NSGA-II and MOPSO based optimization for sizing of hybrid PV/wind/battery energy storage system

Mohamad Izdin Hlal1, Vigna K. Ramachandaramurthya2, Sanjeevikumar Padmanaban3, Hamid Reza Kaboli4, Aref Pouryekta5, Tuan Ab Rashid bin Tuan Abdullah6 1, 2, 5Institute of Power Engineering, Department of Electrical Power Engineering, College of Engineering , Universiti Tenaga Nasional, Malaysia 3Department of Energy Technology, Aalborg University, Denmark 4UM Power Energy Dedicated Advanced Centre (UMPEDAC), Wisma R&D, University of Malaya (UM), Malaysia 6Institute of Energy Policy and Research (IEPRe), Universiti Tenaga Nasional, Malaysia


INTRODUCTION
In recent years, the increasing concern on the depletion of fossil fuel and global warming has catalyzed the growth of renewable energy sources due to their promising economic and environmental benefits [1], [2]. Wind turbines and solar photovoltaic are commonly used in the renewable energy system to supply power to consumers in the remote regions because there is no fuel cost involved, easy to install and are also non-polluting. Nevertheless, designing a renewable energy system can be a challenge. Thus, knowledge of all aspects that influences system performance and component sizing is a precondition for an accurate SHRES design. Large fluctuations in climatic and meteorological conditions cause intermittency of renewable energy sources. Malaysia which lies close to the equator has seasonal wind speed and does not have a comprehensive wind assessment [3]. This problem can practically be overcome by using battery energy storage system [4]. They design and optimization methods are important aspects for SHRES to significant fluctuations due to weather conditions and hence, the constant load demand may not be met. To mitigate this issue, a battery bank can be integrated to the hybrid system. However, the high cost of batteries is an issue in renewable energy systems. Thus, optimizing the size of the PV-WT-BES system becomes essential. These contributions reduce the capital cost and increase the chances of investment in renewable energy plant installation. Therefore, the optimal combination of renewable power resources with appropriate storage sizing, as proposed in this work, will give a vital contribution for the future economic feasibility of such plants, thus making the design more attractive for investors.

Wind turbine modeling
The wind is characterized by its speed and direction and is affected by factors, such as geographic position, meteorological factors and height above ground level. Wind turbine reacts to the wind, capturing a part of its kinetic energy and switching it into usable energy. The output power of wind turbine is determined as a function of the rated wind speed (Vr), the cut-in wind speed (Vci) and the cut-out wind speed (Vco) according to the following (1): Where, PWT is the output power by wind turbine, is the rated wind power, V is the wind speed, , and represent the cut-in wind speed, nominal wind speed, and cut-out wind speed respectively. The turbine cut-in speed is small, which enhances the effective operation of the system even under low wind speed [20]-[23].

Solar PV array modeling
Solar panels are defined as a group of cells connected in parallel and series to generate the required electrical power based on meteorological factors such as solar radiation and temperature. The current model used to predict the output power of a PV module can be expressed through the following (2) and (3) [24]: = Ta+ (0.0256 * G).
Where, PVSTC is the nominal power in (kW), G is the global solar radiation (kW/m2), is the solar radiation under STC (1000/m 2 ), TC is the temperature of PV cell, = 25 C°, is the PV temperature coefficient, 3.7*10 (1/Ċ) and Ta is the surrounding temperature.

Battery storage modeling
The typical batteries that are used for hybrid energy system in areas of low wind speed and intermittent solar radiation conditions are the lead-acid and lithium-based batteries [25]. Commonly, both these batteries are employed in most large-scale energy storage projects because of their low cost, long life span, and durability, in addition to their commercial availability [26]. Membrane based lead acid batteries are also available in the market presently. Battery storage is sized to meet the load demand during a shortage or interruption of renewable energy source, usually referred to as Autonomous Days (AD). Regularly, AD is taken to be one to three days according to (4). Typically battery capacity design depends on the load and AD. Thus, battery capacity can be calculated using the following equation: Where, CB is the battery capacity, EL is the load demand, DOD is the depth of discharge, μbat is the efficiency of battery and μinv is the inverter efficiency. It is noteworthy that, the preceding expression is only used when the hybrid PV/WT system is unable to supply the required energy [20]. The hybrid PV/WT and battery system is formulated as a multi-objective optimization problem to improve the techno-economic performance simultaneously.

