Program on Technology Innovation: Grid Operation
with 100% Inverter-Based Resources
Final Report
2019 TECHNICAL REPORT
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Program on Technology
Innovation: Grid Operation
with 100% Inverter-Based
Resources
Final Report
EPRI Project Manager
E. Farantatos
3420 Hillview Avenue
Palo Alto, CA 94304-1338
USA
PO Box 10412
Palo Alto, CA 94303-0813
USA
800.313.3774
650.855.2121
3002014775
Final Report, January 2019
askepri@epri.com
www.epri.com
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DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES
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Washington State University
NOTE
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e-mail askepri@epri.com.
Electric Power Research Institute, EPRI, and TOGETHER…SHAPING THE FUTURE OF ELECTRICITY are
registered service marks of the Electric Power Research Institute, Inc.
Copyright © 2019 Electric Power Research Institute, Inc. All rights reserved.
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Acknowledgments
The Electric Power Research Institute (EPRI) prepared this report.
Principal Investigators
D. Ramasubramanian
Q. Wang
E. Farantatos
A. Tuohy
E. Ela
The following organization, under contract to the Electric Power
Research Institute (EPRI), contributed to this report:
Washington State University
Pullman, WA, 99163
Principal Investigators
A. Mehrizi-Sani
This report describes research sponsored by EPRI.
This publication is a corporate
document that should be cited in the
literature in the following manner:
Program on Technology Innovation:
Grid Operation with 100% InverterBased Resources: Final Report.
EPRI, Palo Alto, CA: 2018.
3002014775.
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Abstract
The electric power system, once dominated by traditional
synchronous generation, is experiencing a shift toward an increased
share of power electronics interfaced generation. This shift is mainly
due to increased integration of variable renewable energy resources,
such as wind and solar photovoltaic, which use power electronic
based inverters. Several R&D efforts in the industry are presently
investigating the challenges of grid operation with high levels of
inverter based resources (IBR), however whether or not a bulk power
system can operate and how it could operate with 100% generation
from IBR, i.e. without any synchronous generation, remains an open
question. In such a scenario, maintaining the reliability of the bulk
power system would require complex planning and operation
paradigms. This project investigates the operation and associated
reliability implications of an all inverter-interfaced generation system,
given the new operational features and challenges of such a system
(e.g. no inertia, no synchronizing torque, limited short circuit
capacity, no physical link between load/generation and frequency,
etc.).
The work first investigates the dynamic and stability performance of
an all inverter bulk power system. The definition of frequency in a
100% inverter based system is discussed, and a constant frequency
operational paradigm is introduced. New inverter controls have been
designed to support such a grid, and corresponding models in both
positive sequence, as well as three-phase EMT simulation platforms,
have been developed to investigate power sharing among generating
units and voltage and frequency response of the grid under system
disturbances. The performance of the proposed inverter controls and
their interactions with synchronous machine controls are also
evaluated under IBR dominated systems and operational conditions
in which only a small portion of generation is provided by
conventional rotating generators.
The work also investigates steady state and balancing operation of a
100% variable energy resource system. Production cost simulations
for operating scenarios with 100% energy provided by IBR for
temporal intervals during a day have been performed, and the impact
of curtailment and reserve determination strategies is analyzed. The
applicability of traditional unit commitment and economic dispatch
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frameworks is also discussed. Some aspects of market operations with
focus on the behavior of electricity price are also presented.
The work conducted under this project is considered foundational
towards a multi-year R&D plan that is expected to be executed under
various Electric Power Research Institute (EPRI) projects in the near
future. This project does not intend to answer all of the questions for
such a wide and futuristic R&D topic, rather it raises open questions,
presents ideas and conceptual designs for potential operating
schemes, and demonstrates their performance and applicability
through simulations on large scale synthetic bulk power systems.
Keywords
Inverter
Grid forming
Renewable resources
Constant frequency
Resource uncertainty
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EXECUTIVE SUMMARY
Deliverable Number: 3002014775
Product Type: Technical Report
Product Title: Program on Technology Innovation: Grid Operation with 100% InverterBased Resources: Final Report
PRIMARY AUDIENCE: Transmission Operations and Planning Engineers and Executives
KEY RESEARCH QUESTION
The power grid is experiencing a continuously increasing penetration of generating units that are interfaced
to the system through power electronics, the majority of which are renewable energy resources. Several R&D
efforts in the industry are presently investigating the challenges of grid operation with high levels of renewable
resources, however whether or not the system can operate and how it could operate with 100% generation
from inverter based resources (IBR), i.e. without any synchronous generation, remains an open question. In
such a scenario, maintaining the reliability and stability of the bulk power system would require complex
planning and operation paradigms. This project investigates the operation and associated reliability
implications of an all inverter-interfaced generation system given the new operational features and challenges
of such a system (no inertia, no synchronizing torque, limited short circuit capacity, no physical link between
load/generation and frequency, etc.).
RESEARCH OVERVIEW
The work first investigates the dynamic and stability performance of an all inverter bulk power system. The
definition of frequency in such a system is discussed, and an operating paradigm referred to as constant
frequency operation is introduced. The viability and system reliability of constant frequency operation with
respect to stability performance are evaluated based on detailed inverter models and associated inverter
controls that have been developed and used in various simulation scenarios. A phase angle based droop
scheme is proposed to ensure adequate power sharing among all available resources upon a generation/load
imbalance event. Realizing that an all IBR system might be too far in the future, more realistic scenarios of
inverter dominated systems with small percentages of energy provided by rotating generators are also
studied. The work also investigates steady state and balancing operation of a 100% variable energy resource
system. Production cost simulations for operating scenarios with 100% energy provided by IBR for temporal
intervals during a day have been performed, and the impact of curtailment and reserve determination
strategies is analyzed. The applicability of traditional unit commitment and economic dispatch frameworks is
also discussed. Some aspects of market operations with focus on the behavior of electricity price are also
presented.
KEY FINDINGS
• Frequency definition: In a 100% IBR system, the physical link between generation/load and frequency
is lost due to the power electronics interface between the grid and the energy generating source
• Constant frequency operation that restores frequency to nominal within a few seconds
• Design of grid forming inverter controls that perform power sharing among inverter based resources
• Investigation of steady-state balancing and dispatch operations for time periods with very high
penetrations of variable energy resources (VERs), using state-of-the-art production cost
modeling/tools
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EXECUTIVE SUMMARY
WHY THIS MATTERS
Several regions/states internationally are setting targets of 100% energy production from renewable/clean
sources within the next few decades. It is expected that in the future, system operators will have to manage
and securely operate the system for periods of the day with 100% energy provided by VERs, with possible
operating conditions in which all the energy may be produced by IBR. This report addresses the challenges
and associated reliability implications of operating such a transmission grid.
HOW TO APPLY RESULTS
The insights and learnings from this report can be used to guide future research on the topic of grid operation
with 100% variable and inverter based resources.
LEARNING AND ENGAGEMENT OPPORTUNITIES
The work conducted under this project is considered foundational towards a multi-year R&D plan that is
expected to be executed under various Electric Power Research Institute (EPRI)projects in the near future.
This project does not intend to answer all of the questions for such a wide and futuristic R&D topic, rather it
raises open questions, presents ideas and conceptual designs for potential operating schemes, and
demonstrates their performance and applicability through simulations on largescale synthetic bulk power
systems.
EPRI CONTACTS: Evangelos Farantatos, Senior Technical Leader, efarantatos@epri.com
PROGRAM: Technology Innovation
Together...Shaping the Future of Electricity®
Electric Power Research Institute
3420 Hillview Avenue, Palo Alto, California 94304-1338 • PO Box 10412, Palo Alto, California 94303-0813 USA
800.313.3774 • 650.855.2121 • askepri@epri.com • www.epri.com
© 2019 Electric Power Research Institute (EPRI), Inc. All rights reserved. Electric Power Research Institute, EPRI, and
TOGETHER...SHAPING THE FUTURE OF ELECTRICITY are registered service marks of the Electric Power Research Institute, Inc.
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Table of Contents
Abstract ................................................................. V
Executive Summary .............................................. VII
Section 1: Introduction ........................................ 1-1
Section 2: Inverter Modeling and Constant
Frequency Operation of an All
Inverter System .................................. 2-1
Background ............................................................... 2-1
Constant Frequency Operational Paradigm ................... 2-2
Grid Forming Inverter Positive Sequence Modeling ........ 2-3
Voltage & Current Controlled Grid Forming
Inverter ................................................................ 2-4
Constant Frequency Operation - Demonstrating
Results - 433-Machine 2000-Bus System ....................... 2-5
Case 1: Grid Forming Inverter Operation ................ 2-5
Case 2: Under Frequency Trip ............................... 2-7
Case 3: Variation in Size, Location and Number
of Grid Forming Inverters ..................................... 2-10
Case 4: Topology Change................................... 2-11
Inverter Based Resources Dominated Grid ................... 2-12
Modularized Constant Frequency Inverter
Positive Sequence Models .................................... 2-13
IBR Dominated System - Demonstrating Results - 433Machine 2000-Bus System ........................................ 2-15
Scenario 1: System Operation for a Generation
Loss Event .......................................................... 2-16
Scenario 2: Change in Power Command from
the System Operator ........................................... 2-30
Scenario 3: Line fault followed by outage of the
line ................................................................... 2-33
Section 3: Three-Phase Inverter Models for
Constant Frequency Operation ............ 3-1
Inverter Controls ......................................................... 3-1
Inverter Control Objectives..................................... 3-1
Voltage Magnitude Controller ................................ 3-2
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Real Power Sharing Algorithm ................................ 3-3
Angle Droop Algorithm ......................................... 3-5
Parameter Design ................................................. 3-7
Simulation Case Studies .............................................. 3-8
Step Change in Pgs, i* and |vgs, i*| ..................... 3-10
Load Increase ..................................................... 3-10
Dynamic Loads ................................................... 3-11
Power Redispatch ............................................... 3-12
Fault .................................................................. 3-13
Performance Evaluation in the Presence of
Synchronous Generation ........................................... 3-14
Synchronous Generator Connection ...................... 3-15
Load Change ..................................................... 3-16
Fault .................................................................. 3-18
Power Dispatch .................................................. 3-18
Effect of Controller Gains on the Oscillation
Frequency of the SG ................................................. 3-19
Natural Frequencies of the Shaft System ................ 3-20
Changing Control Gains and Their Impacts on
the Oscillation Frequency of the System ................. 3-22
Performance Comparison Between Three-Phase and
Positive-Sequence Inverter Models .............................. 3-25
Section 4: Balancing and Market Operations
of an All Inverter System .................... 4-1
System Operation with 100% VER During Some
Periods of a Week ..................................................... 4-2
Test System and Data Used .................................... 4-2
Results for Case with No Reserves .......................... 4-5
Selection of Curtailment Resources .......................... 4-9
Electricity Price Behavior ...................................... 4-11
Effects of Enabling Technologies ........................... 4-16
Determination and Impact of Reserve
Requirements ...................................................... 4-19
Conceptual Discussion of Electric Power Systems
with 100% VER and Without Dispatchable Thermal
Resources ................................................................ 4-25
Change of SCUC and SCED Models .................... 4-25
Change of Reserve Determination Method ............. 4-26
Electricity Market Design Evolution ........................ 4-27
Section 5: Summary and Future Work ................ 5-1
Section 6: References .......................................... 6-1
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Appendix A: Test Case and Scenarios for
Chapter 4 ........................................... A-1
Test System Description ............................................... A-1
Test Scenarios Description ........................................... A-1
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List of Figures
Figure 1-1 Operating paradigm evolution of power
system with inverter based resources ............................ 1-1
Figure 2-1 Definition and physical links of electrical
frequency in a conventional system .............................. 2-1
Figure 2-2 Definition and physical links of electrical
frequency in an all inverter system................................ 2-2
Figure 2-3 System frequency response for a conventional
system and for an all inverter system with different
types of inverter controls ............................................. 2-3
Figure 2-4 Controlled grid forming inverter positive
sequence model schematic .......................................... 2-5
Figure 2-5 Frequency and angle droop schematic in grid
supporting inverter ..................................................... 2-6
Figure 2-6 Comparison of change in mean system
frequency with and without a grid forming inverter ........ 2-6
Figure 2-7 Voltage magnitude in the system with and
without a grid forming inverter..................................... 2-7
Figure 2-8 Mean system frequency for the stressed
system ...................................................................... 2-8
Figure 2-9 Bus voltage magnitude for the stressed system ..... 2-8
Figure 2-10 Mean system frequency for the stressed
system with generator curtailment and load shedding ... 2-10
Figure 2-11 Mean system frequency with varying
location, number & size of grid forming inverter .......... 2-11
Figure 2-12 Change in power output in Areas 2, 5 & 8
for a 500kV line trip in Area 5 .................................. 2-12
Figure 2-13 Modularized control structure with voltage
source interface ....................................................... 2-13
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Figure 2-14 Modularized control structure with current
source interface ....................................................... 2-13
Figure 2-15 User defined active power controller
structure .................................................................. 2-14
Figure 2-16 Average electrical frequency across the
entire system for two generation trip events ................. 2-16
Figure 2-17 Average frequency in each area in Case 1
for two generation trip event ..................................... 2-17
Figure 2-18 Average frequency in each area in Case 2
for two generation trip event ..................................... 2-18
Figure 2-19 System electrical frequency in the immediate
aftermath of two generation trip event ........................ 2-18
Figure 2-20 Geographic view of the test system ................ 2-20
Figure 2-21 Total active power from all inverter
resources in Area 5, for a two generation trip ............. 2-22
Figure 2-22 Total active power from all inverters
resources in Area 5, when controlled as a current
source and voltage source, for two generation trip ....... 2-23
Figure 2-23 System average electrical frequency for
simultaneous trip of both generators ........................... 2-25
Figure 2-24 Total active power in area 5 and 8 for
simultaneous trip of both generators ........................... 2-25
Figure 2-25 Minimum voltage across the system for
simultaneous trip of both generation ........................... 2-27
Figure 2-26 Total active power in areas 5 and 2 for the
simultaneous trip of both generation ........................... 2-27
Figure 2-27 Minimum voltage across the system for a
change in headroom ................................................ 2-28
Figure 2-28 Total active power in areas 5 and 2 with
the inclusion of tie line deviation control signal ............ 2-29
Figure 2-29 Change in power output in areas 5 and 2
to a change in system operator command ................... 2-31
Figure 2-30 Total power output from areas 5 and 2 for
a change in active and reactive power load, along
with change in power reference................................. 2-32
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Figure 2-31 Total power output from areas 5 and 2 for
a change in only active power load, along with
change in power reference ....................................... 2-33
Figure 2-32 Minimum voltage in the system for a line
fault on an internal area line followed by outage of
the line ................................................................... 2-34
Figure 2-33 Reactive power output of a inverter located
close to the fault ....................................................... 2-35
Figure 2-34 Minimum voltage in the system for a line
fault on a tie line followed by outage of the line .......... 2-36
Figure 2-35 Minimum voltage in the system for a line
fault on a tie line followed by outage of the line, with
few voltage source inverters ...................................... 2-36
Figure 3-1 Generic unit i interfaced to the power system. ..... 3-2
Figure 3-2 Overall structure of the proposed controller. ........ 3-2
Figure 3-3 Proposed voltage magnitude controller and
current limiter............................................................. 3-2
Figure 3-4 Proposed real power controller. ......................... 3-3
Figure 3-5 A sample two-bus system. ................................. 3-4
Figure 3-6 Vector diagrams of the two-bus system in
operating conditions (a) grid-forming unit is large
(see text for definition); (b) grid-forming unit is
limited; and (c) grid-forming unit is limited and
brings δgft to zero...................................................... 3-5
Figure 3-7 (a) proposed angle droop; (b) conventional
frequency droop. ....................................................... 3-6
Figure 3-8 Proposed real power sharing algorithm; (a)
grid-forming unit; and (b) grid-supporting units. ............. 3-7
Figure 3-9 Vector diagrams of the generation units in the
steady state when the grid-forming unit is (a) large
(see text for definition); and (b) limited.......................... 3-8
Figure 3-10 Study system. ................................................ 3-9
Figure 3-11 Measurements as (a) Pgs, 3* changes from
85 to 120 MW at t=0.3 s; (b) vgs, 1* changes from
1.026 to 1.040 pu at t=1.3 s. .................................. 3-10
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Figure 3-12 Generation units measurements for the
system with a (a) large (compared with load
demand) grid-forming unit; (b) small grid-forming
unit. In both systems, the load at bus 6 increases by
15 MW at t=1 s and the load at bus 5 increases by
80 MW at t=3 s. ..................................................... 3-11
Figure 3-13 Measurements of buses 1-3 and machine
loads as IM1 changes from no-load to full-load at
t=1 s and IM2 changes from no-load to full-load at
t=3 s....................................................................... 3-12
Figure 3-14 Measurements at buses 1—3 when Pgf, max
decreases from 192 MW to 120 MW at t=2 s. ........... 3-13
Figure 3-15 Measurements at buses 1—3 when a fault
occurs at t=1.0 s and clears after 100 ms; (a) with
the current limiter; (b) without. ................................... 3-14
Figure 3-16 Modified IEEE/WSCC 9-bus system. .............. 3-15
Figure 3-17 Performance of the controller when the SG
is connected to the system. ........................................ 3-16
Figure 3-18 Performance of the controllers when the
load at bus 6 increases by 20 MW at t=2 s and the
load at bus 5 increases by 70 MW at t=4 s. ............... 3-17
Figure 3-19 Performance of the controllers when a threephase bolted fault occurs at t=1 s at the middle of
the transmission line between bus 8 and bus 9. ........... 3-18
Figure 3-20 Performance of the controllers in a case of
changing P*gs,1 and P*gs,3 ........................................... 3-19
Figure 3-21 Structure of a typical lumped –mass system
model [3-1] ............................................................. 3-20
Figure 3-22 Real power of the system components and
zoom-ins. (a) the real power of three inverters and
the SG (b) the oscillation frequency of the real power
of GS unit (c) the oscillation frequency of the real
power of the GF unit (d) the oscillation frequency of
the real power SG.................................................... 3-24
Figure 3-23 From top to bottom: Real powers of
generation units, bus voltages of generation units,
and system frequency measured at the buses of
generation units in (a) PSPS method and (b) the
proposed method. .................................................... 3-25
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Figure 4-1 Comparison of VG and load in case 1 and
case 2 as the input data in DA .................................... 4-4
Figure 4-2 Comparison of VG and load in case 1 and
case 2 as the input data in RT...................................... 4-5
Figure 4-3 Real-time VER penetration percentages for
different scenarios ...................................................... 4-6
Figure 4-4 Real-time thermal energy percentages for
different scenarios ...................................................... 4-7
Figure 4-5 Comparing the load and VER production in
real-time for one day ................................................ 4-10
Figure 4-6 Curtailment for wind resources in one day ........ 4-11
Figure 4-7 Curtailment for PV resources in one day ........... 4-11
Figure 4-8 DA LMP in one-week period in the system ......... 4-14
Figure 4-9 RT LMP in one-week period for case 4 .............. 4-15
Figure 4-10 Comparing LMPs with and without energy
storage resources ..................................................... 4-18
Figure 4-11 A comparison of hourly aggregated
operation costs in RT for one week ............................. 4-18
Figure 4-12 A comparison of the renewable energy
percentage with and without operating reserves for
case 4 .................................................................... 4-21
Figure 4-13 Comparison of the original case with the
new case that allows renewables to provide reserves ... 4-23
Figure A-1 NREL Reliability Test System ............................. A-1
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List of Tables
Table 2-1 Number, location and size of grid forming
inverter per simulation .............................................. 2-10
Table 2-2 Rate of change of frequency for each case ........ 2-19
Table 2-3 Generators with rate of change of frequency
greater than 0.15 Hz/s in Case 1 ............................. 2-19
Table 2-4 Rate of change of frequency of the 16
synchronous machines in Case 2 and Case 4............... 2-21
Table 2-5 Rate of change of frequency of the 16
synchronous machines for simultaneous two
generation trip ......................................................... 2-24
Table 2-6 Total energy supplied in each case for
simultaneous trip of both generators ........................... 2-26
Table 3-1 Parameters of the Controllers .............................. 3-9
Table 3-2 Inertia constants and torsional stiffness
coefficients of rotor system ........................................ 3-21
Table 3-3 Oscillation frequencies of an inverterdominated power system .......................................... 3-22
Table 4-1 Generation Capacity (MW) in Each Case
(Peak load: 8192 MW) .............................................. 4-3
Table 4-2 Load violation and renewable energy
curtailment analysis .................................................... 4-7
Table 4-3 Existence of intervals with zero system price
(marginal cost) but non-zero costs .............................. 4-13
Table 4-4 Cost and Revenue for case 4 (two-settlement
pricing mechanism was applied while calculating
the revenue) ............................................................ 4-16
Table 4-5 Comparison of solutions for the system with
and without storage.................................................. 4-17
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Table 4-6 Summary of simulation results with four types
of reserves............................................................... 4-22
Table 4-7 Summary of simulation results for case 4 with
and without VER providing reserves ........................... 4-24
Table A-1 Generation Capacity (MW) in Each Case
(Peak load: 8192 MW) .............................................. A-2
Table A-2 Average percentages of Generation in One
Week ....................................................................... A-2
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Section 1: Introduction
The presence of inverter based resources (IBR) in the bulk power system has
been steadily increasing over the past few years. While IBR may include
emerging technologies such as battery technology, the majority of the expected
IBR include variable energy resources (VER), such as wind plants and solar
photovoltaic plants. This trend has in part been supported by government
subsidies and renewable energy mandates directed towards a goal of covering a
certain percentage of energy use from renewable energy sources. This influx of
IBR/VER resources is expected to continue to increase in the United States [1-1]
and around the world, and coupled with the scheduled retirement of
conventional generating plants, is transforming the behavior of the bulk power
system. Note that not all new renewable resources need to be IBR (e.g. hydro,
geothermal, and biomass are typically synchronously connected and
dispatchable), but the majority of the new resources are expected to be wind and
solar PV.
Projecting this scenario few years into the future, it is very likely that system
operators would have to deal with an all inverter based generation and
transmission network, completely isolated from other transmission networks [12], at least for certain periods of a year. The energy source behind the inverter,
being primarily a renewable energy source, is bound to be variable and uncertain.
In such a scenario, maintaining the reliability and economic efficiency of the bulk
power system would require novel, complex planning and operation paradigms.
Figure 1-1
Operating paradigm evolution of power system with inverter based resources
This work investigates characteristics of a transmission system with all inverter
based generation. Both the dynamic behavior and stability performance, as well
as steady-state operation and balancing issues related to integrating these
resources onto the bulk power grid are addressed.
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The report is structured as follows. Chapter 2 first discusses the definition of
frequency in an 100% IBR system, and introduces the constant frequency
operational paradigm. Inverter models developed in positive sequence simulation
platforms are used to evaluate the dynamic performance and stability of such a
grid. Realizing that a 100% IBR operation may occur only temporarily (for a few
hours/days), the proposed inverter controls are also evaluated under operational
conditions with a small portion of generation provided by conventional rotating
generators. Chapter 3 focuses on detailed EMT modeling of the proposed
inverter controls. Chapter 4 addresses steady-state and balancing operation of a
system with periods of 100% IBR/VER, applying a state-of-the-art unit
commitment and economic dispatch framework. In addition, it discusses new
features of market pricing under 100% IBR operation. Chapter 5 summarizes the
report and discusses future work.
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Section 2: Inverter Modeling and Constant
Frequency Operation of an All
Inverter System
Background
In a system with conventional synchronous machines, due to Newton’s laws of
physics, electrical frequency has a physical link with the speed of the rotating
machines and hence the mismatch between generation and load, as shown in
Figure 2-1. However, with IBR, the source of energy is either stationary (e.g.
solar PV and battery) or electrically isolated from the network by the inverter
(e.g. Type 4 wind turbine generator). A change in the electrical frequency of the
power network (due to any system event), would thus be decoupled from the
source, as shown in Figure 2-2. In a 100% IBR system, the notion of frequency is
only the electrical frequency (rate of change of bus voltage angle). Thus, a change
in the injection of current from the inverter sources could change the angles
across the system and thus change the electrical frequency.
Figure 2-1
Definition and physical links of electrical frequency in a conventional system
 2-1 
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Figure 2-2
Definition and physical links of electrical frequency in an all inverter system
Presently, the majority of the IBR sources are primarily controlled in a grid
parallel mode. In this mode, the power output of the inverter does not change
with respect to changes in system conditions, and the sources (solar or wind)
operate according to their maximum power point tracking algorithm. A second
mode of control is known as a grid supporting mode. In this scenario, the power
output of the inverters (possibly both active and reactive) can change upon a
change in grid conditions. Both of these modes are typically collectively referred
to as grid following modes as the inverters require the presence of a grid to
operate. A phase locked loop (PLL) is used to track the voltage & frequency of
the grid at the point of connection. A third operating mode known as grid
forming mode has recently been discussed in microgrid research literature [2-1,
2-2, 2-3]. In this mode, the inverter is controlled as a voltage source (as opposed
to the current source representation in the other two operating modes) and is
responsible for the establishment and maintenance of the grid voltage and
frequency. A system with no synchronous machines would thus require the
presence of grid forming inverters to act as voltage sources to set the system
frequency and voltage which can be tracked by other inverters in the system.
Constant Frequency Operational Paradigm
Presently, multiple criteria exist to ensure that each Balancing Area (BA) [2-4, 25, 2-6] in the system would contribute to the maintenance of system frequency.
However, these criteria have been developed on the basis of the power system
operating upon the principles of conventional synchronous machines. With the
conventional methods of maintaining system frequency well understood, it is
important to understand the impact that grid forming inverters might have in
maintenance of system frequency. In a conventional system, inertial response
occurs in the first few seconds after the disturbance. Following this, primary
frequency response is designed to stabilize the recovery of frequency to an off
nominal value in a duration of around one minute. Slower acting secondary
frequency response then restores the frequency back to nominal in a duration of
around five to ten minutes. With the presence of fast acting grid supporting
inverters, the frequency decline can be arrested faster resulting in a higher nadir
and thus subsequently, faster recovery of frequency to nominal value. However, in
an all inverter system, network electrical frequency across large interconnections
could possibly be restored back to nominal value within seconds. This operational
paradigm is referred to as constant frequency operation. In this work, by bringing
 2-2 
0
about the operation of the system at constant frequency, it is hoped that new
light will be shed on the importance (or unimportance) of frequency. Note that,
when stating the operation as constant frequency, it is understood that there will
be transients in the electrical frequency, however, the value of the electrical
frequency would come back to the nominal value within a few seconds after the
initiation of the transient. An illustrative diagram of this operational behavior is
shown in Figure 2-3.
Figure 2-3
System frequency response for a conventional system and for an all inverter system
with different types of inverter controls
In an all inverter system, power sharing upon a disturbance and frequency control
will depend entirely on the control schemes of the inverters. Presently, inverter
based sources in most balancing areas operate in a fixed non-dispatchable mode.
This can lead to a depletion in the available frequency response. Under constant
frequency operation, legacy frequency droop is not applicable to achieve power
sharing among IBRs. In addition, the traditional mechanisms and concepts of
system stability that rely on rotating machines’ physical inertia, do not apply to
systems with 100% of inverter interfaced generation. Wind generation allows for
non-synchronous operation while solar PV is completely free of rotating parts,
and since these devices are connected to the rest of the grid through power
electronics, there is no physical inertia. Upon a disturbance, the stability of the
system will be characterized by the capability of the inverter control schemes to
ride-through the fault and restore generation/load balance. Thus, system stability
will mainly depend on the controls and physical limitations of the interface
inverters.
Grid Forming Inverter Positive Sequence Modeling
Inverter interfaced renewable energy models presently available in positive
sequence simulation software are representative examples of either grid
supporting voltage source/current source models [2-7, 2-8] or grid paralleling
 2-3 
0
current source models [2-8]. In this work, a positive sequence model for a grid
forming inverter is presented. In terms of modeling and implementation, a grid
forming inverter in positive sequence is simply a controlled voltage source whose
terminal voltage is maintained at a constant value. As the existing literature and
development of a grid forming inverter model for the BPS is still in its infancy, it
must be emphasized that the inverter modeling is simplified under the
constraints of a positive sequence modeling platform. However, due to the
modeling simplifications inherent to the positive sequence modeling platform, a
three-phase point on wave model is also developed and compared with the
positive sequence model in Chapter 3. The positive sequence model is thus
considered sufficiently accurate to accomplish the purpose of this work, which is
to understand the viability and operational implications/limitations of operating
the BPS at constant frequency. The inverter models that have been developed are
used to study the operation of systems in which all the generation resources are
interfaced to the grid though a inverter.
Voltage & Current Controlled Grid Forming Inverter
In this inverter model, the current output of the inverter is controlled to ensure
that there is power sharing between the various sources in the system.
Additionally, a current limit can also be introduced to ensure that the current
output is within expected operational levels. As the frequency of the system is
constant, conventional frequency droop schemes would not allow for post
disturbance steady state sharing of power amongst the various sources in the
system. Thus, an angle droop scheme has been adopted instead. The inverter
model has a PLL to track itself and change its phase angle δ in order to change
its power output. The block diagram of the control scheme is shown in Figure 24. The individual equations describing the blocks in the schematics have been
intentionally omitted in order to reinforce the focus of this section on the
applicability and reliability impact of a constant frequency bulk power system.
 2-4 
0
Figure 2-4
Controlled grid forming inverter positive sequence model schematic
Constant Frequency Operation - Demonstrating Results - 433Machine 2000-Bus System
In this section, the constant frequency operation is studied. To test the
implementation of the inverter model and to understand the dynamics of a large
system, the 2000 bus synthetic Texas system [2-9, 2-10] was used. This system
has 433 in-service energy sources with a total generation of 69 GW, a total load
of 67 GW and 19 Gvar. The load in the entire system is represented as constant
impedance for the transient time domain simulations.
Case 1: Grid Forming Inverter Operation
In this case, one source out of the 433 is represented by the controlled grid
forming inverter model, while the remaining 432 sources are represented by the
grid supporting inverter model in [2-11]. The performance is compared against
the scenario wherein all generation sources are represented by the grid supporting
inverter model. With the presence of the grid forming inverter, a combination of
frequency and angle droop as shown in Figure 2-5 was used in the grid
supporting inverter model, while only frequency droop control was used in the
scenario wherein all sources were grid supporting inverters.
 2-5 
0
Figure 2-5
Frequency and angle droop schematic in grid supporting inverter
In the grid forming inverter model, only angle droop is used. The values of the
controller gains used in the grid forming model were 𝐾𝐾𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 =20, 𝐾𝐾𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 =100,
𝐾𝐾𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 =10, 𝐾𝐾𝛿𝛿 𝑒𝑒𝑒𝑒𝑒𝑒 =0.1, 𝐾𝐾𝑝𝑝𝑝𝑝 =1.0, 𝐾𝐾𝑖𝑖𝑖𝑖 =60.0. The angle droop in the grid supporting
model has the same control gain values with the additional frequency droop (𝑅𝑅𝑝𝑝 )
of 5% on the inverter MVA base. At t = 5s, a generation outage of 2569 MW is
simulated. Figure 2-6 shows the change in system mean frequency for both
scenarios. The mean frequency was calculated by calculating the average of the
frequency from each of the 8 areas. The frequency in each area is obtained as the
rate of change of bus angle at a random 230 kV bus.
Figure 2-6
Comparison of change in mean system frequency with and without a grid forming
inverter
 2-6 
0
It can be seen that even in a large system, with just one grid forming inverter, the
system frequency can be maintained at the nominal value. The grid forming
inverter is however representative of a 1625 MVA generation source. The nadir
of the frequency in both scenarios is around the same value of around 59.75 Hz.
The voltage magnitude at a 230 kV bus in these 8 areas is shown in Figure 2-7.
Figure 2-7
Voltage magnitude in the system with and without a grid forming inverter
In the legend, ‘grdfrm’ corresponds to the scenario with the presence of the grid
forming inverter while ‘nogrdfrm’ corresponds to the scenario with the absence of
the grid forming inverter. It can be seen that transiently, there is minimal
difference in the system voltage between the two scenarios.
From the above, it can be concluded that for normal operation of the system, there
appears to be no reliability risk at operating an all inverter system at constant
frequency. This reliable operating condition is however contingent upon at least
three pre-existing conditions: a) adequate availability of active power reserves, b)
optimally tuned control parameters, and c) sufficient current margin in the inverter.
Additionally, the sharing of power between the areas is in accordance with the
electrical distance between the areas. Thus, the inverters in the disturbance area
tend to respond by a larger amount as compared to the inverters in the other
areas. Such a response can be considered similar to the combinatorial response of
conventional primary and secondary frequency response in which the frequency is
brought back to the nominal value by the generators in the disturbance area.
However, with the grid forming inverter, it is not pure secondary response as the
inverters in other areas still contribute to some extent.
Case 2: Under Frequency Trip
In a conventional system, the lack of availability of adequate reserves can cause
under frequency load shed (UFLS) relays to activate. This action however takes
place in the time frame of conventional primary frequency response. To
 2-7 
0
investigate the effect of constrained active power reserves in the all inverter
system with the presence of a grid forming inverter model, the system is stressed
by preventing grid supporting inverters in an entire area from responding to the
generation outage. Figure 2-8 compares the system mean frequency for the
following conditions:

