Designing of standalone hybrid PV/wind/battery system using improved crow search algorithm considering reliability index
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Abstract
In this paper, the design of a hybrid renewable energy PV/wind/battery system is proposed for improving the load supply reliability over a study horizon considering the Net Present Cost (NPC) as the objective function to minimize. The NPC includes the costs related to the investment, replacement, operation, and maintenance of the hybrid system. The considered reliability index is the deficit powerhourly interruption probability of the load demand. The decision variables are the number of PV panels, wind turbines and batteries, capacity of transferred power by inverter, angle of PV panels, and wind tower height. To solve the optimization problem, a new algorithm named improved crow search algorithm (ICSA) is proposed. The design of the system is done for Zanjan city, Iran based on real data of solar radiation and wind speed of this area. The performance of the proposed ICSA is compared with crow search algorithm (CSA) and particle swarm optimization methods in different combinations of system. This comparison shows that the proposed ICSA algorithm has better performance than other methods.
Keywords
Hybrid PV/wind/battery system Net present cost Reliability index Improved crow search algorithmIntroduction
In recent years, the applications of hybrid renewable energy sources have grown rapidly [1, 2, 3]. The main objective of studies related to hybrid systems is to improve the existing challenges stemming from the optimal sizing of hybrid equipment depending on load demand. Before implementing and installing the hybrid system equipment, it is necessary to determine its capacity using design methods in an optimal manner so as to obtain the capital cost and feasibility studies [4, 5]. Equipment sizing is basically the method of determining the capacity of the hybrid system equipment by minimizing the system cost while preserving the reliability of the load supply. A large size of the equipment will increase the system cost, while a small capacity; this may lead to a failure of the powergeneration system to supply the load [4]. Various methods such as graphical structure, probabilistic approach, iterationbased method, and artificial intelligence (AI) have been used by previous studies to optimally design energy hybrid systems [1, 2, 3, 4, 5, 6]. In the graphical structure method, the problem with two design variables can be solved by a graphical observation of how they change with respect to one another [6]. In [7], a method for optimal sizing of a solar–wind hybrid system is presented, where the optimal combination of the system is obtained by determining the amount of generation cost and the amount of system reliability constraint through preserving the capacity of wind generators and considering deficit powerhourly interruption probability (DPHIP) constraint.
In the optimal design of hybrid energy systems, which is an optimization problem with multiple factors, due to the complexity of the problem, conventional methods are incapable of solving the problem appropriately. For this reason, in recent years, the use of AI methods has been greatly welcomed. Reliability/cost assessment of solar–wind hybrid systems with a fuel cell system to minimize annual costs of the system plus the cost of load energy not supplied considering the reliability constraints of the probability of nonsupplying the load has been studied using particle swarm optimization (PSO) algorithm [8]. The optimal size of a solar–wind hybrid system with fuel cell is presented using imperialist competitive algorithm (ICA) to minimize energy generation costs and the cost of load energy not supplied [9]. Design and management of solar–wind–fuel cell system as a case study for the city of Ardabil, Iran, are proposed using the flower pollination algorithm (FPA) with the aim of minimizing the net present value (NPV) and taking into account two reliability constraints at the same time, namely, loss of expected energy (LOEE), and loss of load expected (LOLE) [10]. The optimal design of a solar–wind–fuel cell hybrid system is presented in [11] using harmony search algorithm (HSA) to minimize the lifespan cost by considering loss of power supply probability (LPSP). The artificial bee colony (ABC) algorithm has been used in [12] to find the optimal size of an independent solar–wind hybrid system based on a storage system by considering the LPSP reliability constraint. The optimal design of a solar–wind–battery hybrid system has been presented in [13] to minimize the annual energy generation costs by taking into account the reliability constraints of the probability of load energy not supplied using the genetic algorithm (GA). The obtained results show that by increasing the reliability of the system, the energy generation cost increases. The optimal design of solar–wind–battery hybrid systems with the aim of minimizing the annual costs of the system considering the power balance constraint was investigated in [14]. The purpose of this study was to determine the number of solar panels, wind turbines, and the number of batteries using the discrete harmonic search algorithm (DHSA). The optimal design of hybrid systems is provided by minimizing total costs and environmental pollution using GA [15]. In [16], the sizing of solar–wind hybrid systems by utilizing a battery bank with the objective of achieving the reliability constraint of desired load supply and the minimum annual system cost is presented using GA. In [17], a threecriterion optimization objective function with the minimization of total costs, environmental fuel emissions, and load power deficiency is proposed using Paretoevolutionary algorithm to determine the optimal size of energy hybrid system. In [18], the combination of PSO algorithm and optimization constraints has been used to determine the optimal size of equipment of hybrid energy systems. In this study, the total system costs are considered as the objective function of the optimization problem and environmental pollution and load energy deficiency were taken into account as constraints. The optimal design of solar–wind–diesel hybrid energy system aiming at minimizing the annual costs of the system considering reliability constraints and fuel emission was performed in [19] using a pseudoevolutionary algorithm. The authors of [20] used the bigbang (BB) algorithm to optimally design of a gridindependent solar–battery hybrid system with battery storage. In this study, the minimization of capital investment and repair and maintenance costs are considered as the objective function of the problem and a reliability index is assumed as the technical constraint of the problem. The optimal design of solar–wind–battery system using evolutionary algorithm (DA) has been studied by minimizing capital investment and repair and maintenance costs of equipment and the probability of notsupplied load constraint and the effects of the mentioned variations on the optimal size of equipment and the cost of the hybrid system have been evaluated [21]. In [22], the optimization of a solar–wind hybrid system with a battery bank has been investigated to minimize the annual cost of the system by considering the power balance constraint using the grey wolf optimizer (GWO) algorithm. In this study, the effect of equipment availability was evaluated by providing a reliability model [22]. The optimal design of a solar–diesel–battery system is presented using the cuckoo search algorithm (CSA) by minimizing the system powergeneration cost and improving the reliability of the load [23]. In [24], the optimal design of a solar–wind–hydro system is presented based on the use of biogeographybased optimization (BBO) algorithm to specify the optimal size of the equipment.
Depending on the algorithm used to solve the design problem of a hybrid system, some of the advantages and disadvantages of these algorithms are described as follows. The GA is very suitable for optimization of problems with discrete quantities. However, when the search space is relatively small, the GA has a slower performance compared to some other similar methods [25]. Despite several benefits, such as sharing information between particles, high convergence rate, and better robustness against trapping at local optimal points, the PSO has disadvantages such as premature integration establishment and population diversity. The main disadvantage of the ICA is its dependence on the initial value of the parameters, and if an inappropriate amount is selected for the initial parameter, it will be trapped in the local optimum. The ABC, HSA, and CSA algorithms have suitable performance for solving optimization problems [25]. They also benefit high computational power and speed. Nevertheless, when the system under study is selected large and the number of optimization variables is high, these methods may become trapped in the local optimum and could not reach the global optimum [3, 4, 26].
From the above description, it is obvious that the competition is about using a method with high convergence accuracy and speed to achieve global optimum. On the other hand, an algorithm may well solve an optimization problem, but fail to solve another problem. As an appropriate solution, researchers examine different solving approaches of a problem to achieve a better solution. Therefore, selecting an appropriate algorithm with high precision and high convergence speed is very important for achieving the optimal size of hybrid systems. This has led to new opportunities for new optimization methods to be utilized in addressing a variety of problems and overcome the disadvantages of the conventional methods. On the other hand, the formulation of most of the reliability constraints used in designing hybrid systems has been implemented based on the concept of the power or energy associated with the load. To design the energy hybrid systems more precisely and to achieve a more reliable system, the concept of load interruption hours should also be considered in the formulation of reliability constraints and considering that it is possible to present the reliability constraint as a combination of power or energy concepts as well as load disruption hours. In addition, the problem of designing optimal solar–wind hybrid systems in a particular region requires the knowledge of sun radiation, temperature, and wind speed data in that area. Therefore, climatic conditions, including solar irradiation and wind speed in each geographic region, have a direct impact on the unit commitment of solar and wind power units in the hybrid system. Consequently, at first, feasibility studies should be made for each region.
