PERFORMANCE EVALUATION OF SOME SELECTED WIND TURBINES IN HEIPANG WIND SPEED REGIME

Heipang in Plateau State is classified under moderate wind speed regime in Nigeria, thus, has high potential for wind electricity generation. Due to high cost, it is difficult to design a wind turbine for a particular site; therefore, the designer of the wind energy project has to choose from the available options in markets, which come in different sizes and speed characteristics. This paper is aimed at evaluating the performance of some selected wind turbines in Heipang wind speed regime. The method used is based on wind speed analysis and computation of the capacity factors of wind turbines expressed as a product of wind turbines’ power output models and probability distribution of wind speed regime of Heipang; and the total annual energy generation of the wind turbines using Wind Energy Resources Analysis (WERA) software. Results showed that Heipang has an annual mean wind speed of 6.3 m/s and its wind speed regime best fitted into Weibull probability distribution function with average Weibull shape and scale parameters of 3.05 and 7.03 m/s respectively at 10 m height. For small (<10kW), medium (10kW-250kW) and large (>250kW) wind turbines classifications; WT4, WT14 and WT25 have the highest capacity factors of 0.61, 0.7 and 0.53 respectively and WT2, WT22, WT27 have the highest total annual energy generation of 0.0054, 1.12 and 4.03 GWh/year respectively. In conclusion, Heipang has high wind speed potential for wind power technology and wind turbines with higher annual energy generation are better options for selections for wind power generation applications.

site, so usually one chooses for a given site the best among existing wind turbines in the market. Selection of the right wind turbine for the right site plays a major role in the success of wind power project (Bencherif et al., 2014). Several wind turbines of the same power class but differing in performance curves may be commercially available, thus, designer of the wind energy project often choose a system from these available options for the project site.
Many procedures have been proposed for investigating the potentiality of a site in relation to wind turbines since 1979 (Chang et al., 2003). Gungor et al, (2020)  This paper is aimed at presenting a simple methodology for analyzing the performance of different wind turbines in the market in wind speed regime of Heipang village for selection among others for wind power project installation in Heipang village in Plateau State. The method used in the analysis was based on the computation of the capacity factors and the total annual energy generation of the wind turbines expressed as a function of the Weibull distribution function and the speed characteristics of the wind turbines using the Wind Energy Resources Analysis (WERA) software. Instead of dealing with tedious bar-chart data of wind distribution and power curves, the WERA application software is fast and simple in carrying out the analysis.
Heipang village is a small community located along Jos-Barkin-Ladi road about 30 km from Jos the state capital of Plateau State. It is located between longitude 8 o 53' E and 8 o 54' E and between latitude 9 o 37' N and latitude 9 o 40' N. The landscape is a plain land with its vegetation characterized by shrubs and grasses with few scattered trees planted by the people in the community (Ajaegbu, 1992), giving it the advantage of siting a Federal Airport Authority.

2.1
Wind speed data The sizing of wind turbine power system depends on the wind speed potential of the site. It has been recommended that a site with an average wind velocity at the height of a wind turbine of at least 3 m/s has the potential for wind electric power generation (Agbetuyi et al., 2012). Long-term wind speed data of ten years or more collected from meteorological stations near the site can be used for making estimates of wind energy potential if there are no measured wind speed data of the site available (Wei, 2010 andMatthew, 2006). Thus, for the analysis of the wind regime of the site, ten year daily average wind velocity data for Heipang village was obtained from the National Meteorology Agency, Abuja.

2.2
Wind Turbines Models Twenty eight models of wind turbines of different velocity characteristics and rated power available in the market were selected for the analysis, see Appendix I. The models of the wind turbines were obtained from the Catalogue of European Urban Wind Turbine Manufacturers and from Mick Sagrillo wind generators catalogue (Sagrillo, 2002).

2.3
Wind Energy Resource Analysis (WERA) Application software Wind Energy Resources Analysis (WERA) software was used to compute the capacity factors and the total annual energy generation of the selected wind turbines, which are indicators of the performance of wind turbines at the site (Matthew, 2006).

