Pijush Dutta∗ and Madhurima Majumder∗∗
[1] M.S. Ismail, M. Moghavvemi, and T.M.I., Mahlia charac-terization of PV panel and global optimization of its modelparameters using genetic algorithm, Energy Conversion andManagement, 73, 2013, 10–25. [2] L.L. Jiang, D.L. Maskell, and J.C. Patra, Parameter estima-tion of solar cells and modules using an improved adaptiveFigure 5. Graph for calculated value of SDM (s75).Figure 6. Graph for calculated value of DDM (s75).differential evolution algorithm, Applied Energy, 112, 2013,185–193. [3] D. Oliva, A.A. Ewees, M.A.E. Aziz, A.E. Hassanien, and M.Per´ez-Cisneros, A chaotic improved artificial bee colony forparameter estimation of photovoltaic cells, Energies, 10, 2017,865. [4] H.M. Hasanien, Shuffled frog leaping algorithm for photo-voltaic model identification, IEEE Transactions on SustainableEnergy, 6, 2015, 509–515. [5] D.F. Alam, D.A. Yousri, and M.B. Eteiba, Flower pol-lination algorithm based solar PV parameter estimation,Energy Conversion and Management, 101, 2015, 410–422.https://doi.org/10.1016/j.enconman.2015.05.074. [6] P. Dutta, R. Agarwala, M. Majumder, and A. Kumar, Pa-rameters extraction of a single diode solar cell model usingbat algorithm, firefly algorithm & cuckoo search optimization,Annals of the Faculty of Engineering Hunedoara, 18, 2020,147–156. [7] D. Miao, W. Chen, W. Zhao, and T. Demsas, Param-eter estimation of PEM fuel cells employing the hybridgrey wolf optimization method, Energy, 193, 2020, 116616.https://doi.org/10.1016/j.energy.2019.116616.220 [8] N. Singh and S.B. Singh, Hybrid algorithm of particle swarmoptimization and grey wolf optimizer for improving convergenceperformance, Journal of Applied Mathematics, 2017, 2017,e2030489. https://doi.org/10.1155/2017/2030489. [9] F.A. S¸enel, F. G¨ok¸ce, A.S. Y¨uksel, T. Yi˘git, Anovel hybrid PSO–GWO algorithm for optimization prob-lems, Engineering with Computers, 35, 2019, 1359–1373.https://doi.org/10.1007/s00366-018-0668-5. [10] I. Pervez, I.H. Malick, M. Tariq, A. Sarwar, and M.Zaid, A maximum power point tracking method using ahybrid PSO and Grey wolf optimization algorithm, 20192nd International Conference on Power Energy, Environ-ment and Intelligent Control (PEEIC), 2019, 565–569.https://doi.org/10.1109/PEEIC47157.2019.8976741. [11] N. Chopra, G. Kumar, and S. Mehta, Hybrid GWO-PSO Al-gorithm for Solving Convex Economic Load Dispatch Problem,2016, 4. [12] U. Jain, R. Tiwari, and W.W. Godfrey, Odor source localizationby concatenating particle swarm optimization and grey wolfoptimizer, in S. Bhattacharyya, N. Chaki, D. Konar, U.K.r.Chakraborty, C.T. Singh (eds), Advanced computational andcommunication paradigms (Singapore: Springer, 2018), 145–153. https://doi.org/10.1007/978-981-10-8237-5 14. [14].Figure 2. Double diode model [14].2.2 Double Diode Model (DDM)In DDM, V–I characteristic equation can be expressed bythe following (2), in Fig. 2IC = Iph − Isd1 expVC + ICRsη1Vt− 1− Isd2 expVC + ICRsη2Vt− 1 −VC + ICRsRsh(2)2.3 PV Module ModelThe single diode model and the double diode model of aPV module which consists of connected cells in series canalso be expressed as (1) and (2), where Vt = NsKT/.3. Objective FunctionFor the single diode model, f(V C, IC, X) and X can be,respectively, expressed as (3)RMSEmin=1NNi=1(Imeasured − Icalculated(Iph, Isd, Rs, Rsh, η))2X = {Iph, Isd, Rs, Rsh, η}(3)For the double diode model, f(V C, IC, X) and X can be,respectively, expressed as:RMSEmin =1NNi=1(Imeasured − Icalculated(Iph, Isd1, Isd2, Rs, Rsh, η1, η2))2X = {Iph, Isd1, Isd2, Rs, Rsh, η1, η2}(4)The smaller objective function value corresponds to betterestimated parameters. Because the objective function isnonlinear and transcendental, this problem is difficult tosolve.4. Proposed Methodology4.1 Improved Grey Wolf OptimizationAs indicated by Talbi [15], two variations can be hy-bridized at a low level or elevated level with hand-off orco-transformative procedures as heterogeneous or homo-geneous. In this content, we hybridize PSO with GWOalgorithm utilizing a low-level co-transformative mixtureso that HPSOGWO, refresh the three specialists’ positionvector of GWO upgraded in the pursuit space. Parameterssetting of each