Microsoft Word - 9-2381_s1_CA Engineering, Technology & Applied Science Research Vol. 9, No. 1, 2019, 3721-3725 3721 www.etasr.com Memon et al.: Assessment of Wind Power Potential Based on Raleigh Distribution Model… Assessment of Wind Power Potential Based on Raleigh Distribution Model: An Experimental Investigation for Coastal Zone Bisharatullah Memon Department of Electrical Engineering, Mehran University of Engineering & Technology, Sindh, Pakistan Mazhar H. Baloch Department of Electrical Engineering, Mehran University of Engineering & Technology, Sindh, Pakistan A. Hakeem Memon Department of Electrical Engineering, Mehran University of Engineering & Technology, Sindh, Pakistan Sajid H. Qazi Department of Electrical Engineering, Mehran University of Engineering & Technology, Sindh, Pakistan Raza Haider Electrical Engineering Department, Baluchistan University of Engineering & Technology, Khuzdar, Pakistan Dahaman Ishak School of Electrical and Electronics Engineering, Universiti Sains Malaysia, Malaysia Abstract—The wind energy share in the global energy production is increasing rapidly. Currently, the Government of Pakistan (GoP) is moving towards renewable energy resources (RER), specifically wind and solar energy. In this paper, the wind energy potential of Tando Ghulam Ali, Sindh, Pakistan is explored. For this purpose, one-year wind speed data are considered at various heights through various probability distribution functions (PDFs). Statistical comparison of Rayleigh, gamma, generalized extreme value (GEV) and lognormal PDFs have been done with two methods, namely root mean square error and (��) in order to select the best PDF. Results showed that the Rayleigh distribution function is the best at the above area for finding various factors like site selection and wind power cost per kWh. Keywords-wind energy; wind probability distribution function; fitting tool I. INTRODUCTION Several countries are investing resources in the direction of RER. Energy sources like biomass, wind energy, hydro energy, and thermal energy have gained interest because of their friendly environment features [1, 21-23]. The wind energy is a drifting RER for production of energy, and can have better results over the reliability and stability of the power system. Wind power recorded a yearly development of 25% rate over the past few years [2, 20] and is based on the wind speed estimation, which is uncertain in considering wind energy and the performance of the wind energy conversion system. Wind speed at a location diverges unsystematically and its deviation in a specific area over a time period and can be characterized by PDFs. Several PDFs are taken to estimate the wind speed features including Rayleigh, Weibull, GEV, lognormal and gamma [3]. To find the most accurate of PDFs, prediction performance tests are suggested. In this paper, root mean square error (RMSE) and coefficient of determination (R 2 ) tests are considered. In [4], it was shown that the outcomes of the Weibull distribution dignified the PDF and are more suitable as compared to the Rayleigh distribution in the peak height region of Nepal [4]. Authors in [5] ranked 7 different methods considering the examined error of calculations regarding wind energy. Authors in [6] found the wind power density in a specific location of Pakistan at various heights and considered different distribution functions for wind speed calculation and from 5 numerical methods. Authors in [7] examined the comparison between the lognormal and Weibull techniques by fitting the curve of observed wind speeds and concluded that the Weibull distribution is more reliable than lognormal distribution to pronounce the performance of wind speed data. Authors in [8] explored the number of distribution techniques to find the exact wind speed data in Hong Kong. This study summarizes the results of wind speed data at Tando Ghulam Ali. This study tries to find the best distribution techniques from various PDFs like: Rayleigh, gamma, GEV and lognormal. From the results, it was proved that the Rayleigh distribution function was the best distribution technique for the studied site. II. MATHEMATICAL PDFS The estimation of wind energy at a particular site involves statistical methods of PDF, which require wind speed data at a meteorological station. Similarly, frequency distribution functions are used to estimate wind power density. Some types of PDFs are chi-squared distribution, Rayleigh distribution, generalized normal, three parameter log-normal, log normal- distribution, gamma distribution, kappa, wake by inverse Gaussian distribution, normal two variable distributions, hybrid distribution, as well as normal square root of wind speed distribution [9-11]. Corresponding authors: M. H. Baloch (mazhar.hussain08ele@gmail.com), D. Ishak (dahaman@usm.my) Engineering, Technology & Applied Science Research Vol. 9, No. 1, 2019, 3721-3725 3722 www.etasr.com Memon et al.: Assessment of Wind Power Potential Based on Raleigh Distribution Model… A. Rayleigh Distribution Model Rayleigh distribution function [12]: ���� � � � � ��� �� (1) The shape parameter (k) is assumed to be 2 and the scale parameter (c) is defined as: � � �������� (2) where (m) is the mean and can be obtained as: � � �� ∑ �� ���� (3) B. Gamma Distribution Model The gamma distribution function can be defined as [13]: ���� � !