of market structure. As noted previously, increasing the size of the wind plant on
the existing system will likely affect the impacts of the wind on system operation
and control. This effect is probably not a linear effect, but rather a step function
that should be investigated. Additionally, other LF reserve strategies should be
investigated to determine the sensitivity of the cost impacts relative to NSP’s
current strategy of not specifically including LF reserves in the day-ahead.
Various strategies should be investigated.
The market structure and transmission tariff under which Xcel operates are
scheduled to change significantly by the end of 2003. Even with the same load
8-5
pattern and wind resource assumed in the study, and the same reliability criteria
for the region, the results in 2004 could be significantly different because the
geographic area that will be balanced and the range of resources available to
accomplish the balancing will both be significantly larger under the new tariff
administered by the Midwest Independent System Operator (MISO). These
factors could tend to decrease the calculated wind integration costs under
favorable conditions. The same basic modeling tool developed here could be
used to study the new configuration. Additional enhancements could be made to
further refine the results. These include a more robust generator re-dispatch
function to represent the potential sources of balancing energy to be dispatched
according to a locational marginal pricing algorithm and a robust transmission
load flow model to capture the limits and costs on either “importing” this
balancing energy or “exporting” the energy imbalances to or from the former
Xcel control area.
•
Inclusion of Actual Transaction Data. As noted, the transaction data used in the
unit commitment simulations are all hypothesized due to the lack of actual NSP
data. Collecting the transaction data and incorporating them into the simulation
will substantially enhance the quality of the solution.
•
Inclusion of Load forecast Inaccuracy. As noted, the inclusion of load forecast
inaccuracy would likely reduce the impacts of wind generation forecasting
inaccuracy. In the future, the developed framework should be enhanced for load
uncertainty modeling to improve the cost impact assessment.
•
Inclusion of More Representative Wind Generation Forecast Error Distribution.
The uniform distribution is utilized for the probability distribution of the wind
generation forecasting error in the existing model for estimating its cost impact
because of its simplicity. Effort is required to determine a realistic distribution for
accurate cost assessment.
•
Impact of Pumped Storage. The daily wind generation pattern is usually diurnal
where energy production picks up at night and dies down during the daytime.
Such a generation pattern is less valuable because the energy price at night is
much lower than in the daytime. Since wind generation is mostly uncontrollable,
this means that wind generation must be taken when it is produced. However,
pumped storage would allow for the storage of the wind produced at night to be
used in the daytime. Performing simulations of scenarios including pumped
storage will provide insight on the value of this option.
•
Impact of Control of Blade Pitch. When a wind turbine is operated in the region
between the cut-in and the rated wind speed, the output of the wind turbine is
directly related to the cube of wind speed. Wind generation exhibits the most
fluctuations because the blade pitch is fixed at an angle to maximize the energy
output. For a large capacity wind plant, the fluctuations significantly increase the
burden on the conventional units to perform regulation. By not operating the
8-6
blade pitch at the position of maximizing its output generation for the current
wind speed, a margin is created which in essence provides room for the turbine to
continuously adjust its blade pitch to reduce the output fluctuation, hence
reducing the regulating reserve requirement. Further research is required to
design the feedback control mechanism and to determine the cost/benefit of this
option.
8-7
8-8
9 References
S. M. Chan, D. C. Powell, M. Yoshimura and D. H. Curtice (1983-1), “Operations
Requirements of Utilities with Wind Power Generation,” IEEE PES 1983, PAS-102 (9):
p. 2850-2860.
M. R. Milligan, A. H. Miller and F. Chapman (1995-1), “Estimating the Economic Value
of Wind Forecasting to Utilities,” presented at Windpower ’95 Conference, March 27-30,
1995, Washington, DC.
E. Hirst and B. Kirby (1995-1), “Electric-Power Ancillary Services,” Oak Ridge National
Laboratory, ORNL, Oak Ridge, TN, February 1996.
M. R. Milligan and M. S. Graham (1996-1), “An Enumerated Probabilistic Simulation
Technique and Case Study: Integrating Wind Power into Utility Production Cost
Models,” presented at IEEE Power Engineering Society, Summer Meeting, July 29August 1, 1996; Denver, Colorado.
E. Hirst and B. Kirby (1996-1), “Ancillary Costs for 12 U.S. Electric Utilities,” Oak
Ridge National Laboratory, ORNL, Oak Ridge, TN, March 1997.
M. R. Milligan and B. Parsons (1997-1), “A Comparison and Case Study of Capacity
Credit Algorithms for Intermittent Generators,” presented at Solar ’97 Conference, April
27-30, 1997, Washington, DC.
M. R. Milligan and M. S. Graham (1997-2), “An Enumerative Technique for Modeling
Wind Power Variations in Production Costing,” International Conference on Probabilistic
Methods Applied to Power Systems, September 21-25, 1997; Vancouver, British
Columbia, Canada.
B. Ernst, Y. Wan and B. Kirby (1999-1), “Short-Term Power Fluctuation of Wind
Turbines: Analyzing Data from the German 250-MW Measurement Program from the
Ancillary Services Viewpoint,” presented at Windpower ’99 Conference, June 20-23,
1999, Burlington, Vermont.
E. Hirst and B. Kirby (2000-1), “Measuring Generator Performance in Providing the
Regulation and Load-Following Ancillary Services,” Oak Ridge National Laboratory,
ORNL, Oak Ridge, TN, December 2000.
M. R. Milligan (2000-1), “Modeling Utility-Scale Wind Power Plants Part 1:
Economics,” National Renewable Energy Laboratory NREL, Golden, Colorado, June
2000.
J. Cadogan, M. R. Milligan, Y. Wan and B. Kirby (2000-1), “Short-Term Output
Variations in Wind Farms – Implications for Ancillary Services in the United States,”
9-1
presented at the Wind Power for the 21st Century Conference, September 26-28, 2000,
Kassel, Germany.
R. Z. Poore and G. Randall (2001-1), “Characterizing and Predicting Ten Minute and
Hourly Fluctuations in Wind Power Plant Output to Support Integrating Wind Energy
into a Utility System,” presented at Windpower 2001 Conference, June 3-7, 2001;
Washington, DC.
Y. Wan and D. Bucaneg (2001-1), “Short-term Power Fluctuation of Large Wind Power
Plants,” National Energy Laboratory NREL, Golden Colorado, June 2000.
R. Hudson, B. Kirby and Y. Wan (2001-1), “Regulation Requirements for Wind
Generation Facilities,” presented at Windpower 2001 Conference, June 3-7, 2001,
Washington. DC.
E. Hirst (2001-1), “Interactions of Wind Farms with Bulk-Power Operations and
Markets,” Consulting in Electric-Industry Restructuring, Oak Ridge, TN 37830, prepared
for Sustainable FERC Energy Policy, Alexandria, Virginia 22314, September 2001.
E. Hirst (1998-1), “Defining Intra- and Inter-hour Load Swings,” IEEE Transactions on
Power Systems 13(4), 1379-1385, November 1998..
9-2
Appendix A: Summary of Related Works
[Chan 1983-1] Development of a probabilistic framework for load-following, operatingreserve, and unloadable-generation requirements for one or more spatially dispersed
wind-turbine clusters under random atmospheric conditions. Wind statistics necessary for
assessing the operating requirements are defined and computed, while a computational
method is developed that translates these wind statistics based on various requirements.
[Milligan 1995-1] The potential value of wind forecast accuracy is identified by using an
electricity production cost model to measure the cost implications of various degrees of
forecast accuracy. The work does not attempt to forecast wind or wind energy, but rather
to analyze the value associated with a particular degree of accuracy in a forecast. The role
of accuracy in wind forecasting is viewed as a function to reduce risk as the utility
attempts to minimize the cost of service to its customers.
[Hirst 1995-1] This report provides a view of different types of ancillary services
required in supporting the transmission of electrical power from seller to purchaser while
maintaining reliable operations of the interconnected transmission system.
