Performance Enhancement of Proposed Namaacha Wind Farm by Minimising Losses Due to the Wake Effect: a Mozambican Case Study

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Article Performance Enhancement of Proposed Namaacha Wind Farm by Minimising Losses Due to the Wake Effect: A Mozambican Case Study

Paxis Marques João Roque 1,* , Shyama Pada Chowdhury 2 and Zhongjie Huan 1

1 Faculty of Engineering and the Built Environment, Department of Mechanical and Mechatronics Engineering, Tshwane University of Technology, Private Bag X680, Pretoria 0001, South Africa; [email protected] 2 Faculty of Engineering and the Built Environment, Department of Electrical Engineering, Tshwane University of Technology, Private Bag X680, Pretoria 0001, South Africa; [email protected] or [email protected] * Correspondence: [email protected]

Abstract: District of Namaacha in Maputo Province of Mozambique presents a high wind potential, with an average wind speed of around 7.5 m/s and huge open fields that are favourable to the installation of wind farms. However, in order to make better use of the wind potential, it is necessary to evaluate the operating conditions of the turbines and guide the independent power producers (IPPs) on how to efficiently use wind power. The investigation of the wind farm operating conditions is justified by the fact that the implementation of wind power systems is quite expensive, and therefore, it is imperative to find alternatives to reduce power losses and improve energy production. Taking into account the power needs in Mozambique, this project applied hybrid optimisation of multiple energy resources (HOMER) to size the capacity of the wind farm and the number of turbines Citation: Roque, P.M.J.; Chowdhury, that guarantee an adequate supply of power. Moreover, considering the topographic conditions S.P.; Huan, Z. Performance of the site and the operational parameters of the turbines, the system advisor model (SAM) was Enhancement of Proposed Namaacha applied to evaluate the performance of the Vestas V82-1.65 horizontal axis turbines and the system’s Wind Farm by Minimising Losses power output as a result of the wake effect. For any wind farm, it is evident that wind turbines’ wake Due to the Wake Effect: A effects significantly reduce the performance of wind farms. The paper seeks to design and examine Mozambican Case Study. Energies the proper layout for practical placements of wind generators. Firstly, a survey on the Namaacha’s 2021, 14, 4291. https://doi.org/ 10.3390/en14144291 electricity demand was carried out in order to obtain the district’s daily load profile required to size the wind farm’s capacity. Secondly, with the previous knowledge that the operation of wind farms Academic Editor: Georg Stadtmann is affected by wake losses, different wake effect models applied by SAM were examined and the Eddy–Viscosity model was selected to perform the analysis. Three distinct layouts result from SAM Received: 30 May 2021 optimisation, and the best one is recommended for wind turbines installation for maximising wind Accepted: 30 June 2021 to energy generation. Although it is understood that the wake effect occurs on any wind farm, it Published: 16 July 2021 is observed that wake losses can be minimised through the proper design of the wind generators’ placement layout. Therefore, any wind farm project should, from its layout, examine the optimal Publisher’s Note: MDPI stays neutral wind farm arrangement, which will depend on the wind speed, wind direction, turbine hub height, with regard to jurisdictional claims in and other topographical characteristics of the area. In that context, considering the topographic and published maps and institutional affil- climate features of Mozambique, the study brings novelty in the way wind farms should be placed iations. in the district and wake losses minimised. The study is based on a real assumption that the project can be implemented in the district, and thus, considering the wind farm’s capacity, the district’s energy needs could be met. The optimal transversal and longitudinal distances between turbines recommended are 8Do and 10Do, respectively, arranged according to layout 1, with wake losses of Copyright: © 2021 by the authors. about 1.7%, land utilisation of about 6.46 Km2, and power output estimated at 71.844 GWh per year. Licensee MDPI, Basel, Switzerland. This article is an open access article Keywords: wind energy; wake effect; wake model; wind turbine performance distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Energies 2021, 14, 4291. https://doi.org/10.3390/en14144291 https://www.mdpi.com/journal/energies Energies 2021, 14, 4291 2 of 22

1. Introduction The growth in power consumption worldwide, combined with the issue of climate changes that concerns all the stakeholders across the globe, has driven renewable energies to play an important role in mitigating environmental impacts and providing universal power access to populations suffering from power poverty [1–6]. Although many countries have a sturdy interest in renewable power technologies, there are still major challenges in the implementation of these alternative energy generations [7,8]. Wind power is a prominent source and has aroused massive attention in the last past decade, but its low capacity factor associated with its high cost of the initial investment, in addition to its maintenance [9,10], has necessitated research to continue with improvement of its performance. Moreover, the unpredictable dynamic behaviour of a wind turbine has not yet been possible to predict properly, considering uncertainties of various operating parameters [1,11,12]. The overall efﬁciency of a wind system depends on several factors, such as aerodynamic and mechanical characteristics of the wind turbine and operating parameters of the electric generator and other auxiliary electric components [13,14]. A selected wind site requires a proper layout for the installation and commissioning of wind generators. There is a research gap in the published literature concerning the layout optimisation for minimising losses due to wake effects to maximise energy output. The following key factors affect the performance of wind for energy generation systems:

I Weather conditions such as wind speed, wind direction, and air density—wind to energy generation, the assessment of wind conditions, and potential wind power evaluation are based mainly on wind speed, spatial distribution, and air density [4,5,15–17]. I The wind turbine’s design such as rotor´s diameter, blade geometry, and wind tower´s height—the fundamentals of aerodynamics have been decisive for the advance of wind turbines [18]. A number of numerical modelling challenges are present in the design of wind turbines, with respect to the aerodynamics of the rotor and blades and stability of the tower under wind gusts and oscillations [17,19]. Depending on the type of turbine, its performance is influenced by other design parameters such as the number of blades and rotor orientation [14,20–22]. I The wind farm layout such as the site´s topographic conditions, the distance between two consecutive turbines, and the erection layout (linear or scattered)—depending on the local wind conditions of the wind site, the design can lead to power loss due to wake effect on the wind farm. Wind turbines’ wake effects significantly reduce the performance of downstream wind turbines [7,23–26]. With the increase in the number of turbines downstream, the influence of the wake effect and load of airflow generated tends to be more significant [7,27]. With regard to the subject of wake effect minimisation, Sun et al. [7] summarised the results of wake losses measurement experiments in distinct wind farms. In general, the experimental measurement results proved that for high wind speeds, the deficits in the wind speed reached approximately 45%, 35%, and 5% at distances of 3Do, 3.5Do, and 5Do, respectively. In addition to the influence of wind speed and distance between turbines, the tests also demonstrated that the wake losses are influenced by the number of turbines in the wind farm as well as the turbine’s rotor diameter Do and hub height. For 20 turbines with a rotor diameter of 76 m, a hub height of 64 m, and turbines spacing of 2.4 Do, results showed that for the wind speed of 11 m/s, the turbulence intensity is about 6.5%. Fei et al. [23] investigated the influence of the rotor diameter on wake width and depth. Results proved that with the increase of downwind distance, the wake width and depth increase regardless of the rotor diameter. However, the growth magnitude is diverse, and thus, the greater the diameter is, the lower the growth magnitude becomes. Dhiman et al. [25] applied a bilateral wake model derived from two benchmark models, namely, Jensen’s and Frandsen’s variation models, to evaluate the wind speed prediction in the presence of wakes for two distinct wind farms composed of 5 turbines (layout A) and 15 turbines (layout B). Results revealed that for layout A, the prediction Energies 2021, 14, 4291 3 of 22

accuracy improved by 10.56%, 10.05%, and 10.48% when the inputs to the forecasting model are from Jensen’s, Frandsen’s, and bilateral wake models, respectively. Similarly, for layout B, an improvement in prediction accuracy by 20.47%, 8.37%, and 46.88% was when the inputs to the forecasting model are from Jensen’s, Frandsen’s, and bilateral wake model, respectively. Ge et al. [26] investigated the interaction between the wind turbine wake and a building array applying large eddy simulation. Results showed that the urban district can considerably inﬂuence the development of the turbine wake, and thus, this proves the inﬂuence of the surrounding environment and landscape on the wind farm performance. Tao et al. [27] examined the performance of three wind farms composed of different numbers of turbines (layout C = 25 turbines, layout D = 45, and layout E = 60). Results demonstrated that with the increase of turbines in the farm, wake losses increase. Note that the results of the studies display diverse trends and emphasise the novelty existing in each wind farm performance assessment as a particular case.

2. Performance Analysis of Wind Technology Aerodynamics

Energies 2021, 14, x FOR PEER REVIEW Thus far, in the field of power generation, different models of wind turbines6 have of 24 been developed. In general, according to the rotation direction, wind turbines can be classified into two major types: horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT) [11,12,28,29]. The aerodynamic performance of the wind turbine where depends greatly on the power extracted from the wind mass and the shape of the blade’s b —is the interference factor. cross section and thus is linked to the power coefficient Cp, which expresses the amount of powerThe extracted maximum from value the of wind Cp occurs [30]. Wind when power b = 1/3 turbines or the far are downstream placed in wide, velocity extended, u3 is fluxes of air movement. The air that passes through the wind turbine cannot, therefore, be one-third of that of the undisturbed wind velocity u1, and therefore, deflected into regions where there is no air already and so there are individual limits to 2 wind turbine efficiency. =−==1116  C p 4 1  0.5926 (15) According to Steiger [31], in Figure33271, the  upwind stream approaching the turbine flows undisturbed with velocity u1, and the downwind stream transited through the Wind velocity usually varies from one location to another and fluctuates over time turbine and flowing with velocity u3 is substantially slowed. Considering that at the disk, in an unpredictable way, affecting the performance of wind technology, and thus, an ac- the flow velocity u2 is the average of the upstream and downstream velocities u1 and u3, it curatecan be evaluation expressed asof follows:wind conditions at the site represents a key step in the placement of wind projects [19]. The Betz criterion providu1 +esu 3the accepted standard of 59% for the max- u2 = [m/s] = (1) imum extractable power and represents the2 power coefficient, C p 0.59 .

