Evaluating the wind speed persistence for several wind stations in Peninsular Malaysia

or Wa saan , Ma Keywords: side he w ns f possib risis th me an potential. The initial investigation should include, for example an effort to understand the dynamics of the wind speed series over time; such an understanding would provide insight in to the temporal distribution and the persistence of this energy resource [3]. Wind speed persistence is one of the dominant factors affecting persistent. Kocak [4] applied three different methods (an autocor- relation function, conditional probability and the wind speed duration curves) to hourly wind speed data available at six mete- orological stations in Turkey and found that wind speed duration curve (WSDC) methods could successfully identify the differences in wind speed persistence between the stations as compared to the other methods. In another study, Kocak [6] studied a systematic analysis used to detect long-term correlations, known as detrended fluctuation analysis (DFA). He applied DFA to wind speed data from * Corresponding author. Tel.: þ60 3 8921 5788; fax: þ60 3 8925 4519. Contents lists available at Ener .e ls Energy 37 (2012) 649e656 E-mail address: [email protected] (N. Masseran). renewable source of energy because it is clean and cost effective for many applications such as electric power production and water pumping. The utilisation of wind as an energy resource has been growing rapidly worldwide because the consumption of other energy resources such as oil-, nuclear-, and coal-based resources contribute to environmental pollution and global warming. Wind energy does not impose a transportation problem and its utilisation does not require advanced technology [2]. In Malaysia, the use of wind energy as an alternative source of energy is still not wide- spread; thus, studies should be undertaken to investigate its involve measurements relative to the stability properties of the entities of interest [4e9]. Many methods have been proposed to determine the persis- tence of wind speed over a given area. Kocak [5], for example, suggested a theoretical ideal wind speed duration curve and compared it with the empirical wind speed duration curve to identify the level of persistence. The measure of error between the empirical speed duration curve and the theoretical ideal speed duration curve is considered the criterion for the existence of wind speed persistence, if the error is small, thewind speed is considered Wind speed Persistence Unit-root test Stationary time series Levene’s test Wind speed duration curve 1. Introduction The growing interest in wind as a producing electricity dates to the oil c 1970’s [1]. Wind energy has beco 0360-5442/$ e see front matter � 2011 Elsevier Ltd. doi:10.1016/j.energy.2011.10.035 exists a significant difference in the variability of wind speed between the different stations. Because the variance of the hourly wind speeds for the Chuping station is the smallest observed, the wind speed observed at this location is the most persistent compared to other locations. However, it is more meaningful to measure the persistence at a particular level of speed, one suitable to generate energy. Accordingly, the wind speed duration curve method is applied to the observed data for each station. Consequently, the wind speed at Mersing is found to be the most persistent, and, consequently, this location has the most potential for energy production compared to other locations. � 2011 Elsevier Ltd. All rights reserved. le source of energy for at occurred in the mid- important alternative the sustainability of wind energy production in any location [4]. The stability and sustainability of a source of energy is an important factor not only for wind energy but also for other energy types [4e6]. Various definitions of persistence have been proposed by researchers in various fields; however, all of these definitions Available online 21 November 2011 station exhibits stationarity. The test for equality of variance, based on Levene’s test, shows that there Accepted 23 October 2011 each station, stationarity and variability are investigated