[Milligan 1996-1], [Milligan 1997-2] A proposed enumerated probabilistic approach and
reduced enumerated probabilistic approach to evaluate the capacity credit of wind power
plants through the use of production costing and reliability modeling. Capacity credit is
defined based on effective load carrying capability. The probabilistic technique is
implemented outside of the production cost model, therefore it is capable of handling
multiple wind power time series. Time series are generated through a Markov wind-speed
simulation model. Two production-cost models are used in this work: Elfin, a loadduration curve model; and P+, a chronological model.
[Hirst 1996-1] Using data, assumptions, and analyses from twelve utilities throughout the
United States, estimates were developed for the cost of each individual ancillary service
and for aggregation of these services. These utilities, although a small and nonrepresentative sample of the industry, account for 28% of U.S. electric-energy
production.
[Milligan 1997-1] Several traditional capacity credit calculations are examined that are
considered minimal in computational effort. An approach based on effective load
carrying capability is used as a reference, and is compared with three other approaches
based on capacity factor. Calculations are included demonstrating these different
approaches as applied to a wind power plant operating within a large generation
company.
[Ernst 1999-1] Individual turbine and aggregate power output data is analyzed from the
German “250-MW Wind” data project. Load following and regulation impacts are
examined as functions of the number and spacing of the turbines in order to quantify the
impacts of aggregation. Results show a significant decrease in the relative system
A-1
regulation burden with increasing number of turbines, even when the turbines are in close
proximity.
[Milligan 2000-1] The basic economic issues associated with electricity production from
several generators, including large-scale wind power plants, are addressed. The roles of
unit commitment and economic dispatch in production-cost models are emphasized.
Overviews and comparisons of the prevalent production-cost modeling methods are
provided, including several case studies applied to a variety of electric utilities.
[Hirst 2000-1] Metrics for two real-power ancillary services are applied and developed
for regulation and load following. This application is based on assuming a small control
area, as well as using system and generator specific data for two 12-day periods. The
metrics is used to quantity the amount of the two ancillary services each generator
actually delivers. One issue addressed is whether the metrics should compare individual
generator performance to overall system performance or should individual generator
performance be compared only to system-operator instructions sent to that generator.
[Cadogan 2001-1] With the arrival of competition in the electrical power marketplace, its
effect on wind and other renewable energy technologies is reviewed. In particular, the
implications of ancillary service requirements on a wind farm and present initial
operating results of monitoring one Midwest wind farm are examined. Another topic is
the role of federal and state policies in the recent wind installations within the United
States. One example of note is the federal energy policy, which states that each generator
must purchase or otherwise provide for ancillary services required to transmit power to
the given load.
[Poore 2001-1] Statistically evaluation of the ten-minute and hourly variations in the
output of a 42-turbine wind power plant and examination of various techniques for using
the current performance of the facility to predict short-term future performance are
investigated. The behavior varies as function of power level, time of day, and season. The
behaviors of small portions of the project are compared to the overall project
performance in order to examine the impact of the plant size on the output characteristics.
[Wan 2001-1] Wind speed and wind generation data collected from two large wind
power plants (Storm Lake and Lake Benton II) was examined. Observations were made
that the actual magnitude of power fluctuations did not appear to be extraordinary as the
spatial diversity played a large role in reducing the variations. Persistency analysis of the
data indicated that the plant’s output power fluctuations are bounded in a narrow range.
On a minute-by-minute basis, operators could expect for 94.5% of time that the power
level change (either up or down) would be less than 1.4% of the total capacity. Given the
knowledge of current power output at a given level, operators could expect that at least
90% of time the output power will remain at the same level. In addition to the limited
range of power changes, the data showed that the rates of power changes are also limited.
For example, a wind plant having a total capacity of 103.5 MW would have 99% of the
apparent power change rates within ±200 kW/sec.
A-2
[Hudson 2001-1] The operational impacts of a wind generation facility on the regulation
requirements of the electric utility grid system were evaluated. Analysis was based on
operations data from a 100 MW wind facility, and showed that the regulation burden, on
a nameplate capacity basis, is inversely proportional to the number of machines due to
the effects of spatial diversity. Furthermore, when a wind facility is integrated into a
utility grid, the additional regulation burden due to wind facility is directly influenced by
the relative magnitude of the regulation burden due to load. In the case study example, a
4.3% wind capacity addition results in only 0.22% increase in system regulation
requirements.
[Hirst 2001-1] A quantitative method is defined and applied that allows for the
integration of a wind power facility into a large electric system. The method focuses on
the real-time and short-term forward markets in a competitive (deregulated) wholesale
electricity industry. The applied method suggests that wind-farm owners can increase
their earnings by scheduling wind output ahead of time rather than having the wind
energy appear entirely in real time, improved forecasting models can increase the
revenues associated with hour-ahead scheduling, and the average revenue per MWh of
wind production declines as the size of the wind facility increases relative to the size of
the electrical system.
A-3
A-4
Appendix B: Unit Commitment Primer
B.1 Background
During the December 13, 2001 UWIG Technical Review Committee (TRC) meeting in
Denver, the question was raised as to whether a unit commitment (UC) program can be
used to determine a unit generation schedule to meet hourly system load requirements
over the study horizon, as well as the intra-hour load change. The answer to this question
is “Yes, if the utility day-ahead operation planner chooses to do so.” UC is able to
schedule unit generation to meet the hourly load requirements with respect to the given
forecasted load profile while enforcing the constraints of inter-hour ramp rate limits of
the generating units on UC. Additionally, if a sufficient amount of regulation and load
following spinning reserve is allocated in the UC, the unit generation levels scheduled by
UC will provide enough total room between unit-generation high and low limits to follow
intra-hour load changes.
It is also possible, however, that a particular operation planner would adopt a different
strategy whereby regulation and load following reserves are not allocated in the dayahead UC scheduling. Due to uncertainty in load forecasting, some utilities may consider
a better strategy to be 1) not fully-committing all units necessary for meeting the intraand inter-hour load ramping requirements and 2) relying on the real-time operator to
revise the unit generation and transaction schedules on near real-time basis as the
operator has more accurate information on actual system load. For example, the utility
operation planner may run unit commitment with reduced spinning reserve requirement.
In such a case, if there is no subsequent real-time operator intervention, the schedule from
unit commitment is not able to support the intra-hour load changes. Examples are
provided in the following sections for illustration. Note that modeling this second
strategy of utility operation for simulation is very difficult. Additionally, there are human
factors involved, and capturing the real-time operator decision process into the simulation
could be rather complicated. Furthermore, there could be several real-time operators each
having a somewhat different strategy.
This appendix provides a simplified explanation of how UC functions to provide
generation schedules to meet inter- and intra-hour load changes. In this explanation, the
following are assumed:
•
•
Day-ahead load forecast is perfect;
It is very expensive for the real-time operator to purchase energy from the spot
market when the utility does not own sufficient generating facilities to meet the
load demand in real time.
Under these assumptions, a utility operation planner opts to use the unit commitment to
provide a generation schedule for meeting the hourly forecasted load as well as to follow
the intra-hour load changes. We will describe how to set up unit commitment constraint
B-1
requirements to achieve such a goal. Without loss of any generality, we assume no wind
generation at all in the utility system for this discussion.
B.1.1 Spinning Reserve Requirement in Real Time
In the WSCC and NERC guidelines, reserve requirement applies only to real-time
operation. There is no guideline on the amount of reserve required in performing UC
planning.
Both WSCC and NERC require the utility to maintain operating reserve of the following
components on a real-time basis:
•
•
•
•
Regulating reserve (spinning) – this is the regulation reserve and load
following reserve in the terminology of our project
Contingency reserve (spinning and non-spinning)
Additional reserve for interruptible imports (spinning and non-spinning)
Additional reserve for on-demand obligation (spinning and non-spinning)
The WSCC guideline specifies the regulating reserve requirement to be the system load
change over the next 10 minutes. This discussion, however, focuses on the regulating
reserve requirement to be used in UC. Furthermore, following the terminology used
throughout the project and this report, the regulating reserve defined by the WSCC and
NERC refers to the total of the regulating reserve and the load following reserve
requirements investigated in this project. For simplicity, illustrative examples presented
in this document use zero values for requirements of all other types of spinning reserve.