algorithm is shown in Table 1.5. Results and DiscussionFor all calculations, the number of maximum iteration andpopulation are set to 5,000 and 100 individually. Becauseof the stochastic nature of metaheuristics, every algorithmruns 20 times. From above Table 2, it may be seen very wellthat the proposed HPSOGWO can arrive at best wellnessesteem (at least RMSE) [16]. For the entirety of theinstances of photovoltaic frameworks, standard deviationsand computational time of HPSOGWO are best for boththe SDM and DDM model.Table 3 shows the optimal parameters of SDM andDDM, while Table 4 represents the total absolute error andaccuracy of single diode and double diode models obtainedby hybrid PSO–GWO algorithm.Figures 3 and 4 represent the comparative study ofrelative error between PSO, GWO, and HPSOGWO, whileFigures 5 and 6 show the experimental and calculated o/pcurrent obtained from all these three algorithms. Eachand every characteristics graph shows HPSOGWO outper-formed than others.Table 1Parameters Setting for Each AlgorithmPSO GWO HPSOGWOInertia weight Number of c1 = c2 = c3 = 0.5may be between wolves is 50.9 and 0.4C1 = C2 = 2 Search domain w = 0.5+ rand s ()/2;is 36 and I =∈ [2,0]218Table 2Comparative Study based on Different Level of Fitness [17]Maximum Minimum Mean Standard Deviation AverageCase Method RMSE RMSE RMSE of RMSE Computational TimeRTC Single Diode GWO 0.01663624 0.001434366 0.003536 0.0078453 98.8936 SecHPSOGWO 0.00151312 0.00095276 0.002012 0.00751123 42.1381 SecPSO 0.00244805 0.001022083 0.002057 0.02896407 169.462 SecRTC Double Diode GWO 0.04214202 0.001993715 0.004019175 0.00768977 167.89 SecHPSOGWO 0.03338124 0.0009842015 0.0037681456 0.00736789 54.3914 SecPSO 0.036029972 0.001184587 0.023682121 0.02646232 294.37 SecTable 3Optimal Parameters for SDM and DDMOptimal Parameters for SDM Optimal Parameters for DDMParameters PSO GWO PSO-GWO Parameters PSO GWO PSO-GWOIph 0.6025 0.76112 0.7632 Iph 0.73 0.7627 0.7664Isd 0.24419 0.44851 0.3287 Isd1 0.928 0.7427 0.8627Rs 0.002757 0.03485 0.0363 Rs 0.0039 0.0313 0.03329Rsh 75.4366 55.2308 56.1813 Rsh 85.32 51.3139 54.828η 1.74815 1.5158 1.5322 η1 1.7 1.5775 1.7078Isd2 0.00026 0.6142 1.497η2 1.8 1.9649 1.482Table 4Comparative Study Based on Total Absolute Error and Accuracy [18]Case Method Total Absolute Error RMSE AccuracyRTC Single Diode GWO 0.027807 1.7861 98.214HPSOGWO 0.0209817 0.7182 99.2818PSO 0.021422 2.896 97.103RTC Double Diode GWO 0.022134 1.7689 98.2311HPSOGWO 0.020150 0.7312 99.2688PSO 0.02431 2.646 97.3546. ConclusionThis paper presents optimal parameters of solar cells fromthe experimental data sets of single diode and double diodeRTC cells for the control and design of a PV system. Theestimated current, as well as power rating of a solar, de-pends upon several input parameters like photo-generatedcurrent, reverse saturation current, series resistance, shuntresistance, and ideality factor which are described in Sec-tion 2.Due to the complexity of the optimization problem, anew multi-objective hybrid optimization method involvingboth PSO and GWO is applied. Moreover, a comparisonbetween the PSO–GWO hybrid on the one hand, and PSOand GWO each used in isolation on the other, is performedfor both the single and double diode objective function.Due to its capability of searching global optimum, theconvergence speed proposed PSO–GWO hybrid algorithmis a fruitful algorithm that can serve as an alternativemethod for finding the modelling parameters of PV mod-ules. As mentioned in Section 5, the proposed hybrid al-gorithm PSO–GWO is efficient other than PSO and GWOusing convergence speed, computational efficiency, root-mean-square error, and accuracy. In this key study, pro-219Figure 3. Comparative study of relative error for SDM.Figure 4. Comparative study for relative error for DDM.posed hybrid algorithm PSO–GWO is applied to extractthe parameters precisely and proficiently of PV modules(S75) verified in Figures 5 and 6.However, one of the significant weaknesses of HP-SOGWO is a relative error and standard deviation. Thereliability and accuracy of the proposed optimization oughtto be additionally improved in the future. Presenting dis-tinctive statement systems and adjustments or hybridiza-tions of the optimization might be a potential methodologyeasing these shortcomings.Conflict of InterestThe authors declare that they have no conflict of interests.References[1] M.S. Ismail, M. Moghavvemi, and T.M.I., Mahlia charac-terization of PV panel and global optimization of its modelparameters using genetic algorithm, Energy Conversion andManagement, 73, 2013, 10–25.