�" ��#� � � $� "% (4) where, & � ��'� (5) ( � '�� (6) where (s) can be obtained as follows: ) � $ ��*�∑ ��� � ������+ % �� (7) C. Lognormal Distribution Model Lognormal distribution can be defined as [14]: ���� � � "√�- .�����/0/0� �*#�" ��1 (8) Parameters from (8) are estimated as: & �23 234 �5�� 6�7�8 (9) ( � 523 23�1 : '���� (10) D. Generalized Extreme Value Distribution (GEV) Model It is a combination of Frechet, Gumbel and Weibull maximum extreme value distributions and can be defined as [15]: ���� � �# $1� ;# �� � <�% ��*� =�$1� ;# �� � <�% ��>if A B 0 (11) With the support of the maximum likelihood method, the parameters of GEV can be obtained as: DD � 23∏ F����; H,J, 2�K0��� � ∑ F����;H, 2�K0��/ /0 (12) III. PROBABILITY DISTRIBUTION MODEL EVALUATION In this paper, for the initial evaluation of the process the graphical display of the wind speed of measured data is being superimposed by the fitted PDFs and visual comparison is done. RMSE and R 2 criteria are considered for choosing the appropriateness of the fit method for the selected three functions along with their ability to estimate the energy and to predict the wind potential. The performance of these functions is analyzed through the following ways [16]: A. Root Mean Square Error (RMSE)Test The value of RMSE that is nearest to the zero indicates a better distribution function. The RMSE is calculated as [17]: LMNO � ��∑ ��� � �����P�+ (13) B. L� Test The R-squared goodness of fit test is hypothesis and comparison testing that determines the correlation between the predicted and observed data. Greater value of R 2 shows better fit of the PDF. It can be defined as [18]: L� � 1 � ∑ �Q�R���STU�∑ �Q�Q���SVU� (14) C. Wind Power Density Function It is defined as the power generated by wind turbine per m 2 . It is helpful in the estimation of wind resources at a site. There are many ways to determine wind power density [6], and it can be defined as follows: WXY � ∑ ��Z��[��������� (15) where the probability of wind speed at the i-th speed value is f(vi). The standard value of air density is considered to be ρ=1.225kg/m 3 . IV. RESULTS AND DISCUSSION The proposed site, Tando Ghulam Ali located near Hyderabad, Sindh province, lies in the southern region of Pakistan, at 24°52’02.025’’N and 66°51’41.983’’E. One year’s wind speed data (from Jan 2017 to Dec 2017), with 10 minute sample intervals were used. The typical hourly and monthly measurements are calculated at the different heights of 80, 60, 40 and 20m. The average wind speed at different heights is shown in Figure 1(a-b). Table I summarizes the average values of wind speed and wind power density for all heights. (a) (b) Fig. 1. (a) Hourly and (b) monthly average wind speed at different heights. V d iu rn a l (m /s ) Engineering, Technology & Applied Science Research Vol. 9, No. 1, 2019, 3721-3725 3723 www.etasr.com Memon et al.: Assessment of Wind Power Potential Based on Raleigh Distribution Model… TABLE I. MONTHLY AVERAGE OF WIND SPEED AND WIND POWER DENSITY Heights 80m 60m 40m 20m Months/Factors Vavg (m/s) WPD(Watts/m 2 ) Vavg (m/s) WPD (Watts/m 2 ) Vavg (m/s) WPD (Watts/m 2 ) Vavg (m/s) WPD (Watts/m 2 ) Jan 5.948 199.339 5.492 146.349 4.631 83.229 3.568 40.876 Feb 6.201 241.862 5.743 178.793 4.753 93.854 3.513 39.094 Mar 5.967 188.372 5.546 147.580 4.897 102.387 3.913 55.409 Apr 7.999 394.927 7.491 326.331 6.824 254.450 5.745 160.253 May 8.623 449.674 8.238 396.278 7.712 330.572 6.662 216.206 June 8.568 485.264 8.206 431.087 7.714 365.560 6.708 245.574 Jul 8.385 464.414 7.997 408.468 7.475 340.660 6.466 224.809 Aug 7.723 362.365 7.309 312.404 6.764 254.442 5.831 168.981 Sep 6.351 181.119 5.908 146.452 5.353 112.059 4.534 71.889 Oct 5.705 166.097 5.171 114.592 4.418 67.361 3.358 30.346 Nov 5.506 176.713 5.082 128.415 4.230 66.299 3.057 23.446 Dec 6.859 271.994 6.141 181.989 5.056 97.521 3.765 42.218 Year 6.990 3.010.112 6.531 243.228 5.824 184.041 4.767 103.934 (a) (b) (c) (d) Fig. 2. Fitting of different PDFs over the data using MATLAB distribution fitting tool. Figure 2 shows the fitting of each PDF over the data. It can be observed that for 80m, 60m, and 40m, the Rayleigh distribution fitted best, followed by gamma, generalized extreme value and lognormal. Due to the lower wind speed at 20m, lognormal fitted best followed by Rayleigh, gamma and generalized extreme value. Table II shows the value of the parameters for each PDF. Table III