Wind Speed Data Analysis and Determination of Weilbull Parameters
The ten year daily average wind speed data of Heipang village were analysed using Microsoft Excel spread sheet to determine the monthly average wind speed for the location under study. Due to the boundary layer effect wind speed increases with height in a logarithmic pattern. Thus, the wind speed data collected at meteorological station height of 10 m was extrapolated to the wind turbine height of 100 m on the basis of the roughness height of the terrain (Matthew, 2006): (1) Where: w z is the wind turbine height and m z is the meteorological station height.
Wind speed distribution is stochastic in nature and can be best expressed as probability distribution function with an acceptable accuracy level (Matthew, 2006 andBoro et al., 2020). To determine the probability distribution of the wind regime, the measured wind speed data was fitted into various probability functions using easyfit software which is an add-on in Microsoft Excel spread sheet, to identify suitable statistical distributions representing the wind speed regime of Heipang village. The easyfit software ranks the fitting of the wind speed data to the various probability distribution function and their parameters.
The probability density function ) (v f indicates the fraction of time (or probability) for which the wind is at a given velocity v (Matthew, 2006 ): is the integral of the probability density function as in (Matthew, 2006): The value of k determines the shape of the curve and hence is called the shape parameter and c is called the scale parameter.
The monthly Weibull shape parameter k and scale parameter c were determined from the wind speed data of Heipang village using equations (4) and (5) respectively (Matthew, 2006;Ohunakin et al., 2011 andAzad et al., 2014): where v  and m v are the standard deviation and the mean wind speed of the location.
The vertical extrapolation of the Weibull parameters at desired elevation, w z above the meteorological height m z were computed using equations (6), (7) and (8) (Kent et al., 2018;Cheggaga, 2017;Pallabazzer, 2003 andFaghani et al., 2018): where, z c and z k are the Weibull scale and shape parameters at desired height respectively, while 10 c and 10 k are the Weibull scale and shape parameters respectively at 10 m height. w z , and 10 z are the desired height and the height at 10 m respectively. The power law exponent  is given as (Boro et al., 2020;Tonsie et al., 2021 andManwell et al., 2005): Where, ref U is the ten-year average wind speed at 10 m height.

Wind Turbines Power Output Models
The important velocity characteristic of wind turbine are its cut-in velocity ) ( c v which is the minimum wind velocity at which system begins to produce power; rated velocity ) ( r v which is the velocity at which the wind turbine operates at its rated power and the cut-out velocity ) ( o v which is the minimum velocity at which the wind turbine furls to protect it from being destroyed by strong wind. The output power curve of wind turbines in the markets are often expressed graphically, however, to compute their capacity factor analytically, their power output curves have to be modeled. The power output models of wind turbines used for the analysis are as given in  Teyabeen et al. (2017). The wind turbines power output is fitted into the proposed wind turbine power curve model given as equation (9) with varying values of the power-velocity proportionality index, n representing the different power output curve models.
are the rated power, cutin, rated and cut-out velocities of the wind turbine respectively and v is the wind velocity.
n is the power-velocity proportionality index. The power output model in equation (9) (10) and (11) below and based on the velocity characteristics, hub heights, the determined power curve model of each of the selected wind turbines; and the Weibull parameters extrapolated at the wind turbines' heights, their capacity factors were computed.
Where c and k are the scale parameter and shape parameter of the site respectively, c v , r v and o v are the cut-in , rated velocity and the cut-out velocity of the wind turbine respectively, n is the power-velocity proportionality index of the wind turbine.
Where R P is the rated power of the wind turbine; T is the time of operation of the wind turbine in this case one year and T E is the total energy developed by the wind turbine 2.6 Matching wind turbines with the wind speed regime The average power produced by a wind turbine can be calculated by integrating the product of the power output curve of the wind turbine and the Weibull probability function of the wind regime where the wind turbine operates as given by equation (12) (Matthew, 2006): is the power output curve of the wind turbine and ) (v f is the Weibull probability function which gives the fraction of the time for which the velocity v prevails in the wind regime. The capacity factor (CF) was calculated from the relation given in equation (13) (Matthew, 2006 andVaughn, 2009): The performance of a wind energy conversion system at a site depends heavily on the efficiency with which the turbine interacts with the wind regime. CF and the annual total energy generation are important indices for assessing the field performance of a wind turbine. The CF of a wind turbine at a given site is defined as the ratio of the energy actually produced by the wind turbine to the energy that could have been produced by it, if the wind turbine would have operated at its rated power throughout the time period (Matthew, 2006). The CF is influenced by the efficient interaction of wind turbine to the prevailing wind in the site. In other words, the functional velocities of the wind turbine ( c v , r v and o v ) should be chosen in such a way that the wind energy available within the wind regime is exploited to its maximum level. The CF of a wind turbine can be estimated using equation (10) expressed as a function of Weibull parameters and wind turbine's velocity characteristics (Matthew, 2006 andBurton et al., 2021).
The total annual energy developed by the wind turbine is computed using equation (11) (Matthew, 2006). It should be noted that in equations (10), CF is independent of R P , but depends only on speeds characteristic of the wind turbine such as cut-in velocity c v , rated velocity r v and cut-out velocity o v and the Weibull distribution function parameters characterizing the site wind energy potentials while the total energy generated depends on the rated power of the wind turbine. The CF reflects how effectively the turbine could harness the energy available in the wind spectra. As pointed out in Mathew, (Matthew, 2006) the CF for a reasonably efficient turbine at a potential site range from 0.25 to 0.4 and CF of 0.4 or higher indicates that the system is interacting with the regime very efficiently.

3.1
Wind Data Analysis Table 1 shows the monthly mean wind speeds distribution of Heipang village with an annual average of 6.3 m/s and standard deviation of 0.39. As it can be seen, the windiest month is November, with peak wind speed of 7.41 m/s, while the calmest month is September with the minimum wind speed of 5.08 m/s. The high wind speed as seen dominant during the dry season of the year between October and May could be due to the north-easterly tropical continental air masses also known as the harmattan which characterized the months (Ajaegbu, 1992). Seasonal winds in Heipang village are strongest in months between October and May, making the location most suitable for establishing wind power plant as wind speed is high and more consistent throughout the year. Incidentally, these months with strong wind speed fall within the dry season of the year, thus the wind energy resources can be harnessed for wind pump technology for dry season farming.

