ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT AZOJETE June 2022. Vol. 18(2):197-208 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 197 ORIGINAL RESEARCH ARTICLE AN INDEPENDENT FRAMEWORK FOR OFF-GRID HYBRID RENEWABLE ENERGY DESIGN USING OPTIMAL FORAGING ALGORITHM (OFA) M. M. Muhammad1*, J. Usman1, I. Mustapha1, M. U. M. Bakura1 and A. T. Salawudeen2 1Department of Electrical and Electronics Engineering, University of Maiduguri, Maiduguri, Nigeria 2Department of Electrical and Electronic Engineering, University of Jos, Jos, Nigeria *Corresponding author’s email address: engr.massa@gmail.com 1.0 Introduction Electricity is requisite for socio-economic development of every society. Unfortunately, sub- Saharan Africa is challenged with different electrification problem. One of the popular technologies which have been widely adopted to improve the electrical energy demand has been based on renewable energy resources especially in remote areas where power generated cannot be supplied to such communities due to difficulties in the transmission and distribution systems (Njoh et al., 2019). Renewable energy generation have identified solution to these problems and as an effective source of energy in such areas. The Off-grid mode of energy generation does not ARTICLE INFORMATION ABSTRACT The rapidly increase in electrical energy demand from residential, commercial and industrial sectors is one of the major challenge in power system, especially in the current period of high oil prices, steadily reducing energy sources and increased concerns about environmental pollution. Renewable energy is considered as one of the solution to this increase in power demand. The conventional method of power system cannot meet the power demand for many reasons such as environmental effects, location of the consumer, price of fuel and others. This paper presents the design of an off-grid Hybrid Renewable Energy System (HRES) for electrification of a typical remote area. The designed hybrid system consists of three different configurations of PV/Battery, Wind/Battery and PV/Wind/Battery systems. The system components are modelled and the objective function is designed as a function of total annualized cost of the system subject to some constraints binding the decision variables. The total annual cost is formulated as a function of annual capital cost and annual maintenance cost of the system subject to some operational constraints. In order to determine the optimal number of the decision variables that would satisfy the load demand in the most cost effect manner, Optimal Foraging Optimization (OFA) algorithm was used. Finally, a simulation experiment shows that the total annual cost obtained by each algorithm for the PV/Battery system is $9,340.42 or N3,876,274.30, $9,446.77 or N3,920,409.55 and $10,076.34 or N4,181,681.1 for OFA, GA and PSO respectively. For the Wind/Battery configuration, the total annual cost obtained by OFA, GA and PSO are $17,508.20 or N7,265,903, $12,493.27 or N 5,184,707.05 and $16,535.93 or N6,862,410.95 respectively. Similarly, the PV/Wind/Battery configuration showed that the OFA, GA and PSO obtained an annualized cost of $15,926.07 or N6,609,319.05, $18,167.09 or N7,539,342.35 and $16,535.93 or N6,862,410,95 respectively. From the results obtained by OFA are compared with that of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm. Results showed that all the algorithm can efficiently size the hybrid system with OFA obtaining the most economical design. Therefore, for economically and efficiently electrification of a remote area in Abuja using an off-grid hybrid renewable energy system, GA optimization algorithm is recommended for wind/Battery system and OFA optimization algorithm is recommended for PV/Wind/Battery system. © 2022 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved. Submitted 7 August, 2021 Revised 21 October, 2021 Accepted 30 October, 2021 Keywords: Optimal Foraging Algorithm (OFA) Stand-alone hybrid energy system Optimal sizing Total Annual Cost Micro-grid http://www.azojete.com.ng/ mailto:engr.massa@gmail.com mailto:engr.massa@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June, 2022; Vol. 