Estimating the potential of wind energy resources using Weibull parameters: A case study of the coastline region of Dar es Salaam, Tanzania

Enock Michael; Dominicus Danardono Dwi Prija Tjahjana; Aditya Rio Prabowo

doi:10.1515/eng-2021-0108

Article Open Access

Estimating the potential of wind energy resources using Weibull parameters: A case study of the coastline region of Dar es Salaam, Tanzania

Enock Michael , Dominicus Danardono Dwi Prija Tjahjana and Aditya Rio Prabowo

Published/Copyright: November 19, 2021

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From the journal Open Engineering Volume 11 Issue 1

Abstract

This study aimed to compare the graphical method (GM) and standard deviation method (SDM), based on analyses and efficient Weibull parameters by estimating future wind energy potential in the coastline region of Dar es Salaam, Tanzania. Hence, the conclusion from the numerical method comparisons will also determine suitable wind turbines that are cost-effective for the study location. The wind speed data for this study were collected by the Tanzania Meteorological Authority Dar es Salaam station over the period of 2017 to 2019. The two numerical methods introduced in this study were both found to be appropriate for Weibull distribution parameter estimation in the study area. However, the SDM gave a higher value of the Weibull parameter estimation than the GM. Furthermore, the five selected commercial wind turbine models that were simulated in terms of performance were based on a capacity factor using the SDM and were both over 25% the recommended capacity factor value. The Polaris P50-500 commercial wind turbine is recommend as a suitable wind turbine to be installed in the study area due to its maximum annual capacity factor value over 3 years.

Keywords: Weibull parameters; numerical methods; wind energy potential; statistical analysis

1 Introduction

Energy is considered as one of the primary benchmarks for the growth of the economic and industrial sectors of a country [1,2]. Among the major energy resources are fossil fuels, but these have reserve limits [3]; the use of fossil fuels, however, is no doubt one of the key factors that contributes to the gases that cause the greenhouse effect [4,5,6,7]. A way to avoid these harmful effects is the utilization of renewable energies, such as hydro [8], biomass [9], geothermal [10], solar [11], and wind energy [12,13,14].

Among these different renewable energy sources, wind energy is noted as a promising source of renewable energy, which has presently gained greater awareness due to its many locations, adequate availabilities, and its sustainable characteristics [15,16,17,18,19,20]. Additionally, wind energy first captured interest in Europe and USA due to the worldwide oil crises in the 1970s and 1980s. In the 1980s and 1990s, the construction of modern wind farms began, which allowed the cumulative installed wind capacity of the whole world to be around 6,100 MW; the installed wind capacity reached 16,863 MW by the end of 2000 [2]. Eighty percent of the installed wind capacity belonged to Germany, USA, Denmark, and Spain at that time [21]. Investments in wind energy worldwide increased 10× by 2010 compared with the end of 2000 [2]. By the end of 2019, worldwide wind capacity installation reached about 622,704 MW for both onshore and offshore farms, as shown in Figure 1 [2].

Figure 1

The global installed wind capacity until the end of 2019.

Wind data analysis is regarded as the first stage of estimation of the future wind energy potential of a study site. For wind speed frequency distribution estimations over a period of time, there are probability distribution functions that can be used, such as the two-parameter Weibull distribution and Rayleigh methods [22,23,24,25,26]. The two-parameter Weibull distribution is considered efficient for wind-data fitting and is also able to provide accurate wind energy potential predictions [27,28]. There are several types of two-parameter Weibull distributions, such as the moment method, energy pattern factor method, graphical method (GM), empirical method of Justus, empirical method of Lysen, standard deviation method (SDM), and the maximum likelihood method [29]. This study used the GM and SDM for wind speed frequency distribution analyses.

