Effect Weibull Distribution Parameters Calculating Methods on Energy Output of a Wind Turbine: A Study Case

Transcription

1 Int. J. of Termal & Environmental Engineering Volume 14, No. 2 (2017) Effect Weibull Distribution Parameters Calculating Metods on Energy Output of a Wind Turbine: Study Case beer Qawasmi, Suil Kiwan Mecanical Engineering Department, Jordan University of Science and Tecnology, Irbid 22110, Jordan bstract Wind energy is an important renewable energy source. It is considered as one of te most significant, freely available and alternative source of energy distributed trougout te world. Te estimation of te potential of wind energy in a site plays a vital role in estimating te energy output of te wind turbines and, terefore, affects economics and decision making. Site caracterization can be expressed matematically in different metods. Weibull distribution is one of te most common metods used to represent wind energy potential in a site. In tis study, wind speed data was collected for year 2013, from Jan 2013 to Dec Te data collected for tree different eigts (20 m, 40 m and 60 m) from measurement station installed at Jordan University of science and tecnology campus area (Irbid, Jordan). Te data recorded based on ten minutes averages using a data logger. Yearly sape factor (k) and scale factor (c), of Weibull distribution for te wind speed are calculated for eac eigt using grapical and standard deviation metods. Bot aritmetic and cubic mean wind speeds were used to estimate Weibull parameters. Ten, te energy outputs of Vestas V wind turbine installed at te site were estimated using calculated Weibull parameters and actual estimation. Te results are compared to ceck te accuracy of metods of estimating Weibull parameters. new metod of caracterizing te site is proposed and tested. Te metod is based on Weibull distribution but te specific power density is te main variable of te distribution. Te results sowed tat tis metod is te most accurate metod among all tested metods. Keywords: Wind power, Weibull distribution, Irbid-Jordan. 1. Introduction Te global energy use as been growing over 45 years and in 2008; te total worldwide energy consumption was 5 x J of wic 80-90% originates from combustion of fossil foil [1]. s te world energy consumption growing especially in te developing countries, te fossil foil consumption increase causing te global warming, by increasing carbon emission to te environment [2]. Uncertainty in oil price and environmental problems as led to energizing of researc in renewable energy. t present, renewable energy availability supply 13.3% of te world primary energy needs and teir future potential observed [3]. Renewable energy tecnologies resources suc as te sun, wind, eart geotermal and biomass ave good * Corresponding autor. Tel.: Fax: ; kiwan@just.edu.jo 2017 International ssociation for Saring Knowledge and Sustainability DOI: /ijtee benefits compared to non-renewable sources. Renewable energy came from continuous source of energy and it is asymmetrically distributed troug over te world. So, every region as some renewable sources [4]. Wind energy is one of te most renewable energy used today and it is one of te fastest growing source of energy by zero emission. Te total installed production capacity of wind energy in te wole world was 432,419 MW at te end of 2015 [5]. Wind energy is mainly used in two purposes; to generate electricity and water pumping. verage wind speed and te wind speed variation affect ow te use of wind power. Many ways are discussed by numerous researcers to find te potential wind site. Te two factors in Weibull distribution c & k are used to estimate te prospective wind site by estimating te wind energy at certain site, and tere are several metods to 163

