BMOTSM: design of a hybrid bioinspired model to determine optimal turbine sizing for capacity maximisation in environment-and-economy aware deployments

ABSTRACT

Multiparametric optimisation determines optimal turbine size for eco-friendly wind farm repowering. This involves identifying turbine ratings, repowering locations, and wind zone analysis for maximum economic efficiency and low environmental impacts. Existing models that perform these tasks are either highly complex or cannot be scaled due to deployment-specific characteristics. Most of these models do not consider economic or environmental impacts when repowering wind farms. This text discusses the design of a novel hybrid bioinspired model to determine optimal turbine sizing in environment- and economy-aware deployments. The model combines GWO, PSO, and GA to optimise turbine ratings, economic impacts, and environmental impacts during the repowering process. GA model optimises new turbine locations, while PSO maximises turbine efficiency. Both these models are internally optimised via GWO due to economic and environmental effects. The GWO model continuously tunes GA and PSO to find the best multiobjective repowering solution. The integrated model was validated on real-time wind farms to evaluate power conversion efficiency, deployment cost, soil fragmentation percentage, and cost-to-power ratios. The proposed BMOTSM model achieved 6.5% higher conversion efficiency, 8.5% lower deployment cost, 15.4% lower soil fragmentation, and 3.5% lower cost-to-power ratio than state-of-the-art models, making it useful for a variety of real-time wind farm repowering scenarios.

KEYWORDS:

• GA
• PSO
• GWO
• fragmentation
• power
• repowering

1. Introduction

Repowering of wind farms is a multi-domain process that requires long-term planning and analysis for improving power conversion efficiency along with low environmental impacts. Repowering models are capable of identifying turbine ratings, and generator locations for maximum power conversion efficiency, with minimum impact to soil, wildlife and plantation habitats. A typical repowering model (Karoui 2019) is depicted in Figure 1, wherein bioinspired optimisation is applied for the preparation of wind turbines, mobilisation of equipments, and other processes.

Figure 1. A typical wind farm repowering model based on bioinspired optimisation process.

The model formulates the use of multiple turbine parameters and incorporates economical impacts of repowering, which assists in improving its efficiency for real-time deployments. Similar models (Zuo 2021; Erlich 2013; Yang 2021) that consider environmental impacts, social impacts, economic viability, power efficiency, etc., are discussed in the next section of this text. This brief discussion evaluates three models in terms of their contextual nuances, application-specific advantages, deployment-specific limitations, and functional future scopes.

2. Literature review

Wind farm optimisation is a relatively new area, thus, most research is done for planning fresh deployments or extending their generation capabilities. For instance, research presented by Zuo (2021); Xu, Geng, and Chu (2021); Erduman (2021) suggests the cross-substation incorporation (CSI) for repowering, the stochastic projected simplex model (SPSM), and the linear optimisation (LO). These models take into account the many different configurations of wind farms in order to estimate the precise locations of generator units. These models can be used to plan generation systems for deployments based on long-term forecasting, but they cannot be used to plan systems for immediate analysis. However, they can be used to plan systems for deployments based on short-term forecasting. In the research presented by Paula (2020), the authors suggest using gradient boosting (GB), neural networks (NN), and random forest (RF) models to estimate future load demands and plan wind farms in accordance with these demands. These models contribute to an increased level of deployment efficiency by allowing for the consideration of potential future requirements during the component selection and placement processes. Similar models that use particle swarm optimisation (PSO) have been discussed by researchers (Asaah, Hao, and Ji 2021), the graph theory-based parthenogenetic model (PGM) has been discussed (Fu 2022), and the superconducting magnetic energy storage model has been discussed (Ngamroo 2019). Machine learning (ML) strategies are utilised in order to optimise the performance of these models for a wide variety of wind farm planning scenarios.

