For proper planning and efficient utilization of wind energy, wind speed predictions are important. In the present study the hourly wind speed data from 1995 to 2001 at three meteorological stations at a height of 14 m above the

ground level have been analysed for fitting autoregressive integrated moving average (ARIMA) models

A, Shamshad

M. A, Bawadi

S. A, Mohd. Sanusi

W. M. A, Wan Hussin

English

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1058 ICAST 2003 ediled by Wan Ramli Wan Daud el. al© Facully of Engineering, Universili Kebangsaan Malaysia1059ev AUTOREGRESSIVE INTEGRATED MOVINGAVERAGE MODEL (ARIMA) FOR FORECASTINGWIND SPEEDShamshad A. I, Wan Hussin W. M. A., Bawadi M. A., Mohd. Sanusi S. A.School of Civil Engineering, University of Science MalaysiaKeywords: ARIMA model, autocorrelation function, Akaike infonnation criteriaABSTRACTFor proper planning and efficient utilization of wind energy, wind speedpredictions are important. In the present study the hourly wind speed data from1995 to 2001 at three meteorological stations at a height of 14 m above theground level have been analysed for fitting autoregressive integrated movingaverage (ARIMA) models. First, the analysis has been carried out to detect anytrend that can be present in the data series using Kendall's tau test. The windspeed data were subjected to standard time series analysis. For fitting the ARlMAmodel to the time series of the wind speed data, the three stage procedure ofmodel identification, estimation of model parameters and diagnostic checking ofthe estimated parameters have been adopted. To detennine the possiblepersistence structure in the data. the autocorrelation function (ACF) and thepartial autocorrelation function (PACF) have been used. The examination of theACF and PACF correlograms revealed that the data have non-stationarity.Therefore. ACF and PACF correlograms with various seasonal and non-seasonaldifferencing schemes have been used. All the possible models have beenidentified for the data series. For checking the adequacy of the model fitted to thedata series, statistical tests have been carried. The Akaike Infonnation Criteria(AIC) has been used to sekct the most appropriate fitted model out of the variouscompeting models.INTRODUCTIONWind is pollution free, inexhaustible and free source of energy that has servedman kind for many centuries by propelling ships and driving wind turbines togrind the grains and pumping the water. The cost of wind energy in the recentpast has reduced. [n spite of the high cost of wind energy as compared to those ofcoal and nuclear, wind may become the major source of energy in the time tocome. Many countries have started to harness the energy from the wind andmany more are trying their best. The modelling and forecasting of wind speeddata is important for designing a proper wind energy system.1062I:: p~7C5:ii7is-;/.. \jG.. - -1063Possible Model ¢, (J, (/), a, Ale RemarksKuala TerengganuARIMA· 0.71 1.00(1,1, I)x(O,O,O)12 136.9ARIMA 0.71 0.62 most appropriate(I,O,O)x(O, 1, I)12 155.8 modelARIMA 0.34 0.65(O,I,I)x(O,l,l)12 151.1ARIMA(0,0,1 )x( 1,1,0) 12 0.58 0.45 115.4ARIMA 0.39(0,0,1 )x(O,I,I) 12 0.42 132.7TABLE 1 Statistical Parameters of the Selected ARIMA Models for Wind SpeedPossible Model ¢, 0, (/J, 8, Ale RemarksFIGURE I ACF and PACF Corrclograms with 95% Confidence Limits forVarious Combinations of Non-seasonal Differencing (d) and SeasonalDifferencing (0) of Wind Speed Time Series at Kuantan'0.950.70 '1.00The results obtained in the study reveal that the ARIMA models provide a usefulquantitative description of the mean monthly wind speed. The technique isaccurate but requires a lot of computational skill. The data should be available insufficient large numbers if possible at least 50 ~lI1d preferably 100 successiveobservations should be used to achieve the appropriate model. The technique issite specific and need to be used carefully and it can not respond to 'what if' typeof questions. The forecasting accuracy of ARIMA model decreases with time;CONCLUSIONIn the next step the parameters of all the tentative selected models have beenestimated using the least square techniques. The AR and MA coefficients havebeen optimized by varying the values within a specified range from -1 to I till thcsum of squares of residuals were minimum. The maximum likelihood estimatesof all the mod~l parameters, corresponding to the minimum sum of squares of theresiduals, have been obtained as shown in Table 1. To cherk the adequacy of themodel the residual autocorrelations have been computed. Two or three models on. each st"iit"ron have shown that the residuals of the· model can be considered aswhite n·oi"se. To further test these models the Akaike infoffilation criteria (AIC)(Akaike, 1974) values have been computed. The model having the minimumvalue of AIC has been selected as the most appropriate model. The best modelsfor Mersing, Kuantan and Terengganu are ARIMA (l,O,O)x(O,I,1 )12, ARIMA(1,I,I)x(0,O,O)12 and ARIMA (l,O,O)x(O,I,I)12 respectively. It is observed that ingeneral the models having both a regular and seasonal components were the mostappropriate models. The observed and fitted values of the most appropriatemodels have been shown in Figure 2. The fitted values are quite close to theobserved values. The models perfonnance for forecasting has been evaluated interms of root mean square error (RMSE). RMSE in each case has been foundnearly 0.30 m/s which is quite satisfactory.most appropriatemodelmost appropriatemodel-62.9-97.1118.0171.873.59153.3146.3144.165.8594.74-77.40.850.720.860.710.770.490.600.480.460.150.290.300.860.420.950.45o330.660.53MersingARIMA(1,1,1 ):«O,O.O)!:ARIMA(1,0, I )x(O.O,O).:ARIMA(I ,O,O)x(O.1 ,I )I~ARIMA(O,I,I)x(O,I,I)I;ARIMA(0,0,1 )x( 1,1,0)1:ARIMA(0,0,1 )x(O, 1,1)12KuantanARIMA(1,1,1 )x(O,O,O)12ARIMA(I,O,O)x(O,I,l )12ARIMA(O,I,I)x(O,l,l)12ARIMA(0,0,1 )x( I, I,0)12ARIMA(0,0,1 )x(O,I.1 )12

Autoregressive Integrated Moving Average Model(Arima)For Forecasting Wind Speed.

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Autoregressive Integrated Moving Average Model(Arima)For Forecasting Wind Speed.

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