Assessment of wind energy potential using wind energy conversion system

Accepted Manuscript Assessment of wind energy potential using wind energy conversion system

Muhammad Shoaib, Imran Siddiqui, Shafiqur Rehman, Shamim Khan, Luai M. Alhems PII:

S0959-6526(19)30145-3

DOI:

10.1016/j.jclepro.2019.01.128

Reference:

JCLP 15515

To appear in:

Journal of Cleaner Production

Received Date:

04 August 2018

Accepted Date:

12 January 2019

Please cite this article as: Muhammad Shoaib, Imran Siddiqui, Shafiqur Rehman, Shamim Khan, Luai M. Alhems, Assessment of wind energy potential using wind energy conversion system, Journal of Cleaner Production (2019), doi: 10.1016/j.jclepro.2019.01.128

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ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT Assessment of wind energy potential using wind energy conversion system Muhammad Shoaiba, Imran Siddiquib, Shafiqur Rehmanc, Shamim Khand, and Luai M. Alhemsc aDepartment of Physics, Federal Urdu University of Arts, Sciences and Technology, Gulshan-e-Iqbal, Karachi 75300, Pakistan bDepartment of Physics, University of Karachi, Karachi 75270, Pakistan cCenter for Engineering Research, The Research Institute King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia; [email protected] (for correspondence) dIslamia College Peshawar, Peshawar Jamrod Road, University Campus, Peshawar, Khyber Pakhtunkhwa 25120, Pakistan Abstract Wind energy, as a renewable resource, is the most rapidly growing source that produces electrical energy using wind turbines. Such a wind energy conversion system is both economical and is environmental friendly. It requires understanding of wind conditions at the site under study. With this intent, wind characteristics of Jhampir (district Thatta Sindh, Pakistan) are investigated and wind energy potential is determined. The study is conducted using 10-minutes averaged wind speed data obtained from Alternate Energy Development Board of Pakistan for a period of three years (2007 to 2010). Monthly, seasonal, and yearly analysis is performed by fitting measured wind speed data to a Weibull distribution function. Weibull shape and scale parameters are determined numerically using Maximum Likelihood Method, Modified Maximum Likelihood Method, and Energy Pattern Factor Methods. The suitability of the fit is assessed using goodness-of-fit tests, such as, Root Mean Square Error, Coefficient of Determination (R2), and Chi-Square (2) tests. In all three data analysis periods, RMSE values varied between 10-2 and 10-4. Similarly, R2 values varied between 0.989 and 0.996 and 2-test between 10-4 and 10-8. For entire data set, all the tests showed better performance of Maximum Likelihood and Modified Maximum Likelihood Methods compared to Energy Pattern Factor. In case of monthly analysis, Maximum Likelihood Method performed better compared to Modified Maximum Likelihood Method and Energy Pattern Factor according to root mean square error and 2 tests results. Seasonal performance of all the methods is found to be similar with marginal superiority of MLM over other methods. A very good agreement is observed between standard deviation values for measured wind speed data distribution and fitted Weibull distribution using Maximum Likelihood Method estimator. Additionally, to understand the optimum directional efficiency, directional wind power densities are calculated. Finally, a wind turbine is used to the seasonal and yearly wind speed data to determine the actual wind energy potential of the site. Extracted wind energy values for four seasons are found to be 1691, 2851, 4572, and 916 kWh with an annual yield of 10054 kWh. Wind energy values obtained for different periods and directions suggest that Jhampir is a suitable site for developing the wind power plant. Keywords: Jhampir; Weibull function; wind power density; wind turbine; wind energy

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ACCEPTED MANUSCRIPT 1. Introduction The industrial growth of any country depends on creating a balance between energy production and its consumption. The production of energy in turn depends on the availability of renewable and non-renewable energy resources. Non-renewable energy resources are in a continuous state of depletion and their scarcity is much felt in countries which are less developed. Furthermore, the adverse effects of fossil-fuel consumption for the energy production results in environmental deterioration (Carbon dioxide emissions). Therefore, the use of renewable energy resources not only helps in reducing the fossil-fuel consumption but also reduces the chances of green-house effect. The renewable energy resources are constantly replenished naturally means a non-ending supply of eco-friendly source of energy is available to humanity. This makes it one of the widely studied source of energy that is rapidly replacing conventional energy sources. According to Global Wind Energy Council (GWEC) report (2014), Pakistan economy is one of the fastest growing economies utilizing wind energy as a major electrical energy resource. The country’s daily power consumption goes beyond 20,000 MW and further increases during summer. This results in a short fall of 4500-5500 MW per day (National Power Policy, 2013). In view of its vast land in Punjab and Khyber Pakhtunkhwa (KPK) and in the presence of long coastal belt in Sindh and Baluchistan, production of energy from wind holds good prospects. PMD (Pakistan Meteorological Department) and AEDB (Alternate Energy Development Board) are working on a number of projects (Putnam, 1948; Johnson, 2001; Kloeffler, et al. 1946) to estimate the wind potentials of different sites all over the country. A reliable estimate of wind potential for the site under study requires a thorough understanding of its wind characteristics. This has motivated researchers all over the globe to conduct studies utilizing short and long-term wind speed data by employing appropriate mathematical functions and distributions to model measured wind speed data. These give reliable wind power estimates of sites for efficient planning and installing wind farms. A twoparameter statistical distribution function known as Weibull function, proposed by Waloddi Weibull (Weibull, 1951) is used to fit the measured wind speed data (Justus, et al., 1978; Rehman et al., 1994; Shoaib et al., 2017). Islam et al. (2011) used a two parameter Weibull function for the estimation of wind energy potential of Kudat and Labuan during 2006-2008. Maximum wind energy obtained at Kudat was 590.40 kWh/m2/year in 2008. The highest wind speeds corresponding to maximum energy calculated at Labuan and Kudat Malaysia, respectively, in the year 2007 were 2.44 m/s and 6.02 m/s. The study concluded that sites are suitable for small scale wind energy generation. Sopian et al. (1995) analyzed wind speed data from ten stations for a period of 10 years during 1982-1991 in Malaysia. Wind speed data was fitted to Weibull function and it was found that Mersing has the highest wind energy potential with mean power density of 85.61 W/m2 using wind speeds recorded at 10 m height. Garcia et al. (1998) used Weibull and Lognormal models to fit hourly mean wind speed data. Goodness-of-fit tests were performed using R2 and nonlinear regression approaches for Weibull and lognormal models. The Weibull model was found to be better than lognormal model. Seguro et al. (2000) investigated wind characteristics by modeling wind speed data using Weibull function. The study showed that MLM works better for time series wind speed data and MMLM for wind speed data in frequency distribution format. Isaac et al. (2000) calculated probability density function using two-parameter Weibull function for a thirty-year long term hourly mean wind speed data measured in open sea area in Hong Kong. Estimated values of shape and scale parameters varied over wide range of 1.63 to 2.03 and 2.76 to 8.92 m/s, respectively. Sulaiman et al. (2002) and Dorvlo (2002) analyzed wind speed data measured at four stations in Oman using Weibull distribution function. Carta et al. (2009) reviewed different probability density functions for describing various wind regimes, viz. null winds, unimodal, bimodal, bitangential regimes, etc. The suitability of distribution function 2

