Assessment of the Wind Energy Potential of Two Burundian Sites

1-year hourly wind speed data from two Burundian stations, namely Bujumbura and Muyinga, have been processed in this work to bring an efficient help for the planning and installation of wind energy conversion systems (WECS) at those localities. Mean seasonal and diurnal variations of wind direction and wind shear exponent have been derived. Two-parameter Weibull probability density functions (PDFs) fitting the observed monthly and annual wind speed relative frequency distributions have been implemented. As shown through three complementary statistical tests, the fitting technique was very satisfactory. A wind resource analysis at 10 m above ground level (AGL) has led to a mean power density at Bujumbura which is almost thirteen fold higher than at Muyinga. The use of the empirical power law to extrapolate wind characteristics at heights from 150 to 350 m AGL has shown that energy potential of hilltops around Muyinga was only suitable for small, individual scale wind energy applications. At the opposite, wind energy potential of ridge-tops and hilltops around Bujumbura has been found suitable for medium and large scale electricity production. For that locality and at those heights, energy outputs and capacity factors (CF or C f ) have been computed for ten selected wind turbines (WTs), together with costs of electricity (COE) using the present value of cost (PVC) method. Amongst those WTs, YDF-1500-87 and S95-2.1 MW have emerged as the best options for installation owing to their highest CF and lowest COE. Moreover, an analysis of those two quantities at monthly basis for YDF-1500-87 WT has led to its best performance in the dry season. Compared to the average present COE of household hydroelectricity consumption, results of this study have evidenced economical feasibility and benefit of WECS setting in selected Burundian sites in order to supplement traditional electricity sources.


Introduction
Almost 98% of the population in Burundi still uses firewood or wood scraps in rural areas and charcoal in urban zones for their main energy needs, which are food cooking, house heating and lighting. In average, less than 5% of that population has access to electricity (with 2% in the rural areas and 52% in the urban ones) [1]. 98.2% of the total electricity consumption (400 GW-hr; 2014's estimate) comes from hydroelectric plants and 1.8% from fossil fuels [2]. The average annual electricity consumption is less than 30 kWh per capita, which is almost five fold lower than the average one in Africa. The electricity production (300 GW-hr; 2014's estimate) is inadequate when it faces up to an increasing energy demand due to industrialization effort and to a high rate of population growth (3.26%; on a total population of 11,099,298; 2016's estimate) [2]. That feature is well illustrated by electricity shortages frequently observed daily in different urban areas. As a consequence and in order to bypass such events, besides country electricity imports (100 GW-hr; 2014's estimate) [2], various firms, institutions or departments resort to motor generators such as Diesel engines, which use imported fossil fuels, particularly refined petroleum products. Like in many other countries, effort is nowadays made in Burundi to increase electricity production and to alleviate the constantly scaling cost and environmental concern of fossil fuels. One way to achieve those objectives and which is clearly stated in the current government's working agenda [1] [3] [4], is to supplement traditional energy sources with free, clean and inexhaustible energy sources, particularly the solar and the wind energy ones.
The present work deals with the possible use of wind energy source in Burundi. An essential stage for that purpose is the selection of the most suitable site to settle a wind energy conversion system (WECS) and the decision about the system's parameters (e.g.: blade shape and size, direction, total capacity, etc.). That requires a good knowledge of various properties of the site and those properties should be found out by using not only wind dynamic and statistical data [5] [6], but also data about climate, e.g.: air density, temperature, humidity, pressure [7] [8], land topography, obstacles and surface roughness [9] [10]. Research papers in that context for Burundian sites are rather scarce, but one should mention a recent study which compares the effectiveness of different PDFs in fitting experimental frequency distributions of wind speed data [11]. The major aim of this work is to provide decision makers with a technical study which should bring an efficient help for the planning and implementation of WECS projects at two Burundian localities, namely Bujumbura and Muyinga. For that purpose, hourly wind speed data recorded over a 1-year period at those sites have been processed