using unit-root tests and the test for equality of variance respectively. Results from the unit-root tests indicated that the hourly wind speed for each Evaluating the wind speed persistence f in Peninsular Malaysia N. Masseran a,*, A.M. Razali a,b, K. Ibrahim a,b, W.Z. a School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebang b Solar Energy Research Center, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor a r t i c l e i n f o Article history: Received 15 March 2011 Received in revised form 21 October 2011 a b s t r a c t An important factor to con this study, persistence of t available at 10 wind statio journal homepage: www All rights reserved. several wind stations n Zin a Malaysia, 43600 Bangi, Selangor, Malaysia laysia r when evaluating wind energy potential is the wind speed persistence. In ind speed in Peninsular Malaysia is investigated based on the hourly data rom 2007 to 2009. To determine the degree of persistence in the data for SciVerse ScienceDirect gy evier .com/locate/energy correlated series in a unit-root test. Thus, correlated series will not affect the asymptotic distribution of the test statistic. The PP test provides an estimation for the equation Dyt ¼ dþ ayt�1 þ 3t . The null and alternative hypotheses for the PP test are given by H0 : a ¼ 0 H1 : a < 0 The test statistic for PP test is given by ~ta ¼ ta � g0 f0 �1 2 � Tðf0 � g0Þðseða^ÞÞ 2f 1=20 s ; (4) where a^ is an estimated value obtained from the Eq. (4), t is the ergy 20 wind generation stations located in the north-western part of Turkey. His results indicated the that recorded wind speed has a crossover in scaling exponent and that for long time scale, the data exhibited long-range correlations. Cancino-Solorzano et al. [10] evaluated persistence properties from a method based on an autocorrelation function, a conditional probability and a curve of speed duration for wind stations in Mexico. Their results indicated that coastal areas have the best conditions for wind speed persistence. In this study, the persistence of wind speed at 10 stations in Peninsular Malaysia is investigated based on stationarity properties and variation in the hourly speed data from 2007 to 2009.Futher- more, a stronger basis for the comparison of persistence between stations is made using WSDC to suggest the location that has the most potential to produce wind energy in Peninsular Malaysia. Here, the persistence is evaluated using a time series approach. It is assumed in this study that, the stationary time series with the minimum variance implies a good persistence. Stationarity is a property of a time series with constant mean and variance. The covariance of time between two periods depends only on the distance or interval between the periods of time considered rather than the actual value of the computed covariance [11]. When two data sets are compared in terms of persistence, the data that exhibit stationarity with a smaller amount of variation are considered more persistent. 2. Study area and data Peninsular Malaysia is a country that lies entirely in the equa- torial zone, situated in the south-east part of Asia, and situated in the northern latitude between 1� and 6� N and the eastern longi- tude from 100� to 103� E. Throughout the year, Malaysia experi- ences wet and humid conditions with daily temperatures ranging from 25.5 �C to 35 �C. The wind that blows across the peninsula is influenced by the monsoon seasons, namely the south-west monsoon, the north-east monsoon and two short inter-monsoon periods. The two monsoons that contribute to rainy seasons are the south-west monsoon, occurring from May to September, and the north-east monsoon, occurring from November to March. The latermonsoon brings heavier rainfall in the peninsula, and themost severely affected areas are in the east and south. Malaysia, a mari- time country is also influenced by the effect of sea breezes and land breezes, especially when the sky is not cloudy. During most after- noons, sea breezes occur with speeds of 10e15 knots. However, at night, the reverse process occurs. Weak land breezes occur in coastal areas. The data used in this