Figure 1. Representation of upwind and down downwindwind stream for wind turbines.

AnalogousDue to the reductionto the power in momentum,coefficient, the the thrust force coefficient F on the turbine (CT) is resultingalso a vital from parameter the air andmass illustrates ﬂow can the be expressedway the fluid as follows: streamlines diverge as a result of deceleration of the fluid

and supports measuring the axial static load• induced by the wind [30]. In a horizontal axis wind turbine, increasing the thrustF =loadm( umay1 − ucause3)[N blade] deflection. Therefore, under-(2) standing the multi-physics phenomena related to blade dynamics which represents is also where a key •aspect for the continuous improvement of wind turbine efficiency, and thus, thrust forcem should—is the be air controlled. mass ﬂow The rate wind [kg/s]; power density at the site can be converted by the windu turbine1—is the and upstream also assessed wind speedusing a [m/s]; probability density function such as Weibull, Ray- leigh,u and3—is Lognormal the downstream [4,15]. windUsing speed the Weibull [m/s]. distribution, Wind power density can be estimated as a function of wind speed u , shape factor k , and scale factor c.

kk−1 ku − u  fukc(,,)=  exp   (16) cc  c 

3. Namaacha District Renewable Power Potential Overview In many studies on Mozambique’s renewable power potential, Namaacha District has been singled out as one of the most prominent districts in terms of wind energy [32– 34]. The district has a combination of reliefs from hills and mountains landscapes to plains and depressions landscapes and extensive lands favourable to the implementation of wind farms. Taking into account the weather conditions and landscape features in the Namaacha District, the National Energy Fund (FUNAE) held a mapping process and estimated the average wind speed and wind power generation potential of promising wind sites. Figure 2a represents the proposed wind site with an estimated area of 14.0 km2 (approximately 4.0 km wide and 3.5 km long), and Figure 2b illustrates the wind farm’s landscape area.

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Assuming that the airﬂow speed at the turbine u2 is uniform, the power extracted by the turbine can be expressed as

• PwT = F · u2 = m(u1 − u3)u2 [W] (3)

where • m—is the air mass ﬂow rate [kg/s]; u1—is the upstream wind speed [m/s]; u2—is the wind speed at the turbine [m/s]; u3—is the downstream wind speed [m/s]. The difference in energy between the upstream and downstream air mass represents the energy extracted from the wind, and therefore,

• m(u2 − u2) P = 1 3 [W] (4) ext 2 where • m—is the air mass ﬂow rate [kg/s]; u1—is the upstream wind speed [m/s]; u3—is the downstream wind speed [m/s]. Considering the energy extracted by the turbine equal to the difference of the upstream and downstream energy of the air mass one can write the following:

• • 2 2 m(u1−u3) m(u1 − u3)u2 = 2 2 2 (5) (u1−u3) 1 (u1 − u3)u2 = 2 = 2 (u1 − u3)(u1 + u3) The rate at which mass streams across the swept area of the rotor is

• m = ρAu2 [kg/s] (6)

where ρ—is the mass ﬂow density [kg/m3]; A—is the swept area of the blades [m2]; u2—is the wind speed in the turbine [m/s]; The power extracted by the turbine can be rewritten as follows:

2 PwT = ρAu2(u1 − u3)[W] (7)

where ρ—is the mass ﬂow density [kg/m3]; A—is the swept area of the blades [m2]; u1—is the upstream wind speed [m/s]; u2—is the wind speed at the turbine [m/s]; u3—is the downstream wind speed [m/s]. From Equation (1), u3 = 2u2 − u1 [m/s] (8) Additionally, this results in

2 PwT = ρAu2[u1 − (2u2 − u1)] 2 (9) PwT = 2ρAu2(u1 − u2)[W] where ρ—is the mass ﬂow density [kg/m3]; A—is the swept area of the blades [m2]; u1—is the upstream wind speed [m/s]; Energies 2021, 14, 4291 5 of 22

u2—is the wind speed at the turbine [m/s]. Taking into account the interference factor, it can be expressed as follows:

u1 − u2 b = ↔ u2 = u1(1 − b) (10) u1 where u1—is the upstream wind speed [m/s]; u2—is the wind speed at the turbine [m/s]. Rearranging the interference factor as per Equation (1) results in the following:

(u − u ) b = 1 3 (11) 2u1 where u1—is the upstream wind speed [m/s]; u3—is the downstream wind speed [m/s]. Reorganising Equation (9) and incorporating the interference factor results in the following: 2 2 PwT = 2ρA(1 − b) u1[u1 − (1 − b)u1] 1 3h 2i (12) PwT = 2 ρA u1 4b(1 − b) [W] where ρ—is the mass ﬂow density [kg/m3]; A—is the swept area of the blades [m2]; u1—is the upstream wind speed [m/s]; b—is the interference factor. Equation (12) consists of two parts: P1, which is the power of the undisturbed upstream air mass and expressed as follows:

1 P = ρA u3 [W] (13) 1 2 1 where ρ—is the mass ﬂow density [kg/m3]; A—is the swept area of the blades [m2]; u1—is the upstream wind speed [m/s]. Additionally, Cp which is the fraction of the extracted power is expressed as follows:

2 Cp = 4b(1 − b) (14)

where b—is the interference factor. The maximum value of Cp occurs when b = 1/3 or the far downstream velocity u3 is one-third of that of the undisturbed wind velocity u1, and therefore,

1 1 2 16 C = 4 1 − = = 0.5926 (15) p 3 3 27

Wind velocity usually varies from one location to another and fluctuates over time in an unpredictable way, affecting the performance of wind technology, and thus, an accurate evaluation of wind conditions at the site represents a key step in the placement of wind projects [19]. The Betz criterion provides the accepted standard of 59% for the maximum extractable power and represents the power coefficient, Cp = 0.59. Analogous to the power coefficient, the thrust coefficient (CT) is also a vital parameter and illustrates the way the fluid streamlines diverge as a result of deceleration of the fluid and supports measuring the axial static load induced by the wind [30]. In a horizontal Energies 2021, 14, 4291 6 of 22

axis wind turbine, increasing the thrust load may cause blade deﬂection. Therefore, understanding the multi-physics phenomena related to blade dynamics which represents is also a key aspect for the continuous improvement of wind turbine efﬁciency, and thus, thrust force should be controlled. The wind power density at the site can be converted by the wind turbine and also assessed using a probability density function such as Weibull, Rayleigh, and Lognormal [4,15]. Using the Weibull distribution, Wind power density can be estimated as a function of wind speed u, shape factor k, and scale factor c.

k u k−1 −u k f (u, k, c) = exp (16) c c c

3. Namaacha District Renewable Power Potential Overview In many studies on Mozambique’s renewable power potential, Namaacha District has been singled out as one of the most prominent districts in terms of wind energy [32–34]. The district has a combination of reliefs from hills and mountains landscapes to plains and depressions landscapes and extensive lands favourable to the implementation of wind farms. Taking into account the weather conditions and landscape features in the Namaacha District, the National Energy Fund (FUNAE) held a mapping process and estimated the average wind speed and wind power generation potential of promising Energies 2021, 14, x FOR PEER REVIEWwind sites. Figure2a represents the proposed wind site with an estimated area of 14.07 km of 242

(approximately 4.0 km wide and 3.5 km long), and Figure2b illustrates the wind farm’s landscape area.

(a) (b)

Figure 2. (a) Proposed site forFigure Namaacha 2. (a) Proposed wind farm. site Courtesy for Namaacha of Google wind Earth, farm. land Cour fortesy wind of farmGoogle allocation Earth, land (25◦ 58for019” wind S, farm 32◦01056” E, elevation 497M);allocation (b) Overview (25°58 of′19 the′′S, wind 32°01 farm’s′56′′E, landscape.elevation 497M); Courtesy (b of) Overview FUNAE [ 32of]. the wind farm’s landscape. Courtesy of FUNAE [32]. Three different wind farm layouts that differ in terms of distance between turbines, the rowThree orientation different angle, wind and farm spacing layouts between that diff rowser in were terms placed of distance in the area,between and turbines, the total energythe row production orientation ofangle, the turbinesand spacing was between evaluated. rows In were order placed to take in full the advantagearea, and the of total the Namaachaenergy production wind potential, of the FUNAEturbines [was32] recommends evaluated. In the order installation to take offull a windadvantage tower of with the aNamaacha height of aboutwind potential, 60 m. Figure FUNAE3 shows [32] the recomme annualnds ﬂuctuation the installation of the wind of a wind speed tower with with the heighta height in of Namaacha. about 60 m. As Figure it is observed, 3 shows the districtannual ´fluctuations average wind of the speed wind isspeed estimated with the at 7.5height m/s. in Namaacha. As it is observed, the district´s average wind speed is estimated at 7.5 m/s.

Figure 3. Namaacha’s annual wind speed profile. Courtesy of FUNAE [32].

Although the daily load curve of the Namaacha power system has not changed its shape in the last years, there has been a considerable increase in terms of peak demand for electricity in the last decade. Figure 4 illustrates the typical daily load profile shape of the system.

