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Wind Speed Distribution and Performance of Some Selected Wind Turbines in Jos, Nigeria

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Wind Speed Distribution and Performance of Some Selected Wind Turbines in Jos, Nigeria Wind speed distribution and performance of some selected wind turbines in Jos, Nigeria Joseph Aidan Federal University of Technology, Yola P. M. B. 2076, Yola, Adamawa State, Nigeria. E-mail: [email protected] (Received 1 May 2011; accepted 26 June 2011) Abstract The wind speed data of Jos have been shown to be either gamma or normally distributed. The wind is available and could be used for both residential and large scale power generation. At respective hub heights of 15m and 100m, at least 23% and 40% of Iskra AT5-1 and Micon NM 82 wind turbines installed capacities can averagely be generated respectively. A Micon NM 82 installed at a height of 100m in Jos can service about 210 homes each consuming at most 3kW of electrical power. The site is therefore good and the performance of the best two wind turbines attractive for investors. Keywords: Wind speed distribution, Turbine performance, Average power output. Resumen Los datos de velocidad del viento de Jos han demostrado ser gamma o una distribución normal. El viento está disponible y puede ser utilizado tanto para la generación de energía residencial y de gran escala. En alturas de hub respectivas de 15m y 100m, por lo menos 23% y 40% de Iskra AT5-1 y Micon NM 82 capacidades de turbinas de viento instaladas que ser pueden generadas respectivamente. Un Micon NM 82 instalado a una altura de 100m en Jos puede abastecer a unas 210 viviendas cada una consume en su mayoría 3kW de energía eléctrica. El sitio es bueno y por lo tanto el rendimiento de las dos mejores turbinas de viento es atractivo para los inversores. Palabras clave: Distribución de la velocidad de viento, Rendimiento de Turbina, Potencia media de salida. PACS: 06.30.Gv, 07.10.Pz ISSN 1870-9095 I. INTRODUCTION 09.867, Longitude: 08.900 and Altitude: 1286m) were used for this study. They were obtained from the Nigerian Investments in wind energy require detail statistical Meteorological Agency, Oshodi, Lagos and are re- assessment of sites’ wind distributions and availability. It structured into a histogram of class interval of 1 in Fig. 1. also requires selection and installation of suitable wind turbines for wind power extraction at the sites. B. Distribution Functions In Nigeria, most of these statistical assessments starts by assuming a Weibull distributed wind speeds [1, 2]. These Four different distribution functions: normal, n (푣), gamma, assumptions might lead to errors of over or under g (푣), Weibull, h (푣) and Rayleigh, R (푣) were fitted and estimation of potentials of candidate sites especially when their probability density function (pdf) expressions for the 푡푕 the distribution of the wind speeds of the sites are not really 푖 wind speed, 푣푖 are given [3] as Weibull. In this work, four distribution functions were fitted unto 1 1 푣 −휇 2 푛 푣 = 푒푥푝 − 푖 , 0 ≤ 푣 ≤ ∞, (1) constructed histogram of the wind speed data of Jos and the 2휋휍 2 휍 푣훼 푣 best fitted distribution function used for its detail energy 푔 푣 = 푖 푒푥푝 − 푖 , 훼, 훽, 푣 > 0, (2) potential assessment. 훽 훼 Γ(훼) 훽 푘 푣 푘−1 푣 푘 푕 푣 = 푖 푒푥푝 − 푖 , 푣 ≥ 0, 푘, 푐 > 0, (3) 푐 푐 푐 2 푣 2 II. MATERIALS AND METHODS 푅 푣 = 푣 푒푥푝 − 푖 , 푣 ≥ 0, 푐 > 0, (4) 푐2 푖 푐 푖 A. Data where 푘, 푐, 휍, 휇, 훼 and β are the parameters of the distribution functions. Ten years (1978-1987) monthly average wind speed data (in ms-1), measured at a height of 3m, in Jos (Latitude: Lat. Am. J. Phys. Educ. Vol. 5, No. 2, June 2011 457 http://www.lajpe.org Joseph Aidan These parameters were determined statistically [3] at where 푃(푣) is the power delivered by a turbine at each various heights from predicted wind speeds 푣푕 at some wind speed and fitted in this work by a third degree selected wind turbines hub heights, h using the Hellmann polynomial as 2 3 power law [4]. 