A growing literature has affirmed with great confidence the feasibility of high penetration levels of wind and solar energy in electric generation under existing technology. This optimism is based in part on the belief that improved forecasting has effectively “solved” the challenge of intermittency. For example, the UK’s Royal Academy of Engineering has recently noted that wind energy’s capacity weighted forecast error of about five percent is evidence that the wind energy forecasts in Great Britain are highly accurate. This paper assesses this claim using data from Great Britain, 50Hertz in Germany, Amprion in Germany, the California ISO, the Bonneville Power Administration, the Midcontinent ISO, France, Western Demark, Eastern Denmark, and Belgium. The analysis proceeds by comparing the forecast accuracy of load, wind, and solar energy with the accuracy of the corresponding persistence forecasts for load, wind, and solar energy. The analysis indicates that while the load forecasts are generally more accurate than a persistence load forecast, the wind and solar energy forecasts are generally less accurate than the corresponding persistence forecasts for wind and solar energy. Specifically, with a persistence forecast as reference, the mean-square-error-skill-score (MSESS) of the load forecasts are generally positive while the MSESS of the wind or solar energy forecast are generally negative. Evidence is also presented that the forecast errors have a systematic component. Modelling of this systematic component can yield short-run solar and wind energy forecasts that are significantly more accurate. This does not resolve the challenge of intermittency but may mitigate matters.

1. The Accuracy of Wind and Solar Energy
Forecasts and the Prospects for
Improvement
Kevin F. Forbes
USAEE Distinguished Lecturer
Associate Professor of Economics
The Catholic University of America
Forbes@CUA.edu
Ernest M. Zampelli
Professor of Economics
The Catholic University of America
Zampelli@CUA.edu
USAEE Distinguished Lecture
Lehigh University Student Chapter of the USAEE
Lehigh University
Bethlehem, Pennsylvania
5 November 2015

2. The Organization of this Talk
1)Why is Forecasting Important?
2) The Literature on Wind and Solar Energy Forecast Accuracy
3) What is the level of forecast skill ? Specifically, what does the Mean Squared Error Skill
Score (MSESS) indicate about the solar and wind energy forecasts? How does this level of
accuracy compare to the accuracy of the load forecasts?
4)From the point of view of a system operator, how does wind energy compare with
conventional forms of generation?
5)What are the prospects for improving the accuracy of the solar, wind, and load forecasts?

3. 1)Why is Forecasting Important?
• The stability of the power grid is enhanced when forecasts are more
accurate. This is important because blackouts have very high societal
costs
• Some forms of balancing technologies such as open-cycle gas turbines
can be very expensive to deploy and also have above average
emissions factors.

4. Errors in the Day-Ahead Load Forecast for New York City and the
Differential between the Real-Time and Day-Ahead Prices in New
York City, 6 August 2009 – 30 June 2013.
Note: Excludes the period of time when operations were affected by Superstorm Sandy in late October 2012

5. The Net Energy Imbalance in Great Britain, 1
January 2012 – 30 June 2014
This figure depicts the net
deployment of balancing power.
Positive values represent the
response to market shortage
while negative values represent
the response to an excess supply.
The root causes of the deployments
include imperfect forecasts and
the failure of suppliers to adhere
to their generation and transmission
schedules.

6. System Frequency in Great Britain, 1
December – 31 December 2013
System frequency in Great Britain varies around the
target of 50 Hz with National Grid being obligated to keep
system frequency within one percent of the 50 Hz target,
i.e. +/- 50 mHz In Great Britain, deviations within
the band +/- 20 mHz are considered normal.
Deviations outside the band +/- 20 mHz do occur.
Specifically, there were 152 cases in December 2013
in which the operational limits were violated.
This appears to be a higher rate of violations than previously.
For example, there was only one violation in December 2012.