Furthermore, this work is a logical part of examining, in detail, the wind energy potential of the coastline region of Dar es Salaam, Tanzania, using an attentive, more extensive, and accurate comparative study of the two numerical methods for Weibull parameter estimation. The wind energy potential of the coast of Dar es Salaam seems promising; however, there have been no previous studies related to the wind energy potential conducted in the area. The yearly mean values estimated from the wind speed data were analyzed in this work to evaluate methods of adjustment for the study site. As the height of the hub of many commercial wind turbines is higher than the height of an anemometer (a device used for the measurement of wind speed), determining yearly wind power density requires exploration of the height of wind-speed data. The GM and SDM were used at a height of 70 m. The obtained results from both the numerical methods were compared for accurate determination. Three statistical tests, namely root mean square error (RMSE), Chi-square error (χ ²), and the determination of the coefficient (R ²) were used to perform the evaluation process. Hence, wind turbine performance assessment was evaluated from the best fit numerical method, based on the capacity factor of the wind turbine using five commercial wind turbine models.

2 Wind energy in Tanzania, Dar es Salaam description, and data collection

The wind resources in Tanzania are very strong, and the wind speeds are between 6 and 8 m/s, particularly in the regions around Rift Valley and the coastline of the country [30]. There have been a number of ongoing research studies for some years, including an exploration program that receives sponsorship from the Tanzania Ministry of Energy and Minerals, Tanzania National Electric Supply Company Limited (TANESCO), and Tanzania Traditional Energy Development Organization as well as technical and financial support from the Denmark National Laboratory (Risø) and the Danish International Development Agency (DANIDA) [30]. The mentioned institutions have conducted a significant amount of work in terms of wind resource assessment and also aim to determine the feasibility of wind energy utilization. The exploration ended in 2003 and produced detailed information for specific locations, as described in Table 1. Presently, the first wind farm operating in Tanzania has been opened and the installed wind capacity of the Mwenga wind farm is 2.4 MW; it is located at Usokami Village in the Mufindi District. The wind farm is a privately owned plant and consists of three 800 kW enecorn wind turbines [31]. The study site location is the region of Dar es Salaam and is located at latitude 6°48′S, longitude 39°17′E, at an altitude of 55 m above sea level, and in the east of the country. The region is 442 km east of the capital, Dodoma, and 625 km south of the headquarters of the East African community, Arusha, as shown on the map of Tanzania in Figure 2. It covers an area of 1,590 km², of which 450 km² is coastline [32]. Additionally, Dar es Salaam has a tropical climate feature with a fairly high temperature and high humidity. The average rainfall in the region is 1,000 mm per year, which occurs throughout the year but primarily during the two rainy seasons [32]. The wind speed data used in this study were provided by the Tanzania Meteorological Authority. The wind speed data were recorded using an anemometer every 3 h at a height of 10 m above the ground over 3 years (from January 2017 to December 2019).

Table 1

Wind resources in Tanzania

Location	Study	10 (m) wind speed (m/s)	30 (m) wind speed (m/s)
Makambako (Njombe)	Original Wind East Africa	7.6	8.7
Singida	Wind East Africa	8.2	9.4
Karatu (Arusha)	DANIDA/Risø/TANESCO	4.9	5.5
Mkumbara (Tanga)	DANIDA/Risø/TANESCO	4.14	4.9
Gomvu (Dar es Salaam)	DANIDA/Risø/TANESCO	3.56	4.28
Litembe (Mtwara)	DANIDA/Risø/TANESCO	3.21	4.47

Figure 2

The map of Tanzania.

3 Weibull distribution method

3.1 Weibull probability density function

The Weibull probability density function is the function where the value at any specified point can be explained by providing a relative likelihood that the random variable value would be equal to that sample. In the context of wind speed, this offers the frequency at which a particular value of wind speed is noticed in a studied region. The Weibull probability density function is given by [33,34,35,36]:

(1) f ( v ) = k c ⋅ v c k − 1 ⋅ exp − v c k ,

where f ( v ) represents the probability of wind speed observation v , k defines the dimensionless Weibull shape parameter, and c defines the Weibull scale parameter in wind speed units [37].