Hybrid energy management system
The uncertainty of renewable energy supplies (ERE) is the main limitation of hybrid renewable energy plants. Therefore, an energy management strategy is required to complement the exchange of power from the generating sources and the load under variable weather conditions. It is calculated using the following (5) and (6): (t) = NWT* EWT (t) + NPV * EPV (t) Where, ∆Enet is the net energy of SHRES, NWT is the number of wind turbines, NPV is the number of PV panel, EWT is the energy generated by the wind turbines, EPV is the energy generated from the PV panels, and EL (t) is the load demand at hour (t) where (t) equals one hour. The following cases are taken into account in this article, to simulate an energy management strategy, as depicted in Figure. 1: a. When the generated power is higher than the load demand, the surplus power is employed to charge the battery bank. b. When the generated power is higher than the load demand and the state of charge of the battery bank is full, the surplus energy is consumed in a dump load. c. When the generated energy is lower than the load demand, the battery bank is discharged to sufficiently supply the load demand.

OPTIMAL CONFIGURATION OF THE STAND-ALONE HYBRID SYSTEM
Once the hybrid component specifications have been determined, two cases will be investigated based on multi-objective optimization using NSGA-II and MOPSO methods. In the first case, the hybrid system will consist of PV panels, WT, and battery bank, while the second case consists of PV panels and battery bank only. The following two sub-sections illustrate the definitions of the objective functions in detail.

Reliability analysis
There are two approaches to determine the long-term performance of LPSP in a stand-alone hybrid system, namely, chronological method and probabilistic techniques [27]. The chronological method is more common and accurate, especially to determine the energy produced from the battery and the computational time is typically larger than that of probabilistic models. It is common in the chronological models to perform a one-year simulation with a one-hour time step. Computation time is especially necessary because this kind of model is generally used for component size optimization that requires several iterations. Hence, the chronological method is utilized in this paper. The LPSP is defined as the probability of unmet load over the  [26], as mentioned in the first objective. The unmet load can be calculated by utilizing the deficit power between the load and sources in SHRES through the following (7) [3] :

Economic analysis
COE is defined as the average cost per kilowatt-hour ($/kWh) of electrical energy produced by the hybrid energy system [24], which can be achieved via the following equations: Where, CRF is the capital recovery factor, which calculates the present value of system components by considering the interest rates (i = approximated as 6%) and project life span (T= 20 years in our case). TAC is the total annualized cost in $. The total annualized cost is the sum of the annualized capital cost (CC), operation and maintenance cost (CO&M) and replacement cost (CR).
Where, CPV, CWT, and Cb, are PV panel unit-price, WT unit-price, and battery unit-price respectively. Also, CINV, CREG_PV, and CREG_WT are inverter unit price, regulator of PV price, and regulator of WT price respectively. In addition, NINV is the number of inverters and equal 2 as well as the cost of the wind tower estimated as 20% of the system capital cost. The CO&M taken as 1% of the total cost as earlier supported [28]. For the Replacement Cost, expressed in (16) and (17). Where SFF expressed as the sinking fund factor, PR_LF is lifespan of components (battery, inverter, and regulators). CRB, CRINV, CR_REG_PV, and CR_REG-WT are the replacement cost of the battery, inverter, PV regulator and WT regulator respectively.
While NREG_PV is the number of voltage regulator and equal 1, NREG_WT is the number of WT regulator and equal 1. Whereas the sinking fund factor is clarified by the following equation: Therefore, the sinking fund factor is clarified by the following equation:

Solution methodology
MOPSO and NSGA-II algorithms work by creating new reliable solutions. However, their working mechanism differs. Table1 shows the differences between the two algorithms.  Capable of finding the local optimum More complex due to mutation and crossover; takes extra time compared to MOPSO.
Fast and easy to implement as only a few parameters need adjustment. In recent years, the implementation of NSGA-II and MOPSO algorithms based on GA and PSO are the foremost techniques adopted for global optimization in various fields, such as business, engineering, and in stochastic nature of renewable energy applications [1]. In this study, the NSGA-II and MOPSO methods are utilized to size the stand-alone hybrid PV/wind systems and these methods are shown to be better than the single-objective methods such as hybrid genetic algorithm (GA) or particle swarm optimization (PSO).