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(a) (b)

Figure 2. (a) Proposed site for Namaacha wind farm. Courtesy of Google Earth, land for wind farm allocation (25°58′19′′S, 32°01′56′′E, elevation 497M); (b) Overview of the wind farm’s landscape. Courtesy of FUNAE [32].

Three different wind farm layouts that differ in terms of distance between turbines, the row orientation angle, and spacing between rows were placed in the area, and the total energy production of the turbines was evaluated. In order to take full advantage of the Namaacha wind potential, FUNAE [32] recommends the installation of a wind tower with

Energies 2021, 14, 4291 a height of about 60 m. Figure 3 shows the annual fluctuation of the wind speed with7 of the 22 height in Namaacha. As it is observed, the district´s average wind speed is estimated at 7.5 m/s.

Figure 3. Namaacha’s annual wind speed profile. proﬁle. Courtesy of FUNAE [32]. [32].

Although the daily load curve of the Namaacha power system has not changed its shape in the last years, there has been a considerableconsiderable increase in terms of peak demand Energies 2021, 14, x FOR PEER REVIEWfor electricity in the last decade. Figure4 illustrates the typical daily load proﬁle shape8 of 24 for electricity in the last decade. Figure 4 illustrates the typical daily load profile shape of the system.

Namaacha´s residential daily load profile 1000 800 600 400

Peak load (kW) load Peak 200 0 123456789101112131415161718192021222324 Hours

Figure 4. Namaacha′s typical residential daily load profile on 15 January. Courtesy of Mozambique Figure 4. Namaacha0s typical residential daily load proﬁle on 15 January. Courtesy of Mozambique Power Company (EDM) [35]. Power Company (EDM) [35].

4.4. Model Model Application Application and and Assessment Assessment of of Wake Wake Effect Effect on on Turbine Turbine Performance Performance InIn this this project, project, HOMER HOMER and and SAM SAM were were used used to to size size a a wind wind system system and and to to examine examine thethe wake wake effect effect on on the the farm. farm. In In HOMER, HOMER, the the determination determination of of wind wind turbine turbine power power output output entailsentails three three steps, steps, namely, namely, wind wind speed speed calculation calculation at at the the hub hub height height of of the the wind wind turbine, turbine, thethe estimation estimation of of power power generated generated by by the the wind wind turbine turbine at at the the wind wind speed speed standard standard air air density,density, and and ﬁnally, finally, the the adjustment adjustment of of that that power power output output value value for for the the actual actual air air density. density. TheThe wind wind speed speed at at the the hub hub height height of of the the wind wind turbine turbine is is calculated calculated through through the the computing computing ofof the the wind wind resource resource data data provided. provided. HOMER HOMER applies applies two two distinct distinct methods methods to to estimate estimate windwind speed: speed: the the logarithm logarithm law law and and the the power power law. la Thew. The ﬁrst first method method is expressed is expressed as follows: as follows: ln Zhub Zo uhub = uanem zhub [m/s] (17) lnlnZanem Zo z = o (167 uuhub anem [/] ms where z ) ln anem uhub—is the wind speed at the hub height of the turbine [m/s]; zo uanem—is the wind speed at the anemometer height [m/s]; whereZhub —is the hub height of the turbine [m]; Zanem—is the anemometer height [m]; u hub —is the wind speed at the hub height of the turbine [m/s];

uanem —is the wind speed at the anemometer height [m/s];

z hub —is the hub height of the turbine [m];

zanem —is the anemometer height [m];

zo —is the surface roughness length [m]. By applying the second method, the wind speed at the hub height of the wind turbine is expressed as follows: γ z = hub uuhub anem [/] ms (18) zanem where

uhub —is the wind speed at the hub height of the turbine [m/s];

uanem —is the wind speed at the anemometer height [m/s];

zhub —is the hub height of the wind turbine [m];

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Zo—is the surface roughness length [m]. By applying the second method, the wind speed at the hub height of the wind turbine is expressed as follows: γ Zhub uhub = uanem [m/s] (18) Zanem Energies 2021, 14, x FOR PEER REVIEW 9 of 24 where uhub—is the wind speed at the hub height of the turbine [m/s]; uanem—is the wind speed at the anemometer height [m/s];

zZanemhub—is—is thethe hubanemometer height of height the wind [m]; turbine [m]; γZanem—is—is the thepower-law anemometer exponent. height [m]; γ—is the power-law exponent. Once the hub height wind speed is calculated, with the help of the wind turbine Once the hub height wind speed is calculated, with the help of the wind turbine power power curve, the expected power of the wind turbine at this wind speed under normal curve, the expected power of the wind turbine at this wind speed under normal temperature temperature and pressure conditions is calculated. If the wind speed at the turbine hub and pressure conditions is calculated. If the wind speed at the turbine hub height is not height is not within the range defined in the power curve, the turbine will not generate within the range deﬁned in the power curve, the turbine will not generate power. Wind power. Wind power technology fundaments the state that wind turbines will not produce power technology fundaments the state that wind turbines will not produce power at powerwind speedsat wind below speeds the below minimum the minimum cut-off orcut-off above or the above maximum the maximum cut-out cut-out wind speeds. wind speeds.Power curvesPower typicallycurves typically specify specify wind turbine wind turbine performance performance under normal under temperaturenormal temper- and aturepressure and conditions.pressure conditions. FigureFigure 55 presentspresents the the power power curve curve of ofthe the selected selected turbine turbine Vestas Vestas V82-1.65 V82-1.65 under under var- yingvarying wind wind conditions. conditions. Table Table 1 presents1 presents the turbine’s the turbine’s operating operating range range of wind of wind speed. speed. Ac- cordingAccording to Chaouachi to Chaouachi et al. et al.and and Veena Veena et etal. al. [36,37], [36,37 ],the the selection selection of of wind wind turbine turbine follows follows threethree criteria: criteria: (1) (1) reliability reliability objective, objective, which which is related is related to the to the impact impact of the of thewind wind system system on theon electricity the electricity network network security security of supply; of supply; (2) the (2) cost the objective cost objective associated associated with the with tech- the nology’stechnology’s investment investment costs costs and andthe electricity the electricity tariff tariff charged; charged; (3) the (3) theperformance, performance, which which is linkedis linked to the to theexpected expected energy energy production production and andthe correlation the correlation of wind of windprofile proﬁle patterns patterns with correspondingwith corresponding load demand. load demand.

FigureFigure 5. 5. VestasVestas V82-1.65 V82-1.65 turbine turbine power power curve. curve. Courtesy Courtesy of of Vestas Vestas Wind Wind System.

TableTable 1. 1. TurbineTurbine operation operation parameters. parameters. Courtesy Courtesy of of Vestas Vestas Wind System.

ParameterParameter Value Value Cut-inCut-in wind speed: wind speed: 3.5 m/s3.5 m/s NominalNominal wind speed: wind speed: 13 m/s 13 m/s Cut-out wind speed 20 m/s Cut-out wind speed 20 m/s Hub height (50 Hz, 230 V) 78 m Hub height (50 Hz, 230 V) 78 m

Taking into account the Namaacha wind profile, it is expected that the selected tur- Taking into account the Namaacha wind proﬁle, it is expected that the selected turbine will operate above its average power capacity for most of the year, with maximum bine will operate above its average power capacity for most of the year, with maximum production in periods of extreme wind speed. Regarding the efficiency of the turbine, it can be perceived from Figure 6 that the district’s wind speed profile allows the turbine to operate at its maximum power coefficient.

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production in periods of extreme wind speed. Regarding the efﬁciency of the turbine, it Energies 2021, 14, x FOR PEER REVIEWcan be perceived from Figure6 that the district’s wind speed proﬁle allows the turbine10 of to24

operate at its maximum power coefﬁcient.

FigureFigure 6. 6. VestasVestas V82-1.65 V82-1.65 turbine turbine power power curve. curve. Courtesy Courtesy Vestas Vestas Wind System.

ToTo adjust adjust to to real conditions, HOMER multiplies multiplies the the power power output output predicted predicted by by the the powerpower curve curve by by the the air air density density ratio, ratio, according according to to the the following following equation:

