Wind Energy Assessment at Bafoussam, Cameroon

Three-hourly wind speed data measured using the Beaufort scale at a height of 10m, from 6am to 6pm local time (5 periods per day), was obtained from the Bafoussam Airport. It was analyzed using the Weibull and Rayleigh probability density models and wind rose plots. It was determined that the lowest wind speeds (most calms) were observed during the first period (6am) and the highest at 3pm (fourth period). The very low morning wind speed adversely affected the daily mean wind speed. Better, but still poor, power density results were obtained at this fourth (3pm) period. The monthly and yearly mean speeds varied between 1.9 and 3.1m/s and with very low standard deviations. The wind rose plots also showed that all the significant winds fell in the first quadrant (NE) and predominantly on angle 10 with some discernibly on 20 and 30, only. Three goodness-of-fit tests: the chi square, coefficient of determination or R and root mean square error, showed the Weibull to be a better fit to the wind regime than the Rayleigh model. The shape parameters were always greater than the scale parameters. Results show that, using the Weibull parameters, the power density of Bafoussam falls in the category 1 of the wind energy resource group and hence is not a very good wind energy exploitable candidate.

connectivity is just about 11%. This lead to the installation of thermal plants but the ever growing population and more energy demanding structures and activities has still not decreased the crisis.
If viable, small scale off-grid installations may curb this debility if local renewable sources are identified and properly harnessed. Among these local sources are organic wastes, solar and wind. As far as wind energy potential studies in Cameroon are concerned, only her northern part of the national territory is fairly covered in the literature. Tchinda and Kaptouom (2003) estimated the mean wind power in the far north province. In another study, Tchinda, Kendjio, Kaptouom, Njomo (2014) analysed wind speed and wind energy distributions in the Adamaoua and North regions. Kaoga, Sergeb, Raidandic, Djongyang (2014), Kaoga, Danwe, Yamigno, Djongyang (2014), Kaoga,, Djongyang, Doka, Raidandi (2014), Kaoga1, Raidandi, Djongyang, Doka, (2014) equally and variously carried out wind energy studies in Kousseri, Maroua and Garoua, all from the northern regions. Their studies showed that the region is not feasible for wind energy exploitation but feasible as water wind mills. In the southern part of Cameroon, only a single case is documented in the literature. Using NASA data, Afungchui and Aban (2014) carried out studies of Bamenda's environ and determined that the wind regime is Weibull representative and hence could be used to model the power density of this locality. However, Satellite data, in general, is always of low resolution albeit indicative of the tendency of wind regime.
In this work we study the wind characteristics of Bafoussam, also in the southern part of Cameroon and about 80km from Bamenda. It is a regional headquarter (of the West Region), heavily populated and with many agro-industrial activities and medium sized industries and structures and, hence, inherently exposed to the same energy demise. In this paper we study the wind characteristics based on the Weibull and Rayleigh probability distribution models and evaluate wind energy potential application of any windmill. We use three goodness-of-fit (gof) tests to discriminate which of the two models best fits the wind regime at this site. Furthermore, we also determine the wind speed classes and the dominant wind directions at this site. Wind directions are important in determining the directions in which the blades of a vertical axis turbine should be facing so as to minimize the wear and tear when turning to face its direction or during furling.

Site Description and Data
Bafoussam is situated on latitude 5.5, longitude 10.4 and at an altitude 1438m and on the Bamboutous highland. The 3-hourly periodically measured daily wind speed data used in this study was obtained from the Bafoussam Airport, Fig.1, for the period 2007 to 20013 spanning a duration of seven years. The wind speed data was measured using the Beaufort scale at an altitude of 10m above the ground. The preprocessing of the data consisted of firstly computing the daily mean speeds. The daily mean speed, , was obtained by using equation (1): where is the daily mean and is the wind speed at time steps of 3 hours from 6am to 6pm, local time. These were then sequentially appended to give the weekly, monthly, etc, rows of daily means. The Weibull, Rayleigh, some other statistics and power density studies were carried out on these mean wind speeds.

Wind Direction (Wind Rose Plots)
In order to obtain information about the wind directions and classes from the five double columns (wind speed and direction, each) of the wind data per day, each was appended sequentially day after day through each week to months and to the rest of each year. This enabled the determination of average directions and classes per period (time of day) per month or per year. Finally, for each day, the pairs of data (direction and wind speed) per period were again appended so as to form two columns (of 5 rows) per day; through the weeks, months, years and for the continuous seven years. The wind rose Matlab program was applied on these columned data to eventually obtain the directions and mean wind speeds per class for the chosen period or duration of studies.