B.1.2 NSP UC Reserve Requirements
As noted in the body of the report, it was difficult to obtain firm information regarding
NSP’s UC setup. At the time that the UC simulations were set up and performed, the
only information obtained was that 160 MW was used for the total spinning reserve
requirement and this amount covered different types of spinning reserve in total. As
noted in the body of the report, subsequent information indicated that only the 160 MW
of contingency reserve is included in the day-ahead UC planning. NSP does not appear
to include load following or regulating reserve requirements in the day-ahead UC
scheduling. Rather, NSP depends on the real-time operator to act to revise the generation
schedule and transaction schedule to meet inter- and intra-hour load changes. As noted,
NSP real-time operators appear to accomplish this by moving the high limits of certain
units from their normal dependable capability (NDC) to their maximum dependable
capability (MDC) and by starting peaking units.
From the NSP hourly historical load data, during the morning load ramp-up the inter-hour
load change from one hour to the next can be as high as 700 MW. The 160 MW spinning
reserve requirement used in NSP’s unit commitment is insufficient for those hours with
rapid intra-hour load ramping. Without the intervention of NSP’s real-time operators, the
generation schedule obtained from the unit commitment would not be able to support the
intra-hour load change in real-time operation. A detailed explanation is given in Section 5
using examples.
B-2
B.2 Unit Commitment in Hourly Resolution
UC study horizon is usually from several days to several weeks. Time resolution is
typically hourly, although some UC programs support half-hour resolution. In this
discussion, an hourly resolution for unit commitment is considered. Since unit
commitment uses hourly resolution, all variables and input quantities are on an hourly
average basis. Consider an actual load profile of 4 hours as shown in Figure B - 1.
Load
(MW)
160
140
120
100
1
2
3
4
Hour
Figure B - 1. Example actual load profile.
During the 4-hour period as shown in the figure, system load continues to ramp up from
90 MW to 160 MW; specifically 90 MW to 110 MW for hour 1, 110 MW to 130 MW for
hour 2, 130 MW to 140 MW for hour 3 and 140 MW to 160 MW for hour 4. System load
ramps at a constant rate during each hour. In performing UC, the following hourly
system load series -- average system load over the entire hour – is used as an input: 100
MW for hour 1, 120 MW for hour 2, 135 MW for hour 3 and 150 MW for hour 4, which
is shown graphically in Figure B - 2.
The unit generation levels obtained from the UC solution are also hourly averages. UC
enforces the inter-hour generating ramp rate constraints of a given unit in the sense that
the change in the unit’s hourly generation levels between two successive hours must be
less than or equal to the hourly ramp rate limit of the applicable raise or lower directions.
B-3
Load
(MW)
160
140
120
100
1
2
3
4
Hour
Figure B - 2. Hourly average load profile for actual load shown in Figure B - 1.
B.3 Example #1 -- Unit Commitment Schedule and IntraHour Real-Time Operation
In this section, it is demonstrated through examples that even with inter-hour unit
ramping constraints being enforced, the UC solution may not be able to support the intrahour load change in real-time operation. The next section shows that in order to insure
that the UC solution is capable of following the intra-hour load change in real-time
operation, appropriate regulating and load following reserve requirements must be
enforced in UC.
In this example, the system load shown in Figure B - 1 and Figure B - 2 is used. Two
generating units are considered. Initially, i.e. prior to hour 1, unit 1 is online with 80 MW
hourly generation and unit 2 is offline. The high limits for unit 1 and 2 are 135 MW and
100 MW, respectively. The low limits of unit 1 and 2 are both 0 MW. The ramp rates
for unit 1 and 2 are 20 MW/hr and 30 MW/hr, respectively, in both the raise and lower
directions. Unit 2 has a very high generation cost at its minimum generation level such
that it should be kept offline as much as possible. Unit 2 can be dispatched immediately
after it is online.
Consider that unit 2 is newly online for a particular hour; hence unit 2 is at minimum
generation at the beginning of the hour. Consider that unit 2 continues to ramp up at the
ramp rate limit until the end of the hour. Therefore the hourly generation of unit 2 for that
hour can be as much as (0.5 * hourly ramp rate + low limit). Consider that the
requirement of regulating reserve and load following is zero, the unit commitment
solution is shown in Figure B - 3.
B-4
Load
(MW)
160
140
120
100
1
2
3
4
Hour
Unit 1 140
(MW)
120
100
Unit 2
(MW)
20
0
Figure B - 3. Graphically representation of UC solution
Figure B - 3 shows that the UC solution is such that unit 1 generation matches the system
load from hour 1 to hour 3 while unit 2 is offline. The inter-hour ramping of unit 1
generation is within the ramping limit. On hour 3, unit 1 hourly generation level reaches
its high limit. On hour 4, since unit 1 hourly generation cannot be increased, unit 2 is
started to provide additional generation to meet the increase in load requirement. Note
B-5
that there is no spinning reserve requirement. In summary, the hourly generation for unit
1 and 2 are given in Table B - 1.
Table B - 1. Summary of UC hourly generation schedule for example #1.
Hour
1
2
3
4
System load hourly MW
100
120
135
150
Unit 1 hourly MW
100 (on)
120 (on)
135 (on)
135 (on)
Unit 2 hourly MW
0 (off)
0 (off)
0 (off)
15 (off)
The UC solution is able to follow intra-hour load change until the mid-point of hour 3 in
real time. During the second half of hour 3, the system load continues to increase,
however. Unit 1 is already at the high limit, and unit 2 has not yet started. Consequently,
there is no generating capacity to follow the intra-hour load change. Figure B - 4 shows
the unit generation in real-time operation for hour 1, 2 and hour 3. Note the total
generation of unit 1 and 2 does not match system load for the second half of hour 3 in
real-time operation.
B-6
Load
(MW)
160
140
120
100
1
2
3
4
Hour
Unit 1 140
(MW)
120
100
Unit 2
(MW)
20
0
Figure B - 4. Real-time comparison of load and generation for hourly UC schedule.
B-7
B.4 Example #2 -- Load Following Reserve for Unit
Commitment
From the previous example, it is clear that extra reserve is required from the UC solution
for intra-hour load following. The amount of reserve required is equal to the intra-hour
maximum minus the hourly average of system load. For hour 3, it is 5 MW. Assuming
that the hourly average is approximately at the mid point between the intra-hour
maximum and minimum, the reserve requirement becomes the average of the system load
intra-hour maximum and minimum. Table B - 2 lists the total intra-hour reserve
(regulating reserve plus the load following reserve) requirement required for each hour in
the UC for the UC solution to adequately follow the intra-hour load changes.
Table B - 2. Total intra-hour reserve required for UC solution of example #1 to adequately follow
intra-hour load changes.
Hour
System load hourly MW
1
2
3
4
100
120
135
150
Reserve requirement in MW for
regulation and load following
10
10
5
10
The next question is what is the reserve contribution from different generating units. Here
we see from the example that in real-time, the system load increases to the intra-hour
maximum from the hourly average level in about half an hour. This means that unit
generation must be able to increase by this much within half an hour for load following.
Thus, the reserve contribution from a generating unit is as follows:
Reserve Contribution = Minimum of (1) high limit – hourly generation, and (2) 0.5 *
hourly ramp rate
With the additional reserve requirement, the new unit commitment solution is given in
the following table. This solution is shown graphically in Figure B - 1.
Table B - 3. Updated UC solution with adequate hourly reserve requirements enforced.
Hr
1
2
3
4
System load
hourly MW
100
120
135
150
Reserve Reqt.