Additional methods that can be used to further improve optimisations include continuous monitoring and control (Zhang, Geng, and Jiang 2020), impedance optimisation of static synchronous compensator for resonance mitigation (Zhang 2021), hybrid grey wolf optimisation (HGWO) with Frandsen–Gaussian (F–G) wake model (Tao and Kuenzel 2019), and genetic algorithm (GA) for overcurrent relay (OCR) optimisation (Rezaei 2019). These methods contribute to the ongoing optimisation of performance in a variety of real-time use cases. Extensions to these models are discussed in Tao and Xu (2020); Huang, Wu, and Zhao (2020); Huang, Wu, and Guo (2020); Deveci (2020), which propose the use of bi-level optimisation by selecting the best cable type with parallel cabling, analytical target cascading method (ATCM), hierarchical active power control (HAPC), and bi-hierarchy optimisation (BHO) in order to optimise placement models. These models are discussed in order to optimise placement models. These models incorporate a variety of high-power optimisation techniques in order to improve the effectiveness of the generators that are utilised in wind farms. As a result, the generators will be able to rotate with as much fluidity as is physically possible in response to the actual wind conditions. Similar models that make use of impedance tuning (Jin 2019), the multiple feature similarity matching method (MSMM) (Peng 2020), model predictive control (MPC) (Huang, Wu, and Bao 2021), cost aware distribution and planning models (CADP) (Sun 2019), and binary most valuable player (BMVP) (Ramli and Bouchekara 2020) have been the subject of discussion among researchers. These models make use of bioinspired computing to improve the placement of wind turbines and the amount of energy they produce in a variety of wind farm layouts. Because these techniques make use of bioinspired models, extensive simulations are required to be run before they can be applied to use cases that take place in the real world.

Discussion is held on models that help improve large-scale deployment capabilities for a variety of wind farm applications. These models make use of the improved equivalent method (IEM) (Han 2020), filters optimised tuning (Shojaei, Samet, and Ghanbari 2021), wind farm self-discipline interval optimisation (Yu 2020), and integrated global optimisation model for cable placements (Yu 2020). A hierarchical inertial control scheme that makes use of a battery energy storage system (BESS) and a mixed integer linear program (MILP) has been proposed as a method for achieving global optimisations in the research presented in Bao (2021) and Perez-Rua (2020). In addition to being discussed and utilised for real-time use cases, these programs also serve to extend the models. But it can be observed that either these models are highly complex or cannot be scaled due to their deployment-specific characteristics. Moreover, most of these models are non-comprehensive and do not consider economic or environmental impacts while repowering wind farms. To overcome these limitations, next section discusses the design of a novel hybrid bioinspired model to determine optimal turbine sizing for capacity maximisation in environment-and-economy aware deployments. The model was evaluated on multiple use cases and compared with different state-of-the techniques under different configurations.

2.1. Research gap and motivation

Based on this literature survey, the following gaps can be evaluated:

• Existing models are highly context-sensitive and thus cannot be used for large-scale deployment scenarios.

• Most of these models are non-comprehensive and do not consider economic or environmental impacts while repowering wind farms.

This can be observed from Table 1.

Table 1. Complexity and space analysis of existing methods.

Parameter	SP SM (Xu, Geng, and Chu 2021)	HW GO FG (Tao and Kuenzel 2019)	BHO (Deveci 2020)	BM OT SM
Time complexity	O (N)	O (N)	O (N!)	O (log(N))
Space complexity	O (N^2)	O (N)	O (N)	O (log(N))

Based on this analysis, we can observe that existing models cannot be scaled, thus, our motivation is to design a novel hybrid bioinspired model to determine optimal turbine sizing for capacity maximisation in environment-and-economy aware deployments. The model must be evaluated under a wide variety of real-time conditions, and its performance must be compared with existing models in terms of power conversion efficiency, deployment cost, fragmentation percentage of underlying soil, and cost-to-power ratios.

2.2. Challenges

The main challenges for this work were:

• Improving scalability while incorporating multiple low-level constraints.

• Designing a comprehensive model that considers both economic and environmental impacts while repowering wind farms.

2.3. Contribution

The following are the main contributions of this paper:

• The paper discusses the design of a fusion of grey wolf optimisation (GWO) along with PSO and GA to optimise turbine ratings, economic impacts and environmental impacts during the repowering process.

• The GA model also assists in the optimisation of new turbine locations, while PSO optimises turbine ratings for maximum efficiency under given conditions.

• Both these models are internally optimised via GWO, which is possible due to the incorporation of economical and environmental effects.

• The GWO model performs continuous tuning of GA and PSO, which assists in obtaining an optimum multi-objective solution for different repowering scenarios.

Due to these optimisations, the model is able to improve efficiency levels for different wind farm deployments.

2.4. Paper organisation

This paper is organised in a reader-friendly manner, where Section 3 discusses the design of a novel hybrid bioinspired model to determine optimal turbine sizing for capacity maximisation in environment-and-economy aware deployments. The model was evaluated under a wide variety of real-time conditions, and its performance was calculated in Section 3, where it was compared with existing models in terms of power conversion efficiency, deployment cost, fragmentation percentage of underlying soil, and cost-to-power ratios. Finally, this text concludes with some context-based observations about the proposed model and also recommends methods to further optimise its performance for large-scale scenarios.