study were obtained from the Malaysian Meteorological Department. Ten stations were selected for this study: Alor Setar, Bayan Lepas, Cameron Highlands, Chuping, Ipoh, Kota Bahru, Kuantan, Malacca, Mersing and Kuala Terengganu Airport (shown in Table 1 and Fig. 1). The wind speed hourly data from 1 January, 2007, to 30 November, 2009, were used. 3. Methods Many methods have been applied to determine the persistence of wind speed at a particular location; [4e6,10]. Three different unit-root tests, including the Augmented DickeyeFuller test, the DickeyeFuller test with generalised least squares (GLS) detrending and the PhillipsePerron test, were applied to test the stationarity in the data for each station, and then, the results were compared. The tests are based on the random walk process. The random walk is defined as a non-stationary stochastic process. If the time series is found to be a significantly a random walk process, then that time N. Masseran et al. / En650 series is said to be non-stationary. 3.1. Unit-root test 3.1.1. Augmented Dickey Fuller test (ADF) ADF is applied when the time series satisfies the autoregressive model. The order of the autoregressive model, lag-k, is determined based on the partial autocorrelation function (PACF) as given by rkk ¼ 8>>>>>>< >>>>>>: r1 if k ¼ 1 rk � Pk�1 j¼1 rk�1;jrk�j 1� Pk�1 j¼1 rk�1;jrj if k ¼ 2;3. (1) with rkj ¼ rk�1;j � rkkrk�1;k�j for j ¼ 1;2;3.k� 1, where rk is the autocorrelation value at lag-k, (for more detail, see [12]). The autoregressive model of order p denoted as AR(p), and can be written as yt ¼ dþ r1yt�1 þ r2yt�2.þ rpyt�p þ 3t (2) ADF is calculated by estimating Eq. (2) after subtracting yt�1 from both sides of Eq. (2). Dyt ¼ dþ ayt�1 þ b1Dyt�1/þ bpDyt�p þ 3t (3) with a ¼ r1�1, the null and alternative hypotheses for ADF are respectively, H0 : a ¼ 0 H1 : a < 0 and they can be evaluated using the t-ratio for a, � ta ¼ a^seða^Þ � . The critical region for this test statistic is based on the MacKinnon critical region [13,14]. 3.1.2. Phillips Perron test (PP) The PP test applies a non-parametric approach to control the Table 1 Geographical coordinate and altitude for each station. Station Latitude Longitude Altitude (m) Alor Setar 6�120N 100�240E 3.9 B. Lepas 5�180N 100�160E 2.8 C.Highlands 4�280N 101�220E 1545.0 Chuping 6�290N 100�160E 21.7 Ipoh 4�340N 101�060E 40.1 Kota Bahru 6�100N 102�170E 4.6 Kuantan 3�470N 103�130E 15.3 Malacca 2�160N 102�150E 8.5 Mersing 2�270N 105�500E 43.6 K.Teregganu 5�230N 103�060E 5.2 37 (2012) 649e656 a t-ratio of a, seða^Þ is the coefficient’s standard error, s is the standard N. Masseran et al. / Energy error of the regression test, g0 is the consistent estimate of error variance and f0 is an estimate of the residual spectrum at frequency zero. The parameter f0 can be estimated using a kernel based on the sum of the covariance or on the autoregressive spectral density estimation [14e16]. 3.1.3. DickeyeFuller test with generalised least squares detrending (DFGLSD) DFGLSD includes a constant, or is constant with a linear time trend in the ADF test regression. The data are detrended so that the explanatory variable is excluded from the data prior to the regression test. The quasi-difference of yt, which on the value of ~a, represents specific point alternatives against the null hypothesis and is given by d � yt ���~a� ¼ � yt if t ¼ 1 yt � ~ayt�1 if t>1 (5) The recommend values for ~a are given by ~a ¼ � 1� 7=T if xt ¼ f1g 1� 13:5=T if xt ¼ f1; tg (6) Fig. 1. Location of wind station 37 (2012) 649e656 651 Ordinary least squares regression of the quasi-difference data dðyt j~aÞ on the quasi-difference dðxt j~aÞ is defined as d � yt ���~a� ¼ d�xt ���~a�0d�~a�þ ht (7) where xt is either constant or a constant with a trend. The param- eter dð~aÞ is the ordinary least squares estimate from the regression. The GLS detrended data are defined as ydt ¼ yt � x0td � ~a � (8) DFGLSD test were performed by estimating the ADF test equa- tion via the detrended data. Dydt ¼ aydt þ b1Dydt�1 þ b2Dydt�2 þ.