2 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) calculate tese parameters suc as, grapical metod, standard deviation metod, moment metod, maximum likeliood metod and energy pattern factor metod [6]. Many researcers developed several metods to analyze wind data from using Weibull distribution. zad et al. [7] developed tree metods to predict wind energy generation in Banglades. Pisgar-Komle et al. [8] analyzed wind speed and power density based on Weibull and Rayleig distributions in Fairouzkoo region of Iran. Benatialla and Sellam [6] use Weibull distribution to discuss te wind potential in Saara site of lgeria and perform a researc on te wind power potential of desert of lgeria. noter case study was done in nkara, Turkey by Levent Bilir et al. [9] using Weibull distribution to predict seasonal and yearly wind speed distribution and power density at tree different eigt (20, 30, 50 m) for data collected for a one year between June 2013 to June 2013, wic tey conclude tat te igest wind power at winter and te lowest one at autumn. Furtermore, it is important to analyze te beavior of wind speed because roug wind is not suitable to install wind turbine for electricity generation. lso, it is important to analyze wind sear for wind data. fter select te potential windy sites and based on te selected site data, a proper wind turbine design needed. In tis study, two numerical metods in several tecniques ave been used for determining te value of Weibull parameters. Tese parameters are used to identify te caracteristics of wind and te potential of wind energy. Tis statistical study involves identifying te most accurate way to apply Weibull distribution to predict te potential of energy in a certain site wit a selective wind turbine [8]. Tis work considers te wind data records wic was collected for year 2013, from Jan 2013 to Dec Te data collected for tree different eigts (20 m, 40 m and 60 m) from measurement station installed at Jordan University of Science and Tecnology campus area (Irbid, Jordan). Te data recorded by a data logger based on ten minutes averages using NRG#40 cupanemometers. Two anemometers were installed at eac eigt. Namely; 20 m, 40 m and 60 m. Metodology One of te most widely statistical metods used in wind data analysis is Weibull distribution. Te Weibull sape factor (k) and scale factor (c) are te main parameters to predict Weibull probability density and cumulative distribution as sown in (equation 1) respectively [10]. distribution parameters are used in tis study; grapical metod and standard deviation metod. Standard deviation metod used several tecniques to estimate te two Weibull distribution factors. Wind data recorded based on ten minutes average was divided into two data seet; te first one as intervals of wind speed and te probability density of Weibull distribution and te second one analyze te data for eac average speed of data recorded. 2.1 Standard deviation metod Te aritmetic mean wind speed (Vm) and te root mean cube wind speed (Vmc) were calculated for te two data seet of wind data, and te variance (σv) for eac average speed also was calculated. Ten for eac average speed and variance te Weibull distribution factors c & k calculated using or a simpler to estimate tem as is discussed below. Te average wind speed calculated for eac data seet by different equations., For interval data te aritmetic mean wind speed and te root mean cube wind speed is calculated as in equation 2a and equation 2b, respectively. Te standard deviation is calculated for mean wind speed and root mean cube wind speed according to equation 3a and equation 3b, respectively. Vm (aritmetic) = (2a) Vmc (root mean cube) = [ ] 1/3 (2b) σv (Vm) = σv (Vmw) = (3a) (3b) Te aritmetic mean wind speed and te root mean cube wind are calculated according to equation 4a and equation 4b, respectively. nd ten te standard deviation is calculated for mean wind speed and root mean cube wind speed: Vm (aritmetic) = Vi (4a) f (v) = ( )k-1 e -(v c )k (1a) Vmc (root mean cube) = [ Vi 3 ] 1/3 (4b) F (v) = 1-e -( ) k (1b) Te standard deviations are calculated using: Were v is te wind speed in m/s, k is te sape factor wic is dimensionless parameter and c is te scale factor in m/s. Two metods for calculating Weibull σv (Vm) = (5a) 164

3 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) σv (Vmw) = (5b) C = ᴦ (8) fter te mean wind speed Vm or Vmc and te variance σv (Vm) or σv (Vmw) of data are known, ten te value of te two factors of Weibull distribution c & k can be calculated. Mainly, te scale parameter c referenced to caracteristics of te wind distribution and te sape factor k referenced to ow peak te wind distribution. Tese two parameters are estimated by two tecniques; (1) using and (2) a simpler (as it will be discussed later). Tese parameters (c and k) will be calculated twice; first time using te aritmetic mean wind speed and te second time using te root mean cubic wind speed. Te value of average wind velocity and variance of wind speed can be calculated using (ᴦ) using: Vm = c ᴦ (1+ ) σv = c [ᴦ (1+ ) - ᴦ2 (1+ 1/2 )] (6b) (6a) Once te values of average wind speed and te variance of wind speed data are known ten (ᴦ) is used to estimate te value of sape factor as in equation 7, and find te value of K by solving te following expression numerically. Te value of scale factor c is estimated according to: ) 2 = ᴦ ᴦ 1 (7) Ten after estimating tese factors, a simpler of is used to estimate te values of te sape and scale factors c & k using [11]: K = ( ) c = Grapical metod (9a) (9b) Te following expressions can be developed from Equation (1b) [11]: P (V < Vi) = P (V 0) {1- exp [- ( ) k ]} (10) Ln {- ln [1- F (v)]} = k ln (vi) - k ln c (11) plot of Ln {- ln [1- F (v)]} vs. ln (Vi) presents a straigt line wit a slope of k and a y-intercept of k ln c. Tis logaritmic transformation is te basis of grapical metod. Grapical metod requires tat te wind speed data be in cumulative distribution format. Best fit line can be drawn using a least square regression. Te following cart summarizes all metods of solutiontecniques used at tis study. 165