3. Design of the proposed hybrid bioinspired model to determine optimal turbine sizing for capacity maximisation in environment-and-economy aware deployments

After referring to existing models for wind farm repowering and placement optimisation, it was observed that they either are highly complex or cannot be scaled due to their deployment-specific characteristics. Moreover, most of these models are non-comprehensive, and do not consider economic or environmental impacts while repowering wind farms. To overcome these limitations, this section discusses the design of a novel hybrid bioinspired model to determine optimal turbine sizing for capacity maximisation in environment-and-economy aware deployments. The flow of the model is depicted in Figure 2, wherein it can be observed that the proposed model uses a fusion of GWO along with PSO and GA to optimise turbine ratings, economical impacts and environmental impacts during the repowering process.

Figure 2. Overall flow of the proposed model for optimum generation locations and configurations.

The GA model assists in the optimisation of new turbine locations, while PSO optimises turbine ratings for maximum efficiency under given conditions. Both these models are internally optimised via GWO, which is possible due to the incorporation of economical and environmental effects. The GWO model performs continuous tuning of GA and PSO, which assists in obtaining an optimum multi-objective solution for different repowering scenarios.

From the figure, it can be observed that the model initially uses a GA for the identification of turbine locations. This model works via the following process:

• Initially, setup the following constants for GA-based optimisation process

  • o Total solutions to be used for optimisation ($N_s$)

  • o Total iterations to be used for optimisation ($N_i$)

  • o Tunable rate at which the model will perform mutation and crossover operations ($L_r$)

  • o Total new turbine generators to be installed $N_t$

  • o Existing locations of turbines ($\mathrm{ET}(X,Y,Z)$)

  • o Temporal dataset of wind flow at each location ($\mathrm{WF}(X,Y,Z)$)

  • o Temporal dataset of previous land shifts at each location ($\mathrm{SL}(X,Y,Z)$)

• To start the optimisation process, set each particle status as ‘mutate’

• Scan each particle for $N_i$ iterations, via the following process

  • o Check if particle status is ‘crossover’, then skip this particle and go to the next one in sequence

  • o Else, mutate this particle via the following process

    • ▪ Evaluate the location of each turbine generator via the following equation: (1) $G(X,Y,Z)=\mathrm{STOCH}(\mathrm{Min}(X,Y,Z),\mathrm{Max}(X,Y,Z))$(1) where $\mathrm{STOCH}$ represents stochastic Markovian process for generation of number sets, while $G(X,Y,Z)$ represents generator location which is recommended by the mutation process.

    • ▪ Evaluate the distance between this location and existing generator locations via the following equation: (2) $D_i=\sqrt{\begin{array}{c}{(G(X)-\mathrm{ET}{(X)}_i)}^2+\\ {(G(Y)-\mathrm{ET}{(Y)}_i)}^2+\\ {(G(Z)-\mathrm{ET}{(Z)}_i)}^2\end{array}}$(2) where $i\in (1,N_e)$ and $N_e$ represents a number of existing turbines.

    • ▪ Accept this location if Equation (3) is satisfied (3) $\begin{array}{rl}& D_i<{\displaystyle \frac{D(R)}{L_r},\mathrm{if}{L}_r<0,}\\ & \mathrm{otherwise}{D}_i<D(r)\ast L_r\end{array}$(3) where $D(R)$ represents recommended distance between two turbines, for minimum shadowing effects.

    • ▪ Based on this location, identify solution fitness via the following equation: (4) $f=\sum _{i=1}^{N_t}{\displaystyle \frac{\mathrm{Min}\left({\bigcup }_{j=1}^{N_t}{D}_j\right)}{\mathrm{Max}\left({\bigcup }_{j=1}^{N_t}{D}_j\right)}\ast {\displaystyle \frac{\mathrm{W}{\mathrm{F}}_i}{\mathrm{S}{\mathrm{L}}_i}\ast \mathrm{GBest}(G_i)}}$(4) where $\mathrm{WF}\mathrm{and}\mathrm{SL}$ represent wind flow and land slide probability at the current generator position, and $\mathrm{GBest}(G)$ represents global best particle fitness of the turbine generator when connected at the current location, which is obtained via the PSO process. The designed fitness function is novel, in a way that it incorporates wind flow, land shifts, and distance between generator positions, which assists in optimising its deployment efficiency levels.