Inverters in all areas respond (Case A),

Inverters only in areas 7 and 8 respond (Case B), and

Inverters only in area 8 respond (Case C),
while Figure 2-9 compares the terminal voltage magnitude at these 8 buses.
Figure 2-8
Mean system frequency for the stressed system
Figure 2-9
Bus voltage magnitude for the stressed system
 2-8 
0
As expected, it can be seen that as the deployable active power reserve decreases,
the frequency response of the system deteriorates with Case C diverging. An
additional effect of this is that the inverters hit their current limits in an effort to
provide more reactive power to prevent the deterioration of the terminal voltage.
The limited injection of current however causes the bus voltage angle to change
rapidly as the solution of the network equation tries to obtain a voltage level
suitable for the power level at that point in time. Thus, this large change in
frequency is an artifact of the changing rate of change of bus voltage angle, which
is in turn caused by limited injection of current into the network by the sources.
It must however not be confused with the ‘out-of-sync’ phenomena observed in a
conventional system wherein synchronous machine rotors fall out of
synchronism.
In order to prevent a system collapse, one can note that just like in a conventional
system, opportunities to apply UFLS are also available in a constant frequency
operation all inverter system. Additionally, in an all inverter system, it is highly
probable that the majority of the resources would be renewable energy resources.
In such a scenario, with many renewable resources operating at their maximum
power point with zero deployable active power reserve, curtailment of these
resources under transient over frequency conditions could also be a feature that
could be exploited.
To allow generation curtailment, the grid supporting inverters were only allowed
to respond to the generation outage if 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐 < 𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟 (Figure 2-5). To illustrate
this, using the conditions of Case C, Figure 2-10 compares the system mean
frequency for the following conditions:
1. Inverters in Areas 1-7 can transiently curtail their output for over frequency
(Case Ca),
2. In addition to curtailment, active power load throughout the system is
reduced by 5%, 1s after the disturbance (Case Cb), and
3. In addition to curtailment, active power load throughout the system is
reduced by 5%, 0.5s after the disturbance (Case Cc).
 2-9 
0
Figure 2-10
Mean system frequency for the stressed system with generator curtailment and load
shedding
Although the applied methodology of reduction of load is not in strict
accordance with the methodology by which UFLS is applied in a conventional
power system, the analysis serves to illustrate the possibility and use of applying
UFLS in the all inverter system to maintain reliable operation at constant
frequency. Additionally, it is entirely possible that with optimal control gains, the
response of Case Ca can be damped to obtain a reliable system operation with no
load reduction.
Case 3: Variation in Size, Location and Number of Grid
Forming Inverters
In the previous two cases, a single large grid forming inverter was placed in Area
7 of the system. To observe the impact of location, size & number of grid
forming inverters, simulations were run as per the setup in Table 2-1. In the first
8 simulations, the source with the lowest MVA in the area was chosen as the grid
forming inverter.
Table 2-1
Number, location and size of grid forming inverter per simulation
Location
MVA
Area 1
12 MVA
Area 2
12 MVA
Area 3
18 MVA
Area 4
11.5 MVA
Area 5
2.0 MVA
Area 6
1.8 MVA
 2-10 
0
Table 2-1 (continued)
Number, location and size of grid forming inverter per simulation
Location
MVA
Area 7
8.2 MVA
Area 8
52.8 MVA
Area 7 – Large Inverter
1625 MVA
2 Small Inverters
Area 5 (2.0 MVA), Area 6 (1.8 MVA)
2 Large Inverters
Area 7 (1625 MVA), Area 8 (1077 MVA)
3 Large Inverters
Area 5 (1209 MVA), Area 7 (1625 MVA),
Area 8 (1077 MVA)
For the same generation outage event, Figure 2-11 shows the system mean
frequency. It can be noticed that impact of the size of the grid forming inverter is
more significant than the impact of the location. The nadir of the mean
frequency is at a higher value with two large grid forming inverters present.
Figure 2-11
Mean system frequency with varying location, number & size of grid forming
inverter
Case 4: Topology Change
While the suggested angle droop method of sharing of power among sources
might be effective for a load/generation event, it could also result in a new
operating point due a change in the topology of the system. Although this
change in operating point might not be large, it could still have implications on
market settlement and economics of operation of the system. As an example, at
t=5s, a 500 kV line in Area 5 carrying ≈ 890 MW/73 MVAr is tripped. Figure 212 shows the change in total power output of Areas 2, 5 & 8. With the presence
of the grid forming inverter, angle droop control was used and without the grid
forming inverter, conventional frequency droop control is used.
 2-11 
0
Figure 2-12
Change in power output in Areas 2, 5 & 8 for a 500kV line trip in Area 5
It can be seen that there is a change in power output in the individual areas to
support the change in losses/load due to change in voltage magnitude and angle.
Inverter Based Resources Dominated Grid
The possibility of the bulk power system being all inverter could be questioned. It
is true that the current power system is far from an all inverter operation, but there
are possibilities where certain isolated power systems may temporarily operate in an
all-inverter mode. Examples are the power grid of the Electric Reliability Council
of Texas (ERCOT) in North America, or island systems such as the power grid of
Ireland. Both these systems presently have a lot of existing wind generation with
more slated to be in the interconnection queue. Ireland is presently curtailing wind
generation to maximum of 65% due to frequency stability concerns.
In a system with a small percentage of synchronous machines still online, the
juxtaposition of fast inverter controls along with slower synchronous machine
control can introduce reliability concerns. In this section, the constant frequency
inverter control scheme described before is used to address the following
questions in an IBR dominated grid:
1. For a large generation loss event, can power be shared in the short term
among all participating inverter resources?
2. Over the long term, can the flows on the tie line interfaces between areas be
restored to the pre-disturbance value?
3. If there are few synchronous machines remaining on the system, will the fast
constant frequency control of the inverters have an adverse impact on the
machines?
4. If the inverter resources receive a schedule change command from the system
operator, can the control system track the change in schedule, and if it can,
how will it behave if a disturbance occurs during the schedule change?
5. If there are severe N-1 line outages, then can the control scheme ride through?
 2-12 
0
Modularized Constant Frequency Inverter Positive Sequence
Models
In this section, a modularized modeling approach of the constant frequency
control scheme is discussed. The modularized setup facilitates experiments with
different control structures, while also making use of existing inverter models. A
broad overview of the modularized setup is shown in Figure 2-13 and Figure 214 wherein a comparison can be made with existing current source inverter
interface model (REGC_A) and new voltage source inverter interface models,
while still using the same outer loop controls.
Figure 2-13
Modularized control structure with voltage source interface
Figure 2-14
Modularized control structure with current source interface
 2-13 
0
The user defined active power controller model is as shown in Figure 2-15. All
quantities in this controller are in per unit on a MW value base which can be
lower than the MVA rating of the inverter.
Figure 2-15
User defined active power controller structure
In order to assess the ability of the control scheme to control the power transfer
between balancing areas, the ‘Tie-line deviation’ control loop was incorporated
′
on a system level, and each inverter resource receives a signal (𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎
) to mimic the
operation of a simple automatic generation control loop. One ‘Tie-line deviation’
block is placed in each area of the system, and its internal algorithm can be
generally described as:
1. Once every 2 seconds evaluate the total tie line power mismatch of the area
2. Compare the mismatch with a tolerance level,
-
If the mismatch is below the tolerance level – do nothing,
-
Else, integrate the difference through a PI controller to obtain a value of
power that has to be raised/lowered in the area.
3. Once every 3 seconds, and through a further first order time constant of 1.0s,
′
to the active power
the value of power evaluated in step 2b is sent as 𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎
controller of every inverter resource in the area.
The user-defined voltage source inverter model used in this study is the detailed
inverter model that was developed in 2018 under the EPRI P173.03 project.
This detailed inverter model is capable of representing the faster phase locked
loop and inner current control dynamics that are of crucial importance while
analyzing the behavior of inverter interfaced generation in low short circuit areas.
Details regarding this model can be obtained in [2-12]. The electrical controller
model REEC_A has been used in local voltage control mode, with Q priority,
and no momentary cessation.
It must be mentioned here that in both modular inverter interface
representations, the dynamics of the dc bus and the source behind the dc bus
 2-14 
0
have been ignored. Additionally, it has been assumed that the dc bus is stiff
and/or the dynamics of the controller controlling the dc bus voltage is fast
enough to cater to the demands of the grid side inverter controllers.
The next section discusses results from implementation of both modular inverter
structures on a 2000 bus Synthetic Texas system.
IBR Dominated System - Demonstrating Results - 433-Machine
2000-Bus System
The same 2000 bus synthetic Texas system is used in this section. The positive
sequence simulations were carried out in GE- PSLF™. Five cases were setup up
as defined below:
1. Case 1: All 433 energy sources were modeled as conventional synchronous
machines with a round rotor generator model (GENROU), a simple
governor model (TGOV1) and a simple static excitation system model
(SEXS)
2. Case 2: 417 energy sources were modeled as inverter interfaced generation
with the voltage source inverter interface model, and the constant frequency
control mode enabled. The remaining 16 energy sources, have an MVA
greater than 500 MVA, and are represented as conventional synchronous
machines, with the same type of models as in Case 1.
3. Case 3: 417 energy sources were modeled as inverter interfaced generation
with the existing current source inverter interface model, but with the
constant frequency control mode enabled. The remaining 16 energy sources,
had an MVA greater than 500 MVA, and were represented as conventional
synchronous machines, with the same type of models as in Case 1.
4. Case 4: 417 energy sources were modeled as inverter interfaced generation
with the voltage source inverter interface model, but with the constant
frequency control model disabled. Only frequency droop control was enabled.
The remaining 16 energy sources, had an MVA greater than 500 MVA, and
were represented as conventional synchronous machines, with the same type
of models as in Case 1.
5. Case 5: 417 energy sources were modeled as inverter interfaced generation
with the existing current source inverter interface model, but with the
constant frequency control model disabled. Only frequency droop control
was enabled. The remaining 16 energy sources, had an MVA greater than
500 MVA, and were represented as conventional synchronous machines,
with the same type of models as in Case 1.
The synchronous machines in Cases 2 – 5 represent approximately 15% of the
capacity (and approximately 11% of MW) of all in service sources. Additionally,
the loads in the system are represented according to the value of active power as:
1. 0.0 MW < 𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ≤ 20.0 MW – Constant Impedance
2. 20.0 MW < 𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 < 60.0 MW – Three phase induction motor (H = 0.5s,
quadratic P vs 𝜔𝜔)
 2-15 
0
3. 𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ≥ 60.0 MW – Composite load model with NERC default data
Below, the various scenarios studied are discussed.
Scenario 1: System Operation for a Generation Loss Event
The two largest generators in this system have approximately 1.2 GW of
generation each. To evaluate the behavior of the system, both these generators
were tripped in a sequential manner at t = 10s and 25s. Since in all five cases
synchronous machines are still present in the system, the electrical frequency of
the system still holds value.
The average electrical frequency across the entire system (average of electrical
frequency evaluated at every bus in the system) is shown in Figure 2-16.
Figure 2-16
Average electrical frequency across the entire system for two generation trip events
It can be seen that with all synchronous machines, the frequency response graph
follows the well-known behavior. In the actual Texas power system, the set point
for under frequency load shedding is 59.3 Hz and has remained at that value
since 2012 [2-13]. Additionally, the nadir of frequency (around 59.7 Hz) is also
approximately equivalent to the nadir observed in studies shown in [2-13] for a
generation trip of this magnitude.
For Case 4 and Case 5, where the inverters were only enabled with frequency
droop response (with the same value of droop gain and headroom as the
corresponding synchronous machine model used in Case 1), the final settling
value of the frequency is the same as in the all synchronous case. These two cases
are provided as reference intermediate cases to highlight the additional
capabilities that can be extracted from inverters. It should be noted that inverters
can have a smaller droop percentage (say 2% droop instead of 6%), which would
result in a higher settling off-nominal frequency, but sensitivity to droop gain is
 2-16 
0
not the objective of this work. This kind of sensitivity analysis is discussed in
detail in [2-14].
In Case 2 and Case 3, where the inverters were also enabled with the constant
frequency control scheme, it can be seen that the electrical frequency is
satisfactorily brought back to the nominal value of 60.0 Hz, within few seconds
of the disturbance. Additionally, even with the presence of the large synchronous
machines, the system frequency does not show any major oscillations that could
be a cause of concern. This is however majorly influenced by the value of the
control gains used in both the inverter and synchronous machine controls.
However, in Case 1 as expected, there is a presence of inter area oscillatory
modes. While these modes are not visible in the system frequency plot, they can
be seen in the plot of each area’s frequency, as shown in Figure 2-17. The
individual area frequencies for Case 2 are shown in Figure 2-18 for the duration
around the first disturbance (i.e. 10s). Due to the fast action of the inverters,
there are minimal inter area oscillations in frequency range that is common in an
all synchronous machine system. This is despite the presence of the fast phase
locked loop and inner current control loop controls in the inverter model. An
interesting observation from Figure 2-18 is that the area where most of the 16
synchronous machines are present is readily observable as the frequency in that
area has a slower rate of change of frequency.
Figure 2-17
Average frequency in each area in Case 1 for two generation trip event
 2-17 
0
Figure 2-18
Average frequency in each area in Case 2 for two generation trip event
While the plots with the large presence of inverters show a stable response, in all
four of them, the rate of change of frequency is much steeper than the all
synchronous machine case, while the nadir is higher. The higher nadir is
attributed to the smaller time constants that are present in the frequency control
path of the inverter model, than the time constant in the governor and machine
models. This allows fast injection of energy from the inverters into the power
system. But, with the chosen values of control gains, this injection of energy from
the inverters is not fast enough to prevent a steep rate of change of frequency.
This steep rate of change of frequency could be a cause of concern for the
remaining 16 synchronous machines. In order to observe the rate of change of
frequency better, the plot of the system electrical frequency in the immediate
aftermath of the first disturbance (the few seconds around 10s) is shown in
Figure 2-19.
Figure 2-19
System electrical frequency in the immediate aftermath of two generation trip event
 2-18 
0
The rate of change of frequency is usually evaluated as a moving average over the
period of 500ms. In this scenario, for each case, the rate of change is evaluated
500ms after the disturbance, as tabulated in Table 2-2.
Table 2-2
Rate of change of frequency for each case
Case
Frequency (Hz)
at 10s
Frequency (Hz)
at 10.5s
1
60.0
59.962
2
60.0
59.94
3
60.0
59.94
4
60.0
59.898
5
60.0
59.898
Rate of change (Hz/s)
59.962 − 60.0
= −0.076
0.5
59.94 − 60.0
= −0.12
0.5
59.94 − 60.0
= −0.12
0.5
59.898 − 60.0
= −0. 204
0.5
59.898 − 60.0
= −0. 204
0.5
While it is expected that with large presence of inverters the rate of change of
frequency will be steeper, the rate of change of system electrical frequency only
shows one side of the picture. Even in an all synchronous system, as seen in
Figure 2-17, the rate of change of frequency is different in different areas of the
system, and the electrical distance of a generator to the disturbance location also
plays a role. In Case 1, for the same generation loss event, the rate of change of
frequency at individual generator terminals was evaluated 500ms after the
disturbance, and the generators with absolute value of rate of change greater than
0.15 Hz/s are tabulated in Table 2-3. It is interesting to note that although the
generation loss event was in Area 5, the largest rate of change is observable in the
adjoining areas of 2 and 8.
Table 2-3
Generators with rate of change of frequency greater than 0.15 Hz/s in Case 1
Bus number
Area number
Rate of change
(Hz/s)
2115
2
-0.1525
2117
2
-0.1536
2118
2
-0.1546
2119
2
-0.1502
2120
2
-0.1541
8129
8
-0.1524
8130
8
-0.1560
8131
8
-0.1529
 2-19 
0
Geographically, the 8 areas in the system are approximately spread out as shown
in Figure 2-20, with the white lines denoting weaker portions of the network.
The demarcation of areas is by no means accurate, and it is a very high level
approximation. However, it shows that generators in Area 2 and 8, especially if
they are at the edge of the areas, can easily be electrically close to the event bus in
Area 5.
Figure 2-20
Geographic view of the test system
With the presence of inverters, the rate of change of frequency at the remaining
16 synchronous machines terminals is tabulated in Table 2-4 for Case 2 and
Case4.
 2-20 
0
Table 2-4
Rate of change of frequency of the 16 synchronous machines in Case 2 and Case 4
Bus
number
Area
number
Rate of change
(Hz/s) for Case 2
Rate of change
(Hz/s) for Case 4
7098
7
-0.1624
-0.1994
7099
7
-0.1624
-0.2112
7208
7
-0.1655
-0.2111
7209
7
-0.1648
-0.2109
7335
7
-0.1648
-0.2109
7353
7
-0.1679
-0.2124
7354
7
-0.1665
-0.2118
7355
7
-0.1665
-0.2118
7356
7
-0.1663
-0.2117
7389
7
-0.1593
-0.2102
7400
7
-0.1626
-0.2104
8071
8
-0.1402
-0.2312
8088
8
-0.1358
-0.2211
8129
8
-0.1357
-0.2303
8130
8
-0.1430
-0.2377
8131
8
-0.1356
-0.2301
Only these two cases were considered because, from Figure 2-19 it can be seen
that the difference between the current source and the voltage source
implementation of the inverter interface occurs only in the first 300ms following
the disturbance. At the time of calculation of the rate of the change of frequency,
there is negligible difference between the current source and voltage source
interface.
In Case 2, with the constant frequency operation of the inverters, the rate of
change of frequency at the terminals of the generators in area 7 have increased in
comparison to their rate of change of frequency in an all synchronous machine
setup. However, the rate of change at the terminals of the generators in area 8
have decreased when compared to the corresponding values (Table 2-3) in an all
synchronous machine system. In Case 4, with the inverters operating only on
conventional frequency droop control, the rate of change of frequency at the
generator terminals has increased in comparison to the all synchronous machine
case.
The difference in the rate of change of frequency between Cases 2 and 4 can be
attributed to the contribution from the inverters in the other areas. As an
example, the total active power output from the inverters in Area 5 for Cases 2
and 4 (excluding the two generation sources that were tripped), is shown in
Figure 2-21.
 2-21 
0
Figure 2-21
Total active power from all inverter resources in Area 5, for a two generation trip
In Case 2, due to the constant frequency control, the inverters in Area 5 inject
more energy into the system during the first 500ms. A similar behavior would
occur in Areas 7 and 8 thereby, arresting the frequency decline at the terminals of
the machine. It goes without saying that the injection of this additional energy is
subject to conditions of a stiff dc bus and availability of energy from the source
behind the inverter. Representation of the dynamics of these loops is a topic that
will be pursued in the future.
However, a question then arises is whether this behavior is strictly due to the
voltage source interface of the inverter. An inverter which is controlled as a pure
voltage source (known as grid forming inverters in some literature), is said to
inject energy into the network without delay upon the occurrence of a
disturbance. It has been postulated in literature that this rapid injection of energy
from a voltage source inverter (subject to the availability of energy from the dc
bus/source behind the inverter) can take the place of conventional inertial energy
to help arrest the frequency decline as this rapid injection of energy is not
possible from traditional current source controlled inverters. In order to test this
hypothesis, Figure 2-22 shows the total active power in Area 5 for Cases 2 and 3
(again excluding the two generation sources that were tripped).
 2-22 
0
Figure 2-22
Total active power from all inverters resources in Area 5, when controlled as a
current source and voltage source, for two generation trip
Both Cases 2 and 3 have the constant frequency control mode enabled, but case 2
uses a voltage source interface inverter while case 3 uses the present state of the
art current source interface inverter. The advantage of the voltage source interface
inverter is observable in the near instant after the disturbance. The voltage source
inverters provide more short circuit current than the current source interface.
However, due to the nature of the energy balance, following the rapid injection
of energy at the instant of disturbance, the injection from the voltage source
interface inverter drops, and the action of the control loops become dominant.
The current source interface inverter on the other hand, is unable to contribute
short circuit at the instant of disturbance, and thus, only the action of the control
loops is present. In both schemes, after the first 100ms, the delivery of energy
into the network is roughly the same, and thus, from the perspective of arresting
the frequency decline, it may be possible to continue to use current source
interface inverters. But, it must be stated that this conclusion is only from the
perspective of arresting the frequency decline, given that the rate of change of
frequency is measured as a moving average over 500ms.
In the real Texas power system, to plan for frequency response reserves, a loss of
2750 MW of generation, with a credit of 1209 MW of fast acting load response,
is the benchmark event for analysis [2-13]. These numbers align with the net
generation loss event that has been analyzed in this scenario. It is worthwhile to
check if the same trend of rate of change holds if both the generators were
tripped at the same time in this scenario. Table 2-5 tabulates the rate of change
of frequency at the terminals of the 16 generator buses for all five cases.
 2-23 
0
Table 2-5
Rate of change of frequency of the 16 synchronous machines for simultaneous two
generation trip
Bus
number
Case 1
Case 2
Case 3
Case 4
Case 5
7098
-0.0232
-0.2846
-0.3129
-0.3578
-0.3766
7099
-0.0366
-0.2915
-0.3168
-0.3890
-0.4062
7208
-0.0279
-0.2951
-0.3205
-0.3863
-0.4040
7209
-0.0284
-0.2942
-0.3192
-0.3864
-0.4038
7335
-0.0309
-0.2933
-0.3177
-0.3867
-0.4037
7353
-0.0282
-0.2989
-0.3249
-0.3882
-0.4062
7354
-0.0291
-0.2968
-0.3222
-0.3877
-0.4053
7355
-0.0291
-0.2968
-0.3222
-0.3877
-0.4053
7356
-0.0292
-0.2966
-0.3218
-0.3876
-0.4052
7389
-0.0444
-0.2873
-0.3082
-0.3879
-0.4022
7400
-0.0310
-0.2913
-0.3149
-0.3865
-0.4029
8071
-0.2497
-0.2786
-0.2685
-0.4621
-0.4521
8088
-0.1997
-0.2659
-0.2601
-0.4368
-0.4319
8129
-0.3078
-0.2748
-0.2649
-0.4663
-0.4558
8130
-0.3147
-0.2882
-0.2810
-0.4804
-0.4716
8131
-0.3091
-0.2748
-0.2656
-0.4665
-0.4566
The two areas where the 16 synchronous machines are present (Area 7 and Area
8) have very different electrical distances with the point of disturbance in Area 5.
Area 8 is electrically closer, while Area 7 is electrically farther away. This is
immediately evident from the results of Case 1 where all the machines in Area 7
have a slow response, while the machines in Area 8 move quickly. In comparison,
when the inverters operate in constant frequency control mode (both voltage
source and current source, Cases 2 and 3), the rate of change of frequency for the
machines in Area 8 reduces, while the rate of change increases quite significantly