þ bpDydt�p þ 3t (9) With a ¼ r�1, the null and alternative hypotheses for DFGLSD are H0 : a ¼ 0 H1 : a < 0 The test statistic is also the t-ratio ta ¼ a^seða^Þ [14,17]. The critical value for this test statistic was computed by using Eviews7. s in Peninsular Malaysia. produced is chosen. The percentage of time that corresponds to the intersection point between the horizontal line and WSDC is the value used to indicate wind persistence, and is denoted as Pwsdc [4,10]. 4. Results and discussion 4.1. Descriptive statistics Before a detailed analysis is made, it is important to evaluate the descriptive statistics to obtain some preliminary information about ergy 37 (2012) 649e656 3.2. Levene’s test Levene’s test is used to assess the equality of variances between different groups of data. If the variances are similar, then the data from k different group are homogeneous. The advantage of Levene’s test is that it does not require the assumption of normality. The null and alternative hypotheses of Levene’s test are given by H0 : s21 ¼ s22 ¼ s23. ¼ s2k H1 : at least one pair of s2i and s 2 j such that s2iss 2 j where isj The test statistic is given by W ¼ ðN � kÞ Xk i¼1 Niðxi � �xÞ2 ðk� 1Þ Xk i¼1 XNi j¼1 � xij � xi 2 (10) with xij ¼ 8< : jyij � yi:j or jyij � ~yi:j ; �x ¼ 1 N Xk i¼1 XNi j¼1 xij xi ¼ 1 Ni XNi j¼1 xij; N ¼ N1 þ N2.þ Nk; where yi is the observed data, yi: is the mean for i-th group, ~yi: is median for i-th group, xij is a new set of data after subtracting either the mean or median of the observed data yi, �x is the overall mean and xi is the mean for i-th group for the data xij. The selection of the mean or median when defining variable xij determines the power and robustness of Levene’s test. The median is usually used when the distribution of the data is not symmetric, and the selection of the mean is appropriate when the data come from a symmetrical distribution. The null hypothesis is rejected at the significance level a if the value of the test statistic is greater than the critical val- ueFða; k� 1;N � kÞ, (see [18,19]). 3.3. Wind speed duration curve (WSDC) WSDC is a graphical method often used in wind engineering. This method shows the accumulated distribution of wind speed over a certain period of time. WSDC is a graph in which the vertical axis represents the wind speed and the horizontal axis represents the percentage of time the wind speed equals or exceeds some specific value [10]. WSDC provides an approximate idea of the nature of the wind regime at each wind station. The flatter the curve, the more regular the wind regime is, while the steeper the curve, the more irregular the wind regime is at each station [20]. To construct the WSDC, estimates ofPðyiÞ ¼ PðY � yiÞ are made using the rank i of the order statisticsyðiÞ. Notably, yi is the observation at time i in the raw data, and yðiÞ is the observed value in the order of i after the data are arranged in ascending order [4]. Each i-th order statistic has its own distribution, (see [21]). The estimates for PðyiÞ are given by P � yðiÞ � ¼ T þ 1� i T þ 1 � 100; i ¼ 1;2.; T (11) where T is the number of observations in the time series data. The graph of WSDC is obtained by plotting yðiÞ on the vertical axis versus Pðy Þ on the horizontal axis. A truncated level on the N. Masseran et al. / En652 ðiÞ vertical axis, which indicates the level at which energy can be the data. The descriptive statistics in Table 2 indicate little differ- ence in terms of the mean and variance of wind speed for each station, which was confirmed by conducting a test to determine whether there was a significant difference between the variances for each station. Kuantan and Alor Setar showed the highest maximum value compared to other stations with wind speeds of 11.8 m/s and 11.5 m/s, respectively. The range of wind speeds that is suitable for turning the windmill and generating energy is usually between 3 m/s and 12 m/s. From Table 2, based on the calculated mean value, it can be observed that none of the stations are suitable for generating wind energy because the mean wind speed for each station does not exceed 3.00 m/s, the minimum value for turning the windmills. However, the maximum value for each station is found to lie in the range of 6.00 m/se12.00 m/s, indicating