Sizing of renewable energy based hybrid system for rural electrification using grey wolf optimisation approach

: The utilisation of renewable energy sources (RES) in increasing drastically because of various issues including depletion of fossil fuels, greenhouse gas emissions, climate change and so on. As the power generated from RES is fluctuating in nature, therefore, the appropriate sizing of the hybrid model based on RES is utmost important. In this study, the grey wolf optimisation, a newly developed approach is used for the optimal sizing of the hybrid model. In this work, the optimal design of solar/biomass/biogas/battery-based hybrid system has been carried out to supply continuous electricity to various households of a cluster of villages of Haryana state of India. The results obtained from the proposed model have been compared with harmony search and particle swarm optimisation and found better.


Introduction
Over the last many years, fossil fuels are the major contributor to power generation throughout the world. However, they are the key reason for greenhouse gas (GHG) emission, global warming and so on. On the contrary, the need for clean, environmentally friendly, sustainable and reliable energy is escalating day-by-day due to various technical, environmental and economical concerns [1]. Under these circumstances, nowadays, there is an inclination towards the power generation through renewable energy sources (RES) such as solar, biomass, wind, biogas and so on globally. It is evident from the literature that the integration of two or more RES called hybrid systems are more efficient due to various factors, including unpredictable nature of RES, climatic conditions, cost and so on [2,3]. Further, these systems diminish carbon emissions and offer more efficient, economical and reliable power systems.
Abdullaha et al. employed HOMER simulation software to inspect the cost-effectiveness of the hybrid solar/hydro system and photovoltaic (PV) system for rural electrification. It has been found that the power generated from the hybrid system is more sustainable due to volatile climatically issues [27,28]. Nouni et al. [29] identified many locations in India wherever off-grid hybrid system is more economical in comparison to grid extension. As a result, micro-hydro, wind generators dual fuel biomass gasifier systems, and solar PV system (SPV) systems could be financially captivating for providing electricity in diminutive remote villages. Phuangpornpitak and Kumar [30] developed solar based hybrid system to fulfil the electricity needs of the rural area in Thailand and also recommended that adding up of diesel generator (DG) to SPV system amends the power supply reliability. Rehman and Al-Hadhrami [31] developed hybrid PV diesel along with a battery system for a rural community at Kingdom as a replacement for existing diesel-generated electricity. The results revealed that existing DG is cost-effective with diesel prices of 0.2 $/l and the hybrid system provides economic power with a diesel price of 0.60 $/l or higher.
Shahzad et al. [32] developed a grid independent SPV/biomass hybrid energy system to electrify the domestic and agricultural sector of the rural area located in Pakistan. It is concluded that the hybrid system composing of 10 kW of SPV, 8 kW of biogas with 32 battery storage system and 12 kW converter was economical with NPC of PKR4.48M. The cost of energy (COE) of the proposed system is 5.51 PKR/kWh as compared to grid supply rate of 10.35 PKR/kWh. Asrari et al. [33] presented a case study for economic assessment of renewable energy based hybrid systems for electrification of a rural area in Iran. HOMER software was used to assess the feasibility of different hybrid DG-RES and grid-RES energy systems. Results revealed that RES based power generation in off-grid and grid-connected scenario makes more cost-effective power system. Bhattacharjee and Dey [34] carried out the techno-economic feasibility of grid-connected hybrid PV/ biomass system to fulfil the electricity requirement of rice mill of Tripura state in India. The COE was computed as 0.143 $/kWh with a renewable fraction of 91%. Sensitivity analysis was also carried out to find the effects of varying solar irradiation; load demand electricity price and maximum yearly capacity shortage. Padrón et al. [35] also employed HOMER software to develop an optimal hybrid system to provide a reliable power supply to Autonomous reverse osmosis desalination system located at Lanzarote and Fuerteventura.
Bala et al. [36] employed GA to design an optimal hybrid minigrid system comprising of SPV and DG for a fishing society in an isolated island Sandwip in Bangladesh. Results showed that the major contribution of cost through SPV panels and battery. Mostofi and Shayeghi [37] optimised the hybrid SPV-wind-fuel cell (FC)hydro system utilising GA. The results were compared with HOMER and found it more accurate. Koutroulis and Kolokotsa [38], Yang et al. [39,40], Nafeh [41], Abdullrahman and Addoweesh [42], and Tégani et al. [43] also utilised GA for size optimisation of SPV-wind hybrid systems for various rural applications in respect of minimising cost. Further, particle swarm optimisation (PSO) technique was used by Pirhaghshenasvali and Asaei [44] to achieve optimal sizing of system components of offgrid hybrid SPV-battery-wind system while minimising cost. Maleki and Askarzadeh [45] assessed the performance of four different heuristic algorithms namely PSO, Tabu Search (TS), simulated annealing (SA) and HS for optimal sizing of hybrid systems of SPV-wind-FC and SPV-wind-battery in order to continuously satisfied the load with minimum total annualised cost. It has been found that PSO provides more promising results.