ρρ = = [ ] PwTPwTPPWwT wT(()stp stp ) []W (19)(19) ρρo o wherewhere PwT—is the wind turbine power output [W]; PwT —is the wind turbine power output [W]; PwT(stp)—is the wind turbine power output at standard temperature and pressure —is the wind turbine power output at standard temperature and pressure conditionsPwT() stp [W]; conditionsρ—is the[W]; actual air density [kg/m3]; 3 ρo—is the airactual density air density at standard [kg/m temperature3]; and pressure conditions [kg/m ]. In a real wind farm, the wind energy density experienced by individual wind turbines ρ —is the air density at standard temperature and pressure conditions [kg/m3]. can differo significantly. In that context, the power output of a wind turbine may be affected by theIn a wake real effectwind farm, of other the wind windturbines, energy de andnsity thus, experienced in the design by individual of wind farms,wind tur- it is binesrecommended can differ tosignificantly. give an appropriate In that contex distancet, the between power twooutput consecutive of a wind turbines turbine tomay avoid be affecteddisturbances by the in wake the performanceeffect of other of wind the downstreamturbines, andturbine thus, in[ the38]. design Features of wind of the farms, wind itfarm is recommended that needs to beto consideredgive an appropriate include fluctuations distance between of wind two speed, consecutive wind direction, turbines and to avoidaverage disturbances wind speed in [5the]. Windperformance turbine of farm the modelsdownstream investigate turbine the [38]. profile Features of the of wind the windspeed farm deficit that downstream needs to be ofconsidered the rotor thatinclud is capturede fluctuations by the of subsequent wind speed, turbine. wind direction, A precise andwake average model wind is critical speed for [5]. the Wind mathematical turbine farm modelling models investigate of a wind the farm profile and theof the optimal wind speedplacement deficit of downstream wind turbines of [the27]. rotor Considering that is captured the configuration by the subsequent of the wake, turbine. three A types pre- ciseof models wake model are presented: is critical for one-dimensional the mathematical wake modelling model, of two-dimensional a wind farm and wake the optimal model, placementand three-dimensional of wind turbines wake [27]. model. Considerin The one-dimensionalg the configuration wake modelof the wake, is the well-knownthree types ofJensen’s models model, are presented: the two-dimensional one-dimensional wake wake model model, is the two-dimensional Gaussian variation wake of Jensen’smodel, andmodel, three-dimensional named Jensen–Gaussian wake model. model, The one-dimensional and the three-dimensional wake model wake is the modelwell-known is the Jensen’sGaussian model, wake modelthe two-dimensional [27]. wake model is the Gaussian variation of Jensen’s model,Given named the thrustJensen–Gaussian coefficient curvemodel, of and the windthe three-dimensional turbine and the wind wake farm model design, is the the Gaussianwake effect wake models model can [27]. estimate the wake losses for each turbine. Apart from a reduction of theGiven turbine’s the thrust power coefficient generated, curve the of wake the wi effectnd turbine also leads and the to a wind dynamic farm loaddesign, on the the wakedownstream effect models turbine can [25 estimate]. SAM presentsthe wake threelosses different for each waketurbine. effect Apart methods from a to reduction estimate ofthe the effect turbine’s of upwind power turbines generated, in downwind the wake turbine effect also performance leads to asa dynamic follows: load on the

downstreamI Simple waketurbine model—applies [25]. SAM presents a thrust three coefficient different to calculatewake effect the methods wind speed to estimate deficit in the effecteach of turbine upwind due turbines to the wakein down effectwind of theturbine upwind performance turbines; as follows: .I SimpleWind resourceswake model assessment,—applies siting, a thrust and coefficient energy model to calcul (WAsPate model)—usesthe wind speed a declinedeficit inconstant each turbine to estimate due to thethe windwake speedeffect of deficit the upwind behind turbines; each turbine and computes the . Windoverlap resources of that assessment, wake profile siting, with theand downwind energy model turbine (WAsP to calculate model)—uses the wind a decline speed constantat the downwind to estimate turbine; the wind speed deficit behind each turbine and computes the I overlapEddy–viscosity—is of that wake analogousprofile with to the the down WAsPwind model, turbine and besidesto calculate that, the the wind wind speed speed atshortage the downwind behind eachturbine; turbine is presumed to have a Gaussian shape; . Eddy–viscosity—is analogous to the WAsP model, and besides that, the wind speed shortage behind each turbine is presumed to have a Gaussian shape; . Constant loss—estimates wake loss as a constant percentage reduction in the wind farm output.

Energies 2021, 14, 4291 10 of 22

I Constant loss—estimates wake loss as a constant percentage reduction in the wind farm output. According to Shao et al. and Dhiman et al. [39,40], in the simple wake model, the wind speed in the wake uΨ is a function of the thrust coefﬁcient (CT), and wake decline and is computed as follows:

" 2# p ro uΨ = uo 1 − 1 − 1 − CT [m/s] (20) ro + φx

−y2 Ct ( ) ∆u = e 2δ2x2 [m/s] (21) 4δ2x2

where Ct—is the thrust coefficient; x—is the downwind distance between two consecutive wind turbines [m]; y—is the crosswind distance between two consecutive√ wind turbines [m]; δ—is the local turbulence coefficient estimated as 50/ uo. In the WAsP method, the effective wind speed deficit at the downwind turbine is calculated using the following equation:

2 p ro Aoverl uΨ = uo 1 − 1 − CT [m/s] (22) ro + φx A1

where uo—is the inflow velocity [m/s]; CT—is the thrust coefficient; x—is the downwind distance behind two consecutive wind turbines [m2]; ro—is the rotor radius [m]; φ—is the decay coefficient (k = 0.075 for onshore wind farms) and (k = 0.05 for offshore wind farms); Aoverl—is the overlapped area of the swept area of the rotors; A—is the swept area of the upwind turbine’s rotor. Regarding the Eddy–viscosity wake model which has a Gaussian shape, the studies in [25,27] present the following equation to estimate the wind velocity at the downstream wind turbine: " s ! 2 # CT −r = − − − 2σ2 [ ] uΨ uo 1 1 1 2 e m/s (23) 8(σ/2ro) where CT—is the thrust coefficient; ro—is the rotor radius [m]; x—is the downwind distance between two consecutive wind turbines [m]; σ—is the wake wide [m]. In this study, the investigation began with the calculation of wind farm capacity by applying HOMER. Considering the daily load profile of the Namaacha District provided by EDM [35], the wind speed profile provided by FUNAE [32], and investment costs Energies 2021, 14, 4291 11 of 22

per kW power of wind technology presented by IRENA [41,42] and Mazzeo et al. [43], HOMER sized the 33 MW wind farm for the district composed of 20 V82-1.65 MW turbines. Then, by introducing the turbine type and other input data in the SAM, the three distinct wind farm layouts were examined. The Eddy–viscosity model presented by SAM was applied considering the following losses evaluated by SAM: wake losses, availability losses, electrical losses, turbine performance losses, environmental losses, and operational strategies losses. These distinct categories of losses are expressed as a percentage of the total annual system output before losses and are deﬁned to work in parallel with operating system uncertainties. Table2 presents the assumed percentage of losses.

Table 2. System’s estimated losses and operating uncertainties.

Designation Estimated Value (%) Turbine’s availability losses 5.0 Electrical losses 3.0 Turbine performance losses 4.0 Environmental losses 2.5 Operational strategies losses 2.0 Operating system uncertainties 7.5

Losses effectively influence the optimal generation dispatch [44]. During the wind farm evaluation phase, environmental losses due to icing and other atmospheric conditions need to be assessed. The environmental losses estimation incorporates relatively great uncertainties due to the complexity of atmospheric phenomena. From Turkia et al. [45], environmental losses can vary from 4 to 17%. Namaacha does not experiment with severe atmospheric conditions, and therefore, environmental losses are considered to be 2.5%. Electrical losses in power systems are inevitable and occur due to the resistance of the current flowing in the circuit. In wind farms, annual electrical losses range from 2 to 3% [46], and performance losses can reach 6% [47]. With the assumed losses, the wind farm’s wake losses were examined. Apart from the assumed losses, the wind farm layout was changed, and the effect of the losses on the system’s power output was optimised. The alteration in the layout of the wind farm was based on the arrangement of the erection of the turbines by modifying the distance between turbines and rows as well as the row orientation. With the change in orientation, the scattering of the turbines increases, and some turbines are not positioned behind the others. The desire of reducing the placement of the turbines one behind the other can also be achieved using the offset option of the rows. Figure7 illustrates the primary design of the wind farm composed of 20 turbines; a major disturbance in the performance of the wind farm can occur in the downstream turbines. The primary distance between the turbines in each row and the spacing between rows was demarcated as a function of the rotor diameter Do. The row orientation was defined to be 0◦, and thus, the lines are parallel to the equator. Regarding the offset of the rows, the value was set to L = 0 and the wind direction equal to ϕ = 0◦. In Figures8 and9, it can be observed that with the change in row orientation, the wind farm’s size increases. In a real wind farm, since wind direction continuously changes, the position of downstream turbines varies according to wind direction, and the wake effect in the wind farm also changes [48]. Energies 2021, 14, 4291 12 of 22 EnergiesEnergies 202120212021,, , 14 1414,, , x xx FOR FORFOR PEER PEERPEER REVIEW REVIEWREVIEW 131313 of ofof 24 2424

FigureFigure 7.7. OptimalOptimal wind windwind farm farmfarm (layout(layout 1)1) withwith thethe distancedistance betweenbetween turbines turbines equal equal to to 8D 8D0000,, , the thethe distance distancedistancedistance between rows equal to 10D0, and wind direction angle equal to 30°.◦ betweenbetween rowsrows equalequal toto 10D10D000,,, andandand windwindwind directiondirectiondirection angleangleangle equalequalequal tototo 3030°.30°..

Figure 8. Modified wind farm (layout 2), considering row orientation angle. FigureFigure 8.8. ModiﬁedModified windwind farmfarm (layout(layout 2),2), consideringconsidering rowrow orientationorientation angle.angle.

FigureFigure 9.9. ModifiedModified windwind farmfarm (layout(layout 3)3) consideringconsidering rowrow offset.offset. FigureFigure 9.9. ModiﬁedModified windwind farmfarm (layout(layout 3)3) consideringconsidering rowrow offset.offset.

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The wind speed in thethe farmfarm waswas assumedassumed toto varyvary betweenbetween 4.44.4 toto 88 m/s;m/s; FigureFigure 1010 illustrates the the distribution distribution of of the the wind wind speed’s speed’s probability probability of of occurrence. occurrence. From From Figure Figure 6,6 it, itis isobserved observed that that the the V82-1.65 V82-1.65 turbine turbine presen presentsts better better values values of power of power for forwind wind speed speed be- betweentween 4 to 4 to10 10m/s. m/s.