Optimal configuration based on NSGA_II algorithm
In 2002, Deb proposed the use of NSGA-II algorithm [29], in which the population is distributed into several non-domination levels and each solution is assigned a fitness equal to its non-domination level. The algorithm can be summarized as follows [19]: a. In the first step, the requested input data are provided. This data involves the specifications of the hybrid system (hourly radiation, temperature and wind speed) and also load demand, data to compute the technical and economic functions and data to assess the constraint situations. b. Upper and lower bound of the number of PV-WT and BES c. The energy output of PV and wind turbine are calculated through the PV and wind models by using (1)(2)(3). The model of energy storage battery by using (4) with the total capacity (CB) is allowed to charge and discharge up to a limit defined by the maximum depth of discharge (DOD), by using (5, 6) and Figure 1. d. A random parent population (Pi) is created with size N. Then, the population of children (Qi) including N solutions is produced through genetic manipulation (crossover and mutation). e. Calculate the objective functions for each individual of Pi population (LPSP and COE) using (7)(8)(9)(10)(11)(12)(13)(14). f.
The two populations are combined to form the (Ri) population with size 2N. g. Classification of the Ri population is made in accordance with the Pareto front on the bases of fitness (non-dominated sorting is performed to determine the rank (front) of each population member). h. The next population of one of the fronts is built according to priorities by performing a general comparison of the members of the Ri population. i.
Since the size of Ri is equal to 2N, the remaining solutions can simply be ignored because it is impossible to place all members in the new population (Pi+1). j.
The end, if the maximum number of iterations referred in Step 3 is reached, the non-dominated sorting resolution at the last iteration was achieved as the optimal sizing and design for the SHRES. Otherwise go back to number 2. Figure 2 displays the NSGA-II algorithm application approach. This approach is aimed at finding the numbers of variables that depend on the state of NPV, NWT, and NBES in order to meet the minimized system LPSP and COE. This is executed by using NSGA-II optimization toolbox in MATLAB, with a selected population size of 200, the crossover value of 0.8, and the maximum simulation generation number set at 500.

Optimal configuration based on MOPSO algorithm
In 1995, Kenney and Eberhart showed that the Particle Swarm Optimization (PSO) has two separate concepts: a) social interaction which is exhibited by swarming and b) field of evolutionary calculation. In PSO, the two best values will determine the position of each particle.
PSO is an AI approach which is based on the swarm social interaction within a field of evolutionary calculation, as proposed [30]- [32]. The algorithm determines the two best positions for each particle. Initially, the best value is obtained, called the individual best (pbest), and is retained by the particle, while the next value is determined by the PSO optimization algorithm within a global best populations. Individual particle position defines the particles variable target values and velocity that is applied to monitor the overall global best value (gbest). The fitness equation of this algorithm is to search the best solution from amongst all possible available options, with additional constraints added. The algorithm is based on each particle fitness appraisal, individual and global best fitness update, alongside with particle position and velocity.
During the operation of the algorithm, each particle keeps the best fitness value that it has achieved. The particle with the best fitness value is calculated and updated during iterations. In this case, each particle represents a potential configuration of the PV-wind turbine and battery hybrid system: NPV, NWT and NBES, and the search space dimension are three. Then, the objective function of each particle is computed, corresponding to each scenario configuration (LPSP and COE). The following steps illustrate utilized this method for HRES as the following:a. In the first step: Initialization, the requested input data are provided. This data involves the specifications of the hybrid system (hourly radiation, temperature and wind speed) and also load demand, data to compute the technical and economic functions and data to assess the constraint situations. b. Upper and lower bound of the number of PV-WT and BES c. The energy output of PV and wind turbine are calculated through the PV and wind models by using (1)(2)(3). The model of energy storage battery by using (4) with the total capacity (CB) is allowed to charge and discharge up to a limit defined by the maximum depth of discharge (DOD), by using (5, 6) and Figure 1. d. Constants : -Personal and global coefficients, C1 = C2 =2.
-Inertia weight, w = 0.9. e. The position and velocity of particles are randomly selected in order to generate the initial population and then applied to the objective functions to find the optimum fitness value, by using (7)(8)(9)(10)(11)(12)(13)(14). f.
Evaluate the fitness value, with minimum LPSP and COE g. Calculate and update (Pbest and gbest) h. Calculate and update velocity and position of each particle i.
Apply the updated value to find optimum value of LPSP and COE j.
The end, if the maximum number of iterations referred in Step 3 is reached, the non-dominated sorting resolution at the last iteration was achieved as the optimal sizing and design for the SHRES. Otherwise go back to number 2. The sizing model of the hybrid PV/wind energy systems is more complex than the single-source generation systems. This is because the variables must be considered for system optimization. Moreover, system performance over a long-term, economic parameters, and reliability objectives should be well thought-out in order to achieve a suitable compromise between COE and LPSP. NSGA-II and MOPSO are the appropriate methods with regards to global optimization and the random nature of renewable power sources. These methods have been used in many hybrid applications in recent years [4], [33], [34] In this paper, the NSGA-II and MOPSO algorithms were applied to size the stand-alone hybrid PV/WT and battery system. In principle, these algorithms aim to find the optimum number of PV panels, wind generation, and batteries to minimize the LPSP and COE. The optimization method was done using MATLAB software by executing the same number of iterations and population in both algorithms. Finally, the results were compared and the algorithm with the best result was identified.
The optimization method starts with the following input values: hourly output power for PV, WT and load profile. Then, the loop iterates the NSGA-II or MOPSO algorithms. The optimum results generated by the two algorithms are converted to the nearest integer values. This gives the sizing of the generating source. The optimum sizing along with COE and LPSP values are recorded for each run and stored in an array for each iteration. Finally, all appropriate solutions are obtained through non-dominated optimal called Pareto front [35]. The number of each generating units are provided. Flow charts of the NSGA-II and MOPSO algorithms are shown in Figure.