Estimation of Wind Potential
The theoretical available power, , at each wind speed is given by where A is the rotor swept area and is the air density. Thus, power is about cubes of wind speed. The power density is defined by power per unit area. The air density is taken as a constant at 1.225kg/m3 for the simulations in this work. The power per unit area transported by a fluid system is related to the cube of the fluid speed, Kamau, Kinyua, Gathua (2010). Hence, for the spectrum of wind speeds, the total power density at an observation site is given by where is the probability density distribution, PDF, of wind speed. Its forms are determined by the probability distribution that best fits the wind regime. For simple PDFs, such as the Weibull or Rayleigh distributions, equation (3) can be solved analytically for their various parameters.

Modeling and Evaluation Techniques of Wind Speed
There are many probability distributions or density functions available, but not all are suitable for fitting wind speed. The statistical distributions included in this research are the Weibull and the Rayleigh distributions because most wind regimes in the world almost accurately are modeled by these two models. Rahbari, Vafaeipour, Fazelpour, Feidt, Rosen (2014) determined that the Weibull distribution is a very appropriate model fit in many situations. The Weibull function has much flexibility and simplicity and provides a logical fit to experimental data when applying to wind data as given in G. Johnson (2006). Equation (4) represents the 2-parameter Weibull probability function with the dimensionless shape parameter, k and scale parameters, c, measured in m/s.

Determination of the Weibull Parameters
where > 0 and > 0.
The Weibull PDF is derived from its CDF and has the form: The m th moment of the Weibull distribution provides a means of analytically determining some of its statistics, as earlier mentioned. Hence, for example, from its general m th moment equation (6), the mean can be obtained as in equation (7).
where Γ . represents the gamma function. The standard deviation is derived from equation (8).
The standard deviation used in this work is simply the square root of equation (8).
Both the Weibull and Rayleigh models for the power density make use of k and c, whereas for the Rayleigh function, c is replaced by b. Hence, they have to be determined in order to model the power density in accordance with their respective density distributions.
Numerical techniques are the most used methods for the determination of the shape parameter, k and finally, the scale parameter, c, of the Weibull probability density function. Comparing 7 different methods, Paulo, de Sousa, de Andrade, da Silva (2012) determined that the most accurate values and Weibull fittings were observed on methods applying iterative routines on their more complex non-close form mathematical expressions.
The maximum likelihood estimation procedure for the 2-parameter Weibull function in equation (9), Azad, Rasul, Yusaf (2014) has been an extensively used method for estimating the parameters of the Weibull distribution due to, among many others, this particular desirable property. The commonly used procedure to determine k is the Newton-Raphson routine on equation (9): c is then obtained by substituting k in equation (10): where n is the length of data.

Weibull Power density Model
The expected monthly or annual wind power density per unit area, , of a site based on a Weibull probability density function, can be expressed as given by Bhattaracharya and Bhattacharjee (2010) in equation (11): The parameters and are related to the mean wind speed through

Rayleigh Model
The Rayleigh distribution is a special case of the Weibull distribution where the shape factor k is set to 2. Its CDF and PDF, Gupta and Biswas (2010), are determined by equations (13) and (14), respectively.
And its probability density by where b, in m/s, is its scale parameter. As earlier mentioned, it is the counterpart of the scale parameter, c, of the Weibull scale parameter.

Rayleigh Power Density Model
Putting k=2 in equation (12) and finally in equation (11), we obtain the Rayleigh power density model; given by:

Goodness-of-Fit (gof) Tests
In order to deduce the degree of convergence of the various distributions to the actual measured data, the following three tests were performed on each of the probability distribution functions; namely R 2 , rmse and X 2 .

The Coefficient of Determination (COD or R 2 )
The R 2 , as provided in Carillo, Cidras, Diaz-Dorado, Obando-Montano (2014) is one of the best probability distribution hypothesis tests because of its quantification of the correlation between observed and predicted probabilities and is given by: The larger the value of , the better is the fit of the model under consideration.

The Root Mean Square Error
The root mean square error is given by Abbas et al. (2012) as: where , and , in m/s, in equations (16) and (17) are the observed, estimated and mean of the data, respectively.

The Minimum Chi Square Method
The Chi-Square method is used for testing the predicted against the actual wind distribution. The least determined value, among the distributions, on this model, normally chooses it as the best probability representative candidate. In Abbas et al. (2012) the Chi-square χ² is equally given by where Oi, Ei and k are the observed, expected frequencies and k the number of bins.
The least value of RMSE and indicates a better fit of the model.