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 198 require complex interconnections of power systems generation equipment like the main grid. One of the major challenges which have hinder harnessing renewable energy to full capacity is the weather conditions. The total dependency of wind and solar energy on weather and climatic conditions has been a major drawback in total harvesting their energy to full capacity (Ogunjuyigbe et al., 2016) . The energy generated from the individual sources may not be sufficient for a considerable amount of time. To address these challenges several researches have proposed hybridizing different renewable energy sources to compensate for energy shortage that arise from individual sources. To efficiently and economically utilize the hybrid energy systems, a proper sizing mechanism is important (Ogunjuyigbe et al., 2019). Several studies related to the optimal sizing of stand-alone hybrid energy systems have been conducted in the literature. Dong et al. (2016) reported an improved Ant Colony Optimization (ACO) algorithm for optimizing a multi-objective stand-alone hybrid PV/wind/battery/hydrogen system with major focus on reliability and economy of supply. The loss of power supply and total annual cost were modelled as a dual objective function which the ACO was used to minimize. An optimized hybrid renewable energy system of PV/wind/battery for electrification of a remote area in Iran using particle swarm optimization technique was proposed in (Askarzadeh, 2015).The particles of PSO probe the search space to minimize the life cycle cost (LCC), at the same time maintaining a reliable system. In (Kanase-Patil et al., 2010) LINGO software was used to analyzed integrated renewable energy systems for off-grid rural electrification of remote area in India. The optimal system cost, reliability and cost of energy were evaluated for four different renewable energy technologies which include biomass, micro hydro, solar and wind. In Maleki et al. (2014), a discrete harmony search (DHS) optimization algorithm was used to optimally size an off-grid of PV/wind/diesel system with battery storage. For performance evaluation, the results of DHS are compared with results found by a discrete simulated annealing (DSA) algorithm. The proposed methods minimize the total annual cost (CT) of the off-grid system effectively. Although various aspects of HRES system have been studied, useful and interesting model and efficient optimization tool for optimal sizing is still a major challenge for researchers. In this regard, this paper presents an efficient sizing technique for optimal sizing of off grid hybrid renewable energy system using Optimal Foraging Algorithm (OFA). The HRES model is designed to incorporate photovoltaic system, wind energy and energy storage. Different configurations including PV/Battery, Wind/Battery and PV/Wind/Battery were considered to analyze the effectiveness of OFA in solving the HRES problem. Each configuration of HRES system is optimization considering total annualize cost as a metric. For performance evaluation the results of OFA are compared with that of found by Particle Swarm Optimization and Genetic Algorithm. The outline of this paper is organized as follows: The modelling of the hybrid energy system is given in section 2. Section 3 presents the hybrid renewable energy optimization problem formulation. Section 4, present the Optimal Foraging Algorithm (OFA). Section 5 gives the simulation results. Finally, a conclusion for this work is stated in section 6. 2. Materials and methods The hybrid energy system is made up of photovoltaic modules and wind turbines (WTs) as renewable energy sources and battery bank for excessing energy storage. The battery bank helps to maintain constant power supply when the power generated by the renewable energy sources is less than the power demand. If the power generated by the renewable energy sources is higher than the load demand, then excess energy is stored in the battery bank. The schematic representation of the hybrid renewable energy system is shown in Figure 1. file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:engr.massa@gmail.com Muhammad et al: An Independent Framework for Off-Grid Hybrid Renewable Energy Design Using Optimal Foraging Algorithm (OFA). AZOJETE, 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 199 Figure 1. Schematic description of the PV/wind/battery based hybrid system (Gil Mena et al., 2021). 