The Accuracy of Wind and Solar Energy

Forecasts and the Prospects for Improvement

Kevin F. ForbesUSAEE Distinguished Lecturer

Associate Professor of EconomicsThe Catholic University of America

Forbes@CUA.edu

Ernest M. ZampelliProfessor of Economics

The Catholic University of AmericaZampelli@CUA.edu

USAEE Distinguished Lecture Lehigh University Student Chapter of the USAEE

Lehigh UniversityBethlehem, Pennsylvania

5 November 2015

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?

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.

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

The Net Energy Imbalance in Great Britain, 1 January 2012 – 30 June 2014

This figure depicts the netdeployment of balancing power.Positive values represent the response to market shortagewhile negative values representthe response to an excess supply.

The root causes of the deployments include imperfect forecasts andthe failure of suppliers to adhere to their generation and transmission schedules.

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.

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.

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 %.

CapacityInstalled

T

ForecastActual

CWRMSE

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ProducedEnergyMean

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ForecastActual

EWRMSE

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tt

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CWRMSE vs EWRMSE

CWRMSE will be substantially less than EWRMSE when capacity factors are low.

3) Using The Mean-Squared-Error Skill Score (MSESS) to Assess Forecast AccuracyA 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 −𝑀𝑆𝐸𝐹

𝑀𝑆𝐸𝑃

Where 𝑀𝑆𝐸𝐹 is the mean squared error of the forecast that is being evaluated and 𝑀𝑆𝐸𝑝is 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.

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

Mean Squared Error Skill Scores (MSESS) with a Persistence Forecast as Reference

Control

Area/Zone Forecast Type Sample Period Observations GranularityMSESS

50Hertz

(Germany) Day-Ahead Load

1Jan2011 –

31Dec2013104,590

Quarter-Hour -62.7486

Day-Ahead

Wind

1Jan2011 –

31Dec2013104,590

Quarter-Hour -31.3501

Day-Ahead Solar

1Jan2011 –

31Dec201354,545

Quarter-Hour -5.26831

Amprion

(Germany) Day-Ahead Load

1Jan2011 –

31Dec2013103,326 Quarter-Hour

-12.3308

Day-Ahead

Wind

1Jan2011 –

31Dec2013103,326 Quarter-Hour

-14.5887

Day-Ahead Solar1Jan2011 –

31Dec201355,498 Quarter-Hour

-11.20691

Mean Squared Error Skill Scores (MSESS) with a Persistence Forecast as Reference (Continued)

Control

Area/Zone Forecast Type Sample Period Observations GranularityMSESS

California ISO Day-Ahead Load1Jan2013 –

31Dec20138,760 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

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-Hourly0.3842

Day-Ahead Wind 1Jan2012 – 31Dec2013 17,349 Hourly-5.7375

Hour 1 Same Day, Wind1Jan2012 – 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 Wind1Jan2011 – 31Dec2013

26,105 Hourly-3.6749

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 Wind1Jan2012 – 31Dec2013 16,847 Hourly -0.81342

Great BritainDay-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.

Actual Wind Energy and the Hour-Ahead Forecast of Wind Energy in the Bonneville Power Administration, 1 Jan 2012 – 31 December 2013.

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Hour-Ahead AVG Forecasted Wind Energy (MW)

MSESS = -0.8134

EWRMSE = 23.1%

Day-Ahead Forecasted Wind Energy in Great Britain and Actual Wind Energy Outturn, 1 January 2012 – 31 December 2013

The EWRMSEof the day-ahead forecastis about 25 percent. The CWRMSE is about 6.8 percent.

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Day-Ahead Forecasted Wind Energy (MW)

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

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.

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.