Then, the cumulative distribution function is determined as follows [38,39,40]:

(2) F ( v ) = 1 – exp − v c k .

3.2 Mean wind power density and energy density

The mean wind power density can be defined using the equation below [41]:

(3) P D = P ( V ) A = 1 2 ρ V m 3 ,

where P ( V ) is defined as the wind power (in watt), P D is defined as the power density of the wind (watt per square meter), ρ is defined as the site density of air that is assumed to be 1.225 kg/m³ in this study, and A is the rotor blades’ swept area (in square meter).

The energy density can be defined using the following expression [42]:

(4) E D = 1 2 ρ c 3 Γ 1 + 3 k T ,

where Γ is defined as a gamma function and T is the specific period of time.

3.3 Weibull parameter variation with height

Generally, available wind speed data are measured at a height that is different from that of the hub height of a wind turbine. It is noted that wind speed in this regard, for wind power applications, is the wind speed at the hub height. Thus, the available wind speeds are converted to the wind turbine hub height using the polar law expression [43,44,45]:

(5) V V 0 = h h 0 α ,

where v is defined as the wind speed hub height ( h ), v o is defined as wind speed original height ( h o ), and α is defined as the surface roughness coefficient and is commonly assumed to be 0.143 (1/7) [46].

Wind speed placed at a given height ( h 0 ), when it is measured by an anemometer, has a Weibull probability density function with the recognized parameters k and c and can be used to extrapolate the wind speed values at different heights. The Weibull distribution parameters k ( h ) and c ( h ) for altitude h above the level of an anemometer can be obtained using the expression of the following relationship [47]:

(6) k ( h ) = k 0 1 − 0.088 ln h 0 10 1 − 0.088 ln h 10 ,

(7) c ( h ) = c 0 h h 0 n ,

(8) n = [ 0.37 − 0.088 ln ( c 0 ) ] / 1 − 0.088 ln h 10 .

4 Methods used for estimation of Weibull distribution parameters

As is known, there are several Weibull distribution methods that can be used in shape and scale Weibull factor determination for wind-speed measurements. In this study, the GM and the SDM were used to estimate the Weibull probability density function parameters. The Sections 4.1 and 4.2 summarize these two Weibull distribution methods.

4.1 The GM

The GM requires wind speed to be in the format of a cumulative frequency distribution. In this distribution method, the wind-speed data are interpolated using a straight line and the concept of least squares regression was used. Logarithmic transformation is the foundation of this method. By converting equation (1) into a logarithmic form, equation (9) is obtained [48]:

(9) ln [ − ln ( 1 − F ( v ) ) ] = k ln ( v ) – k ln ( c ) .

The Weibull shape and scale factor parameters were used for estimation by graphing ln ( v ) against ln [ − ln ( 1 − F ( v ) ) ] , for which a straight line was determined. For generating the best fit line, observations of calms should be left out of the data. The Weibull shape parameter k is defined as the line gradient and the y -intercept is defined as the value of the term – k ln( c ) [49].

4.2 The SDM

In the SDM, the wind speed average and the standard deviation values are used to estimate the Weibull distribution function. Shape k and scale c coefficients can be estimated, as in equations (10) and (11) [46]:

(10) k = ( σ / V m ) − 1.086 ,

(11) c = V m Γ 1 + 1 k ,

where σ is the standard deviation, V m is the average wind speed (in m/s) and Γ ( x ) is the gamma function, which is defined as [46,50]:

(12) Γ ( x ) = ∫ ∞ 0 t x − 1 e t d t .