2.1 Modelling A brief modelling of the hybrid system which consist of PV modules, the wind turbines, the battery storage as being used in the algorithm is as presented. 2.1.1 Photovoltaic System The output power of every PV system (𝑃𝑃𝑉) at time step t can be calculated from the solar radiation using: ( ) ( )pv pvP t I t A    (1) Where I is the solar radiation (W/m2), A symbolizes the area of PV (m2) and Ƞ𝑃𝑉 is the efficiency of the PV’s modules. It is assumed that the PV panels is embedded with maximum power point tracking (MPPT) system. 2.1.2 Wind Turbine Low speed winds usually don’t have sufficient power to subdue friction of the wind turbine. Therefore, at wind speed less than the cut-in wind speed (𝑉𝑐𝑖) no power is generated. With increase in velocity greater than the cut-in wind speed, the power generated by the wind turbine generator rises as the cube of wind speed. As the wind speed increase continuously, up to the rated value say (𝑉𝑟), the generator produces as much power it is designed for say (𝑃𝑟) in kW. At a certain level, when the wind speed is so high it becomes a threat to the wind turbine. At this wind speed, named the cut-out wind speed (𝑉𝑐𝑜), the wind turbine needs to be shut down to prevent it from damaging (Maleki et al., 2016). Hence, the output power is zero. Mathematically, this behavior can be expressed as follows: 𝑃𝑊𝑇(𝑡) = { 0 𝑃𝑟 𝑃𝑟 𝑣3(𝑡)−𝑉𝑐𝑖 3 𝑉𝑟 3−𝑉𝑐𝑖 3 𝑣(𝑡) ≤ 𝑉𝑐𝑖 𝑜𝑟 𝑣(𝑡) ≥ 𝑉𝑐𝑜 𝑉𝑐𝑖 < 𝑣(𝑡) < 𝑉𝑟 𝑉𝑟 < 𝑣(𝑡) < 𝑉𝑐𝑜 (2) http://www.azojete.com.ng/ mailto:engr.massa@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June, 2022; Vol. 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 200 Where 𝑣(𝑡) is the wind speed in m/s at time t. The rated power of the wind turbine generator (𝑃𝑟) is defined as a function of the air density (𝜌𝑎 ), the swept rotor area occupied by the rotating wind turbine blades (𝐴𝑤 ), the power coefficient (𝐶𝑝) and the wind turbine generator efficiency (Ƞ𝑔) as follows: 31 2 r a w p g rP A C V       (3) 2.1.4 Battery The battery is used to store the excess generated power by the renewable resources and also cut power mismatch between generation and load demand. State of Charge (𝑆𝑂𝐶) of battery in accordance with productivity and consumption period can be obtained when the total output power of the hybrid system is greater than the load demand, 𝑒𝑃𝑉(𝑡) + 𝑒𝑊𝑇(𝑡) > 𝐸𝐿𝑜𝑎𝑑(𝑡), The charge quantity of the battery at time t can be written as (Maleki et al., 2014): ( ) ( ) ( 1) (1 ) [ (t) ( )) ]Load BC inv E t eBat t eBat t ePV ewT t           (4) Where 𝑒𝐵𝑎𝑡(𝑡) and 𝑒𝐵𝑎𝑡(𝑡 − 1) are the charge quantities of the battery bank at time 𝑡 and 𝑡 − 1, σ is the hourly self-discharge rate, Ƞ𝐼𝑛𝑣 is the inverter efficiency, 𝐸𝐿𝑜𝑎𝑑(𝑡) is the load demand for a particular hour and Ƞ𝐵𝐶 is the charge efficiency of the battery bank. When the total output power of hybrid system is less than the load demand, 𝑒𝑃𝑉(𝑡) + 𝑒𝑊𝑇(𝑡) < 𝐸𝐿𝑜𝑎𝑑(𝑡), the battery bank is in discharging state. The charge quantity of the battery at time t can be obtained as: ( ) ( ) ( 1) (1 ) ( ) ( ))Load Inv E t eBat t eBat t ePV t eWT t              (5) Where Ƞ𝐵𝐷 is the discharging efficiency of the battery bank which ranges from 0-100%. In this research, the value is assumed to be 100%. 2.1.5 Load Profile The load profile defines the requirements of power supply from the off-grid PV/wind hybrid energy system. The hourly load profile for a residential building collected through questioner (Figure 2). The study of the load profile reveal that the households wake up in the morning to prepare for business, work and school (more electricity is needed to prepare for hot showers and breakfast). People then leave for business, work and school typically at 7:00hr and close by 18:00hr on weekdays. At around this time, most households switch on lighting points, fans, prepare for dinner and watch TV up to around 22:00hr before bed time. file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:engr.massa@gmail.com Muhammad et al: An Independent Framework for Off-Grid Hybrid Renewable Energy Design Using Optimal Foraging Algorithm (OFA). AZOJETE, 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 201 Figure 2. Hourly load profile 3. Problem formulation 3.1 