7. 2) The Literature on Forecast Accuracy
Some researchers calculate a root-mean-squared error of the forecasts and then weight it by the capacity of
the equipment used to produce the energy. The reported capacity weighted root mean squared errors
(CWRMSE) are usually less than 10 percent. Adherents of this approach include Lange, et al. (2006, 2007),
Cali et al. (2006), Krauss, et al. (2006), Holttinen, et al. (2006), Kariniotakis, et al. (2006), and even NERC
(2010, p. 9).
In a publication entitled, “Wind Power Myths Debunked,” Milligan, et al. (2009) draw on research from
Germany to argue that it is a fiction that wind energy is difficult to forecast. In their words: “In other
research conducted in Germany, typical wind forecast errors for a single wind project are 10% to 15% root
mean-squared error (RMSE) of installed wind capacity (emphasis added) but drop to 5% to 7% for all of
Germany.” (Milligan, et al. 2009, p. 93)
The UK’s Royal Academy of Engineering (2014, p. 33) has noted that wind energy’s capacity weighted
forecast error of about five percent is evidence that that the wind energy forecasts are highly accurate.
A report by the IPCC ( 2012 p, 623) on renewable energy indicates that wind energy is moderately
predictable as evidenced by a capacity weighted RMS forecast error that is less than 10%. Solar energy is
reported to be even more accurate.

8. The Literature on Forecast Accuracy
(Continued)
NREL (2013) implicitly endorses capacity weighted RMSEs for wind
energy but makes use of energy weighted RMSEs when discussing
the accuracy of load forecasts.
In contrast, Forbes et. al. (2012) calculate a root-mean-squared
forecast error for wind energy in nine electricity control areas. The
RMSEs are normalized by the mean level of wind energy that is
actually produced. The reported energy weighted root mean squared
errors (EWRMSE) are in excess of 20 %.

9. CapacityInstalled
T
ForecastActual
CWRMSE
T
t
tt )(
1
2



ProducedEnergyMean
T
ForecastActual
EWRMSE
T
t
tt )(
1
2



CWRMSE vs EWRMSE
CWRMSE will be substantially less than EWRMSE when capacity factors are low.

10. 3) Using The Mean-Squared-Error Skill Score
(MSESS) to Assess Forecast Accuracy
A useful alternative to both the energy weighted and capacity weighted RMSE is
the mean-squared-error skill score (MSESS). With this metric, one can evaluate the
skill of a forecast as compared to a persistence forecast, a persistence forecast
being a period-ahead forecast that assumes that the outcome in period t equals
the output in period t-1. The MSESS with the persistence forecast as a reference is
calculated as follows:
𝑀𝑆𝐸𝑆𝑆 = 1 −
𝑀𝑆𝐸 𝐹
𝑀𝑆𝐸 𝑃
Where 𝑀𝑆𝐸 𝐹 is the mean squared error of the forecast that is being evaluated and
𝑀𝑆𝐸 𝑝is the mean squared error a persistence forecast. A perfect forecast would
have a MSESS equal to one. A MSESS equal to zero indicates that the forecast skill is
equal to that of a persistence forecast. A negative MSESS indicates that the
forecast under evaluation is inferior to a persistence forecast.

11. How accurate are the forecasts?
• MSESS were computed for the following zones and/or control areas:
• Bonneville Power Administration
• CAISO: SP15 and NP15
• MISO
• PJM
• 50Hertz in Germany
• Amprion in Germany
• Elia in Belgium
• RTE in France
• National Grid in Great Britain
• Finland
• Sweden
• Norway
• Eastern Denmark
• Western Denmark
• When possible the MSESS are reported for Wind, Solar, and Load

12. Mean Squared Error Skill Scores
(MSESS) with a Persistence Forecast as Reference
Control
Area/Zone Forecast Type Sample Period Observations Granularity
MSESS
50Hertz
(Germany) Day-Ahead Load
1Jan2011 –
31Dec2013
104,590
Quarter-Hour -62.7486
Day-Ahead
Wind
1Jan2011 –
31Dec2013
104,590
Quarter-Hour -31.3501
Day-Ahead Solar
1Jan2011 –
31Dec2013
54,545
Quarter-Hour -5.26831
Amprion
(Germany) Day-Ahead Load
1Jan2011 –
31Dec2013
103,326 Quarter-Hour
-12.3308
Day-Ahead
Wind
1Jan2011 –
31Dec2013
103,326 Quarter-Hour
-14.5887
Day-Ahead Solar
1Jan2011 –
31Dec2013
55,498 Quarter-Hour
-11.20691