Sites and Basic Data
As an African country with a total (land and water) area of 27,834 km 2 and a population density of 432.22 persons per km 2 [2], Burundi is located closely to the equatorial zone, at latitudes (φ) between 2˚10'S and 4˚30'S, and longitudes (L) between 28˚50'E and 30˚53'E. Long-term records of the wind speed and wind direction have been performed at different stations and then collected and kept within the Geographical Institute of Burundi (IGEBU). The records were made daily between 6:00 and 18:00 local time (LT) by the means of an anemometer fitted with an integrating device. Proper calibration of that device allowed the derivation of wind speed data (v, in m/s) averaged over a 1-hour or 3-hour period. For most of the stations, wind speed measurements were referred to 2 m height above the ground level (AGL). Exceptionally, wind speed data were available at 2 m and 12 m AGL for only two stations, namely Bujumbura (airport; L = 29˚21'E; φ = 3˚23'S; z' = 783 m) and Muyinga (airport; L = 30˚21'E; φ = 2˚51'S; z' = 1755 m), which are shown in Figure 1. The quantity z' is the altitude of the station. The measured hour-by-hour wind speed data used to implement Weibull distributions of section 2.2 refer to 12 m height AGL at the two previous sites and to a 1-year period of continuous records with a minimum number of missing data. Moreover, the wind shear exponent (α) data quoted in section 2.3 have been derived from wind speed measurements at heights z 1 = 2 m and z 2 = 12 m AGL for any of the two sites, together with the next expression extracted from the common empirical power law [9] and ( ) where c and k are the Weibull scale parameter (m/s) and modulus or shape parameter (dimensionless), respectively. The different techniques quoted in the literature to estimate the two previous parameters include notably the graphical method, maximum likehood method, modified maximum likehood method, standard deviation method, power density method, moments method, equivalent energy method, Justus's empirical method, Lysen's empirical method [ [20] and median rank regression method [21]. In the present study, once the mean ( v ) and variance ( 2 σ ) of the observed wind speed frequency distribution were known, the following relationships have been used to determine the Weibull shape and scale parameters [22] [23]: and where Г(x) is the gamma function of a real variable x, for which values are available in tables [24].

Tests of the Effectiveness of the Fitting Technique
and where ,

Wind Speed and Weibull Parameters Variation with Height
As the values of average wind speed and power density increase with height, higher WT tower hub heights are preferred to obtain higher wind energy densities. In this study, the empirical power law has been used to extrapolate the wind speed variation with height. It is expressed as where v is wind speed estimated at a given height, z; v 0 is wind speed at reference height, z 0 ; and α is the ground surface friction coefficient, also called power law exponent or wind shear exponent. In several works, the reference height is 0 10 m z = AGL as recommended by the World Meteorological Organization (WMO) [5]. The exponent α varies with height, time of day, season, nature of the terrain, wind speed and temperature. For the period and the two sites of this study, the use of the field data quoted at the end of Section 2.1 has led to the annual mean value 0.25 Owing to Equations (4)-(5), for relatively low heights AGL, the shape parameter (k) remains almost constant when the height increases, while the scale parameter (c) varies with height at the same rate as the wind

Wind Power and Energy Content
Following the WD, different characteristics of the wind power and energy content are described in this section.
The average wind power density, p (in W/m 2 ) is given by the next relationship [9] [10] [12] [23]: where the mean air density, ρ, which depends on the site's altitude, air pressure and temperature, is usually taken as equal to 1.225 kg/m 3 [6] [29].
According to the Betz's limit, the average maximum wind power density which can be extracted from a WT is expressed as [6]: Once the average wind power density of a site is known, the wind energy density for a given duration T (in hours) can be calculated (in W-hr/m 2 ) as [7] [10] [15]: At its turn, the wind energy pattern factor, E PF is expressed as [9]: The most probable or most frequent wind speed, which refers to the maximum of the Weibull PDF, is given by the next relationship [6]: while the optimum wind speed, or wind speed of maximum energy carrier, is expressed as [7] [15] [22]:

Wind turbine energy output and capacity factor
In most cases, a WT operates at increasing power, P CR (v) between cut-in and rated wind speeds (v C and v R , respectively) and at constant rated power, P R with maximum efficiency between rated and cut-off wind speeds (v R and v F , respec- Different WTs have different power output performance curves, so the models to describe those curves are different. For the function P CR (v) in particular, quadratic [12], cubic [15] and 3-degree polynomials [7] have been used, as well as various other expressions [5] [9] [10] [31].
Once the function P T (v) is known, the actual wind energy output from a WT over a given duration T (in hours) is calculated as [15]: where f(v) is the actual site's wind speed PDF (Equation (3)).
In this work, a model WT is assumed with the quantities P R , P T (v) and E TA /T in Equations (17)-(18) representing the rated electrical power (P eR ), electrical power output (P e ) and average electrical power output (P e,ave ), respectively. The model is simulated using the next relationships [31] [32]: and , e e e where P eCR represents the quantity P CR (v) of Equation (17). At its turn, the WT capacity factor, C f is given by the ratio of the average electrical power output to the rated electrical power of the WT [15] [31] [32]: , e ave f eR