(MW)
10
10
5
10
Unit 1
hourly MW
100 (on)
120 (on)
130 (on)
135 (on)
B-8
Unit 2
hourly MW
0 (off)
0 (off)
5 (on)
15 (on)
Total spin
reserve MW
10
10
20
15
Load
(MW)
160
140
120
100
1
2
3
4
Hour
Unit 1
(MW)
140
120
100
Unit 2
(MW)
20
0
Figure B - 5. Graphical representation of UC solution with adequate hourly reserve requirements
enforced.
Note that due to the additional reserve requirement, unit commitment starts up unit 2 on
hour 3 instead of hour 4. With unit 2 online for hour 3 and 4, a sufficient amount of
generating capacity is available for intra-hour load following in real-time operation.
Figure B - 6 shows the unit generation in real-time operation for the updated UC solution.
B-9
Load
(MW)
160
140
120
100
1
2
3
4
Hour
Unit 1
(MW)
140
120
100
Unit 2
(MW)
20
0
Figure B - 6. Real-time comparison of load and generation for update hourly UC schedule including
adequate reserve requirement.
B-10
Appendix C: Y2000 NSP Hourly Wind Generation Data
This appendix provides a graphical view of the NSP Year 2000 hourly-resolution wind
generation data used to generate the hourly STM.
C.1 January 2000- April 2000
250
200
150
100
50
0
1/1/00 0:00
1/8/00 0:00
1/15/00 0:00
1/22/00 0:00
1/29/00 0:00
250
200
150
100
50
0
2/1/00 0:00
2/8/00 0:00
2/15/00 0:00
2/22/00 0:00
2/29/00 0:00
250
200
150
100
50
0
3/1/00 0:00
3/8/00 0:00
3/15/00 0:00
3/22/00 0:00
3/29/00 0:00
250
200
150
100
50
0
4/1/00 0:00
4/8/00 0:00
4/15/00 0:00
C-1
4/22/00 0:00
4/29/00 0:00
C.2 May 2000- August 2000
250
200
150
100
50
0
5/1/00 0:00
5/8/00 0:00
5/15/00 0:00
5/22/00 0:00
5/29/00 0:00
250
200
150
100
50
0
6/1/00 0:00
6/8/00 0:00
6/15/00 0:00
6/22/00 0:00
6/29/00 0:00
250
200
150
100
50
0
7/1/00 0:00
7/8/00 0:00
7/15/00 0:00
7/22/00 0:00
7/29/00 0:00
8/8/00 0:00
8/15/00 0:00
8/22/00 0:00
8/29/00 0:00
250
200
150
100
50
0
8/1/00 0:00
C-2
C.3 September 2000 – December 2000
250
200
150
100
50
0
9/1/00 0:00
9/8/00 0:00
9/15/00 0:00
9/22/00 0:00
9/29/00 0:00
250
200
150
100
50
0
10/1/00 0:00
10/8/00 0:00
10/15/00 0:00
10/22/00 0:00
10/29/00 0:00
250
200
150
100
50
0
11/1/00 0:00
11/8/00 0:00
11/15/00 0:00
11/22/00 0:00
11/29/00 0:00
250
200
150
100
50
0
12/1/00 0:00
12/8/00 0:00
12/15/00 0:00
C-3
12/22/00 0:00
12/29/00 0:00
C-4
Appendix D: Summary of Related Works
The following provides a brief description of ABB’s CougerPlus, which is the program
used in the unit commitment portion of the project. The material is adopted from the
CougerPlus descriptions posted on ABB’s website.
ABB’s CougerPlus is a comprehensive operations scheduling program that determines
optimal resource schedules in order to minimize utility/GenCo operating costs and
maximize profits. The CougerPlus coordinates the scheduling of all resources including
thermal, hydro and combined cycle generating units, and coordinates opportunities for
purchases and sales of bulk power at electric utility control centers and GenCo trading
floors.
CougerPlus is the industry standard for resource scheduling software with installations
throughout the world. In the US, utilities and GenCo’s scheduling approximately 50% of
the nation’s electric production assets use the CougerPlus software.
The program can operate in stand-alone or client-server architecture, and offers a
comprehensive and user-friendly graphic interface for data entry and operation. Program
operation and data flow can also be controlled through text files, interfacing in this
manner allows for large numbers of cases to be run without requiring human intervention.
Advanced features of the program include:
•
•
•
•
•
•
•
•
Emission Dispatch – Schedule generation and assets that are subject to emission
limits and constraints
Auto Transaction Analysis – Provide fast and accurate cost/value evaluation on
individual transactions or multiple blocks of power
Multi Area Model – Enable a utility or GenCo to optimize asset commitment and
dispatch subject to transmission constraints
Risk Manager – Calculate costs and risk values for multiple operations (load
forecasts, availability, etc.)
Post Analysis – Provide capabilities to calculate actual trading profit and loss and
compare actual system operations against best practice
Fuel Allocation – Schedule generation resources subject to varying fuel
availability and cost
Combined Cycle – Model complex combined cycle plant characteristics
Annual Model – Model seasonal and annual planning horizons
D-1
D-2
Appendix E: Sample CougerPlus Solution Output
This appendix presents the complete hourly generation schedule obtained from the UC simulation for the
winter scenario, no wind case.
__________________________________
The following lists the generation pattern from the solution of the unit commitment run for the 3-day period
of Jan 2 to 4. Notice that SHC1, SHC2 and SHC 3 under unit name stand for Sherco 1, 2 and 3 respectively.
Purch01 stands for the first energy purchase block and Purch 02 for the second etc. Pur means total
purchase.
Note that the energy sale is not shown. For any hour that total generation exceeds total load, the
difference is the total energy sale.
Printed 17-APR-02 ( 9:12)
cougerplus
version
6.76
PAGE
78
Output 4.1 - MW Loading Summary for Tue 2JAN01-Day 1
Area= SYSTEM
Period= ALL-WEEK
Case=ABB-UCP VERSION 5.9
Unit
ASK1
BDS3
BFT4
BFT5
BFT6
FEN1
HBR5
HBR6
LCG1
PR1
PR2
MNN1
REW1
REW2
RIV1
RIV2
SHC1
SHC2
SHC3
WLM1
WLM2
Purch01
Gen
-Therm
-Pur+UP
TotGen *
Load
-Native
TotLoad*
------ MW Generation/Purchase (+) or Pumping/Sale (-) in Hour -----------------------------1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
0.
0.
0.
0.
0.
0.
0.
64.
64.
64.
64.
64.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
510.
510.
510.
510.
510.
510.
570.
662.
662.
662.
662.
662.
530.
530.
530.
530.
530.
530.
570.
662.
662.
662.
662.
662.
754.
755.
755.
755.
755.
755.
802.
871.
871.
871.
871.
871.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
1.*
0.
0.
0.
0.
0.
0.
25.*
228.*
367.*
327.*
390.*
4561.
1.
----4562.
4561.
0.
----4561.
4561.
0.
----4561.
4561.
0.
----4561.
4561.
0.
----4561.
4561.
0.
----4561.
4708.
0.
----4708.
5025.
25.
----5050.
5025.
228.
----5253.
5025.
367.
----5392.
5025.
327.
----5352.
5025.
390.
----5415.
3798.
----3798.
3682.
----3682.
3630.
----3630.
3612.
----3612.
3740.
----3740.
4035.
----4035.
4708.
----4708.
5050.
----5050.
5253.
----5253.
5392.
----5392.
5352.
----5352.
5415.
----5415.
E-1
Printed 17-APR-02 ( 9:12)
cougerplus
version
6.76
PAGE
79
Output 4.1 - MW Loading Summary for Tue 2JAN01-Day 1
Area= SYSTEM
Period= ALL-WEEK
Case=ABB-UCP VERSION 5.9
Unit
ASK1
BDS3
BFT4
BFT5
BFT6
FEN1
HBR5
HBR6
LCG1
PR1
PR2
MNN1
REW1
REW2
RIV1
RIV2
SHC1
SHC2
SHC3
WLM1
WLM2
Purch01
Purch02
------ MW Generation/Purchase (+) or Pumping/Sale (-) in Hour -----------------------------13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
24:00
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
64.
