a comparison of long-term wind speed forecasting models

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Petros P. Kritharas1e-mail: [email protected] J. Watsone-mail: [email protected] for Renewable Energy SystemsTechnology (CREST),Department of Electronic and Electrical

Engineering,Loughborough University,Loughborough LE11 3TU, UKA Comparison of Long-Term WindSpeed Forecasting ModelsThis paper presents a time series analysis of historical observations of wind speed inorder to project future wind speed trends. For this study, 52 years of data havebeen usedfrom seven suitable stations across the UK. Four parsimonious models have been employed,and the data were split into two different segments: the training and the valida

tiondata sets. During the fitting process, the optimum parameters for each model weredetermined in order to minimize the mean square error in the predictions. The resultssuggest that the seasonal pattern in wind speeds is the most important factor but thatthere is some monthly autocorrelation in the data, which can improve forecasts.This isconfirmed by testing the four models with the model having considered both autocorrelationand seasonality achieving the smallest errors. The approach proposed for forecasting

wind speeds a month ahead may be deemed useful to suppliers for purchasing baseload in advance and to system operators for power system maintenance schedulingup toa month ahead. DOI: 10.1115/1.40023461 IntroductionWind generators, in order to avoid being penalized for any mismatchin the power contracted to be delivered and that was actuallydelivered, use several forecasting techniques. The value ofwind power forecasting has a twofold importance. First, knowledgeof the expected generation output from wind power plantsprovides confidence to the system operators SOs when trying toachieve reliable and secure operation of the network. Second, it

enhances the value of wind generated electricity by giving vitalinformation when participating in an energy market such as themarket in Great Britain. This can be achieved both by providinghigher value contracts due to better bidding strategies and byminimizing imbalance costs. Specifically, in a deregulated market,generators and suppliers to whom the imbalance risk is oftentransferred can avoid being penalized by choosing an optimumbidding strategy. However, this also depends on the market inquestion. As stated in Ref. 1, the rules can influence the selectionof an appropriate bidding strategy. Findings vary depending on theselected approach statistical or physical, the time horizon of thepredictions, or the area covered single wind turbine/farm, subregion,region, or country. An up-to-date comparison and evaluation

of the state-of-the-art of forecasting systems can be found inRef. 2. In addition, for a comprehensive overview of predictionmodels, we refer to Refs. 35. However, these models tend to


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predict wind conditions, thus wind power, only a week ahead dueto the difficulties of forecasting the state of the atmosphere beyond10 days. Nevertheless, any reference for the future state ofwind conditions is crucial since it will provide suppliers with vitalinformation with regard to the optimum purchasing of base load

6. Moreover, it will contribute to the maintenance schedule forwind farms, the whole operation of which can be time consuming

and expensive. Also, wind power forecasting will allow SOs toevaluate the potential wind energy production and schedule powersystems in a more effective way 7. The use of wind indices hasbeen proposed in Ref. 8 since they provide suppliers/generatorsand SOs with estimates regarding the long-term production fromwind farms 9. In one research project, three parsimonious methodsfor estimating monthly wind energy were compared. Fromthis comparison, it was shown that an hourly based approach anda linear regression method performed similarly. This conclusionestablished the linear regression method, despite its simplicity, foruse in estimating wind energy at monthly time scales 10. In Ref.

11, it was shown that it was feasible to predict to a reasonable

degree the monthly electricity production from wind farms in LaVenta, Oaxaca, Mexico. The authors compared two methods: autoregressiveintegrated moving average ARIMA and artificialneural network ANN models. The results indicated in this casethat the seasonal ARIMA SARIMA models performed betterthan the ANN models. In another study, a probabilistic model wasproposed for use in long-term energy resource planning 12. Duringthe study, both autoregressive AR and autoregressive movingaverage ARMA models were tested for generating windspeed time series. The wind speed was converted into power, andby employing a spatial smoothing technique, the individual poweroutput from a wind turbine was extrapolated across geographicallydisperse wind farm sites. However, some other studies doubt

the efficacy of ARIMA models when compared with the ANNmodel. In Ref. 13, feed forward and recurrent networks havebeen developed for predicting wind speed at a monthly time scaleand have been compared with ARIMA models. This comparisonshowed that ANN models performed better. Also, in Ref. 14, theauthors developed an ANN model and compared it with an ARmodel. The results again indicated the superiority of ANN modelsfor predicting wind speed on a monthly basis. Similarly, Ref. 15proposed two multilayered network architectures for predictingmonthly mean wind speed with satisfactory results, while in Ref.

