# A Multi-Objective Hybrid BESSA Optimization Scheme for Parameter Extraction from PV Modules
## 1 Introduction  
Predictive performance tools determine the success of any technology. Consumers can now obtain and analyze optimized performance evaluations of their PV modules. The high growth rate in the utilization of PV energy has led researchers to develop novel photovoltaic cells and to develop theoretical analyses for forecasting the performance estimation, sizing, and optimization of PV energy systems [1]. In order to extract maximum power, the PV module must to be operated at its Maximum Power Point (MPP). This requires an MPP Tracker, which then demands a meticulous and accurate analytical modelof PV cells for analysis and testing. A photovoltaic module operating at a temperature of 25 \({}^{\circ}\)C and irradiance of 1000 W/m\({}^{2}\) is said to be operating in Standard Operating Condition (SOC) [2]. Again, it is well known that the manufacturer's data sheet provides limited information regarding the operational data of a PV module [2], as they only include PV module performance information operating in SOC. The data sheet provides information on short circuit current (ISC), open circuit voltage (VOC), maximum power (PMPP), voltage at PMPP (i.e., VMPP), and current at PMPP (i.e., IMPP) only when operating in SOC. In actuality, PV panels are subjected to operating conditions which differ from SOC. This requires a reliable PV model for apprehending electrical performance other than that achieved in SOC [2]. It has been reported that PV modules can be modelled theoretically via many methods [1]. It has also been reported that PV modelling based on two diode models is a mathematically rigorous and difficult process. As a result, the single-diode model has been adopted by most researchers worldwide for research and analysis [3]. Without illumination, PV cells operate as diodes. When the PV cell is operated in illumination, it yields photocurrent. This leads the PV cell to be modelled in the form of a current source parallelly connected with a diode in series with resistance (\(\mathcal{R}_{S}\)) and in shunt to resistance(\(\mathcal{R}_{Q}\)) [4]. The above-mentioned resistances model the dissipative effect and constructional defects, if any, that can cause a parasitic current. Figure 1 shows the electrical equivalent of single-diode PV model incorporating its five parameters, i.e., \(\mathcal{R}_{g}\), \(\delta\), \(\mathcal{R}_{S}\), \(I_{\Delta}\), and \(I_{\beta}\). The PV cell performance is evaluated by visualizing it in the form of an electrical equivalent circuit including five parameters; these are \(I_{\beta}\), \(I_{\Delta}\), \(\mathcal{R}_{S}\), \(\mathcal{R}_{g}\), and \(\delta\). It is to be noted that the manufacturer's datasheet does not provide information on these parameters. Hence, these parameters must be extracted using suitable techniques for the subsequent correct modelling and analysis of a PV module. Researchers have detailed many techniques for the parameter extraction and modeling of PV modules. These include the Modified Gromov, Derivative \(\alpha\), and Simple Conductance [5] methods, the penalty-based differential evolution algorithm [6], the Newton-Raphson technique [7], and using the Ant Lion Optimizer [8]. Optimization algorithms [9; 10] are an efficient method for finding solutions to many nonlinear real-world [11; 12] problems. As the NFL (No Free Lunch) theory explains that one single optimization algorithm cannot provide satisfactory results for all types of problems, there is always the opportunity to discover and advance new optimization techniques that suit a particular problem [13]. This is the motivation for this present research work. Optimization techniques [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29] are nature-inspired optimisation technique are broadly categorized into three categories. These are evolutionary methods, trajectory methods, and swarm methods [14; 15; 16]. [PERSON] et al. [17] introduced Bald Eagle Search optimization technique. In 1983, [PERSON] [18] developed Simulated Annealing technique to solve real world problem.