In this paper, the optimal design of a PV/WT/Battery hybrid system is presented to minimize the NPCS with regard to hybrid constraint of deficit powerhourly interruption probability (DPHIP) for a case study in the city of Zanjan, Iran, for a 20year study horizon. To determine the system parameters, including the optimal number of solar panels and wind turbines, the number of batteries, power transfer capacity of the inverter, solar array angle, and wind turbine height, a novel algorithm known as improved crow search algorithm (ICSA) has been introduced. The traditional CSA algorithm is inspired by the social behavior of crows in concealing their food. To improve the performance of the traditional CSA method, the mutation and crossover operators of GA method are employed to improve its performance in terms of increasing convergence speed, preventing trapping in local optima, and achieving accurate global optimum, based on which the ICSA algorithm is established. In the current research, the optimal design of the system in various combinations including solar–battery (PV/Batt) system, wind–battery (WT/Batt) system, and solar–wind–battery (PV/WT/Batt) system is performed considering the NPCS and DPHIP and the best combination for Zanjan is determined evaluating economic and technical indices. Moreover, in this paper, the effect of DPHIP constraint variations on the design of different system combinations is investigated. In addition, the capability of ICSA method in the design of hybrid systems is compared with a traditional CSA algorithm as well as with the PSO algorithm having high computational accuracy and power in solving optimization problems.
 1.
The optimal design of a hybrid system for Zanjan city to minimize the NPCS considering the DPHIP hybrid constraint
 2.
The use of ICSA metaheuristic algorithm for designing the hybrid system
 3.
Determination of the best combination of an hybrid system for Zanjan based on the real data of solar radiation and wind speed
 4.
Comparison of capabilities of the ICSA method with wellknown methods like PSO and CSA when designing the hybrid system
 5.
Investigation of the effects of DPHIP variations on system design, NPCS, and DPP.
Case study: Zanjan City
Iran has a high potential for deploying a variety of renewable energy sources and implement hybrid energy systems. In this study, solar radiation and wind speed data of Zanjan were used to design a solar–wind–battery hybrid system and feasibility study on the implementation of renewable energy systems in this city was investigated. Zanjan city is located in the northwest of Iran in the Azarbaijan area, with (Northern) latitude of \( 36^{ \circ } 68^{{\prime }} \) and (Eastern) longitude of \( 48^{ \circ } 50^{{\prime }} \), and is 1650 m above sea level [27].
The studied renewable energy system
System configuration
System operation
The operation of PV/WT/Batt energy system is such that the whole load is supplied (DPHIP = 0) when total generated power by solar arrays and wind turbines are equal to the load demand. In the case the overall generated power by PVs and wind turbines is greater than the load demand, the excessive power is injected into the battery and it will be in charging mode (DPHIP = 0). On the other hand, when the generated energy by PV and wind units is lower than the load demand, then the load deficiency is compensated by battery discharge. When the produced power by PVs and WTs as well as battery power are unable to fully supply the load, a part of the load is curtailed, and under such conditions, a reliability index is proposed as DPHIP index (\( 0 \le {\text{DPHIP}} \le 1 \)). DPHIP is a combined reliability index representing the probability of load deficit power to the total load powerhourly load interruption probability to the total load hours.
System equipment modeling
This section presents the modeling of all PV/WT/Batt system equipment.
Solar panel
Wind turbine
Battery bank

Battery charging mode

Battery discharging mode
Objective function and problem constraints
The purpose of design is to determine the optimization variables including the number of solar arrays, wind turbines, batteries, inverter’s transfer power, solar panel angle, and the height of wind tower considering the objective function of minimizing NPCS and satisfying the reliability hybrid constraint, known as DPHIP. In this study, the data related to solar radiation and wind speed in Zanjan city are chosen for optimal design of the PV/WT/Batt system.