16 a feed forward, back propagation network was developed forthe same purpose. It is clear from the above discussion that thereis not yet consensus as to which approach

nonlinear or stochastic

model produces the better result.This paper presents a statistical analysis of wind speeds over aperiod of 52 years for the UK. Based on autoregressive techniquesand by using the seasonal patterns identified in the time series,monthly wind speed forecasts have been generated. The modelsdeveloped in this study are compared, and it is found that the bestforecasts are made when the seasonal component is taken intoaccount.2 Data Collection and AnalysisObservations of several meteorological parameters, such aswind speed, have been retrieved from the Met Office IntegratedDatabase Archive System MIDAS17 and have been collected

from a wide range of locations across the UK, including synopticand climatological stations. The data used in this paper include1Corresponding author.


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Contributed by the Solar Energy Division of ASME for publication in the JOURNALOF SOLAR ENERGY ENGINEERING. Manuscript received September 8, 2009; finalmanuscript received June 22, 2010; published online October 4, 2010. Assoc. Editor:Spyros Voutsinas.Journal of Solar Energy Engineering Copyright 2010 by ASME NOVEMBER 2010, Vol. 132 / 041008-1

Downloaded 19 Jan 2011 to 203.200.35.31. Redistribution subject to ASME licenseor copyright; see http://www.asme.org/terms/Terms_Use.cfmonly the wind speed records and have been analyzed statisticallyin order to identify repeating patterns and autocorrelation. Observationsfrom the MIDAS database go back to the late 1940s, andthe records were stored as 10 min averages made on the hour. Inorder to accomplish homogeneity between the different stations interms of time, the year 1957 was set as the starting year for allstations used in this analysis. In the present study, we were interestedin demonstrating the existence of repeating patterns of windspeed as a way of forecasting but modified for any observed autocorrelation.From over 50,000 stations, varying in type and location,

we selected seven sites, which were suitable for analysis.One of the criteria for selecting these specific stations was thecompleteness of the data recorded and stored for each station.Another criterion set was that the stations used in the study arestill carrying out observations and hence are active. Also, prior tothe selection of the stations, a quality assessment was applied onthe data to avoid discrepancies and missing or duplicated values.The requirement set was the total recorded hours to be 75% ofthe total theoretical hours for the 52 years. Table 1 shows thepercentage of the available data for the stations used.A fast Fourier transform FFT was applied to generate a windspeed frequency spectrum. Figure 1 clearly shows the existence oftwo strong peaks. The first peak appears at 24 h and the second

peak at 1 year due to diurnal and annual variation in wind speed18, respectively. In Fig. 1, the stations are split into three cases:1. strong diurnal peak and strong annual peak2. strong diurnal peak and weak annual peak3. weak diurnal peak and strong annual peakAfter generating the wind speed spectrum and observing thestrong patterns on a daily and yearly basis, a time series analysiswas applied on the wind speed data. As Fig. 2 confirms, the analysisshowed that the time series are nonstationary. Analyzing themonthly mean wind speed averaged over all years per stationresulted in the observation of a similar seasonal behavior for eachstation see Fig. 3. It is clear that during the summer, where thelowest wind speeds occur, and during the winter, where the highestwind speeds have been recorded, all the stations showed similarperiodic variations.A popular and established way to identify and measure the periodicitywithin the time series is by determining the correlationbetween different data values at varying time lags for this study,time lags are in months. Figure 4a shows significant seasonalityin the time series. The standard errors SEs in the correlogramrepresent the white noise estimates, while Q stands for the BoxLjung test statistic, which is among the portmanteau tests. TheBoxLjung test statistic is used to identify how well fitted a timeseries model is and is based on the autocorrelation plot. As Fig.4a confirms, if the value for the significant autocorrelation p is

found to be relatively small, it is considered that the model haspassed the test 19. Figure 4b shows the partial autocorrelationfunction PACF plot, which suggests that correlation in the data