푃 푣 = 푎0 + 푎1푣 + 푎2푣 + 푎3푣 , (12) 훾 푕 where 푎0, 푎1, 푎2 and 푎3 are coefficients determined from 푣푕 = 푣푔 , (5) 푕푔 fitted polynomial unto the performance data [8, 9] of the selected wind turbines. The list of the selected turbines and where 푣푔 is the reference wind speed measured at the their characteristics are given in Table I. reference height, 푕푔(= 3m) from the ground surface and 훾 is In Jos, since the maximum recorded wind speed, 푣푚푎푥 the ground surface friction coefficient (taken as 0.2 for Jos). excluding gust, is less than most turbine’s rated wind speed, -1 These distribution functions were validated with some 푣푟 (12-15ms ), Eq. (11) was simply evaluated. statistical goodness-of-fit tests: Chi-square, Kolmogorov- Smirnov (KS) and Anderson-Darling (AD) tests. The TABLE I. Characteristics of some selected wind turbines. details of these statistics could be found elsewhere [3, 5, 6]. -1 -1 Turbine vin (ms ) vr (ms ) Hub, ht (m) C. Wind Power Densities Small- turbines Proven WT 6000 2.5 12 9-15 BWC Excel-S 3.5 13.8 18-30 The extractible root-mean-cube wind power, 푃 at a rotor 푟푚푐 Jacobs WTIC-29 3.0 14 36.6 efficiency, 퐶푃 = 50% is given [4] as Whisper H 175 3.0 12 15 AOC 15/50 4.6 11.3 30 1 3 푃푟푚푐 = 휌퐴푣푟푚푐 , (6) Iskra AT5-1 3.5 11 12-30 4 Nordtank 65 kW 4.0 12 23 Medium size turbines and the root-mean-cube wind speed, 푣 for the best fitted 푟푚푐 Suzlon S. 64/950 3.5 13 64.5 distribution function, f(푣) is given as Suzlon S 64/1000 3.5 13 64.5 Bonus 300 Mk II 4.6 15.5 30 1 ∞ 3 Nordtank 150 kW 4.0 12 24.5 푣 = 푣 푓 푣 푑푣 3 . (7) 푟푚푐 0 푖 Turbowinds T600 3.5 12.5 50-60 Micon 108kW 4.0 15 23 Hence the root-mean-cube extractible power density, 푃푠 is Large turbines then Suzlon S 62/1000 3.5 14 64.5 Suzlon S 88/2100 4.6 14 80 푃푟푚푐 1 3 GE 1.5 SL 77 3.5 12 85/100 푃 = = 휌푣 (8) 푠 퐴 4 푟푚푐 , Nordex S 77 4.6 14 80 Micon NM 82 4.0 14 70-100 3 where 푣푟푚푐 is derived from fitted gamma distribution Nordex N 90 4.6 15 80/100 function as (Sources: INL, Sayler, Manufacturers websites [8, 9]). 3 3 푣푟푚푐 = 훽 훼 훼 + 2 훼 + 1 . (9) between 푣푖푛 and 푣푟 such that And the corresponding mean wind speed, 푣 is given by 0, 푣 < 푣 , 푖 푖푛 ∞ 2 푃 푣 = (13) 푃푟 , 푣푖푛 < 푣푖 ≤ 푣푚푎푥 , 푣푟 . 푣 = 0 푣푓 푣 푑푣 = 훼훽 . (10) D. Turbine Electrical Power Output Using the values of the coefficients for each of the selected wind turbines and the corresponding values of 훽 at the The extractible wind power given by equation (8) does not fixed shape parameter, 훼 Eq. (11) was then solved automatically translate into electrical power output of numerically at various heights for the yearly average turbines due to transmission and generator losses. The electrical power output for each of the selected wind electrical output powers depend upon turbines turbines. characteristics and their performance at each wind speed. E. Turbine Capacity Factor The annual average electrical power output, 푃푎 of a turbine between its cut-in, 푣푖푛 and cut-out, 푣표푢푡 wind speeds is given [7] as Wind turbines performance are measures of how much of their rated powers are relatively generated at a site per 푣표푢푡 annum. The capacity factor, CF (%) is the figure of merit 푃푎 = 푃 푣 푓 푣 푑푣 , (11) 푣푖푛 that determines these measurements [4] and is simplified as 푃푎 퐶퐹 = . (14) 푃푟 Lat. Am. J. Phys. Educ. Vol. 5, No. 2, June 2011 458 http://www.lajpe.org Wind Speed Distribution and Performance of Some Selected Wind Turbines in Jos, Nigeria III. RESULTS AND DISCUSSION TABLE II. Statistical goodness-of-fit tests for fitted distribution functions. The fitted distribution functions unto the constructed histogram of the measured or observed wind speed data of pdf K-S test Anderson-Darling test Jos is given in Fig. 1. Table II gives corresponding values Test Decision Test CV Decision of their relative goodness-of-fit test results. value Rule value rule It could be visually seen that gamma and normal -5 distribution functions are better fitted to the constructed h (v) 0.115 reject 2.7x10 0.050 reject histogram than Rayleigh and Weibull distribution functions. g (v) 0.056 accept - - - R (v) 0.342 reject 2.9x10-49 0.050 reject n (v) 0.075 accept 0.5811 0.747 accept CV 0.1257 0.8 observed gamma Rayleigh It is seen that the average minimum wind speed is greater -1 0.6 normal than 4ms hence a suitable cut-in for most modern wind Weibull turbines. With these range of power densities at the various heights, the wind in Jos could be considered available for 0.4 most categories of wind turbines. Also in Table III are the pdf values of the 훽 parameter of the gamma distribution 0.2 function at different heights. The values of the modal wind speeds given in Table III give estimates of the speeds at which the wind blows most of the time and at the various 0 heights in Jos. 3.5 4.5 5.5 The goodness of their fits is indicated by the values of wind speed (ms-1) the coefficient of determination, 푅2 which were obtained to FIGURE 1.
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