It should be noted that in optimal designing of hybrid energy systems, it is necessary to provide an optimization objective function and the other to provide a reliability constraint. In all hybrid system designing studies, the objective function is presented as an economic index that is, cost. And, the reliability constraint is also expressed as a technical index. The economic index refers to the cost of the net present cost of the load supply, as presented in Eq. (11). The technical index refers to the system load supply, which is presented in Eqs. (20) and (21).
Objective function
Constraints
Proposed method for solving optimization problem
The optimal design of PV/WT/Batt system based on economic and technical indices is a nonlinear optimization problem. A metaheuristic method known as improved crow search algorithm (ICSA) has been used in this study to solve the mentioned problem, which will be described in the following subsection.
Crow search algorithm (CSA)
Crow search algorithm (CSA) is a metaheuristic method inspired by intelligent behavior of crows, which was introduced by Askarzadeh in 2016 [29]. Since crows are voracious, they follow other crows in search of better quality food. Of course, finding the concealed food is not a simple task. If a crow follows another crow with the aim of discovering the hidden food, two phases are established on the basis of awareness probability. The first phase is when the crow is unaware of being followed by another crow, and as a result, the follower will discover the food cache. Consequently, the search process commences in a local area. The second phase is when the crow is aware of being followed by another crow or a flock of crows. In this case, a random position is established, where the search space occurs in a global area [29, 30].
If the number of crows is assumed to be N, then the position of crow i in the iteration iter will be a vector as \( X^{{i,{\text{iter}}}} \left( {i = 1,2, \ldots ,N;{\text{iter}} = 1,2, \ldots ,{\text{iter}}_{\rm {max} } } \right), \) where \( {\text{iter}}_{\rm {max} } \) is the maximum number of iterations and \( X^{{i,{\text{iter}}}} = \left[ {x_{1}^{{i,{\text{iter}}}} ,x_{2}^{{i,{\text{iter}}}} , \ldots ,x_{d}^{{i,{\text{iter}}}} } \right] \). It is assumed that the d dimension space includes the number of crows. One of the best experiences of the crow is stored in its memory. In the next iteration, the previous position is remembered and announced by \( m^{{i,{\text{iter}}}} \). Crows displace between the areas around themselves and search these areas to reach more food sources than the available food. Memory of crow j is updated when followed by crow i for discovering the food cache.
The CSA starts with a group of random solution. Then, the new position is created with help of awareness probability (AP) and the optimal solution is obtained by searching the problem space. Parameters of the CSA include flight length (FL) and AP. Two phases are defined in the CSA according to AP [29, 30]:
Phase 2 Crow j is aware of being followed by crow i. Hence, it attempts to deceive crow i by changing its position in the search space to protect its food source.
Improved CSA (ICSA) for optimal design of the system
In this study, crossover and mutation operators of GA have been used to improve the performance of the CSA method. CSA benefits a suitable capability of making a balance between exploration and exploitation, such that it explores the search space and exploits acceptable areas that have suitable solution. Nevertheless, in largescale optimization problems, the CSA may be unable to reach a fast convergence and trap in local optimum. That is the reason why improved CSA (ICSA) has been presented. The ICSA method was introduced to overcome some challenges of optimization methods when the dimension of the problem increases and to achieve a faster convergence. Thus, the ICSA method has been proposed to ensure appropriate coverage of search space related to the range of optimization variables and reaching a suitable convergence of global optimum.
Step 1 Initialization of hybrid system data: In this step, solar radiation and wind speed data of Zanjan city as well as load demand information and economic and technical parameters of the design are applied to the program.
Step 2 Initialization of algorithm parameters: First, flock size (algorithm population), maximum number of iterations, FL, AP, crossover probability (P_{c}), and mutation probability (P_{m}) (based on trial and error and experience) are determined. In addition, the variables, i.e., the size of hybrid system equipment, are randomly determined for the algorithm population.
