Investigating Seasonal Wind Energy Potential in Vredendal, South Africa

Volume 29 Number 2

Investigating seasonal wind energy potential in Vredendal, South Africa

Thapelo Mosetlhe1,*, Adedayo Ademola Yusuff2, Yskandar Hamam1 1. Department of Electrical Engineering/French South African Institute of Technology, Tshwane University of Technology, Private Bag X680, Pretoria 0001, South Africa 2. Department of Electrical and Mining Engineering, University of South Africa, P O Box 392, Unisa 0003, South Africa

Abstract sible to harness wind power effectively. During sum- Global warming and the energy crisis have necessi- mer and spring, there was a high potential for wind tated an urgent exploitation and utilisation of renew- power availability compared with that of winter. able energy. Wind energy has gained popularity over the years because of vast availability of its re- Keywords: stochastic; weather; renewable energy source. A study was carried out to investigate the stochastic characteristics of the available wind energy at installation sites. Data for a ten-minute interval wind speed collected over a period of five years and measured at a height of 10, 40 and 62 m in Vredendal was considered. Wind speed data was arranged in seasonal format and its statistical distribution investigated based on Weibull, lognormal and gamma distributions. The Anderson-Darling test and Akaike information criterion were used to evaluate the goodness of fit. The results showed that wind power at different heights and time stamps exhibited different statistical distribution. It was found that wind turbines in Vredendal must be installed as high as pos-

Journal of Energy in Southern Africa 29(2): 77–83 DOI: http://dx.doi.org/10.17159/2413-3051/2017/v29i2a2746 Published by the Energy Research Centre, University of Cape Town ISSN: 2413-3051 http://journals.assaf.org.za/jesa Sponsored by the Department of Science and Technology

* Corresponding author: +27 71 185 4301; email: [email protected]

77 Journal of Energy in Southern Africa • Vol 29 No 2 • February 2018

1. Introduction the lowest wind energy potential. It was also noted The utilisation of renewable energy sources (RESs) that the wind energy potential in Tehran was not has been a burning issue in research and energy pro- substantial enough to warrant a large-scale wind duction. Different types of RES, such as solar, wind, farm, or integration into the grid. and biomass have been exploited as alternatives to Wind is used in Turkey to augment electric the burning of fossil fuels to generate electric power. power supply. At Iskenderun, Weibull and Ray- In the past two decades, efforts were made on effec- leigh’s distributions were used to model wind speed tively integrating RESs into the grid (Mosetlhe et al., data over one year (Celik, 2004). Measurements 2017; Ayodele et al., 2012), with wind energy show- were taken on an hourly basis to obtain wind speed ing great potential in electricity generation. As wind time-series data. The Weibull model gave a better energy depends primarily on the behaviour of wind representation of the intermittent behaviour of wind it has stochastic characteristics, and it is imperative speed at the site. that these are known for a given installation, so that Hourly mean wind speed data was collected at the wind energy is effectively utilised. Kirklareli, also in Turkey (Gokcek et al., 2007), and Modelling of RESs has attracted a great interest, in Rwanda (Safari & Gasore, 2010). The goodness with an attempt to describe their stochastic behav- of fit of the data for Weibull and Raleigh distributions iour. Algorithms such as autoregressive integrated were analysed to estimate available wind power at moving average were used with success in modelling selected sites. In both Turkey and Rwanda, the re- solar radiation data by Ranganai & Nzuza (2015). sults based on correlation coefficient (R2) showed Regression models estimated the intermittent nature that Weibull might sometimes perform badly in of RES. In Vhembe region, Mulaudzi et al. (2013) other sites. The appropriateness of Weibull was used regression models to estimate and predict the compared with Rayleigh and gamma distribution availability of RESs. The correlation coefficient for (Olaofe & Folly, 2012), where data were collected the developed models was above 0.9, which vali- at 10, 50, and 70 m above sea levels. Chi-squared dated the results and indicated that the models could test and R2 were used to estimate the goodness of fit be approximated to real-world measurements at different height levels. It was found that Rayleigh (Taylor, 1990). distribution function gave a better estimate of wind Artificial intelligence techniques such as neural speed than Weibull and gamma distribution func- networks have been used because of their reliability tion. Weibull distribution proved to be an appropri- in predicting time-series data (Dombaycı & Gölcü, ate function to model long-term wind speed data av- 2009). A multi-layer neural network of at least three eraged on an hourly basis (Ayodele et al., 2013), layers was proposed to estimate and predict the sto- whereas artificial neural networks showed its effec- chastic behaviour of wind energy by Nogay et al. tiveness for short-term (i.e., daily, monthly) model- (2012). The revision of this proposed methodology ling (Özgür, 2014; Nogay et al., 2012). was found to give satisfactory performance for fore- The present study investigated the possibility of casting short-term data (Özgür, 2014). using statistical distributions to model short-term A statistical approach shows efficiency in model- (seasonal) wind speed data. The appropriateness of ling long-term wind speed data, although the artifi- statistical distributions (Weibull, lognormal and cial intelligence techniques give satisfactory results gamma) was evaluated using the test of Anderson for short-term data analysis. Economic evaluation of and Darlington (1952) and the information criterion wind energy potential and its importance is, conse- of Akaike (2011). A model was formulated to quan- quently, realised. A Weibull model for wind speed tify the availability of wind energy at different data collected over a period of five years in Zahedan heights, based on the distribution functions. Sections (Iran) was developed based on a statistical approach 2 and 3 give theoretical background for the estima- (Mostafaeipour et al., 2014). Wind energy density tion of the stochastic characteristics of potential wind and wind energy potential from the model were energy at Vredendal, Western Cape province, South quantified, and four different types of wind turbines Africa. Data collection and results of statistical anal- were considered to evaluate the economic prospects ysis are presented in Sections 4 and 5 respectively. of Zahedan. A 2.5 kW model wind turbine showed Discussion and conclusions are presented in Sec- great economic viability when installed on the same tions 6 and 7. site. Long-term wind speed data was collected over a 2. Theoretical background period of eleven years in Tehran (Keyhani et al., The stochastic characteristics of wind speed at a site 2010), where measurements of the mean wind depend on weather conditions, so they can be con- speed were taken three-hourly. The data was used sidered as a random variable. In probability theory, to estimate the range of dimensionless Weibull a random variable ( ) is defined by an event , shape parameter (k) and Weibull scale parameter which assigns values to possible outputs (Alberto, (c). The results showed that April and August had 2008; Hsu, 1997). A𝑥𝑥 probability𝜁𝜁 is assigned for allζ 𝑥𝑥