  • o Evaluate this fitness for each solution and identify iteration fitness via the following equation: (5) $f_{\mathrm{th}}=\sum _{i=1}^{N_s}{f}_i\ast {\displaystyle \frac{N_s}{L_r}}$(5)

• Once an iteration is completed, then change status of particles to be ‘mutate’, if $f<f_{\mathrm{th}}$, otherwise change status of particles to ‘crossover’

Once all solutions are scanned for $N_i$ iterations, identify the solution with maximum fitness and use its particle positions in order to place the wind generators. Due to this process, the wind generator position with high wind flow and low environmental impact is evaluated, which is further tuned by the GWO-based optimisation process. The GA model uses the efficiency of the generator, which is optimised via PSO that works via the following process:

• Initially, setup the following constants for PSO process

  • o Total particles to be used for optimisation process ($N_p$)

  • o Total iterations for which the PSO model will be evaluated ($N_i$)

  • o Learning rate with which each PSO particle will learn from itself $L_c$

  • o Learning rate with which each PSO particle will learn from other particles $L_s$

  • o Minimum and Maximum hub height for turbine $\mathrm{Min}(h),\mathrm{Max}(h)$

  • o Minimum and Maximum surface roughness for turbine $\mathrm{Min}(\mathrm{SR}),\mathrm{Max}(\mathrm{SR})$

  • o Minimum and Maximum horizontal-axis wind turbine (HAWT) rotor diameter ($\mathrm{Min}(d),\mathrm{Max}(d)$)

• Initially, generate all particles via the following process

  • o For each generator, setup its ratings via Equations (6), (7), and (8), as follows: (6) $\mathrm{H}{\mathrm{T}}_i=\mathrm{STOCH}(\mathrm{Min}(h),\mathrm{Max}(h))$(6) (7) $\mathrm{S}{\mathrm{R}}_i=\mathrm{STOCH}(\mathrm{Min}(\mathrm{SR}),\mathrm{Max}(\mathrm{SR}))$(7) (8) $\mathrm{HAW}{\mathrm{T}}_i=\mathrm{STOCH}(\mathrm{Min}(d),\mathrm{Max}(d))$(8) where $\mathrm{HT},\mathrm{SR}\mathrm{and}\mathrm{HAWT}$ represent hub height, surface roughness and HAWT diameter for the turbine generator, and $i\in (1,N_t)$

  • o Based on this configuration, identify turbine efficiency factor ($\mathrm{tef}$) for each turbine, which is evaluated via the following equation: (9) $\mathrm{tef}=\left[1-\sqrt{1-\mathrm{SR}}\right]\ast {\displaystyle \frac{\mathrm{HAWT}}{{\left(\begin{array}{c}\mathrm{HAWT}+\\ 2\ast \mathrm{WER}\end{array}\right)}^2}}$(9) where $\mathrm{WER}$ represents wake expansion rate and is evaluated via the following equation: (10) $\mathrm{WER}={\displaystyle \frac{0.5}{\log \left({\displaystyle \frac{\mathrm{HT}}{\mathrm{SR}}}\right)}}$(10)

  • o Based on $\mathrm{tef}$, calculate the maximum achievable velocity ($\mathrm{mav}$) of generator via the following equation: (11) $\mathrm{mav}=\mathrm{iv}\ast \left[1-\sqrt{\sum _{j=1}^{N_T}\begin{array}{c}\mathrm{MIS}\\ \ast \mathrm{te}{\mathrm{f}}^2\end{array}}\right]$(11) where $\mathrm{MIS}$ represents maximum inflow speed and is evaluated via the following equation: (12) $\mathrm{MIS}=\left({\displaystyle \frac{X_{\mathrm{overlap}}}{\mathrm{Width}}+{\displaystyle \frac{Y_{\mathrm{overlap}}}{\mathrm{Height}}}}\right)\ast \mathrm{HAWT}\ast \mathrm{WER}$(12) where $X_{\mathrm{overlap}}\mathrm{and}{Y}_{\mathrm{overlap}}$ represent the overlap of current wind generator with other generators along the X and Y axis, $\mathrm{Width}\mathrm{and}\mathrm{Height}$ represent the width and height of the generator configurations.