Step 3 Memory of every crow at the first iteration has been set randomly according to the estimation of its initial position.
Step 4 Calculation of the NPCS objective function for each member of the ICSA population: In this step, the value of the objective function is calculated for each member of the algorithm population (crows).
Step 5 Definition of the best member among the population: In this step, the values of the NPCS objective function for each member of the algorithm population are evaluated and a member (crow) with the minimum NPCS is selected as the best solution.
Step 6 Generation of a new position: In this step, crows establish new positions in the search space in case they are being followed. The obtained new position is determined according to Eq. (30).
Step 7 Feasibility study of new positions: Feasibility of new positions of crows is investigated. If the new position of a crow is feasible, then the crow updates its position; otherwise, it remains in the current position and will not move towards the new formed position.
Step 8 Calculation of NPCS for new positions of crows: The value of objective function is calculated for all new members of the updated population.
Step 10 Determination of the best solution: By evaluating and comparing the objective function in steps 6–9, the obtained solution will replace the solution of Step 5 if the former is better than the latter.
Step 11 Implementation of operators of GA method for algorithm population: In this step, crossover and mutation operators of GA method are used for all members of the CSA population to improve its performance, which includes preventing trapping in local optima and achieving the global optimum accurately. In this step, the best solution replaces the obtained solution from Step 10, in case the former is better than the latter.
Step 12 Have convergence conditions (achieving minimum NPCS (the best memory position) and execution of the maximum number of iterations for the algorithm) been verified? If yes, then go to Step 13, otherwise go to Step 6.
Step 13 Stop the algorithm and determine the best optimal variables corresponding to the best value of NPCS and print the results.
Results and discussion
System data
The specification of the hybrid system
Device  Investment cost (US$/unit)  Replacement cost (US$/unit)  Maintenance and repair cost (US$/unityr)  Rated capacity (%) (kW)  Efficiency (%)  Lifetime (Year) 

Wind turbine  3200  3200  100  1  –  20 
PV panel  2000  2000  33  1  –  20 
Battery  280  280  5  1  85  10 
Inverter  700  700  8  1  90  15 
The lifetime of the PV/WT/Batt system and interest rate is 20 years and 6%, respectively [10]. The performance of the proposed algorithm in PV/WT/Batt designing is compared with conventional CSA and PSO algorithms. Each of the optimization methods is implemented 20time independently in simulation environment. In this paper, the maximum population and the number of iteration of algorithms are considered 50 and 100, respectively. The decision variables include the number of wind turbines and the number of PV panels and number of batteries, the inverter capacity, the PV panel angle, and the height of the wind turbine tower. The maximum values of these variables are 1000, 1000, 1000, 50, 90, and 50, respectively, and their minimum amount is zero.