[2] L.L. Jiang, D.L. Maskell, and J.C. Patra, Parameter estima-tion of solar cells and modules using an improved adaptiveFigure 5. Graph for calculated value of SDM (s75).Figure 6. Graph for calculated value of DDM (s75).differential evolution algorithm, Applied Energy, 112, 2013,185–193.[3] D. Oliva, A.A. Ewees, M.A.E. Aziz, A.E. Hassanien, and M.Per´ez-Cisneros, A chaotic improved artificial bee colony forparameter estimation of photovoltaic cells, Energies, 10, 2017,865.[4] H.M. Hasanien, Shuffled frog leaping algorithm for photo-voltaic model identification, IEEE Transactions on SustainableEnergy, 6, 2015, 509–515.[5] D.F. Alam, D.A. Yousri, and M.B. Eteiba, Flower pol-lination algorithm based solar PV parameter estimation,Energy Conversion and Management, 101, 2015, 410–422.https://doi.org/10.1016/j.enconman.2015.05.074.[6] P. Dutta, R. Agarwala, M. Majumder, and A. Kumar, Pa-rameters extraction of a single diode solar cell model usingbat algorithm, firefly algorithm & cuckoo search optimization,Annals of the Faculty of Engineering Hunedoara, 18, 2020,147–156.[7] D. Miao, W. Chen, W. Zhao, and T. Demsas, Param-eter estimation of PEM fuel cells employing the hybridgrey wolf optimization method, Energy, 193, 2020, 116616.https://doi.org/10.1016/j.energy.2019.116616.220[8] N. Singh and S.B. Singh, Hybrid algorithm of particle swarmoptimization and grey wolf optimizer for improving convergenceperformance, Journal of Applied Mathematics, 2017, 2017,e2030489. https://doi.org/10.1155/2017/2030489.[9] F.A. S¸enel, F. G¨ok¸ce, A.S. Y¨uksel, T. Yi˘git, Anovel hybrid PSO–GWO algorithm for optimization prob-lems, Engineering with Computers, 35, 2019, 1359–1373.https://doi.org/10.1007/s00366-018-0668-5.[10] I. Pervez, I.H. Malick, M. Tariq, A. Sarwar, and M.Zaid, A maximum power point tracking method using ahybrid PSO and Grey wolf optimization algorithm, 20192nd International Conference on Power Energy, Environ-ment and Intelligent Control (PEEIC), 2019, 565–569.https://doi.org/10.1109/PEEIC47157.2019.8976741.[11] N. Chopra, G. Kumar, and S. Mehta, Hybrid GWO-PSO Al-gorithm for Solving Convex Economic Load Dispatch Problem,2016, 4.[12] U. Jain, R. Tiwari, and W.W. Godfrey, Odor source localizationby concatenating particle swarm optimization and grey wolfoptimizer, in S. Bhattacharyya, N. Chaki, D. Konar, U.K.r.Chakraborty, C.T. Singh (eds), Advanced computational andcommunication paradigms (Singapore: Springer, 2018), 145–153. https://doi.org/10.1007/978-981-10-8237-5 14.[13] A.M. Abdelshafy, H. Hassan, and J. Jurasz, Optimal de-sign of a grid-connected desalination plant powered by renew-able energy resources using a hybrid PSO–GWO approach,Energy Conversion and Management, 173, 2018, 331–347.https://doi.org/10.1016/j.enconman.2018.07.083.[14] S. Xu and Y. Wang, Parameter estimation of photovoltaicmodules using a hybrid flower pollination algorithm, EnergyConversion and Management, 144, 2017, 53–68.[15] E.-G. Talbi, A taxonomy of hybrid metaheuristics, Jour-nal of Heuristics, 8, 2002, 541–564. https://doi.org/10.1023/A:1016540724870.[16] P. Dutta and A. Kumar, Modeling and optimization of a liquidflow process using an artificial neural network-based flowerpollination algorithm, Journal of Intelligent Systems, 29, 2018.https://doi.org/10.1515/jisys-2018-0206.[17] P. Dutta and A. Kumar, Modelling of liquid flow con-trol system using optimized genetic algorithm, Statistics,Optimization & Information Computing, 8, 2020, 565–582.https://doi.org/10.19139/soic-2310-5070-618.[18] P. Dutta and A. Kumar, Application of an ANFIS modelto optimize the liquid flow rate of a process control sys-tem, Chemical Engineering Transactions, 71, 2018, 991–996.https://doi.org/10.3303/CET1871166.
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