  • o Using these values, evaluate the power generated by the turbine via Equation (13), which assists in estimation of particle fitness levels (13) $P=E\ast 0.5\ast {\mathrm{\partial }}^{\mathrm{AIR}}\ast \left[\pi \ast {\displaystyle \frac{\mathrm{HAW}{\mathrm{T}}^2}{2}}\right]\ast \sum \mathrm{ti}{\mathrm{f}}^3$(13) where $E$ represents the maximum efficiency of turbine generators, and ${\mathrm{\partial }}^{\mathrm{AIR}}$ represents the density of air that varies with different wind farm scenarios.

  • o Evaluate generation cost via the following equation: (14) $\mathrm{Cost}=N_t\ast \left[{\displaystyle \frac{2}{3}+{\displaystyle \frac{1}{3}\ast \exp (-C\ast N_t^2)}}\right]$(14) where $C$ represents generator cost, which is calculated as per the context of the deployments.

  • o Based on these evaluations, calculate particle fitness via the following equation: (15) $\mathrm{pf}=\mathrm{Cost}\ast {\displaystyle \frac{1000\ast N_t}{{\sum }_{i=1}^{N_t}{P}_i}}$(15)

• To start with, mark each particle’s current configuration as $\mathrm{PBest}$, while we evaluate $\mathrm{GBest}$ via the following equation: (16) $\mathrm{GBest}=\mathrm{Max}\left(\underset{i=1}{\overset{N_p}{\cup }}\mathrm{PBest}\right)$(16)

• Now, scan each particle for $N_i$ iterations and modify its configuration via the following equation: (17) $P(\mathrm{New})=P(\mathrm{Old})\ast r+L_c\ast (P(\mathrm{Old})-\mathrm{PBest})+L_s\ast (P(\mathrm{Old})-\mathrm{GBest})$(17) where $r$ is a stochastic number between (0,1), while $P$ represents configuration parameter $P\in (\mathrm{HT},\mathrm{SR},\mathrm{HAWT})$, while $P(\mathrm{Old})andP(\mathrm{New})$ represent old and new configurations for the given parameter sets.

• After repeating this process for $N_i$ iterations, identify the particle with maximum fitness levels and use its generator configuration for optimised performance.

Based on this process, the model is capable of generating highly optimised configurations for turbine generators. These configurations are further tuned via a GWO-based continuous learning process. This assists in the identification of optimal learning rates for GA and PSO models, and works via the following process,

• Number of optimisation wolves ($N_w$) are initially marked as ‘Delta’ and are scanned for $N_i$ iterations via the following process

  • o If the Wolf is currently marked as ‘Delta’, then generate its configurations via the following process

    • ▪ Identify GA learning rate and PSO learning rates via the following equation: (18) $L_r(M)=\mathrm{STOCH}(0.1,1)$(18) where $L_r(M)$ represents the learning rate for the model $M$, and $L_r(M)\in (L_r,L_c,L_s)$.

    • ▪ Based on this learning rate, evaluate the GA and PSO Models and estimate wolf fitness levels via the following equation: (19) $f_w=\mathrm{GBest}(\mathrm{PSO})+\mathrm{Max}(f(\mathrm{GA}))$(19) where $\mathrm{GBest}(\mathrm{PSO})and\mathrm{Max}(f(\mathrm{GA}))$ represent global best fitness levels of PSO and maximum fitness of GA optimisation process.

  • o Evaluate this fitness for all wolves and then estimate fitness threshold via the following equation: (20) $f_{\mathrm{th}}=\sum _{i=1}^{N_w}{f}_i\ast {\displaystyle \frac{L_r}{N_w}}$(20)

  • o Based on this threshold, change the status of each wolf, via the following process:

    • ▪ Wolf is marked as ‘Alpha’, if $f>2\ast f_{\mathrm{th}}$

    • ▪ Else, wolf is marked as ‘Beta’, if $f>f_{\mathrm{th}}$

    • ▪ Else, wolf is marked as ‘Gamma’, if $f>L_r\ast f_{\mathrm{th}}$

    • ▪ Otherwise, it is marked as ‘Delta’

• This process is repeated for all iterations, and wolf with maximum fitness levels is selected for tuning the GA and PSO processes.

Based on this process, the internal parameters of PSO and GA are tuned to obtain high wind generation efficiency, with low-cost and low environmental impacts. This performance is evaluated in terms of conversion efficiency, deployment cost, fragmentation percentage of the underlying soil, and cost-to-power ratio parameters. These parameters were evaluated for different locations and compared with a different state-of-the art models, in the next section of this text.

