Optimum Operational Conditions for Power Generation for Ngong Hill Wind Farm

doi:10.21203/rs.3.rs-5185248/v1

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Optimum Operational Conditions for Power Generation for Ngong Hill Wind Farm

https://doi.org/10.21203/rs.3.rs-5185248/v1

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The Ngong Hill Wind Farm, in Kenya, represents a significant investment in renewable energy aimed at reducing the country's dependence on fossil fuels and enhancing sustainable power generation. In order to model an optimized wind farm layout, it is crucial to accurately measure, describe, and analyze the statistical properties of the wind available in the site. This research investigates the optimal operational conditions for effective power generation at the Ngong Hill Wind Farm. The analysis is based on long-term data spanning from 2010 to 2019 and consists of ten-minute mean wind measurements and validation data collected for three months of the year 2022. The power loss due to wake effects is analysed using the Jensen wake models, and simulation for power output done with simulations in PHYTON libraries. The study shows that the yearly average Weibull shape and scale parameters are 3.29 and 9.81 m/s, respectively. The maximum power extractable at optimum efficiency is 509 W/m², corresponding to wind power class V. Predominant wind directions are from North-East to South-East. The simulation for Annual Energy Produced (AEP) at the Ngong wind farm under wake interference conditions shows a significant power loss of 28.209%, reducing AEP from 61.86 GWh to 44.41 GWh. The actual net output is 12 GWh, much lower than expected due to wake effects and turbine downtime. From the study, turbine efficiency and the overall wind farm performance is maximized by addressing wake interference and optimizing maintenance scheduling.

Renewable Resources

optimization

simulation

Jensen

wake effects

maintenance scheduling

The growing alarm and awareness over increased atmospheric warming due to the greenhouse gases emissions, environmental pollution and sustainability of energy resources have led to heightened interest in the establishment of renewable and environmentally safe sources of energy. These environmentally friendly and widely available energy sources including harnessing power from the sun, wind, hydro, geothermal and biomass; are considered better alternatives to the conventional sources of energy [19]. Harnessing wind power with modern technology and emergent energy conversion systems continues to be well established in the recent years [20]. Rapid technical and economic sustainability has enabled the harnessed wind power to be deployed on a large scale, thereby contributing a large percentage to national energy consumption in some countries [18]. However, power from wind greatly relies on the unpredictable weather and geographic conditions that fluctuates so much as compared with some other renewable energy sources such as hydropower. There is an increasing share of wind power in the power market across the globe, resulting into a large amount of wind power being integrated into existing grids. Given the technological developments, there is a growing concern that the current electrical grid infrastructure may face challenges in efficiently managing and integrating the increasing renewable energy capacity. However, wind power being an intermittent source due to the unpredictability of the resource, both grid stability and system security should be addressed as one of the means to prepare for the situation [19].

The wind resource being site specific, deriving profitable energy is primarily limited to specific geographical sites which more often than not are inaccessible since they are located in deep remote areas [13]. Wind energy projects require large amount of capital, starting from acquiring land for the wind farm and the other hardware rendering upfront investment to be high [9]; however, compared to other energy sources, the maintenance, servicing and other operational costs of the farms are decent and hence manageable and can be easily achieved. However, with the booming wind power industry, there is a challenge in attaining a situation with a feasible reduction in the cost of generating wind power, which has been a major focus in the recent years. The generation of Wind power’s fixed costs are quite high with relatively low variable costs [19].

Over the years, a large percentage of Kenya’s electric power comes from hydropower plants, which accounted for 45.422% of the total installed capacity in 2020 [15], however, in 2008, Vision 2030, saw Kenya come up with a power generation target of 23,000MW of energy. This target is up to about ten times more in energy capacity of what the country was able to produce by 2008. Strategies are put in place to achieve this energy target by the integration of the renewable energy resources which include the hydro, geothermal, solar, wind, and coal [11]. Kenya’s wind energy resources remain unexploited; the potential to generate electricity out of wind power is so high; with a total of 346 Wm^− 2; which if harnessed can sustain power requirements for the entire nation at an affordable price [21]. Geographically, Kenya is endowed with distinct locations with profitable wind resources most part of the year, which mainly is a result of its complex topographical characteristics with mountainous regions and valleys [11]. The northwest regions of the country and most edges of the Rift Valley are endowed with high wind speed (with average wind speeds of over 9m/s at a hub height of 50 m). The coastal region’s wind speeds are lower however promising (about 5-7m/s at 50 m hub height). It is expected that about 25% of the country will be suited to current wind technology. The largest wind power project in Africa was unveiled in 2019; the Lake Turkana Wind Power farm; which is comprising of 365 turbines with a total energy capacity of 310 megawatts. The wind power provides reliable, low-cost energy to the national grid [1].