Results of hybrid system design for DPHIP_{max} = 1%
Results of optimal design of hybrid combinations using different methods (DPHIP_{max} = 1%)
System variables  PV/Batt  PV/WT/Batt  WT/Batt  

ICSA  CSA  PSO  ICSA  CSA  PSO  ICSA  CSA  PSO  
\( N_{\rm {WG}} \)  –  –  –  0  1  0  805  805  805 
\( N_{\rm {PV}} \)  417  421  418  415  482  420  –  –  – 
\( N_{\rm {Bat}} \)  295  291  292  297  235  289  220  234  223 
\( P_{\rm {Inv}} \left( {\text{kW}} \right) \)  29.75  31.85  30.00  29.99  30.35  30.00  30.62  30.41  30.00 
\( \theta_{\rm {PV}} \left( {\text{m}} \right) \)  20.55  13.89  19.73  20.80  13.89  16.40  –  –  – 
\( h_{\rm {Tower}} \left( {\text{m}} \right) \)  –  –  –  –  10.01  –  49.98  49.98  50.00 
\( {\text{DPP}} \)  0.0053  0.0055  0.0056  0.0054  0.0064  0.0056  0.0067  0.0067  0.0067 
\( {\text{HIP}} \left( {\text{h/year}} \right) \)  87  87  87  83  83  83  87  87  87 
\( {\text{NPCS}} \left( {{\text{M}}\$ } \right) \)  1.166  1.176  1.169  1.167  1.292  1.175  3.636  3.642  3.637 
According to Table 2, NPCS for the PV/WT/Batt system using ICSA, CSA, and PSO methods are 1.167, 1.292, and 1.175 M$, respectively, for the PV/Batt system for each method, the values are 1.166, 1.176, and 1.169 M$ and for the WT/Batt system for ICSA, CSA, and PSO methods, there are 3.636, 3.642, and 3.637 M$, respectively. According to the results, it is clear that the ICSA method in all of the system combinations has less NPCS than CSA and PSO methods. In addition, the results show that the ICSA method is achieved desirable reliability indices compared to the other methods. Another important result is that the results of the PV/Batt and PV/WT/Batt in view of NPCS are almost the same, and virtually no wind turbines are used in the best combination for power generation. This is due to the weak wind potential in Zanjan. In the combination of WT/Batt, which the program has to use wind turbines to supply, system costs have risen by more than 200%, due to the high utilization of the battery system due to its low wind potential in Zanjan. Therefore, implementation of energy system based on wind energy for Zanjan is not economical. The value of the DPP index, obtained using the ICSA, CSA, and PSO method, in PV WT/Batt system designing, is 0.0054, 0.0064 and 0.0056, respectively. The DPP index value is calculated using the ICSA, CSA, and PSO method in designing of the PV/Batt system, equal to 0.0053, 0.0055, and 0.0056, respectively. Also, the value of the HIP index is 87 h for the PV/WT/Batt system designing using the ICSA, CSA, and PSO method and for the PV/Batt system is 83 h.
Results of hybrid system design for DPHIP_{max} = 3%
Optimal design results of hybrid system using different methods (DPHIP_{max} = 3%)
System variables  PV/Batt  PV/WT/Batt  WT/Batt  

ICSA  CSA  PSO  ICSA  CSA  PSO  ICSA  CSA  PSO  
\( N_{\rm {WG}} \)  –  –  –  0  4  0  258  260  257 
\( N_{\rm {PV}} \)  339  421  341  339  350  337  –  –  – 
\( N_{\rm {Bat}} \)  438  448  428  438  371  445  506  496  508 
\( P_{\rm {Inv}} \left( {\text{kW}} \right) \)  30.12  31.51  30.00  30.52  32.90  30.69  29.64  31.30  31.00 
\( \theta_{\rm {PV}} \left( {\text{m}} \right) \)  19.16  20.13  19.28  21.78  17.15  16.51  –  –  – 
\( h_{\rm {Tower}} \left( {\text{m}} \right) \)  –  –  –  –  48.86  –  49.93  49.80  50.00 
\( {\text{DPP}} \)  0.0180  0.0182  0.0182  0.0179  0.0187  0.0181  0.0219  0.0221  0.0220 
\( {\text{HIP}} \left( {\text{h/year}} \right) \)  262  262  262  261  261  262  262  262  261 
\( {\text{NPCS }}\left( {{\text{M}}\$ } \right) \)  1.050  1.053  1.051  1.052  1.061  1.054  1.398  1.406  1.401 
Table 3 shows the NPCS value for the PV/WT/Batt system using ICSA, CSA, and PSO methods that is 1.052, 1.061, and 1.054 M$, respectively, for the PV/Batt system, for each method, the NPCS values are 1.050, 1.053, and 1.051 M$; and for the WT/Batt system for the ICSA, CSA, and PSO methods, there are 1.398, 1.406, and 1.401 M$, respectively. According to the results, it is clear that the ICSA method in all of the system combinations has less NPCS than CSA and PSO methods. Similarly, the results of PV/Batt and PV/WT/Batt are roughly the same, and due to the low wind potential in Zanjan, wind turbines are not used in the best combination for energy generation. In addition, the cost of the system has increased in the combination of WT/Batt, which the program has to use with wind turbines to supply the load. The value of the DPP index, using the ICSA, CSA, and PSO method, in PV/WT/Batt, is 0.0179, 0.0187, and 0.0181, for PV/Batt is 0.0180, 0.0182, and 0.0182, and also for WT/Batt system, it is 0.0219, 0.0221, and 0.0220, respectively. In addition, the value of the HIP index is 262 h using the ICSA, CSA, and PSO method in PV/Batt system design.