Figure 10. Distribution of the wind speed’s probability of occurrence.

In this study, thethe followingfollowing threethree differentdifferent windwind farmfarm layoutslayouts werewere analysed:analysed: I. LayoutLayout 1 1:: examined examined the the influence influence of of the the increased increased distance distance between between turbines turbines and and the spacingthe spacing between between lines. lines. The Thedistances distances between between turbines turbines used used were were 2Do 2D, 4Do,o, 4D 6Doo,, 6Dando, 8Dando, while 8Do, while the spacing the spacing between between rows used rows was used 2D waso, 4D 2Do,o 6D, 4Do, o8D, 6Do, 10Do, 8Do, oand, 10D 12Do, ando. In this12D layout,o. In this in layout, addition in to addition varying to the varying distance the between distance turbines between and turbines lines, andthe lines,wind directionthe wind varied direction from varied 0° to from 60°. SAM 0◦ to 60cons◦. SAMiders considerswind direction wind equal direction to 0° equal when to the 0◦ windwhen blows the wind from blows north from to south. north toRow south. orientation Row orientation angle and angle row and offset row was offset main- was tainedmaintained as β =as 0°β and= 0 L◦ and= 0, respectively. L = 0, respectively. I. LayoutLayout 2 2:: examined examined the the influence influence of of changing changing the the row row orientation orientation angle. The The follow- follow- inging angles angles were were used: used: 5°, 5◦ 10°,, 10◦ 15°,, 15 ◦20°,, 20 ◦25°,, 25 and◦, and 30°. 30 The◦. The optimal optimal distance distance between between the turbinesthe turbines and and the therows, rows, as aswell well as asthe the wind wind direction, direction, was was maintained maintained at 8D8Doo, 10D10Doo, andand 30°, 30◦, respectively. respectively. I. LayoutLayout 3 3:: examined examined the the influence influence of of increased increased scattering scattering of the turbines byby changingchanging thethe row row offset. The followingfollowing offsetoffset rowsrows werewere used:used: 0,0, 0.5D 0.5Doo,D, Doo 1.5D1.5Doo,, 2D2Doo,, 2.5D2.5Doo, andand 3D 3Doo.. The The optimal optimal distance distance between between the the turbines turbines and the rows, as well asas thethe windwind ◦ direction,direction, was was maintained maintained at 8D oo,, 10D 10Doo, ,and and 30°, 30 ,respectively. respectively.

5. Results and Discussion Taking intointo accountaccount thethe dailydaily variationvariation ofof energyenergy consumption,consumption, thethe district’sdistrict’s windwind energy potential, and costs of the wind technology, HOMERHOMER estimatedestimated that the necessary capacity ofof thethe windwind farm farm is is about about 33 33 MW, MW, comprising comprising 20 V82-1.6520 V82-1.65 MW MW turbines. turbines. Given Given the thrustthe thrust coefficient coefficient curve curve of the of wind the wind turbine turb andine the and wind the farm wind design, farm design, wake effect wake models effect canmodels estimate can estimate the wake the losses wake in losses the wind in the farm. wind Apart farm. from Apart a reductionfrom a reduction of turbines of turbines power generation,power generation, the wake the effect wake also effect leads also to leads a dynamic to a dynamic load on load the on downstream the downstream turbine turbine [25]. Figure 11 illustrates the wind site’s power generation according to the wind direction. [25]. When the wind direction is zero (from north to south), the disturbances in the air masses in Figure 11 illustrates the wind site’s power generation according to the wind direc- the downstream turbines are more intense. Different from traditional energy resources, the tion. When the wind direction is zero (from north to south), the disturbances in the air wind resource has single features because of its temporal and seasonal variation. Therefore, masses in the downstream turbines are more intense. Different from traditional energy wind power output technology fluctuates more strongly than traditional fossil fuel energy resources, the wind resource has single features because of its temporal and seasonal var- sources [16]. The change in wind direction creates temporary modifications in the wind iation. Therefore, wind power output technology fluctuates more strongly than traditional

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Energies 2021, 14, 4291 14 of 22 fossil fuel energy sources [16]. The change in wind direction creates temporary modifica- fossil fuel energy sources [16]. The change in wind direction creates temporary modifications in the wind farm layout and consequently the variation in power generation. From tions in the wind farm layout and consequently the variation in power generation. From farmthe analysis, layout and it was consequently observed that the variationthe highest in rate power of energy generation. production From theoccurs analysis, from ita wind was the analysis, it was observed that the highest rate of energy production occurs from a wind observeddirection thatof 30°. the highest rate of energy production occurs from a wind direction of 30◦. direction of 30°.

Layout-1: System's power output with wind Layout-1: System's power output with wind direction direction 75,000 75,000 70,000 70,000 65,000 65,000 60,000 60,000 55,000 55,000 50,000

Power outpou (MWh) Power outpou 50,000

Power outpou (MWh) Power outpou 0 10203040506070 0 10203040506070 Wind direction (degree) Wind direction (degree)

Figure 11. System’s power output for different wind directions. FigureFigure 11. 11.System’s System’s power power output output for for different different wind wind directions. directions. Taking into account the distance between the turbines and the lines assumed in lay- Taking into account the distance between the turbines and the lines assumed in layout Taking1 of the into wind account farm, theFigures distance 12 and between 13 illustrate the turbines the system’s and the power lines assumed output and in layout wake out 1 of the wind farm, Figures 12 and 13 illustrate the system’s power output and wake 1losses, of the windrespectively. farm, Figures As can 12 beand perceived, 13 illustrate by the increasing system’s the power distance, output the and power wake losses,can be losses, respectively. As can be perceived, by increasing the distance, the power can be respectively.improved and As wake can be losses perceived, reduced, by increasing but an ex thecessive distance, increase the powerin the candistance be improved between improved and wake losses reduced, but an excessive increase in the distance between andlines wake can lossescause reduced,a decline but in anpower excessive generation increase since, in the in distancea real wind between farm, lines the candecline cause in alines decline can in cause power a generationdecline in power since, in generation a real wind since, farm, in the a declinereal wind in powerfarm, the generation decline isin power generation is due to both the wake effect and the decrease of the wind mass load. duepower to bothgeneration the wake is due effect to andboth the the decrease wake effe ofct the and wind the decrease mass load. of the On wind the other mass hand, load. On the other hand, although there is a marked gain in power generation and reduction of althoughOn the other there hand, is a marked although gain there in power is a marked generation gain andin power reduction generation of wake and effect reduction with the of wake effect with the distance between turbines from 2Do to 4Do, in contrast to that, with distancewake effect between with turbinesthe distance from between 2Do to 4D turbineso, in contrast from 2D too that, to 4D witho, in the contrast distance to that, between with the distance between turbines from 4Do to 8Do, the power generated remains practically turbinesthe distance from between 4D to 8D turbines, the power from generated4Do to 8Do remains, the power practically generated constant. remains practically constant. o o constant.

Layout 1: System's power output Layout 1: System's power output 74,000 74,000 67,000 67,000 60,000 60,000 53,000 53,000 46,000 46,000 39,000 39,000 32,000 32,000

Power output (MWh) Power output 25,000

Power output (MWh) Power output 25,000 2Do 4Do 6Do 8Do 10Do 12Do 2Do 4Do 6Do 8Do 10Do 12Do Rows distance Rows distance Turbines distance=2Do Turbines distance=4Do Turbines distance=2Do Turbines distance=4Do Turbines distance=6Do Turbines distance=8Do Turbines distance=6Do Turbines distance=8Do

Figure 12. System’s power output for different distances between turbines and rows. FigureFigure 12. 12.System’s System’s power power output output for for different different distances distances between between turbines turbines and and rows. rows.

For row spacing of 2Do and distance between turbines of 8Do, maximum wake loss is For row spacing of 2Do and distance between turbines of 8Do, maximum wake loss is about 50%. A similar study [7] found a maximum wind deficit of approximately 45%, at a about 50%. A similar study [7] found a maximum wind deficit of approximately 45%, at a

Energies 2021, 14, x FOR PEER REVIEW 16 of 24

downstream distance of 2.5Do, and 35% at 3.5Do. Therefore, it is assumed that the optimal distance between turbines is 8Do, and the optimal spacing between rows is 10Do since this Energies 2021, 14, 4291 combination presents the highest energy production (71,844.0 MWh) and the lowest15 ofwake 22 loss (1.7%). In terms of surface, layout 1 occupies approximately 6. 46 km2 (46.1%) of the Energies 2021, 14, x FOR PEER REVIEWavailable land. 16 of 24

Layout 1: System's wake losses downstream distance of 2.5Do, and 35% at 3.5Do. Therefore, it is assumed that the optimal 70 distance between turbines is 8Do, and the optimal spacing between rows is 10Do since this combination60 presents the highest energy production (71,844.0 MWh) and the lowest wake loss (1.7%).50 In terms of surface, layout 1 occupies approximately 6. 46 km2 (46.1%) of the available40 land. 30 20 Layout 1: System's wake losses

Wake losses (%) 10 700 60 2Do 4Do 6Do 8Do 10Do 12Do 50 Rows distance 40 30 Turbines distance=2Do Turbines distance=4Do 20 Turbines distance=6Do Turbines distance=8Do

Wake losses (%) 10 Figure 013. System’s wake losses for different distances between turbines and rows. Figure 13. System’s2Do wake losses 4Do for different 6Do distances between8Do turbines 10Do and rows. 12Do Taking into account all the variableRows assumed distance losses, Figure 14 specifies the probabil- For row spacing of 2Do and distance between turbines of 8Do, maximum wake loss is aboutity density 50%. A function similar studyof the [annual7] found energy a maximum delivered wind and deﬁcit estimates of approximately the predicted 45%, losses. at aIn downstreamthis layout, distanceconsideringTurbines of 2.5D p50 distance=2Doo, probability, and 35% at 3.5D annualo.Turbines Therefore, gross energy distance=4Do it is assumed is about that89.49 the GWh, optimal and predicted losses are around 17,653.2 MWh. distance between turbinesTurbines is distance=6Do 8Do, and the optimalTurbines spacing betweendistance=8Do rows is 10Do since this combination presents the highest energy production (71,844.0 MWh) and the lowest wake 2 lossFigure (1.7%). 13. System’s In terms wake of surface,losses for layoutdifferent 1 occupiesdistances between approximately turbines 6.and 46 rows. km (46.1%) of the available land. Taking intointo accountaccount allall thethe variablevariable assumed assumed losses, losses, Figure Figure 14 14 speciﬁes specifies the the probability probabil- densityity density function function of the of the annual annual energy energy delivered delivered and and estimates estimates the predictedthe predicted losses. losses. In this In layout,this layout, considering considering p50 probability, p50 probability, annual annual gross energy gross isenergy about 89.49is about GWh, 89.49 and GWh, predicted and lossespredicted are aroundlosses are 17,653.2 around MWh. 17,653.2 MWh.