The Revised Generation Schedules vs Actual Generation: The Case of Coal in Great Britain

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Scheduled Generation including Balancing Actions (MWh)

EWRMSE = 2.5 %

The Revised Generation Schedules vs Actual Generation: The Case of Combined Cycle Gas Turbines in Great Britain

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Scheduled Generation including Balancing Actions (MWh)

EWRMSE = 5.6%

Actual vs. Scheduled Generation: The Case of Nuclear Energy in Great Britain

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Scheduled Generation (MWh)

EWRMSE = 7.4 %

The Revised Generation Schedules vs Actual Generation: The Case of Wind Energy in Great Britain, 1 Jan 2012 – 31 2013

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Scheduled Generation including Balancing Actions (MWh)

EWRMSE= 18 %

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

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

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.

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

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

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

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

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 beendeleted.

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Day-Ahead Forecasted Solar Energy (MW)

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 beendeleted.

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Hour-Ahead Forecasted Solar Energy (MW)

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 beendeleted.

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Modified Forecast of Solar Energy (MW)

Day-Ahead Forecasted and Actual Wind Energy in SP15, 1 January – 30 September 2015

EWRMSE = 49.4 % MSESS = -5.43

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CAISO's Day-Ahead Wind Energy Forecast (MW)

Hour-Ahead Forecasted and Actual Wind Energy in SP15, 1 January – 30 September 2015

EWRMSE = 37.1 % MSESS = -2.62

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CAISO's Hour-Ahead Wind Energy Forecast (MW)

Actual Wind Energy and a Revised Wind Energy Forecast for SP15, 1 January – 30 September 2015

EWRMSE = 15.8 % MSESS = 0.34

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Modified Hour-Ahead Forecast (MW)

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-AheadSolar Energy Forecast

6,541 0.84 16.4

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-AheadWind

6559 0.23 16.0 %

Out of Sample Results for Wind Energy in Great Britain, 1 Jan 2014 – 30 June 2014Forecast 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 %

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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References (Continued)

Hannale Holttinen, Pirkko Saarikivi, Sami Repo, Jussi Ikäheimo, Goran Koreneff, 2006. Prediction Errors and Balancing Costs for Wind Power Production in Finland. Global Wind Power Conference, Adelaide

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Bernhard Lange, Kurt Rohrig, Bernhard Ernst, Florian Schlögl, Umit Cali, Rene Jursa, and Javad Moradi, 2006. Wind power prediction in Germany – Recent advances and future challenges, Zeitschrift für Energiewirtschaft, vol. 30, no 2, at115-120. At http://www.iset.uni-kassel.de/abt/FB-I/publication/Lange-et-al_2006_EWEC_paper.pdf <last accessed 15 feb 2012>

References (Continued)

Bernhard Lange, Kurt Rohrig, Florian Schlögl, Umit Cali,and Rene Jursa, 2007. Wind Power Forecasting, in Renewable Electricity and the Grid, Godfrey Boyle, Ed. Sterling,VA: Earthscan, London, at 95-120.

David Milborrow, 2007. Wind Power on the Grid, in Renewable Electricity and the Grid, Godfrey Boyle, Ed. Sterling,VA: Earthscan, London, at 31-54

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References (Continued)

National Grid, 2009. Operating the Electricity Transmission Networks in 2020: Initial Consultation. At http://www.nationalgrid.com/NR/rdonlyres/32879A26-D6F2-4D82-9441-40FB2B0E2E0C/39517/Operatingin2020Consulation1.pdf <last accessed 15 feb 2012>

North American Electric Reliability Corporation, 2009b. Accommodating High Levels of Variable Generation, April. At http://www.nerc.com/files/IVGTF_Report_041609.pdf <last accessed 15 feb 2012>

NERC, 2010. IVGTF Task 2.1 Report: Variable Generation Power Forecasting for Operations. At http://www.nerc.com/files/Varialbe%20Generationn%20Power%20Forecasting%20for%20Operations.pdf <last accessed 15 feb 2012>

Jennifer Rodgers and Kevin Porter, 2009. Central Wind Power Forecasting Programs in North America by Regional Transmission Organizations and Electric Utilities.

Royal Academy of Engineering, 2014, Wind Energy : Implications of Large-Scale Deployment on the GB Electricity System http://www.raeng.org.uk/publications/reports/wind-energy-implications-of-large-scale-deployment