ACCEPTED MANUSCRIPT was judged by estimating R2 test. The study concluded that Weibull probability density function performed better than all other density functions. Chang (2011) used six different numerical methods to estimate shape and scale parameters of the Weibull function and compared these methods using Monte Carlo technique. Their study revealed that maximum likelihood method is better than other estimation methods followed by Modified Maximum Likelihood Method and Method of Moment. Additionally, the Monte Carlo simulation has wide ranging applications associated with project management, financial issues and decisionmaking problems (Mahdiyar et al. 2017, Blom et al. 2006, Armaghani et al. 2016). Smith and Caracoglia (2011) performed ‘‘fragility analysis’’ of high-rise structures in the presence of turbulent wind loading using Monte Carlo method. Akdağ and Dinler (2009) used a new method known as power density (PD) for the estimation of Weibull parameters. Akdağ et al. (2010) performed statistical analysis of nine bouys data in Ionian and Aegean Sea. Authors used wind regimes containing zero percentage of null speeds and wind speed data was fitted Weibull function and two-component mixture Weibull function. Suitability of fitted distributions was checked using R2 and RMSE tests and concluded that Weibull function was a better choice for approximating recorded wind speed data. Rocha et. al. (2012) used wind speed data obtained from Camocim and Paracuru cities in Brazil to determine Weibull parameters using seven numerical methods. Analysis of variance, RMSE, and 2 tests were used to check the goodness-of-fit. Chang (2011a) reviewed five different mixture probability density functions fitted to the 10 min intervals wind speed data during the period 2006-2008 at three different wind farms in Taiwan. The test statistics showed that the mixture models fitted well compared to the conventional Weibull function. Akgül et al. (2016) modeled the wind speed data using inverse Weibull function and compared with the conventional Weibull function. Based on error analysis the study concluded that inverse Weibull performed better than Weibull function. Arslan et al. (2017) proposed generalized Lindley and power Lindley distribution function as an alternative to Weibull function for modeling wind speed data. Various error estimates were used and based on root mean square error and coefficient of determination tests generalized Lindley function fitted better, whereas power Lindley function was better in terms of power density error criterion. Dongbum et al. (2018) investigated the measured five-year wind speed data for Jeju Island, South Korea by fitting to Weibull function. Authors used six different methods for the estimation of Weibull parameters and discussed their accuracy by taking different bin sizes. The study showed that the choice of bin size greatly affects the accuracy of graphical method but has no effect on maximum likelihood method. Environmental factors such as air temperature and pressure differences produce continuous and rapid variations in wind speeds resulting in a non-linear behavior of wind energy systems. These non-linear wind conditions are modelled using neuro fuzzy logic and artificial neural network algorithms. Accordingly, estimation of power coefficients of wind turbines (Dalibor et al. 2013), extraction of wind energy from turbines and the management of wind energy conversion system (Dalibor et al. 2014) can be performed using adaptive neuro fuzzy inference system (ANFIS). On the other hand, such rapid fluctuations in wind speeds lead to instabilities in the wind energy conversion systems. Improvements in the estimation of wind speed fluctuations can also be performed using fractal interpolation technique (Dalibor et al. 2017). Additionally, surface roughness and different heights at which wind speeds are measured also affects the wind speed variability. Influence of such factors on the prediction of reliable wind speed and fractal nature of wind speed can be studied using neuro fuzzy method (Nikolic´ et al. 2017). Proper design of a wind energy conversion system requires identification of suitable wind factors which are relevant for an efficient conversion system. Nikolić et al. (2016) developed a systematic methodology for identification of such factors and designing an innovative wind production system. Dalibor et al. (2016) used adaptive neuro-fuzzy inference 3

ACCEPTED MANUSCRIPT system (ANFIS) to assess the efficiency of wind power production system. Two main objectives were discussed in the study, reducing the cost of production and maximizing the energy production. The results indicated that the method was effective in achieving the objectives of the study. Hossain et al. (2017) investigated the power output of photovoltaic system using Extreme Learning Machine (ELM) approach and proposed a model for forecasting power output of a grid-connected photovoltaic system. The comparison of the proposed ELM method with other models showed relatively better accuracy. Fallah et al. (2018) studied smart energy management grid system by utilizing machine learning approach, that is, a computationally intelligent load forecasting approach in terms of a sustainable energy management system. The present study is aimed at (i) investigating the wind characteristics of the site under study by fitting monthly, seasonal, and yearly wind speed data to a Weibull function (ii) assessing the suitable Weibull parameter estimation method, and (iii) studying the directional properties of wind and estimating of wind power potential as a function of wind direction. Using the results obtained, a suitable wind turbine is employed to extract wind energy by fitting the continuous Weibull function to the power curve of the wind turbine. 2. Weibull function Weibull function is used as an empirical model to approximate the measured wind speed data for the chosen site. The two model parameters shape (k - dimensionless) and scale (c – m/s) are estimated using different numerical methods. Fitted Weibull function thus used to calculate wind power potential of the site. Weibull pdf and cdf as a function of wind speed v are given as follows: k v f(v)    cc

k 1

  v k  exp       c  

  v k  F(v)  1  exp       c  

(1) (2)