that there may be some stations that are suitable for generating wind power, at certain times only. Thus, the persistence of wind speed for each station should be evaluated to provide some meaningful information as to whether wind power can be generated. The coefficient of skewness for each station is found not to be approx- imately zero, indicating that the data do not follow a normal distribution. In fact, in many cases, the wind speed data are well fit to the Weibull distribution. Many geographical factors contribute to the wind speed magnitude at each station, including factors such as altitude and surface roughness index. Although the Cameron Highlands station is located high above sea level, the wind speed observed was low because the value of the surface roughness index (0.6), was rela- tively high. Aside from experiencing low temperatures (ranging from 10 �C to 20 �C), this location also experiences the highest rainfall in the country. The combined effect of low temperature and high humidity causes the wind speed to be low. 4.2. Unit-root test The Ipoh station was chosen as an example to show how the detailed analysis was carried out; the same method was followed for other stations. Fig. 2 shows the time series plot for Ipoh station. The X-axis indicates the time (hours), while the Y-axis indicates the observed wind speed value. The fluctuation in the wind speeds recorded for Ipoh station indicated that there are some observa- tions that deviate from calculated mean value of 1.64 m/s. The Table 2 Descriptive statistics for each station. Station Mean (m/s) Variance (m/s)2 Minimum (m/s) Maximum (m/s) Skewness Coef. Curtosis Coef. Alor Setar 1.74 1.69 0.00 11.80 1.08 4.25 B. Lepas 1.92 2.20 0.00 10.00 0.74 3.01 Chuping 1.03 0.75 0.00 6.00 0.42 2.31 Ipoh 1.64 1.05 0.00 9.50 0.97 5.18 C.Highland 1.90 1.66 0.00 9.20 0.96 4.50 Kota Bahru 2.18 2.10 0.00 9.70 0.42 3.32 Kuantan 1.55 1.48 0.00 11.50 1.04 3.72 Malacca 1.98 1.86 0.00 8.90 0.66 3.56 Mersing 2.82 1.95 0.00 9.80 0.66 3.83 Dydt ¼ � 0:063ydt � 0:481ydt�1 � 0:419Dydt�2 Fig. 2. Wind speed time series plot for Ipoh station. N. Masseran et al. / Energy calculated variance for wind speed is 1.05 (m/s)2. The plot also indicates that the data do not show any increasing or decreasing trends. Furthermore, the seasonal and cyclical component are also absent in the series. These features imply that the series experi- ences a stationary condition. The unit-root test is performed to determine whether the stationarity of time series is significant. 4.2.1. ADF test Before the DickeyeFuller test is performed, the autoregressive model for the time series data of Ipoh must be identified. From Fig. 3, the partial autocorrelation function (PACF) is found truncated at lag-24. Based on this characteristic, the appropriate model for these data is AR (24). Estimation of the coefficient a in Eq. (3) is determined based on a regression method. If a is found to be significantly greater than zero, the series of data is non-stationary. The estimated AR(24) model is found to be Fig. 3. Partial autocorrelation plots for Ipoh station. þ.� 0:089Dydt�24 The null and alternative hypotheses are given by H0 : a ¼ 0 H1 : a < 0 The test statistic is the t-ratio ta ¼ a^seða^Þ ¼ �0:0626 0:008203 ¼ �7:64 At a 5% level of significance, the critical region was �1.94. Thus, the null hypothesis was rejected. The DFGLSD test also states that the time series plot of wind speed data for the Ipoh station is stationary. 4.2.3. PP test To confirm the result of the earlier tests (that the time series for the Ipoh wind speed data is stationary), a comparison was made between the results based on the DF, DFGLSD and PP tests. In most cases, the PP test provides a conclusion similar to those of the ADF and DFGLSD tests; however, if there are differences in the results of any two tests, the stationarity of time series can be questioned. The null and alternative hypotheses for the PP test are given by H0 : a ¼ 0 H1 : a < 0 respectively. The test statistic is given by ~ta ¼ ta � g0 f0 �1 2 � Tðf0 � g0Þðseða^ÞÞ 2f 1=20 s It was found that the standard error of the coefficient a^ was 