64.
64.
64.
89.
258.
258.
225.
64.
64.
0.
0.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
662.
662.
662.
662.
662.
662.
662.
662.
662.
662.
559.
510.
662.
662.
662.
662.
662.
662.
662.
665.
664.
662.
570.
530.
871.
871.
871.
871.
871.
871.
871.
871.
871.
871.
795.
755.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
274.*
222.*
211.*
228.*
400.*
400.
400.
400.*
400.*
124.*
2.*
0.
0.
0.
0.
0.
0.
179.*
115.*
0.
0.
0.
0.
0.
E-2
Printed 17-APR-02 ( 9:12)
cougerplus
version
6.76
PAGE
80
Output 4.1 - MW Loading Summary for Tue 2JAN01-Day 1
Area= SYSTEM
Period= ALL-WEEK
Case=ABB-UCP VERSION 5.9
Unit
Gen
-Therm
-Pur+UP
TotGen *
Load
-Native
TotLoad*
------ MW Generation/Purchase (+) or Pumping/Sale (-) in Hour -----------------------------13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
24:00
5025.
274.
----5299.
5025.
222.
----5247.
5025.
211.
----5236.
5025.
228.
----5253.
5050.
400.
----5450.
5219.
579.
----5798.
5219.
515.
----5734.
5189.
400.
----5589.
5027.
400.
----5427.
5025.
124.
----5149.
4691.
2.
----4693.
4561.
0.
----4561.
5299.
----5299.
5247.
----5247.
5236.
----5236.
5253.
----5253.
5450.
----5450.
5798.
----5798.
5734.
----5734.
5589.
----5589.
5427.
----5427.
5149.
----5149.
4691.
----4691.
4244.
----4244.
E-3
Printed 17-APR-02 ( 9:12)
cougerplus
version
6.76
PAGE
81
Output 4.1 - MW Loading Summary for Wed 3JAN01-Day 2
Area= SYSTEM
Period= ALL-WEEK
Case=ABB-UCP VERSION 5.9
Unit
ASK1
BDS3
BFT4
BFT5
BFT6
FEN1
HBR5
HBR6
LCG1
PR1
PR2
MNN1
REW1
REW2
RIV1
RIV2
SHC1
SHC2
SHC3
WLM1
WLM2
Purch01
Gen
-Therm
-Pur+UP
TotGen *
Load
-Native
TotLoad*
------ MW Generation/Purchase (+) or Pumping/Sale (-) in Hour -----------------------------1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
0.
0.
0.
0.
0.
0.
0.
64.
64.
64.
64.
64.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
510.
510.
510.
510.
510.
510.
570.
662.
662.
662.
662.
662.
530.
530.
530.
530.
530.
530.
570.
662.
662.
662.
662.
662.
755.
755.
755.
755.
755.
755.
826.
871.
871.
871.
871.
871.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
1.*
0.
0.
0.
0.
2.*
0.
210.*
193.*
255.*
271.*
232.*
4561.
1.
----4562.
4561.
0.
----4561.
4561.
0.
----4561.
4561.
0.
----4561.
4561.
0.
----4561.
4561.
2.
----4563.
4732.
0.
----4732.
5025.
210.
----5235.
5025.
193.
----5218.
5025.
255.
----5280.
5025.
271.
----5296.
5025.
232.
----5257.
3944.
----3944.
3816.
----3816.
3738.
----3738.
3654.
----3654.
3760.
----3760.
4101.
----4101.
4732.
----4732.
5235.
----5235.
5218.
----5218.
5280.
----5280.
5296.
----5296.
5257.
----5257.
E-4
Printed 17-APR-02 ( 9:12)
cougerplus
version
6.76
PAGE
82
Output 4.1 - MW Loading Summary for Wed 3JAN01-Day 2
Area= SYSTEM
Period= ALL-WEEK
Case=ABB-UCP VERSION 5.9
Unit
ASK1
BDS3
BFT4
BFT5
BFT6
FEN1
HBR5
HBR6
LCG1
PR1
PR2
MNN1
REW1
REW2
RIV1
RIV2
SHC1
SHC2
SHC3
WLM1
WLM2
Purch01
Gen
-Therm
-Pur+UP
TotGen *
Load
-Native
TotLoad*
------ MW Generation/Purchase (+) or Pumping/Sale (-) in Hour -----------------------------13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
24:00
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
64.
64.
64.
64.
64.
215.
225.
131.
64.
44.
0.
0.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
662.
662.
662.
662.
662.
662.
662.
662.
662.
662.
519.
510.
662.
662.
662.
662.
662.
662.
663.
668.
662.
674.
530.
530.
871.
871.
871.
871.
871.
871.
871.
871.
871.
871.
755.
755.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
143.*
98.*
37.*
20.*
171.*
400.*
400.*
400.*
288.*
2.*
2.*
2.*
5025.
143.
----5168.
5025.
98.
----5123.
5025.
37.
----5062.
5025.
20.
----5045.
5025.
171.
----5196.
5176.
400.
----5576.
5187.
400.
----5587.
5098.
400.
----5498.
5025.
288.
----5313.
5017.
2.
----5019.
4570.
2.
----4572.
4561.
2.
----4563.
5168.
----5168.
5123.
----5123.
5062.
----5062.
5045.
----5045.
5196.
----5196.
5576.
----5576.
5587.
----5587.
5498.
----5498.
5313.
----5313.
5017.
----5017.
4570.
----4570.
4151.
----4151.
E-5
Printed 17-APR-02 ( 9:12)
cougerplus
version
6.76
PAGE
83
Output 4.1 - MW Loading Summary for Thu 4JAN01-Day 3
Area= SYSTEM
Period= ALL-WEEK
Case=ABB-UCP VERSION 5.9
Unit
ASK1
BDS3
BFT4
BFT5
BFT6
FEN1
HBR5
HBR6
LCG1
PR1
PR2
MNN1
REW1
REW2
RIV1
RIV2
SHC1
SHC2
SHC3
WLM1
WLM2
Purch01
Gen
-Therm
-Pur+UP
TotGen *
Load
-Native
TotLoad*
------ MW Generation/Purchase (+) or Pumping/Sale (-) in Hour -----------------------------1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
0.
0.
0.
0.
0.
0.
0.
64.
64.
64.
64.
64.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
510.
510.
510.
510.
510.
510.
590.
662.
662.
662.
662.
662.
530.
530.
530.
530.
530.
530.
598.
662.
662.
662.
662.
662.
755.
755.
754.
755.
755.
755.
847.
871.
871.
871.
871.
871.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
2.*
2.*
0.
0.
0.
2.*
2.*
209.*
170.*
231.*
264.*
259.*
4561.
2.
----4563.
4561.
2.
----4563.
4560.
0.
----4560.
4561.
0.
----4561.
4561.
0.
----4561.
4561.
2.
----4563.
4801.
2.
----4803.
5025.
209.
----5234.
5025.
170.
----5195.
5025.
231.
----5256.
5025.
264.
----5289.
5025.
259.
----5284.
3885.
----3885.
3785.
----3785.
3757.
----3757.
3730.
----3730.
3830.
----3830.
4179.
----4179.
4801.
----4801.
5234.
----5234.
5195.
----5195.
5256.
----5256.
5289.
----5289.
5284.
----5284.
E-6
Printed 17-APR-02 ( 9:12)
cougerplus
version
6.76
PAGE
84
Output 4.1 - MW Loading Summary for Thu 4JAN01-Day 3
Area= SYSTEM
Period= ALL-WEEK
Case=ABB-UCP VERSION 5.9
Unit
ASK1
BDS3
BFT4
BFT5
BFT6
FEN1
HBR5
HBR6
LCG1
PR1
PR2
MNN1
REW1
REW2
RIV1
RIV2
SHC1
SHC2
SHC3
WLM1
WLM2
Purch01
Gen
-Therm
-Pur+UP
TotGen *
Load
-Native
TotLoad*
------ MW Generation/Purchase (+) or Pumping/Sale (-) in Hour -----------------------------13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
24:00
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
490.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
76.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
13.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
14.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
22.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
58.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
112.