Economic Analysis
Amongst the different ways of estimating the economics of WTs, the method used in this study is the specific cost per kW-hr of electrical energy generated by a WT, which is defined as the ratio of the present value of cost (PVC) to the energy output during the WT lifetime. The PVC is expressed as [10] [31] [32]: In that relationship, I is the investment cost of the WT (the price of the WT in addition with 20% for civil works and other connections). The prices of WTs based on the rated power are indicated in Table 1. C omr represents the operation, maintenance and repair costs (15% of I); S is the scrap value (10% of I); n is the WT lifetime (20 years) and the discount rate, r is expressed as: where i 0 is the nominal interest rate (12%) and i represents the inflation rate (5%).
The total energy output over the WT lifetime (in kW-hr) is computed as: where A (=95%) is the availability of the wind power resource for generating electricity. Therefore, the cost of electricity (COE) per unit kW-hr in the PVC method is given by:

On the Wind Shear Exponent
All the values of the wind shear exponent (α) obtained in this study lie in the range [0.10; 0.40] in accordance with results from other works [33] [34] [35].
The monthly and annual averages shown in Table 2  In mean seasonal trends, the driest months (from August to October) are the windiest (with lowest α or highest v values) at the two sites. Table 3 indicates at its turn that, in mean diurnal trends, the half-day period is windier than the

On the Average Wind Direction
An analysis of the data quoted in Section 2.1 shows that the average wind direction at Bujumbura is north (N) in the morning and south (S) in the afternoon.
Nevertheless, the morning wind direction at that site is sometimes (but seldom) S, south-west (SW) or north-west (NW). At the opposite, the average wind direction at Muyinga is S all along the day. The wind direction's inversion phenomenon observed at the midday for Bujumbura should be ascribed to the alternation between the land's breeze and the lake's breeze (that site is located at the border of the Tanganyika lake). Table 4(a) and Table 4 Muyinga, the highest mean wind speeds are noticed both in the dry season (July and September) and in the rainy one (April). The Weibull PDFs fitting the observed monthly and annual frequency distributions of wind speed data at the two sites are closer to Rayleigh PDFs than to exponential PDFs, since the shape parameter (k) is closer to 2 than to 1 in most of the cases. Moreover, any of the 26 Weibull PDFs implemented in this study is a very good fit of the related observed frequency distribution of wind speed data. As a matter of fact, for each data set, the MBE is found equal (or very close) to zero, the RMSE is very low and values of the t-statistics are either equal to zero or much lower than their critical counterparts. Figure 2 and Figure 3 illustrate some of those fits for the two sites, respectively.

On the Wind Power and Energy Content
The average wind speed ( v ), Weibull shape and scale parameters (k and c), power and energy densities ( p and e ), energy pattern factor (E PF ), most probable and optimum wind speeds (v mp and v op ) at reference height z 0 = 10 mAGL are summarized in Table 5(a) and  the highest wind power (or energy) potential at Bujumbura. In the same kind of order, the six months with the highest wind power (or energy) potential at Muyinga are July, September, April, March, January and May. Nevertheless, the annual mean wind power (or energy) density at reference height AGL is about thirteen fold greater at Bujumbura than at Muyinga.

At Small, Individual Scale
Following the Pacific Northwest National Laboratory's classification of sites according to their annual mean wind speed and power density [38], at 10 m height AGL, any of the two sites of this study falls under class 1 and is an unsuitable location for generating electricity. Instead of direct electricity production, the wind energy potential at those sites is high enough to power simple machines of less than 5 kW in rated power capacity. Those machines could be associated with full energy charging and storage in chemical storage batteries, together with load distributors for individual premises. Through those distributors, the energy extracted from the wind would be channeled into different useful purposes in the dwellings and barns. The use of those machines in water pumping for irrigation would be an alternative to battery storage [39]. This feature would be particularly relevant for the agricultural area localities in the surroundings of the data collection station of Bujumbura, where the dry season encloses the windiest months of the year. For all those purposes, simple and inexpensive locally manufactured designs having very low cut-in wind speeds (<2 m/s) and which can withstand high wind gusts (>25 m/s), could be used.

