The Smart Grid and the Imperative for
Improved Modeling of Electricity
Transmission Flows
Kevin F. Forbes
The Catholic University of America
Washington, DC 20064 USA
Forbes@CUA.edu
O.C. St. Cyr
Department of Physics
The Catholic University of America
and
NASA-Goddard Space Flight Center
SIXTH ANNUAL CARNEGIE MELLON CONFERENCE ON THE ELECTRICITY
INDUSTRY
9 March 2010
Research Supported by the National Science Foundation
Back Ground
y
y
y
Many markets are self-correcting. When a market is in
disequilibrium in the sense that demand is not equal to
supply, there are forces at work that will move the
system to a new equilibrium.
A decrease in the supply of, say, bananas could lead to
a shortage of bananas but the shortage is likely to be
short lived as the price of bananas changes and
producers and consumers respond to the new price.
In any event, a short-lived banana shortage is probably
not a big deal.
Electricity is Different
y
y
y
There are very large societal costs associated
with blackouts.
Avoiding these costs requires that system
frequency be maintained at its setpoint value of
60 Hz (50 Mz in most of the rest of the world)
Maintaining system frequency at its setpoint
value requires that the demand for electricity
match the supply. Specifically, the amount of
power generation in a balancing area needs to
match exactly, on a near-instantaneous basis,
the system load, net of losses and interchange
with other balancing areas.
Challenges to Reliability
Load Forecasting Errors.
y Wind Forecasting Errors
y Issues with Conventional
Generation
y Transmission Issues
y
Challenges to Reliability
y
Load Forecasting Errors. Depending on
the system operator, the root-meansquared errors of the day-ahead forecasts
are usually between 3- 5 percent but can
be as high as 10 percent.
Actual and Day-Ahead
Forecasted Load in PJM, 1 June
– 7 June 2009
120000
100000
MWh
80000
60000
40000
20000
0
Forecasted Load 11:45 AM
Forecasted Load 5:45 PM
pjm_actual_load
0
2
4
Percent
6
8
10
A Histogram of Day-Ahead Load Forecasting
Errors by PJM, 1 May 2005 – 11 August 2009
-10000
-5000
0
5000
da_load_forecast_error
10000
0
5
Percent
10
15
A Histogram of Day-Ahead Load
Forecasting Errors by the California
ISO, 1 April 2009 - 31 January 2010
-4000
-2000
0
2000
da_load_forecast_error
4000
6000
0
2
Percent
4
6
8
A Histogram of Day-Ahead Load
Forecasting Errors for France, 1 November
2003 – 31 December 2008
-10000
-5000
0
5000
french_load_forecast_error_mw
10000
0
2
Percent
4
6
8
A Histogram of Day-Ahead Load
Forecasting Errors for the Midwest ISO,
1 April 2005 – 31 December 2008
-5000
0
5000
load_forecast_error_mwh
10000
Load Forecasting Errors
y
While the “average error” may seem
small, there are a nontrivial number of
days in which the errors are quite
large
y
The is preliminary evidence that a
portion of the errors is systematic.
This may make it possible to reduce
the errors by modifying forecasts
based on the systematic component of
the errors
Challenges to Reliability
y
Wind Energy. It is not uncommon for
the root-mean-squared errors of the
day-ahead wind energy forecasts to
be larger than 30 percent of actual
wind energy.
Actual vs Day-Ahead Forecasted Wind
Energy in ERCOT, 2 November – 30
November 2009
7000
6000
5000
MW
4000
3000
2000
1000
0
Actu al W in d
D ay Ah ead S T W P F H R 15
0
2
Percent
4
6
8
A Histogram of Day-Ahead Wind
Forecasting Errors in ERCOT, 13
June 2009 – 31 January 2010
-4000
-2000
0
2000
da_forecast_error_hr_12
4000
6000
Day-Ahead Wind Forecasting Errors
in Germany, 1 January -15
December 2009
40
35
30
Percent
25
20
15
10
5
0
Amprion (formerly known as TransPower (formerly known
RWE)
as E.ON Netz)
RMSE Relative to the Average Level of Wind Energy
Vattenfall
Mean Absolute Percent Error
Challenges to Reliability (Continued)
Unscheduled Electricity Flows (aka
Loop Flows) between Control Areas. It
is not uncommon on alternating current
transmission systems for the root-meansquares of the unscheduled electricity
flows between control areas to exceed
100 percent.