Figure 14. System’s predicted losses considering wake losses (layout 1). The performance of wind turbines is governed by both external conditions and turbine operation parameters, and thus, wind farm design uncertainties result in distinct factors such as wind speed measurement process, wake effects, terrain effects, extreme events, aerodynamics, and control [49]. Figure 15 displays year 1 probability distribution for the wind farm. In the wake losses analysis, the P50 energy production level is the mean Figureenergy 14. productionSystem’s predicted estimation, losses consideringassuming a wake 50% losses probability (layout 1).of achieving annual power Figure 14. System’s predicted losses considering wake losses (layout 1). The performance of wind turbines is governed by both external conditions and turbine The performance of wind turbines is governed by both external conditions and tur- operation parameters, and thus, wind farm design uncertainties result in distinct factors bine operation parameters, and thus, wind farm design uncertainties result in distinct fac- such as wind speed measurement process, wake effects, terrain effects, extreme events, tors such as wind speed measurement process, wake effects, terrain effects, extreme aerodynamics, and control [49]. Figure 15 displays year 1 probability distribution for the events, aerodynamics, and control [49]. Figure 15 displays year 1 probability distribution wind farm. In the wake losses analysis, the P50 energy production level is the mean energy for the wind farm. In the wake losses analysis, the P50 energy production level is the mean energy production estimation, assuming a 50% probability of achieving annual power

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generation.generation. A probabilityA probability factor factor greater greater than than 50, 50, such such as asp95, p95, represents represents more more uncertainties uncertainties production estimation, assuming a 50% probability of achieving annual power generation. presumedpresumed and and therefore therefore high high predicted predicted losses. losses. On On the the contrary, contrary, probability probability factor factor minor minor A probability factor greater than 50, such as p95, represents more uncertainties presumed thanthan 50 50 such such as asp16 p16 represents represents slight slight uncertainties uncertainties presumed presumed and and therefore therefore small small pre- pre- and therefore high predicted losses. On the contrary, probability factor minor than 50 such dicteddicted losses. losses. as p16 represents slight uncertainties presumed and therefore small predicted losses.

Figure 15. System’s P16, P50, P84, P95, P99 probability of annual energy production (layout 1). FigureFigure 15. 15.System’s System’s P 16P16,P, P5050,P, P8484,P, P9595,,P P99 probabilityprobability of of annual annual energy energy production production (layout (layout 1). 1).

FigureFigureFigure 1616 16 presentspresents presents the the the fluctuation fluctuation fluctuation of of ofthe the the power power power output output output system system system and and and wake wake wake losses losses losses with with with rowrowrow orientation. orientation. orientation. The TheThe analysis analysisanalysis was was performed performed performed to tocompare to compare compare the the thewake wake wake losses losses losses in inlayout inlayout layout 1 and1 and 1 layoutandlayout layout 2. 2.From From 2. the From the analysis, analysis, the analysis, it isit isobserved observed it is observed that that the the that minimum minimum the minimum losses losses verifiedlosses verified verifiedwith with modifi- modifi- with cationmodificationcation of ofrow row orientation of orientation row orientation are are of ofa higherarea higher of amagn higher magnitudeitude magnitude than than the the thanminimum minimum the minimum losses losses in inlayout losses layout 1. in 1. ◦ WithlayoutWith rows 1.rows With orientation orientation rows orientation angle angle β =β 0°, angle= 0°, layout layoutβ = 1 0 predicted 1, layoutpredicted 1 losses predicted losses in inthe losses the order order in of the of1.7%, order1.7%, and ofand with 1.7%, with ◦ theandthe variation with variation the of variation ofthe the row’s row’s of theorientation, orientation, row’s orientation, the the angle angle theβ =β angle 20°= 20° presented βpresented= 20 presented losses losses in inthe losses the order order inthe of of 2.3%.order2.3%. of 2.3%.

LayoutLayout 2: 2: System's System's power power output output and and wake wake losses losses 72,00072,000 1414 70,50070,500 1212 69,000 69,000 1010 67,50067,500 8 8 66,00066,000 6 6 64,50064,500 4 4

63,000 (%) losses Wake

63,000 (%) losses Wake Power output (MWh) output Power 61,500(MWh) output Power 61,500 2 2 60,00060,000 0 0 00 5 5 10 10 15 15 20 20 25 25 30 30 35 35 RowRow orientation orientation (º) (º)

System'sSystem's power power output output System'sSystem's wake wake losses losses

Figure 16. System’s power output for different rows orientation angles. FigureFigure 16. 16.System’s System’s power power output output for for different different rows rows orientation orientation angles. angles.

TakingTakingTaking into into accountaccount account allall theall the the assumed assumed assumed variables, variables, variables, layout layout layout 2 presented 2 presented2 presented an annual an an annual annual predicted pre- pre- dictedlossdicted of loss about loss of ofabout 18103.2 about 18103.2 18103.2 MWh MWh (see MWh Figure(see (see Figure Figure17). 17). In 17). this In Inthis layout, this layout, layout, annual annual annual power power power production production production in

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in year 1 is estimated as 71.39 GWh, and in terms of surface, layout 2 occupies approxi- in year 1 is estimated as 71.39 GWh, and in terms of surface, layout 2 occupies approxi- yearmately 1 is 11.12 estimated km2 (79.4%) as 71.39 of GWh, the available and in terms land. of surface, layout 2 occupies approximately 2 mately11.12 km 11.122 (79.4%) km (79.4%) of the availableof the available land. land.

FigureFigure 17. 17.System’s System’s predicted predicted losses losses considering considering wake wake losses losses (layout (layout 2). 2). Figure 17. System’s predicted losses considering wake losses (layout 2). WakeWake losses losses in in layout layout 2 2 are are signiﬁcant significant when when the the wind wind direction direction coincides coincides with with the the Wake losses in layout 2 are significant when the wind direction coincides with the directiondirection comprising comprising the the largest largest number number of of turbines, turbines, as as presented presented in in Figure Figure 18 18.. direction comprising the largest number of turbines, as presented in Figure 18.

Figure 18. The region with intense wake effect in the layout 2. FigureFigure 18. 18. TheThe region region with with intense intense wake wake effect effect in in the the layout layout 2. 2. RegardingRegarding layout layout 3, 3, Figure Figure 19 19 displays displays the the variation variation of of the the power power output output system system and and Regarding layout 3, Figure 19 displays the variation of the power output system and wakewake losses losses with with row row offset. offset. The The analysis analysis aims aims to to compare compare the the system’s system’s performance performance in in wake losses with row offset. The analysis aims to compare the system’s performance in layoutlayout 1 1 and and layout layout 3. 3. From From the the results, results, it is it observed is observed that thethat minimum the minimum losses losses veriﬁed verified with layout 1 and layout 3. From the results, it is observed that the minimum losses verified rowwith offset row areoffset of aare higher of a higher magnitude magnitude than the than minimum the minimum losses inlosses layout in layout 1 with rows1 with offset rows with row offset are of a higher magnitude than the minimum losses in layout 1 with rows Loffset = 0. Applying L = 0. Applying the strategy the stra of rowtegy offset,of row the offset, minimum the minimum losses are losses achieved are achieved with L = 0.5Dwitho L offset L = 0. Applying the strategy of row offset, the minimum losses are achieved with L and= 0.5D represento and represent 2.3%. However, 2.3%. However, this percentage this percenta is abovege is above the minimal the minimal losses losses obtained obtained in = 0.5Do and represent 2.3%. However, this percentage is above the minimal losses obtained layoutin layout 1. In1. termsIn terms of of surface, surface, layout layout 3 occupies3 occupies approximately approximately 6.82 6.82 km km2 (48.7%)2 (48.7%) of of the the in layout 1. In terms of surface, layout 3 occupies approximately 6.82 km2 (48.7%) of the availableavailable land. land. available land.