5 Performance analyses of the models

Usually, the RMSE, Chi-square error (χ ²), and the determination of the coefficient ( R 2 ) are used to evaluate the performance of numerical methods. They are expressed as [38,50,51]:

(13) RMSE = 1 N ∑ i = 1 n ( y i − x i ) 2 ,

(14) χ 2 = ∑ i = 1 n ( y i − x i ) 2 x i ,

(15) R 2 = ∑ i = 1 n ( y i − v ¯ ) 2 − ∑ i = 1 N ( y i − x i ) 2 ∑ i = 1 n ( y i − v ¯ ) 2 ,

where y i , x i , v ¯ , and n are defined as the observation frequency, Weibull frequency, average wind speed, and the constant number used, respectively.

6 Wind turbine performance assessment

For determining the most efficient and suitable type of wind turbine based on the studied area, five wind turbine models (small to medium sizes) with a rated power between 50 and 1,000 kW were simulated, and their performances were based on a capacity factor. The capacity factor, C f , is defined as the ratio of average power output ( P e .ave ) to rated electric power ( P eR ) of a wind turbine.

The mean power output, P e .ave , and the capacity factor ( C f ) of a wind turbine can be calculated using the following expressions [41,46]:

(16) P e = 0 , v < v c P eR v k − v c k v R k − v c k , v c ≤ v ≤ v R P eR , v R ≤ v ≤ v F 0 , v F < v ,

(17) P e .ave = P eR e − V c c k − e − V r c k V r c k − V c c k − e − V f c k ,

(18) C f = P e .ave P eR ,

where V c , V r , and V f are the cut-in wind speed, rated wind speed, and cut-off wind speed, respectively. As a recommendation, the capacity factor of the wind turbine should be greater than 0.25 for low-cost wind power investments.

7 Results and discussion

7.1 Comparison based on Weibull distribution parameter estimation

An average monthly Weibull distribution parameter for all years (2017–2019), as estimated by both methods, is shown in Table 2 for an anemometer that was placed at a height of 10 m. In addition, extrapolated wind characteristics obtained for a 70 m height are also shown in the same table. The Weibull distribution parameter variation depended on the month. The highest monthly Weibull shape factor k was observed in January and the lowest monthly Weibull shape factor k was observed in October for the SDM. The highest monthly Weibull shape factor k and lowest shape factor k were observed in October and November, respectively, for the GM. Both these records were obtained when the anemometer was placed at a height of 10 m (as shown in Figure 3). For an extrapolated wind height of 70 m, the highest and lowest Weibull shape factor k for the SDM were recorded in January and October, respectively, while for the GM, the highest and lowest Weibull shape factor k were recorded in October and November, respectively, as shown in Figure 4. At 10 and 70 m, the highest Weibull scale factor ( c ) was observed in January, and for 10 and 70 m the lowest Weibull scale factor ( c ) was recorded in November; this result was obtained from the SDM, as shown in Figures 5 and 6. While the GM gives a lower value Weibull scale parameter when compared to the SDM, after the GM was used, the highest Weibull scale factor ( c ) for both (10 and 70 m) heights was recorded in February. The lowest scale factor ( c ) for the GM at 10 and 70 m was observed in January, as shown in Figures 5 and 6. For Weibull shape k and scale c factors, for both heights, comparison between the two numerical methods showed that the SDM gave the highest value for both Weibull parameter shape and scale estimations and the GM provided the lowest value for Weibull parameter shape and scale estimations. Comparison based on wind power density between both the numerical methods, for both wind speed heights (10 and 70 m) showed that the SDM gave the highest average monthly wind power density, while the GM gave the lowest average monthly wind power density, as shown in Table 2.