Using the fitted Weibull function wind characteristics such as mean wind speed (Vm), most probable wind speed (Vmp), and wind power density PD are estimated from Eqs. 3-5. In order to compare the estimated wind characteristics, actual wind power density, PA, is determined using Eq. 6 (Justus et al., 1978; Isaac et al., 2000; Chang 2011b).  1 Vm  cΓ 1    k

Vmp PD 

 k 1  c   k 

(3)

1/ k

(4)

ρa c  3  Γ 1   2  k

(5)

1 3 ρa v 2

(6)

PA 

where PA is the actual wind power and ρa is the air density which is 1.225 kg/m3. Variance and standard deviation for Weibull distribution function is expressed as,

4

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

2 W

W

2  2   1       c Γ  1       1     k   k      

(7)

2  2   1       c Γ  1       1     k   k      

(8)

2

2

where Gamma function (z) is obtained using the following equation: 

Γ(z)   x z 1e  x dx

(9)

0

2.1 Weibull shape and scale parameters In this communiqué, Weibull k and c values are estimated using three different methods namely, Modified Maximum Likelihood Method (MMLM), Maximum Likelihood Method (MLM), and Energy Pattern Factor Method (EPFM). Mathematical expressions for these methods are given in Table 1 and to check their suitability Monte Carlo technique is used. Based on Monte Carlo simulations, MLM method is selected to determine Weibull parameters in the present study (Arslan et al, 2014; Kantar and S-enoglu 2008). Table 1: Weibull parameters estimation methods. Method of estimation Mathematical expression of k and c  n    vik ln vi   n 1  i  1 k   ln vi  n n   i 1 vik      i 1 



Maximum Likelihood Method (MLM)





1

1 n  c    vik   n i 1 

n  n k    vi ln(vi )f(vi )  ln(vi )f(vi )   k   i 1 n  i 1   f(v  0) k   v i f (v i )   i 1 

Maximum Likelihood Method (MMLM)

n  1  c   vik f (vi )    f(v  0) i 1 

Energy Pattern Factor Method (EPFM)

E pf

1/k

1

1/k

1 n 3  vi 1 n i 1 3.69 c   , and  k  1  3 2 n E n 1  pf   vi   n i 1 

 v   i 1  n

1/k

k i

2.2 Error analysis In order to assess the suitability of Weibull function as a fitted model to the observed wind speed data, goodness-of-fit tests are used. The tests included are R2, RMSE and 2 and are discussed in the sections below. 5

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2.2.1 Coefficient of determination (R2) R-squared (R2) test measures a proportion of variance if the dependent variable predicted using independent variable, that is, n

R2 

 y i 1

n

 z i     y i  xi  2

i

2

i 1

n

 y i 1

i

 zi 

(10)

2

where n is the number of data points, yi is the predicted value of xi and zi is the mean wind speed. The values for R2 range between 0 and 1, a high value of R2 implies better prediction whereas a low value means a poor prediction. RMSE test is a measure of difference between the values obtained from fitted function and observed values. RMSE is given by the following expression:

1 n 2 RMSE     y i  xi    n i 1 

1/ 2

(11)

2.2.2 Chi-Squared (2) Test Chi-squared is a goodness-of-fit test and is used to assess correlation between two set of values. It can be determined using the following equation: n

  2

O  E  i

2

i

(12) Ei where Oi is the observed value and Ei is the expected value. A low value of χ2-test implies a good correlation between two sample distributions. i 1

2.2.3 Monte Carlo Simulation The performance comparison of three Weibull parameter estimation methods is checked using Monte Carlo (MC) simulation. Synthetic wind speed data is generated using Weibull cdf for wind speed v using a random number generator Rn in the range [0,1].   1 v  c ln   1  Rn

  

1/ k

(13)

The efficiencies of Weibull parameters estimation methods are assessed by computing mean bias error (MBE) and mean square error (MSE) using the relations MBE (kˆ)  E (kˆ)  k (14)

MSE (kˆ)  E ([kˆ  k ]2 )

(15)

ˆ where k is the estimated value of shape parameter using Monte Carlo simulation procedure and k is the observed shape parameter obtained using iterative method of Weibull parameters estimation method. In order to calculate MBE and MSE, simulated values of shape factor are 6

ACCEPTED MANUSCRIPT obtained by running MC [[100,000/n]] number of times. Here [[·]] denotes the integer value function and n is the number of wind speed values being simulated. RMSE measures the deviation of the fitted distribution from the actual data distribution, whereas R2 statistics tests the reliability of the fit. χ2 statistics tests how well the fitted distribution follows variability in the actual data distribution contrary to R2 test which gives quantification of this variability. χ2 statistics performs better for a large data sample size. Monte Carlo analysis, on the other hand, tests the unbiasedness of Weibull parameters estimators for various sample sizes. 2.4 Wind energy production system In order to have a reliable estimate of the energy content of wind, the data obtained from the site is fitted to a continuous distribution function. Weibull distribution function is used for fitting and then is integrated over the wind turbine power curve (Shoaib et al., 2016, Eqs. 26, 27) to obtain the actual wind energy ETA. The actual power (PAT) generated by a wind turbine depends on the performance curve and is given by: v  vcin 0 P P  C r vcin  v  v r PAT   (16) P v  v  v r r co  0 v  vco where PC is the mathematical function characterizing wind turbine performance curve. In the present case a cubic polynomial is fitted to the performance curve of the selected wind turbine. The turbine characteristic curve, so obtained, is given by: PC  0.003031x 3  0.07521x 2  0.4528 x  0.8347 (17) and Pr is the rated power given by: Pr 

1  a Av r3 2

(18)

where A is the turbine rotor intercept area, vr is the rated velocity, vcin and vco are the cut-in and cut-off speeds of the selected turbine. The actual wind energy is then calculated by multiplying the PAT with the fitted wind speed probability distribution function f(v) using the following integral equations: vco vco v    r  (19) ETA  T  PAT (v) f (v)dv  TPr   PC f (v)dv   f (v)dv    vcin v v r  cin  and vr

EWTA  TPr



vcin

k v PC   c c

k 1

v

k 1   v k    v k  k v     dv exp    dv TPr exp    c   c  c c       vr



(20)

where EWTA is the actual wind energy obtained using Weibull distribution function.