4 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) Grapical metod Standard deviation metod Interval data veraged data ritmetic mean (Vm, σv) Root mean cube (Vm, σv) ritmetic mean (Vm, σv) root mean cube (Vm, σv) (c & k) (c & k) (c & k) (c & k) to find (c & k) to find (c & k) to find (c & k) to find (c & k), In summary, tere are eigt tecniques to find (c & k) and eigt value of (c) and eigt values of (k) at eac eigt in te site, ten te potential wind power and energy predicted of te site of a selective turbine can be calculated as te values of c & k are known. new metod of estimating te energy output of a certain wind turbine installed in a specific site is proposed and tested. Tis metod relies on te fact tat care is always needed in estimating wind speeds in a site is because of teir energy content. Since te wind power varies wit te cube of te wind speed, ten design/selection of a wind turbine based on matematical average wind speed may lead to an improper utilization of wind potential at te site [12]. Te proposed metod still rely on Weibull distribution to describe te wind caracteristics of te site but it uses te specific power density (cube of wind speed) rater tan te wind speed. Te potential wind power at a given speed is given as: P V (12) Specific power density is given as: P 1 V 2 3 (13) Or for simplicity use of specific power density according to: P 0.5 V 3 (14) Te measured data for V is used to calculate te values of according to Equation (14). Te Weibull distribution is used to model te distribution of as follows: f k k 1 k c e (15) c c Te metods used for calculating te values of c and k for v-based Weibull distribution can be used to calculate c and k for -based Weibull distribution. To calculate te energy produced from a certain wind turbine located in a site described by c and k te following equation is used: 0 f V E P V dv (16) Were PV is te variation of te power output of a specific wind turbine wit te variation of te wind speed. Similarly, te energy output is calculated using te -based Weibull distribution according to: E PP f d (17) 0 Were PP is te power output of a specific wind turbine wit te variation of te specific power density of te site, i.e. wit V

5 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) To ceck te accurcy of te used metods to describe te caracteristics of te site, a wind turbine is selected. Ten, te energy output is estimated using te values of k and c calculated earlier for te site and compared wit te actual energy output based on instantenous measured wind speeds. For tis purpose, te power curve of a 2 MW Vestas V wind turbine is used to represent an actual wind turbine. It as te following specifications [13]: cut in, rated and cut-out velocities 4 m/s, 16 m/s and 25 m/s, respectively. Its power curve expressed in kw is given accordng to Equation (18) as: P V (18) av bv cv d V 4 4 V V V Were a, b, c and d are constats evaluated using best curve fit. Teir associated values are a=2.9626, b=83.583, c= and d= Energy produced from te wind turbine is estimated based on site specifications using Weibull based and EES (Engineering Equation Solver) [14] by solving equations (16) and (17). 1. Results and Discussion In tis study, ten minutes time series wind speed data ave been collected at different eigts in Irbid, Jordan. Te data as been sorted out according to annually mean wind speed for te selected site. Figure 1(a, b and c) sows te wind speed probability distribution based on 1m/s bin widt at eigts of 60, 40 and 20 m in te site, respectively. HOURS / YER HEIGHT 60 M FREQUENCY 1, , , , WIND SPEED (VI) Fig. 1(a): Wind speed probability at 60m eigt HOURS / YER Fig. 1(b): Wind speed probability at 40 m eigt HOURS / YER HEIGHT 40 M FREQUENCY WIND SPEED (VI) 1, , , , HEIGHT 20 M FREQUENCY WIND SPEED (VI) Fig. 1(c): Wind speed probability at 20 m eigt Based on frequency distribution and cumulative distribution te values of te wind speed average (Equation (2a)), root mean cube (Equation (4b)) and standard deviations (Equations (3)) are calculated using te center of te interval as a pivot. Equations (7-8) are ten used to calculate a set of values of c and k labeled as Gamma in Table 2. noter set of c and k are obtained by using Equations (9). Tis set is labeled as pproac in Table 1. Tus, four pairs of (c, k) at eac eigt are obtained. Te results are sown in Table 1. It is clear from te results obtained tat te values based on root mean cube are iger tan tose values obtained based on aritmetic mean. Te two sets are re-calculated but based on te mean average and cube mean average and standard deviations obtained from te measured data directly. Te results obtained are sown in Table 2. One can also notice tat te values of c and k based on Vrmc are iger tan tose 167