Results of hybrid system design for DPHIP_{max} = 5%
Optimal designing results of hybrid combinations using different methods (DPHIP_{max} = 5%)
System variables  PV/Batt  PV/WT/Batt  WT/Batt  

ICSA  CSA  PSO  ICSA  CSA  PSO  ICSA  CSA  PSO  
\( N_{\rm {WG}} \)  –  –  –  0  5  0  258  258  259 
\( N_{\rm {PV}} \)  339  344  337  333  338  335  –  –  – 
\( N_{\rm {Bat}} \)  350  330  355  389  340  369  402  402  390 
\( P_{\rm {Inv}} \left( {\text{kW}} \right) \)  29.49  30.03  32.54  29.52  30.83  29.56  30.35  33.07  29.99 
\( \theta_{\rm {PV}} \left( {\text{m}} \right) \)  19.54  17.71  21.30  20.21  13.07  18.58  –  –  – 
\( h_{\rm {Tower}} \left( {\text{m}} \right) \)  –  –  –  –  45.66  –  49.98  49.99  50 
\( {\text{DPP}} \)  0.0326  0.0338  0.0339  0.0327  0.0333  0.0338  0.0409  0.0409  0.0411 
\( {\text{HIP}} \left( {\text{h/year}} \right) \)  438  438  438  438  438  438  438  438  438 
\( {\text{NPCS }}\left( {{\text{M}}\$ } \right) \)  1.0097  1.0118  1.0105  1.0108  1.0202  1.0128  1.3480  1.3510  1.3500 
Comparison the results due to different Variations
NPCS under conditions of DPHIP_{max} variations
NPCS values in different combinations of hybrid systems considering different DPHIP_{max}
System variables  Algorithm  DPHIP_{max} = 1%  DPHIP_{max} = 3%  DPHIP_{max} = 5% 

PV/Batt  ICSA  1.166  1.050  1.0097 
CSA  1.176  1.053  1.0118  
PSO  1.169  1.051  1.0105  
PV/WT/Batt  ICSA  1.167  1.052  1.0108 
CSA  1.292  1.061  1.0202  
PSO  1.175  1.054  1.0128  
WT/Batt  ICSA  3.636  1.398  1.348 
CSA  3.642  1.406  1.351  
PSO  3.637  1.401  1.350 
DPP in terms of DPHIP_{max} variations
DPP values in different combinations of hybrid systems considering different DPHIP_{max}
System variables  Algorithm  DPHIP_{max} = 1%  DPHIP_{max} = 3%  DPHIP_{max} = 5% 

PV/Batt  ICSA  0.0053  0.0180  0.0326 
CSA  0.0055  0.0182  0.0338  
PSO  0.0056  0.0182  0.0339  
PV/WT/Batt  ICSA  0.0054  0.0179  0.0327 
CSA  0.0064  0.0187  0.0333  
PSO  0.0056  0.0181  0.0338  
WT/Batt  ICSA  0.0067  0.0219  0.0409 
CSA  0.0067  0.0221  0.0409  
PSO  0.0067  0.0220  0.0411 
Battery bank energy variations in different combinations
Energy management of hybrid system
Sensitivity analysis
In the previous section, it was shown that the combination of hybrid PV/Battery system is the best option to implement the hybrid renewable energy systems in Zanjan. Therefore, in this section, the effect of variations in inverter efficiency, initial cost system, and load are investigated on the hybrid PV/Battery system.