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only exists up to one time step ahead. This fact was used to determinethe order of the simple exponential smoothing SES andsimple seasonal SS models see Sec. 4.3 Seasonal DecompositionThe fundamental principle of time series forecasting dependson identifying a pattern in the series and then, based on the historyof incidents over time, to forecast ahead. Generally, a time series

pattern discloses subpatterns such as trends with cyclic or periodicpatterns, random or sporadic variations, seasonal, level shifts, etc.,or, in some cases, a combination of the above subpatterns. Also, atime series often exhibits periodic fluctuations, which should beeliminated when investigating the existence of trends within theseseries. This can be achieved by removing any seasonality. Theprocedure commonly used is a way to identify and analyze theseries characteristics rather than forecasting directly and is calledseasonal decomposition. For an additive decomposition, as in thisstudy, removing the seasonal component means subtracting itfrom the original data:Yt St = Tt + Et 1

Where Yt is the actual value at period t, St is the seasonal componentat period t, Tt is the trend cycle at period t, and Et is theirregular component at period t.Applying smoothing to the series such as a moving average

MA filter can help estimate the trend cycle Tt. Randomness ofthe time series should be eliminated as the order of the smoothingincreases. Nevertheless, the drawback in increasing the number ofterms in the MA filter is that more information is lost in theaveraging process. For that reason, along with the fact that in thisstudy we are dealing with monthly data the order of the MA filterwas chosen to be 12. Figure 5 shows the monthly mean windspeed at the Stornoway Airport station after having beensmoothed by removing the seasonal component.

4 Model Selection and FittingThe next step in this study was the model selection, whichincludes the choice of one or more forecasting models and theirfitting to the data. The forecasting models chosen for this paperare the following.4.1 1 month Persistence. This forecasting model is based onthe assumption that the forecasted value at time t+1 will be thesame as the value at the previous time step t:Y t+1 = Yt 2whereY t+1, is the forecast value at period t+1, and Yt is the actualvalue at period t.4.2 12 month Persistence. This forecasting model is basedon the assumption that the forecasted value at time t+h will be thesame as the value at time t, where h represents the periods aheadof the forecast h=12 for monthly data:Y t+h = Yt 3where Y t+h is the forecast value at period t+h, and Yt is the actualvalue at period t.4.3 SES. This forecasting model is based on two factors, theforecast from the previous period and the actual value in the previousperiod. This model is equivalent to an ARIMA model,

ARIMA0,1,1, and its mathematical expression is as follows:Y t+1 = Yt + 1 Y


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t 4where is the smoothing factor, 01, Y t+1 is the forecastvalue at period t+1, Y t is the forecast value at period t, and Yt isthe actual value at period t.Table 1 Data quality assessment

Cases Stations Total hoursAvailability

%1 Lerwick 453,254 99.4Stornoway Airport 450,842 98.9Valley 454,958 99.82 Aldergrove 455,570 99.9Boscombe Down 452,144 99.13 Aberporth 454,495 99.7Tiree 453,902 99.5041008 2 / Vol. 132, NOVEMBER 2010 Transactions of the ASMEDownloaded 19 Jan 2011 to 203.200.35.31. Redistribution subject to ASME license

or copyright; see http://www.asme.org/terms/Terms_Use.cfm4.4 SS. This forecasting model is similar to the simple exponentialsmoothing model with the addition of a seasonal component.This model is equivalent to an ARIMA0,1,s+10,1,0smodel, and following Ref. 20 its mathematical expression is asfollows:Y t+h = Lt + St+hs 5where Y t+h is the forecast value at period t for a lead time t+h,and Lt denotes the series level at time t and the data after removingthe seasonal component:Lt = Yt Sts + 1 Lt1 + bt16