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Figure 1a: Jhampir located in the wind corridor of Sindh (Pakistan Meteorological Department)

Figure 1b: Jhampir-FFC mast location (AEDB-Pakistan) 3 Results and Discussion: Case Study: Jhampir – Fauji Fertilizer Company (FFC) 3.1 Data description and Methodology The assessment of wind energy potential of Jhampir-FFC (Sindh, Pakistan) is performed using wind speed data collected from AEDB (Alternate Energy Development Board) Pakistan. The coordinates of site are 25◦ 04' 33.20'' N and 67◦ 58' 22.20'' E (Fig. 1a & 1b). Jhampir mast site has a hard and rocky surface with roughness class of 1.5 and surface roughness length of 0.055 m. Wind speed data is recorded using a combined speed-direction anemometer with measurable velocity range between 0 to 30 m/s with a threshold of 0.00345 m/s and a resolution of 0.056 m/s. The data was saved as ten minutes averages at 80 m above ground level (AGL) over a period of three years, starting from 28/05/2007 and ending on 30/04/2010. The acquired wind 8

ACCEPTED MANUSCRIPT speed data is pre-processed by converting it into a set of hourly averaged values. The analysis is carried out for three data regimes viz.; monthly, seasonal, and yearly. Four seasons investigated are December to February (season 1), March to May (season 2), June to September (season 3) and October to November (season 4). Fig. 2 gives the complete graphical layout of the methodology followed to process raw wind speed data and obtain Weibull wind characteristics and extraction of wind energy using a wind turbine.

Figure 2. Flow chart of the methodology to process wind speed data 3.2 Descriptive Statistics The descriptive statistics on monthly, yearly, and seasonal basis are summarized in Tables 2 and 3. The monthly mean wind speed varied between a minimum of 5.83 m/s and a maximum of 10.37 m/s corresponding to the months of February and May during the year. The monthly ranges (difference between maximum and minimum wind speed over the month) are found to be 8.11 m/s in October and 12.18 m/s in August during the year. In general higher wind speed values are observed during summer months and relatively low in winter time which is a positive point having concurrency with usual load pattern. Monthly distributions are mixtures of flat and peaked distribution as observed in Figs. 3-14. In most of the months (with the exception of February, April, May, and July corresponding to Figs. 4, 6, 7, and 9; respectively), the distributions are observed to be slightly skewed either positively or negatively. In both the cases, the majority of the wind speed data lies around the monthly mean wind speed values. The monthly mean wind power density (Column 8, Table 2) are found to vary between a minimum of 121.7 W/m2 in February and maximum of 684.0 W/m2 in May with an overall 9

ACCEPTED MANUSCRIPT annual mean value of 287.5 W/m2. Like wind speed, the wind power density also found to be higher in summer time relative to wintertime. The seasonal mean wind speeds in four seasons are 6.65 m/s, 8.24 m/s, 9.00 m/s and 6.27 m/s, respectively (Table 3). In season 3, the wind speed values are distributed symmetrically around the mean but have a light tail. The estimated seasonal power densities are 179.77, 342.16, 446.75, and 151.08 W/m2 corresponding to seasons 1-4. This implies that the period from June to September (season 3) is the best from wind power harnessing point of view while season 2 (March to June) is the second best period. In a way, the entire period from March to September seems to be good at Jhimpir site for wind power realization. The annual mean wind speed at 80 m height (Table 2) is 7.77 m/s with standard deviation (σ) of 2.31 m/s and a confidence interval (C.I.) of 0.05 at 95.00% C.L. The coefficient of variation (CV) for the specified number of data points in one complete year period is 29.73 %. This means that ca. 70% of the wind speed data points lie around mean wind speed and fall within a window of C.I. of 0.05. The distribution is slightly skewed (S = 0.08) suggesting that the majority of data points are evenly distributed about mean and therefore the measured wind speed distribution can be modeled by a normal distribution function. For yearly data distribution, the Kurtosis (K) of -0.44 implies a nominally flat distribution compared to a normal distribution and light tails, (Fig. 15). The statistics suggests that annual wind speed variability around mean is low and ca. 70% of time wind speed remains on the average ca. 7 m/s, which is a significant and advantageous statistic for stable wind power generation throughout the year. Table 2: Monthly descriptive statistics Period Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Yearly

Mean V (m/s) 7.09 5.83 6.67 7.65 10.37 9.19 9.21 9.17 8.42 6.14 6.40 6.93 7.77

Range (m/s) 9.60 8.36 11.8 5 10.7 9 11.3 3 8.68 10.2 8 12.1 8 8.95 8.11 8.82 11.3 8 14.1 3

 (m/s) 1.90 1.60 2.06 1.94 1.93 1.60 1.89 1.85 1.45 1.48 1.67 2.35 2.31

K

S

-0.37 -0.38 -0.33 -0.23 0.10 -0.22 -0.04 -0.38 0.08 -0.29 -0.54 -0.72 -0.44

-0.09 0.20 0.14 0.20 -0.40 -0.05 -0.21 -0.05 0.07 -0.14 0.11 0.12 0.08

K

S

-0.43 -0.59 -0.15 -0.37

0.21 0.06 0.00 0.03

PD (W/m2) 218.4 1 121.6 6 181.6 0 273.7 1 683.9 7 476.1 1 478.7 1 471.5 8 365.9 8 142.0 4 160.8 1 204.0 7 287.4 8

CV % 26.80 27.42 30.96 25.36 18.65 17.45 20.47 20.20 17.21 24.11 26.05 33.94 29.73

C.I. (95.0%) 0.14 0.12 0.15 0.14 0.14 0.12 0.14 0.13 0.11 0.11 0.12 0.17 0.05

Table 3: Seasonal descriptive statistics Seasons 1 2 3 4

Mean V (m/s) 6.65 8.24 9.00 6.27

Range (m/s) 11.38 13.09 12.18 9.04

 (m/s) 2.06 2.53 1.74 1.58

10

PD (W/m2) 179.77 342.16 446.75 151.08

CV % 31.00 30.73 19.34 25.20

C.I. (95.0%) 0.09 0.11 0.06 0.08

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Fig. 3. Histogram and pdf, cdf curves for January