64.
64.
64.
64.
64.
189.
156.
64.
64.
0.
0.
0.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
462.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
542.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
584.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
124.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
226.
662.
662.
662.
662.
662.
662.
662.
662.
662.
650.
510.
510.
662.
662.
662.
662.
662.
662.
662.
676.
662.
669.
530.
530.
871.
871.
871.
871.
871.
871.
871.
871.
871.
871.
755.
754.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
9.
242.*
159.*
98.*
64.*
186.*
400.*
400.*
400.*
198.*
0.
1.*
0.
5025.
242.
----5267.
5025.
159.
----5184.
5025.
98.
----5123.
5025.
64.
----5089.
5025.
186.
----5211.
5150.
400.
----5550.
5117.
400.
----5517.
5039.
400.
----5439.
5025.
198.
----5223.
4956.
0.
----4956.
4561.
1.
----4563.
4560.
0.
----4560.
5267.
----5267.
5184.
----5184.
5123.
----5123.
5089.
----5089.
5211.
----5211.
5550.
----5550.
5517.
----5517.
5439.
----5439.
5223.
----5223.
4956.
----4956.
4507.
----4507.
4129.
----4129.
E-7
E-8
Appendix F: Description of Economic Dispatch Tool
This appendix presents the economic dispatch formulation used in the NSP case study,
along with a simple example to illustrate the implementation in the Matlab environment.
F.1 Economic Dispatch Formulation
The Economic Dispatch formulation with multiple types of reserve constraints is as
follows:
Let n be the number of units (input data)
Let ld be the load demand plus scheduled interchange (input data)
Let rrureq be the up-direction regulating reserve requirement (input data)
Let rrdreq be the down-direction regulating reserve requirement (input data)
Let rcreq be the spinning contingency reserve requirement (input data)
Let rfreq be the up-direction load following reserve requirement (input data)
Let i be the index of generating unit with i = 1…n
Let gi be the generation variable of unit i (variable)
Let gd be the variable for generation deficit (variable)
Let rrui be the regulating reserve up-direction variable of unit i (variable)
Let rrud be the variable for regulating reserve up-direction deficit (variable)
Let rrdi be the regulating reserve down-direction variable of unit i (variable)
Let rrdd be the variable for regulating reserve down-direction deficit (variable)
Let rci be the contingency reserve variable of unit i (variable)
Let rcd be the variable for contingency reserve deficit (variable)
Let rfi be the load following reserve variable of unit i (variable)
Let rfd be the variable for load following reserve deficit (variable)
Let Ci(gi) be the cost function of unit i generation gi (input data)
Let Cg,d(gd) be the cost function of generation deficit gd (input data)
Let Crru,d(rrud) be the cost function of regulating reserve up-direction deficit rrud (input
data)
Let Crrd,d(rrd) be the cost function of regulating reserve down-direction deficit rrd (input
data)
Let Crc,d(rcd) be the cost function of contingency reserve rcd (input data)
Let Crf,d(rfd) be the cost function of load following reserve deficit rfd (input data)
Let gcbi,max and gcbi,min be capability high and low limits of generating unit i (input data)
Let gopi,max and gopi,min be operating high and low limits of generating unit i (input data)
Let gdspi,max and gdspi,min be dispatchable high and low limits of generating unit i (input
data)
Let rrui,max be the maximum contribution to regulating reserve up-direction from unit i
(input data)
F-1
Let rrdi,max be the maximum contribution to regulating reserve down-direction from unit i
(input data)
Let rci,max be the maximum contribution to contingency reserve from unit i (input data)
Let rfi,max be the maximum contribution to load following reserve from unit i (input data)
Let upfi be the penalty factor of unit i (input data)
Let upfd be the penalty factor of the generation deficit (input data)
We assume the ordering of the time period in increase direction for the deployment of
different types of reserve is 1) regulating, 2) contingency and 3) load-following. It
follows that
rri,max ≤ rci,max ≤ rfi,max
(1)
The optimization problem is formulated mathematically as follows:
Min (Σi = 1,…,n Ci(gi)) + Cg,d(gd) + Crru,d(rrud) + Crc,d(rcd) + Crf,d(rfd) + Crru,d(rrdd)
(2)
Subject to
(Σi = 1,…n (1/upfi)*gi) + (1/upfd)*gd ≥ ld
(coupling constraint)
(3)
(Σi = 1,…n rrui) + rrud ≥ rrureq (coupling constraint)
(4)
(Σi = 1,…n rrdi) + rrdd ≥ rrdreq (coupling constraint)
(4a)
(Σi = 1,…n rci) + rcd ≥ rcreq
(coupling constraint)
(5)
(Σi = 1,…n rfi) + rfd ≥ rfreq
(coupling constraint)
(6)
gopi,min ≤ gi - rrdi
i = 1,…,n
(individual unit constraint)
(7)
gi + rrui + rfi + ≤ gopi,max
i = 1,…,n
(individual unit constraint)
(7a)
0 ≤ rrui ; 0 ≤ rci ; 0 ≤ rfi
i = 1,…,n
(individual unit constraint)
(8)
0 ≤ rrdi
i = 1,…,n
(individual unit constraint)
(8a)
rrui ≤ rrui,max
i = 1,…,n
(individual unit constraint)
(9)
rrdi ≤ rrdi,max
i = 1,…,n
(individual unit constraint)
(9a)
rci ≤ rci,max
i = 1,…,n
(individual unit constraint)
(9b)
rfi ≤ rfi,max
i = 1,…,n
(individual unit constraint)
(9c)
F-2
rrui + rci ≤ max(rrui,max , rci,max) i = 1,…,n
(individual unit constraint)
(10)
rrui + rfi ≤ max(rrui,max , rfi,max) i = 1,…,n
(individual unit constraint)
(10a)
rci + rfi ≤ max(rci,max , rfi,max) i = 1,…,n
(individual unit constraint)
(10b)
rrui + rci + rfi ≤ max (rrui,max , rci,max , rfi,max )
i = 1,…,n
(individual unit constraint)
(11)
gi + rrui + rci + rfi ≤ gcbi,max i = 1,…,n
(individual unit constraint)
(12)
gdspi,min ≤ gi
i = 1,…,n
(individual unit constraint)
(13)
gi ≤ gdspi,max
i = 1,…,n
(individual unit constraint)
(13a)
F.2 Some Implementation Details
The following details relate to the implementation of the economic dispatch formulation
presented above in the MatLab operating environment for the simulations performed in
the NSP case study:
1.
The deployment time for each reserve type is specified as input data. For each
unit and for each type of reserve, the maximum reserve contribution from the unit is
calculated as the unit ramp rate multiplied by the reserve deployment time.
2.
Incremental cost curve for each generating unit is assumed to be incremental nondecreasing, stepwise constant; in other words, the curve is in an upward staircase
shape. The curve is defined from low limit gmin to high limit gmax for each generating
unit. When converting the EDC problem into a linear programming formulation, one
variable is defined for each segment (step) of the increment cost curve, say x1, x2 and
xm where m is the total number of segments. These variables will be used instead of
variable g. Variables x1, x2 and xm correspond to segments from left to right with
lowest incremental cost for x1 and highest incremental cost for xm. Each variable is
bound between 0 and the length of the segment. The total length of all segments must
be equal to the difference between gmax and gmin. Finally, g - gmin is replaced by x1 +
x2 +… + xm.
3.
Let cj be the incremental cost associated with segment j of the incremental cost
curve. Hence c1 < c2 < …< cm. The cost function C (g) = C (gmin + x1 + x2 +… + xm)
of generating unit is
C(g) = constant + c1∗x1 + c2∗x2 +… + cm∗xm
The constant value is generating unit specific.