78 Journal of Energy in Southern Africa • Vol 29 No 2 • May 2018 outputs generated by a random variable. A real [ ( )] = 2 (6) number called a distribution function is assigned to ln 𝑣𝑣−𝜇𝜇 1 � � each event as a probability measure . The density 2 𝑓𝑓 √2𝜋𝜋 𝜎𝜎 𝑣𝑣 𝑒𝑒 of this probability can be defined as Equation 1. where and are respectively the parameters of 𝑃𝑃 lognormal distribution representing the scale and = ( + ) = ( + ) shape parameter.𝜇𝜇 𝜎𝜎 ( ) (10) 𝑥𝑥 𝑑𝑑𝐹𝐹 𝑃𝑃 𝑥𝑥 ≤ 𝑋𝑋 ≤ 𝑥𝑥 𝑑𝑑𝑑𝑑 𝑃𝑃 𝑋𝑋 ≤ 𝑥𝑥 𝑑𝑑𝑑𝑑 − (c) Gamma distribution 𝑃𝑃As𝑋𝑋 wind≤ 𝑥𝑥 speed is collected and varies over time Mosetlhe et al. (2016) used gamma distribution to T, it is classified as a random process (Liptser & estimate the characteristics of time series data and Shiryaev, 2013). An approach to define a random given by Equation 7 (Saucier, 2000). process considers a function ( ) as a random process for time . A random variable = ( ) can = (7) be described by its cumulative𝑋𝑋 distribution𝑡𝑡 function 𝛼𝛼− (1 ) 𝑣𝑣 1 1 1 𝑣𝑣 �𝛽𝛽� 𝑡𝑡 𝑋𝑋 𝑋𝑋 𝑡𝑡 𝛼𝛼 (CDF) ( , ) according to Equation 2. 𝑓𝑓 𝛽𝛽 𝛤𝛤 𝛼𝛼 𝑒𝑒 where ( ) is a gamma function defined by Equa- 𝑥𝑥 1 1 ( , 𝐹𝐹) =𝑥𝑥 P𝑡𝑡{ ( ) } (2) tion 8. Γ 𝛼𝛼 𝑥𝑥 1 1 1 1 where𝐹𝐹 𝑥𝑥 𝑡𝑡 ( , 𝑋𝑋) is𝑡𝑡 a ≤first𝑥𝑥-order distribution of ( ), ∞ c−1 (−x) (8) while second-order distribution of ( ) is given by Γ(c) = ∫ dx 𝑥𝑥 1 1 x e Equation𝐹𝐹 3.𝑥𝑥 𝑡𝑡 𝑋𝑋 𝑡𝑡 0 𝑋𝑋 𝑡𝑡 ( , ; , ) = P{ ( ) ; ( ) } (3) and the parameters and are the shape and the scale parameters respectively. 𝑥𝑥 1 1 2 2 1 1 2 2 𝛼𝛼 𝛽𝛽 where𝐹𝐹 𝑥𝑥 𝑡𝑡for𝑥𝑥 a 𝑡𝑡given time𝑋𝑋 𝑡𝑡 ≤and𝑥𝑥 𝑋𝑋, 𝑡𝑡 =≤ 𝑥𝑥( ) and