13. Mean Squared Error Skill Scores (MSESS)
with a Persistence Forecast as Reference (Continued)
Control
Area/Zone Forecast Type Sample Period Observations Granularity
MSESS
California ISO Day-Ahead Load
1Jan2013 –
31Dec2013
8,760 Hourly
0.6026
NP15 Day-Ahead Wind
1Jan2013 –
31Dec2013 8,704 Hourly -6.1401
NP15 Hour-Ahead Wind
1Jan2013 –
31Dec2013 8,704 Hourly -2.3605
NP15 Day-Ahead Solar
1Jan2013 –
31Dec2013 8,666 Hourly -3.2002
NP15 Hour-Ahead Solar
1Jan2013 –
31Dec2013 8,666 Hourly -2.4846
SP15 Day-Ahead Wind
1Jan2013 –
31Dec2013 8,752 Hourly -4.8210
SP15 Hour-Ahead Wind
1Jan2013 –
31Dec2013 8,752 Hourly -2.1894
SP15 Day-Ahead Solar
1Jan2013 –
31Dec2013 8,752 Hourly 0.7050
SP15 Hour-Ahead Solar
1Jan2013 –
31Dec2013 8,752 Hourly 0.7972

14. Mean Squared Error Skill Scores (MSESS)
with a Persistence Forecast as Reference (Continued)
Control Area/Zone Forecast Type Sample Period Observations Granularity MSESS
Belgium
Day-Ahead Solar 1Jan2013 – 31Dec2013 17,921 Quarter-Hour -12.2621
Intra-Day Solar 1Jan2013 – 31Dec2013 11,278 Quarter-Hour -9.7931
France Day-Ahead Load 1Jan2012 – 31Dec2013 35,088 Half-Hourly
0.3842
Day-Ahead Wind 1Jan2012 – 31Dec2013 17,349 Hourly
-5.7375
Hour 1 Same Day, Wind
1Jan2012 – 31Dec2013
15,109 Hourly -5.2889
Norway Day-Ahead Load 1Jan2011 – 31Dec2013 26,160 Hourly 0.1870
Sweden Day-Ahead Load 1Jan2011 – 31Dec2013 26,160 Hourly 0.2008
Finland Day-Ahead Load 1Jan2011 – 31Dec2013 26,159 Hourly 0.0486
Eastern Denmark Day-Ahead Load 1Jan2011 – 31Dec2013 26,160 Hourly 0.3953
Day-Ahead Wind 1Jan2011 – 31Dec2013 26,107 Hourly -2.7507
Western Denmark Day-Ahead Load 1Jan2011 – 31Dec2013 26,160 Hourly 0.6560
Day-Ahead Wind
1Jan2011 – 31Dec2013
26,105 Hourly
-3.6749

15. Mean Squared Error Skill Scores (MSESS)
with a Persistence Forecast as Reference (Continued)
Control
Area/Zone Forecast Type Sample Period Observations Granularity MSESS
MISO Day-Ahead Wind Energy 1Jan2011 – 31Dec2013 26,303 Hourly -4.3873
PJM Day-Ahead Load 1Jan2011 – 31Dec2013 26,160 Hourly 0.4727
New York City Day-Ahead Load 1Jan2011 – 31Dec2013 25,675 Hourly 0.1703
Bonneville Power Five Minute-Ahead Wind 1Jan2012 – 31Dec2013 206,477 Five minutes -36.25762
Hour-Ahead Wind
1Jan2012 – 31Dec2013 16,847 Hourly -0.81342
Great Britain
Day-Ahead Load 1Jan2012 – 31Dec2013
30,477
Half-Hourly 0.62
Day-Ahead Wind
1Jan2012 – 31Dec2013
30,477
Half-Hourly
-19.032
1 Daylight portion of the sample period
2MSESS calculation excludes periods in which wind energy production was curtailed by the
system operator.