Results and Discussions
In this study, we used Matlab R2013b and Microsoft Excel 2010 for all simulations and calculations. Table 1 shows the simulation results carried on some of the afore mentioned equations on the yearly mean speeds for the variously concerned periods of measurement.
The following observations may be extracted from the table: (i) The gof results (higher R2, lower rmse and X2, in each case) overwhelmingly show that the Weibull model better fits the wind regime than the Rayleigh model.
(ii) The mean, M, speeds are all less than 3.2m/s. Good wind energy exploitative turbines have a cut-in wind speeds of more than 3.5m/s.
The standard deviations, SD, are low indicating low amplitude of stochastic oscillations about the mean and are consequently almost stationary and, hence, reliable.
(iv) The shape parameter, k, is always greater than the scale parameter, c. This inadvertently affects the value of power density as evidenced in equation (11).
(v) The theoretical power densities, Pd, are very low and always almost identical with the model predictions Pw, of the Weibull model, but, both, are always less than that of the Rayleigh model, P R .  Figure 2 shows, for visual comparison of fitness, the composite qualitative results of the simulations of the Weibull and the Rayleigh models for contiguous 7 years. With respect to the PDFs, the Weibull probability density function well fits the histogram, whereas the Rayleigh underestimates it. From the same figure and with respect to their CDFs, the Rayleigh equally demonstrates a radical departure of its curve from the empirical CDF or ECDF, while the Weibull CDF well fits it. Since in both situations, quantitative and qualitative, the Rayleigh function always dramatically demonstrates this lack of fitness or coincidence with the characteristics of the wind regime, henceforth the Rayleigh studies shall be discontinued. We, thus, where necessary, continue investigations only with the Weibull function. We next carry out quantitative and qualitative simulations on monthly means for each year. The quantitative results are presented in Tables 2 to 9. Similar results, as in Table 1, are observed in these tables. Mean speeds are between 1.9 and 3.1 m/s, low SDs, always higher shape than the scale parameters, Pb and P W are almost same, albeit low. With respect to the gof results, the R2 values, in particular, also show that the wind regime is Weibull representative.  We choose only one year, year 2010, to demonstrate the graphical presentations of the qualitative simulations results of the monthly mean wind speed. Figure 3 shows that the PDF curves for each month for that year are almost bell-shaped, like for a normal distribution; depicting high shape parameter values. Figure 4 shows the corresponding CDFs and are relatively steep, which still validates the (high) range values of the shape parameter.  Figure 7, there are only two main directions and with low wind speeds, as observed from the wind rose legend. Generally, it was observed that most calms occurred at 6am; increasing gradually to a maxim at 3pm and falling again at 6pm. However, the highest frequency of winds at 6am and 9am flow in at angle 30 o , albeit very low wind speeds. Studying the legends in general, it is observed that the highest wind speeds are between 8 and 9m/s. These numerical results were displayed to two decimal places because at only one decimal place, some values become visibly negligible but are indicated by wind rose plots.
Tables 9 and 10 show frequencies for each wind speed in each range and average directions, respectively. The frequencies are observed directly below each with speed range; to the right of first column, which is the average wind speed direction. The last column is the sum of the frequencies of each wind speed range for the average direction. It is observed from the two tables that (

Conclusion
We studied the Wind characteristics of Bafoussam airport, Cameroon, based on three-hourly wind speeds, measured five times a day starting at 6am local time and at a height of 10m. The speeds were determined using the Beaufort scale and in m/s. The gof results determine the Weibull PDF to be a good representative distribution function for the wind pattern of Bafoussam. Bafoussam is characterized by very low wind speeds whose means vary between 1.9 and 3.1m/s in all cases considered. Using the Theoretical and the Weibull power density formulations, it was observed that Bafoussam is a poor wind energy potential site with the highest value being 19.8W/m2 in March 2008 and the lowest being 4.0W/m2 in August 2011 using the Weibull power model. Either the Theoretical or the Weibull power could be used as their values were almost identical.
The Wind roses results showed, averagely, that all winds were from the NE (first quadrant), with a predominance at angle 10 o and some at 20 o and 30 o , each year for the seven years and for the contiguous seven years. However, determining these directions during the periodic time steps, it was determined that most of winds came in at angle 30 o during the 6am and 9am time steps. The angles gradually changed to 10 o and 20 o for the last three measurements of the periods of the day. Also, the highest wind speeds were measured at 3pm and most calms were observed at 6am.
This study is imbued with some inherent shortcomings. The 3-hourly time steps greatly diminish the stochastic nature of wind speeds and directions at shorter sampling times. The Beaufort scale is equally generally subjective and, hence, less accurate. The height of evaluation of energy potential assumes zero surface roughness. A longer duration of data gives a more dependable picture about the average values of parameters at a site. Based on these assumptions and inadequacies, we thus provide the following recommendations for future studies at this site: (i) Evaluations at higher heights using, at least, any of the power laws that take care of the effect of surface roughness.
(ii) Coming back after a considerable number of years for a longer duration of data that takes care of local (weather) changes and seasonality, hence, giving a more vivid picture about the average parameters described in this work.
(iii) The Weibull PDF clearly better fits the wind pattern than the Rayleigh model but could be inadequate compared with other probability density functions. Thus, further studies are recommended by applying the broader spectrum of probability density functions to determine that which actually best describes the wind regime at Bafoussam.
(iv) A higher sampling rate describes a better stochastic nature of wind directions and speeds than the average values in the 3-hourly time steps used in this study. Thus, a revisit is advised for the short duration measurement of wind speeds and direction with the newly installed instruments at the Bafoussam airport.