6 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) obtained based on te aritmetic mean. One can also notice tat te sets of c and k obtained for te same eigt using bot metods are close to eac oter. Te sets of c and k are obtained using te grapical metod as follows: Equation (11) for eac eigt is plotted as sown in Figure 2. best curve fit equation is obtained. Ten value of c & k are obtained as described earlier. Table 3 sows te values of c & k at eac eigt tat estimated using grapical metod. Te total actual energy output from Vestas V generated by te turbine over a period can be computed by adding up te energy corresponding to all possible wind speeds in te regime, at wic te system is operational as sown in Figure 3. Vestas V wind turbine constant parameters from 3 rd order relation between wind speed and power output are sown in Figure 4. Te energy generated from te turbine is calculated using te actual measured velocities. Te results are sown in Table 4. Tis data is labeled as actual energy output. It sould be mentioned tat even toug te diameter of te selected wind turbine is 80 m, wic is iger tan te ub eigt, te actual energy is calculated. Te results sould be read as te energy output if te wind turbine is erected at eigts aving te values of c and k same as tose at 20 m or 40m eigts. It sould be noted tat in reality te actual energy output will be less tan tis value. Te reason is tat te calculations do not take into consideration te variation of te wind direction. Te calculations of te energy produced by te wind turbine assumes tat te wind speed is always normal to te blade. Tis in reality is impossible. Table 1: Weibull distribution constants using frequency distribution and standard deviation metod 60 m 40 m 20 m ritmetic mean Root mean cube ritmetic mean Root mean cube ritmetic mean Root mean cube Vm = Vmw = Vm = Vmw = Vm = Vmw = σv = C = Simp ler appro ac σv = σv = σv = σv = σv = K = Table 2: Weibull distribution constants using actual measured wind and standard deviation metod 60 m 40 m 20 m ritmetic mean Root mean cube ritmetic mean Root mean cube ritmetic mean Root mean cube Vm = Vmw = Vm = Vmw = Vm = Vmw = σv = c = k = Simp ler appro ac σv = σv = σv = σv = σv =

7 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) LN { LN (1 F(V)) M HEIGHT y = x R² = LN(VI) Fig. 2(a) Grapical metod to estimate c & k at 60 m LN { LN (1 F(V)) M HEIGHT y = x R² = LN(VI) Fig. 2(c) Grapical metod to estimate c & k at 40 m eigt LN { LN (1 F(V)) M HEIGHT y = x R² = LN(VI) Fig. 2(b) Grapical metod to estimate c & k at 20 m eigts Table 3: Weibull parameters using grapical metod 60 m 40 m 20 m c k c k c k

8 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) Power output KW , Wind speed m/s power output y = x x x R² = wind velocity Fig. 3 Power curve for Vestas V Fig. 4 Te relationsip between wind speed and power output between cut-in and rated speeds for V wind turbine Table 4: Te actual energy output for all eigts 60 m Heigt 40 m Heigt 20 m Heigt ctual energy (Mw)/year ctual energy (Mw)/year ctual energy (Mw)/year EES software is used to calculate te energy output from te selected wind turbine located in te site using several relation and expressions including integral expression to estimate te energy of te turbine for nonlinear relation and using c & k as entered values to calculate te energy as sown in Figure (4). Table 5 sows te energy output from te selected wind turbine using grapical metod (Table 6) and standard deviation metod for te four tecniques used; interval wind speed (Table 5a) and te average wind speed (Table 5b) data collected at eac eigt of 60, 40, 20 m wic compared wit te actual energy about for eac eigt Te error in predicting te actual energy output for eac tecnique using is calculated and tabulated. It is clear from te table tat te tecniques based on te average wind speed are very accurate (error less tan 5%) in predicting te energy output. 60 m 40 m 20 m Table 5a: Standard deviation metod used interval wind speed tecnique SD-Interval wind speed Energy output ctual energy Mw/year Mw/year Error % ritmetic % mean % Root mean % cube % ritmetic % mean % Root mean % cube % ritmetic % mean % Root mean % cube % 170