16. Actual Wind Energy and the Hour-Ahead Forecast of Wind Energy in the Bonneville Power
Administration, 1 Jan 2012 – 31 December 2013.
0
1000200030004000500060007000
ActualWindEnergy(MW)
0 1000 2000 3000 4000 5000 6000 7000
Hour-Ahead AVG Forecasted Wind Energy (MW)
MSESS = -0.8134
EWRMSE = 23.1%

17. Day-Ahead Forecasted Wind Energy in Great
Britain and Actual Wind Energy Outturn, 1
January 2012 – 31 December 2013
The EWRMSE
of the day-ahead forecast
is about 25 percent.
The CWRMSE is
about 6.8 percent.
0
200040006000
0 2000 4000 6000
Day-Ahead Forecasted Wind Energy (MW)

18. Day-Ahead Forecasted Load vs. Actual Load in
Great Britain, 1 January 2012 – 31 December
2013 The EWRMSE of the day-ahead load
forecast is about 1.8 percent. The
CWRMSE is about 0.45 percent based
on a proxy of the installed capacity of
the equipment that consumes electricity.
The point of this slide and the previous
slide is that day-ahead wind energy
forecasts in Great Britain are
substantially less accurate than day-
ahead load forecasts regardless of
whether one measures forecast accuracy
using EWRMSE or CWRMSE

19. Why are the MSESSs for Solar and Wind
Energy so Large?
• Meteorologists have historically largely focused on forecasting
temperature as compared to cloud cover and wind speeds.
• Changes in cloud cover and wind speeds can be more volatile than
changes in temperature.
• For example, the diurnal correlation in the hourly average
temperature between hour k and hour k -24 in Chicago was about
0.92 over the period April 2013 – December 2014. Over the same
period, the diurnal correlation in hourly cloud cover and wind speed
between hour k and hour k -24 was about 0.221 and 0.227,
respectively.

20. 4)From the point of view of a system operator, how does wind
energy compare with conventional forms of generation?
Evidence from Great Britain
• In Great Britain, each generating station informs the system operator of its
intended level of generation one hour prior to real-time. This value is known
as the final physical notification (FPN).
• Generators also submit bids (a proposal to reduce generation) and offers (a
proposal in increase generation) to provide balancing services
• During real-time, the system operator accepts the bids and offers based on
system conditions.
• In short, the revised generation schedule equals the FPN plus the level of
balancing services volume requested by the system operator.
• Failure to follow the revised generation schedule gives rise to an electricity
market imbalance that needs to be resolved by other generators.

21. The Revised Generation Schedules vs Actual
Generation: The Case of Coal in Great Britain
0
2000400060008000
1000012000
MeteredGeneration(MWh)
0 2000 4000 6000 8000 10000 12000
Scheduled Generation including Balancing Actions (MWh)
EWRMSE = 2.5 %

22. The Revised Generation Schedules vs Actual
Generation: The Case of Combined Cycle Gas
Turbines in Great Britain
0
250050007500
1000012500
MeteredGeneration(MWh)
0 2500 5000 7500 10000 12500
Scheduled Generation including Balancing Actions (MWh)
EWRMSE = 5.6%

23. Actual vs. Scheduled Generation: The Case of
Nuclear Energy in Great Britain
0
10002000300040005000
MeteredGeneration(MWh)
0 1000 2000 3000 4000 5000
Scheduled Generation (MWh)
EWRMSE = 7.4 %

24. The Revised Generation Schedules vs Actual Generation: The Case of
Wind Energy in Great Britain, 1 Jan 2012 – 31 2013
0
500
10001500200025003000
MeteredGeneration(MWh)
0 500 1000 1500 2000 2500 3000
Scheduled Generation including Balancing Actions (MWh)
EWRMSE= 18 %

25. Average Imbalances by Fuel in Great Britain, 1
Jan 2012- 31 December 2013

26. A Closer look at the Wind Energy Imbalances,
1 Jan 2012 – 30 June 2014

27. 5) The Prospects for Improving the Forecasts
• Significant improvements in day-ahead forecasts will probably require
major advances in meteorological research. One obvious place to
begin is to note that the heat trapping properties of Greenhouse
gases most likely have implications for wind speeds.
• Significant improvements in very short run forecasts (e.g. one or two
hours ahead) are possible by exploiting the systematic nature of the
existing forecast errors.