For remote areas of Iran, the optimal size of a hybrid system consisting of SPV, wind, battery storage was performed by Maleki et al. [46] via comparing different optimisation techniques such as PSO, modified PSO, PSO-RF, PSO-CF, PSO-W, HS, TS and SA. Results indicated that PSO-CF is most auspicious technique compare to others. Askarzadeh [24] employed discrete harmony search (DHS) based algorithm for optimal sizing of solar arrays and wind turbines of the hybrid system. Chauhan and Saini [47] also utilised DHS algorithm for optimal sizing of SPV/wind/ biomass/biogas/micro-hydro/battery hybrid system with and without demand response (DR). Results revealed that a substantial amount of savings in system sizes and costs are attained with DR strategy instead of without DR. Additionally, the various combinations of the hybrid system were optimised in terms of power reliability at 0 and 5% unmet load.
Upadhyay and Sharma [48] performed a comparative analysis of PSO, GA and HOMER techniques for the size optimisation of a hybrid system. It has been found that PSO provides more promising results than GA and HOMER. The same authors also explored an optimal hybrid model by considering three energy management strategies including cycle charging, peak shaving load and load following. The cycle charging strategy gave more economical results compared to the other two strategies [49]. Singh et al. utilised artificial bee colony (ABC) algorithm for optimal sizing of hybrid system components to accomplish the electrical load demand of a rural community of India. Obtained results were compared with PSO and HOMER and found more accurate [50]. González et al. [51] employed GA to optimise the size of gridconnected hybrid SPV/wind system to electrify the rural area in Spain. Sensitivity analysis was also performed to inspect the accurateness of the system. It was revealed that the calculated net present value is directly proportional to cost and inversely proportional to the efficiency of renewable energy systems. Zebarjadi and Askarzadeh [52] presented harmony search (HS) based size optimisation of a grid-connected PV-based power plant for a set of six houses situated in Iran. Results revealed that investment in PV system installation might economical in the case electricity prices escalate from the current perspective. Mohamed et al. [53] applied the PSO based algorithm for the optimal design of grid-dependent hybrid PV/wind energy system to minimise the COE and maximised the reliability. The optimised hybrid system was compared with the actual utility grid in terms of cost savings.
Sawle et al. [54] presented an optimal sizing of standalone HRES to power the remote area of Barwani district India using different optimisation approaches such as GA, PSO, butterfly PSO and teaching learning-based optimisation (TLBO) in terms of minimising multi-objective function. The multi-objective function includes technical, economical and social factors. Different configurations are selected and found the most optimal. Results indicated that TLBO performs better followed by BFPSO, PSO and GA.
Abdelshafya et al. [55] used a hybrid PSO-GWO (grey wolf optimisation) approach to develop an optimal grid-connected PV/ wind hybrid system to power the reverse osmosis desalination plant. In this regard, two different configurations such as PV/wind/ battery and PV/wind/hydrogen storage system are compared in respect of minimising cost as well as CO 2 emission. Results revealed that PV/wind along with battery storage system is more cost-effective and environmentally friendly. Also, the hybrid PSO-GWO approach is compared with PSO and GWO alone and found more superior. It is also found that the cost can also be reduced by adding DG. Moreover, a sensitivity analysis was also performed to find out the effects of variations of solar radiation and wind speed in cost and found that solar radiation affects more than wind speed.
Based on the literature, it has been revealed that intelligent techniques provide more promising results than simulation software. Further, most of the work has been done for optimisation of off-grid hybrid systems. Also, most of the analysis related to the grid-connected scenario has been done using HOMER simulation software. The area of use of intelligent optimisation techniques for grid-connected systems has rarely explored. In recent years, numerous intelligent techniques inspired by natural phenomenon such as a neural network (NN), GA, differential evolution, PSO, ant colony optimisation algorithm, harmony search (HS), BBO and so on are being largely explored by the researchers for optimisation. A GWO approach is a recently developed evolutionary approach proposed by Mirjalili et al. [56]. This approach is motivated by the social behaviour of the grey wolf and its prey methodology. Grey wolves are acme predators' means they are at the summit of the chow sequence. Grey wolves generally have a preference to live in a crowd or group. The crowd size is on average 2-12. They have a very stern social dominant hierarchy due to their particular interest. GWO approach has many advantages like good computational efficiency along with qualitative results, easy to implement with a few parameters and so on [56]. Therefore, intelligent techniques GWO has been employed for optimal sizing and design of the hybrid system in this paper.
This paper deals with the size optimisation of off-grid and grid connected hybrid system for selected study areas. Based on the availability of RES, configurations are selected to meet the load demand of the selected rural areas. Finally, the size of different generators has been calculated using a recently developed GWO algorithm. Further, the results have been compared with PSO and HS in MATLAB.