Fig. 4. Histogram and pdf, cdf curves for February

Fig. 5. Histogram and pdf, cdf curves for March

Fig. 6. Histogram and pdf, cdf curves for April

Fig. 7. Histogram and pdf, cdf curves for May

Fig. 8. Histogram and pdf, cdf curves for June

Fig. 9. Histogram and pdf, cdf curves for July

Fig. 10. Histogram and pdf, cdf curves for August

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Fig. 11. Histogram, pdf, cdf curves for September

Fig. 12. Histogram, pdf, cdf curves for October

Fig. 13. Histogram, pdf, cdf curves for November

Fig. 14. Histogram, pdf, cdf curves for December

Fig. 15. Histogram and pdf, cdf curves for one year

3.3 Monte Carlo simulation of Weibull parameters Monte Carlo simulation is used to assess the suitability of EPFM, MMLM and MLM for the estimation of Weibull parameters on yearly and seasonal (for season 1 only) wind speed data sets. In the case of yearly simulations, the sample sizes taken are n = 7500(500)9500. For each sample size, the shape parameter values used are in the range of k = 2.30(0.50)4.30 for EPFM, k = 2.79(0.50)4.72 for MMLM and k = 2.73(0.50)4.73 for MLM. The scale parameter values for the three methods are kept constant for respective methods as c = 8.75, 8.71, and 8.61 m/s. In case of seasonal simulation of season 1 data set, the samples sizes are chosen as n = 1500(500)3500 with shape parameter values in ranges of k = 2.20(0.50)4.20, 2.61(0.50)4.61, 2.55(0.50)4.55 and constant scale parameter values of c = 7.50, 7.63, 7.38 m/s for EPFM, MMLM, and MLM. The MBE and MSE values for yearly and season 1 data sets are found to be minimum for MLM compared to other two methods used (Figs. 16a-16d). Thus, MLM is a superior choice for the determination of k and c parameters over MMLM and EPFM.

12

ACCEPTED MANUSCRIPT Furthermore, for yearly and seasonal data sets, MBE becomes more and more negative with increasing number of data points (means more and more negatively biased). Additionally, MSE is found to be minimum for MLM with varying number of data points compared to the same variation of number of data points for EPFM and MMLM. It is found to be comparatively less sensitive to the variation in number of data points. This suggests that MLM is less biased and more consistent compared to EPFM and MMLM.

Fig. 16. MBE and MSE with number of data points for yearly (a, b) and season 1 (c, d) data sets 3.4 Weibull wind characteristics Monthly, seasonal, and yearly wind speed data sets are fitted to Weibull function and wind characteristics are determined over entire data collection period (May 2007 to April 2010). Weibull k and c parameters are determined using MLM, MMLM and EPFM and pdf and cdf for monthly and yearly (Table 4) and seasonal (Table 5) data sets. Based on these estimated values of c and k; the mean wind speed (Vm), most probable wind speed (Vmp), standard deviation (w) and wind power density (PD) are calculated and are summarized in Table 4. The maximum energy carrying and most probable wind speed values show a seasonal trend with lower values in wintertime and higher in summertime. The maximum values of these two parameters are obtained in May while the minimum in February. This simply implies that mean 13

ACCEPTED MANUSCRIPT and the most probable wind speed of around 10 m/s fall in the month of May during the year. The wind power density show an increasing trend from January until mid of the year and then a decreasing towards the end of the year (Table 4, column 9). The coefficient of determination R2 (Table 4, column 10) between the estimated and measured wind speed data are observed to be always more than 0.99 irrespective of the Weibull parameter calculation method. This suggests that R2 test results showed that a good correlation exists between the measured and fitted distributions. Table 4: Wind characteristics for monthly and yearly regimes and test statistic values. Period Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Yearly

Methods

Hours

k

EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM

743 743 743 671 671 671 743 743 743 719 719 719 743 743 743 719 719 719 743 743 743 743 743 743 719 719 719 743 743 743 719 719 719 743 743 743 8759 8759 8759

3.51 4.23 3.87 3.45 4.02 3.39 3.22 3.59 3.57 3.59 4.33 3.51 4.05 6.31 6.25 4.10 6.40 4.52 3.93 5.57 5.44 3.94 5.65 5.56 4.12 6.33 5.64 3.69 4.73 4.26 3.55 4.29 3.94 3.03 3.28 3.31 3.30 3.73 3.72

c (m/s) 7.97 7.80 7.83 6.56 6.43 6.11 7.53 7.40 7.61 8.58 8.38 7.95 11.57 11.15 11.11 10.24 9.85 9.58 10.29 9.96 10.42 10.23 9.90 10.16 9.38 9.02 9.04 6.88 6.71 6.33 7.19 7.03 6.89 7.85 7.74 7.98 8.75 8.61 8.71

Vm (m/s) 7.10 7.02 7.01 5.84 5.77 5.43 6.68 6.60 6.79 7.65 7.55 7.08 10.39 10.27 10.23 9.20 9.08 8.65 9.22 9.11 9.52 9.17 9.06 9.29 8.43 8.31 8.27 6.15 6.08 5.70 6.41 6.34 6.17 6.94 6.87 7.09 7.77 7.70 7.78

Vmp (m/s) 7.24 7.31 7.25 5.94 5.99 5.51 6.71 6.75 6.95 7.83 7.89 7.22 10.78 10.85 10.81 9.57 9.60 9.06 9.54 9.61 10.04 9.50 9.57 9.81 8.77 8.78 8.73 6.32 6.38 5.95 6.55 6.61 6.39 6.88 6.92 7.16 7.84 7.92 8.01

w (m/s)

2.26 1.89 2.05 1.89 1.63 1.79 2.30 2.06 2.13 2.39 1.99 2.26 2.91 1.92 1.93 2.55 1.67 2.20 2.66 1.91 2.04 2.63 1.87 1.95 2.33 1.55 1.71 1.87 1.48 1.53 2.02 1.68 1.77 2.53 2.33 2.38 2.62 2.32 2.36

PD (W/m2) 290.49 261.59 269.53 163.15 147.87 132.17 251.70 231.02 252.44 360.79 323.99 288.23 861.00 745.06 737.26 595.72 514.05 480.73 608.83 531.99 609.88 599.17 523.05 565.37 457.67 394.38 397.64 185.04 164.46 140.10 213.01 191.73 182.72 291.87 271.64 297.01 392.70 361.30 373.51

