The Smart Grid and the Imperative for Improved
Modeling of Electricity Transmission Flows:The Case of
Denmark and its Trading Partners
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
34rd IAEE International Conference
Stockholm, Sweden
June 2011
Research Supported by the National Science Foundation
Back Ground
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 Hz
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.
Wind Forecasting Errors
Issues with Conventional
Generation
Transmission Issues
Transmission – the problem of
Unscheduled flows
On most alternating current transmission systems,
the actual flow of electricity at a given interchange is
not equal to the scheduled flow.
The difference between the scheduled and actual
flow is known as the unscheduled flow (also known
as loop flow)
It is not uncommon on alternating current
transmission systems for the root-mean-squares of
the unscheduled electricity flows between control
areas to exceed 100 percent.
System Operators have had difficulty modeling these
flows.
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
8
6
Percent
4
Note: the
figure does
not reflect
2
dynamically
scheduled flows
0
-4000 -2000 0 2000
inadvertent_interchange_mwh
Actual Imports Scheduled
Actual vs Scheduled Electricity Flows
Between Ontario and Michigan, 1 Oct – 31
Oct 2005
1500
1000
500
MWH per Hour
0
-500
-1000
-1500
-2000
Scheduled Flow Actual Flow
Net Unscheduled Flows Between
Finland and Sweden, November
2008
800
600
400
200
MWh
0
-200
-400
The Imbalance Power Market
between Finland and Sweden
To manage the unscheduled flows
between the two systems, the system
operators in Sweden and Finland have
established a market for imbalance power.
Over the period 1 Jan 2008 – 31
December 2009, peak hourly purchases of
imbalance power by Fingrid was 1,400
MWh.
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
700
USD per MWh
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 PJM Service Territory in the
United States
The Magnitude of the Challenge: 1 June
2007 – 31 December 2008
InterChange InterChange Absolute Root-Mean- Simple
With PJM Abbreviation Value of Square of the Correlation
Scheduled Inadvertent between
Trade Flow Relative Actual and
(MWh per to Mean of Scheduled
Hour) the Absolute Flow
Value of the
Scheduled
Flow (in
percent)
Alliant East PJM/ALTE 216 277 % 0.1080
Alliant West PJM/ALTW 192 117 % 0.3766
Ameren (Illinois) PJM/AMIL 139 659 % 0.2890
Cinergy 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 Root-Mean-Square Simple
Value of of the Inadvertent Correlation
Scheduled Flow Relative to between
Trade Mean of the Actual and
(MWh per Absolute Value of Scheduled
Hour) the Scheduled Flow Flow
Indianapolis PJM/IPL 217 273 % 0.2088
Power and Light
LG&E Energy PJM/LGEE 180 117 % 0.3953
MidAmerican PJM/MEC 458 100 % 0.5654
Energy
Michigan Electric PJM/MECS 371 482 % -0.0165
Coordinated
System
NEPTUNE PJM/NEPT 599 0.2 % 1.00
Northern Indiana PJM/NPIS 112 322 % 0.0789
Public Service
New York ISO PJM/NYIS 954 78 % 0.6174
The Magnitude of the Challenge: 1 June
2007 – 31 December 2008
InterChange InterChange Absolute Root-Mean- Simple
Value of Square of the Correlation
Scheduled Inadvertent between
Trade (MWh Flow Relative to Actual and
per Hour) Mean of the Scheduled
Absolute Value Flow
of the
Scheduled Flow
(in percent)
Ohio Valley PJM/OVEC 1045 36 % 0.3947
Electric
Corporation
Tennessee Valley PJM/TVA 484 125 % 0.6711
Authority
Wisconsin PJM/WEC 114 416 % 0.1446
Energy
Corporation
Modeling Loop Flows
Ambient temperature is probably an important
factor. The relationship is probably nonlinear.
Nonthermal transmission constraints are most likely
also important
“Network effects” are probably very important.
Geomagnetic Storms and
Loop Flows
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).
These currents have the potential to
induce transmission constraints
which in turn can affect transmission
flows.
Geomagnetically Induced
Currents and Transformers
GICs in the UK Power Grid, Oct 30
2003
Source: Alan Thompson of the BGS
The Peer Reviewed Literature
GICs have been found to be statistically
related with various measures of real-time
operations in 12 power grids including
PJM, NYISO, New England, England and
Wales, New Zealand, Australia, Ireland,
and the Netherlands.
It may also be relevant to note that the
Hydro-Quebec system collapsed in 1989
during a geomagnetic storm.
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
700
USD per MWh
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
900
Rate of Change in the Horizontal Component of the
250
800
700
Geomagnetic Field(nT/min)
200
USD per MWh
600
500 150
400
100
300
200
50
100
0 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 dH/dt - OTT
This paper examines electricity
flow issues between Denmark
and its Trading Partners
Electricity Flows Between Western
Denmark and its Trading Partners,
1 June 2001- 31 December 2007
Trading Partner Average of Root-Mean- Simple
the Absolute Square of Correlation
Value of the between
Scheduled Unscheduled Actual and
Trade (MWh Flow Scheduled
per Hour) Relative to Flow
Mean of the
Absolute
Value of the
Scheduled
Flow (in
percent)
Germany 641 16.8 0.9913
Norway 559 22.2 0.9813
Sweden 248 45.7 0.9415
Total 555 31.9 0.9648
Unscheduled Electricity Flows
between Western Denmark
and its Trading Partners
25
20
15
Percent
10
5
0
-1000 -500 0 500 1000 1500
net_unscheduled
Unscheduled Electricity Flows
between Western Denmark
and its Trading Partners
The range of the difference between the
actual and scheduled flows for Western
Denmark exceeded 2,800 MWh over the
sample period 1 June 2001- 31 December
2007.
Explanatory Variables in a Model of
Electricity Flows Between Denmark
and its Trading Partners
Scheduled Transmission Flows
Proxies for transmission constraints
Wind Energy Production Levels
Binary variables to represent the hour of
the day, the month of the year, and the
year of the sample.
A GIC proxy
The Model
The Model was estimated using hourly
data over the period 1 January 2001 – 31
December 2007
Results
The correlation coefficient between the
predicted and actual flow is 0.97
The coefficients on the explanatory
variables are highly statistically significant
There is evidence of network effects in
the sense that the level of scheduled
flows between Eastern Denmark and
Germany has implications for the level of
actual flows to/from Western Denmark.
Unexpected Flows
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-mean-squared-
error was calculated.
This error was compared to the error
one obtains when comparing the actual
vs. scheduled flow
Results
The predicted value was compared to the
actual flow and the root-mean-squared-
error was calculated.
The RMSE was found to 13 percent lower
when the actual flows are compared to
the predicted flows instead of the
scheduled flows.
This decline is less dramatic but is none
the less consistent with findings for PJM
The Root-Mean-Squares
of the Unexpected Flows for selected
Interchanges in the United States
2000
1800
Root Mean Squared Errors (MWh per Hour)
1600
1400
1200
1000
800
600
400
200
0
CIN MEC MECS NY TVA
Actual Flow vs Model Predicted Actual Flow vs Scheduled
The Range in the Electricity
Flow “Errors” for Western
Denmark – a decline of 20%
3000
2500
2000
MWh
1500
1000
500
0
Range in Actual vs Scheduled Flow Range in Actual vs Model Predicted Flow
Next Steps
Incorporate additional measures of expected
power grid conditions into the model
Perform “out of sample” testing of the model’s
forecasting performance