0.00541, the standard error of the regression test was 0.9123, the consistent estimates of error variance was 0.8322, the number of observations was 25,560 and the estimator of residual spectrum at frequency zero was 0.919. Thus, our test statistic value was Dyt ¼ 0:052� 0:316yt�1/� 0:074Dyt�24 For testing stationarity based on ADF, the null and alternative hypotheses are given by H0 : a ¼ 0 H1 : a < 0 respectively. Using the estimated parameter value found from the fitted model, we have ta ¼ �0:3160:0145 ¼ �21:79 To determine the rejection region, Mackinnon critical values were applied. At a 5% significance level, the MacKinnon critical region was �2.861. Thus, the null hypothesis was rejected. There- fore, the time series for the Ipoh data is not a randomwalk process; that is, it has stationary wind speed data at this station. 4.2.2. DFGLSD test An estimate of regression equation using detrended data for the Ipoh station is given by 37 (2012) 649e656 653 ~ta ¼ �94:40: At a 5% level of significance, the MacKinnon critical region was �2.861. Therefore, the null hypothesis was rejected. After an allowance was made for the serial correlation in the time series, the wind speed data for Ipoh station was also found to be stationary. Figs. 4 and 5 show the time series plots and the partial auto- correlation function plots for other stations. From Fig. 4, it can be observed that there are no increasing or decreasing trends and no seasonal or cyclical components during the past three years for the data of all stations. From Fig. 5, we observe that PACF truncated at lag-46 for Kota Bahru station, truncated at lag-29 for Chuping station, truncated at lag-31 for Alor Setar station and truncated at lag-48 for Kuala Terengganu station; for other stations, PACF was truncated at lag-47. Based on the truncated lags identified using the PACF, suitable autoregressive models for each station were chosen before the unit-root test was performed. Table 3 shows the results of the unit-root tests for all stations. At a 5% level of significance, the MacKinnon critical region was �2.861. We found that wind speed data at all stations were stationary. Because all the series were stationary, it was informative to identify the station with the smallest variance. To investigate the differences in variance between stations, Levene’s test was performed. A comparison was made of the variability in the data to determine the degree of persistence. When the variations of two data sets are compared based on the measure of variance, the data set with a smaller variance is the more persistent. 4.3. Levene’s test Levene’s test cab suitably be used to test the variance because the data are not normally distributed, indicated by the coefficient of skewness for all stations in Table 2. If the variances of wind speed between stations are significantly different, we can conclude that there exists a difference in persistence of wind speed among the station. When the Yij variation in two data sets are compared based on the measured of variance, the data set with a smaller variance is more persistent. Let denote the observedwind speed at time j for the i-th station, where i¼ 1,2,.10 and j¼ 1,2,.T. After applying Eq. (10) to the data Yij, and with the appropriate transformation, we have W ¼ ð255600� 10Þ � 25560 P10 i¼1ðxi � 0:989Þ2 ð10� 1ÞP10i¼1 P25560j¼1 �Xij � xi 2 ¼ 634:31 Because the test statistic was quite large, we rejected H0, implying that the variance was significantly different between stations. This result indicated that there exist some differences in persistence between stations. Because the wind speed at Chuping station was found to have the smallest variance about the mean as compared to other stations, the speed is most persistent at this station. Unfortunately, the mean speed for Chuping station was approximately 1.03m/s, which is below theminimum threshold for N. Masseran et al. / Energy 37 (2012) 649e656654 Fig. 4. Wind speed time seri es plot for each station. Fig. 5. Partial autocorrelation Table 3 Summary of unit-root test for each wind stations. Station Test statistics 5% significant level 1% significant level Result