R2

RMSE

0.993 0.993 0.993 0.990 0.989 0.989 0.993 0.993 0.993 0.993 0.993 0.993 0.996 0.996 0.996 0.995 0.994 0.994 0.995 0.994 0.995 0.995 0.995 0.995 0.995 0.994 0.994 0.991 0.990 0.989 0.992 0.991 0.991 0.992 0.992 0.992 0.994 0.994 0.994

2.69E-03 1.47E-03 4.79E-03 2.94E-03 6.02E-03 3.41E-03 2.63E-03 2.40E-03 3.53E-03 6.45E-03 3.38E-03 3.60E-03 5.16E-03 5.49E-03 1.29E-02 1.05E-02 7.66E-03 5.34E-03 6.32E-03 5.17E-03 3.73E-03 5.94E-03 4.87E-03 6.63E-03 1.14E-02 2.99E-03 6.77E-03 6.70E-03 7.42E-03 3.45E-03 2.21E-03 6.08E-03 7.14E-03 1.67E-03 1.70E-03 1.45E-03 3.58E-04 2.29E-04 2.26E-04

2 (α=0.05) 7.22E-06 2.16E-06 2.29E-05 8.63E-06 3.63E-05 1.16E-05 6.94E-06 5.77E-06 1.25E-05 4.17E-05 1.14E-05 1.30E-05 2.66E-05 3.02E-05 1.66E-04 1.10E-04 5.87E-05 2.85E-05 4.00E-05 2.67E-05 1.39E-05 3.53E-05 2.37E-05 4.40E-05 1.30E-04 8.93E-06 4.59E-05 4.50E-05 5.51E-05 1.19E-05 4.88E-06 3.70E-05 5.10E-05 2.78E-06 2.91E-06 2.10E-06 1.28E-07 5.22E-08 5.09E-08

The pdf and cdf obtained using three Weibull parameter estimation methods and measured wind speed histograms on monthly, yearly, and seasonal basis are depicted in Figs. 3-14, Fig. 15, and Figs. 17-20; respectively. A close look of these plots indicates that the performance of MLM is better than the other two methods. This claim is justified by comparing spread in wind speed values around mean or standard deviation for measured data distribution () and for 14

ACCEPTED MANUSCRIPT fitted Weibull distribution function (w) (compare Tables 2 and 3 column 4 and Tables 4 and 5 column 8) for monthly, yearly and seasonal data sets. It is observed that the calculated 2test values for all data sets (Table 4 and 5, column 12) suggest better performance of MLM compared to MMLM and EPFM Weibull parameters estimators. For a significance value α = 0.05 and for a minimum of 61 observations, the p-value quoted in 2 table (Appendix Table A.5, Walpole et al. 2007) is 79.082. The present study is based on sample sizes of 700 for monthly, 1400-3000 for seasonal and 8000 for yearly wind speed data points. With these sizes the 2 test statistics determined lie in the range from 10-4 to 10-8, which is considerably smaller than the reported p-values in the 2-tables. Therefore, the initial assumption about Weibull distribution function as a best fit function is accepted. In all four seasons (Table 5), the distribution of wind speeds is almost symmetrical with mean wind speeds lying in the range from 6 to 9 m/s. Highest wind speed is observed in season 3 and corresponding to a large value of wind power density of 493 W/m2 when Weibull parameters are estimated using MLM method. Table 5: Wind characteristics for four seasons and test statistic values Seasons 1

2

3

4

Methods

Hours

k

c (m/s)

Vm (m/s)

Vmp (m/s)

w (m/s)

PD (W/m2)

R2

RMSE

EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM EPFM MLM MMLM

2159 2159 2159 2207 2207 2207 2927 2927 2927 1463 1463 1463

3.20 3.55 3.61 3.24 3.63 3.68 3.99 5.73 5.63 3.61 4.43 3.97

7.50 7.38 7.63 9.29 9.14 9.38 10.04 9.71 9.89 7.03 6.87 6.48

6.65 6.58 6.81 8.24 8.16 8.38 9.00 8.90 9.05 6.27 6.20 5.81

6.67 6.72 6.98 8.29 8.37 8.61 9.34 9.39 9.55 6.43 6.49 6.02

2.30 2.08 2.12 2.82 2.52 2.56 2.56 1.82 1.88 1.95 1.60 1.66

249.22 230.54 253.83 472.05 435.37 468.78 564.19 493.00 520.93 198.50 178.28 151.79

0.991 0.991 0.991 0.994 0.994 0.994 0.995 0.995 0.995 0.991 0.991 0.990

2.68E-03 5.53E-04 9.57E-04 7.68E-04 1.07E-03 9.83E-04 3.41E-03 3.14E-03 1.04E-03 2.43E-03 6.63E-04 1.57E-03

Fig. 17. Histogram and pdf, cdf curves for the season 1 (December to February)

2 (α=0.05) 7.20E-06 3.06E-07 9.17E-07 5.91E-07 1.14E-06 9.66E-07 1.16E-05 9.88E-06 1.08E-06 5.91E-06 4.40E-07 2.47E-06

Fig. 18. Histogram and pdf, cdf curves for the season 2 (March to May)

15

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Fig. 19. Histogram and pdf, cdf curves for the season 3 (June to September)

Fig. 20. Histogram and pdf, cdf curves for the season 4 (October to November)