At Medium and Large Scales
From the 10 m AGL data of Table 5(a) and Muyinga data collection station is unsuitable for medium and large electricity generation. Instead of that, small and individual scale wind energy applications such as those described in sub-section 3.5.1 should be foreseen for that locality.
As shown in Table 6, ten WTs have been selected for possible installation at the above-mentioned sites around Bujumbura. All of them have pitch control system, with rated power ranging from 9.7 to 3000 kW, hub heights between 25 and 80 m, and power curves as provided in the relevant references (cited websites) [40]- [47].
Annual average power and energy outputs, capacity factors, together with average costs of electricity's estimates of those selected WTs at exposed ridge-tops and hilltops in the surroundings of Bujumbura, are shown in Table 7, where E out is the WT's energy output during one year.  Within the setting on ridge-tops and hilltops 150 m AGL around Bujumbura, YDF-1500-87 should be selected owing to its high capacity factor and low cost of electricity. These quantities have been computed on monthly basis and results are shown in Figure 4.
The minimum capacity factor (33.01%) and maximum cost of electricity (0.094 US $/kW-hr) occur simultaneously in February. At the opposite, the highest capacity factors (with maximum of 56.96% in August) and the lowest costs of electricity (with minimum of 0.050 US $/kW-hr in the same month) are observed in the dry season (from June to November). From Figure 4, it is shown that any increase of the CF occurs simultaneously with a decrease of the COE. At the opposite, when the CF decreases, the COE increases. Those features are well in accordance with the relationships (21) and (25) defining the CF and the COE, respectively. As a matter of fact, in those equations, the rated electrical power (P eR ) )and the present value of cost (PVC; Equation (22)) are unchanging parameters for a given WT. At the opposite, the WT's average electrical power output (P e,ave ; Equation (20)) and the WT's total energy output (E WT ; Equation (24)) are changing quantities which exhibit the same seasonal variations.
The average monthly household hydroelectricity consumption in Burundi is 150 kW-hr for a present cost of 33,100 BIF (local currency). As the present local rate of exchange ranges from 2200 BIF (official rate) to 3400 BIF (black market rate) for 1 US $, that means a local average COE (hydroelectricity) which ranges from 0.065 to 0.100 US $/kW-hr. A comparison of those features with COE data from Table 7 and Figure 4 leads to the following evidence: the option of installing WECS as clean energy sources in order to supplement traditional ones is economically feasible in well selected Burundian sites. That should be particularly beneficent in reducing electricity shortages commonly observed in different localities, especially during the dry season. Those WECS should be planned for not only onshore setting, but also for offshore setting, for example in the Tanganyika lake and other lakes in the North-East region of the country.

Conclusions
The present wind resource analysis for Bujumbura and Muyinga has led to the following results. The average shear exponent is 0.25 at any of those sites. The driest months are the windiest, and the half-day period is windier than the morning and evening periods. The average wind direction at Muyinga is south all along the day, while average wind directions at Bujumbura are north in the morning and south in the afternoon. Since Bujumbura is located near the Tanganyika lake, that midday inversion phenomenon should be ascribed to the alternation between the land's and lake's breezes.
All the 26 two-parameter Weibull PDFs implemented to fit the related ob- At the same heights AGL, exposed ridge-tops and hilltops in the surroundings of Bujumbura are contrarily wind sites of classes from 3 to 6, which are suitable for medium and large scale electricity generation.
Amongst ten WTs (with rated capacity ranging from 9.7 to 3000 kW and hub heights between 25 and 80 m) selected for possible installation at the previous ridge-tops and hilltops, YDF-1500-87 and S95-2.1 MW have emerged as the best candidates owing to their highest capacity factors and lowest costs of electricity per unit energy output. From a monthly basis analysis, it has also been shown that the best performance of YDF-1500-87 WT is observed during the dry season (from June to November), with maximum capacity factor (56.96%) and minimum cost of electricity (0.050 US $/kW-hr) in August. Furthermore, the analysis has evidenced economical feasibility and benefit of setting WECS in selected Burundian sites in order to supplement traditional electricity sources.