Kota Bahru ADF �11.48 �2.861 �3.43 Reject Ho PP �57.22 �2.861 �3.43 Reject Ho DFGLS �7.071 �1.94 �2.57 Reject Ho Malacca ADF �9.47 �2.861 �3.43 Reject Ho PP �59.31 �2.861 �3.43 Reject Ho DFGLS �5.378 �1.94 �2.57 Reject Ho Kuantan ADF �14.98 �2.861 �3.43 Reject Ho PP �60.59 �2.861 �3.43 Reject Ho DFGLS �5.69 �1.94 �2.57 Reject Ho Mersing ADF �8.94 �2.861 �3.43 Reject Ho PP �65.21 �2.861 �3.43 Reject Ho DFGLS �6.60 �1.94 �2.57 Reject Ho Cameron Highlands ADF �15.06 �2.861 �3.43 Reject Ho PP �59.78 �2.861 �3.43 Reject Ho DFGLS �10.77 �1.94 �2.57 Reject Ho Bayan Lepas ADF �12.12 �2.861 �3.43 Reject Ho PP �59.80 �2.861 �3.43 Reject Ho DFGLS �3.49 �1.94 �2.57 Reject Ho Chuping ADF �10.03 �2.861 �3.43 Reject Ho PP �58.31 �2.861 �3.43 Reject Ho DFGLS �6.93 �1.94 �2.57 Reject Ho Alor Setar ADF �16.66 �2.861 �3.43 Reject Ho PP �57.15 �2.861 �3.43 Reject Ho DFGLS �5.82 �1.94 �2.57 Reject Ho Kuala Terengganu ADF �10.74 �2.861 �3.43 Reject Ho PP �83.74 �2.861 �3.43 Reject Ho DFGLS �8.30 �1.94 �2.57 Reject Ho N. Masseran et al. / Energy 37 (2012) 649e656 655 generating energy. However, the observed maximum value was found to be 6.00 m/s, implying that the Chuping station is capable of generating energy at certain times. To investigate in more detail whether Chuping station has the potential to produce energy, we function for each station. Fig. 6. WSDC for Ipoh, Kota Bahru, Melaka, Kuantan and Mersing. ergy evaluated the persistence of wind speed at a certain truncated level based on the wind speed duration curve. 4.4. Wind speed duration curve (WSDC) The persistence analysis on energy production for each station is determined using the wind speed duration curve. Figs. 6 and 7 show some features of the wind regimes at all stations studied. The vertical axis represented the value of wind speed in ascending order, and the horizontal axis represents the percentage of time the wind speed equals or exceeds some specific value of wind speed. In this graph, the flatter the curves, the more regular are the wind regimes, while the steeper the curve, the more irregular are the wind regimens for each station. For most wind turbines, the range Fig. 7. WSDC for Alor Setar, Bayan Lepas, C. Highlands and K.Terengganu. N. Masseran et al. / En656 of cut-inwind speed for energy production is 3m/se4.5m/s [22]. In this study, 4.00 m/s was chosen as the truncated level on the vertical axis because this level is commonly suitable for generating wind energy in Malaysia. The persistence level of wind energy at each station can be determined by using the percentage of the time that the speed is greater than 4.00 m/s, which can be computed using the graph of WSDC. The percentage of time corresponds to the areas beyond the intersection point between the horizontal line, and the WSDC is defined as the persistence value, Pwsdc. From Figs. 6 and 7, the corresponding value of Pwsdc for each station can be determined. The value of Pwsdc for the Mersing station is the highest at 18.2. The wind speed at the Mersing station exceeded 4.0 m/s, 18.2% of the time during the three-year period. This percentage is relatively small; thus, the observed persistence level of wind speed is not significant enough to ensure a sustainable energy supply. Only at certain times does the value of wind speed at the Mersing station exceed 4.00 m/s. The result from the wind speed duration curve indicated a lack of energy persistence for each station studied. 5. Conclusion Based on the assessment of stationarity and variation in the wind speed data at all the stations considered, the speed at the Chuping station was found to be the most persistent. However, when the stations were compared in terms of the potential for methods for wind persistence: their application in assessing the best site for a wind farm in the state of Veracruz, Mexico. Renewable Energy 2010;35: [17] Elliott Graham, Rothenberg Thomas J, James HS. Efficient tests for an autor- egressive unit root. Econometrica 1996;64:813e36. [18] Carrol RJ, Schneider H. A note on levene’s test for equality of variances. Statistics & Probability Letters 2003;3(Issue 4):191e4. [19] Lim TS, Loh WY. A comparison of test of equality of varians. Computational Statistics & Data Analysis 1996;22:287e301. [20] Cellula M, Cirrincione G, Marvuglia A, Miraoui A. Wind speed spatial esti- mation for energy planning in Sicily: introduction and statistical analysis. Renewable Energy 2008;33:1237e50. [21] Hogg RV, Tanis EA. Probability and statistical inference. 