Description of study area
A case study of the total 533 households of the group of four villages situated at Sonipat district of Haryana state in India has been selected in this paper. The selected area is located at latitude and longitude of 28.98°N and 77.02°E, respectively [57]. The geographical location of the study area is shown in Fig. 1. Due to the variations in temperature during the year have an effect on energy consumption, three seasons; season I (April-July), season II (August-November) and season III (December-March) have been considered in this study. The average daily energy demand of the study area has been calculated as 2997.58, 2357.98, 1286.149 kWh/day during seasons I-III, respectively. Furthermore, the potential of RES such as solar radiation, biogas and biomass has been estimated based on the collected data. It has been found that mean daily radiation of this location is 5.26 kWh/m 2 /day. Biogas of 820.24 m 3 /day from cattle dung and biomass of 470.19 tons/year from crop residues have been computed in the selected area.

Mathematical modelling of hybrid system components
Mathematical modelling is one of the indispensable steps for designing and developing an optimal model and sizing of the hybrid system. Therefore, the mathematical modelling of each hybrid system component is described as follows.

Solar PV system
PV system composed of PV panels connected in series and parallel. The output power of the PV system (P PV (t)) is evaluated as [38] where N PV stands for the number of PV panels, V OC (t) and I SC (t) represent an open-circuit voltage (V) and short-circuit current (A) of SPV panels, respectively, FF defines fill factor. V OC (t) and I SC (t) of an SPV panel can be calculated as [38] V where V OCS (t) represents open-circuit voltage (V) under standard test conditions (STC), I SCS (t) is short-circuit current (A) under STC. τ depicts an open-circuit voltage temperature coefficient (V/°C ), ς stands short-circuit current temperature coefficient (A/°C), Q PV (t) is global solar irradiance (W/m 2 ) incident on SPV panels, T PV (t) is solar cell operational temperature and T PVnm (t) is nominal temperature of solar cell in °C, respectively, T amb (t) is an ambient temperature (°C).
Further, the FF of the SPV panel is computed as where V mpp and I mpp depict voltage and current at the maximum power point, respectively. Finally, energy generated by the PV system (E PV (t)) in kWh at hour 't' is evaluated as where Δt represents the time step considered as 1 h in this work.