shows the statistical errors for the different distribution functions and the value of both RMSE and R 2 goodness of fit tests. For economical evaluation the cost of each turbine is considered as $1.5/W, other initial costs like transportation, installation, grid integration etc. are taken as 40% of the turbine’s cost, the cost of the maintenance and operations is 1.5% of the turbine’s cost at interest rate of 10% and the turbine life span is taken as 20 years. TABLE II. PARAMETERS OF DIFFERENT PDFS PDF 20m 40m 60m 80m Rayleigh A 2 2 2 2 � 3.7314 4.4750 4.9820 5.3376 Gamma α 4.402 4.9230 4.9692 4.72186 ( 1.082 1.1832 1.3144 1.4805 GEV K 0.00223 -0.1254 -0.19450 -0.2173 Α 1.7813 2.2135 2.5327 2.7809 l 3.7259 4.7945 5.49120 5.8888 Lognormal α 1.443 1.6571 1.7727 1.8350 β 0.506 0.4932 0.5001 0.5172 TABLE III. STATISTICAL ERRORS AT EACH HEIGHT Height Method RMSE R 2 80m Rayleigh 0.010418 0.954265 Gamma 0.019615 0.840719 Gen Extreme Value 0.019931 0.834948 Lognormal 0.026673 0.713073 60m Rayleigh 0.010568 0.960678 Gamma 0.018961 0.875165 Gen Extreme Value 0.02168 0.841316 Lognormal 0.02644 0.761952 40m Rayleigh 0.010357 0.969184 Gamma 0.014716 0.937879 Gen Extreme Value 0.021199 0.879976 Lognormal 0.022046 0.862584 20m Lognormal 0.00994 0.978188 Rayleigh 0.010305 0.976476 Gamma 0.010919 0.972912 Gen Extreme Value 0.01923 0.921165 D e n si ty D e n si ty D e n si ty Engineering, Technology & Applied Science Research Vol. 9, No. 1, 2019, 3721-3725 3724 www.etasr.com Memon et al.: Assessment of Wind Power Potential Based on Raleigh Distribution Model… V. PERFORMANCE AND COST ASSESSMENTS The investment cost of a wind power plant is extremely high, it is therefore important to estimate the cost of the energy generated by a turbine in $/kWh, which can be calculated by (16) [19]: \ � P]^_+` a �bcdef$1 + �g�����h*�������h i% (16) where PR is the rated turbine power, Cf is capacity factor, m is the cost of operation and maintenance, i is the rate of interest and I is the investment cost. To assess the performance and economical evaluation of wind turbines at the candidature site, five different turbines were considered whose specifications are given in Table IV. Each turbine comes with different hub heights. The performance of wind turbines is taken at the hub height of 80m. Estimated capacity factor, annual energy output (kWh/year) and cost/kWh in dollars, for each wind turbine are shown in Table V. The Gamesa G128/4500 wind turbine minimum cost is $0.05453 per kWh of energy generated, with a capacity factor of 40.87%. Nordex N90/2500 model also costs minimum at $0.05453 per kWh with a capacity factor of 32.88%. The highest cost of $0.08019 per kWh energy generated by Vestas V112/3000 with a capacity factor of 27.78%. TABLE IV. WIND TURBINES SPECIFICATIONS Model Enercon E82 Gamesa G128 Nordex N90 Repower MM82 Vestas V112 Rated power (kW) 2300 4500 2500 2050 3000 Rotor diameter (m) 82 128 90 82 112 Hub height (m) 138, 78 140, 120, 81 120,100, 80, 75 100, 59 119, 84 Cut-in wind speed (m/s) 2 1.05 3 3.5 3.5 Rated wind speed (m/s) 14 12 13-14 15 15.5 Cut-out wind speed (m/s) 25 25 25 22 25 TABLE V. ESTIMATED COST PER KWH Turbine Model Power generated (kW) Energy produced (MWh) Capacity factor Cost/k Wh Gamesa G128 183913.03 1611078.14 40.870 0.05453 Nordex N90 82216.61 720217.50 32.887 0.05453 Repower MM82 65076.14 570066.99 32.538 0.06849 Enercon E82 73937.89 647695.92 32.147 0.06932 Vestas V112 83367.15 730296.23 27.789 0.08019 VI. CONCLUSION The study concludes that the proposed site can be utilized for commercial purpose. Government of Pakistan (GoP) can exploit this site for wind energy power generation. Four techniques, gamma distribution, Rayleigh distribution, lognormal distribution, and generalized extreme value distribution were employed and their statistical evaluation was conducted by RMSE and R 2 through Matlab distribution fitting tool. The following points are concluded: • In comparison to other PDFs, the Rayleigh distribution function fits more accurately to the wind probability distribution at higher altitudes. While at lower wind speeds, lognormal showed better fitting. • The Gamesa G128 wind turbine model is recommended, having lower cost regarding generated energy, with highest capacity factor of 40.8 %. • More feasibility study of wind power project is required, to exploit wind potential at the proposed site. • Results showed that the highest wind potential is available during the summer season, during May-July and can be used for power generation. Calculations were made to obtain the parameter of each PDF, and then the best fitted distribution technique was used to determine the wind potential. This site is in the premises of the National Grid which is another advantage of installing wind projects there. Finally, this site can be employed for commercial purposes. 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