for the machines in Area 7. However, the increase in Area 7 is only large in
comparison to the corresponding value in the all synchronous machine case while
it is comparable to the values of rate of change of frequencies for the machines in
Area 8. With the inverters in only frequency droop control mode (Cases 4 and
5), the rate of change of frequency is expectedly larger than the constant
frequency control mode as the injection of energy by the inverters is lower in the
frequency droop control mode. The system electrical frequency for this event is
shown in Figure 2-23. The system electrical frequencies for Cases 1, 2 and 3
intersect at around 500ms after the event.
 2-24 
0
Figure 2-23
System average electrical frequency for simultaneous trip of both generators
For all five cases, the total active power in Area 5 (excluding the two generation
sources that tripped) and Area 8 is shown in Figure 2-24.
Figure 2-24
Total active power in area 5 and 8 for simultaneous trip of both generators
In Area 5, immediately upon the occurrence of the disturbance, the large amount
of energy supplied by the synchronous machines in Case 1 is clearly observable.
However, as time advances, the inverters catch up in energy injection. In Area 8,
in Cases 2 – 5 with the large presence of inverters, the 5 remaining machines
(buses 8071, 8088, 8129, 8130 and 8131) constitute approximately 64% (both by
capacity and MW) of entire area’s in service generation. Hence, when the
inverters in Area 5 are slow to begin injection of energy, the machines in Area 8
inject more energy than they did in Case 1.
 2-25 
0
But, the question then is, how much additional/reduced energy is injected in each
case? In order to approximately compute the energy injected, the total active
power curve in Area 5 was integrated over the duration of the simulation using a
composite trapezoidal numerical integration rule, and the results are tabulated in
Table 2-6. In addition to evaluating the energy injected over the entire duration
of the simulation, the energy injected immediately after the disturbance (from
9.99s to 10.50s and from 9.99s to 11.014s) was also approximately calculated.
The energy values in the table are in units of MWs approximated to the nearest
integer.
Table 2-6
Total energy supplied in each case for simultaneous trip of both generators
Time duration
Case 1
Case 2
Case 3
Case 4
Case 5
0s to 30s
316113
322585
322212
317174
317095
9.99s to 10.50s
5540
5439
5413
5355
5338
9.99s to 11.014s
10665
10913
10892
10653
10638
It can be seen that in Area 5, although the synchronous machines in Case 1 inject
a large amount of power immediately upon the occurrence of the disturbance to
arrest the frequency decline, the energy injection in comparison to the energy
injection of the all inverter situations of Cases 2 and 3, is almost similar in the
first 500ms after the disturbance. This is also confirmed from Figure 2-23
wherein the system frequency in Cases 1, 2 and 3 intersect at around 500ms after
the disturbance. The energy evaluation also provides an idea of the additional
MWs of energy required from inverter resources to be operated in the constant
frequency control mode, as opposed to operation in a frequency droop control
mode.
At every time step, the minimum voltage magnitude across the entire system for
this event is shown in Figure 2-25. It can be seen that for all the inverter cases,
the voltage control is stricter. This is due to two primary reasons:
1. In the synchronous machines case, although the machines inject energy in
the first 500ms after the disturbance, the energy injection reduces in the
subsequent couple of seconds as is seen from Figure 2-24. This reduction in
energy injection few seconds after the disturbance would cause the angles to
spread across the system which causes the voltages to reduce. In the cases
with the inverters, although the inverters have a slightly slower rate of
injection of energy, there is no reduction in energy once the energy injection
has begun. This is of course under the assumption that the controllers of the
inverter plants are well tuned. In the first 500ms when there is a slower rate
of energy injection from the inverters, the angles across the systems do spread
faster, and this is observable from the greater rate of change of voltage in that
small time frame.
2. The static excitation system used for the synchronous machines have not
been tuned to optimal values which could otherwise possibly allow faster
voltage control.
 2-26 
0
Figure 2-25
Minimum voltage across the system for simultaneous trip of both generation
With the operation of the constant frequency control established, and the
implications on frequency response discussed, henceforth, Cases 4 and 5 will not
be considered in the discussion. With constant frequency operation, upon the
occurrence of a disturbance (generation or load change), a valid concern is
whether all areas will share the burden of the disturbance (as it presently occurs
nowadays due to frequency droop control). In the constant frequency control
scheme, based upon the proportion of the deviation of the terminal voltage bus
angle from a set reference, the power command of the inverters is changed. With
such a control, it is possible to share the burden of a disturbance among the
various sources in the system. For the two generation trip event, the total active
power in Areas 5 and 2 is shown in Figure 2-26. The sharing of power across the
areas can be inferred from this figure.
Figure 2-26
Total active power in areas 5 and 2 for the simultaneous trip of both generation
 2-27 
0
As the sharing of power is now linked to the deviation of bus voltage angle, the
topology of the electrical network would now play a large role in determining the
areas which are able to share more proportion of the burden.
With a large portion of the fleet being inverter interfaced sources, the
implications of uncertainty in input energy have to also be analyzed. In 2017, a
stochastic based framework was explored to look into the various combinations of
input energy uncertainty that can occur with a large fleet of inverter based
generation, but a small system was used in the study with the inverters on
conventional frequency droop control. In this report, the aim is to study the
impact of the uncertainty on the constant frequency control scheme, when spread
across the large system. In comparison to a scenario where there is sufficient
available headroom, if the available energy headroom on inverters is suddenly
limited, then angles across the system would change faster and by a larger
magnitude, causing inverters which have available headroom to pick up more of
the burden. This happens even in a conventional frequency droop control
scheme. However, due to the fast nature of the controls on the inverter, it is
possible that this fast change in angle can cause a fast voltage reduction in the
system.
For the same two generation trip event, a simulation was carried out for Cases 2
and 3, but with the headroom of the inverters in Areas 2 and 5 reduced by 20%,
one second after the occurrence of the disturbance. Area 2 was chosen in addition
to Area 5 as pre-disturbance, Area 5 imports active power from it. While it could
be rare that there is a sudden decrease in available energy across a vast
geographical area (as is the geographical spread of these two areas), such a
scenario serves as a benchmark test case. Figure 2-27 shows the minimum voltage
magnitude across the system for both cases in comparison to the minimum
voltage magnitude when the headroom is sufficient.
Figure 2-27
Minimum voltage across the system for a change in headroom
 2-28 
0
As the headroom decreases in these areas, the voltage across the system becomes
increasingly oscillatory, and as expected, the magnitude of the sag deepens. In
these scenarios, the inverters were operated in a Q priority mode, wherein, during
the disturbance, priority is given to the injection of reactive current over the
injection of active current.
In the present power system, the deviation in frequency is used as an integral
component in the calculation of area control error (ACE) which drives the
implementation of secondary frequency control. But in the constant frequency
control model implemented here, the frequency deviation is essentially zero
within a few seconds after the disturbance. In such a situation, the research
question that arises is would the tie line deviation error be a sufficient signal for
the implementation of the secondary frequency control?
By enabling the ‘Tie line deviation’ control block, Figure 2-28 shows the total
active power output in Areas 5 and 2 for the two generation trip event. It can be
seen by just using the tie line deviation as a signal, the individual areas are able to
respond to the changes in command to either increase or decrease their power
output resulting in the sources in Area 5 having to increase their power output by
almost the total generation loss, while the sources in Area 2, after having initially
shouldered part of the burden to bring the frequency back to nominal, go back to
their pre-disturbance values.
Figure 2-28
Total active power in areas 5 and 2 with the inclusion of tie line deviation control
signal
 2-29 
0
To conclude this scenario, few take away points are:
1. The constant frequency control mode is able to bring the entire system
electrical frequency back to the nominal value within a few seconds after the
disturbance, even with the presence of synchronous machines.
2. With constant frequency control mode, apart from the first 200-300ms after
a disturbance, there is little difference between the workings of a current
source interface inverter and a voltage source interface inverter.
3. With rate of change of frequency evaluated 500ms after the disturbance,
operation of a majority inverter dominant system, results in no significant
change in the rate of change of frequency at the synchronous machine
terminals that are located electrically close to the point of disturbance.
However, for machines that located electrically farther away, an increase in
the rate of change is observed.
4. Evaluation of the energy injected by the inverters in the few milli-seconds
after the disturbance provides an insight into the capacity planning
requirements for the satisfactory operation of a inverter dominated power
system.
5. The angle droop control mode allows for inverters in all areas to share the
burden of generation – load imbalance.
6. Only tie – line active power deviation could be used successfully as a control
signal for secondary frequency control.
Scenario 2: Change in Power Command from the System
Operator
A crucial portion of the constant frequency control mode is the change in power
command of the inverter in proportion to the deviation of the terminal bus
voltage angle, in reference to a constant value of angle. Few questions that then
arise are,
1. What is the constant value of angle?
2. How is it set?
3. Can it be changed based upon a dispatch setting from the system operator?
In the control scheme developed, the angle reference (𝛿𝛿𝑟𝑟𝑟𝑟𝑟𝑟 in Figure 2-15), is the
angle of the terminal bus voltage of the inverter itself at a previous point in time,
when the system was in steady state. However, in a practical system, it is
impossible to define a pure steady state, as there are always minute load variations
occurring across the system. Thus, to define the value of 𝛿𝛿𝑟𝑟𝑟𝑟𝑟𝑟 with respect to a
practical system, the angle reference variable tracks the angle of the inverter as
long as the frequency deviation is within a tolerance value. Once the frequency
deviation exceeds the tolerance, the value of 𝛿𝛿𝑟𝑟𝑟𝑟𝑟𝑟 is frozen at the value just before
the larger deviation in frequency, and is held frozen at this value, until the
frequency deviation is lower than the tolerance. This operation can be expressed
by following pseudo-code, with the variables in reference to Figure 2-15,
 2-30 
0
𝑖𝑖𝑖𝑖 (|𝑓𝑓 − 1.0| < 𝑑𝑑𝑑𝑑𝑑𝑑) 𝑡𝑡ℎ𝑒𝑒𝑒𝑒 (𝛿𝛿𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑠𝑠2 )
Eq. 2-1
With this expression, the reference angle does not have to be compared with any
other system reference, and thus no wide area communication system is required.
Admittedly, the variable 𝑠𝑠2 is not a true representation of the terminal bus
voltage angle of the inverter, but it is the controller’s interpretation of the
terminal bus voltage angle.
As the angle is not a true representation of the terminal bus voltage angle, there
is a cause of concern whether the control scheme can accept change in power
reference commands from the system operator. In a conventional frequency
droop scheme, the change in power reference commands are implemented by
shifting the 𝑓𝑓 − 𝑃𝑃 droop curve up or down, in parallel to the present set point
droop curve. By shifting the curve, the value of 𝜔𝜔𝑟𝑟𝑟𝑟𝑟𝑟 changes, while keeping the
slope of the curve the same, thereby resulting in a new active power level at
nominal frequency. Additionally, with knowledge of the new active power set
point, and the slope of the droop curve, the new value of 𝜔𝜔𝑟𝑟𝑟𝑟𝑟𝑟 can be easily
calculated. This kind of maneuvering could be quite tedious in the constant
frequency control scheme, as 𝛿𝛿𝑟𝑟𝑟𝑟𝑟𝑟 and 𝑠𝑠2 are in a way internal variables of the
control scheme. However, the same result of change in output power to system
operator command can be achieved by adjusting the value of 𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 in the control
scheme, and then due to the self-angle tracking algorithm, the controller would
reset itself to be ready for the next event that occurs at the new operating point.
The working of this mechanism is illustrated in Figure 2-29 for Cases 2 and 3
wherein the total active power of Areas 5 and 2 are shown for a change in system
operator command. The total active power in Area 5 was commanded to
decreased by 5 MW at each inverter, over a period of 10s, while during the same
time interval, the inverters in Area 2 were commanded to increase their active
power by 5 MW each.
Figure 2-29
Change in power output in areas 5 and 2 to a change in system operator
command
 2-31 
0
For this scenario, the ‘Tie line deviation’ control block was disabled, as the
change in system operator command was issued without consideration of
maintaining tie line flows. Additionally, due to this, the inverters in other areas
also respond by changing their power outputs.
If a disturbance occurs during the ramp change, and also after the change, is the
controller able to handle these situations? For the same change in system
operator command, Figure 2-30 shows the total active power in Areas 5 and 2 for
Cases 2 and 3. However, this time, midway through the ramp change, the entire
static load in the system (both active and reactive power) was increased by 1%,
and after the end of the ramp change, the static load was further increased by 2%.
It can be seen that the constant frequency control is fairly robust and stable to
track system operator commands, and address any sudden disturbance that might
occur during a change, and after a change. The reason for the difference between
Cases 2 and 3 is due to the difference in performance of the voltage source
interface as compared to the current source interface. As the load change is
applied, the voltages across the system change differently whether the sources are
voltage sources or current sources as the network impedance is different in both
cases, with the voltage source interface introducing its source impedance in the
system. This variation in voltage, is more prominent when only the active power
load is increased, as shown in Figure 2-31. While the performance of the voltage
source interface inverter remains roughly the same as before, the current source
interface inverter shows a much varied change in output. Another contributing
factor to this difference is that in the voltage source interface, the input frequency
to the power controller is the phased locked loop calculated frequency, while in
the current source interface, the network bus frequency is the input to the
controller.
Figure 2-30
Total power output from areas 5 and 2 for a change in active and reactive power
load, along with change in power reference
 2-32 
0
Figure 2-31
Total power output from areas 5 and 2 for a change in only active power load,
along with change in power reference
Further investigation into this difference between the voltage source and current
source inverter performance is yet to be carried out, however, it can be concluded
that both inverter interfaces, when operating in the constant frequency control
mode, are able to follow dispatch commands from the system operator, and reset
their control references to be ready for the next event.
Scenario 3: Line fault followed by outage of the line
In scenario 1, the response of the constant frequency control scheme to
generation trip events was discussed. In this scenario, the behavior to a line fault,
followed by outage of the line will be discussed. In general, the 2000 bus
Synthetic Texas system is robust to a N – 1 line outage. To determine the
weakest lines, a brute force continuation power flow solution was carried out for
every line in the system according to the following algorithm:
1. Load the base case power flow file, and make the status of a branch 0
2. Solve the power flow
3. Increase all active and reactive power load by 1%
4. Increase all generation active power by 1%, as long as the maximum limit is
not violated
5. Solve power flow
6. If a successful solution is obtained, go back to step 3.
7. If a solution is not obtained, record the total amount of load increase, and go
back to Step 1 to proceed to the next branch.
Using this method, it was found that for the outage of almost all branches, the
system could handle an approximate 10% increase in total active and reactive
power load. However, there were two branches in the system, upon whose
 2-33 
0
outage, the resultant system couldn’t handle a large increase in load. For one of
these branches, a tie line between Area 1 and Area 3, the system could only
handle a load increase of 2%, while for the other branch, a branch internal to
Area 3, the system could only handle a load increase of 4%.
The minimum voltage in the system for Cases 1, 2 and 3 for a 6 cycle fault at the
center of the branch between buses 3041 – 3046 (branch internal to Area 3),
followed by outage of the branch, is shown in Figure 2-32.
Figure 2-32
Minimum voltage in the system for a line fault on an internal area line followed by
outage of the line
It can be seen that the voltage source interface inverter is the most controlled
response. The current source interface response was numerically unstable for the
immediate duration around the fault, but since recovered. The synchronous
machines response, while being oscillatory, is also stable. The oscillatory behavior
can be attributed to the settings of the excitation system of the machine. Due to
the fault occurring at one of the weaker locations in the system, fast voltage
support is required to prevent the spread of the angles across the system. The
voltage source interface inverter, is able to provide this fast response, while the
current source interface is unable to do so quickly. The reactive power output of
an inverter located close to the faulted bus is shown in Figure 2-33 for Cases 2
(blue curve) and 3 (red curve).
 2-34 
0
Figure 2-33
Reactive power output of a inverter located close to the fault
The sluggishness of the current source interface and the rapid injection of current
from the voltage source interface is observable from the figure. This rapid
injection of reactive current from the voltage source interface inverter is crucial in
order to help support the voltage at nearby buses in the system. The inverters are
able to inject reactive current, as they were operating in a Q-priority mode.
However, even with operation in a P-priority mode, the frequency control loop
reduces the active power command during the fault, as upon inception of the
fault, the frequency rises in the system. As the active power command reduces,
and the voltage reduces, the active current command will reduce, providing more
room for reactive power command to be injected. Thus, even in the P – priority
mode, the inverters are able to provide voltage support.
For the outage of the tie line between Areas 1 and 3, the minimum voltage in the
system for Cases 2 and 3 for a 6 cycle fault at the center of the branch between
buses 1081 – 3058 followed by outage of the branch, is shown in Figure 2-34.
The outage of this tie line, causes an extreme low voltage condition in the vicinity
of the boundary buses between the two areas. Area 1 exports power to Area 3,
and thus, with the outage of this tie line, the power (around 410 MW) is routed
through other tie line paths, which causes the transmission bus voltages to drop.
This reduction in the transmission bus voltages impacts the motor loads in this
region. Case 1 for this event had rotor angle instability issues, and is thus, not
shown in the figure. The rotor angle instability in Case 1 for all synchronous
machines could be prevented by increasing the speed of response of the static
excitation system on the machines in Area 1, but the oscillations were still
undamped. From the figure, it can be seen that Case 2, with the voltage source
interface inverter, is the most robust source, for this event.
 2-35 
0
Figure 2-34
Minimum voltage in the system for a line fault on a tie line followed by outage of
the line
It is possible that the current source interface inverter’s gains can be tuned to be
stable for this event. As an alternative, the sources in Area 1 whose MVA was
greater than 150.0 MVA were replaced by the voltage source interface inverter.
Thus, in this temporary setup (labeled as Case 2a), there were now 16
synchronous machines, 13 voltage source inverter interfaces, and the remaining
404 sources were represented by the current source interface inverter. For the
same tie line outage, Figure 2-35 shows the minimum voltage across the system.
Figure 2-35
Minimum voltage in the system for a line fault on a tie line followed by outage of
the line, with few voltage source inverters
The voltage source interface inverters, by rapidly injecting current into the system
upon the occurrence of the fault, are able to reduce the drop in voltage, and this
contributes towards a more stable response. Thus, it is possible that the entire
system may need only few voltage source interfaced inverters to prevent a system
collapse, while the other inverters can be current source interfaced, with all the
inverters operating on a constant frequency control scheme.
 2-36 
0
Section 3: Three-Phase Inverter Models for
Constant Frequency Operation
In this chapter, detailed three-phase EMT-type inverter models with controls
that enable constant frequency operation, as described in the previous chapter,
are presented.
Inverter Controls
Inverter Control Objectives
Figure 3-1 shows a generic generation unit interfaced to the power system via an
inverter [as a voltage-sourced inverter (VSC)] and an RLC filter. The control
objective of the inverter is to regulate real power Pi(t) and voltage magnitude
�𝑣𝑣𝑠𝑠,𝑖𝑖 (𝑡𝑡)�|vt (t)| to their reference set points Pi* and �𝑣𝑣𝑠𝑠,𝑖𝑖 (𝑡𝑡)�*. The instantaneous
three-phase output voltages of the inverter are
𝑣𝑣𝑡𝑡𝑡𝑡,𝑖𝑖 (𝑡𝑡) = �𝑣𝑣𝑡𝑡,𝑖𝑖 (𝑡𝑡)� 𝑐𝑐𝑐𝑐𝑐𝑐 �𝜃𝜃𝑡𝑡,𝑖𝑖 (𝑡𝑡)�
𝑣𝑣𝑡𝑡𝑡𝑡,𝑖𝑖 (𝑡𝑡) = �𝑣𝑣𝑡𝑡,𝑖𝑖 (𝑡𝑡)� 𝑐𝑐𝑐𝑐𝑐𝑐 �𝜃𝜃𝑡𝑡,𝑖𝑖 (𝑡𝑡) −
𝑣𝑣𝑡𝑡𝑡𝑡,𝑖𝑖 (𝑡𝑡) = �𝑣𝑣𝑡𝑡,𝑖𝑖 (𝑡𝑡)� 𝑐𝑐𝑐𝑐𝑐𝑐 �𝜃𝜃𝑡𝑡,𝑖𝑖 (𝑡𝑡) +
2𝜋𝜋
3
2𝜋𝜋
3
�
Eq. 3-1
�.
These voltages can be constructed at the inverter terminals via a modulation
method by specifying |𝑣𝑣𝑡𝑡 (𝑡𝑡)| and 𝜃𝜃𝑡𝑡 (𝑡𝑡), whose reference points are determined
by the proposed power sharing algorithm. Figure 3-2 shows the overall structure
of the associated controller. In a system at constant frequency 𝑓𝑓0 , 𝜃𝜃𝑡𝑡,𝑖𝑖 (𝑡𝑡) is
𝜃𝜃𝑡𝑡,𝑖𝑖 (𝑡𝑡) = 𝛿𝛿𝑡𝑡,𝑖𝑖 (𝑡𝑡) + (2𝜋𝜋)𝑓𝑓0 𝑡𝑡.
Eq. 3-2
In the proposed control architecture, units need access to accurate time. While it
is possible to receive time t from GPS at every time step of 50us (GPS data is
typically accurate to within 40 ns), another approach would be to run a local
timer which is synchronized with GPS periodically. This method helps with
occasional loss of data due to for example equipment malfunctioning. Modern
power systems extensively use GPS data for measurement and control purposes.
 3-1 
0
Figure 3-1
Generic unit i interfaced to the power system.
Figure 3-2
Overall structure of the proposed controller.
Voltage Magnitude Controller
Figure 3-3 shows the proposed voltage magnitude controller. When the selector
is in +1 state, the controller uses an integral controller with gain G1 to determine
the inverter terminal voltage �𝑣𝑣𝑡𝑡,𝑖𝑖 (𝑡𝑡)�. However, if current magnitude �𝑖𝑖𝑡𝑡,𝑖𝑖 (𝑡𝑡)�
exceeds its limit �𝑖𝑖𝑡𝑡,𝑖𝑖 (𝑡𝑡)�max , the selector switches to -1 state, when the controller
decreases the inverter terminal voltage with the gain G1G2 until it limits �𝑖𝑖𝑡𝑡,𝑖𝑖 (𝑡𝑡)�.
Figure 3-3
Proposed voltage magnitude controller and current limiter.
 3-2 
0
Real Power Sharing Algorithm
The underlying idea behind the proposed real power sharing algorithm is that the
injected real power of a generating unit at the transmission level can be controlled
by adjusting its voltage angle. We assume each grid-supporting unit has a
∗
preferred real power set point 𝑃𝑃𝑔𝑔𝑔𝑔
that depends on factors such as maximizing
profit, required power reserve, available power, and possibly operator commands.
The proposed algorithm needs to ensure that the allocation of power to gridforming and grid-supporting units can meet the total load demand. It calculates
the modified power set point for each grid-supporting unit as
∗
∗
𝑃𝑃𝑔𝑔𝑔𝑔 ,∗𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 (𝑡𝑡) = 𝑃𝑃𝑔𝑔𝑔𝑔
+ ∆𝑃𝑃𝑔𝑔𝑔𝑔
(𝑡𝑡)
Eq. 3-3
∗
∗
∑ ∆𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
= 𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 – 𝑃𝑃𝑔𝑔𝑔𝑔 − ∑ 𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
Eq. 3-4
∗
where 𝑃𝑃𝑔𝑔𝑔𝑔 ,∗𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 (𝑡𝑡) is the is the modified set point due to droop, and ∆𝑃𝑃𝑔𝑔𝑔𝑔
(𝑡𝑡) is
its adjustment. The sum of these adjustments should equal the difference
between the total demand and sum of the power supplied by the grid-forming
unit and the preferred powers of the grid-supporting units:
where 𝑃𝑃𝑔𝑔𝑔𝑔 ≤ 𝑃𝑃𝑔𝑔𝑔𝑔,max .
In the proposed power sharing algorithm, we follow the following design
principles:

Principle 1: The power limits of all grid-forming and grid supporting units
should be met.

Principle 2: The reference set points of grid-supporting units should not
deviate from the preferred set points unless needed to meet power demand.
-

Principle 2*: The algorithm should also be able to enable participation of
grid-forming and grid-supporting units, irrespective of their preferred set
points, in power sharing.
Principle 3: The share of grid-supporting units in power sharing should be
based on their droop characteristic.
If the grid-forming unit is large enough, the grid-supporting units continue to
∗
. In this case, the grid-forming unit's
inject their preferred real power values 𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
voltage angle 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) is maintained at zero, and the angles 𝛿𝛿𝑔𝑔𝑔𝑔,𝑖𝑖 (𝑡𝑡) of grid∗
as
supporting units are changed in a ramp at rate at C1 until 𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖 (𝑡𝑡) reaches 𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
shown in Figure 3-4.
Figure 3-4
Proposed real power controller.
 3-3 
0
However, if the grid-forming unit is not large enough or if its 𝑃𝑃𝑔𝑔𝑔𝑔,max is lowered
to redispatch power, the grid-supporting units do need to participate in power
sharing. We first discuss the proposed power sharing algorithm for the two-bus
system shown in Figure 3-5, in which the power generated by one inverter is
consumed by the other (e.g., an island consisting of a PV unit and a battery unit)
and then extend it to a generic power system. For simplicity, we assume we start
from a steady-state in which 𝛿𝛿𝑔𝑔𝑔𝑔 = 0; then the grid-supporting unit increases its
∗
∗
power output to 𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
. To meet 𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
, the controller of the grid-supporting unit
(similar to the controller shown in Figure 3-4) ramps its angle 𝛿𝛿𝑔𝑔𝑔𝑔,𝑖𝑖 (𝑡𝑡) at a rate of
C1. Simultaneously, the grid-forming unit monitors its output power and
∗
compares it with the limit |𝑃𝑃𝑔𝑔𝑔𝑔,max |. If |𝑃𝑃𝑔𝑔𝑔𝑔
| < |𝑃𝑃𝑔𝑔𝑔𝑔,max |, we have the same
controls as the large grid-forming case discussed above. Figure 3-6(a) shows the
vector diagram for this operating condition in the dq frame synchronized to
∗
| > |𝑃𝑃𝑔𝑔𝑔𝑔,max |, i.e., the power by the grid-supporting unit
(2πf0)t. However, if |𝑃𝑃𝑔𝑔𝑔𝑔
exceeds the capability of the grid-forming unit, as soon as |𝑃𝑃𝑔𝑔𝑔𝑔 | > |𝑃𝑃𝑔𝑔𝑔𝑔,max |, the
controller of the grid-forming unit changes its angle 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) to avoid further
increase of its power and violating the limit. Figure 3-6(b) shows the vector
diagram for this operating condition. If 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) is ramped at a rate C2>C1,
𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) − 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) changes at the rate C2–C1 until |𝑃𝑃𝑔𝑔𝑔𝑔 (t)|= |𝑃𝑃𝑔𝑔𝑔𝑔 (t)|=| 𝑃𝑃𝑔𝑔𝑔𝑔,max |.
Then the controller of the grid-supporting unit continues to ramp up
∗
𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡)δgs (t), but it cannot regulate 𝑃𝑃𝑔𝑔𝑔𝑔 (t) to 𝑃𝑃𝑔𝑔𝑔𝑔
because 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) − 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) is
influenced by the grid-forming unit and C2 > C1. As a result, both 𝑣𝑣𝑔𝑔𝑔𝑔 (𝑡𝑡) and
𝑣𝑣𝑔𝑔𝑔𝑔 (𝑡𝑡) vectors rotate in the dq frame at a speed of C1 rad/s. Therefore, the system
frequency 𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠 changes such that |𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠 - f0|=C1/2π.
∗
| <= |𝑃𝑃𝑔𝑔𝑔𝑔,max |, at which point it is preferred to bring
Eventually, we have |𝑃𝑃𝑔𝑔𝑔𝑔
𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) back to zero to maximize power sharing capability reserves. However,
changing 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) should not affect the ability of the grid-supporting unit to
control its power 𝑃𝑃𝑔𝑔𝑔𝑔 (t). Therefore, C0 should be smaller than C1 so that while the
grid-forming unit adjusts 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡), the grid-supporting unit can adjust its angle
relative to 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡). Figure 3-6(c) shows the vector diagrams for this operating
condition.
Figure 3-5
A sample two-bus system.
 3-4 
0
Figure 3-6
Vector diagrams of the two-bus system in operating conditions (a) grid-forming unit
is large (see text for definition); (b) grid-forming unit is limited; and (c) grid-forming
unit is limited and brings 𝜹𝜹𝒈𝒈𝒈𝒈 (𝒕𝒕) to zero.
Angle Droop Algorithm
To avoid steady-state deviation of 𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠 from f0, we define upper and lower trigger
∗
when 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡)
points for 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡). In the angle droop implementation, we reduce 𝑃𝑃𝑔𝑔𝑔𝑔
∗
is outside these trigger points. The adjustment ∆𝑃𝑃𝑔𝑔𝑔𝑔 in (3) is calculated as
⎧ 0,
⎪
∗
∆𝑃𝑃𝑔𝑔𝑔𝑔
= 𝐷𝐷 �𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 − 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡)�,
⎨
⎪𝐷𝐷 �𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 − 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡)�,
⎩
𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 < 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡) < 𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚
𝛿𝛿𝑔𝑔𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚 < 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡)
Eq. 3-5
𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 > 𝛿𝛿𝑔𝑔𝑔𝑔 (𝑡𝑡)
where D is the angle droop gain. With multiple grid-supporting units, D of each
unit determines its power share.
Figure 3-7 compares the droop characteristic of the proposed angle droop
algorithm with conventional frequency droop. The angle droop characteristic,
Figure 3-7(a), has a soft limiter shape (in governor terminology, this type of
limiter is called a non-step deadband) while the frequency droop characteristic,
Figure 3-7(b), is primarily a straight sloped line. However, practically, the
frequency droop characteristic also has a small dead band of around 0.017 –
0.036 Hz to prevent unnecessary movement of the governor of machines. The
use of the dead band in the angle droop path of the grid supporting inverters is to
allow the grid forming inverter control to react first, while allowing for a
stabilizing effect on the entire system control. This is because in frequency droop
all units naturally stabilize to settle at the same frequency as frequency is a system
wide variable. However, voltage angles are a local property in the power system,
and in order to ensure transfer of power, a difference must exist in value of the
angles, and thus in order to stabilize the system after a disturbance, the dead
band in the controller plays a role. For symmetry, in the remainder of this report,
we assume 𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 = - 𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 but the proposed angle droop algorithm can
operate without this assumption. The choice of 𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 is a trade-off between
 3-5 
0
power sharing accuracy based on D coefficients and the time it takes to reach the
steady state. This is discussed later in detail under parameter selection.
Figure 3-8 shows the overall real power sharing algorithm generalized to multiple
grid-supporting units. The hysteresis band prevents interference of the power
limiting and angle control features of the grid-forming unit. A bandwidth too
large has allows |𝑃𝑃𝑔𝑔𝑔𝑔 (t)| to exceed 𝑃𝑃𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 ; a bandwidth too small may result in
system instability due to frequent changes in the control mode. Therefore, the
bandwidth should be chosen as a modest fraction of 𝑃𝑃𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 , e.g., 1%.
In the proposed method, communication error in the GPS signal, e.g., delay or
corrupted signal) does not affect real power tracking: Due to closed loop control
of P as shown in Figure 3-8, P tracks its reference. Therefore, a delay or
miscommunication in t does not affect δ in the steady state. However, it can
change δi, which has no effect on our real power control. However, it changes the
share of inverter i in power sharing. Nevertheless, the inverter units can continue
their operation with their internal clock until a trusted signal is received.
Figure 3-7
(a) proposed angle droop; (b) conventional frequency droop.
 3-6 
0
Figure 3-8
Proposed real power sharing algorithm; (a) grid-forming unit; and (b) gridsupporting units.
Parameter Design
As mentioned above, the proposed angle droop algorithm ensures voltage angles
are within their limits. However, the ramp rates Ci to change angles are finite to
accommodate the physical capabilities of the prime mover and possibly stability
considerations. The limits for Ci in this work are based on values found
heuristically, but if needed, studies can be performed to find the theoretical
limits. Because the angles change with a certain rate, it takes some finite time for
the voltage vectors to rotate and reach the steady state. Without extra measures,
during this time, the real powers of grid-supporting units are uncontrolled and
may exceed their limits even though their reference values are limited. To prevent
this, a variable gain is adopted: If the real power of a grid-supporting unit reaches
its limit, the ramp rate is changed from C1 to a larger value C3. If C3 > C2, real
power limiting scheme of the grid-forming unit is no longer able to change the
real power of the grid-supporting unit because the voltage vector of the gridsupporting unit will rotate at the speed of C3 - C2. Therefore, the grid-supporting
unit can limit its output real power during this time. Therefore, these parameters
should be chosen such that C0<C1<C2<C3. (Note that the same should be true for
each individual inverter when there are multiple inverters.)
 3-7 
0
To determine the share of each grid-supporting unit in supplying the needed real
power 𝑃𝑃𝑔𝑔𝑔𝑔−𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡−𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 can be defined as
∗
*
𝑃𝑃𝑔𝑔𝑔𝑔−𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡−𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ∑ 𝛥𝛥𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
= ∑ 𝐷𝐷𝑖𝑖 (𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 − 𝛿𝛿𝑔𝑔𝑔𝑔,𝑖𝑖 ) Pgs-total-change = ∑ ∆Pgs,i
=
∑ Di (δgs,min -δave )
Eq. 3-6
If 𝑃𝑃𝑔𝑔𝑔𝑔−𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡−𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 0, i.e., the grid-forming unit is large enough to supply the
power demand beyond the preferred set points of the grid-supporting units, 𝛿𝛿𝑔𝑔𝑔𝑔 =
0 and all
𝑣𝑣𝑔𝑔𝑔𝑔,𝑖𝑖 vectors cluster around it as shown in Figure 3-9(a). Otherwise, as shown in
Figure 3-9(b), voltage vectors cluster around a hypothetical vector at
𝛿𝛿𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 (𝛿𝛿𝑔𝑔𝑔𝑔,𝑖𝑖 ). If Di values are small, |𝛿𝛿𝑎𝑎𝑎𝑎𝑎𝑎 | is large and for all gridsupporting units
𝛿𝛿𝑔𝑔𝑔𝑔,𝑖𝑖 ≈ 𝛿𝛿𝑎𝑎𝑎𝑎𝑎𝑎 . Therefore,
∗
𝑃𝑃𝑔𝑔𝑔𝑔−𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡−𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ∑ 𝛥𝛥𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
= ∑ 𝐷𝐷𝑖𝑖 (𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 − 𝛿𝛿𝑎𝑎𝑎𝑎𝑎𝑎 )
Eq. 3-7
Subsequently,
𝐷𝐷
∗
𝛥𝛥𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
= ∑ 𝑖𝑖 𝑃𝑃𝑔𝑔𝑔𝑔−𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡−𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
𝐷𝐷𝑖𝑖
Eq. 3-8
That is, the real power change of each grid-supporting unit is (approximately)
proportional to its droop gain Di.
Figure 3-9
Vector diagrams of the generation units in the steady state when the grid-forming
unit is (a) large (see text for definition); and (b) limited.
Simulation Case Studies
Several case studies are conducted to evaluate the performance of the proposed
algorithms in different operating conditions. The software tool
PSCAD/EMTDC is employed to model the fast, electromagnetic transients of
power electronics-based inverters. Figure 3-10 shows the study system chosen as
the three-machine, IEEE/WSCC nine-bus system. The base values of the
 3-8 
0
voltage and power used for per-unit calculations are 230 kV and 100 MVA. The
rated powers of the generation units at buses 1-3 are 250 MVA, 192 MVA, and
128 MVA. Per-unit currents are calculated on the base of their associated
generator. The loads are modeled as a constant impedance calculated at the
nominal voltage, except for the section where induction motor loads are used. All
three generation units are interfaced to the grid via an inverter. The generation
unit at bus 2 is chosen as the grid-forming unit (gf), and the generation units at
buses 1 and 3 are chosen as grid-supporting units (gs1 and gs3). Initially, buses
1-3 regulate their output real power and bus voltage magnitudes to the rated
values of the nine-bus system. Table 3-1 shows the controller parameters.
Figure 3-10
Study system.
Table 3-1
Parameters of the Controllers
G1= 10, G2= 2
𝑖𝑖𝑡𝑡𝑡𝑡,𝑡𝑡ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑜𝑜𝑜𝑜𝑜𝑜 = 1.5 pu (i=1, 2, 3)
Voltage controller
Real power controller
𝑃𝑃𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 = 192 MW
D1=5*103
Angle droop
 3-9 
0
C0= 0.75, C1= 1,
C2= 1.25, C3= 5
𝑃𝑃𝑔𝑔𝑔𝑔,1,𝑚𝑚𝑚𝑚𝑚𝑚 = 250 MW, 𝑃𝑃𝑔𝑔𝑠𝑠,3,𝑚𝑚𝑚𝑚𝑚𝑚 = 128 MW
𝑀𝑀𝑀𝑀
𝑟𝑟𝑟𝑟𝑟𝑟
, D3=2.5*103
𝑀𝑀𝑀𝑀
𝑟𝑟𝑟𝑟𝑟𝑟
𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 = − 𝛿𝛿𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 = 0.75 rad
Step Change in 𝑷𝑷∗𝒈𝒈𝒈𝒈,𝒊𝒊 and |𝒗𝒗∗𝒈𝒈𝒈𝒈,𝒊𝒊 |
In this case study, initially the grid-supporting units output their preferred real
∗
∗
increases in a step by 35 MW, and at t=1.3 s, |𝑣𝑣𝑔𝑔𝑔𝑔,1
|
powers. At t=0.3 s, 𝑃𝑃𝑔𝑔𝑔𝑔,3
increases in a step by 0.014 pu. The loads do not change. Figure 3-11 shows
voltage, current, real power, and frequency at buses 1—3. 𝑃𝑃𝑔𝑔𝑔𝑔,3 (𝑡𝑡) tracks its set
∗
with a rise time of 150 ms (inversely proportional to C1) and
point 𝑃𝑃𝑔𝑔𝑔𝑔,3
∗
| with a rise time of 50 ms. During transients, the current
|𝑣𝑣𝑔𝑔𝑔𝑔,1 (𝑡𝑡)| tracks |𝑣𝑣𝑔𝑔𝑔𝑔,1
magnitudes change smoothly. Because the load is unchanged, after the increase
in 𝑃𝑃𝑔𝑔𝑔𝑔,3 (𝑡𝑡), 𝑃𝑃𝑔𝑔𝑔𝑔 (𝑡𝑡) decreases to maintain power balance. The system frequency
returns to its rated value (60 Hz) in the steady state.
Figure 3-11
Measurements as (a) 𝑷𝑷∗𝒈𝒈𝒈𝒈,𝟑𝟑 changes from 85 to 120 MW at t=0.3 s; (b) 𝒗𝒗∗𝒈𝒈𝒈𝒈,𝟏𝟏
changes from 1.026 to 1.040 pu at t=1.3 s.
Load Increase
In this case study at t=1s the real power of the load at bus 6 increases by 15 MW,
and at t=3s, the real power of the load at bus 5 increases by 80 MW. This
scenario is simulated once assuming the grid-forming unit can accommodate the
whole load change (𝑃𝑃𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 is large) and once when it cannot. Figure 3-12 shows
the results. In both cases, the first load increase is supported by an increase in
𝑃𝑃𝑔𝑔𝑔𝑔 (𝑡𝑡) because �𝑃𝑃𝑔𝑔𝑔𝑔 (𝑡𝑡)� < 𝑃𝑃𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 .
However, the two systems respond differently to the second load increase. In the
system with the large grid-forming unit, the load increase is supported by an
increase in 𝑃𝑃𝑔𝑔𝑔𝑔 (𝑡𝑡) and in the steady state, 𝑃𝑃𝑔𝑔𝑔𝑔 =264 MW. In the system with the
small grid-forming unit, the load increase is initially responded to by an increase
in 𝑃𝑃𝑔𝑔𝑔𝑔 (𝑡𝑡) until 𝑃𝑃𝑔𝑔𝑔𝑔 (𝑡𝑡)= 𝑃𝑃𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 . Then, 𝑃𝑃𝑔𝑔𝑔𝑔,1 (𝑡𝑡) and 𝑃𝑃𝑔𝑔𝑔𝑔,3 (𝑡𝑡) ramp up. It takes
approximately 1.5 s for the grid-supporting units to reach their new reference
power set points. During this time, 𝑃𝑃𝑔𝑔𝑔𝑔,1 (𝑡𝑡) and 𝑃𝑃𝑔𝑔𝑔𝑔,3 (𝑡𝑡) are not under control
∗
∗
=48 MW and ∆𝑃𝑃𝑔𝑔𝑔𝑔,3
=23
but are within their limits. In the steady state, ∆𝑃𝑃𝑔𝑔𝑔𝑔,1
∗
∗
MW. The ratio ∆𝑃𝑃𝑔𝑔𝑔𝑔,1 / ∆𝑃𝑃𝑔𝑔𝑔𝑔,3 is 2.09, which is very close to the ratio 𝐷𝐷1 /𝐷𝐷3 =
 3-10 
0
2.00 (4.5% error). Choosing smaller a 𝐷𝐷𝑖𝑖 results in more precise power sharing
but a longer response time. The frequency returns to 60 Hz in both cases.
Figure 3-12
Generation units measurements for the system with a (a) large (compared with
load demand) grid-forming unit; (b) small grid-forming unit. In both systems, the
load at bus 6 increases by 15 MW at t=1 s and the load at bus 5 increases by 80
MW at t=3 s.
Dynamic Loads
This case study investigates the performance of the proposed algorithm in the
presence of dynamic loads with inertia. Two induction motors (IM) are
connected to bus 6 (15 MW, IM1) and bus 5 (80 MW, IM2). Initially, both IMs
run at no-load conditions. IM1 is loaded at t=1 s, and IM2 is loaded at t=3 s.
Both loads are linear with a mechanical torque proportional to speed. Figure 313 shows the results.
The grid-forming unit provides the power needed by IM1 without exceeding its
real power limit. However, loading of IM2 needs power to be provided by the
grid-supporting unit and hence, results in increase of 𝑃𝑃𝑔𝑔𝑔𝑔,1 (𝑡𝑡) and 𝑃𝑃𝑔𝑔𝑔𝑔,3 (𝑡𝑡).
During start-up, the rotor speeds of the IMs are smooth, but their
electromagnetic torques oscillate. Subsequently, their real powers (product of
electromagnetic torque and rotor speed) oscillate too, resulting in small
oscillations in the voltage and real power. These oscillations are related to the
mechanical modes of the IMs and their analysis is beyond the scope of this work.
The proposed algorithm performs effectively with dynamic loads represented by
induction machines.
 3-11 
0
Power Redispatch
In this case study, initially the grid-supporting units output their preferred real
powers and the grid supporting unit provides 170 MW. At t=2 s, 𝑃𝑃𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚
decreases from 192 MW to 120 MW. Subsequently, a portion of the load
initially supplied by the grid-forming unit has to be provided by the gridsupporting units. Figure 3-14 shows that after the reduction in 𝑃𝑃𝑔𝑔𝑓𝑓,𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑃𝑃𝑔𝑔𝑔𝑔,1 (𝑡𝑡)
and 𝑃𝑃𝑔𝑔𝑔𝑔,3 (𝑡𝑡) increase by 33 MW and 17 MW. This change is proportional to the
droop gains of the grid-supporting units as expected.
Figure 3-13
Measurements of buses 1-3 and machine loads as IM1 changes from no-load to
full-load at t=1 s and IM2 changes from no-load to full-load at t=3 s.
 3-12 
0
Figure 3-14
Measurements at buses 1—3 when 𝑷𝑷𝒈𝒈𝒈𝒈,𝒎𝒎𝒎𝒎𝒎𝒎 decreases from 192 MW to 120 MW
at t=2 s.
Fault
This case study evaluates the system response to a fault. Initially, the system
operates at nominal conditions when a three-phase bolted fault occurs at t=1.0 s
in the middle of one of the double transmission lines between buses 4 and 5 (this
second line is added for this case study). After 100 ms, the fault is cleared by the
circuit breakers at the two ends of the line. Figure 3-15(a) shows the system
response. The current limiting function of the controller activates when the
current reaches the threshold value. This threshold in general depends on the
rating of the switches (with respect to the inverter rating), cooling mechanism,
and system considerations. In this paper, this limit is chosen heuristically. The
limiter is clearly not a replacement for protection or the current limitation
provided by limiting the reference current values.
The maximum instantaneous current magnitude is 1.8 pu. Moreover, minimum
and maximum voltage voltages of the generation buses are 0.2 pu and 1.1 pu,
respectively. When the fault is cleared, the system returns to its normal
operation. Figure 3-15(b) shows the result of the same case study if the proposed
 3-13 
0
voltage controller is not augmented with a current limiter. The maximum current
is 4.8 pu, and the minimum and maximum voltages are 0.5 pu and 2.0 pu.
Figure 3-15
Measurements at buses 1—3 when a fault occurs at t=1.0 s and clears after 100
ms; (a) with the current limiter; (b) without.
Performance Evaluation in the Presence of Synchronous
Generation
The previous sections focused on an angle droop-based power sharing method
for a 100% inverter-based power system, which is an extreme operating scenario
and presently may occur only a few hours during a day. In this section, the
interactions between the proposed controllers of inverters and SG controls is
investigated, using the EMT-type models described before. This study is
important because the proposed angle droop-based method enables constant
frequency operation of the power system, but the speed—droop controller of the
synchronous generator (SG) changes its real power when its frequency changes.
Thus, studying the potential interaction between the angle droop-based method
in inverter-based units and the SG controller in systems with a small percentage
of synchronous generation is required.
To evaluate the performance of the proposed controllers for an inverterdominated power system, different case studies are simulated in
PSCAD/EMTDC software for the modified IEEE/WSCC nine-bus system.
Figure 3-16 shows the study system with four generation units. Three generation
units at bus 1-3 are integrated to the system via a VSC unit. Based on IEEE 9bus system, the generation unit at bus 2 with the rated power of 192 MVA is
considered as the grid-forming unit, and generation units at buses 1 and 3 with
the rated power of 250 MVA and 128 MVA are considered as grid-supporting
units. A synchronous generator (SG) with a rated power of 33 MVA is
connected to bus 6. The base values of power and voltage for per-unit
calculations are 100 MVA and 230 kV. Per-unit currents are calculated based on
their own generation units.
 3-14 
0
Figure 3-16
Modified IEEE/WSCC 9-bus system.
Synchronous Generator Connection
This case study evaluates the performance of the proposed controller for the
inverter-based power system when an additional SG is connected to bus 6. In
this case, the SG is synchronized to the network at t=1 s and its input torque is
ramped up at t = 2 s and reaches the rated value at t=3.5 s. Figure 3-17 shows the
real power, frequency, current magnitude, and voltage magnitude of buses 1—3
and 6. The SG provides 33 MW of power. Thus, to maintain power balance, the
real power controller of the grid-forming unit reduces 𝑃𝑃𝑔𝑔𝑔𝑔 (t) with a constant rate
of C2, and the real power controllers of grid-supporting units track their defined
set point values, which confirms the performance of the controller to maintain
power balance. In addition, the voltage controller of all generation units regulate
∗
| at rated values, which confirms the performance of
the amplitude voltages |𝑣𝑣𝑠𝑠,𝑖𝑖
the voltage controller.
Note that because synchronization does not occur exactly at the moment of zero
power transfer (when the angles on the sides of the switch are the same), there is
some exchange of power immediately after switch closure. Compared to the
results presented later in this subsection, e.g., load change and power redispatch,
more deviation in delta is experienced in the case presented here.
 3-15 
0
Figure 3-17
Performance of the controller when the SG is connected to the system.
Load Change
This case study evaluates the performance of the proposed controllers when loads
change. Initially the system operates at nominal conditions. The load at bus 6
increases by 20 MW at t=2 s and the load at bus 5 increases by 70 MW at t=4 s
respectively. Figure 3-18 shows the response of the controllers. When the load at
bus 6 increases, the grid-forming unit responds by increasing 𝑃𝑃𝑔𝑔𝑔𝑔 (t), and it can
support the whole load change. When the second load is added to the system, the
grid—forming unit initially responds by increasing 𝑃𝑃𝑔𝑔𝑔𝑔 (t) until |𝑃𝑃𝑔𝑔𝑔𝑔 (t)|=
𝑃𝑃𝑔𝑔𝑔𝑔,𝑚𝑚𝑚𝑚𝑚𝑚 . Thus, the angle droop controller of the grid supporting units responds