Biomass generator (BMG) system
The power generated by the BMG system (P M (t)) at hour 't' is computed as [59] where Q AM denotes yearly available biomass (tons/yr). F M stands for the calorific value of biomass (4015 kcal/kg). η M stands for overall conversion efficiency from biomass to electricity of BMG system (20%). H M denote operating hours per day of BMG system. Finally, energy generated by BMG system (E M (t)) at hour 't' has been evaluated using the following equation:

Biogas generator (BG) system
The output power (P G (t)) of the BG system is estimated using the following equation [26]: where Q G represents the availability of biogas per day (m 3 /day), F G is biogas calorific value (4700 kcal/m 3 ), η G is overall conversion efficiency from biogas to electricity production (28%). H G represents operating hours of BG per day. Finally, the energy generated (E G (t)) by BG system at hour 't' has been evaluated as

Battery system
Sometimes, the energy generated from RES (E gen (t)) may or may not be capable to fulfil the hourly load demand (E D (t)) and that needs a suitable size of the battery bank. A comprehensive study of the battery charging and discharging states is summarised as • When hourly generated power is more than load demand, i.e. E gen (t) > E D (t), then the extra amount of energy will be stored in the battery. During charging state, the battery capacity can be obtained as follows: where γ denotes the self-discharging rate of battery at hour t; E B (t) denotes the amount of energy stored in the battery in kWh.
and E XG (t) represent the amount of excess energy generated by PV, wind, BMG and BG system after meeting the load demand, respectively, (kWh) and η ch denotes charging efficiency. • When E D (t) > E gen (t), then the amount of deficit energy will be supplied by the battery. During discharging state, the battery capacity can be evaluated using the following equations: where η dh and η inv are discharging efficiency of battery and inverter efficiency, respectively. E df (t) is an unmet demand that is not fulfiled by RES (kWh).

Utility grid
In the first state, demand is more than generation and battery available storage; the deficit energy will be purchased from the grid and can be obtained as follows: where E GP (t) denotes deficit energy to be purchased from the grid (kWh) and E Bmn denotes minimum values of battery storage capacity.
In the second state, demand is less than the generation and the battery bank is fully charged, the excess energy will be sold to the grid that can be computed using the following equation: where E GS (t) represents excess energy to be sold to the grid (kWh) and E Bmx is the maximum value of battery storage capacity.

Economical parameters of hybrid system components
In this work, the net present cost (NPC) has been considered for the economic analysis of the hybrid system. Therefore, mathematical expressions for the NPC of individual system components have been developed as.

PV panels
In this work, the project lifetime has been taken equal to the lifetime of PV panels. Further, solar irradiance acts as a fuel to generate electricity, which is free of cost. Therefore, replacement and fuel costs will be zero. Thus, the NPC of PV panels (NPC PV ) involves capital cost (C P ), operation and maintenance (O&M) cost (OM PV ) and salvage values (SV PV ) only and are computed as The capital cost of PV panels has been calculated as where Ψ PV represents an initial cost of individual PV panel ($/kW). P panel represents the power of one PV panel (kW/panel). Further, O&M cost (OM PV ) of PV panels has been evaluated using the following equation: (18) where ϖ PV , ζ PV , R represent O&M cost, escalation rate and interest rate of PV panels, respectively. μ is the project lifetime in years.
The salvage value, i.e. the resale value of PV panels (SV PV ) after project lifetime has been determined using the following equation: where ɛ PV is the resale price of PV panel ($/kW) after completing their life and λ is an inflation rate (0.05).