Table 2

Yearly shape k and scale c Weibull factor parameters and wind density in the coastline region of Dar es Salaam at two heights of 10 and 70 m

Method	Month	k 10	c 10	P 10 (W/m²)	Method	Month	k 70	c 70	P 70 (W/m²)
SDM	Jan	3.25	6.81	138.34	SDM	Jan	3.92	10.91	473.84
	Feb	3.02	6.42	115.23		Feb	3.65	10.42	407.52
	Mar	2.76	5.75	80.77		Mar	3.33	9.55	303.13
	Apr	2.85	5.85	86.62		Apr	3.44	9.68	321.91
	May	2.96	5.66	78.88		May	3.58	9.44	297.42
	Jun	2.82	6.18	102.46		Jun	3.41	10.11	368.24
	Jul	2.61	5.69	78.41		Jul	3.15	9.47	297.42
	Aug	2.62	5.67	77.95		Aug	3.16	9.44	295.16
	Sep	2.72	5.64	77.48		Sep	3.28	9.41	294.03
	Oct	2.49	5.72	80.29		Oct	3.01	9.51	300.84
	Nov	2.62	5.23	61.58		Nov	3.16	8.85	242.21
	Dec	2.65	6.11	98.06		Dec	3.21	10.02	356.59
GM	Jan	2.21	3.63	100.25	GM	Jan	2.66	6.63	364.33
	Feb	1.91	5.46	79.82		Feb	2.31	9.16	300.84
	Mar	1.71	4.53	53.61		Mar	2.06	7.89	216.45
	Apr	2.08	4.24	56.19		Apr	2.51	7.51	223.88
	May	1.89	4.71	52.89		May	2.28	8.16	213.71
	Jun	1.86	4.82	66.48		Jun	2.24	8.29	257.37
	Jul	1.94	3.95	47.69		Jul	2.34	7.08	196.01
	Aug	1.72	4.62	47.02		Aug	2.08	8.03	194.29
	Sep	1.89	4.47	49.04		Sep	2.28	7.82	200.34
	Oct	2.34	4.06	46.36		Oct	2.83	7.25	191.74
	Nov	1.68	3.79	36.89		Nov	2.03	6.87	158.32
	Dec	1.91	4.29	60.01		Dec	2.29	7.57	237.29

Figure 3

Time variation of Weibull shape factor k at a height of 10 m.

Figure 4

Time variation of Weibull shape factor k at a height of 70 m.

Figure 5

Time variation of Weibull scale factor c at the height of 10 m.

Figure 6

Time variation of Weibull scale factor c at a height of 70 m.

7.2 Comparison based on the monthly average wind speed

The monthly average wind speed for all years (2017–2019) at heights of 10 and 70 m were also observed for both numerical methods. For the SDM, the highest and lowest monthly average wind speeds at 10 m were 6.09 and 4.65 m/s in January and November, respectively, while for the GM, at the same height, the highest and lowest average wind speeds were observed as 5.47 and 3.92 m/s (also in January and November, respectively) as shown in Figure 7. The highest and lowest monthly average wind speeds at a height of 70 m were observed using the SDM and were 9.18 and 7.34 m/s, which were both recorded in January and November, respectively, as shown in Figure 8. For the same height of 70 m, using the GM, the observed highest and lowest average wind speeds were 8.41 and 6.37 m/s in January and November, respectively, as shown in Figure 8. For both wind speed heights (10 m and 70), the SDM provided the highest number of average monthly wind speed when compared with the GM, as shown in Figures 7 and 8.

Figure 7

Average monthly wind speed characteristics at a height of 10 m.

Figure 8

Average monthly wind speed characteristics at a height of 70 m.

7.3 Comparison based on the actual wind speed data

The Weibull distribution plots of the wind speeds at a height of 10 m are presented in Figure 9a–c. The histogram plots show the values of the actual wind speed data, and are illustrated in the figures for comparison of the obtained results of the SDM and the GM. The observed results show that the SDM provides a satisfactory result for all years (2017–2019), while the GM provides weak results for all years (2017–2019).

Figure 9

Comparison of Weibull distribution of actual wind speed data and the two numerical methods. (a) year 2017, (b) year 2018, and (c) year 2019.