Objective function The optimization problem is to minimize the total annual cost ( )TAC of system. The TAC consists of annual capital cost ( )ACC and annual maintenance cost ( )AMC . To optimally size the stand-alone hybrid energy system, the following cost function is minimized using Optimal Foraging Algorithm (OFA). (Kellogg et al., 1998). AC AMTAC C C  (6) Capital cost take place at the starting of a project while maintenance cost take place during project life. To transform the initial capital cost to the annual capital cost, the capital recovery factor (𝐶𝑅𝐹) is expressed by equation (7). (Belfkira et al., 2014). (1 ) (1 ) 1 n n i i CRF i     (7) Where, 𝑛 denotes the life span of the system and 𝑖 is the interest rate. The duration of the proposed hybrid energy system is assigned to be 20 years. Some of the hybrid system components is expected to be changed during the project’s lifetime. The lifetime of a battery is assumed to be 5 years. Using single payment present worth factor, we have (Eltamaly et al., 2016): 0,5,10,15 1 (1 ) Bat Bat k k C P i     (8) Where 𝐶𝐵𝑎𝑡 is the present worth of battery and 𝑃𝐵𝑎𝑡 is the battery price. Similarly, the duration of converters is assumed to be 10 years. We can calculate the converter cost as 0,10 1 (1 ) conv conv k k C P i     (9) Where 𝐶𝐶𝑜𝑛𝑣/𝐼𝑛𝑣 is the present worth of converter/inverter components and 𝑃𝐶𝑜𝑛𝑣/𝐼𝑛𝑣 is converter/inverter price. http://www.azojete.com.ng/ mailto:engr.massa@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June, 2022; Vol. 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 202 Thus, the total annual capital and maintenance cost are obtained by equations (10) and (11) relatively. AC pv WT Bat convC CRF nPV C nWT C nBat C nConv C           (10) Where 𝑛𝑃𝑉 is the number of PV panels, 𝐶𝑃𝑉 is unit cost of PV panel, 𝑛𝑊𝑇 is the number of wind turbines, 𝐶𝑊𝑇 is the unit cost of wind turbine, 𝑛𝐵𝑎𝑡 is the number of batteries and 𝑛𝐶𝑜𝑛𝑣 is the number of converter/inverter systems. AM pv Mtn pv WT Mtn WTC C N C N     (11) Where 𝐶𝑃𝑉−𝑀𝑡𝑛 and 𝐶𝑊𝑇−𝑀𝑡𝑛 are the annual maintenance cost of PV panel and wind turbine respectively. The maintenance costs of battery and converter/inverter systems are ignored. 3.2 Constraints For the stand-alone PV/wind/Storage energy system, the following decision variable constraints should be satisfied: min max ,nPV nPV nPV nPV Integer   (12) min max ,nWT nWT nWT nWT Integer   (13) min max ,nBat nBat nBat nBat Integer   (14) Where 𝑛𝑃𝑉𝑚𝑎𝑥, 𝑛𝑊𝑇𝑚𝑎𝑥 and 𝑛𝐵𝑎𝑡𝑚𝑎𝑥 are the upper bound of the PV panels, Wind turbines and Batteries respectively. Then, 𝑛𝑃𝑉𝑚𝑖𝑛, 𝑛𝑊𝑇𝑚𝑖𝑛 and 𝑛𝐵𝑎𝑡𝑚𝑖𝑛 are the lower bound of PV panels, Wind turbines and Batteries respectively. Moreover, at any time, the quantity of charge in the battery bank should satisfy: min max( ) ( ) ( )eBat t eBat t eBat t  The maximum charge quantity of the battery bank 𝑒𝐵𝑎𝑡𝑚𝑎𝑥 takes the value of nominal capacity of battery bank (𝑆𝐵𝑎𝑡𝑡) and the minimum charge quantity of the battery bank 𝐸𝑚𝑖𝑛 is obtained by maximum depth of discharge (𝐷𝑂𝐷). min (1 ) BatteBat DOD S   (15) 4. Optimal Foraging Algorithm (OFA) The OFA is a metaheuristic algorithm developed from the idea of Optimal Foraging Theory (OFT). Optimal foraging theory is a concept that described the dietary patterns of biology organisms towards food (Salawudeen et al., 2018, Mu'azu et al., 2018) . When a biological organism searches for food, three important questions must be considered. These questions are: i. where is best suitable to search for food? ii. At what point/time should a new source of food be searched? and iii. what kind of food sources should be exploited? Organisms employ these three rules to maximize the net energy acquired during foraging process. This concept was used to develop the OFA by Zhu and Zhang. (Ahmed T S et al., 2020) and (Zhu et al., 2017). In OFA, individual foragers select areas to forage using a certain rule. After foraging a new search space, the individual foragers decide whether the food energy in this area is beneficial or not. Other foragers are attracted to the new area if the food energy is valuable thus increasing the diversification of the algorithm. Now, assume there are N individual foragers in a group foraging in D-dimensional search space. The initial positions of the foragers ,1 ,2 ,[ , ,..., ]t t t