# A Multi-Objective Hybrid BESSA Optimization Scheme for Parameter Extraction from PV Modules
## 9 Discussion  
A multi-objective parameter extraction scheme based on the Hybrid BESSA and BES for PV modules is discussed in this work. In the first stage, the efficacy of the Hybrid BESSA was analyzed with testing on unimodal benchmark functions, fixed dimensional benchmark functions, and fixed dimensional multimodal benchmark functions, as discussed in Section 6. The statistical results of the Hybrid BESSA technique was compared with those of the BES, Hybrid Water Cycle--Moth Flame Optimization Algorithm (WCMFO) [21], Artificial Bee Colony (ABC) algorithm [22], Cuckoo Search (CS) [23], Particle Swarm Optimization and Gravitational Search Algorithm (PSOGSA) [24], Meth Flame Optimization (MFO) [25], Gravitational Search Algorithm (GSA) [26], Water Cycle Algorithm (WCA) [27], Dragonfly Algorithm (DA) [28], and Whale Optimization Algorithm(WOA) [29] as detailed in [9]. For all of the above analyses, the maximum number of search particles taken and total iteration counts were limited to 100 and 1000, respectively, and these are common parameters for all of the algorithms mentioned above. To reach the right conclusion, the number of runs for each algorithm was fixed at 30. Figure 15: Simulation and experimental results for the \(PV\) curve of Module AS-M3607-S at a temperature of 28 \({}^{\circ}\)C and an irradiance of 480 W/m\({}^{2}\). It was observed that the Hybrid BESSA produced better results and was able to find global optima for all of the unimodal functions when compared to the BES, CamWOA, and all of the other above-mentioned techniques [9]. The statistical outcomes from the Hybrid BESSA technique obtained by testing multimodal functions revealed that the Hybrid BESSA technique produced better results for all of the mentioned functions except function \(f_{13}(p)\). For function \(f_{13}(p)\), the BES produced better results than the Hybrid BESSA and CamWOA. For function \(f_{10}(p)\), the results were comparable. When tested upon the fixed dimensional multimodal functions, it was found that the Hybrid BESSA and BES techniques were both able to find global optima for functions \(f_{16}(p)-f_{19}(p)\). For functions \(f_{14}(p)\), \(f_{15}(p)\), \(f_{17}(p)\), \(f_{19}(p)\), and \(f_{20}(p)\), the Hybrid BESSA produced better results than the BES, CamWOA, and all of the other mentioned 10 optimization techniques [9]. For functions \(f_{16}(p)\) and \(f_{18}(p)\), the proposed BESSA was able to find global optima. For functions \(f_{21}(p)\), \(f_{22}(p)\), and \(f_{23}(p)\), CamWOA provided better results. From the above analysis, it is evident that the Hybrid BESSA has a better exploration capability when compared to the BES, CamWOA, and other techniques. Thus, it was concluded that the Hybrid BESSA has better exploration and exploitation capabilities when compared to the BES, CamWOA, WCMFO, ABC, CS, PSOGSA, MFO, GSA, WCA, DA, and WOA. Again, by studying the convergence characteristics in Section 6, it was found that the convergence capability of the Hybrid BESSA was better and faster than that of the BES. This is due to the hybridization of a global search (i.e., BES) with local search (i.e., SA) techniques. The Hybrid BESSA was also used for parameter extraction for the PV Module AS-M3607-S in a MATLAB/SIMULINK environment. It was found that single-diode PV modeling based on parameters extracted from the Hybrid BESSA was more robust and accurate than that based on the BES-based extracted parameters. The efficacy of the modeling was tested in two ways. The first was by varying temperature from\(-\)30 \({}^{\circ}\)C to 0 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, 30 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, and 70 \({}^{\circ}\)C while keeping irradiance fixed at 1000 W/m\({}^{2}\). In the second set of tests, the temperature was kept fixed at 25 \({}^{\circ}\)C and the irradiance varied by four values, i.e., 400 W/m\({}^{2}\), 600 W/m\({}^{2}\), 800 W/m\({}^{2}\), and 1000 W/m\({}^{2}\).