7th ed. Upper Saddle River, NJ: Pearson Prentice Hall; 2006. [22] Lu Lin, Hongxing Hang, John Burnett. Investigation on wind power potential on Hong Kong islands - an analysis of wind power and wind turbine char- 2844e52. [11] Gujarati D. Essentials of econometrics. 2nd ed. Boston: Irwin/ McGraw-Hill; 1999. [12] Bowerman BL, O’Connell RT, Koehler AB. Forecasting, time series and regression, an applied approach. 4th ed. Belmont, CA: Thomson Brooks/Cole; 2005. [13] Dickey DA, Fuller WA. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 1979; 74:427e31. [14] Eviews7. Quantitative micro software, LLC. 4521 campus drive, #336, Irvine, CA 92612e92621. URL, http://www.eviews.com; 2009. [15] Andrews DWK. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 1991;59:817e58. [16] Phillips PCB, Perron P. Testing for a unit root in time series regression. Bio- metrika 1988;75:335e46. energy production, Mersing had the most potential. The potential for energy production was determined using the wind speed duration curve. The percentage of the time the wind speed at Mersing can produce energy was 18.2%, which was low. All the stations were found to be persistent in terms of the wind speed; however, the average speed observed was quite low. Thus, more effort must be made to identify locations before erecting wind turbines. Acknowledgement The authors are indebted to the staff of the Malaysian Meteo- rology Department for providing the hourly mean wind speed data that made this paper possible. This research would also not have been possible without the sponsorship from Universiti Kebangsaan Malaysia and Ministry of Higher Education, Malaysia (grant number UKM-GUP-TK-08-16-061 and UKM-GUP-2011-213). The authors are also indebted to the anonymous reviewer for their critical comments and views that led to the improvement of this paper. References [1] Sesto E, Casale C. Exploitation of wind as an energy source to meet the world’s electricity demand. Journal of Wind Engineering and Industrial Aerodynamics 1998;74e76:375e87. [2] Ilkilik C, Turkbay I. Determination and utilization of wind energy potential for Turkey. Renewable and Sustainable Energy Review 2010;14:2202e7. [3] Ewing BT, Kruse JB, Schroeder JL, Smith DA. Time series analysis of wind speed using VAR and the generalized impulse response technique. Journal of Wind Engineering and Industrial Aerodynamics 2007;95:209e19. [4] Kocak Kasim. Practical ways of evaluating wind speed persistence. Energy 2008;33:65e70. [5] Kocak Kasim. A method for determination of wind speed persistence and its application. Energy 2002;27:967e73. [6] Kocak Kasim. Examination of persistence properties of wind speed record using detrended fluctuation analysis. Energy 2009;34:1980e5. [7] Dias DA, Marques CR. Using mean reversion as measure of persistence. Economic Modeling 2010;27:262e73. [8] Fletcher J, Forbes D. An exploration of the persistence of UK unit trust performance. Journal of Empirical Finance 2002;9:474e93. [9] Noriega AE, Ramos-Francia M. The dynamic of persistence in US inflation. Economic Letter 2009;105:168e72. [10] Cancio-Solorzano Y, Gutierrez-Trashorras AJ, Xiberta-Bernat J. Analytical 37 (2012) 649e656 acteristics. Renewable Energy 2002;27:1e12. Evaluating the wind speed persistence for several wind stations in Peninsular Malaysia 1. Introduction 2. Study area and data 3. Methods 3.1. Unit-root test 3.1.1. Augmented Dickey Fuller test (ADF) 3.1.2. Phillips Perron test (PP) 3.1.3. Dickey–Fuller test with generalised least squares detrending (DFGLSD) 3.2. Levene’s test 3.3. Wind speed duration curve (WSDC) 4. Results and discussion 4.1. Descriptive statistics 4.2. Unit-root test 4.2.1. ADF test 4.2.2. DFGLSD test 4.2.3. PP test 4.3. Levene’s test 4.4. Wind speed duration curve (WSDC) 5. Conclusion Acknowledgement References