= ( ) are two random variables. Therefore, 1 2 1 1 the CDF of a random𝑡𝑡 process𝑡𝑡 can𝑋𝑋 be defined𝑋𝑋 𝑡𝑡 by 2.2 Goodness of fit 2 2 The AD and AIC were used in this work to evaluate Equation𝑋𝑋 𝑡𝑡ℎ𝑋𝑋 𝑡𝑡4. 𝑛𝑛 the goodness of fit using Equation 9. ( , … , , , … , ) = P{ ( ) , … , ( ) } (4) = ln ( ) + ln (1 𝑥𝑥 1 𝑛𝑛 1 2 1 𝐹𝐹 𝑥𝑥 𝑥𝑥 𝑡𝑡 𝑡𝑡 𝑋𝑋 𝑡𝑡 ≤ ( 2 ) 𝑁𝑁 2𝑖𝑖−1 1 𝑛𝑛 𝑛𝑛 𝑁𝑁 ) 𝑖𝑖=1 𝑖𝑖 (9) 𝑥𝑥Weibull𝑋𝑋 𝑡𝑡distribution≤ 𝑥𝑥 is generally used to describe 𝐴𝐴 −𝑁𝑁 − ∑ 𝑁𝑁 � �𝐹𝐹 𝑋𝑋 � − 𝑁𝑁+1−𝑖𝑖 wind speed data as a random process, hence it was where𝐹𝐹 𝑋𝑋 <� < are ordered sample data and compared with lognormal and gamma distributions is the number of samples. A deviation of the model 1 𝑁𝑁 to describe wind speed data in this work. These dis- derived𝑋𝑋 from⋯ probability𝑋𝑋 distribution from true dis-𝑁𝑁 tributions and their properties are outlined in this tribution is measured using the AIC according to section. Furthermore, the goodness of these distri- Equation 10. 𝑓𝑓 butions is tested using the Anderson-Darling (AD) 𝑔𝑔 and Akaike information criterion (AIC) tests. = log ( ) log ( ) (10)

𝑔𝑔 𝑓𝑓 2.1 Probability distribution fitting 𝐴𝐴𝐴𝐴𝐴𝐴where E𝐸𝐸 is the𝑋𝑋 expectation− 𝐸𝐸 𝑋𝑋with respect to the true (a) Weibull distribution distribution of (Akaike, 2011). The Weibull probability density function (PDF) is calculated by Equation 5 (Ayele et al., 2018). 𝑔𝑔 𝑋𝑋 3. Estimation of wind power density = (5) The available wind power density in W/m2 is given 𝑘𝑘−1 𝑣𝑣 𝑘𝑘 𝑣𝑣 −�𝑐𝑐� by Equation 11 (Olaofe & Folly, 2012). 𝑐𝑐 𝑐𝑐 = where𝑓𝑓 � is� �the� probability𝑒𝑒 of describing the wind 1 3 (11) speed . The parameters and are the shape and 𝑎𝑎 𝑃𝑃 2 𝜌𝜌 𝑣𝑣 the scale𝑓𝑓 parameter of Weibull distribution respec- where is the air density of the site, and is the wind power density. To obtain more accurate wind tively. 𝑣𝑣 𝑘𝑘 𝑐𝑐 𝑎𝑎 𝜌𝜌 𝑃𝑃 power density, Equation 11 becomes Equation 12 (b) Lognormal distribution to take into consideration the time variation of the Lognormal distribution has been used mostly to wind speed and air density. evaluate the time series data (Saucier, 2000). Its two parameters PDF are described by Equation 6. = (12) 1 𝑁𝑁 3 𝑃𝑃𝑎𝑎 2𝑁𝑁 ∑𝑖𝑖=1 𝜌𝜌𝑖𝑖𝑣𝑣 𝑖𝑖