9 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) m 40 m 20 m Table 5b: Standard deviation metod used averaged wind speed tecnique. Energy output ctual energy SD-verage wind speed Error % Mw/year Mw/year ritmetic % mean % Root mean % cube % ritmetic mean Root mean cube ritmetic mean Root mean cube % % % % % % % % Table 6: Energy output using te grapical metod Grapical metod Energy output Mw/year ctual energy Mw/year Error % 60 m % 40 m % 20 m % For te -based Weibull distribution metod, te caracteristics of te site are calculated based on and listed in Table 7. Te power curve for te wind turbine Vestas V is reproduced in terms of. Fig. 5 sows te variation of te power output in te region between cut-in and rated wind speeds for Vestas V turbine., power output (kw) y = 4E 08x 3 5x x R² = Specific power density X Fig. 5: 3 rd order relation between power and cubic wind speed Table 7: Wind data analysis for cubic wind speed using standard deviation metod. 60 m 40 m 20 m verage cubic wind speed Vm = σv = GM M functio n C = K = Simple r approa c verage cubic wind speed Vm = σv = GM M functio n Simple r approa c verage cubic wind speed Vm = σv = GM M functio n Simple r approa c

10 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) Table 8: Comparison between -based analysis and actual energy output for Vestas V wind turbine SD-verage cubic wind speed Energy output Mw/year ctual energy Mw/year Error % 60 m % % 40 m % % 20 m % % Close inspection of Table 8, one can see tat te -based analysis metods ave te igest accuracy among oter metods. 2. Conclusion Te potential of wind energy output from Vestas V wind turbine at tree different eigts (60, 40, 20 m) of te certain site ave been studied in tis researc using v-based and -based Weibull distribution s. Different metods are used to calculate Weibull parameters (c & k). Te grapical and standard deviation metods are used based on te aritmetic mean and root mean cube. Relative percentage of error in estimating energy output using selected wind turbine as been analyzed and compared. Obtained results indicated tat all metods based on Vrmc are 50% away from te actual results. Wile results based on aritmetic averages, in general, are accurate. It is also found tat among te tecniques of estimating te Weibull parameters, te grapical tecnique is less accurate tan te standard deviation metod. new metod of caracterizing te site is proposed and tested. Te metod is based on Weibull distribution but te specific power density is te main variable of te distribution. Te results sowed tat tis metod is te most accurate metod among all tested metods. References [1] Energy Consumption Consumption by fuel, (XLS), Statistical Review of World Energy 2009, BP. July 31, 2006 (accessed ). [2] Zang, X., Zao, X., Smit, S., Xu, J., & Yu, X. (2012). Review of R&D progress and practical application of te solar potovoltaic/termal (PV/T) tecnologies. Renewable and Sustainable Energy Reviews, 16(1), [3] Hasan, M.., & Sumaty, K. (2010). Potovoltaic termal module concepts and teir performance analysis: review. Renewable and Sustainable Energy Reviews, 14(7), [4] Bull, S. R. (2001). Renewable energy today and tomorrow. Proceedings of te IEEE, 89(8), [5] ttp:// date: 11 Feb [6] Dabi, M., Benatialla,., and Sellam, M. (2013). Te analysis of wind power potential in Saara site of lgeria-an estimation using te Weibull density. Energy Procedia, 36, [7] zad,. K., Rasul, M. G., Islam, R., & Sisir, I. R. (2015). nalysis of wind energy prospect for power generation by tree Weibull distribution metods. Energy Procedia, 75, Cicago [8] Ounakin, O. S. and kinnawonu, O. O. (2012) ssessment of wind energy potential and te economics of wind power generation in Jos, Plateau State, Nigeria, and Energy for Sustainable Development. 16, [9] Bilir, L., İmir, M., Devrim, Y., and lbostan,. (2015). Seasonal and yearly wind speed distribution and wind power density analysis based on Weibull distribution. International Journal of Hydrogen Energy, 40(44), [10] zad, K. (2012), Statistical Weibull s Distribution nalysis for Wind Power of Te Two 1.668Dimensional Ridge reas, International Journal of dvanced Renewable Energy Researc (IJRER). 1,

11 Qawasmi and Kiwan / Int. J. of Termal & Environmental Engineering, 14 (2017) [11] Matew, S. (2006), Wind Energy: Fundamentals, Resource nalysis and Economics, Springer-Verlag Berlin Heidelberg, p 84. [12] Wagner, H-J. and Matur J. (2009), Introduction to Wind Energy Systems: Basics, Tecnology and Operation, Springer-Verlag Berlin Heidelberg, p.38 [13] System dvisor Model Software, Version , free software [14] Engineering Equation Solver (EES) Software, 173