A 2020 study by [7] analysed 5 years of wind speed data in Djibouti City to assess its wind energy potential. The study found that despite low monthly wind speeds, the Polaris P12-25 turbine was the most effective, with an annual energy production of 2.1 x 10⁴ MWh and a 9.629% capacity factor. The research supports the proposal to install micro wind turbines, highlighting the need for hub heights above 30.5 meters for optimal energy generation. A study by [10] assessed Marsabit, Kenya's wind energy potential for power generation and water pumping. Using wind data from 2001–2006, the study found average wind speeds over 11 m/s at 10 meters height and power densities between 1776 W/m² and 2202 W/m² at 100 meters, placing the area in wind classes 7 and 8. The analysis showed consistent wind direction and frequency, indicating the site’s suitability for grid-connected power generation and standalone systems for battery charging and water pumping. [14] explored the viability of Small Wind Turbine Generators (SWTG) for powering the rural Mwingi-Kitui plateau in Kenya. Wind speed data, collected over a year at 20 and 40 meters, showed mean speeds of 4.24 m/s and 4.88 m/s, respectively, with power densities up to 115 W/m² at 100 meters. The study indicated that the region, with its consistent wind flow, is suitable for small wind turbines, providing a potential solution for electricity access in this underserved area.

This study provides an analysis of the optimal operational conditions for effective power generation at the Ngong Hill Wind Farm, examining optimal conditions for harnessing wind energy effectively.

2.1 Description of the Study Site

The Ngong Wind Farm, the first wind park to be developed in East Africa, is located in Kajiado county in the northern slopes of Ngong Hills at 1°22'51.9"S, 36°38'08.0"E [5]. It comprises thirty wind turbines with a total installed capacity of 25.5 MW: 14 -Vestas (V52/850 kW) installed at a hub height of 49 m; and 16-Gamessa (G52/850 kW) at 55 m; each with a rotor radius of 26 m and name plate capacity of 850kW. The turbines produce electricity at 690V, which is initially stepped up to 11kV at the substation. From there, power transformers boost the voltage to 66kV for seamless integration into the national grid. The facility houses three power transformers for this purpose [12].

2.2 Wind data

To determine the characteristics of the respective wind farm sites, and to analyze the power potential of the wind farm location, historical data for Ngong Hills wind farm obtained from Kenya Electricity Generating Company (KenGen) archives database, for 10-year period between January 2010 to Dec of 2019 was analyzed. To validate the historical data, wind measurements for the site for the months of March, July and November of 2022 was done at 10 m height. By taking advantage of python and its libraries, various operations were performed to depict various objectives including generation of wind data distributions, normalization of distributions, and annual energy produced from the site.

2.3 Wind Shear

This is a variation of wind speed with elevation, and describes the change in wind speed as it varies with the height above the ground [9]. The height differences for the incoming average speeds were accounted for using wind shear exponent for the sites; taking into consideration the hub height for the towers in the sites. The relationship of wind speed and height was evaluated using the power law [13] as illustrated in Eq. 1:

\(\:\frac{{v}_{2}}{{v}_{1}}=\:{\left(\frac{{h}_{2}}{{h}_{1}}\right)}^{\gamma\:}\) ……………………………………………………………….……….. 1

where v₂ and v₁ are wind speeds at heights h₂ and h₁, and γ is the wind shear exponent, which defines the variation of wind speed with height. The vertical wind shear is an important design parameter, as it directly determines the overall productivity of a wind turbine on a tower of certain height. The shear exponent value used for the extrapolation of wind speed is 0.2, since the site has tall vegetation cover [13]. The wind speeds measured at 10 m height were extrapolated using to shear exponent to 49 m and 50m heights which is the turbine tower heights at the site.