79 Journal of Energy in Southern Africa • Vol 29 No 2 • May 2018 The expected value of the cube of the wind speed 4. Methodology is given by Equation 13 (Ayodele et al., 2012). The wind speed data over a period of five years: 01/01/2011–31/12/2015 was collected at Vreden- = ( ) (13) dal. Measurements were taken at intervals of ten 3 ∞ 3 minutes and height levels of 10, 40, and 62 m. The 0 where𝑣𝑣 (∫ ) 𝑣𝑣is 𝑓𝑓wind𝑣𝑣 𝑑𝑑 distribution𝑑𝑑 . Substituting Equa- data collected is divided into seasonal groups ac- tion 13 into 11 gives Equation 14. cording to season: summer (December–February), 𝑓𝑓 𝑣𝑣 autumn (March–May), winter (June–August) and spring (September–November). The data collected = ( ) (14) for these seasons is tested based on the three distri- 1 ∞ 3 𝐷𝐷 2 0 butions described in Section 2. Estimating𝑃𝑃 𝜌𝜌 wind∫ 𝑣𝑣 power𝑓𝑓 𝑣𝑣 𝑑𝑑 𝑑𝑑density using gamma distribution is achieved by substituting Equation 7 in 5. Results Equation 14, which yields Equation 15. The results of goodness of fit test performed for all the seasons based on Section 2.2 are presented in = [ ( + 1)( + 2)] (15) Tables 1, 2, 3 and 4. The seasonal wind power den- 1 3 sities at 10, 40 and 62 m calculated using Equation 𝐺𝐺 2 For𝑃𝑃 Weibull𝜌𝜌 𝛽𝛽distribution,𝛼𝛼 𝛼𝛼 Equation𝛼𝛼 4 is substituted in 8 are presented in Tables 5, 6 and 7, together with Equation 14 to obtain Equation 16. wind power densities based on wind distribution in Equations 11 and 12. The variation of the distribu- = 1 + (16) tion and their probabilities for Summer and Winter 1 3 3 at 40 m are shown in Figures 1, 2, 3 and 4. 𝑊𝑊 𝑃𝑃 2 𝜌𝜌𝑐𝑐 𝛤𝛤 � 𝑘𝑘� Table 1: Goodness of fit test for summer. Height 10 m 40 m 62 m dist. Wei Log Gam Wei Log Gam Wei Log Gam AD 20.44 13.95 4.85 80.68 119.5 85.94 120.7 141.4 119.2 P <0.01 0.00 <0.005 <0.01 0.00 <0.005 <0.01 0.00 <0.005 AIC 13802 136575 13567 6430 65089 64485 64166 64914 64379 Best fit Gamma Weibull Weibull AD = Anderson and Darlington, P = P Value, AIC = Akaike information criterion, Dist. = Distribution name, Wei. = Weibull, Log = Lognormal, Gam. = Gamma

Table 2: Goodness of fit test for autumn. Height 10 m 40 m 62 m dist. Wei Log Gam Wei Log Gam Wei Log Gam AD 101.8 40.96 161.0 27.16 45.60 11.98 37.49 36.71 11.48 P <0.01 0.00 <0.005 <0.01 0.00 <0.005 <0.01 0.00 <0.005 AIC 50036 48887 21723 54685 55009 54480 55543 55739 55300 Best fit Gamma Gamma Gamma AD = Anderson and Darlington, P = P Value, AIC = Akaike information criterion, Dist. = Distribution name, Wei. = Weibull, Log = Lognormal, Gam. = Gamma