to load increase by increasing the Pgs,1(t) and Pgs,2(t), and they reach their new
∗
power set point approximately within 1.5 s. In this case, ∆𝑃𝑃𝑔𝑔𝑔𝑔,1
= 23 MW and
∗
∗
∗
∆𝑃𝑃𝑔𝑔𝑔𝑔,3 =13MW (∆𝑃𝑃𝑔𝑔𝑔𝑔,1 /∆𝑃𝑃𝑔𝑔𝑔𝑔,3 = 2.09). and this ratio is close to D1/D2 = 2 (4.54%
error), which confirms the performance of the real power controllers. In this case,
when the loads are added to the system, the SG increases its reactive power to try
to remedy the initial drop in the terminal voltage. Because the excitation of the
 3-16 
0
SG has a high gain, and other generation units contribute to power sharing, the
SG’s terminal voltage returns to the nominal value. In addition, when the loads
increase, the system frequency deviates from 60 Hz. Thus, the angle droop
activates, the real power of the generation units changes, and the frequency
returns to 60 Hz.
Note that, as shown in Figure 3-18. the phase angle of the grid-forming unit (and
hence, its frequency) does not change unless the power delivered by this unit is
about to exceed it maximum permissible power. This, however, does not imply that
Pgf does not change because this power depends on the angle differences in the
system and the angles (and frequencies) of the grid supporting units do change.
Figure 3-18
Performance of the controllers when the load at bus 6 increases by 20 MW at t=2
s and the load at bus 5 increases by 70 MW at t=4 s.
 3-17 
0
Fault
This case study evaluates the performance of the proposed controllers when a
fault occurs in the system. Initially the system operates at nominal conditions.
Two parallel lines with similar parameters are assumed as the transmission line
between buses 8 and 9. A three-phase bolted fault at t=1 s occurs at the middle of
one of them, and this fault is cleared after 100 ms by opening the circuit breakers.
Figure 3-19 shows the response of the controllers. During the fault, there are
some oscillations in the system, but when the fault is cleared, the system returns
to its nominal condition.
Figure 3-19
Performance of the controllers when a three-phase bolted fault occurs at t=1 s at
the middle of the transmission line between bus 8 and bus 9.
Power Dispatch
This case study evaluates the performance of the studied controller to track a
change in P*gs,i. In this case, initially the system operates at nominal conditions.
∗
∗
changes from 71.6 MW to 96.6 MW and 𝑃𝑃𝑔𝑔𝑔𝑔,3
changes from 85
At t=2 s, 𝑃𝑃𝑔𝑔𝑔𝑔,1
MW to 120 MW. Figure 3-20 shows that the real power controller of grid∗
supporting units track their reference value 𝑃𝑃𝑔𝑔𝑔𝑔,𝑖𝑖
which is proportional to their
droop gains, and 𝑃𝑃𝑔𝑔𝑔𝑔 (t) reduces from 142 MW to 82 MW, which confirms the
performance of the real power controllers. Since the system has a constant
frequency at 60 Hz, the SG does not contribute to power sharing.
 3-18 
0
Figure 3-20
Performance of the controllers in a case of changing P*gs,1 and P*gs,3
Effect of Controller Gains on the Oscillation Frequency of the
SG
This section studies the effect of the gains of the inverter controllers on the
oscillation frequency of the SG in an inverter-dominated power system.
The rotor of the SG is a complex mechanical system. The rotor contains shaft
sections with different sizes and couplings. This rotor system has a large number
of torsional vibration frequencies both above and below the rated frequency.
Figure 3-21 shows the structure of a shaft system model. The five torsional
masses include the rotors of the generator, two low-pressure (LP) turbine
sections, an intermediate-pressure (IP) turbine section, and a high-pressure (HP)
turbine section.
 3-19 
0
Figure 3-21
Structure of a typical lumped –mass system model [3-1]
The shaft system dynamic characteristics are defined by three sets of parameters:
inertia constant H of the individual masses, torsional stiffness K of shaft sections
connecting adjacent masses, and damping coefficient D associated with each
mass [3-1]. The linearized equations of the complete rotor system by ignoring
damping factor can be summarized as
SG:
𝑑𝑑�∆ωsg �
𝐾𝐾4𝑆𝑆𝑆𝑆
𝑑𝑑𝑑𝑑
=
𝑑𝑑(∆ω1 )
𝐾𝐾21
=
𝑑𝑑𝑑𝑑
𝑑𝑑(∆ω2 )
=
𝑑𝑑𝑑𝑑
2HSG
2H2
𝐾𝐾4𝑆𝑆𝑆𝑆 +𝐾𝐾𝑠𝑠
2HSG
�∆𝜔𝜔sg �𝜔𝜔0
Turbine 1:
2H1
𝐾𝐾21
(Δσ4) -
(Δσ2) -
(Δσ1 ) +
𝐾𝐾21
2H1
(Δσ1)
𝑑𝑑(∆𝜎𝜎1 )
Turbine 2:
𝐾𝐾23
2H2
(Δσsg)
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
𝐾𝐾 +𝐾𝐾21
2H2
(Δσ2)
𝑑𝑑(∆𝜎𝜎2 )
=
(Δσ3)
𝑑𝑑(∆𝜎𝜎3 )
=
𝑑𝑑𝑑𝑑
Turbine 3:
𝑑𝑑(∆ω3 )
=
𝑑𝑑𝑑𝑑
𝐾𝐾32
2H3
(Δσ2) +
𝐾𝐾34
2H3
𝐾𝐾 +𝐾𝐾34
(Δσ4) - 32
(∆𝜔𝜔3 )𝜔𝜔0
2H3
𝑑𝑑𝑡𝑡
Turbine 4:
𝒅𝒅(𝚫𝚫𝛚𝛚𝟒𝟒 )
𝒅𝒅𝒅𝒅
=
𝑲𝑲𝟒𝟒𝟒𝟒𝟒𝟒
𝟐𝟐𝐇𝐇𝟒𝟒
(Δσsg) +
𝑲𝑲𝟒𝟒𝟒𝟒
𝟐𝟐𝐇𝐇𝟒𝟒
(Δσ3) -
𝑲𝑲𝟒𝟒𝟒𝟒𝟒𝟒 +𝑲𝑲𝟒𝟒𝟒𝟒
(∆𝝎𝝎𝟒𝟒 )𝝎𝝎𝟎𝟎
𝟐𝟐𝐇𝐇𝟒𝟒
=
= (∆𝜔𝜔1 )𝜔𝜔0
(Δσ3) - 23
(∆𝜔𝜔2 )𝜔𝜔0
𝑑𝑑(∆𝜎𝜎sg )
(Δσ4)
𝒅𝒅(𝚫𝚫𝝈𝝈𝟒𝟒 )
𝒅𝒅𝒅𝒅
=
Natural Frequencies of the Shaft System
The natural frequencies of the shaft system of the SG can be calculated by
writing the rotor system equations in the state-space form 𝑥𝑥̇ = 𝐴𝐴𝐴𝐴. The state
variables are thus the speed deviations ∆𝜔𝜔i and the rotor angle Δσi with i = 1 to 5
(four turbines and one SG). The elements of the state matrix A of the rotor
system depend on the torsional stiffness coefficients, the inertia constants of the
individual masses, and the generator synchronizing torque coefficient Ks. The
parameters of an example complete rotor system are shown in Table 3-2.
 3-20 
0
Table 3-2
Inertia constants and torsional stiffness coefficients of rotor system
H (s)
H1= 0.124
H2= 0.232
H3= 1.155
H4= 1.192
HSG=0.855
K (pu)
K12= 21.8
K23=48.4
K34=75.6
K4SG= 62.3
Ks=1.98
The eigenvalues of matrix A give the natural frequencies of the shaft system. Considering the parameters given in Table 3-2, matrix A is
A=[
0
0
0
0
0 -87.9032
87.9032
0
0
0
0
0
0
0
0 46.9828
-151.2931 104.3103
0
0
0
0
0
0
0
0
20.9524
-53.6797 32.7273
0
0
0
0
0
0
0
31.7114
-57.8440 26.1326
0
0
0
0
0
0
0
0
36.4327 -37.590
376.9910
0
0
0
0
0
0
0
0
0
0 376.9910 0
0
0
0
0
0
0
0
0
0 376.9910 0
0
0
0
0
0
0
0
0
0 376.9910 0
0
0
0
0
0
0
0
0
0 376.9910 0
0
0
0
0]
 3-21 
0
0
Since we are considering a rotor with five masses, there are five oscillation modes.
The natural frequencies, as given by the imaginary components of the eigenvalues
of the matrix A, are 1.611 Hz, 16. 376 Hz, 24.123 Hz, 30.326 Hz, and 43.996
Hz.
Changing Control Gains and Their Impacts on the Oscillation
Frequency of the System
This subsection studies the impact of controller gains on the oscillation
frequencies of the system. The oscillation frequencies of different parameters are
measured by changing the gains of real power controllers. The oscillation
frequency is measured for different parameters as shown in Table 3-3. 𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆 , 𝑓𝑓𝑆𝑆𝑆𝑆 ,
and 𝜔𝜔𝑆𝑆𝑆𝑆 are the mechanical torque, the frequency, and the speed of the SG,
respectively. In addition, 𝑓𝑓𝑖𝑖𝑖𝑖𝑖𝑖 , 𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖,𝑔𝑔𝑔𝑔 , and 𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 are the frequency and real
power of the grid-supporting units and the real power of grid-forming unit,
respectively. This value of inverter frequency is however calculated at the terminal
of the inverter, outside the control architecture. The parameters shown in Table
3-3 are defined in Figure 3-3 and Figure 3-8.
Table 3-3
Oscillation frequencies of an inverter-dominated power system
Oscillation frequency of different variables by changing C1and C2 (Hz)
Gridsupporting
unit gains
𝐺𝐺1 =10
C1=1
𝐺𝐺1 =10
C1=5
𝐺𝐺1 =10
C1=10
Quantity
C2=1.25
C2=5
C2=10
𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆
1.11
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
𝑓𝑓𝑖𝑖𝑖𝑖𝑖𝑖
1.1, 30.59
1.05, 31.5
1.1, 31.8
30.44
30.7
30.7
𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 𝑔𝑔𝑔𝑔
1.11, 30.1
1.1, 30.9
1.1, 31.9
𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆
1.1
1.1
1.1
𝑓𝑓𝑆𝑆𝑆𝑆
1.1
1.1
1.1
1.1
1.1
1.1
𝑓𝑓𝑖𝑖𝑖𝑖𝑖𝑖
1.1, 32.79
1.1, 31.2
1.1, 31.8
30.55
31.7
31.9
𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 𝑔𝑔𝑔𝑔
1.1, 32.56
1.1, 31.7
1.1, 31.8
𝑇𝑇𝑚𝑚𝑆𝑆𝑆𝑆
1.1
1.1
1.1
𝑓𝑓𝑆𝑆𝑆𝑆
1.1
1.1
1.1
1.1
1.1
1.1
𝑓𝑓𝑖𝑖𝑖𝑖𝑖𝑖
1.1, 31.44
1.1, 31.63
1.1, 31.4
31.5
31.54
31.5
𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 𝑔𝑔𝑔𝑔
1.1, 31.5
1.1, 31.56
1.1, 31.5
𝑓𝑓𝑆𝑆𝑆𝑆
𝜔𝜔𝑆𝑆𝑆𝑆
𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 𝑔𝑔𝑔𝑔
𝜔𝜔𝑆𝑆𝑆𝑆
𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 𝑔𝑔𝑔𝑔
𝜔𝜔𝑆𝑆𝑆𝑆
𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖 𝑔𝑔𝑔𝑔
 3-22 
0
The steady-state simulation results for different values of controller gains show
that when the real power controller gains change between their original design
value (C1=1 and C2=1.25) and 10, the oscillation frequency of the SG’s real power
is 1.1 Hz, which is close to the oscillation frequency of the SG calculated from
rotor equations (1.611 Hz). In addition, the oscillation frequencies of real powers
of the inverters are approximately 1.1 Hz and 31 Hz, which are also close to the
oscillation frequencies of the SG calculated from rotor equations (1.611 Hz and
30.326 Hz).
In addition, Figure 3-22 shows the real power of the all generation units when
the controller gain C1 has a value greater than 10 (e.g., C1=15) and C2=20. As it
shown in this figure, there is an oscillation frequency in the real power of
inverters and the SG. All the generation units have the oscillation frequency close
to 30 Hz, which is close to the oscillation frequency of the SG calculated from
the shaft system (30.326 Hz). In addition, the real powers of the GF unit and the
SG have the oscillation frequency of 1.1 Hz (1.611 Hz), which is close to the
calculated oscillation frequency of the shaft system. The frequencies of the gridsupporting units also oscillate at 1.1 Hz.
While our results in these particular case studies do not show resonance or
instability due to the proposed power sharing strategy, some high frequency
oscillations, such as those shown in Figure 3-22(a), have a large magnitude (50
MW peak to peak at 30 Hz) which is likely to be prone to exciting rotor modes.
More studies are needed to achieve conclusive evidence about such stability
concerns.
 3-23 
0
Figure 3-22
Real power of the system components and zoom-ins. (a) the real power of three
inverters and the SG (b) the oscillation frequency of the real power of GS unit (c)
the oscillation frequency of the real power of the GF unit (d) the oscillation
frequency of the real power SG.
 3-24 
0
Performance Comparison Between Three-Phase and PositiveSequence Inverter Models
In this subsection the performance of the EMT-type inverter models is
compared with the positive-sequence models described in chapter 2.
Figure 3-23 shows the results of both models. In this study, the disturbance
applied is a load change. The ratios for the droop gains in the positive sequence
model are the same as the ratios in the EMT models. In steady state after the
load change, both methods effectively perform power sharing. In positive
sequence the frequency recovers to 60 Hz and power sharing is performed in only
0.2 s after the load change, while for the EMT model it takes 1.2 s. This is
because the control in the EMT model relies on small variations of the angles. A
0.05 rad change in angle, which occurs very quickly, completely changes the
power sharing (at the same time it can quickly make the system unstable).
300
300
200
100
100
0
0
2
4
6
8
Voltages (pu)
1.04
1.02
10
Time (s)
12
7
6.5
6
5.5
5
14
16
18
20
1.02
1
0.98
0.98
60.2
4.95
0
2
4
6
8
5
10
Time (s)
5.05
12
5.1
14
5.15
16
18
20
60.2
60
59.9
59.8
59.8
0
2
4
6
8
5
200
100
0
0
2
4
6
8
5.5
10
Time (s)
12
6
6.5
14
(a)
7
16
1.02
18
20
5
10
Time (s)
5.5
6
12
14
6.5
7
16
18
20
18
20
18
20
1.04
1.02
1
1
0.98
60.2
5
4.95
0.98
60.1
60
300
100
1.04
1.04
1
200
0
Voltages (pu)
0
Frequency (Hz)
Real Power (MW)
200
Frequency (Hz)
Real Power (MW)
300
0
2
4
6
8
10
Time (s)
5.15
5.1
5.05
12
14
16
60.1
60.2
60
60
59.9
59.8
59.8
0
2
4
6
8
5
5.5
10
Time (s)
12
6
6.5
14
7
16
(b)
Figure 3-23
From top to bottom: Real powers of generation units, bus voltages of generation
units, and system frequency measured at the buses of generation units in (a) PSPS
method and (b) the proposed method.
 3-25 
0
0
Section 4: Balancing and Market
Operations of an All Inverter
System
The previous chapters focused on the dynamics and stability performance of an
all IBR system. This chapter focuses on steady state operations and market
operations. The feasibility of a 100% renewable power system has been discussed
for many regions. For example, the recent bill SB100 in California committed to
100 percent clean energy for the state by 2045 [4-5] (note clean energy includes
non-inverter based resources, but it is expected that variable energy resources
(VER) such as wind and solar power will make up a large portion of the
requirement). The Hawaii Public Utilities Commission mandated the state to
achieve 100 percent renewables (again, this could include non-inverter based
resources) by 2040 [4-6]. However, there still is a long way to go for the current
utilities to be converted to 100% VER power systems, where wind and solar may
make up large portions of the annual demand. If these systems were to be
operated at a very high renewable energy penetration level, it is very likely that
they reach 100% VER in some hours of the year 1.
This chapter investigates two subjects. First, we investigate how the system
would operate with periods of very high VER penetrations, such that penetration
levels, or at least available energy from wind and solar, may reach 100% during
some periods of the year. In this first section, we use a production cost simulation
tool to demonstrate how current unit commitment and economic dispatch
models might behave at such a high renewable penetration level, and study the
associated issues related to scheduling, renewable curtailment, reserve
requirements, and pricing. Second, we describe how the existing power system
operation paradigms might change if the system had 100% renewables all the
time, with wind and solar providing much or all of the demand (with some
potential ability to store energy or shift demand required). This section is focused
on a conceptual discussion rather than any new modeling, but should provide
numerous ideas for future research.
1
Note that the work in this chapter focuses more on the variability and uncertainty related issues,
and not the fact that these resources are inverter based, and so the focus here is on variable energy
resources (VER) rather than inverter based resources (IBR). While these may be the same type of
resource (e.g. wind and solar PV) as the IBR investigated in the remainder of the report, the more
important aspect is their variability.
 4-1 
0
Note both of these subjects focus only on short term operations (days and
minutes) and steady-state balancing and dispatch, and does not examine issues
such as resource adequacy, network capacity requirements, revenue sufficiency for
generation, system protection or system stability, the last of which is investigated
in other parts of this report. These issues also need to be studied, and will be
described in future work. The purpose here is less to focus on specific results
from the analysis, but rather the methodology and types of results that are being
examined, to determine how such a system may operate and the important
factors that will need to be considered.
System Operation with 100% VER During Some Periods of a
Week
In this section, the utilization of state-of-the-art production cost simulation tools
for a system that reaches 100% generation from VER for some periods during a
day, is investigated. Results from production cost modeling/operational
simulation are investigated, where there is sufficient energy available from VERs
to meet 100% of demand in some hours, and typical unit commitment and
economic dispatch procedures as used today are carried out. Here, that includes
an hourly day ahead security-constrained unit commitment (SCUC) using
forecasted information representative of current forecasting performance, and
then a five-minute real time security-constrained economic dispatch (SCED)
with realized values. This mimics a simplified version of how U.S. independent
system operators and regional transmission organizations operate today and
allows us to explore challenges with both variability (system conditions are
changing through time) and uncertainty (system conditions are different from
what was expected in advance). The aim is to understand system operations if the
current status quo procedure were continued to be used to operate such a system.
Test System and Data Used
Four test cases have been developed for analysis, with the average renewable
energy generation for the week ranging from 13.3% to 53.5% of total demand.
Details on the test cases can be found in Appendix A – they are based on the
IEEE RTS-96 system [4-7], with modifications provided by NREL [4-8]. The
installed capacity is provided in Table 4-1. In case 2, the renewable energy
penetration is high, but the nuclear units are set to must-run in the simulation,
resulting in likely curtailment. In case 3, the nuclear units are allowed to be
cycled on and off with associated commitment constraints (long start-up times,
minimum run times, and minimum down times) so that they can be utilized only
when their energy is needed. In case 4, the nuclear resources are removed
completely. The hydro energy in case1, case2 and case3 was modeled as timeseries input.
 4-2 
0
Table 4-1
Generation Capacity (MW) in Each Case (Peak load: 8192 MW)
Cap. (MW)
CC
CT
STEAM
Hydro
Nuclear
VER
Case 1
3550
1545
1362
1000
400
2133
Case 2&3
3550
1645
830
1000
400
11948
Case 4
3550
1645
0
0
0
11948
 4-3 
0
For each case, a day ahead (DA) SCUC run was made using a DA forecast of
wind, solar and load, to determine unit commitment of all resource requiring
more than an hour of start-up notification. Then, real time (RT) SCED was ran
based on the 5-minute realized wind, solar and load to determine the actual
dispatch of the resources. A comparison of available VER, based on the day
ahead (DA) forecast, assumed to be made at noon on the previous day, and
system demand for case 1 and case 2 is shown in Figure 4-1 (note that cases 3
and 4 have identical VER inputs as case 2 and demand is the same for all).
Similarly, Figure 4-2 shows the RT available resources at a 5-minute resolution
for VG and system demand. Compared with the DA forecast, there are more
intervals in RT on Day 1, Day 6 and Day 7 in which the VER is greater than the
system demand; this is due to a forecast error underestimating RT; in other
periods, this error may overestimate VER in DA so this would also need to be
considered but is not shown in the data used here. The mean absolute error
(MAE) for DA VER forecast is 212 MW (approximately 10%) and 662
(approximately 5%) MW in case 1 and case 2, respectively; the lower error in the
second case is due to the diversity in the renewables reducing the relative error as
errors at individual plants are not perfectly correlated.
Note that in this first set of runs, no reserves are carried to manage contingencies
or to manage forecast error from DA to RT; this is examined later. These results
will provide simple insights on commitment and dispatch of such large amounts
of VER and the potential implications, which we will later build on to show how
the imbalances and economic challenges (including curtailment) can be mitigated
through additional procedures, like additional reserve.
Figure 4-1
Comparison of VG and load in case 1 and case 2 as the input data in DA
 4-4 
0
Figure 4-2
Comparison of VG and load in case 1 and case 2 as the input data in RT
Results for Case with No Reserves
Some of the more interesting results to examine for this type of study relate to
how different resources would operate, whether there are violations of supplydemand balance, and how different assumptions about resource flexibility impact
results. Figure 4-3 and Figure 4-4 show the real-time penetration levels in the
four cases for VER and thermal units respectively; this is the outcome of the
model and includes any curtailment or load shortfalls required to balance supply
and demand while respecting generation constraints such as minimum up and
down time, startup time and minimum stable output level. The transmission
network is also included, using a DC power flow. The tool used here is the
Power Systems Optimizer tool by Polaris. 2
In case 1, the renewable energy penetration level is low, and the percentage of
thermal generation is relatively less variable throughout the week. In case 2, there
is significant curtailment when VER levels are high, due to the must-run nature
of nuclear and the commitment constraints of the fossil resources. By allowing
nuclear to be dispatchable in case 3, the system has higher renewable energy
generation during afternoon hours where solar generation is high; however, the
fact that fossil and nuclear units cannot be turned off due to long start up times
and a need to be kept online for later needs leads to VER levels that cannot reach
100%. In addition, thermal generators were committed in DA, and the
commitment decision was fixed in RT. As a result, thermal generation was still
online when the VER is greater than demand during some hours of the day; this
forecast error caused a reduction in VER output. If the system operators could
manually decommit the thermal units in real-time in those hours, the percentage
2
Details for this tool can be found at http://psopt.com/pso/.
 4-5 
0
of VG can be 100%. This may show a need for future systems to potentially make
decisions closer to real time as forecasts are often more accurate. Hydro was
counted as VER in the results; it has fixed output profile in the data used here,
such as would be the case with run-of-river hydro. Case 4 shows that allowing for
the removal of the nuclear provides additional flexibility to the system and
reduces the curtailment levels of wind and solar, allowing for 100% penetration
(note again we have no reserve requirements in these simulations); the removal of
hydro would also impact the results by changing the shape of the VER.
RT VER Percentage
120
case 1
case 2
110
case 3
case 4
100
90
80
Percentage (%)
70
60
50
40
30
20
10
200
400
600
800
1000
1200
1400
1600
5min intervals in one week
Figure 4-3
Real-time VER penetration percentages for different scenarios
 4-6 
0
1800
2000
RT Thermal Percentage
100
case 1
case 2
90
case 3
case 4
80
70
Percentage (%)
60
50
40
30
20
10
200
400
600
800
1000
1200
1400
1600
1800
2000
5min intervals in one week
Figure 4-4
Real-time thermal energy percentages for different scenarios
The next results examine violations in supply-demand balance. A load violation
occurs when the power balance equation in the RT cannot be met. In practice,
this may result in area control error (ACE), frequency error, or if large enough,
involuntary load shedding. However, these imbalances would more than likely
result in reserve shortage had we modeled reserve in this first set of simulations.
In the high renewable energy cases, load violation occurred in the form of load
shortages (insufficient capacity to meet demand). The system does not have
sufficient flexibility to ramp up the existing generation fleet to meet large changes
in net load. The reasons why the load violation could not be relieved by release of
wind and solar curtailments were because: 1) the network constraints prohibited
the transmission of curtailed energy to the destination, and 2) the DA
commitment decision was passed to and fixed in RT where resources couldn’t be
turned on in time to manage a forecast error. The balance violations for each case
in DA and RT are shown in Table 4-2.
Table 4-2
Load violation and renewable energy curtailment analysis
Case 1
Case 2
Case 3
Case 4
RT Violations (GWh)
0.3
14.1
25.6
87.8
RT load shortfall (% of
demand)
0.04%
2.4%
4.3%
14.7%
RT Renewable Curtailment (%
of available generation)
2.5%
40.0%
37.2%
26.0%
 4-7 
0