y System Operators have had difficulty
modeling these flows.
y
Percent
4
6
8
Histogram of Inadvertent Interchange ( the sum of the Loop
Flow over all Interchanges) in the PJM Power Grid Over those
Hours in Which PJM was a Scheduled Net Importer, 1April
2002-30 April 2004
0
2
Note: the
figure does
not reflect
dynamically
scheduled flows
-4000
-2000
0
inadvertent_interchange_mwh
Actual Imports < Scheduled
2000
Actual Imports > Scheduled
Actual vs Scheduled Electricity Flows
Between Ontario and Michigan, 1 Oct –
31 Oct 2005
1500
1000
MWH per Hour
500
0
-500
-1000
-1500
-2000
Scheduled Flow
Actual Flow
Challenges to Reliability can Result in Price Spikes
The Day-Ahead and Real-Time Reference Price in the New York ISO,
January 1-31 2005
1000
900
800
USD per MWh
700
600
500
400
300
200
100
0
1/1/05
1/4/05
1/7/05
1/10/05 1/13/05 1/16/05 1/19/05 1/22/05 1/25/05 1/28/05 1/31/05
Real-Time Price
Day-Ahead Price
Another Possible Outcome when
Reliability is Challenged
What is the Magnitude of the
Transmission Challenge?
The Root Mean Squared Error of
the Flows
The Magnitude of the Challenge: 1
June 2007 – 31 December 2008
InterChange
With PJM
InterChange
Abbreviation
Absolute
Value of
Scheduled
Trade (MWh
per Hour)
Root-MeanSquare of the
Inadvertent
Flow Relative
to Mean of
the Absolute
Value of the
Scheduled
Flow (in
percent)
Simple
Correlation
between
Actual and
Scheduled
Flow
Alliant East
PJM/ALTE
216
277 %
0.1080
Alliant West
PJM/ALTW
192
117 %
0.3766
Ameren
(Illinois)
Cinergy
PJM/AMIL
139
659 %
0.2890
PJM/CIN
626
114 %
0.4561
Duke Energy
PJM/DUK
579
113 %
0.8549
First Energy
PJM/FE
329
361 %
0.0438
The Magnitude of the Challenge: 1
June 2007 – 31 December 2008
InterChange
InterChange
Absolute
Value of
Scheduled
Trade
(MWh per
Hour)
Simple
Correlation
between
Actual and
Scheduled
Flow
217
Root-Mean-Square
of the Inadvertent
Flow Relative to
Mean of the
Absolute Value of
the Scheduled
Flow
273 %
Indianapolis
Power and Light
PJM/IPL
LG&E Energy
PJM/LGEE
180
117 %
0.3953
MidAmerican
Energy
PJM/MEC
458
100 %
0.5654
Michigan
Electric
Coordinated
System
NEPTUNE
PJM/MECS
371
482 %
-0.0165
PJM/NEPT
599
0.2 %
1.00
Northern
Indiana Public
Service
New York ISO
PJM/NPIS
112
322 %
0.0789
PJM/NYIS
954
78 %
0.6174
0.2088
The Magnitude of the Challenge: 1
June 2007 – 31 December 2008
InterChange
InterChange
Absolute
Value of
Scheduled
Trade (MWh
per Hour)
Root-MeanSquare of the
Inadvertent
Flow Relative
to Mean of the
Absolute Value
of the
Scheduled
Flow (in
percent)
Simple
Correlation
between
Actual and
Scheduled
Flow
Ohio Valley
Electric
Corporation
PJM/OVEC
1045
36 %
0.3947
Tennessee
Valley Authority
PJM/TVA
484
125 %
0.6711
Wisconsin
Energy
Corporation
PJM/WEC
114
416 %
0.1446
Modeling Loop Flows
y
y
y
Ambient temperature is probably an important
factor. The relationship is probably nonlinear.
Nonthermal transmission constraints that are
terrestrial in origin are most likely also important
“Network effects” are probably very important.