t i i i N Dx x x x can be generated as (Zhang et al., 2017, Zhu et al., 2017 and Salawudeen et al., 2021): file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:engr.massa@gmail.com Muhammad et al: An Independent Framework for Off-Grid Hybrid Renewable Energy Design Using Optimal Foraging Algorithm (OFA). AZOJETE, 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 203  1 t L U L i i i ix x r x x    (16) The objective function of this initial position is computed as  ( ) min ( ), , 1,2,3,...,t L t U i x R i i if x f x R x x x i D     (17) where R is the constrain space, L ix and U ix are the lower and upper bound values, 1r is a random number generated within the range of 0 and 1. As the foragers in OFA iterate during the optimization process, the best foragers in the group forage using 1 2 3( ) ( )t t t t t t i i i worst i worstx x k r x x k r x x          (18) The remaining individual in the foraging group forage using 1 3 5( ) ( )t t t t t t i i random i random ix x k r x x k r x x          (19) where k is defined as max/k t t , t is the current iterations, tmax is the maximum iteration number, r2, r3, r4 and r5 are all randomly generated number. In OFA, the position of foragers obtained after t iterations is regarded as unprofitable position, and the corresponding fitness is regarded as unprofitable fitness ( t jF ). Similarly, the positions of foragers after iteration t+1 is regarded profitable prey location and the corresponding fitness can be represented as 1t jF  . Based on this information, the positions of current foragers are updated if the following equation is satisfied (Eltamaly et al., 2016) and (Zhang et al., 2017). 1 1 11 ( 1) t t t i j j t i F F tt           (20) where  is a random number. If the above equation (22) is not satisfied the previous position of the foragers are retained 5. Results and discussion This section discourses the results of the hybrid renewable energy system obtained by the optimal foraging algorithm in comparison with genetic algorithm and particle swarm optimization. The hybrid system design was implemented in MATLAB R2020b simulation platform. As input, the model employed data of wind speed and solar irradiance measured in in Abuja, Nigeria (latitude: 9.08200 N, Longitude: 8.67530 E). The hybrid resources component parameters have been given in Table 1. The parameter settings of the OFA, GA and PSO are as follows. OFA: 𝑘 = 𝑖𝑡𝑒𝑟/𝑖𝑡𝑒𝑟𝑚𝑎𝑥 𝑁 = 50, 𝑖𝑡𝑒𝑟𝑚𝑎𝑥 = 30,000, PSO: 𝑁 = 50, 𝑐1 = 2, 𝑐2 = 2, 𝜔 = 1, 𝑖𝑡𝑒𝑟𝑚𝑎𝑥 = 300,000; GA: 𝑁 = 50, 𝑖𝑡𝑒𝑟𝑚𝑎𝑥 = 300,00. The lower and upper bounds of the decision variables were set to 0 and 300 respectively. At the initial stage, it is assumed that the battery is charged at 30% of its nominal capacity. The average (Avg), best (Best) and standard deviation (Std) performed over 30 independent runs are summarized in Table 2. http://www.azojete.com.ng/ mailto:engr.massa@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June, 2022; Vol. 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 204 Table 1: Component Parameters Parameters Value Parameters Value Parameters Value I n PV panel rated power A ȠPV CPV CPV-Mtn Life span Power Conv/Inv Rated power inv /conv invP Life span 5% 20years 260 W 1.656m2 15.7% 585 $ 21 $ 20 years 3 kW 95% 2000 $ 10years Diesel generator PDR CDiesel CDiesel-Mtn Life span PFuel Wind turbine rated power (Pr) ciV coV rV WTC CWT-Mtn Life span 1.9 kW 1713.15$ 0.2 $/h 8760 h 1.24 $/l 1 kW 2.5 m s 13m s 11m s 2313$ 40$ 20 years Battery Voltage SBatt ȠBC ȠBD PBatt DOD σ Life span 12 V 2.4kWh 85% 100% 170 $ 0.8 0.0002 5 years Table 2. The mean, standard deviation, best and worst performances of the algorithms HRES Index Algorithms OFA GA PSO PV/wind/battery PV/battery Wind/battery Average rank Final rank Mean Std Best Worst Rank Mean Std Best Worst Rank Mean Std Best Worst Rank 17,957.19 2,601.833 15,926.07 21,765.71 1 10,601.46 1,274.94 9,340,42.00 11,223.17 1 18,527.51 1,492.00 17,508.20 19,759.55 3 2.5 1 18,720.07 543.67 18,167.09 19,331.17 3 10,601.46 1224.256 9,446.77 10,601.46 2 13,527.51 705.512 12,493.27 13,527.51 1 3 2 17,549.15 1,066.27 16,535.93 18,948.22 2 10,178.25 102.47 10,076.34 10,319.43 3 17,745.15 933.5633 16,535.93 18,075.15 2 3.5 3 The breakdown of the statistical results obtained by the algorithms on each sizing