BMG system
The NPC of BMG system (NPC M ) is evaluated by considering capital cost (C M ), the net present value of O&M cost (OM M ), salvage value (SV M ) with fuel cost (F M ) and is given as [25] NPC where ψ M is the initial cost of the BMG system ($/kW). P M denotes the generated power of the BMG system (kW). Further, the net present value of O&M cost of BMG system has been calculated as follows: where ϖ FM and ϖ VM denote yearly fixed and variable O&M cost of BMG system, respectively. P AM W represents the yearly working power of BMG system in kWh/year. ζ M denote the escalation rate of BMG system (0.075). Further, the net present value of resale of the BMG system (SV M ) has been obtained using the following equation: where ɛ M denotes the cost of resale of BMG system ($/kW). By considering the biomass fuel cost and yearly biomass needed, the net present value of fuel cost (F M ) has been calculated by where ξ M denotes the biomass fuel cost ($/ton); and F MR represents yearly biomass needed (ton/year).

BG system
Based on the same pattern of BMG system, the NPC of the BG system (NPC G ) has been computed as where the capital cost of the BG system is given as where ψ G denotes the initial cost of the BG system ($/kW). P G is generated power by the BG system (kW). Further, the net present value of O&M cost of BG system is computed as follows: where ϖ FG and ϖ VG are yearly fixed and variable O&M cost of BG system, respectively. P W AG denotes yearly working power of BG system in kWh/year. ζ G is an escalation rate of BG system (0.075). Further, the net present value of resale of the BG system (SV G ) has been obtained as where ɛ G denotes the resale price of the BG system ($/kW). P G represents the power of BGs (kW). By considering the biogas fuel cost and yearly biogas needed, the net present value of fuel cost (F G ) has been calculated by (29) where ξ G and F GR represent biogas fuel cost ($/m 3 ) and the annual amount of biogas required in a year, respectively.
In the case of BG, the net present value of revenue (RE G ) generated from the organic manure is obtained as where ϕ G and d G are the cost of produced manure ($/ton) and the annual amount of manure produced (ton/year), respectively.

Battery
The NPC of the battery bank (NPC B ) includes capital cost (C B ), O&M cost (OM B ), replacement cost (RP B ), salvage value (SV B ) and can be evaluated as where ψ B is the cost of one battery ($). ϖ B and ζ B denote annual O&M cost ($/year) and escalation rate (0.075) of batteries, respectively. ɛ B denotes the resale value of one battery ($). In this study, the life of the battery (μ B ) has been assumed as 5 years, which is less than the project lifetime of 25 years. Therefore, the battery needs to be replaced after every 5 years. The number of replacements of the battery (N RB ) is calculated as The net present value of replacement cost of the battery is evaluated as

Inverter
The NPC of the inverter (NPC inv ) has been evaluated as where C inv , OM inv , RP inv and SV inv represent a capital cost, O&M cost, replacement cost and salvage value of inverter, respectively, where ψ inv is the initial cost of the inverter ($/kW). The lifetime of inverter assumed as 10 years is less than the project lifetime (25 years). Thus, the net present value of replacement cost is

Grid sale and purchase capacity
In the grid-connected scenario, the net present value of selling price (C GS ) and purchasing (C GP ) cost of electricity from or to the grid has been determined using the following equations: where θ GS and θ GP are unit cost of sale and purchase of electricity to or from the grid ($/kWh), respectively Finally, the COE of the proposed hybrid system has been obtained as where E AD is an annual energy demand (kWh/year). C RS is a capital recovery factor of the hybrid system and can be evaluated as

Objective function and constraints
This research aims to minimise the NPC of the system and is defined as This NPC is to be minimised subject to the system components' limits and boundary constraints as described in the following sections.