RESULT AND DISCUSSION
The methodology was applied to find the optimal size for SHRES. The load profile for a typical rural village in Malaysia consisting of 20 households is shown in Figure 4 and the total energy consumption per day is 138.4 kWh [36]. The maximum solar radiation was approximately 1050 W/m 2 and the maximum wind speed was recorded at 5m/sec. The annual meteorological conditions in Malaysia, and solar radiation and wind speed are illustrated in Figure 5a and 5b, respectively. The data was obtained from the Malaysian Meteorological Department. Table 2 indicates the parameters of PV panels, wind, battery and inverters.  In this paper, two scenarios are investigated to determine the optimal sizing of SHRES. In the first case, the hybrid system consists of PV panels, wind turbines, and battery bank, while the second case comprised of PV panels and battery bank only. The output power curve generated by the first and second case of SHRES and the state of charge and discharge of the battery on an hourly basis under the best configuration are represented in Figure 6a and 6b, respectively. Even though the total energy generated was sufficient to cover the peak load in the evening, the surplus power was employed to charge the battery bank. These figures clearly indicated that the battery, in the period from 7 PM to 7 AM, was state of discharge and it satisfied the load demand, while the period from 7 AM to 7 PM was state of charge. In consonance with the two case studies, the contributions of output PV, wind turbine and battery bank through a one-year period are shown in Figure 7a and 7b. Based on Figure 6, it can be seen that the area had low wind speed and high solar radiation. Further, it was evident that the use of PV panels has a great advantage because the renewable energy for this location will enable the communities to access energy for their daily living. For the first case study, the set of solutions obtained from the NSGA-II and MOPSO approaches for one year are shown in Figure 7a and Figure 7b, respectively. Each solution represents the LPSP and COE that demonstrate the minimum value of the multi-objective optimization set of solutions known as a Paretooptimal set or Pareto front. This technique selects one of the different solutions and makes decision on LPSP against COE based on the number of PV (NPV), wind turbine (NWT) and battery energy storage (NBES). Any of the solutions can be considered optimum, which means that no improvement can be achieved on one of the objective functions without aggravating the other objective function. In order to make the best decision, a number of points on the Pareto front was selected, and then the optimal solutions were chosen based on the tradeoff between cost and reliability. Figure 8c shows the comparison of space of operating points (non-dominated); the matching between two methods of optimization results was quite close. The NSGA-II algorithm had good global search ability but a slower convergence speed than MOPSO. Figure 9a and Figure 9b show the Pareto optimum final value for the second case study. Once again, it proved that, compared to MOPSO, the NSGA-II algorithm had a robust search capability but a slower convergence speed. The optimal sizing solution obtained by the multi-objective NSGA-II and MOPSO algorithms for the first and second case study is illustrated in Table 3; the two case studies were compared according to the two algorithms, in terms of LPSP, COE and the total cost (CTOTAL). When the two hybrid system designs with minimum LPSP and COE were considered, it was clear that the contribution from PV energy was high. However, the energy mix in the first case study was quite low for wind turbine compared to PV.

CONCLUSION
This paper presented the optimal sizing of SHRES for a rural area settlement in Malaysia under the prevalent solar and wind conditions. The NSGA-II and MOPSO optimization techniques were used to optimize the sizing. The hybrid power system modeling was conducted in MATLAB using two case studies to select the best configuration in order to find the optimum number of variables; the first case study consisted of PV/WT and BES, while the second case study consisted of PV/BES to minimize LPSP and COE.
The results showed that the comparison between the two algorithms was successful in supplying household load with two operation scenarios, and in varying the availability of solar and wind power during the entire one-year period. Also, the proposed performance model for the two modes were presented, where the NSGA-II method has more robust performance, while the MOPSO was faster in implementing the optimization. The difference between these two methods in terms of number of variables, as well as LPSP and COE is not significant. Thus both these methods can be used for techno-economic optimization of SHRES. The second case study has proved to be a more efficient solution to meet the energy demand of the remote areas in this location. For the wind turbines have proved to be ineffective and it's not reliable due to low wind speed and also high installation and operational cost, but its utilization may be highly expanded in the future. As conclusion, the proposed system can fulfill the targeted constraints for rural electrification and ensure that the load demand is met.