Proxies for the Expected
Conductivity of the Power Grid
PJM reports day-ahead electricity prices that
are location specific.
y As of 1 June 2007, these prices have three
components: a pure energy component, a
congestion cost component, and a marginal
transmission loss component.
y The congestion cost and transmission loss
components reflect the expected conductivity
of the transmission system
y We use 40 of these reported day-ahead
measures as proxies for the conductivity of the
power grid
y
Examples of Proxies for the
Expected Conductivity of the
Power Grid
Day-Ahead Congestion and Losses at
Chicago Hub
y Day-Ahead Congestion and Losses at
the PJM/New York Interface
y Day-Ahead Congestion and Losses at
the AEP Dayton Hub
y Day-Ahead Congestion and Losses at
the Interface with MISO
y
Day-Ahead Congestion Costs, June
2007
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60
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-20
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da_rto_MCC
da_southexp_MCC
da_ovec_MCC
da_nyis_MCC
da_northwest_MCC
da_nipsco_MCC
da_neptune_MCC
da_miso_MCC
da_michfe_MCC
da_imo_MCC
da_southimp_MCC
da_aep_dayton_hub_MCC
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da_chicago_hub_MCC
da_chicago_hub_MCC
da_dominion_hub_MCC
da_eastern_hub_MCC
da_new_jersey_hub_MCC
da_northern_ill_hub_MCC
da_ohio_hub_MCC
da_western_hub_MCC
da_western_int_hub_MCC
Day-Ahead Marginal Losses, June
2007
20
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5
0
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da_nipsco_MLC
da_neptune_MLC
da_miso_MLC
da_michfe_MLC
da_imo_MLC
da_southimp_MLC
da_aep_dayton_hub_MLC
da_aep_gen_hub_MLC
da_chicago_hub_MLC
da_chicago_gen_hub_MLC
da_dominion_hub_MLC
da_eastern_hub_MLC
da_new_jersey_hub_MLC
da_northern_ill_hub_MLC
da_ohio_hub_MLC
da_western_hub_MLC
da_western_int_hub_MLC
Geomagnetic Storms and
Loop Flows
y
Geomagenetic storms are
disturbances in the Earth’s magnetic
field that are largely caused by
explosions in the Sun’s corona that
spew out solar particles.
Solar Activity and the Earth’s
Magnetic Field
Source: NASA
Geomagnetic Storms and
Loop Flows
Power Grids are vulnerable to
geomagnetic Storms because the
power transmission grid acts as an
‘‘antenna’’ of sorts, picking up
geomagnetically induced currents
(GICs).
y These currents have the potential
to induce transmission constraints
which in turn can affect
transmission flows.
y
The Peer Reviewed Literature
GICs have been found to be
statistically
related with various measures of realtime operations in 12 power grids
including PJM, NYISO, New England,
England and Wales, New Zealand,
Australia, Ireland, and the
Netherlands.
y Many individuals openly scoff at these
findings
y
Yet, the relationship is fairly robust:
The Day-Ahead and Real-Time Reference Price in the New York ISO,
January 1-31 2005
1000
900
800
USD per MWh
700
600
500
400
300
200
100
0
1/1/05
1/4/05
1/7/05
1/10/05 1/13/05 1/16/05 1/19/05 1/22/05 1/25/05 1/28/05 1/31/05
Real-Time Price
Day-Ahead Price
The Rate of Change in the Geomagnetic Field and the
Real-Time Reference Price in the New York ISO,
January 1-31 2005
1000
300
250
800
700
USD per MWh
200
600
150
500
400
100
300
200
50
100
0
1/1/05
0
1/4/05
1/7/05
1/10/05 1/13/05 1/16/05 1/19/05 1/22/05 1/25/05 1/28/05 1/31/05
Real-Time Price
Day-Ahead Price
dH/dt - OTT
Rate of Change in the Horizontal Component of the
Geomagnetic Field(nT/min)
900
The Model and Sample
Period
The model was estimated for five
interfaces over the period 1 June 2007
– 31 December 2008 using hourly
data. There are 12,956 observations
The model includes 113 explanatory
variables
The Modeled Interfaces
Cinergy (CIN)
y MidAmerican Energy (MEC)
y Michigan Electric Coordinated
System(MECS)
y New York(NY)
y Tennessee Valley Authority (TVA)
y
0
2
Percent
4
6
8
10
A Histogram of the Inadvertent Electricity Flow
Between PJM and Cinergy, 1 June 2007 – 31
December 2008
-4000
-2000
0
cin_inadv
2000
4000
0
2
Percent
4
6
8
10
A Histogram of the Inadvertent Electricity Flow
Between PJM and MidAmerican(MEC), 1 June 2007
– 31 December 2008
-2000
-1000
0
1000
mec_inadv
2000
3000
0
2
Percent
4
6
8
A Histogram of the Inadvertent Electricity Flow Between
PJM and Michigan Electric Coordinated System, 1 June
2007 – 31 December 2008
-4000
-2000
0
mecs_inadv
2000
4000
0
2
Percent
4
6
8
A Histogram of the Inadvertent Electricity Flow Between
PJM and the New York ISO, 1 June 2007 – 31 December
2008
-3000
-2000
-1000
0
nyis_inadv
1000
2000
0
2
Percent
4
6
8
A Histogram of the Inadvertent Electricity Flow
Between PJM and TVA, 1 June 2007 – 31 December
2008
-2000
-1500
-1000
-500
tva_inadv
0
500
Results
y
y
y
y
The multivariate analysis indicated that electricity
flows are statistically related with a proxy for
geomagnetically induced currents.