Upper and lower limits on the number of system components
In the proposed system, the size of system components, i.e. N PV , N B , P M and P G may vary to meet the load demand. Therefore, the upper and lower limits of these components are defined as

Storage limits on battery
To operate the battery securely, the minimum and maximum capacities of battery bank storage system have been considered as one of the constraints and is expressed as where E Bmn and E Bmx denote, respectively, minimum and maximum values of battery storage capacity that can be computed using the following equations [41]: where V B is a voltage of the battery (V), Q B is the capacity of the battery (Ah), Q Bmn and Q Bmx define the minimum and maximum state of charge of batteries, respectively.

Power reliability constraint
Loss of power supply probability (LPSP) has been taken as power reliability constraint in the present work. When load demand exceeds the available generation, the user suffers from nonavailability of electricity. Accordingly, LPSP is computed [38] by the following equation: Unmet load for a year Total load for a year (54)

Land requirement
To consider social and environmental concerns, the land needed for the development of the hybrid system (L H ) has been taken in the optimisation as where L K denotes land needed for installation of 1 kW of the kth RES in m 2 /kW, Z K is the optimal size of the kth RES, N ES is number of RESs considered in the proposed hybrid system. The land needed for the design of 1 kW of each renewable energy based system is given in Table 1.

GWO approach
In this optimisation approach, the population is categorised into four groups such as alpha (α), beta (β), delta (δ) and omega (ω). α wolves are known to be a leading wolf and are most accountable for making decisions about the dormant place, hunting and all other tricks. β wolves are next to α wolves in making help in supervisory or other group activity. β wolves admire the α wolves but give the order to other wolves, which are low in the chain of command. Basically, β wolves play the role of consultant to α wolves and discipliner for the whole group. Further, δ plays a character of scapegoat. It may emerge that δ wolves are not very important in the whole group, but the whole group faces internal combat and grief in the absence of δ wolves. α, β, δ wolves give guidance to other wolves, i.e. ω towards promising area of the search space. Further, the hierarchy of α, β, δ and ω wolves is shown in Fig. 2.
To mathematical model the social behaviour of grey wolves, while designing the GWO algorithm, α is considered to be the fittest solution. β and δ are assumed as second and third best solutions, respectively. ω consists of the remaining candidate solution.
To perform optimisation, three main steps of hunting, searching for pray, encircling or trapping and attacking pray are used.
Encircling or trapping behaviour of grey wolves for pray during hunting is computed using the following equations [60]: X GW (t + 1) = X Pr (t) − eG (57)  where G, A and e indicate the coefficient vectors, X Pr represents the position vector of pray, X GW indicates the position vector of the grey wolf. t denotes the current iteration.
Further, e and A are evaluated using the following equations: where a component of q diminishes linearly in the range of 2 to 0 during iterations. R 1 and R 2 represent random vectors that permit the wolves to arrive at any position between the prescribed points. A grey wolf can update its position based on the position of the prey. By setting the value of e and A vectors, the different places in the region of the best agent can be attained concerning the current position. Hence, the position of the grey wolf inside the space around the prey in any random location can be updated by using (56) and (57).
Grey wolves can figure out their prey. The hunting is generally led by α. Sometimes, β and δ also play a role in hunting. However, there is no idea of the location of the prey in the abstract search space. Thus to mathematical model the hunting behaviour, we assume that α, β and δ wolves have good estimates for the potential location of prey. Therefore, the first three best solutions are recorded to lead the other search agents (ω) to update their position based on the position of the best search agent. The operation of the score and position of α, β and δ wolves (first three search agents) can be done using the following equations: where A 1 , A 2 , A 3 indicate the random vectors. The position vector of prey concerning α, β and δ wolves can be computed as where X α , X β , X δ represent the positions of α, β and δ wolves, respectively. e 1 , e 2 , e 3 indicate the random vectors and t defines the number of iterations. The best position can be computed by taking mean of α, β and δ wolves as given below: Searching for prey indicates exploration capability while attacking the prey represents exploitation capability. e is a random value from −2q to +2q. During optimisation, it diminishes from 2 to 0. When |e| is less than one, grey wolves are enforced to attack the prey. The random values of e are used to enforce the search to move away from the prey. When |e| is greater than one, the members of the population are forced to deviate from the prey. In a nutshell, the search process initiates by creating a random population of grey wolves (candidate solutions) in the GWO approach. During the iterations, α, β and δ wolves estimate the possible location of prey. Each candidate solution updates its distance from the prey. Parameter e is condensed from 2 to 0 to put emphasis on exploration and exploitation. Candidate solutions tend to move away from the prey if |e| is greater than 1 and converge to the prey if |e| is less than 1. In the end, the GWO algorithm is terminated by fulfilling the final criterion. Further, the flowchart of the GWO approach is depicted in Fig. 3.