7.4 Comparison based on the statistical tests

Wind-speed frequency evaluation for the numerical methods was made using three different statistical tests, namely, the RMSE, Chi-square error (χ ²), and the determination of coefficient ( R 2 ) ; the observed results show that both the SDM and the GM provided a better fit for the wind speed data, as shown in Table 3.

Table 3

Statistical test for yearly performance evaluation using two Weibull numerical methods at a height of 10 m

Year	Method	RMSE	χ ²	R 2
2017	SDM	0.0322	0.0105	0.9999
	GM	0.0009	0.0098	0.9995
2018	SDM	0.0271	0.0075	0.9999
	GM	0.0026	0.0279	0.9987
2019	SDM	0.0313	0.0099	0.9999
	GM	0.0012	0.0125	0.9994

7.5 Performance of wind turbine based on the annual power output and capacity factor ( C f )

There were five commercial wind turbine models that ranged in size from small to medium and had a rated power range between 50 and 1,000 kW that were selected and simulated to determine their performance at the study location. The selected commercial wind turbines were: the Polaris P15-50, Bonus 300 kW/33, Polaris P50-500, Bonus 1 MW/54, and WWD-1-60 and their performances are shown in Table 4.

Table 4

The selected wind turbine performance

	Polaris P15-50	Bonus 300 kW/33	Polaris P50-500	Bonus 1 MW/54	WWD-1-60
Rated power (kW)	50	300	500	1,000	1,000
Hub height (m)	30	30	50	45	70
Rotor Diameter (m)	15.2	33.4	50	54	60
Cut-in wind speed (m/s)	2.5	3	2.5	3	3.6
Rated wind speed (m/s)	10	14	12	14	12.5
Cut-out wind speed (m/s)	25	25	25	25	25

The average annual energy output, based on the SDM for all commercial wind turbine models, showed that the Bonus 1 MW/54 recorded the maximum value when compared with the other four commercial wind turbine models, after recording an average annual power outputs of 331.594, 359.1664, and 352.7686 MW h/year, in 2017, 2018, and 2019, respectively, as shown in Figure 10. Using the Bonus 1 MW/54 commercial wind turbine, the month of October recorded the highest average monthly energy output of 362.808 MW h/month and the month of May recorded the lowest average monthly energy output of 296.459 MW h/month, based on the SDM, as shown in Figure 11.

Figure 10

Average annual power output.

Figure 11

Average monthly power output.

The capacity factor based on the SDM showed that the Polaris P50-500 recorded the highest maximum values of 41.14, 43.84, and 43.25% in 2017, 2018, and 2019, respectively, as shown in Figure 12. Furthermore, the Polaris P50-500 commercial wind turbine recorded the highest average monthly capacity factor of 44.25% in the month of October, and May recorded the lowest average monthly capacity factor of 37.63%, based on the SDM, as shown in Figure 13.

Figure 12

Yearly capacity factor.

Figure 13

Average monthly capacity factor based on years.

8 Conclusion

In this study, the investigation of the yearly characteristics of wind speed and potential wind energy using the Weibull distribution method for a coastline of the Dar es Salaam region was performed. In addition, analysis and efficient comparison between the SDM and the GM were determined. The results obtained from this study showed that the SDM gave a higher value than the GM in the Weibull distribution parameter analysis. Furthermore, a recommended suitable commercial wind turbine was obtained using the SDM. The recommended commercial wind turbine for wind power production was obtained after a simulated performance using five different commercial wind turbines (Polaris P15-50, Bonus 300 kW/33, Polaris P50-500, Bonus 1 MW/54, and WWD-1-60), in which the Polaris P50-500 stands out as the recommended commercial wind turbine, which is suitable for the study area due to its highest value of the capacity factor, for all 3 years.

Conflict of interest: Authors state no conflict of interest.

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Received: 2021-07-14

Revised: 2021-09-29

Accepted: 2021-10-26

Published Online: 2021-11-19

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2021-0108

Keywords for this article

Weibull parameters; numerical methods; wind energy potential; statistical analysis

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