St stands for the seasonal component of the series at time t:0 4 45 447 4467 44668 45131900.511.522.533.544.5HoursPower densityPeriodogramLERWICKSTORNOWAY AIRPORTVALLEY1 day1 year(a)0 5 50 501 5012 50119 52188800.51

1.522.5


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3HoursPower densityPeriodogramALDEGROVEBOSCOMBE DOWN1 year

1 day(b)0 4 45 447 4467 44668 45084401234567Hours

PeriodogramPower densityABERPORTHTIREE1 day 1 year(c)Fig. 1 Wind power spectra at 10 m height agl: a strong diurnal peak and strong annual peak, bstrong diurnal peak and weak annual peak, and c weak diurnal peak and strong annual peakJournal of Solar Energy Engineering NOVEMBER 2010, Vol. 132 / 041008 3Downloaded 19 Jan 2011 to 203.200.35.31. Redistribution subject to ASME licenseor copyright; see http://www.asme.org/terms/Terms_Use.cfm

St = Yt Lt + 1 Sts 7bt is the trend of the series:bt = Lt Lt1 + 1 bt1 8

, , and are the smoothing factors, s represents the number ofseasons in a year, and h represents the period ahead for theforecast.In order to evaluate the performance of the models, the datawere separated into two subsets: a training and a testing subset. Inthis study, we have focused on training the models using a longdata set while at the same time evaluating their performance overa relatively long time horizon. For this reason, from 52 years ofdata, 44 years have been used for training and 8 years for testingthe models. The models were fitted to the data for the trainingperiod and then employed and monitored for their performanceover the testing period. During the fitting process, the criterion forselecting the optimum parameters for each model was the minimizationof the mean square error MSE. Figures 69 show theperformance of each forecasting model for the testing period. Thestation selected to be presented below as an example is StornowayAirport although all the results are shown in Table 2.5 Model Validation and Statistical ErrorsIn the present study, we were interested in evaluating the performanceof the selected forecasting models. To accomplish this,we use the following metric:Fig. 2 Yearly mean wind speed per station

Fig. 3 Monthly mean wind speed averaged over all years per station041008 4 / Vol. 132, NOVEMBER 2010 Transactions of the ASMEDownloaded 19 Jan 2011 to 203.200.35.31. Redistribution subject to ASME license


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or copyright; see http://www.asme.org/terms/Terms_Use.cfmMSE =1nt=1n

Yt Y

t2 9From this evaluation, as can be seen in Table 2, the SES modelachieved smaller errors than a 1 month persistence for all the casestudies. It is also worth noting that for case 3, the models accountingfor monthly seasonality perform better than those that do not.This is expected since the annual peak in the power spectrum islarge. This emphasizes the importance of the seasonal componentin these forecasts. However, the model that combined both autocorrelationand seasonality SS surpassed the other models tested.Consequently, it is shown that though seasonality is importantwhen trying to predict the wind speed a month ahead, there issome autocorrelation in the data, which is important to consider in

the forecast.Table 2 also shows the average mean error ME for all models:ME =1nt=1n

Yt Y t10Assessing the ME is a way to identify if the forecasts are biased.As Table 2 indicates, the ME is very close to zero, which meansthat the forecasts generated by the models are not biased.In addition to Table 2, Fig. 10 below serves as a direct visual

comparison of the models used in this study since it shows theConf. Limit1.0 0.5 0.0 0.5 1.0015 +,162 ,039614 +,301 ,039713 +,429 ,039712 +,543 ,039711 +,458 ,039810 +,333 ,03989 +,190 ,03988 +,064 ,03997 ,046 ,03996 ,072 ,03995 ,056 ,04004 +,097 ,04003 +,193 ,04002 +,370 ,04011 +,572 ,0401Lag Corr. S.E.0930,1 0,000913,4 0,000856,0 0,000739,0 0,000