F-3
4.
The cost function of the deficit variable is modeled as linear function with a large
valued multiplier.
F.3 Implementation Example
We next describe the implementation of a simple example through Matlab. The generic
form of the LP (linear programming) formulation in Matlab is
Min cTx
x
subject to
Ax ≤ b
vlb ≤ x ≤ vub
where x is the vector variable, A and b are given matrix and vector inputs for linear
coupling constraints , vlb and vub are given vector inputs respectively for the lower and
upper bounds of x. The values of A, b vlb and vub are passed as parameters in calling
Matlab LP subroutine.
We consider an example containing two generating units with all 3 types of reserve
constraints. If one type of reserve is not modeled in the EDC problem, it is always the
reserve variables and the equations of the last reserve type first to be removed from the
EDC formulation.
F.4 Example
Number of generating units n = 2
Load demand plus scheduled interchange ld = 100 MW
REGULATING UP RESERVE REQUIREMENT RRREQ = 10 MW
REGULATING DOWN RESERVE REQUIREMENT RRREQ = 15 MW
Contingency Spinning Reserve Requirement rcreq = 30 MW
Load following Requirement rfreq = 20 MW
Generating unit 1
PENALTY FACTOR = 1.1
DISPATCHABLE MINIMUM = 25 MW
DISPATCHABLE MAXIMUM = 115 MW
OPERATING MINIMUM = 20 MW OPERATING MAXIMUM = 120 MW
Capability minimum = 10 MW Capability maximum = 140 MW
Maximum Reserve Contribution:
Regulating up = 20 MW
Regulating down = 50 MW
Contingency = 40 MW
Load following = 60 MW
Incremental Cost Curve (2 segments):
MW segment
Incremental cost ($/MWh)
[25, 80]
30
[80, 115]
50
F-4
Generating unit 2
Penalty factor = 0.95
Dispatchable minimum = 35 MW
Dispatchable maximum = 95 MW
Operating minimum = 30 MW
Operating maximum = 100 MW
Capability minimum = 15 MW
Capability maximum = 130 MW
Maximum Reserve Contribution:
Regulating up =10 MW
Regulating down = 25 MW
Contingency = 20 MW
Load following = 30 MW
Incremental Cost Curve (3 segments):
MW segment
Incremental cost ($/MWh)
[35, 50]
10
[50, 70]
40
[70, 95]
70
Generating unit 3
Penalty factor = 1.05
Dispatchable minimum = 10 MW
Dispatchable maximum = 40 MW
Operating minimum = 10 MW
Operating maximum = 40 MW
Capability minimum = 5 MW
Capability maximum = 50 MW
Maximum Reserve Contribution:
Regulating up = 4 MW
Regulating down = 10 MW
Contingency = 0 MW
Load following = 8 MW
Incremental Cost Curve (1 segment):
MW segment
Incremental cost ($/MWh)
[10, 40]
5
Incremental cost for deficit variables:
Generation:
100 $/MWh
Regulating up Reserve: 50 $/MWh
Regulating down Reserve: 30 $/MWh
Contingency Reserve: 45 $/MWh
Load following Reserve: 40 $/MWh
Penalty factor for generation deficit: 1.2
Assignment of variable x in Matlab LP formulation
x1
x2
x3
x4
x5
x6
x7
x8
: unit 1 generation dispatched on the 1st segment minus the segment lower bound
: unit 1 generation dispatched on the 2nd segment minus the segment lower bound
: unit 1 regulating reserve up-direction contribution
: unit 1 contingency reserve contribution
: unit 1 load following reserve contribution
: unit 1 regulating reserve down-direction contribution
: unit 2 generation dispatched on the 1st segment minus the segment lower bound
: unit 2 generation dispatched on the 2nd segment minus the segment lower bound
F-5
x9
x10
x11
x12
x13
: unit 2 generation dispatched on the 3rd segment minus the segment lower bound
: unit 2 regulating up reserve contribution
: unit 2 contingency reserve contribution
: unit 2 load following reserve contribution
: unit 2 regulating down reserve contribution
x14
x15
x16
x17
x18
: unit 3 generation dispatched on the 1st segment minus the segment lower bound
: unit 3 regulating up reserve contribution
: unit 3 contingency reserve contribution
: unit 3 load following reserve contribution
: unit 3 regulating down reserve contribution
x19
x20
x21
x22
x23
: system generation deficit
: system regulating up reserve deficit
: system contingency reserve deficit
: system load following reserve deficit
: system regulating down reserve deficit
Consider the object function cTx:
c1
c2
c7
c8
c9
c14
= 30
= 50
= 10
= 40
= 70
=5
c18
c19
c20
c21
c22
= 100
= 50
= 45
= 40
= 30
The remaining ci for i between 1 and 18 are set to zero.
Consider the lower vlb and upper bound vub of x
vlb1 =
vlb2 =
vlb3 =
vlb4 =
vlb5 =
vlb6 =
0
0
0
0
0
0
vlb7 = 0
vlb8 = 0
≤ x1
≤ x2
≤ x3
≤ x4
≤ x5
≤ x6
≤
≤
≤
≤
≤
≤
vub1 = 55
vub2 = 35
vub3 = 15
vub4 = 40
vub5 = 60
vub6 = 50
≤ x7 ≤
≤ x8 ≤
vub7 = 15
vub8 = 20
F-6
vlb9 = 0
vlb10 = 0
vlb11 = 0
vlb12 = 0
vlb13 = 0
≤ x9 ≤
≤ x10 ≤
≤ x11 ≤
≤ x12 ≤
≤ x13 ≤
vub9 = 25
vub10 = 10
vub11 = 20
vub12 = 30
vub13 = 25
vlb14 = 0
vlb15 = 0
vlb16 = 0
vlb17 = 0
vlb18 = 0
≤ x14
≤ x15
≤ x16
≤ x17
≤ x18
≤
≤
≤
≤
≤
vub14 = 30
vub15 = 4
vub16 = 0
vub17 = 8
vub18 = 10
vlb19 = 0
vlb20 = 0
vlb21 = 0
vlb22 = 0
vlb23 = 0
≤ x19
≤ x20
≤ x21
≤ x22
≤ x23
≤
≤
≤
≤
≤
vub19 = large #
vub20 = large #
vub21 = large #
vub22 = large #
vub23 = large #
NOTE THAT FOR VARIABLES HAVE LOWER BOUNDS TO BE ZERO. THE UPPER BOUNDS OF XI I = 1, 2, 6, 7, 8 ARE THE
RANGE OF THE CORRESPONDING INCREMENTAL COST CURVE SEGMENTS. FOR VARIABLES WITHOUT UPPER
BOUNDS, THEIR VUB VALUES ARE SET TO LARGE NUMBER.
WE NEXT DESCRIBE THE CALCULATION OF THE COEFFICIENTS OF THE MATLAB EQUATION AX ≤ B
CONSIDER EQUATION (3)
(1/1.1)*X1 + (1/1.1)*X2 + (1/0.95)*X7 + (1/0.95)*X8 + (1/0.95)*X9 + (1/1.05)*X14 + (1/1.2)*X19 ≥ 30.05
NOTE THAT THE VALUE AT RHS IS THE GENERATION REQUIREMENT MINUS THE TOTAL OF DISPATCHABLE MINIMUM
GENERATION OF ALL UNITS. EQUIVALENTLY, ARRANGING THE PREVIOUS EQUATION IN MATLAB STANDARD FORM, IT
BECOMES
(-1/1.1)*X1 + (-1/1.1)*X2+ (-1/0.95)*X7 + (-1/0.95)*X8 + (-1/0.95)*X9 + (-1/1.05)*X14 +
(-1/1.2)*X19 ≤ -30.05
HENCE
A1,1 = -1/1.1, A1,2 = -1/1.1, A1,7 = -1/0.95, A1,8 = -1/0.95, A1,9 = -1/0.95, A1,14 = -1/1.05,
A1,19 = -1/1.2, B1 = -30.05, AND
A1,J = 0 FOR OTHER J BETWEEN 1 AND 23
NOTE THE ROW INDEX FOR THE ELEMENTS OF A MATRIX AND B VECTOR IS 1 BECAUSE THIS IS THE FIRST
EQUATION.