Balancing violations were observed for all cases in RT. The RT violations were
calculated by the summation of RT violations in each 5-min interval divided by
12 (one hour has 12 five-minute intervals). The total system demand in this week
was 596 GWh. The ratios of RT violation quantity to the total system demand
are shown in the second row of Table 4-2. At case 4, the RT load violations can
be close to 15% of the total system demand, which would be unacceptably high.
It is observed in the table that the quantity of balancing violation in the real-time
is higher when the renewable energy penetration is allowed to get very high in
the model; this shows that one may still need generators committed in DA to
manage variability and uncertainty in RT and shows the importance of properly
set operating reserve requirements for VER and load forecast error. Table 4-2
also shows the percentage of RT renewable energy curtailment for each case. In
the low renewable energy case (case 1), the percentage of curtailment is low. Case
2, case 3 and case 4 have the same available VER, but case 2 has more VER
curtailment than case 3 because nuclear energy is must run, and case 4 has less
VER curtailment than both as the nuclear and hydro were not part of the
solution to cause minimum generation constraints. While the curtailment rate
decreases from case 2 to case 4, the reliability in terms of load balance violations
also decreases. This is due to there being less dispatchable resources available in
RT to accommodate the variability and uncertainty that occurs.
The results shown here may show that in future high VER systems, there is a
trade-off between reliability and the ability to integrate large amounts of VER
without curtailment – this will depend on the specific flexibility of the fleet, and
also will require operating reserves and other factors that may be able to mitigate
the reliability violations. Other mitigation factors such as utilization of energy
storage, which can potentially support reliability and reduce curtailment while
not necessarily adding carbon to the mix, will also impact outcomes. Finally, the
results for the simulations show here are for a system with centralized DA and
RT clearing mechanisms such as in North American ISO/RTO regions or in
most vertically integrated utilities. In other regions, such as Europe, the decision
to commit and decommit or to curtail may be taken by market participants,
where they have to provide sufficient energy to balance some supply requirements
they have. As such, alternative methods to commit and dispatch resources may
need to be evaluated in future work. The results in these examples are highly
simplified and were presented primarily to provide a high-level insight into the
potential for load imbalances and curtailment potential on these very high
penetration VER systems. They primarily show that mitigation strategies, many
of which are already being implemented in regions across the world, are required
to avoid load balance and reliability violations and VER curtailment. We next
discuss some of the most beneficial mitigation strategies (many others have been
presented in other EPRI research) and some unique phenomena that may occur
during steady-state and market operations of these very high VER penetration
systems.
 4-8 
0
Selection of Curtailment Resources
Renewable energy resources are usually curtailed for economic reasons due to
local congestion or system balancing requirements to manage the oversupply
issues. During hours when the demand is low (e.g., midnight) or renewable
energy output is high (e.g., summer afternoon), the output of VER is reduced far
below the available energy. Curtailing renewables results in a lost opportunity for
clean resources to generate carbon-free power. When more renewables are
integrated into the system, oversupply may happen more frequently, and
curtailment of VER may become more common practice. While VER
curtailment occurs in measurable ways on existing systems, it is most often due to
transmission congestion where one or a few VER resources are able to manage
the congestion specifically. In the above examples, VER curtailment is occurring
much more frequently due to oversupply in larger regions where multiple VER
plants must be curtailed to resolve the load balance. With so many VER that can
be used to resolve this imbalance, and all operating at generally the same cost
($0/MWh), how to choose which resources to curtail and when becomes an
important factor that has not been considered in great detail before.
During times of oversupply, the market clearing engines competitively select the
highest cost power resources to be curtailed. VER often offer energy costs into
the market that reflect their willingness to continue producing. These values can
be low positive numbers to reflect variable O&M costs, zero, or negative to
reflect production-based subsidies that the resources receive when producing.
These same decisions and costs are reflected in non-market regions.
When a resource submits zero or negative valued cost offers, the optimization
engine will try to use the resource’s capability as much as possible. Regardless of
the offer of VER or other resources, all the resources are compensated with the
uniform market clearing price, which in existing markets is usually positive for
most parts of the day. However, when the system has 100% renewables for large
periods of time, the market clearing price could often be zero or negative. 3 When
this occurs for increasing portions of the year, revenue of all resources for energy
provision may be significantly decreased, and it is possible that new offering
strategies by resource owners as well as new market designs and products by the
ISO are employed.
As VER curtailments occur more as a solution to large-region over supply
balance resolution, the selection of units to be curtailed is an interesting issue to
be studied. When VER curtailments occur for local congestion, it is usually
obvious which VERs can be curtailed based on their contribution to the
congested lines. But for oversupply, they may all be able to resolve the issue
through curtailment in the same manner and for the same cost. We selected oneday data from Case 4 for demonstration. Figure 4-5 shows the load, available
VER, and actual production of VER in a day. VER oversupply occurred from
Note that, as tax credits and other subsidies expire, the negative pricing issue may be reduced or
disappear.
3
 4-9 
0
8am-3pm in the day, and as a result the oversupplied VER was curtailed to meet
the demand in this period.
Figure 4-5
Comparing the load and VER production in real-time for one day
In the above test case, we assume that all the renewable resources have zero
energy cost. 4 Figure 4-6 and Figure 4-7 show the curtailment of individual wind
and solar units respectively. Since all the units have the same curtailment costs,
the optimization engine will not select resources based on costs. Instead, there
may be multiple equivalent solutions to the problem, and the current UC/ED
engine must only find one. It is necessary to find out proper rules to prioritize the
VER curtailments when its penetration level is high and costs to resolve the
imbalance are the same. These may need to be determined outside the market to
avoid potentially unfair treatment of VER plants in the market.
In reality, there are some specific rules that guide the VER curtailments. For
instance, wind plants in Germany rolling off the first set of subsidy contracts are
going merchant with positive marginal costs (to cover the cost of extended life
warranties and servicing from OEMs). These will naturally curtail early in such
an event. In addition, there are systems with curtailment rules already in place
based connection offer priority schemes, e.g. non-firm or flexible connections.
Other utilities may curtail in order of their interconnection date. A simple
market solution would be that all VER that can be curtailed to solve the solution
In ISO markets, the VERs may not all have the same offers, and the different offers being
provided by different VER can determine who gets curtailed. However, as the true cost of VERs is
essentially the same, and may often be the case that many VER have the same offer costs, this
condition is still worth further study.
4
 4-10 
0
be curtailed pro-rata. This may not always occur automatically through existing
market clearing algorithms.
Figure 4-6
Curtailment for wind resources in one day
Figure 4-7
Curtailment for PV resources in one day
Electricity Price Behavior
The wholesale electricity markets operated by ISOs use locational marginal prices
(LMP) to reflect the value of electric energy at different locations, accounting for
the patterns of load, generation, and the transmission line constraints. Resources
are paid LMP at their location multiplied by their energy output for all hours
 4-11 
0
that they generate. It is possible that VER are the marginal unit, and as a result
set the system LMP. On systems with very high penetrations of VER, the LMP
may become zero or negative for increasing portions of the year. We explore
these conditions with the cases described earlier. Table 4-3 shows the hourly
load, generation dispatch, LMP and total costs for case 4 in one day. The
demand was 100% supplied by renewables from hour 08:00 to 13:00, and the
LMPs and total costs are zero in this period. However, it was observed that at
hour 14:00, the LMP is zero, but the total cost is non-zero. At this hour, the
VER penetration is still high (97%), but some thermal generation units were still
required. The reason is that the VER output is expected to decline after hour 14.
Due to ramp up time limits of thermal units, the system cannot call up them
immediately when they are needed. As a result, the SCUC will select the thermal
units to pre-ramp up to meet the upcoming VER output declining. In traditional
marginal cost pricing (sometimes called traditional LMP), the price is set by the
incremental cost to serve the next increment of load, which in any case where
there is VER curtailment, would be the VER unit. This is true even when other
units are online but are at minimum generation. In hour 14, the marginal unit is
still the VER unit, so the LMP is still $0/MWh. However, when units are
producing energy at costs above the LMP as directed by the ISO (and not selfscheduled), they must be made whole. This results in ‘uplifts’ to the system, and
“make whole payments” are enabled to compensate the monetary loss of the
thermal generator that was online. 5 Many of such intervals with zero LMP and
non-zero costs were observed in the simulations. These results show that overall
revenues could be significantly decreased in the energy market both for VER and
other resources. This may warrant new offering strategies by asset owners or new
market designs by ISOs. In fact, many ISOs have recently implemented new
pricing designs which may allow certain sets of resources at minimum generation
to set price and for additional costs like start-up and no-load costs to be factored
in to the price [4-9]. It is unclear how these designs may be impact future
systems with very high VER penetrations, and whether other revenues through
ancillary service markets, capacity markets, or out-of-market contracts may
provide the needed revenue to remain in the market and recover fixed and
variable costs. Further research into this is definitely required.
5
Note that in most cases, make whole payments are netted across a day or commitment period, so
it may only receive the make whole payment if its profits were negative throughout the entire day
or commitment period.
 4-12 
0
Table 4-3
Existence of intervals with zero system price (marginal cost) but non-zero costs
Time
Load
(MW)
Thermal
Gen (MW)
VER Gen
(MW)
LMP
($/MW)
Total
Cost ($)
2024.04.08 00:00
3100
2838
263
31
79069
2024.04.08 01:00
3073
2862
211
31
79861
2024.04.08 02:00
3077
2759
319
31
76580
2024.04.08 03:00
3150
2664
486
30
73700
2024.04.08 04:00
3331
2785
546
31
77414
2024.04.08 05:00
3554
2124
1430
28
59210
2024.04.08 06:00
3732
833
2899
27
25829
2024.04.08 07:00
3879
51
3827
26
1963
2024.04.08 08:00
4001
0
4001
0
0
2024.04.08 09:00
4069
0
4069
0
0
2024.04.08 10:00
4070
0
4070
0
0
2024.04.08 11:00
4043
0
4043
0
0
2024.04.08 12:00
4011
0
4011
0
0
2024.04.08 13:00
3963
0
3963
0
0
2024.04.08 14:00
3927
112
3815
0
31469
2024.04.08 15:00
3896
1008
2888
27
198166
2024.04.08 16:00
3901
2051
1850
30
55684
2024.04.08 17:00
4131
2620
1511
36
91642
2024.04.08 18:00
4417
2758
1659
107
88381
2024.04.08 19:00
4355
2532
1823
36
71710
2024.04.08 20:00
4014
2033
1981
28
55616
2024.04.08 21:00
3603
1376
2227
23
37914
2024.04.08 22:00
3293
903
2390
13
25625
2024.04.08 23:00
3159
708
2451
23
18892
Figure 4-8 compares the average DA LMP across the network for one week for
case 1 (low VER) and case 4 (high VER). It is observed that even in the low
VER case, the LMP could be zero, as shown in hour 84 and 85 for case 1. In
these hours, there existed VER curtailment due to the commitment status of
thermal units (for example, there are minimum on/off time requirements for
thermal units). In the high VER case, the LMP is zero during much more hours.
In addition, the LMP switches from zero to high values more frequently, because
quick start units with higher marginal costs will be called on more frequently or
penalty prices from infeasibilities (which will most likely be reserve shortages)
that occur more often. As a result, the market may have significantly higher price
volatility at higher VER penetrations.
 4-13 
0
DA LMP
100
DA LMP for case 1
90
DA LMP for case 4
80
70
Price ($/MWh)
60
50
40
30
20
10
0
20
40
80
60
100
120
140
160
Hour in one week
Figure 4-8
DA LMP in one-week period in the system
Figure 4-9 shows the real-time LMP for case 4. The RT LMP switches between
zero and a very high penalty price (≥$1000/MWh 6) very frequently. Compared
with the DA price, the RT LMP has more extreme values. The reason is that in
real-time horizon, the system condition is more variable and has less options to
correct errors than are available in the DA (i.e., most units cannot be called on or
off in RT). As a result, there may exist lots of violations on these systems. These
load violations would typically result in ACE, (or frequency deviations in
practice), but if large enough could lead to involuntary load shedding, but most
often would result in being short on reserve. Having such high prices due to these
administratively set penalty prices has as much implications for revenue adequacy
as do the large increase in zero or negative prices. In some cases, it may balance
out the average price to similar values as to what they are in existing lower VER
penetration systems. More research into appropriate values and how often these
penalty conditions occur on higher VER penetration systems is required.
These penalty prices are typically based on reserve shortage price values. They typically range from
a few hundred dollars per MWh to as much as $2,000/MWh.
6
 4-14 
0
RT LMP
2500
2000
Price ($/MWh)
1500
1000
500
0
200
400
600
800
1000
1200
1400
1600
1800
2000
5min Intervals in one week (case4)
Figure 4-9
RT LMP in one-week period for case 4
The revenue of the thermal units can be directly impacted by these potentially
large changes in LMPs. The significant increase in zero-or negative LMPs can
cause thermal units to lose money in the market because its revenue is zero but
the cost might not be zero. On the contrary, when the LMP is set to a high
penalty price, a thermal unit’s revenue in the market can be much higher than its
operation cost. Table 4-4 shows the cost, revenue and net benefit in DA and RT
for case 4 in one week. The revenue was calculated by the summation of the
product of LMP and thermal unit dispatch in each interval, and was done
separately for both DA and RT which is different from the two-settlement
revenue used in actual ISOs. The net benefit was the difference between the
revenue and the cost. In DA, the revenue was much smaller than the cost, thus
the net benefit was negative. The reason for small revenues in DA was because
the LMP in DA was relatively small. The revenue in RT was calculated by the
two-settlement pricing mechanism, i.e. the revenue is the product of RT LMP
and the quantity difference between DA and RT dispatch. When the RT (hourly
integrated) dispatch is less than the DA schedule, the revenue of a generator is
negative in RT. The RT revenue in Table 4-4 was a negative number whose
absolute value is large. This was caused by the large LMPs with penalty values
($1000/MWh) in RT. Large make whole payments were needed to compensate
the generators in this case. The assumptions of not including reserve to allow for
more resources to accommodate the forecast uncertainty and the lack of virtual
trading would significantly alter these results and should be looked at further.
Nonetheless, compared to the current situation, RT markets may become even
more volatile and an even more important source of revenue for certain
technologies. Additional research on price setting, settlement rules, additional
market products, and offering strategies and allowance should be conducted to
ensure that resources needed for reliability are able to recover costs without
 4-15 
0
excessive costs incurred by consumers on these very high VER penetration
systems. Further analysis on the revenues such as the impact of price caps and
other factors is also warranted.
Table 4-4
Cost and Revenue for case 4 (two-settlement pricing mechanism was applied while
calculating the revenue)
Cost ($)
Revenue ($)
Net benefit ($)
DA
9.5M
1.6M
-7.9M
RT
8.6M
-135M*
-143.6M
The absolute value of the revenue is large because the RT LMP is the penalty value
(>1000/MWh) in many intervals.
*
Effects of Enabling Technologies
Demand response and energy storage resources are playing an increasingly
important role in power systems to balance the power supply and demand and
create a more flexible and reliable grid. Demand response providers with the
ability to aggregate customers capable of reducing their electric demand can
participate in the wholesale markets and provide the flexibility to adjust their load
in response to market schedules and dispatches. Energy storage resources can
either provide energy (in discharging mode) or consume energy (in charging
mode) to the power grids. Both resources are also typically very responsive, able
to adjust power output in short periods of time (i.e., they have very high ramp
rates). Thus, they have more flexibility in the electricity market and power system
operation.
In this section, we mainly focused on how energy storage resources can impact
system balancing, the curtailment of VER and the LMP when the system has
high levels of VER. To this end, we added 1883 MW (about 11% of the total
generation capacity) energy storage resources with maximum energy of 18835
MWh (10 hours of energy) to case 4. A comparison of dispatch results of the
system with and without energy storage resources is shown in Table 4-5. By
adding 11% storage to the system, the load violation ratio reduced from 14.7% to
0.9%, and the VER curtailment quantity reduced from 120 GWh (26%) to 73
GWh (16%). The reason for the reduced curtailment is that when there is more
supply than demand (which usually causes curtailments), the excess electricity
generation can be used to charge storage. Figure 4-10 compares the DA and RT
LMPs for case 4 with and without energy storage resources being added on it.
The average DA LMP reduced from $24.2/MWh to $13.2/MWh, and the
average RT LMP reduced from $2529.3/MWh to $550.8/MWh. In addition,
the price spikes also have significant reductions. For instance, the RT intervals
with price spikes (higher than $1000/MWh) significantly reduced from 979 to
210 5-minute intervals.
The RT production costs for the system with and without energy storage
resources are compared in Table 4-5. The total generation cost for the original
case was $8.6M in the studied week. When adding 11% energy storage devices,
 4-16 
0
the weekly generation cost was reduced to $4.4M (decrease by 49%); note this
included 10 hours of energy, which is a longer duration than typical storage that
is currently being built; future work may look at different power versus energy
ratios. A comparison of the hourly aggregated generation cost between these two
cases is shown in Figure 4-12. In some hours, the cost with storage can be
higher, but for most of the hours the cost is significantly reduced. This reduction
in costs from a relatively small amount of ESRs is significant. It is primarily due
to the large charging/discharging hours we assumed for the energy storage
devices (they can charge/discharge at the maximum capacity for 10 hours), as
well as the reduced VER curtailment and thermal unit de-commitments.
Table 4-5
Comparison of solutions for the system with and without storage
Without Storage
Load violation in RT
87.8 GWh
(14.7% of load)
5.1 GWh
(0.9% of load)
Curtailment in RT
120 GWh
(26% of total available
VER)
73 GWh
(16% of total
available VER)
DA mean LMP
($/MWh)
24.2
13.2
RT mean LMP ($/MWh)
599.3
167.8
RT price spike
(>$1000/MWh)
intervals
348
248
RT Generation costs ($)
8.6M
4.4M
 4-17 
0
With Storage
DA LMP
600
DA LMP without storage
500
DA LMP with storage
Price ($/MWh)
400
300
200
100
0
20
40
60
80
100
120
140
160
Hour in one week
RT LMP
2500
RT LMP without storage
RT LMP with storage
2000
Price ($/MWh)
1500
1000
500
0
200
400
600
800
1000
1200
1400
1600
5min intervals in one week
Figure 4-10
Comparing LMPs with and without energy storage resources
Figure 4-11
A comparison of hourly aggregated operation costs in RT for one week
 4-18 
0
1800
2000
Determination and Impact of Reserve Requirements
Operating reserves refer to the generating capacity available above and below that
scheduled to meet demand in case the scheduled or forecasted supply or demand
of power is disrupted. A shortage of deployable active power reserve may cause
significant ACE, frequency deviation, reliability compliance violations, load
shedding, or even blackouts. In steady-state, VERs increase the variability and
uncertainty of the system and hence impact the amount of operating reserves that
need to be held to maintain system reliability. It is a challenge for system
operators to determine how much each reserve product needs to be increased
with high VER penetration levels [4-10][4-11]. Previous results in this study, as
mentioned, do not consider reserves, for a first order evaluation into economic
supply-demand balancing issues. However, in order to provide more realistic
results, we now also examine how reserve requirements impact and mitigate
issues for system operations at very high VER penetrations.
In this section, we conducted the study by adding four types of operating reserves
to case 4: regulation up reserve, regulation down reserve, spinning reserve, and
supplemental reserve. EPRI has developed a reserve determination tool called
Dynador [4-3] to calculate the system reserve requirement based on input system
demand and VER data. Similar concepts were used here to determine reserve
requirements as are used in that tool, though less detailed consideration was
given compared to the methods used within Dynador. Whereas Dynador
forecasts the reserve requirement for the following day or hour, based on
projected system conditions, here we used a relatively simple method to provide a
brief examination of how reserves help mitigate the issues described in the
previous sections. Dynador and similar methods have been shown to improve
upon the existing methods, but that was not the focus of this study. In this study,
the requirement for each type of reserve is calculated as follows:

Regulation up reserve
We adopted the method used in the Southwest Power Pool to calculate the
regulation up reserve [4-2]. The regulation reserve is determined by four
components: load magnitude, load variability, renewable energy resource
magnitude and renewable energy resource magnitude. The total regulation
reserve requirement is calculated by the summation of each component times
a coefficient, as shown in Equation 4-1:
up
RegReq
=
a up LF (t ) + bup [ LF (t + 1) − LF (t )] + cup RF (t ) + d up [ RF (t + 1) − RF (t )]
Eq. 4-1
where LF(t) is the load forecasting at time t, RF(t) is the renewable energy
resource forecasting at time t, and aup, bup, cup, and dup are coefficients to
determine the weight of each component. The typical values used in SPP of
aup, bup, cup, and dup is 1%, 1%, 5% and 10%, respectively, as shown in [4-2].
 4-19 
0

Regulation down reserve
The regulation down reserve requirement can be calculated using Equation
4-2:
down
RegReq
=
a down LF (t ) − b down [ LF (t + 1) − LF (t )] + c down RF (t ) − d down [ RF (t + 1) − RF (t )]
Eq. 4-2
where aup, bup, cup, and dup are coefficients to weight each component. Their
values were also set to 1%, 1%, 5% and 10%, respectively, in the simulations.

Spinning reserve
The spinning reserve is used to manage instantaneous contingency events on
the system, and typically in the US is required to respond within 10 minutes.
We set the spinning reserve requirement equal to the largest single
contingency (in MW) in the system, similar to many regions.