There is strong evidence of “network effects” in the
sense that actual flows are related with its
scheduled flows to other interfaces
A number of the proxies for the day-ahead expected
conductivity of the grid are highly statistically
significant.
Not surprisingly, temperature also is affects the
flows
PJM’s Actual Flows with Cinergy
are highly statistically related
with
y PJM scheduled flows with Carolina
Power and Light (both East and
West), City Water Light and Power,
East Kentucky Power Cooperative,
and Alliant Energy East
y Day-ahead congestion costs with
MISO
y Day-Ahead losses for the PJM system
as a whole, losses at the FE
interchange, the Chicago Hub and the
AEP Dayton Hub
PJM’s Actual Flows with
MidAmerican Energy are highly
sensitive to
PJM’s scheduled flows with Carolina
Power and Light West, Ameren
(Illinois), East Kentucky Power
Cooperative, First Energy, and TVA
y Day-Ahead Congestion Costs with
Ohio Valley Electric Corporation.
y PJM’s System wide Day-Ahead
Losses losses at the Chicago Hub,
and Losses at the MISO Interface.
y
PJM’s Actual Flows with Michigan
Electric Coordinated System are
highly sensitive to
PJM’s scheduled flows with East
Kentucky Power Cooperative, First
Energy, MidAmerican Energy,
Carolina Power and Light West, City
Water Light and Power,
y Congestion Costs at AEP Dayton
y Day-Ahead Losses at the Chicago
and Ohio Hubs, and the MISO, First
Energy and Northern Indiana
y
PJM’s Actual Flows with New
York are highly sensitive to
y
y
y
PJM’s scheduled flows with Carolina Power and
Light West, First Energy, Indianpolis Power and
Light, East Kentucky Power Cooperative, Cinergy,
Ameren, Michigan Electric Coordinated System ,
Northern Indiana Public Service
Day-Ahead congestion costs at the AEP Hub and
First Energy and Ontario Interfaces
Day-Ahead Losses at the New York and MISO
interfaces and the Chicago Hub
PJM’s Actual Flows with TVA
are highly sensitive to
y
y
y
PJM’s scheduled flows with Carolina Power
and Light West, City Water Light and
Power, East Kentucky Power Cooperative ,
MidAmerican Energy
Day-Ahead congestion costs at the Chicago
and AEP Hubs
Day-Ahead system wide losses, Losses at
the Chicago Hub, losses at the interface
with Northern Indiana Public Service
Unexpected Flows
y
For each modeled interface, the
predicted electricity flow was
calculated for each hour of the sample
The predicted value was compared to
the actual flow and the root-meansquared-error was calculated.
y This error was compared to the error
one obtains when comparing the
actual vs. scheduled flow
y
The Root-Mean-Squares
of the Unexpected Flows
2000
Root Mean Squared Errors (MWh per Hour)
1800
1600
1400
1200
1000
800
600
400
200
0
CIN
MEC
MECS
Actual Flow vs Model Predicted
NY
Actual Flow vs Scheduled
TVA
Next Steps
y
y
y
y
y
Refine the model to account for nonlinearities
Incorporate additional measures of conductivity
into the model(e.g. MISO’s day-ahead measures
of losses and congestion)
Incorporate PJM’s measures of ground currents
into the model
Perform “out of sample” testing of the model’s
forecasting performance
Assess the feasibility of forecasting the GIC
proxy and/or PJM’s ground currents based on
Space Weather Forecasts.