component is presented in Table 2. From this table, the algorithms are ranked based on the best results obtained for each configuration. It can be observed that the OFA obtained the best final rank with a rank of 1. Whereas the GA and PSO obtained a rank of 2 and 3 respectively. This shows that, for the hybrid system design in this paper, the OFA appears to be the suitable algorithm for obtaining the most economical system. This further justifies the acceptability of the algorithms in solving the HRES problem, the characteristics of the algorithms were generated. The superimposed convergence graph of the algorithms on each hybrid system configuration is given in Figure 3, Figure 4 and Figure 5 for PV/Battery, Wind/Battery and PV/Wind/Battery, respectively. file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:engr.massa@gmail.com Muhammad et al: An Independent Framework for Off-Grid Hybrid Renewable Energy Design Using Optimal Foraging Algorithm (OFA). AZOJETE, 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 205 It is seen from Tables 3-5, that economically the PV/battery configuration obtained the best annualized cost for supplying the load demand. The total annual cost obtained by each algorithm for the PV/Battery system is $9,340,42, $9,446.77 and $10,076.34 for OFA, GA and PSO respectively. For the Wind/Battery configuration, the total annual cost obtained by OFA, GA and PSO are $17,508.20, $12,493.27 and $16,535.93 respectively. Similarly, the PV/Wind/Battery configuration showed that the OFA, GA and PSO obtained an annualized cost of $15,926.07, $18,167.09 and $16,535.93 respectively. The optimal size of the hybrid resources obtained by the OFA are as follows. PV/Batter: nPV = 102, nBat = 35, Wind/Battery: nWT = 101, nBat = 99 and PV/Wind/Battery: nPV = 125, nWT = 18, nBat = 115. The cost of other components has also been given in the table. Table 3. Summary of the best results obtained for PV/Battery System HRES OFA GA PSO NPV NWT NBatt NConv/Inv PV cost ($) WT cost ($) Battery cost ($) Conv/Inv cost ($) Total annual cost ($) 102 -- 35 4 6,930.07 -- 1,374.00 1,036.04 9,340,42 66 -- 100 4 4,484.17 -- 3,926.57 1,036.04 9,446.77 77 -- 97 4 5,231.52 -- 3,808.78 1,036.04 10,076.34 Table 4. Summary of the best results obtained for Wind/Battery System HRES OFA GA PSO NPV NWT NBatt NConv/Inv PV cost ($) WT cost ($) Battery cost ($) Conv/Inv cost ($) Total annual cost ($) -- 101 99 3 -- 11,988.00 4,673.20 847.51 17,508.20 -- 77 115 3 -- 6,941.67 4,515.56 1,036.04 12,493.27 -- 75 102 3 -- 6,761.37 4,005.10 1,036.04 11,802.51 Table 5. Summary of the best results obtained for PV/Wind/Battery System HRES OFA GA PSO NPV NWT NBatt NConv/Inv PV cost ($) WT cost ($) Battery cost ($) Conv/Inv cost ($) Total annual cost ($) 125 18 115 5 8,492.74 1,622.73 4,515.56 1,295.05 15,926.07 25 140 65 5 1,698.55 12,621.23 2,552.27 1,295.05 18,167.09 39 107 75 5 2,649.73 9,646.22 2,944.93 1,295.05 16,535.93 http://www.azojete.com.ng/ mailto:engr.massa@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June, 2022; Vol. 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 206 Figure 3: Convergence on PV/Battery Configuration Figure 4: Convergence on Wind/Battery Configuration Figure 5: Convergence on PV/Wind/Battery Configuration From the convergence plots given in Figures 3 to 5, it can be observed that the OFA converges faster in Wind/Battery and PV/Wind Battery configurations. For the PV/Battery Configuration, only GA has a better convergence over OFA. file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:engr.massa@gmail.com Muhammad et al: An Independent Framework for Off-Grid Hybrid Renewable Energy Design Using Optimal Foraging Algorithm (OFA). AZOJETE, 18(2):197-208. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: engr.massa@gmail.com 207 6. Conclusion This paper presents an off-grid hybrid renewable energy system for electrification of a remote area in Abuja, Nigeria. The hybrid system was formulated into an optimization problem where the annualized cost serves as the objective function to be minimized. The optimization problem was solved using optimal foraging optimization algorithm and results was compared with genetic algorithm and particle swarm optimization. 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