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LayoutLayout 3: 3: System's System's power power output output an an wake wake losses losses 73,00073,000 1010 71,500 71,500 8 8 70,00070,000 6 6 68,50068,500 4 4 67,00067,000 Wake losses (%) 65,500 2 2 Wake losses (%) Power output (MWh) Power output 65,500 Power output (MWh) Power output 64,00064,000 0 0 0.00.0 1.0 1.0 2.0 2.0 3.0 3.0 4.0 4.0 5.0 5.0 6.0 6.0 RowRow offset offset (Do) (Do)

System'sSystem's power power output output System'sSystem's Wake Wake losses losses

Figure 19. System’s power output for different row offset. FigureFigure 19.19.System’s System’s powerpower outputoutput forfor differentdifferent row row offset. offset.

ConsideringConsideringConsidering the thethe variable variablevariable assumed, assumed,assumed, layout layoutlayout 3 33presented presentedpresented an anan annual annualannual predicted predictedpredicted loss lossloss of ofof aboutaboutabout 18,117.0 18,117.0 18,117.0 MWh, MWh, MWh, as as as illustrated illustrated illustrated in in Figure Figure 2020. 20.. InIn In thisthis this layout,layout, layout, annualannual annual power power power production production production in inyearin year year 1 1 is is1 estimated isestimated estimated as as71.37 as 71.37 71.37 GWh. GWh. GWh.

Figure 20. System’s predicted losses considering wake losses (layout 3). FigureFigure 20. 20. System’s System’s predicted predicted losses losses considering considering wake wake losses losses (layout (layout 3). 3). 6. Conclusions 6. 6.Conclusions Conclusions The study investigated the wake effect in the wind farm in the District of Namaacha dueThe toThe thestudy study wind investigated investigated farm’s layout. the the wake wake Considering effect effect in in th the the winde wind constraint farm farm in in ofthe the land District District availability, of of Namaacha Namaacha three duedifferentdue to to the the dispositionswind wind farm’s farm’s oflayout. layout. the turbines Considering Considering in the th wind the constrainte constraint farm were of of land studied land availability, availability, in order tothree three find dif- outdif- ferenttheferent placement dispositions dispositions that of wouldof the the turbines turbines minimise in in the wakethe wind wind losses farm farm with were were efficient studied studied utilisation in in order order to ofto find land.find out out From the the placementtheplacement results, that that it waswould would concluded minimise minimise that wake wake the losses influence losses with with of efficient theefficient wake utilisation utilisation effect is of unpredictable of land. land. From From the but the results,canresults, be it minimised itwas was concluded concluded with anthat that adequate the the influence influence disposition of of the the wake of wake the effect turbineseffect is isunpredictable unpredictable and optimal but distancing. but can can be be minimisedRegardingminimised with the with spacingan an adequate adequate between disposition disposition turbines, of layoutof the the turbines 1turbines demonstrated and and optimal optimal that distancing. the distancing. optimal Regard- distance Regard- ingbetweening the the spacing spacing turbines between between is about turbines, turbines, 8Do and layout layout the optimal 1 1de demonstratedmonstrated distance betweenthat that the the optimal rows optimal is arounddistance distance 10D be- be-o. tweenThetween examination turbines turbines is isabout of about the 8D longitudinal 8Do ando and the the optimal distance optimal distance betweendistance between thebetween turbines rows rows showed is isaround around that 10D the10Do. wakeoThe. The

Energies 2021, 14, 4291 19 of 22

effect begins to decline from 4Do, and the tendency continues until 10Do. After 10Do, the energy losses due to the wake effect begin to increase again. In relation to the transversal distance between the turbines, the wake effect would start to reduce from 6Do, but the optimal transversal distance being about 8Do. The increment of the transversal distance above 8Do brings a slight gain of power production associated with high use of land, and therefore, it is not recommended. It is noted that layout 1, compared with layout 2, shows a minor percentage of loss (1.7%) and also lower use of available land (46%). In layout 2, due to the rotation of the rows, in the diagonal line of the wind farm, the wind mass crosses a greater number of turbines, and consequently, there is an increase in power losses as a result of the wake effect. The wake losses in layout 2 are around 2.3%, and therefore, the study proves that in real wind farms, when the wind direction coincides with the line comprising the largest number of turbines, wake losses can be signiﬁcant, and this usually occurs in the diagonal lines of the wind farm. On the other hand, in the diagonal line, in addition to the superior number of turbines, the spacing between two consecutive turbines exceeds the optimum distance of 10Do, and thus, in addition to the increase in losses, there is an inefﬁcient use of land. With respect to the comparison between layout 1 and layout 3, the results emphasise the robustness of layout 1, since the layout continues to present minor wake losses and percentage of used land. Note that layout 3 presents losses in the order of 2.3%, as well as layout 2, but land occupation is 48.7%. However, in terms of preference between layout 2 and layout 3, the last one presents less land occupation which is an advantage.

Author Contributions: Conceptualisation, P.M.J.R., S.P.C. and Z.H.; Methodology, P.M.J.R. and S.P.C.; Validation, P.M.J.R., S.P.C. and Z.H.; formal analysis, P.M.J.R., S.P.C. and Z.H.; investigation, P.M.J.R., S.P.C. and Z.H.; resources, P.M.J.R.; data curation, P.M.J.R., S.P.C. and Z.H.; writing—original draft preparation, P.M.J.R. and S.P.C.; writing—review and editing, P.M.J.R., S.P.C. and Z.H.; visualisation, P.M.J.R., S.P.C. and Z.H. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Informed Consent Statement: The authors hereby agree to publish this paper as Co-Authors in the sequence of Names as above on the basis of our (1) contributions and participations in formulating the research problem, or analysing and interpreting the data or have made other substantial scholarly effort or a combination of these; and/or (2) participations in writing the paper; and (3) approvals of the final version for publication and preparedness to defend the publication against criticisms. Data Availability Statement: Data collected from FUNAE, Mozambique with permission. Acknowledgments: The authors would like to acknowledge the Tshwane University of Technology, Departments of Electrical and Mechanical and Mechatronics Engineering, Pretoria, South Africa, for all the conditions provided in order to conduct the research and writing of this paper. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

u1 Upstream wind speed approaching the turbine [m/s] u2 Wind speed at the rotor [m/s] u3 Downstream wind speed [m/s] • m Air mass ﬂow rate [kg/s] F Force on the turbine resulting from the air mass ﬂow [N] PwT Power extracted by the turbine [W] Pext Energy extracted from the wind [W] ρ Air density [kg/m3] A Swept area of the blades [m2] 2 Aoverl Overlapped area of the swept area of the rotors [m ] Energies 2021, 14, 4291 20 of 22

b Interference factor P1 Power of the undisturbed upstream air mass Cp Power coefficient k Shape factor c Scale factor uhub Wind speed at the hub height of the turbine [m/s] uanem Wind speed at the anemometer height [m/s] Zhub Hub height of the turbine [m] Zanem Anemometer height [m] Zo Surface roughness length [m] γ Power law exponent PwT(stp) Turbine power output at standard temperature and pressure conditions [W] 3 ρo Air density at standard temperature and pressure conditions [kg/m ] CT Thrust coefficient ro Rotor radius [m] φ Decay coefficient x Downwind distance between two consecutive wind turbines [m] y Crosswind distance between two consecutive wind turbines [m] δ Local turbulence coefficient σ Wake wide [m] ϕ Wind direction [◦] β Turbines row orientation angle [◦] Do Rotor diameter [m] L Row offset distance [m]

References 1. Moussa, M.O. Experimental and numerical performances analysis of a small three blades wind turbine. Energy 2020, 203, 117807. [CrossRef] 2. Wilkie, D.; Galasso, C. Impact of climate-change scenarios on offshore wind turbine structural performance. Renew. Sustain. Energy Rev. 2020, 134, 110323. [CrossRef] 3. Nazir, M.S.; Alturise, F.; Alshmrany, S.; Nazir, H.M.J.; Bilal, M.; Abdalla, A.N.; Sanjeevikumar, P.; Ali, Z.M. Wind generation forecasting methods and proliferation of artificial neural network: A review of five years research trend. Sustainability 2020, 12, 3778. [CrossRef] 4. Ulazia, A.; Ibarra-Berastegi, G.; Sáenz, J.; Carreno-Madinabeitia, S.; González-Rojí, S.J. Seasonal Correction of Offshore Wind Energy Potential due to Air Density: Case of the Iberian Peninsula. Sustainability 2019, 11, 3648. [CrossRef] 5. Guo, P.; Chen, S.; Chu, J.; Infield, D. Wind direction fluctuation analysis for wind turbines. Renew. Energy 2020, 162, 1026–1035. [CrossRef] 6. Urabe, C.T.; Saitou, T.; Kataoka, K.; Ikegami, T.; Ogimoto, K. Positive Correlations between Short-Term and Average Long-Term Fluctuations in Wind Power Output. Energies 2021, 14, 1861. [CrossRef] 7. Sun, H.; Gao, X.; Yang, H. A review of full-scale wind-field measurements of the wind-turbine wake effect and a measurement of the wake-interaction effect. Renew. Sustain. Energy Rev. 2020, 132, 110042. [CrossRef] 8. Veludurthi, A.; Bolleddu, V. Experimental buckling analysis of NACA 63415 aerofoil wind turbine blade. Mater. Today Proc. 2021, 46, 205–211. [CrossRef] 9. Rahgozar, S.; Pourrajabian, A.; Kazmi, S.A.A. Performance analysis of a small horizontal axis wind turbine under the use of linear/nonlinear distributions for the chord and twist angle. Energy Sustain. Dev. 2020, 58, 42–49. [CrossRef] 10. Fant, C.; Gunturu, B.; Schlosser, A. Characterizing wind power resource reliability in southern Africa. Appl. Energy 2016, 161, 565–573. [CrossRef] 11. Jin, G.; Zong, Z.; Jiang, Y.; Zou, L. Aerodynamic analysis of side-by-side placed twin vertical-axis wind turbines. Ocean Eng. 2020, 209, 107296. [CrossRef] 12. Leelakrishnan, E.; Kumar, M.S.; Selvaraj, S.D.; Vignesh, N.S.; Raja, T.A. Numerical evaluation of optimum tip speed ratio for darrieus type vertical axis wind turbine. Mater. Today Proc. 2020, 33, 4719–4722. [CrossRef] 13. Vergaerde, A.; De Troyer, T.; Muggiasca, S.; Bayati, I.; Belloli, M.; Kluczewska-Bordier, J.; Parneix, N.; Silvert, F.; Runacres, M.C. Experimental characterisation of the wake behind paired vertical-axis wind turbines. J. Wind. Eng. Ind. Aerodyn. 2020, 206, 104353. [CrossRef] 14. Boudounit, H.; Tarfaoui, M.; Saifaoui, D. Modal analysis for optimal design of offshore wind turbine blades. Mater. Today Proc. 2020, 30, 998–1004. [CrossRef] 15. Ouammi, A.; Dagdougui, H.; Sacile, R.; Mimet, A. Monthly and seasonal assessment of wind energy characteristics at four monitored locations in Liguria region (Italy). Renew. Sustain. Energy Rev. 2010, 14, 1959–1968. [CrossRef] Energies 2021, 14, 4291 21 of 22