3.5 Estimation of directional Wind Power Density The entire wind speed data is distributed into separate wind direction bins of width 10 degrees each, yielding a total of 36-wind speed bins. Bins 1-10, 331-340, 341-350 and 351-360 degrees are unpopulated. In each bin, wind speed data points are approximated by the Weibull function which is constructed by estimating its shape and scale (k and c) parameters using maximum likelihood method (as this method has been found the best among others and will be used in rest of the analysis). Table 6 lists the number of data points, Weibull mean velocity and Weibull power density for each bin. Higher mean wind speeds of more than 7 m/s (Fig. 21) and wind power densities of > 300 W/m2 (Fig. 22) are observed in wind speed bins from 21 – 50 degrees and from 221-290 degrees (Table 6, columns 1, 3, and 4). In season 1, the wind speed (Fig. 23) and the wind power density (Fig. 24) remained above 7.0 m/s and 300 W/m2 only in wind speed bins of 21- 50 (Table 6, columns 1, 6, and 7) and much less than 200 W/m2 in rest of the bins. The situation changed in season 2 with higher wind speeds (> 7 m/s, Fig. 25) and wind power densities (> 300 W/m2, Fig. 26) are seen in wind speed bins from 221-280 degrees. The wind speed (> 8 m/s, Fig. 27) and wind power density values (> 450 W/m2, Fig. 28) are found to be dominant in wind speed bins starting from 131 and ending at 300 degrees in season 3 (Table 6, columns 1, 12, and 13). Although the wind speed is seen to be blowing all along east to west through south directions (Fig. 29) and has almost a flat wind power density distribution (Fig. 30). Table 6: Distribution of wind speeds in 10 degrees bins and corresponding average speed and power density values in each bin Monthly Characteristics

DEg 1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 101-110 111-120 121-130 131-140

Seasonal Characteristics Season 2 Season 3

Season 1

Dp

Vavg

Pd

Dp

Vavg

Pd

17 231 266 253 152 107 57 64 103 207 265 232 208

6.2 9.2 7.96 7.07 6.13 5.61 5.01 4.7 6.44 6.81 6.27 6.06 5.97

178.28 531.22 358.06 252.83 165.38 131.68 95.24 82.47 205.31 235.46 187.8 171.82 173.87

15 217 248 223 131 89 48 44 52 106 150 142 115

6.65 9.3 8.14 7.27 6.24 5.6 4.93 4.4 5.97 6.56 5.96 5.98 5.99

218.59 545.68 375.89 269.55 173.66 131.07 89.55 67.88 159.36 216.02 162.93 160.6 156.05

Dp

Vavg

Pd

Dp

Vavg

Season 4 Pd

Dp

Vavg

Pd

13 7 8 3

4.12 5.81 4.3

50.55 139.88 59.02

7 15 24 14 12 20

5.05 7.24 7.05 6.88 6.32 4.82

106.53 264.45 250.66 243.06 201.06 83.44

16

16

9.9

630.15

9 20 16 16 6 11 34 75 99 74 54

6.06 5.3 5.46 5.49 5.3 5.18 6.6 6.98 6.59 5.99 5.13

7.5 156.92 103.6 106.65 123.23 105.87 94.84 225.04 245.77 209.92 156.16 96.17

289.83

ACCEPTED MANUSCRIPT 141-150 151-160 161-170 171-180 181-190 191-200 201-210 211-220 221-230 231-240 241-250 251-260 261-270 271-280 281-290 291-300 301-310 311-320 321-330 331-340 341-350 351-360

170 173 173 292 394 304 271 290 289 611 1250 1061 574 332 186 111 52 25 7

5.93 6.3 6.61 7.17 6.86 6.35 6.74 6.76 7.42 8.67 9.41 8.99 8.23 7.82 7.17 6.55 6.07 5.52 6.04

182.4 215.8 238.86 285.82 247.09 190.05 251.82 242.95 308.83 473.55 590.66 520.04 412.08 358.39 276.96 205.53 162.94 134.85 144.08

71 43 35 42 71 67 49 36 31 24 11 7 13 12 13 12 8 3

5.32 5.2 5.02 5.56 6.03 5.49 5.36 5.12 5.47 5.53 6.06 5.44 5.95 6.38 5.59 5.35 4.91 2.81

120.99 106.67 95.58 129.64 168.93 122.56 117.19 98.9 126.2 128.59 169.25 103.86 142.98 212.83 115.53 110.58 78.14 14.09

41 37 27 67 94 84 63 69 56 133 413 378 284 166 88 44 19 4

6.27 6.05 6.14 6.62 6.33 6.2 6.52 5.97 7.36 8.91 10.24 9.31 8.36 7.59 6.9 6.43 6.02 4.81

232.92 167.73 179.41 228.93 196.28 175.52 200.66 173.74 301.89 542.25 745.2 579.55 431.21 328.53 236.5 191.14 155.47 69.73

7 30 34 120 133 82 71 107 154 404 748 628 214 110 39 11

9.13 9.12 8.95 8.69 8.03 7.49 8.47 8.19 8.24 9.06 9.28 9 8.8 8.94 8.76 8.09

496.51 553.32 484.61 439.23 363.38 285.96 465.29 386.21 390.67 505.76 549.4 510.1 474.15 491.14 467.95 370.71

48 60 74 60 93 68 85 75 45 47 75 45 60 41 43 41 22 16 6

5.81 5.7 6.35 5.76 6.28 5.94 6.2 6.15 5.84 6.15 6.49 6.58 5.93 5.89 6.65 6.46 6.2 6.07 5.89

153.85 141.03 202.97 141.18 179.64 150.41 177.59 160.22 147.08 172.99 197.37 203.49 147.72 141.02 198.83 179.51 170.22 165.2 133.65

Fig. 21. Wind rose for entire data set

Fig. 22. Directional wind power density for entire data set

Fig. 23. Wind rose for season 1

Fig. 24. Directional wind power density

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Fig. 25. Wind rose for season 2

Fig. 26. Directional wind power density

Fig. 27. Wind rose for season 3

Fig. 28. Directional wind power density

Fig. 29. Wind rose for season 4

Fig. 30. Directional wind power density

3.6 Wind Energy Production The actual wind energy calculations are performed by fitting a wind turbine system to the wind speed data sets. A wind turbine of 2.5 kW rated power from Nordex N100/2500 is used for the assessment of wind energy yield. The turbine specifications are given in Table 7. The power curve of the turbine is overlaid on the seasonal and yearly pdfs, as shown in Fig. 31. It is evident from Fig. 31 that season 3 (June – September) pdf has a maximum overlap with the turbine 18

ACCEPTED MANUSCRIPT power curve, consequently giving a maximum energy yield of 4571.55 kWh compared to other seasons (Table 8). The annual energy production is found to be 10054.27 kWh. The plant capacity factor achieved is around 53% in season 3, highest among all seasons. Table 7: Nordex N100/2500 Wind Turbine Specification Turbine Characteristics Rated Power Rotor Diameter Swept area Cut in wind speed Cut out speed Rated speed Rotor hub height