Effect of inverter efficiency variations on the hybrid system designing
Effects of inverter efficiency variations on hybrid system designing (DPHIP = 1%)
System variables  PV/Batt  

90%  95%  100%  
\( N_{\rm {PV}} \)  417  400  394 
\( N_{\rm {Bat}} \)  295  267  222 
\( P_{\rm {Inv}} \left( {\text{kW}} \right) \)  29.75  29.64  29.17 
\( \theta_{\rm {PV}} \left( {\text{m}} \right) \)  20.55  20.22  22.45 
\( {\text{DPP}} \)  0.00553  0.00553  0.00536 
\( {\text{NPCS }}\left( {{\text{M}}\$ } \right) \)  1.167  1.112  1.077 
The effect of load variations on the hybrid system designing
Effect of load variations on the hybrid systems designing (DPHIP = 1%)
System variables  PV/Batt  

0.9 * P_{load} (kW)  P_{load} (kW)  1.1 * P_{load} (kW)  
\( N_{\rm {PV}} \)  416  417  418 
\( N_{\rm {Bat}} \)  293  295  297 
\( P_{\rm {Inv}} \left( {\text{kW}} \right) \)  30.04  29.75  30.03 
\( \theta_{\rm {PV}} \left( {\text{m}} \right) \)  18.32  20.55  19.37 
\( {\text{DPP}} \)  0.00559  0.00553  0.00557 
\( {\text{NPCS }}\left( {{\text{M}}\$ } \right) \)  1.165  1.167  1.173 
Effects of initial cost system variations on the hybrid system designing
Effect of variations in the initial investment cost of the storage system on the hybrid system designing (DPHIP = 1%)
System variables  PV/Batt  

280 ($/kWh)  380 ($/kWh)  480 ($/kWh)  
\( N_{\rm {PV}} \)  417  420  439 
\( N_{\rm {Bat}} \)  295  287  238 
\( P_{\rm {Inv}} \left( {\text{kW}} \right) \)  29.75  29.99  29.64 
\( \theta_{\rm {PV}} \left( {\text{m}} \right) \)  20.55  18.77  20.06 
\( {\text{DPP}} \)  0.00553  0.00568  0.00649 
\( {\text{NPCS }}\left( {{\text{M}}\$ } \right) \)  1.167  1.214  1.264 
Conclusion
In this paper, the design of an optimal hybrid PV/wind/battery system is presented for load demand considering actual data related to the annual solar radiation and wind speed in Zanjan, Iran. The optimum capacity of the hybrid system component is determined with the aim of minimizing NPCS and improving the reliability index (DPHIP) using the new ICSA metaheuristic algorithm. The optimum capacity of the hybrid system components is presented in various combinations and in different amounts of DPHIP constraint. Simulation results showed that hybrid PV/Batt system compared to the other combination in terms of NPCS and DPHIP is more economical and more reliable for Zanjan city. The performance of the algorithm presented in this study is compared with the conventional CSA and PSO optimization methods. The obtained results showed that ICSA algorithm has more convergence speed, lower NPCS, and better reliability in designing different combinations of the hybrid systems. The results also showed that the cost of designing the WT/Batt system for Zanjan is higher than the other combinations and it is not economic that one of the important reasons is the weak wind potential in Zanjan city and the dependence of this combination to the highlevel storage for load supply. In addition, effect of the important technical factors including the inverter efficiency variations and the investment cost of the storage system along with the load variations is evaluated on the hybrid system designing using the ICSA method. The results showed that increased inverter efficiency reduces NPCS and improves reliability. Increasing the storage investment cost increases the NPCS and undermines reliability. The NPCS is also increased with increasing the load demand.
Notes
Funding
This research has not received any specific grant from funding agencies in the public, commercial, or notforprofit sectors.
Compliance with ethical standards
Conflict of interest
The authors confirm that there are no known conflicts of interest associated with this publication.
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