4. Result analysis and comparison

The proposed BMOTSM model is capable of integrating GA and PSO with GWO-based optimisation techniques, which assists in the identification of optimum turbine configurations and locations for high-efficiency, low-cost and low environmental impacts. To estimate performance of the proposed model, its conversion efficiency (CE), deployment cost (DC), fragmentation percentage of underlying soil (FPS), and cost-to-power ratio (CPR) were evaluated for various locations throughout the country. Each of these locations, along with their power capacity, was simulated in MATLAB for performance evaluation under various generator configurations. The results are tabulated in Table 2.

Table 2. Locations used for simulation.

Name	Location	Stn.	Power (MW)
Bercha Wind Park	Ratlam	MP	50
Dangiri Wind Farm	Jaiselmer	RJ	54
Acciona Tuppadahalli	Chitra Durga District	KA	56.1
Welturi	Welturi	MAH	75
Jath	Jath	MAH	84
Damanjodi Wind Power Plant	Damanjodi	OD	99
Anantapur Wind Park	Nimba-gallu	AP	100
Mamatkheda Wind Park	Mamatkheda	MP	100.5
Vaspet	Vaspet	MAH	144
Vankusawade Wind Park	Satara District	MAH	259
Dhalgaon windfarm	Sangli	MAH	278
Brahmanvel windfarm	Dhule	MAH	528
Jaisalmer Wind Park	Jaisalmer	RJ	1064
Muppandal windfarm	Kanya Kumari	TN	1500

These locations were simulated in MATLAB, and maximum number of generators (MaxG) was varied between 3 and 25 for each of the locations. For each of these variations, values of conversion efficiency (CE), deployment cost (DC), fragmentation percentage of underlying soil (FPS), and cost-to-power ratio (CPR) were averaged at each of these locations to estimate real-time performance under different generator configurations. Based on this strategy, conversion efficiency (CE) was evaluated via the following equation: (21) $\mathrm{CE}={\displaystyle \frac{\mathrm{PG}}{\mathrm{Max}(P)}}$(21) where $\mathrm{PG}$ represents power generated by the model, while $\mathrm{Max}(P)$ represents maximum power generation that is theoretically possible with the given wind farm configurations. Variation of these efficiency levels w.r.t. Maximum Generators (MaxG) is tabulated in Table 3.

Table 3. Conversion efficiency levels for different wind farm optimisation models.

MaxG	CE (%) SPSM (Xu, Geng, and Chu 2021)	CE (%) HWGO FG (Bao 2019)	CE (%) BHO (Deveci 2020)	CE (%) BMO TSM
3	87.10	86.99	91.63	93.24
4	87.70	87.16	92.03	93.65
5	88.31	87.36	92.46	94.08
6	88.93	87.53	92.87	94.50
8	89.13	87.72	93.08	94.71
9	89.46	87.88	93.34	94.97
10	89.87	88.06	93.64	95.28
12	90.36	88.23	94.00	95.64
13	90.96	88.41	94.40	96.06
14	91.43	88.58	94.74	96.40
15	91.90	88.76	95.08	96.75
16	92.38	88.93	95.42	97.10
18	92.85	89.11	95.77	97.45
19	93.33	89.28	96.11	97.79
20	93.80	89.46	96.45	98.14
22	94.27	89.63	96.79	98.49
23	94.75	89.80	97.13	98.83
24	95.22	89.98	97.47	99.18
25	95.69	90.15	97.81	99.53

Because of the utilisation of a variety of different configuration and location optimisation procedures, this evaluation and Figure 3 led to the discovery that the proposed model possesses 3.9% better power conversion efficiency than SPSM (Xu, Geng, and Chu 2021), 8.5% better power conversion efficiency than HWGO FG (Tao and Kuenzel 2019), and 1.5% better power conversion efficiency than BHO (Deveci 2020). These results are attributable to the fact that the proposed model uses a combination of these operations. This makes it easier to deploy the model for large-scale use cases, which typically call for higher levels of power efficiency. Similarly, deployment cost (DC) needed to obtain optimum power generation capability was evaluated via Equation (22) and can be observed from Table 3. (22) $\mathrm{DC}=\sum _{i=1}^{N_t}{\displaystyle \frac{C_i}{C(\mathrm{Max})}}$(22) where $C\mathrm{and}C(\mathrm{Max})$ represents the current cost of deployment, and maximum deployment cost, which is required if the model was not used for optimisation operations.