CONSIDER EQUATION (4)
X3 + X10 + X15 + X20 ≥ 10
OR EQUIVALENTLY IN MATLAB STANDARD FORM
(-X3) + (-X10) + (-X15 ) + (-X20) ≤ -10
HENCE
A2,3 = -1, A2,10 = -1, A2,15 = -1, A2,20 = -1, B2 = -10, AND
A2,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (5)
X4 + X11 + X16 + X21 ≥ 30
OR EQUIVALENTLY IN MATLAB STANDARD FORM
F-7
(-X4) + (-X11) + (-X16) + (-X21) ≤ -30
HENCE
A3,4 = -1, A3,11 = -1, A3,16 = -1, A3,21 = -1, B3 = -30, AND
A3,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (6)
X5 + X12 + X17 + X22 ≥ 20
OR EQUIVALENTLY IN MATLAB STANDARD FORM
(-X5) + (-X12) + (-X17) + (-X22) ≤ -20
HENCE
A4,5 = -1, A4,12 = -1, A4,17 = -1, A4,22 = -1, B4 = -20, AND
A4,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (4A)
X6 + X13 + X22 + X23 ≥ 15
OR EQUIVALENTLY IN MATLAB STANDARD FORM
(-X6) + (-X13) + (-X22) + (-X23) ≤ -15
HENCE
A5,6 = -1, A5,13 = -1, A5,22 = -1, A5,23 = -1, B5 = -15, AND
A5,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (7)
FOR GENERATING UNIT 1
X1 + X2 – X6 ≥ -5
X7 + X8 + X9 – X13 ≥ -5 FOR GENERATING UNIT 2
FOR GENERATING UNIT 3
X14 – X18 ≥ 0
NOTE THAT THE VALUE OF RHS IS THE UNIT GENERATION OPERATING MINIMUM MINUS DISPATCHABLE MINIMUM OF
THE CORRESPONDING UNIT.
OR EQUIVALENTLY IN MATLAB STANDARD FORM
(-X1) + (-X2) + X6 ≤ 5
(-X7) + (-X8) + (-X9) + X13 ≤ 5
(-X14) + X18 ≤ 0
FOR GENERATING UNIT 1
FOR GENERATING UNIT 2
FOR GENERATING UNIT 3
HENCE
A6,1 = -1, A6,2 = -1, A6,6 = 1, B6 = 5, AND
A6,J = 0 FOR OTHER J BETWEEN 1 AND 23
A7,7 = -1, A7,8 = -1, A7,9 = -1, A7,13 = 1, B7 = 5, AND
A7,J = 0 FOR OTHER J BETWEEN 1 AND 23
A8,14 = -1, A8,18 = 1, B8 = 0, AND
A8,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (7A)
X1 + X2 + X3 + X5 ≤ 95
X7 + X8 + X9 + X10 + X12 ≤ 65
X14 + X15 + X17 ≤ 30
FOR GENERATING UNIT 1
FOR GENERATING UNIT 2
FOR GENERATING UNIT 3
HENCE
A9,1 = 1, A9,2 = 1, A9,3 = 1, A9,5 = 1, B9 = 95, AND
A9,J = 0 FOR OTHER J BETWEEN 1 AND 23
A10,7 = 1, A10,8 = 1, A10,9 = 1, A10,10 = 1, A10,12 = 1, B10 = 65, AND
A10,J = 0 FOR OTHER J BETWEEN 1 AND 23
A11,14 = 1, A11,15 = 1, A11,17 = 1, B11 = 30, AND
A11,J = 0 FOR OTHER J BETWEEN 1 AND 23
F-8
NOTE THAT THE VALUE OF RHS IS THE GENERATION OPERATING MAXIMUM MINUS DISPATCHABLE MINIMUM OF THE
CORRESPONDING UNIT.
CONSIDER EQUATION (10)
X3 + X4 ≤ 40
X10 + X11 ≤ 20
X15 + X16 ≤ 4
FOR GENERATING UNIT 1
FOR GENERATING UNIT 2
FOR GENERATING UNIT 3
HENCE
A12,3 = 1, A12,4 = 1, B12 = 40, AND
A12,J = 0 FOR OTHER J BETWEEN 1 AND 23
A13,10 = 1, A13,11 = 1, B13 = 20, AND
A13,J = 0 FOR OTHER J BETWEEN 1 AND 23
A14,15 = 1, A14,16 = 1, B14 = 4, AND
A14,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (10A)
X3 + X5 ≤ 60
X10 + X12 ≤ 30
X15 + X17 ≤ 8
FOR GENERATING UNIT 1
FOR GENERATING UNIT 2
FOR GENERATING UNIT 3
HENCE
A15,3 = 1, A15,5 = 1, B15 = 60, AND
A15,J = 0 FOR OTHER J BETWEEN 1 AND 23
A16,10 = 1, A16,12 = 1, B16 = 30, AND
A16,J = 0 FOR OTHER J BETWEEN 1 AND 23
A17,15 = 1, A17,17 = 1, B17 = 8, AND
A17,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (10B)
X4 + X5 ≤ 60
X11 + X12 ≤ 30
X15 + X17 ≤ 8
FOR GENERATING UNIT 1
FOR GENERATING UNIT 2
FOR GENERATING UNIT 3
HENCE
A18,4 = 1, A18,5 = 1, B18 = 60, AND
A18,J = 0 FOR OTHER J BETWEEN 1 AND 23
A19,11 = 1, A19,12 = 1, B19 = 30, AND
A19,J = 0 FOR OTHER J BETWEEN 1 AND 23
A20,15 = 1, A20,17 = 1, B20 = 8, AND
A20,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (11)
FOR GENERATING UNIT 1
X3 + X4 + X5 ≤ 60
X10 + X11 + X12 ≤ 30 FOR GENERATING UNIT 2
X15 + X16 + X17 ≤ 8 FOR GENERATING UNIT 3
HENCE
A21,3 = 1, A21,4 = 1, A21,5 = 1, B21 = 60, AND
A21,J = 0 FOR OTHER J BETWEEN 1 AND 23
A22,10 = 1, A22,11 = 1, A22,12 = 1, B22 = 30, AND
A22,J = 0 FOR OTHER J BETWEEN 1 AND 23
A23,15 = 1, A23,16 = 1, A23,17 = 1, B23 = 8, AND
A23,J = 0 FOR OTHER J BETWEEN 1 AND 23
CONSIDER EQUATION (12)
X1 + X2 + X3 + X4 + X5 ≤ 115
X7 + X8 + X9 + X10 + X11 + X12 ≤ 95
X14 + X15 + X16 + X17 ≤ 40
FOR GENERATING UNIT 1
FOR GENERATING UNIT 2
FOR GENERATING UNIT 3
NOTE THAT THE VALUE OF RHS IS THE GENERATION CAPABILITY MAXIMUM MINUS DISPATCHABLE MINIMUM OF THE
CORRESPONDING UNIT.
F-9
HENCE
A24,1 = 1, A24,2 = 1, A24,3 = 1, A24,4 = 1, A24,5 = 1, B24 = 115, AND
A14,J = 0 FOR OTHER J BETWEEN 1 AND 23
A25,7 = 1, A25,8 = 1, A25,9 = 1, A25,10 = 1, A25,11 = 1, A25,12 = 1, B25 = 95, AND
A25,J = 0 FOR OTHER J BETWEEN 1 AND 23
A26,14 = 1, A26,15 = 1, A26,16 = 1, A26,17 = 1, B26 = 40, AND
A26,J = 0 FOR OTHER J BETWEEN 1 AND 23
F-10