Supplemental reserve
Supplemental reserves must be able to become synchronized with the grid
and ramp to a specified output level within 30 minutes. Its requirement can
be calculated based on historical data. For example, in ERCOT it is
calculated by using the 70th to 95th percentile (depending on the risk of net
load ramping) of hourly net load uncertainty (load minus the estimated uncurtailed total output from Intermittent Renewable Resource) from the same
month of the previous three years. In ISO New England, it is set as 50% of
the second-largest system contingency. Due to data unavailability, we simply
use the ISO New England method for the supplemental reserve requirement
in the simulation.
Using the reserve calculation methods mentioned above, we can obtain the
requirement for each type of reserve in the test system. We assume here that
all of the reserves are provided by thermal generators, and VER cannot
provide operating reserves. By adding those reserve requirements, we rerun
the production cost model for case 4. A comparison of the renewable energy
percentages in real-time between the original case (i.e. case 4) and the new
case with calculated reserves is shown in Figure 4-12. It is observed that the
maximum renewable energy penetration is 57% in the new case, without any
100% VER generation intervals, which is less than the previous cases. This
result is as expected, because thermal generators have to be committed to
provide operating reserves even in the intervals where VER alone are
sufficient to meet the demand. Obviously, this may show the need for more
flexible thermal plants that have lower minimum generation levels, or energy
storage or demand response resources that could provide such reserves, and
thus allow for greater penetration of renewables. Also note that, as systems
get larger, the impact of largest contingencies typically gets smaller on a
percentage basis and therefore reserves may not have quite as large an impact.
It may also show the benefits of having VER provide various types of
operating reserve.
 4-20 
0
Figure 4-12
A comparison of the renewable energy percentage with and without operating
reserves for case 4
A summary of the studied case with four types of reserves is shown in Table 4-6.
Compared with the results in Table 4-4 (the “without storage” case), the load
violations in RT were reduced significantly by carrying reserves (note there are
significant reserve shortfalls instead). The average LMP in DA and RT and the
RT price spikes were also reduced (albeit with additional reserve shortage prices).
This indicates that the reserves in the system can help reduce price volatility and
improve the generation and demand balance. However, there is a cost for doing
so. The total production cost in RT increased from $8.6M to $12.6M.
Additionally, the curtailment ratio of VER was increased. This was because more
thermal generation (and less VER) was dispatched when reserves were
considered. While the VER input did not change, the VER curtailment
increased. The average RT prices and the total reserve shortage for the four types
of reserves are also shown in Table 4-6. The reserve prices were relatively high;
this was because of reserve shortages in many intervals where the reserve prices
were the penalty price, e.g. $1000/MWh. When not counting the reserve
shortage intervals, the average reserve price for regulation up, regulation down,
spinning and non-spinning is $2.4/MWh, $12/MWh, $1.8/MWh and
$0.2/MWh, respectively. The large amount of reserve violations and the high
reserve prices indicate that the conventional reserve determining method might
not be suitable in the VER case. For example, the regulation requirement
formulation from (1)-(2) depends on the demand variability. However, the
variability of net demand should be more significant in this case. As a result, a
new reserve determination tool such as the Dynador is required for high VER
cases.
 4-21 
0
Table 4-6
Summary of simulation results with four types of reserves
Case 4 – no
reserves
Items
Case 4- with
reserves
Load violation in RT
87.8 GWh
(14.7% of load)
3GWh (0.5% of
load)
Curtailment in RT
120 GWh (26% of
total available VER)
251 GWh (54% of
total available VER)
DA mean LMP ($/MWh)
24
15
RT mean LMP ($/MWh)
599
159
RT price spike
(>$1000/MWh) intervals
348
199
Total RT Production costs
($)
8.6M
12.6 M
RT mean regulation up
reserve price ($/MWh)
-
408
RT mean regulation down
reserve price ($/MWh)
-
322
RT mean spinning reserve
price ($/MWh)
-
118
RT mean supplemental
reserve price ($/MWh)
-
82
Total regulation up reserve
shortage in RT
-
2840 MWh
Total regulation down
reserve shortage in RT
-
6120 MWh
Total spinning reserve
shortage in RT
-
892 MWh
Total supplemental reserve
shortage in RT
-
747 MWh
In the above simulation, we assumed that VER cannot provide operating
reserves. However, VER can be dispatched at any value up to the forecasted
energy output. Thus, they can provide all types of operating reserves defined
above as long as system operators have the confidence that they can deliver in
real-time. The case was modified to allow VER to provide reserves, and the
production cost simulation reran. A comparison of renewable energy percentages
between the original case and the modified case is shown in Figure 4-13. The
results between the two cases are very close. The system can still achieve 100%
VER in many intervals when reserves requirements were enforced and VERs
were allowed to provide those reserves.
 4-22 
0
A summary of the simulation results by allowing VER to provide reserves is
shown in Table 4-7. The values in this case are close to the original case 4 results.
There still exists lots of load and reserve shortage in the system, but there is no
shortage on regulation down reserve. The total amount of reserves shortage is
higher when allowing VER to provide reserves. The reason was because in the
100% VER intervals all the VERs have been dispatched at the maximum
capability so there is no head room to ramp up. In addition, no thermal
generators were dispatched at 100% VER intervals. As a result, the capacity for
providing regulation up, spinning (up) and supplemental (up) reserves in the
system is zero at those intervals. On the contrary, the VERs can be dispatched
down, thus there exists sufficient regulation down reserve capacity. This indicates
that although allowing VER to provide reserve can provide some benefits, there
are consequences are well, in particular a shortfall in reliability due to the
uncertainty related to wind and solar power. This also indicates that the current
UC/ED model may needed to be changed to allow VERs to provide reserves
properly when the system demand is 100% supplied by VERs. Further
investigation is needed on how to correctly model VER providing reserves in
future work, as it is not clear that the model is performing as would be expected
here.
Figure 4-13
Comparison of the original case with the new case that allows renewables to
provide reserves
 4-23 
0
Table 4-7
Summary of simulation results for case 4 with and without VER providing reserves
VER providing
reserves
Items
VER does not
provide reserves
Load violation in RT
7.2GWh (1.2% of
load)
3GWh (0.5% of
load)
Curtailment in RT
122 GWh (26.4% of
total available VER)
251 GWh (54% of
total available VER)
DA mean LMP ($/MWh)
23.8
15
RT mean LMP ($/MWh)
581
159
RT price spike
(>$1000/MWh) intervals
340
199
Total RT Production costs ($)
$8.9M
$12.6 M
RT mean regulation up
reserve price ($/MW)
581
408
RT mean regulation down
reserve price ($/MW)
0
322
RT mean spinning reserve
price ($/MW)
841
118
RT mean supplemental
reserve price ($/MW)
552
82
Total regulation up reserve
shortage in RT
8301 MWh
2840 MWh
Total regulation down
reserve shortage in RT
0 MWh
6120 MWh
Total spinning reserve
shortage in RT
29482 MWh
892 MWh
Total supplemental reserve
shortage in RT
8724 MWh
747 MWh
These results thus show how different aspects of operations will need to be
considered in the future. As the case with reserves is more realistic to how the
system would be operated in reality, it shows that the curtailment levels are not
purely a function of supply-demand balancing but will also need to consider other
issues such as forecast error and within interval variability and uncertainty, as well
as aspects like frequency response. In some aspects, case 2 and 3 may be already
carrying headroom that will provide similar results as the case with reserves,
except that when reserves are required additional headroom is often created.
Allowing storage on the system, or allowing VERs to provide reserves, can help
mitigate the situation, allowing for curtailment of renewables to be used to
provide reserves or to be stored for future use. Overall, the amount of
curtailments, steady-state reliability and violations, economics and production
costs, and prices/revenues will be dependent on many different conditions, and it
 4-24 
0
is important to understand the details of these conditions first in order to
understand the most beneficial mitigation strategies.
Conceptual Discussion of Electric Power Systems with 100%
VER and Without Dispatchable Thermal Resources
In this section, we provide some additional insights on the types of operating
paradigms and software that may be evolving along with the potential move to
very high VER penetration systems. Each are discussed qualitatively in brief. We
recommend further research on these sections to understand quantitatively the
impacts and what, if any, solutions may be required.
Change of SCUC and SCED Models
SCUC and SCED are key models in today’s electricity markets to manage the
resources and balance the demand. The SCUC is used in the day-ahead market
to meet the forecasted demand and ancillary service requirements subject to unit
and transmission constraints. The SCED is used to achieve real-time reliable
grid operation at the lowest costs.
With more VER being integrated into the grid, the operation paradigm is
expected to experience significant changes. VERs have no startup and shut down
time, minimum generation level, minimum on and off time, or start up and shut
down costs. These features are significantly different from conventional thermal
generators. When a system has 100% VERs for an entire horizon, the SCUC is
no longer required for system operations. Even for systems with very high
penetrations or those with 100% penetrations during only one or a few hours of
the horizon, there may be substantial changes to SCUC. In today’s market
operations, fast start units can be called up during intra-day and just tens of
minutes before to meet the load imbalance caused by uncertainty. In a 100%
VER system, the logic to call up quick start resources may be different and will
depend on available headroom in VERs, as the release of curtailment may also
act similar to fast-start resources. In general, it is likely that UC becomes less
relevant, and more about ensuring that storage, demand response and curtailed
VER are used in the most efficient manner to mitigate variability and uncertainty
challenges.
The SCED model should also have significant changes, with RT operations
becoming significantly more complex. During intervals where only the zero-cost
resources need to provide energy, there is no cost for SCED to minimize. The
optimization engine may randomly select resources to be curtailed, or have some
pre-ordained order (location may also impact due to congestion). As a result,
there may be multiple solutions to the SCED model. It is important to identify
new rules for determining which units are selected for curtailments. A solution
might be changing the objective from minimizing the operation costs to
minimizing the curtailment in the system.
On a VER, DR and storage system, the optimization algorithm also becomes
much different. The objective may be to reduce DR calls and store the most
 4-25 
0
storage throughout the horizon, rather than minimize costs. This algorithm has
many implications. What should the prices be? How difficult will it be to solve?
What parameters are required from the participating resources? Many more of
these types of questions can come up with this and the many other types of
resource mix and operational algorithms that best utilization those mixes. Further
research is definitely needed to understand how these may work.
Change of Reserve Determination Method
In a power system where the demand is 100% supplied by VER, solar and wind
resources form the baseload. In case of low wind and solar irradiation, the system
must carry sufficient extra capacity to reliably operate the grid under all possible
scenarios. This requires ensuring VER capacity well beyond the reserves required
from thermal plants. Overbuilding capacity is an option, but for scenarios with
high wind and solar irradiation, this will lead to extensive curtailments. Besides
overbuilding capacity, other measures to ensure sufficient reserves in the grid is
massive storage deployment, demand side resources and integration with other
energy systems such as transport and heat requirements.
How and who to provide the reserve needs in a grid with 100% VER is an
important issue in the future power systems. Traditionally, the operating reserves
have been provided by conventional generators such as thermal and hydro units,
and in some cases demand response. In the 100% renewable energy systems,
those reserves need to be provided by demand response, energy storage and VER
themselves.
One significant difference from traditional operation paradigm is that there may
be no need to have various types of reserve products in the 100% VER power
systems. In conventional power systems, different types of reserves need to be
defined because the thermal generators have different response time. For
example, those units with AGC are qualified to provide regulation reserve,
because they can respond to ISO’s setpoint signal in a few seconds. Units with
longer start up (or ramp up) time may be qualified to provide spinning or
supplemental reserves. However, VER have different capabilities than the
conventional generators when they are inverter based. They can respond to the
setpoints immediately. In addition, they have negligible start up or ramp up time.
Considering these features of VER, we might consider two types of operating
reserves to the system:

Load following reserve: It refers to the capacity available during normal
conditions for assistance in active power balance to correct future anticipated
imbalance in the system.

Contingency reserve: It refers to the capacity available for assistance in active
power balance during infrequent events that are more severe than balancing
needed during normal conditions and are used to correct instantaneous
imbalances. The contingency reserve can be set to the size of the largest
resource in the system.
 4-26 
0
The load following reserve should consider the variability and uncertainty of the
load and renewable energy generations. As discussed in a previous EPRI report
[4-3], there are three central needs for operating reserves:
1. Hold capacity now to meet the variability that occurs within the scheduling
time interval. (Intra-interval variability need)
2. Hold capacity now to meet the variability that occurs beyond the scheduling
time interval. (Inter-interval variability need)
3. Hold capacity now to meet the uncertainty that occurs within and beyond
the scheduling time interval. (Uncertainty need)
In a system with very high VER penetration, the net load can be negative in most
hours. The forecast error may not be meaningful if the error is less than the
amount that is planned to be curtailed, because all of the VER can simply avoid
curtailment without impact to the system. Thus, the amount of VER curtailed
must be used along with the VER forecasting data to calculate the reserve
capacity need for intra-interval variability, inter-interval variability and
uncertainty.
The contingency reserve requirement can be defined as the capacity of the largest
unit in the system. With large VER connections that can trip offline, these large
“mega farms” might set the contingency reserve requirement. However, it may be
likely in these cases that the VER forecast error magnitude may dominate the
need for reserve compared to instantaneous loss of a unit. The requirements may
need to be considered together and used as a shared product. This is similar to
how there may not be much need for VER forecast error induced reserve on low
VER penetration systems today. The existing fleet and residual headroom
typically can take care of those impacts.
Electricity Market Design Evolution
The impacts of zero and negative prices and high price spikes was discussed
earlier. The ways in which the market creates incentives for both short-term
reliability needs and long-term resource adequacy may be a lot different on these
high VER penetration systems. The existing market design which is dominated
by energy market revenues, was put in place when variable costs were a large part
of overall electricity costs and incentives to get fuel for less and improve heat rates
were the main drive of electricity market design and deregulation. These drivers
may be losing importance on a system with high VER penetrations. Instead,
there may be a whole set of other incentives for these systems as shown below:

Decrease capital costs including O&M costs

Decrease T&D losses

Decrease needs for additional infrastructure

Increase capacity factor, capacity value and geographic diversity

Provide as much energy as anticipated (decrease forecast error)

Provide energy at not necessarily same times as others
 4-27 
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
Provide reliability services

Provide energy during extreme conditions when needed
There has been some initial discussions in industry over what market designs may
work best on these very high VER penetration systems. The following are some
examples of the different alternatives from a generally high-level:

Use existing energy market dominated electricity markets as is. Make sure
that shortage pricing reflects true value or get price responsive demand to
come in and potentially set the price as often as generation.

Introduce configuration-based markets – forward markets that get the right
resources built in time that are configured to have the attributes that are
required on this system. These may be similar to capacity markets but
emphasize that capacity is not as important of an attribute. The residual
energy market may still exist but is mostly for ensuring reliability and is not
important in terms of investments and revenue.

Reregulation occurs – some say there is less need to have competitive markets
where most resources have the same costs and lower benefit to economic
dispatch and marginal cost pricing. This may still allow competitive RFPs for
technologies as determined by utilities and/or government organizations.
There is much more research required on how these markets evolve and what
might lead to the most efficient resource mix that can ensure long-term reliability
and how those resources can be operated to ensure short-term reliability. It is
important to start thinking about those potential designs earlier than later, as
immediate changes to the market structure can create distortions and poor
decisions. The technical details along with the high level structures are both
important to study further with these potential evolutions.
 4-28 
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Section 5: Summary and Future Work
This project investigates the operation and the associated reliability implications
of an all inverter-interfaced generation system given the new operational features
and challenges of such a system.
First, an operating paradigm of an all IBR system at constant frequency was
discussed, that was conceptualized based on an attempt to fully utilize the fast
control capability of inverter sources without restricting their behavior to mimic a
synchronous machine response. Its viability and system reliability with respect to
stability performance were evaluated based on detailed inverter models and
associated inverter controls that have been developed and used in various
simulation scenarios. It has been observed that such a constant frequency
operational paradigm could be feasible without jeopardizing grid reliability. A
phase angle based droop scheme was proposed to ensure adequate power sharing
among all available resources upon a generation/load imbalance event. It was
observed that the resource located electrically closer to the event would
experience the larger burden, and any topology changes would change the power
flows across the system, thus, practicality of such a scheme requires further
investigation.
Realizing that an all IBR system might be too far in the future, more realistic
scenarios of inverter dominated systems with small percentages of energy
provided by rotating generators were also studied. Interactions of the fast inverter
controls with the slower synchronous machines controls were investigated, and
preliminary results do not indicate any reliability concerns.
With respect to grid forming inverters, further R&D and industry engagement
and collaboration is required to define performance specifications of such inverter
controls. Based on these, representative inverter models can be developed to
perform planning studies on actual systems to investigate potential reliability
benefits that grid forming inverters may result in, in relation to their number and
locations. Also the impact of the dynamics of the inverter dc bus and the source
behind it should be considered for more detailed studies.
Finally, steady-state and balancing operational challenges of an all variable energy
resource (VER) system were also investigated. Preliminary simulation results
indicate that state-of-the-art production cost simulation tools can handle such
scenarios. By simulating several cases with different VER penetration levels, it
was observed that the factors affecting time intervals during a day for which
100% energy is provided by VER include the existence of must-run units,
whether there are long minimum on and off time units and system reserve
 5-1 
0
requirements and determination methods. It was discussed that traditional unit
commitment and economic dispatch models may need to be revised, since VER
have zero marginal costs and very quick start up time. Unlike the synchronous
generator dominated power systems, the commitment decisions become less
critical. Minimizing curtailment may be a better alternative than minimizing
operating cost. It was also observed that under 100% VER scenarios the system’s
LMPs are more variable with frequent changes from zero to extreme penalty
prices. Demand response and energy storage resources could help reduce price
volatility, load violations and renewable energy curtailments.
Future work under this topic may include market design and price formation
evolution, further analysis of revenue implications, more detailed investigation of
storage and demand response ability to support system balance, further
understanding of the reliability implications and how load and reserve shortfalls
manifest themselves, and handling the increased levels of uncertainty and
variability with advanced models. Other related work might include resource
adequacy methods for 100% or very high VER penetrations, understanding how
resource planning may be impacted at such high penetrations, and methods and
tools for optimizing the resource mix (including generation, transmission,
distribution and demand side resources) for high renewable futures.
 5-2 
0
Section 6: References
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G. Barbose, “U.S. Renewables Portfolio Standards - 2016 Annual Status
Report,” 2016.
[1-2]
B. Kroposki, B. Johnson, Y. Zhang, V. Gevorgian, P. Denholm, B. M.
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G. Denis, T. Prevost, P. Panciatici, X. Kestelyn, F. Colas and X.
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R. A. Mastromauro, “Voltage control of a grid-forming inverter for an
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[2-4]
NERC Subcommittee, “Balancing and Frequency Control,” 2011.
[2-5]
“Real Power Balancing Control Performance,” 2012.
[2-6]
I. Howard F. Illian, “Frequency Control Performance Measurement and
Requirements,” 2010.
[2-7]
D. Ramasubramanian, Z. Yu, R. Ayyanar, V. Vittal and J. Undrill,
“Inverter Model for Representing Inverter Interfaced Generation in
Large Scale Grid Simulations,” IEEE Transactions on Power Systems,
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P. Pourbeik, J. Sanchez-Gasca, J. Senthil, J. Weber, P. Zadehkhost, Y.
Kazachkov, S. Tacke, J. Wen and A. Ellis, “Generic Dynamic Models
for Modeling Wind Power Plants and other Renewable Technologies in
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Conversion, vol. PP, pp. 1-1, 2016.
 6-1 
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[2-9]
A. B. Birchfield, T. Xu, K. M. Gegner, K. S. Shetye and T. J. Overbye,
“Grid Structural Characteristics as Validation Criteria for Synthetic
Networks,” IEEE Transactions on Power Systems, vol. 32, pp. 32583265, 7 2017.
[2-10] Texas 2000-Bus System: ACTIVSg2k.
[2-11] D. Ramasubramanian, “Impact of Inverter Interfaced Generation and
Load on Grid Performance,” 2017.
[2-12] Guidelines for Studies on Weak Grids with Inverter Based Resources: A Path
from Screening Metrics and Positive Sequence Simulations to Point on Wave
Simulations. EPRI, Palo Alto, CA: 2018. 3002013639.
[2-13] 2017 NERC Frequency Response Annual Analysis:
https://www.nerc.com/comm/OC/BAL0031_Supporting_Documents_2
017_DL/2017_FRAA_Final_20171113.pdf
[2-14] Frequency Response Primer: A Review of Frequency Response with Increased
Deployment of Variable Energy Resources, EPRI, Palo Alto, CA: 2018.
3002014361.
[3-1]
P. Kundur, Power System Stability and Control. New York, NY:
McGraw-Hill, 1994.
[3-2]
D. Ramasubramanian, E. Farantatos, S. Ziaeinejad, and A. MehriziSani, “Operation paradigm of an all inverter interfaced generation bulk
power system,” IET Gener. Transm. Distrib., Aug. 2018, accepted for
publication (GTD-2018-5179.R1).
[3-3]
R. R. Kolluri, I. Mareels, T. Alpcan, M. Brazil, J. de Hoog, and D. A.
Thomas, “Power sharing in angle droop controlled microgrids,” IEEE
Trans. Power Syst., vol. 32, no. 6, pp. 4743–4751, Nov. 2017.
[3-4]
H. Moussa, A. Shahin, J. P. Martin, S. Pierfederici, and N. Moubayed,
“Optimal angle droop for power sharing enhancement with stability
improvement in islanded microgrids,” IEEE Trans. Smart Grid, vol. 9,
no. 5, pp. 5014–5026, Sep. 2018.
[3-5]
B. John, A. Ghosh, and F. Zare, “Load sharing in medium voltage
islanded microgrids with advanced angle droop control,” IEEE Trans.
Smart Grid, accepted for publication, Jun. 2017.
[4-1]
FERC Open Access Transmission Tariff.
https://www.ferc.gov/industries/electric/indus-act/oatt-reform/order890/pro-forma-oatt-rehearing.pdf?csrt=5308760181500748066.
[4-2]
The Evolution of Ancillary Services to Facilitate Integration of Variable
Renewable Energy Resources. EPRI, Palo Alto, CA, 3002008987, 2016.
 6-2 
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[4-3]
An Enhanced Dynamic Reserve Method for Balancing Areas. EPRI, Palo
Alto, CA. 2017, 3002010941.
[4-4]
NERC. Balancing and frequency control. Princeton, NJ. January 26, 2011.
[4-5]
Senate Bill No. 100.
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20180SB100.
[4-6]
Planning Hawaii's grid for future generations, Integrated Grid Planning
Report, Mar. 1, 2018.
[4-7]
C. Grigg, et al., The IEEE Reliability Test System-1996. A report
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Systems, vol. 14, no. 3, pp.1010-1020, Aug. 1999.
[4-8]
https://github.com/GridMod/RTS-GMLC.
[4-9]
R. Hytowitz,B. Frew, G. Stephen, E. Ela, J. Lau, N. Singhal and A.
Bloom. Impacts of Price Formation Efforts Considering High
Renewable Penetration Levels and System Resource Adequacy Targets.
NREL Technical Report, October 2018.
[4-10] EPRI Video Tutorial - Illustrating Operating Reserve Needs and
Methods- Operating Reserve and Operational Support Tools to Help
Meet Variability and Uncertainty, Palo Alto, CA, 2016.
[4-11] E. Ela, Dynamic Operating Reserve and Advanced Scheduling Techniques to
Support Variability and Uncertainty in Power Systems Case Studies on the
Western Interconnection, EPRI, Palo Alto, CA, 3002008366, 2016.
 6-3 
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Appendix A: Test Case and Scenarios for
Chapter 4
Test System Description
The IEEE reliability test system (RTS-96), recently augmented by NREL to
include additional renewables, was used for the analysis 7. Its one-line diagram is
shown in Figure A-1. It has 121 branches, 74 substations, and 278 generation
injections, which consist of 72 thermal units, 1 nuclear unit, 6 wind units, 20
hydro units, 70 PV and 109 rooftop PV. Three load zones are included to mimic
the grids in LA Division of Water and Power, Nevada Energy, and Arizona
Public Service Company, respectively. The peak load of the system is 8192 MW.
Figure A-1
NREL Reliability Test System
Test Scenarios Description
Based on the original data, four different cases are developed, as shown below:

Case 1: Low renewable energy penetration case.

Case 2: High renewable energy penetration case.

Case 3: Nuclear resource set as non-Must Run in Case 2.

Case 4: Nuclear and Hydro units in Case 2 removed.
7
More information and the test system details can be found at https://github.com/GridMod/RTS-GMLC.
 A-1 
0
Case 1 is a low renewable energy penetration case, which includes lots of thermal
generators. Case 2 is a high renewable energy penetration case, in which a
significant amount of renewable energy resources has been added to the system.
In both case 1 and case 2, there is a 400 MW nuclear power plant which is
simulated as must-run unit in the study. To eliminate the impact of must-run
units to the system operation, in Case 3 the nuclear resource was set as non-must
run (nuclear can still be economically dispatched between the minimum and
maximum capacity) based on case 2. To further remove the impacts of nuclear
units and focus on non-hydro renewable energy resources, Case 4 was created by
removing all the nuclear and hydro units of Case 2.
The generation capacity of the various resources in each case is shown in Table
A-1. A one-week production cost simulation was conducted for each case. The
average percentages of generation of different resources for each case are shown
in Table A-2.
Table A-1
Generation Capacity (MW) in Each Case (Peak load: 8192 MW)
Cap.
(MW)
CC
CT
STEAM
Hydro
Nuclear
VER
Case 1
3550
1545
1362
1000
400
2133
Case 2&3
3550
1645
830
1000
400
11948
Case 4
3550
1645
0
0
0
11948
Table A-2
Average percentages of Generation in One Week
Case 1
Case 2
Case 3
Case 4
Thermal (%)
68.6
37.2
32.5
31.2
Hydro (%)
18.1
14.1
14.6
0.0
VER (%)
13.3
46.4
48.6
53.2
 A-2 
0
0
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