2.3 Wind Distribution

Wind speed is a stochastic quantity. The wind speed for any specified location is represented by density functions. The most common being the Weibull distribution, whose probability density function pd(v) is given in Eq. 2 as:

\(\:pd\left(v\right)=\:\frac{k}{c}\:.\:{\left(\frac{v}{c}\right)}^{k-1}.{e}^{\left(-{\left(\frac{v}{c}\right)}^{k}\right)}\) ……….……………………………………… 2

where v is the wind speed and c and k are the scale and shape parameters, respectively; the parameter k determines the shape the curve takes and c determines the curve distribution [9]. To analyze a wind regime through the Weibull distribution, it is essential to compute the Weibull parameters k and c.

2.4 Wind Power Generation

The electric power P that can be extracted by a wind turbine is directly proportional to the cube of the wind speed [8] as represented by Eq. 3:

\(\:P=\:\frac{1}{2}\rho\:A{v}^{3}{C}_{p}\) ………………………………………………………………… 3

where ρ is the air density, A is the area swept by rotor, v is the incident wind velocity and C_p is the power coefficient. This power output from a wind turbine is proportional to the wind speed incident at the turbine rotor [4]. C_p is known as the Betz coefficient which defines the highest efficiency of any rotor disk type energy extracting device that is placed in the path of flow of a fluid. Using the concepts of conservation of mass, momentum, and energy, Albert Betz, postulated 59.3% of energy as the maximum extractable power for an ideal rotor from a mass of air that is incident at the turbine [9].

2.5 Wind Variability

The constant fluctuations in wind speed and direction, driven by turbulence and daily, seasonal, and annual changes, make predicting energy capture challenging and maintaining a stable power supply to the grid complicated [8]. Wind speed also depends on topography and ground cover, while wind direction changes over similar time scales, with seasonal shifts ranging from 30° to 180° [13].

2.6 Wake Modelling

The power loss due to wake effects is evaluated using wake models, classified as either computational or analytical models. In this study an analytical wake model referred to as the Jensen wake model, was used, which when compared with other analytical models, is capable of predicting the power losses with a high level of accuracy [3]. The Jensen model is a mass-conserving engineering wake model employed to compute the quantification of reduction of the wind velocity of downstream wind turbines from a particular incident wind speed as given in Eq. 4 [6]:

\(\:{V}_{x}=\:{V}_{in}\left[\left\{1-\left(1-\sqrt{1-{C}_{t}}\right){\left(\frac{D}{{D}_{x}}\right)}^{2}\right\}\right]\) …………………..…………………………. 4

where V_in (m/s) is the free stream incoming wind speed, V_x (m/s) is the velocity deficit, Ct is thrust coefficient, \(\:{D}_{x}=D+2{k}_{x}\) and k is wake decreasing constant.

3.1 Mean Wind Speed

The assessment of the wind potential at the chosen location involved an analysis of wind characteristics, including wind speed, prevailing direction, duration, availability, and the resulting power density. By using the measured frequencies, the frequency distribution of wind speed and direction was obtained and represented as a histogram as shown in Fig. 1.

The Fig. 1 illustrates highest frequency of wind speed occurring between 4m/s to 6 m/s, indicating the most common wind speeds in the dataset. The frequency of the highest wind speed between wind speeds of 14 m/s to 16 m/s suggesting that very high wind speeds are rare in this dataset. Extrapolation of the wind speed using the power law Eq. 1, the calculated mean wind speed at 50 m height is 9.38 m/s while the standard deviation is 3.46. Maximum and minimum windspeed were 17.1 m/s and 2.1 m/s respectively. However, this calculated mean may not represent the actual distribution of windspeed and hence a cumulative frequency was determined.

3.2 Wind Speed Variability

The variations for wind energy characteristics for monthly and daily situations, for wind speed and direction at the Ngong wind farm were established and the information represented in time series graphs. Wind speed and direction variation for the year 2020, with the month of January taken to be the reference point through December were represented in graphs. These variations in wind direction and speed are represented in Fig. 2 (a) and (b) respectively. These fluctuations in the wind speed results in the power from an individual wind turbine and therefore from the entire wind park having big variations. Short-term fluctuations in wind power are stochastic in nature, but distinctive patterns exist for longer-term fluctuations [8].