Techno-economic input parameters
The techno-economic input parameters are required for the optimal sizing of the selected hybrid system which is given as

Electrical load demand (kW)
The hourly electrical load demand during seasons I-III of the selected area is demonstrated in Fig. 4 and also provided in Table 2. The maximum load demand in seasons I-III has been computed as 217.59, 217.59 and 146.59 kW, respectively.

Mean solar irradiance (kWh/m 2 /day)
The monthly daily average solar irradiance for the given area is depicted in Fig. 5 and also provided in Table 3. It is evident that the highest solar irradiance of 6.74 kWh/m 2 /day is available in May, whereas the lowest solar irradiance of 3.53 kWh/m 2 /day is available in December.

Average ambient temperature (°C)
The average ambient temperature of the study area is depicted in Fig. 6 and also given in Table 4. It is evident that the ambient temperature varies from 4 to 43°C during the year.

Scheduling of BMG and BG
In this work, BG and BMG are scheduled for operation during peak load hours in each season and are demonstrated in Figs. 7 and 8, respectively.

Parameters of GWO algorithm
To optimise the objective function, the algorithm parameters have been set as itr max = 100, Run = 30.

Cost parameters of hybrid system components
Economical parameters comprise of capital cost, O&M cost, salvage value and fuel cost of individual system components are given in Table 5. Also, the specification of different system components has been provided in Table 6.

Project parameters
In this work, the life duration of the proposed system has been taken as 25 years. Annual real interest rate of 11% is considered.

Result and discussion
In this study, an attempt has been made to get the optimal design and sizing of the hybrid system considering the different types of RESs. At first, three configurations of the hybrid system in off-grid mode have been considered as (a) Configuration I: Biomass-SPV-battery-based hybrid energy system. (b) Configuration II: Biogas-SPV-battery-based hybrid energy system. (c) Configuration III: Biomass-biogas-SPV-battery-based hybrid energy system.
All off-grid configurations are optimised using GWO algorithm and compared in terms of technical and economical concerns and found the most suitable. Further, the best-off grid configuration is compared with a grid-connected hybrid system and found the most optimal solution. Finally, the result has been compared with HS and PSO optimisation techniques.

Optimisation results of off-grid configuration
The considered off-grid configurations are successfully simulated to meet the full hourly demand of the area for 0% unmet load by the GWO algorithm in MATLAB. After hourly simulation, the IET Energy Syst. Integr. This is an open access article published by the IET and Tianjin University under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/) optimisation result of off-grid configuration has been presented in Table 7.
From Table 7, it is observed that the configuration I has least NPC and COE. The most optimal off-grid configuration consists of 234.53 kW PV array, 164 kW biomass system, 513.6 kWh battery storage and 100 kW converter. The NPC and COE are computed as $807,692.30, $0.118/kWh, respectively.

Optimisation results of considered grid-connected configuration
The objective function (NPC) has been optimised using the GWO algorithm in MATLAB. After hourly simulation, the optimum sizes obtained are given in Table 8. The most optimal configuration comprised of 235 kW PV panels, 10 kW biogas system, 55 kW biomass system, 28.8 kWh battery bank storage and 100 kW converter. The total NPC and COE are estimated as $636,923.07 and 0.088 $/kWh, respectively.