Figure 3. Conversion efficiency levels for different wind farm optimisation models.

Due to the integration of cost components while estimating generator configurations, it was found that the proposed model has a deployment cost that is 16.5% lower than SPSM (Xu, Geng, and Chu 2021), 12.5% lower than HWGO FG (Tao and Kuenzel 2019), and 15.4% lower than BHO (Deveci 2020). This was observed based on this evaluation, as well as Figure 4, and it was found that the proposed model requires a deployment cost that is 12.5% lower than HWGO FG (Tao and Kuenzel 2019). This makes it easier to deploy the model for use cases that require lower costs and higher power efficiency. Similarly, fragmentation percentage of soil (FPS) during deployment of the wind generators was evaluated via Equation (23) and can be observed from Table 4. (23) $\mathrm{FPS}=\sum _{i=1}^{N_t}{\displaystyle \frac{\mathrm{S}{\mathrm{M}}_i}{\mathrm{Max}(\mathrm{SM})}}$(23) where $\mathrm{SM}\mathrm{and}\mathrm{Max}(\mathrm{SM})$ represent soil movements due to deployment of the model, and maximum allowed soil movements, which are decided by government authorities.

Figure 4. Deployment cost needed for different wind farm optimisation models.

Table 4. Deployment cost needed for different wind farm optimisation models.

MaxG	DC (%) SPSM (Xu, Geng, and Chu 2021)	DC (%) HWGO FG (Tao and Kuenzel 2019)	DC (%) BHO (Deveci 2020)	DC (%) BMO TSM
3	77.42	71.01	79.67	62.16
4	77.96	71.15	80.03	62.43
5	78.50	71.31	80.40	62.72
6	79.04	71.45	80.75	63.00
8	79.22	71.61	80.93	63.14
9	79.52	71.74	81.16	63.32
10	79.88	71.88	81.43	63.52
12	80.32	72.02	81.74	63.76
13	80.85	72.17	82.09	64.04
14	81.27	72.31	82.38	64.27
15	81.69	72.45	82.68	64.50
16	82.11	72.60	82.98	64.73
18	82.53	72.74	83.27	64.96
19	82.96	72.88	83.57	65.20
20	83.38	73.02	83.87	65.43
22	83.80	73.17	84.17	65.66
23	84.22	73.31	84.46	65.89
24	84.64	73.45	84.76	66.12
25	85.06	73.60	85.06	66.35

Due to the incorporation of environmental impact analysis into the estimation of generator locations, the proposed model was found to result in 12.5% lower soil fragmentation than SPSM (Xu, Geng, and Chu 2021), 10.5% lower soil fragmentation than HWGO FG (Tao and Kuenzel 2019), and 12.4% lower soil fragmentation than BHO (Deveci 2020). This was observed based on this evaluation, as well as Figure 5, and it was determined that the proposed model is responsible for these results. This makes it easier to deploy the model for use cases that require lower costs, less negative impact on the environment, and higher power efficiency. Similarly, cost-to-power ratio (CPR) during deployment of the wind generators was evaluated via Equation (24) and can be observed from Table 5. (24) $\mathrm{CPR}={\displaystyle \frac{1}{2}\ast \sum _{i=1}^{N_t}{\displaystyle \frac{C_i}{C(\mathrm{Max})}+{\displaystyle \frac{\mathrm{Max}(P)}{P_i}}}}$(24) where $C\mathrm{and}P$ represent cost and power levels for the generator configurations (Table 6).

Figure 5. Fragmentation percentage of soil due to wind farm optimisation models.

Table 5. Fragmentation percentage of soil due to wind farm optimisation models.

MaxG	FPS (%) SPSM (Xu, Geng, and Chu 2021)	FPS (%) HWGO FG (Tao and Kuenzel 2019)	FPS (%) BHO (Deveci 2020)	FPS (%) BMO TSM
3	40.98	39.45	42.72	30.99
4	41.15	39.50	42.84	31.07
5	41.31	39.60	42.97	31.17
6	41.89	39.66	43.31	31.42
8	42.03	39.78	43.44	31.52
9	42.16	39.84	43.54	31.59
10	42.27	39.92	43.64	31.66
12	42.41	40.00	43.76	31.74
13	42.77	40.08	43.99	31.91
14	43.00	40.16	44.15	32.03
15	43.22	40.24	44.31	32.15
16	43.45	40.32	44.47	32.26
18	43.67	40.39	44.63	32.38
19	43.89	40.48	44.79	32.49
20	44.12	40.55	44.95	32.61
22	44.34	40.63	45.11	32.73
23	44.56	40.71	45.27	32.84
24	44.79	40.79	45.43	32.96
25	45.01	40.87	45.59	33.07

Table 6. Cost to power ratio due to wind farm optimisation models.