The Fig. 2 (a) shows wind direction over the year fluctuates between 0° and 250°, with occasional peaks near 250°. Early in the year, there is some stabilization between 50° and 150°. Mid-year, shows increased variability, with frequent and rapid fluctuations, indicating a turbulent wind pattern, while late mid-year sees a reduction in the range of fluctuations, mainly between 50° and 200°. Toward the end of the year, the wind direction stabilizes further, with most values falling between 50° and 150°. The pattern suggests seasonal influences, with the mid-year period experiencing more dynamic shifts in wind direction, possibly due to changing weather patterns during that time. Figure 2 (b), illustrates significant fluctuations in wind speed (m/s) over the year, ranging from 4 m/s to 16 m/s. It features multiple peaks at around 16 m/s, indicating high wind days, and troughs at approximately 4 m/s, representing calm days. The recurring patterns suggest seasonal variations influenced by meteorological factors and turbulence [13].

3.3 Wind Direction.

A wind rose diagram is a useful diagram which illustrates wind speed frequency and wind direction all together in one diagram [13]. Determining the wind speed according to wind direction is important to analyze wind energy potential and also shows the impact of geographical features on the wind. Analyzing the wind direction is useful for understanding the wake effect, which turbines could be on the path of the other turbines which could result in a reduction of wind speed. Wind speed rose, provides appropriate knowledge on the predominant wind direction of the site which is a vital factor in determining the direction from which maximum possible wind energy can be harnessed. The observed wind direction for the three months were organized at varying intervals for wind speed for each direction was analyzed and represented in Table 1.

Table 1

Cumulative Wind Speed for Each Direction
	N	NE	E	SE	S	SW	W	NW
Count	60	1568	9890	1021	28	144	86	47
cumulative	112.9	12567.4	97805.6	10075.8	61.6	446.7	187.3	72.5
Average	1.88	8.02	9.89	9.87	2.2	3.10	2.17	1.54

The results in Table 1 show that the East, North East, and South East directions are the predominant wind directions and experience average speeds of 8-9.9 m/s. By studying the hourly wind roses can help determine the best location for the wind turbines. The wind rose for the site is given in the Fig. 3.

The wind rose diagrams shown in Fig. 3 for the Ngong wind farm, provide a visual representation of the wind patterns over the course of 2022, broken down into daily and monthly mean values. The daily mean wind rose indicates that the most frequent wind directions are from the North-east (NE) and South-east (SE). The highest frequency of wind appears to occur at speeds between 6.0 to 9.0 m/s from the NE direction. Both charts show a strong preference for wind coming from the northeastern directions throughout the year. While the predominant speed ranges are similar, the monthly mean chart shows a slightly broader range of higher wind speeds compared to the daily mean, which suggest greater variability in wind speed on a monthly basis compared to daily observations.

3.4 Probability Density Function

The average wind speed of the site is not sufficient to fully understand the available wind potential. To overcome the unpredictability of wind characteristics, a statistical analysis was deemed essential, consequently, Weibull distribution model was used. Weibull model shape parameter k, and scale parameter, c, were determined from the data and the respective distribution curves drawn as illustrated in Fig. 4.

The Fig. 4 illustrates the probability density function which shows the probability of occurrence of each observed wind speed. Weibull probability density curve provide the ability of determining likelihood of wind blowing at a certain speed in any given time [9]. The curve is unimodal, peaking at a wind velocity of about 9 m/s, indicating this as the most common wind speed, which is near the mean wind speed of 9.38 m/s. Probability decreases for wind speeds lower or higher than this peak, which shows that the wind speed is more likely to be near the average value than significantly different from it, and it has an almost equal chance of being lower or higher than the average [13].

3.5 Power Density

The scale and shape parameters were also used to calculate the site’s localized power density. The shape and scale parameters of 3.29 and 9.81m/s respectively and the site’s air density whose value is 1.29g/l were used which gave a theoretical power density of 858W/m². This power was noted to be almost the same as calculated power if the wind was blowing at the average speed of 9.38 m/s. To achieve the maximum power that can be extracted, Betz's limit was taken into consideration, which estimates power output at 59.34% [9], resulting in 509 W/m² as maximum power extractable at the optimum efficiency lying within wind power class V.