28. The Systematic Nature of the Existing Day-Ahead Forecast
Errors for Wind Energy: Evidence from Great Britain

29. The Systematic Nature of the Existing Forecast
Errors for Solar Energy: Evidence from 50Hertz in
Germany

30. The Systematic Nature of the Existing Forecast Errors for Solar
Energy: Evidence from SP15 in California over the time period 1 Jan
2013- 31 December 2014

31. Actual Solar Energy in 50Hertz and an Out-of-
Sample Econometrically Modified Solar Energy
Forecast, 1 July 2013 – 3 March 2014
For the daylight period:
EWRMSE = 4.8 %
MSESS = 0.768

32. Day-Ahead Forecasted and Actual Solar Energy in
SP15, 1 January – 30 September 2015
EWRMSE = 23.3 %
MSESS = .684
Note: 3 highly anomalous
observations have been
deleted.
0
1000200030004000
0 1000 2000 3000 4000
Day-Ahead Forecasted Solar Energy (MW)

33. Hour-Ahead Forecasted and Actual Solar Energy in
SP15, 1 January – 30 September 2015
EWRMSE = 17.9 %
MSESS = 0.813
Note: 3 highly anomalous
observations have been
deleted.
0
1000200030004000
0 1000 2000 3000 4000
Hour-Ahead Forecasted Solar Energy (MW)

34. Actual Solar Energy and a Revised Solar Energy
Forecast for SP15, 1 January – 30 September 2015
EWRMSE = 10.7 %
MSESS = 0. 933
Note: 3 highly anomalous
observations have been
deleted.
0
1000200030004000
0 1000 2000 3000 4000
Modified Forecast of Solar Energy (MW)

35. Day-Ahead Forecasted and Actual Wind Energy in
SP15, 1 January – 30 September 2015
EWRMSE = 49.4 %
MSESS = -5.43
0
500
1000150020002500
0 500 1000 1500 2000 2500
CAISO's Day-Ahead Wind Energy Forecast (MW)

36. Hour-Ahead Forecasted and Actual Wind Energy in
SP15, 1 January – 30 September 2015
EWRMSE = 37.1 %
MSESS = -2.62
0
500
1000150020002500
0 500 1000 1500 2000 2500
CAISO's Hour-Ahead Wind Energy Forecast (MW)

37. Actual Wind Energy and a Revised Wind Energy
Forecast for SP15, 1 January – 30 September 2015
EWRMSE = 15.8 %
MSESS = 0.34
0
500
1000150020002500
0 500 1000 1500 2000 2500
Modified Hour-Ahead Forecast (MW)

38. Out of Sample Results for Solar Energy in NP15 in
California, 1 Jan 2015 – 30 September 2015
Forecast Type Number of Observations MSESS EWRMSE
CAISO’s Day-Ahead Solar
Energy Forecast
6,541 -1.45 64.1
CAISO’s Hour-Ahead
Solar Energy Forecast
6,541 0.18 37.0
Modified Hour-Ahead
Solar Energy Forecast
6,541 0.84 16.4

39. Out of Sample Results for Wind Energy in NP15 in
California, 1 Jan 2015 – 30 September 2015
Forecast Type Number of Observations MSESS EWRMSE
CAISO’s Day-Ahead Wind
Forecast 6559
-5.81 47.9 %
CAISO’s Hour-Ahead
Wind Forecast
6559 -2.18 32.7 %
Modified Hour-Ahead
Wind
6559 0.23 16.0 %

40. Out of Sample Results for Wind Energy in
Great Britain, 1 Jan 2014 – 30 June 2014
Forecast Type Number of Observations MSESS EWRMSE
Day-Ahead Wind Forecast 8,571 -35.05 31.9 %
Forecast equal to the
levels of generation
declared by operators
one hour prior to real-
time
8,571 -19.71 24.2 %
Modified Forecast:
available to system
operator 30 min prior to
real-time
8,571 -1.95 9.1 %

41. Summary and Conclusions
• With few exceptions, the load forecasts examined in this study have
positive skill scores relative to a persistence load forecast.
• With few exceptions, the solar and wind forecasts examined in this study
have negative skill scores relative to the corresponding persistence
forecasts.
• Evidence has been presented that the forecast errors have a systematic
component
• Evidence has also been presented that modelling of this systematic
component can yield very short-run solar and wind energy forecasts that
are significantly more accurate. This does not resolve the challenge of
intermittency but may mitigate matters.

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