Table 3. Goodness of fit test for winter. Height 10 m 40 m 62 m dist. Wei Log Gam Wei Log Gam Wei Log Gam AD 127.5 61.43 41.58 37.16 36.87 11.70 26.03 47.99 20.57 P <0.01 0.00 <0.005 <0.01 0.00 <0.005 <0.01 0.00 <0.005 AIC 43734 42199 42780 48981 48981 48584 47270 47754 47319 Best fit Gamma Gamma Weibull AD = Anderson and Darlington, P = P Value, AIC = Akaike information criterion, Dist. = Distribution name, Wei. = Weibull, Log = Lognormal, Gam. = Gamma

80 Journal of Energy in Southern Africa • Vol 29 No 2 • May 2018 Table 4: Goodness of fit test for spring. Height 10 m 40 m 62 m dist. Wei Log Gam Wei Log Gam Wei Log Gam AD 127.5 61.43 41.58 37.16 36.87 11.70 26.03 47.99 20.57 P <0.01 0.00 <0.005 <0.01 0.00 <0.005 <0.01 0.00 <0.005 AIC 43734 42199 42780 48981 48981 48584 47270 47754 47319 Best fit Gamma Gamma Weibull AD = Anderson and Darlington, P = P Value, AIC = Akaike information criterion, Dist. = Distribution name, Wei. = Weibull, Log = Lognormal, Gam. = Gamma

Figure 1: Probability density of summer.

Figure 2: Probability of summer.

Figure 3: Probability density of winter.

81 Journal of Energy in Southern Africa • Vol 29 No 2 • May 2018 Figure 4: Probability of winter.

Table 5: Seasonal wind power density at 10 m. Summer Autumn Winter Spring

2 Pa (W/m ) 168.55 104.87 86.64 151.23 2 PD (W/m ) 74.18 98.29 81.22 142.39

Pa = Available wind power density, PD = Probability distribution wind power density

Table 6: Seasonal wind power density at 40 m. Summer Autumn Winter Spring

2 Pa (W/m ) 318.32 193.32 181.80 275.12

2 PD (W/m ) 301.96 186.54 172.38 264.67

Pa = Available wind power density, PD = Probability distribution wind power density

Table 7: Seasonal wind power density at 62 m. Summer Autumn Winter Spring

2 Pa (W/m ) 318.32 193.32 181.80 275.12

2 PD (W/m ) 336.68 213.80 204.13 313.13

Pa = Available wind power density, PD = Probability distribution wind power density

speed distribution at different heights. It is, therefore, 6. Discussion imperative to investigate the statistical properties of Wind speed data at different heights of the same site installation sites for varying heights. can have dissimilar distributions. Seasonal wind Summer and spring have a better wind energy speed data considered at Vredendal at different potential. It is easily observed in Tables 1–4 that, for heights showed different characteristics. The good- all the seasons, there is an increase in wind energy ness of fit test in Tables 1–4 indicates that gamma potentials as the installation height increases. Wind distributions gave a better estimation of seasonal turbines must, therefore, be installed as high as pos- data than Weibull and lognormal. Weibull distribu- sible to harness wind power effectively at Vredendal. tion for summer seasons gave a better estimation as compared to gamma and lognormal distributions for wind speed at 40 and 62 m. Figures 1–4 show that 7. Conclusions the data estimated by the probabilities is relatively Wind energy potential at Vredendal was investi- close to the original data. The wind speed data at gated by outlining the theoretical background for the different height levels at the same site exhibited dif- proposed model and adopting the goodness of fit ferent distributions, implying that a single probability tests. Parameters of the distributions were estimated. distribution could not be used to generalise wind From the results, it can be deduced that, for effective

82 Journal of Energy in Southern Africa • Vol 29 No 2 • May 2018 exploitation of wind energy in Vredendal in the Hsu, H. P. 1997. Theory and problems of probability, Western Cape province of South Africa, turbines random variables, and random processes. Schaums must be installed as high as possible. Furthermore, Outline Series. it can be concluded that the site can contribute Keyhani, A., Ghasemi-Varnamkhasti, M., Khanali, M. & more energy towards the overall electrical power Abbaszadeh, R. 2010. An assessment of wind energy supply during the summer and spring than in win- potential as a power generation source in the capital of Iran, Tehran. Energy 35(1): 188-201. ter and autumn. https://doi.org/10.1016/j.energy.2009.09.009

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83 Journal of Energy in Southern Africa • Vol 29 No 2 • May 2018