MaxG	CPR (%) SPSM (Xu, Geng, and Chu 2021)	CPR (%) HWGO FG (Tao and Kuenzel 2019)	CPR (%) BHO (Deveci 2020)	CPR (%) BMO TSM
3	81.96	78.91	85.44	74.38
4	82.30	79.00	85.67	74.57
5	82.63	79.21	85.95	74.80
6	83.77	79.33	86.61	75.41
8	84.06	79.55	86.89	75.65
9	84.31	79.68	87.09	75.82
10	84.54	79.84	87.29	75.99
12	84.81	80.00	87.52	76.17
13	85.54	80.15	87.99	76.59
14	86.00	80.32	88.31	76.87
15	86.44	80.47	88.62	77.15
16	86.89	80.63	88.94	77.43
18	87.34	80.79	89.26	77.70
19	87.78	80.95	89.58	77.98
20	88.23	81.11	89.90	78.26
22	88.68	81.27	90.22	78.54
23	89.13	81.42	90.54	78.82
24	89.57	81.59	90.86	79.10
25	90.02	81.74	91.18	79.37

As a result of the incorporation of environmental impact analysis while estimating generator locations and the use of low-cost components while identifying generator configurations, the proposed model was found to have cost requirements that are 10.5% lower than those of SPSM (Xu, Geng, and Chu 2021), 1.9% lower than those of HWGO FG (Tao and Kuenzel 2019), and 12.5% lower than those of BHO (Deveci 2020). This was discovered based on this evaluation, as well as Figure 6, and it was found that the proposed model has cost requirements that are 10.5% lower than those of this makes it easier to deploy the model for use cases that require lower costs, less negative impact on the environment, and higher power efficiency. Because of these benefits, the model is able to be deployed for use cases involving highly efficient wind farms. Additionally, it is capable of being deployed for a wide variety of scenarios that have lower environmental and economic impacts, which makes it useful for use cases involving large-scale applications.

Figure 6. Cost to power ratio due to wind farm optimisation models.

5. Conclusion and future work

The proposed model combines optimisation techniques to identify environmentally friendly, low-cost, high-efficiency wind generator locations and configurations. GWO, PSO, and GA were integrated for continuous parameter optimisation. GA model optimises new turbine locations, while PSO optimises turbine ratings for maximum efficiency under predetermined conditions. GWO optimises both models by incorporating economic and environmental factors. The GWO model tunes GA and PSO to find the best multi-objective repowering solution. The proposed model outperformed SPSM (Xu, Geng, and Chu 2021), HWGO FG (Tao and Kuenzel 2019), and BHO (Deveci 2020) in power conversion efficiency by 3.9%, 8.5%, and 1.5%, respectively. Combining configuration and location optimisation helped due to the integration of cost components during generator configuration estimation, the proposed model had lower deployment costs than SPSM (Xu, Geng, and Chu 2021), HWGO FG (Tao and Kuenzel 2019), and BHO (Deveci 2020). Incorporating environmental impact analysis into the model’s generator location estimates resulted in 12.4% less soil fragmentation than BHO (Deveci 2020), 10.5% less than HWGO FG (Tao and Kuenzel 2019), and 12.5% less than SPSM (Xu, Geng, and Chu 2021).

The proposed model has 10.5% lower cost requirements than SPSM (Xu, Geng, and Chu 2021), 1.9% less than HWGO FG (Tao and Kuenzel 2019), and 12.5% less than BHO (Deveci 2020). This is because environmental impact analysis and affordable components were considered when estimating generator locations and configurations. This makes it easier to deploy the model in lower cost, environmentally friendly, and energy-efficient use cases. The model can be used for highly efficient wind farm use cases and a wide range of scenarios with lower environmental and economic impacts. In the future, researchers can integrate low-complexity models for the optimisation of locations and generator configurations. These models must be validated on large-scale scenarios and can be further improved via the integration of deep learning techniques, including auto encoders, long-short-term memory (LSTM), generative adversarial network (GAN), and other techniques. Moreover, the performance can be further tuned via the use of Q-learning, and other incremental learning methods, that can be applied to large-scale use cases.