Comparison between off-grid and grid connected configurations 8.3.1 NPC and COE:
The grid-connected configuration has been compared with best off-grid configuration in terms of NPC and COE. From Tables 7 and 8, it is evident that the grid-connected configuration has less NPC and COE compared to off-grid. Therefore, the grid-connected configuration is better in terms of economical concerns.

Total land requirement:
It has been found that the total land requirement for installation of grid-connected configuration and off-grid configuration is 13,451 and 21,828.7 m 2 , respectively. Therefore, there is a saving of 8377.7 m 2 in land use are obtained with grid-connected configuration.
Based on the obtained results, grid-connected hybrid system consisting of SPV, wind, biomass, biogas, and battery is proposed for selected sites. Further, the schematic diagram of the proposed system is depicted in Fig. 9.

Comparison of different optimisation algorithms
Finally, a comparison of different optimisation algorithms has also been carried out to obtain the most optimised results for the best configuration.
The results of the proposed GWO algorithm are compared with HS and PSO for 0% LPSP and given in Table 9. It has been revealed that GWO provides more optimised results compared to HS and PSO.
Also, some other parameters are also compared and demonstrated in Table 10 and evident that GWO performs better.  Further, the convergence curve of PSO, HS and GWO for NPC is shown in Fig. 10. It is revealed from Fig. 10 that GWO provides an optimal solution before ten iterations. However, HS and PSO converged to a fixed value after 90 iterations that show GWO converges faster than other optimisation approaches.

Component wise breakdown of annual energy generation
The percentage wise contribution of different renewable energy technologies in annual power generation is shown in Fig. 11. PV array produced the highest amount of electricity of 450,570 kWh/ year followed by biogas with 15,830 kWh/year and biomass with 12,735 kWh/year.

Cost wise breakdown of total NPC
The share of the capital cost, O&M cost, fuel cost, salvage value, grid purchase and grid sale in total NPC of the hybrid system are illustrated in Table 11. It is found that the cost of grid purchase has the highest share of $433,692.31 among all the system components.

Grid purchase and grid sale
The total cost of grid purchase and revenue generated from grid sale in the considered configuration are calculated as $433,692.31 and $55,792.31, respectively. Further, the annual energy purchase and sold through utility grid is 330,111 and 46,006 kWh/year, respectively. Also, the season-wise energy purchased and sold to the utility grid are indicated in Table 12.
It has been observed that the hybrid system purchases more energy in the season I followed by seasons II and III. It is due to higher energy demand during season I. Further, grid sale and grid purchase are less in season III compared to seasons I and II due to less energy demand.

Season wise battery input and output power
Season-wise battery input and output power are given in Table 13. It has been observed that the battery input power is higher in season III compared to seasons I and II due to high energy demand.

Conclusion
In this study, the optimal sizing of grid-connected solar/biomass/ biogas/battery-based hybrid system has been carried out for rural areas located in Haryana state (India). Different configurations in the off-grid and grid-connected scenario are considered and compared using the GWO algorithm. Grid-connected configuration comprising of solar/biomass/biogas/battery found as the best configuration for the study area. Based on the hourly simulation, the optimum size of the hybrid system in grid scenario for study     area has been obtained as 235 kW PV array, 10 kW biogas system, 55 kW biomass system, 28.8 kWh battery bank storage and 100 kW converter. The total NPC and COE are estimated as $636,923.07 and 0.088 $/kWh, respectively. Further, results have also been compared with PSO and HS and found more appropriate. The land use for installation of the proposed hybrid system for the study area is 13,451 m 2 . The present study may be useful for the development of a hybrid system for the other similar areas and helpful in fulfilling the Indian Government mission of providing 24 × 7 power to all.