16. Feroz, R.M.A.; Javed, A.; Syed, A.H.; Kazmi, S.A.A.; Uddin, E. Wind speed and power forecasting of a utility-scale wind farm with inter-farm wake interference and seasonal variation. Sustain. Energy Technol. Assess. 2020, 42, 100882. [CrossRef] 17. Longo, R.; Nicastro, P.; Natalini, M.; Schito, P.; Mereu, R.; Parente, A. Impact of urban environment on Savonius wind turbine performance: A numerical perspective. Renew. Energy 2020, 156, 407–422. [CrossRef] 18. Regodeseves, P.G.; Morros, C.S. Unsteady numerical investigation of the full geometry of a horizontal axis wind turbine: Flow through the rotor and wake. Energy 2020, 202, 117674. [CrossRef] 19. Ali, Q.S.; Kim, M.H. Unsteady aerodynamic performance analysis of an airborne wind turbine under load varying conditions at high altitude. Energy Convers. Manag. 2020, 210, 112696. [CrossRef] 20. Hohman, T.; Martinelli, L.; Smits, A. The effect of blade geometry on the structure of vertical axis wind turbine wakes. J. Wind. Eng. Ind. Aerodyn. 2020, 207, 104328. [CrossRef] 21. Pallotta, A.; Pietrogiacomi, D.; Romano, G. HYBRI—A combined Savonius-Darrieus wind turbine: Performances and flow fields. Energy 2020, 191, 116433. [CrossRef] 22. Wang, Z.; Wang, S.; Ren, J.; Meng, X.; Wu, Y. Model experiment study for ventilation performance improvement of the Wind Energy Fan system by optimizing wind turbines. Sustain. Cities Soc. 2020, 60, 102212. [CrossRef] 23. Fei, Z.; Tengyuan, W.; Xiaoxia, G.; Haiying, S.; Hongxing, Y.; Zhonghe, H.; Yu, W.; Xiaoxun, Z. Experimental study on wake interactions and performance of the turbines with different rotor-diameters in adjacent area of large-scale wind farm. Energy 2020, 199, 117416. [CrossRef] 24. Abraham, A.; Hong, J. Dynamic wake modulation induced by utility-scale wind turbine operation. Appl. Energy 2020, 257, 114003. [CrossRef] 25. Dhiman, H.S.; Deb, D.; Foley, A.M. Bilateral Gaussian Wake Model Formulation for Wind Farms: A Forecasting Based Approach. Renew. Sustain. Energy Rev. 2020, 127, 109873. [CrossRef] 26. Ge, M.; Zhang, S.; Meng, H.; Ma, H. Study on interaction between the wind-turbine wake and the urban district model by large eddy simulation. Renew. Energy 2020, 157, 941–950. [CrossRef] 27. Tao, S.; Xu, Q.; Feijóo, A.; Zheng, G.; Zhou, J. Wind farm layout optimization with a three-dimensional Gaussian wake model. Renew. Energy 2020, 159, 553–569. [CrossRef] 28. Saad, A.S.; El-Sharkawy, I.I.; Ookawara, S.; Ahmed, M. Performance enhancement of twisted-bladed Savonius vertical axis wind turbines. Energy Convers. Manag. 2020, 209, 112673. [CrossRef] 29. Dorel, S.F.; Mihai, G.A.; Nicusor, D. Review of Specific Performance Parameters of Vertical Wind Turbine Rotors Based on the SAVONIUS Type. Energies 2021, 14, 1962. [CrossRef] 30. Sedighi, H.; Akbarzadeh, P.; Salavatipour, A. Aerodynamic performance enhancement of horizontal axis wind turbines by dimples on blades: Numerical investigation. Energy 2020, 195, 117056. [CrossRef] 31. Twidell, J.; Weir, T. Renewable Energy Resources, 2nd ed.; Renewable Energy Resources in ASEAN; Taylor and Francis: 2018. pp. 4–10. Available online: http://www.uobabylon.edu.iq/eprints/publication_4_10679_78.pdf (accessed on 14 July 2020). 32. Fundo Nacional de Energia. Renewable Energy Atlas of Mozambique; Gesto Energia S.A.: Maputo, Mozambique, 2014. 33. Minister of Energy Mozambique, Riso National Laboratoty-Denmark. Support for Wind Power Development in Mozambique Final Report (Draft) June 2008; DNER Risø Danida: Copenhagen, Denmark, 2008. 34. Mokveld, K.; von Eije, S. Final Energy Report Mozambique; Netherlands Enterprise Agency: Assen, The Netherlands, 2018; pp. 1–43. 35. EDM. Annual Statistical Report 2016; EDM: Maputo, Mozambique, 2016. 36. Chaouachi, A.; Covrig, C.F.; Ardelean, M. Multi-criteria selection of offshore wind farms: Case study for the Baltic States. Energy Policy 2017, 103, 179–192. [CrossRef] 37. Veena, R.; Manuel, S.; Mathew, S.; Petra, I. Parametric Models for Predicting the Performance of Wind Turbines. Mater. Today Proc. 2020, 24, 1795–1803. [CrossRef] 38. Sun, H.; Yang, H. Numerical investigation of the average wind speed of a single wind turbine and development of a novel three-dimensional multiple wind turbine wake model. Renew. Energy 2020, 147, 192–203. [CrossRef] 39. Shao, Z.; Wu, Y.; Li, L.; Han, S.; Liu, Y. Multiple Wind Turbine Wakes Modeling Considering the Faster Wake Recovery in Overlapped Wakes. Energies 2019, 12, 680. [CrossRef] 40. Dhiman, H.S.; Deb, D.; Balas, V.E. Supervised learning for forecasting in presence of wind wakes. In Supervised Machine Learning in Wind Forecasting and Ramp Event Prediction; Academic Press: Cambridge, MA, USA, 2020; pp. 141–169. 41. International Renewable Energy Agency. Renewable Power Generation Costs in 2017; IRENA: Abu Dhabi, United Arab Emirates, 2018. 42. International Renewable Energy Agency. Electricity Storage and Renewables: Costs and Markets to 2030; IRENA: Abu Dhabi, United Arab Emirates, 2017. 43. DMazzeo, D.; Baglivo, C.; Matera, N.; De Luca, P.; Congedo, P.M.; Oliveti, G. Energy and economic dataset of the worldwide optimal photovoltaic-wind hybrid renewable energy systems. Data Brief 2020, 33, 106476. [CrossRef] 44. Farahmand, H.; Warland, L.; Huertas-Hernando, D. The Impact of Active Power Losses on the Wind Energy Exploitation of the North Sea. Energy Procedia 2014, 53, 70–85. [CrossRef] 45. Turkia, V.; Huttunen, S.; Wallenius, T. Method for Estimating Wind Turbine Production Losses due to Icing; VTT Technical Research Centre of Finland: Espoo, Finland, 2013. Energies 2021, 14, 4291 22 of 22

46. Colmenar-Santos, A.; Campíñez-Romero, S.; Enríquez-Garcia, L.A.; Pérez-Molina, C. Simpliﬁed analysis of the electric power losses for on-shore wind farms considering weibull distribution parameters. Energies 2014, 7, 6856–6885. [CrossRef] 47. Byrne, R.; Astolﬁ, D.; Castellani, F.; Hewitt, N.J. A Study of Wind Turbine Performance Decline with Age through Operation Data Analysis. Energies 2020, 13, 2086. [CrossRef] 48. Ge, X.; Chen, Q.; Fu, Y.; Chung, C.Y.; Mi, Y. Optimization of maintenance scheduling for offshore wind turbines considering the wake effect of arbitrary wind direction. Electr. Power Syst. Res. 2020, 184, 106298. [CrossRef] 49. Premkumar, P.S.; Nadaraja P., S.; Arunvinthan, S.; Sivaraja, S.; Vinayagamurthy, G.V.; Peradotto, E.; Panunzio, A.M.; Salles, L.; Schwingshackl, C.; Bacharoudis, K.C.; et al. Uncertainty and Risk Assessment in the Design Process for Wind. J. Adv. Res. Dyn. Control Syst. 2015, 9, V07AT30A013.