3.6 Turbine Placement Evaluation

The layout in Fig. 5 illustrates the spatial arrangement of 30 points representing wind turbines at the Ngong wind farm obtained through a detailed analysis using data with specific geographical coordinates (X and Y positions) from the KenGen archives database. By visualizing the coordinates using Python programming language a layout of the spatial distribution was generated. The data was processed and visualized in Matplotlib Python libraries.

The distances between turbines vary, and their orientation follow a staggered pattern based on topography. Additionally, the turbine distribution does not follow a strict grid but rather takes the landscape's natural features into account. This graphical representation provides an essential tool for further analysis of the AEP by each turbine and the overall farm. Future studies could integrate this layout with wind flow simulations to optimize turbine positioning for reduced power loss. Similarly, the simulated power curves for each turbine shown in Fig. 6, assessed individual performance, helping to identify potential areas for optimization in energy production to improve turbine efficiency and maximizing the farm's AEP.

When considering all turbines to be in operation, the simulation for AEP for the Ngong wind farm when the wind turbines have interference due to wake is found as 44.41 GWh, reducing wake interference increases the AEP to 61.86 GWh, reflecting a 28.209% power loss due to wake effects. The actual annual net output from the farm is 12 GWh [12] much lower than the expected output from the farm, resulting from wake interfering and downtime due to turbines downtime, since not all turbines are operational throughout the year. Wake interference occurs when the wind flow behind a turbine is disrupted by its blades, creating turbulence and reducing the wind speed for downstream turbines [2]. This effect leads to a significant reduction in the AEP, as evidenced by the 28.209% power loss in the scenario. The difference between the AEP with wake interference (44.41 GWh) and the potential AEP with reduced wake interference (61.86 GWh) highlights the importance of addressing this issue. The power losses due to the wake effects can be minimized so that the expected power output is maximized [16]. Strategies to reduce wake interference, such as optimizing the placement of turbines and utilizing advanced control systems [17], can lead to substantial gains in energy output.

An important aspect that has not been addressed by other studies is optimizing maintenance scheduling, which is key to minimizing downtime and maximizing turbine efficiency and in turn, wind farm efficiency can be enhanced, maximizing AEP potential. This approach minimizes energy losses and ensures turbines are fully operational during optimal wind conditions, thus increasing the AEP. Scheduling maintenance when turbines are already less efficient due to wake interference can further reduce its impact on overall energy production.

In conclusion, this study has provided an evaluation of the operational conditions for power generation at Ngong Hill Wind Farm in Kenya. By analyzing long-term wind data and utilizing the Jensen wake model and taking advantage of the PHYTON libraries, significant power losses due to wake interference have been highlighted, which have a notable impact on the Annual Energy Produced (AEP). The simulations reveal that wake effects alone account for a 28.209% reduction in AEP, emphasizing the importance of optimizing turbine placement and minimizing downtime through improved maintenance scheduling. Although the wind resource at Ngong shows promising potential, with Weibull shape and scale parameters of 3.29 and 9.81m/s, and extractable power of 509 W/m², the actual energy output falls short of projections due to these inefficiencies. Addressing wake effects and enhancing turbine performance will be crucial in maximizing the wind farm’s contribution to Kenya’s renewable energy goals and improving the sustainability of the country’s power generation infrastructure.

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The authors declare no competing interests.

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Optimum Operational Conditions for Power Generation for Ngong Hill Wind Farm

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Version 1

Abstract

Figures

1. Introduction

2. Methodology

2.1 Description of the Study Site

2.2 Wind data

2.3 Wind Shear

2.3 Wind Distribution

2.4 Wind Power Generation

2.5 Wind Variability

2.6 Wake Modelling

3. Results and Discussion

3.1 Mean Wind Speed

3.2 Wind Speed Variability

3.3 Wind Direction.

3.4 Probability Density Function

3.5 Power Density

3.6 Turbine Placement Evaluation

4. Conclusion

References

Additional Declarations

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