Values 2500 KW 100 m 7854 m2 3 m/s 20 m/s 13 m/s 80 m IEC 2a

Table 8. Wind energy estimation for Jhimpir using Weibull distribution function. (Turbine Power Curve fitted to Cubic function) Period

Vm (m/s)

Mean Energy Density (kWh/m2)

Ideal Wind Energy (kWh)

Actual Wind Energy (kWh)

Availability F (%)

Efficiency ε (%)

Capacity Factor CF (%)

Season 1

6.58

498.00

3940.50

1691.00

95.99

43.12

31.46

Season 2

8.16

961.30

7475.14

2851.36

98.26

38.14

51.66

Season 3

8.90

1443.52

11434.50

4571.55

99.88

39.98

52.55

Season 4

6.20

261.00

2066.80

915.86

97.50

44.31

25.02

Yearly

7.70

3165.02

24934.38

10054.27

98.06

40.32

45.91

Fig. 31. Probability density function (pdf) and the wind turbine power curve The energy output results with existing studies conducted earlier on other sites in the same corridor are compared in Table 9. The present study gives a comprehensive account of wind energy potential using a wind turbine on monthly and seasonal timescales. Higher annual wind 19

ACCEPTED MANUSCRIPT speed and wind power potential is observed for Jhampir-FFC site, giving planners and investors an opportunity for setting up a wind energy conversion system in Jhampir. Table 9. Annual wind speed and wind power potential for different sites in the wind corridor Heigh Vavg. Wind Reference Wind Site t (m/s Potential ) (m) (W/m2) 6.86 Shoaib et al. Baburband 80 196.18 2017a 6.60 Shoaib et al. Keti Bandar 60 176.06 2017b 5.94 Hawksbay 80 197.19 Khahro et al. 2013 Jhampir7.77 FFC 80 287.40 Present work 4. Conclusions In the present paper, wind speed data obtained from AEDB for a period of three years was preprocessed and converted into an hourly averaged data set. Based on this hourly averaged data, monthly and the seasonal data sets were obtained. Next, Weibull function was fitted to monthly, seasonal, and yearly wind speed data sets and wind characteristics were determined. Based on performance evaluation parameters, MLM method found to be best compared to other two methods. Monthly, seasonal, and yearly wind power densities were determined. Additionally, directional power densities in seasonal and yearly domains were also estimated. This is followed by the extraction of wind energy on seasonal and annual basis. Following points are concluded from the study:  Modeling measured wind data sets using Weibull function is most reliable when parameters are estimated using MLM. This was concluded based on minimum values of MBE and MSE obtained for Monte Carlo simulation method. In case of MLM, MBE was less negative and more stable for a varying number of input data points compared to other methods, EPFM and MMLM.  The study indicated that the period from May to October was windier compared to the rest of the months and consequently higher wind power density values were obtained during the period. Maximum wind power density of 745.06 W/m2 was obtained in the month of May using MLM method.  Directional data analysis revealed that for the entire data set the wind was found to be blowing mostly in the third quadrant around 250 degrees. It simply suggests that higher wind energy can be extracted from this sector during the year. In season 1 (December to February) higher and more wind were blowing from 21-30 degrees direction, resulting in higher value of directional wind power density of 545.68 W/m2. In season 2 (March to May) more wind was concentrated in third quadrant with higher speed values, resulting in a directional power density of 745.2 W/m2 along 241-250 degrees direction. In season 3 (June to September) wind was found to be predominant from third quadrant with almost similar wind speed values, resulting in a flat distribution of wind power densities. In season 4 (October to November) wind was distributed almost equally in the lower half of the wind rose with comparatively smaller wind speed values, resulting in lower wind power density values in this season.

20

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A wind turbine with rated power of 2.5 kW was fitted to the wind speed (yearly and seasonal) data sets. Based on entire data set, the actual wind energy extracted was 10054.27 kWh with an availability factor of ca. 98%. The efficiency of wind turbine for the site under study was 40% and a plant capacity factor of 46%. Season 3 was much windier than the other seasons and actual wind energy extracted was 4571.55 kWh. The season 3 had an exceptionally high availability factor of 99.88%.

Based on the comprehensive analysis presented in this study, it is concluded that Jhampir is suitable for setting up of wind farms for green and clean energy utilization. Acknowledgment The authors are indebted to Federal Urdu University of Arts, Science and Technology (FUUAST) for research support and to the Alternate Energy Development Board (AEDB) for providing wind speed data for the study. Authors also acknowledge the support provided by King Fahd University of Petroleum and Minerals, Dhahran-31261, Saudi Arabia for their help in accomplishing this study. Glossary V ρa σ σW CV C.I. K S R2 RMSE 2 PD Pdf cdf Vm Vmp (z) PA PF Pw

Average measured wind speed (m/s) Air density (kg/m3) Standard Deviation (m/s) Standard Deviation of Weibull Distribution Function (m/s) Coefficient of Variation Confidence Interval Kurtosis Skewness Coefficient of Determination Root-Mean-Square-Error Chi-Square test Power Density (W/m2) Probability Density Function Cumulative Distribution Function Weibull Mean wind speed (m/s) Weibull Most Probable wind speed (m/s) Gamma function Wind Power Density (W/m2) calculated using measured wind speed data Wind Power Density (W/m2) using fitted distribution function Weibull Wind Power Density (W/m2)

References AEDB-Pakistan. Official website of Alternate Energy Development Board, Pakistan. http://www.aedb.org. (accessed on 20.06.2018) Akdağ, S.A., Dinler, A., 2009. A new method to estimate Weibull parameters for wind energy applications. Energy Conversion & Management 50(7), 1761-1766. Akdağ, S.A., Bagiorgas, H.S., G. Mihalakakou, G., 2010. Use of two-component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean. Applied Energy 87(8), 2566-2573.

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Highlights     

Weibull function is used to analyze wind speed data Suitability is assessed using well known methods RMSE, R2, and goodness-of-fit Directional power densities are calculated to find optimum directional efficiency Annual yield of 10054.27 kWh may be realized from a 2500 kW rated wind turbine The site under investigation is found to be suitable for wind farm development