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Vm (m/s) 6.42 6.91 6.91 6.75 6.13 5.83 5.85 5.74 5.08 6.37 7.41 6.82 Figure 1 shows the display of the fitting of the wind speed data of Heipang village into thirty-five different probability distribution functions. The result shows that the wind speed regime best fitted into Weibull probability distribution function as it is ranked highest in the order of best fit with Weibull shape parameter and scale  Table 2 shows the extrapolation of Weibull parameters to varying heights. The results show that the Weibull shape parameter increases by 2% (from 3.05 to 3.11) from a height of 10 m to 100 m while the Weibull shape parameter increases by 61% (from 7.03 to 11.33 m/s) from 10 m to 100 m. A higher value of k , such as k >2.5 indicates a site where the variation of hourly mean wind speed about the annual mean is small (Burton et al., 2021).

Probability Distribution Function of the Wind Speed Regime
The coefficient of determination 2 R and Mean Absolute Percentage Error (MAPE) used to describe the Correlation between the instantaneous power predicted by the different power output curve models in the range of cut-in and rated velocities and the manufacturers' power output values are shown in Table 3. From Table 3, the values of coefficient of determination and the mean average percentage error that are closer to 1 and 0 respectively were selected as the best fitted models.
The results show that 54%, 14%, 21%, and 11% of the selected wind turbines are fitted into quadratic model, general model, linear model and cubic model respectively. The capacity factors and total annual energy generation of the selected small, medium and large wind turbines are shown in Figures 3, 4 and 5 respectively. In Figure 3, the wind turbines WT4 has the highest capacity factor of 0.61 and WT1 has the lowest capacity factor of 0.29, while WT2 has the highest total annual energy generation of 0.0054 GWh/year and WT3 has the lowest total annual energy generation of 0.0011 GWh/year. In Figure 4, the wind turbines WT14 has the highest capacity factor of 0.7 and WT23 has the lowest capacity factor of 0.28, while WT22 has the highest total annual energy generation of 1.12 GWh/year and WT8 has the lowest total annual energy generation of 0.04 GWh/year. Similarly, in Figure 5, the wind turbine WT25 has the highest capacity factor of 0.53 and WT26 has the lowest capacity factor of 0.27. WT27 has the highest total annual energy generation of 4.03 GWh/year and WT24 has 0.92 GWh/year.    Wind turbines performance in a site depends on the efficiency with which the turbines interact with the wind regime. The capacity factor of wind turbines having the same rotor size, rated power, and conversion efficiency are influenced by the availability of the turbine to the prevailing wind, which depends on the functional velocities of the wind turbine, i.e., cut-in, rated and cut-out velocities (Matthew, 2006). The capacity factor and energy generation of wind turbine decreases with increase in cut-in velocity; decreases with increase in rated velocity and slightly increases with increase in cut-out velocity (Matthew, 2006). This is further verified by the result in Figure 4 comparing WT18 and WT19 which have the same rated and cut-out velocities and rated power but different cut-in velocities of 2.7 and 3 m/s respectively.

Figure 1: Fitting of the wind speed regime of Heipang village into probability distribution function
While WT18 has capacity factor and total annual energy generation of 0.58 and 0.51 GWh/year respectively; WT19 has capacity factor of 0.55 and total annual energy generation of 0.  (2006). The capacity factor for a reasonably efficient turbine at a potential site ranges from 0.25 to 0.4 and capacity factor of 0.4 or higher indicates that the system is interacting with the regime very efficiently. However, when selecting from collection of wind turbines with the same power rating but different performance characteristic, the wind turbine with higher capacity factor and energy generation should be selected against those with lower values apart from other factors such as availability and cost of the system and maintenance. For example, from Figure 3 the wind turbine WT4 which has rated power 2.5kW, capacity factor 0.61 and total annual energy generation of 0.0013 GWh/year should be selected against WT3 which has rated power 2.5 kW, capacity factor 0.51 and total annual energy generation of 0.0011 GWH/year. Similarly, in Figure 4, WT14 with rated power 50 kW, capacity factor 0.7, and total annual energy generation 0.31 GWh/year should be selected over WT15 with rated power 50 kW, capacity factor 0.63, total annual energy generation 0.28 GWh/year and WT16 with rated power 50 kW, capacity factor 0.44 and total annual energy generation of 0.19 GWh/year. Based on the same aforementioned reasons, in Figure 5 WT27 should be selected over WT28.4.

CONCLUSION
The following conclusions can be drawn from this work: Heipang village has relatively high potential for wind power technology for generating electricity as indicated by its high annual mean wind speed of 6.3 m/s; The wind regime of Heipang village fits into Weibull probability distribution function; most wind turbines in the market can interact with the wind speed regime of Heipang village very efficiently as indicated by their high capacity factors thereby making the village viable for using wind energy conversion systems to generate electricity.