552,5 0,000420,0 0,000349,9 0,000


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327,2 0,000324,7 0,000323,4 0,000320,1 0,000318,1 0,000312,2 0,000288,9 0,000

203,4 0,000Q p(a) (b) Conf. Limit1.0 0.5 0.0 0.5 1.0015 ,016 ,040214 ,001 ,040213 ,004 ,040212 +,236 ,040211 +,227 ,040210 +,192 ,04029 +,173 ,0402

8 +,137 ,04027 +,054 ,04026 +,026 ,04025 ,150 ,04024 ,011 ,04023 ,063 ,04022 +,065 ,04021 +,572 ,0402Lag Corr. S.E.Fig. 4 Correlograms of monthly wind speed at Stornoway Airport: a autocorrelationfunction and b partial autocorrelationfunctionFig. 5 Removing the seasonal component of wind speed at Stornoway

AirportJournal of Solar Energy Engineering NOVEMBER 2010, Vol. 132 / 041008 5Downloaded 19 Jan 2011 to 203.200.35.31. Redistribution subject to ASME licenseor copyright; see http://www.asme.org/terms/Terms_Use.cfmabsolute error AE for the validation data set. As can be seen,Fig. 10 confirms that the minimum errors occurred when the SSmodel was used.6 ConclusionsIn this paper, 52 years of wind speed records were studied forseven different locations across the UK. A statistical analysis ofthese data was made, and the stations were subdivided into categorieswhere seasonality was weak, average, and very strong. Acorrelogram based on monthly averaged wind speed data revealedthat significant seasonality existed in the time series while thepartial autocorrelation plot showed that significant correlation existedup to 1 month ahead. These plots were used to determine theorder of the forecasting models tested in this study, namely, 1month persistence, 12 month persistence, simple exponentialsmoothing, and simple seasonal. From the comparison and evaluationof these models, it was suggested that the simple seasonalmodel accounting for monthly seasonality and autocorrelation oflag one month gave the best performance in terms of a meansquared error. This approach proposed for forecasting the monthlymean wind speed shows merit on both a financial and technicallevel.

Fig. 6 1 month ahead wind speed forecasts at Stornoway Airport actualversus 1 month persistenceFig. 7 1 month ahead wind speed forecasts at Stornoway Airport actual


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versus 12 month persistence041008 6 / Vol. 132, NOVEMBER 2010 Transactions of the ASMEDownloaded 19 Jan 2011 to 203.200.35.31. Redistribution subject to ASME licenseor copyright; see http://www.asme.org/terms/Terms_Use.cfmTable 2 Errors achieved from the forecasting modelsStations1 month 12 month SES SS

MSE ME MSE ME MSE ME MSE MELerwick 1.368 0.020 1.382 0.003 1.360 0.021 0.754 0.005Stornoway Airport 1.359 0.001 1.501 0.048 1.010 0.024 0.850 0.059Valley 2.333 0.025 2.656 0.017 2.005 0.046 1.339 0.026Aldergrove 0.589 0.003 0.703 0.025 0.543 0.011 0.358 0.024Boscombe Down 0.937 0.018 0.894 0.022 0.734 0.019 0.458 0.020Aberporth 1.728 0.022 1.599 0.011 1.654 0.031 0.833 0.006Tiree 1.946 0.031 1.749 0.069 1.706 0.046 1.041 0.045Fig. 8 1 month ahead wind speed forecasts at Stornoway Airport actualversus SESFig. 9 1 month ahead wind speed forecasts at Stornoway Airport actualversus SS

Journal of Solar Energy Engineering NOVEMBER 2010, Vol. 132 / 041008 7Downloaded 19 Jan 2011 to 203.200.35.31. Redistribution subject to ASME licenseor copyright; see http://www.asme.org/terms/Terms_Use.cfmReferences

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a comparison of long-term wind speed forecasting models

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