AN IMPROVED GREY WOLF OPTIMIZATION TECHNIQUE FOR ESTIMATION OF SOLAR PHOTOVOLTAIC PARAMETERS

Pijush Dutta∗ and Madhurima Majumder∗∗

References

  1. [1] M.S. Ismail, M. Moghavvemi, and T.M.I., Mahlia characterization of PV panel and global optimization of its model parameters using genetic algorithm, Energy Conversion and Management, 73, 2013, 10–25.
  2. [2] L.L. Jiang, D.L. Maskell, and J.C. Patra, Parameter estimation of solar cells and modules using an improved adaptive Figure 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. [3] D. Oliva, A.A. Ewees, M.A.E. Aziz, A.E. Hassanien, and M. Peréz-Cisneros, A chaotic improved artificial bee colony for parameter estimation of photovoltaic cells, Energies, 10, 2017, 865.
  4. [4] H.M. Hasanien, Shuffled frog leaping algorithm for photovoltaic model identification, IEEE Transactions on Sustainable Energy, 6, 2015, 509–515.
  5. [5] D.F. Alam, D.A. Yousri, and M.B. Eteiba, Flower pollination 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. [6] P. Dutta, R. Agarwala, M. Majumder, and A. Kumar, Parameters extraction of a single diode solar cell model using bat algorithm, firefly algorithm & cuckoo search optimization, Annals of the Faculty of Engineering Hunedoara, 18, 2020, 147–156.
  7. [7] D. Miao, W. Chen, W. Zhao, and T. Demsas, Parameter estimation of PEM fuel cells employing the hybrid grey wolf optimization method, Energy, 193, 2020, 116616. https://doi.org/10.1016/j.energy.2019.116616. 220
  8. [8] N. Singh and S.B. Singh, Hybrid algorithm of particle swarm optimization and grey wolf optimizer for improving convergence performance, Journal of Applied Mathematics, 2017, 2017, e2030489. https://doi.org/10.1155/2017/2030489.
  9. [9] F.A. S¸enel, F. Gök¸ce, A.S. Yüksel, T. Yi˘git, A novel hybrid PSO–GWO algorithm for optimization problems, Engineering with Computers, 35, 2019, 1359–1373. https://doi.org/10.1007/s00366-018-0668-5.
  10. [10] I. Pervez, I.H. Malick, M. Tariq, A. Sarwar, and M. Zaid, A maximum power point tracking method using a hybrid PSO and Grey wolf optimization algorithm, 2019 2nd International Conference on Power Energy, Environment and Intelligent Control (PEEIC), 2019, 565–569. https://doi.org/10.1109/PEEIC47157.2019.8976741.
  11. [11] N. Chopra, G. Kumar, and S. Mehta, Hybrid GWO-PSO Algorithm for Solving Convex Economic Load Dispatch Problem, 2016, 4.
  12. [12] U. Jain, R. Tiwari, and W.W. Godfrey, Odor source localization by concatenating particle swarm optimization and grey wolf optimizer, in S. Bhattacharyya, N. Chaki, D. Konar, U.K.r. Chakraborty, C.T. Singh (eds), Advanced computational and communication paradigms (Singapore: Springer, 2018), 145– 153. https://doi.org/10.1007/978-981-10-8237-5 14.
  13. [14]. Figure 2. Double diode model [14]. 2.2 Double Diode Model (DDM) In DDM, V–I characteristic equation can be expressed by the following (2), in Fig. 2 IC = Iph − Isd1 exp VC + ICRs η1Vt − 1 − Isd2 exp VC + ICRs η2Vt − 1 − VC + ICRs Rsh (2) 2.3 PV Module Model The single diode model and the double diode model of a PV module which consists of connected cells in series can also be expressed as (1) and (2), where Vt = NsKT/. 3. Objective Function For the single diode model, f(V C, IC, X) and X can be, respectively, expressed as (3) RMSEmin = 1 N N i=1 (Imeasured − Icalculated(Iph, Isd, Rs, Rsh, η)) 2 X = {Iph, Isd, Rs, Rsh, η} (3) For the double diode model, f(V C, IC, X) and X can be, respectively, expressed as: RMSEmin = 1 N N i=1(Imeasured − Icalculated (Iph, Isd1, Isd2, Rs, Rsh, η1, η2))2 X = {Iph, Isd1, Isd2, Rs, Rsh, η1, η2} (4) The smaller objective function value corresponds to better estimated parameters. Because the objective function is nonlinear and transcendental, this problem is difficult to solve. 4. Proposed Methodology 4.1 Improved Grey Wolf Optimization As indicated by Talbi
  14. [15], two variations can be hybridized at a low level or elevated level with hand-off or co-transformative procedures as heterogeneous or homogeneous. In this content, we hybridize PSO with GWO algorithm utilizing a low-level co-transformative mixture so that HPSOGWO, refresh the three specialists’ position vector of GWO upgraded in the pursuit space. Parameters setting of each algorithm is shown in Table 1. 5. Results and Discussion For all calculations, the number of maximum iteration and population are set to 5,000 and 100 individually. Because of the stochastic nature of metaheuristics, every algorithm runs 20 times. From above Table 2, it may be seen very well that the proposed HPSOGWO can arrive at best wellness esteem (at least RMSE)
  15. [16]. For the entirety of the instances of photovoltaic frameworks, standard deviations and computational time of HPSOGWO are best for both the SDM and DDM model. Table 3 shows the optimal parameters of SDM and DDM, while Table 4 represents the total absolute error and accuracy of single diode and double diode models obtained by hybrid PSO–GWO algorithm. Figures 3 and 4 represent the comparative study of relative error between PSO, GWO, and HPSOGWO, while Figures 5 and 6 show the experimental and calculated o/p current obtained from all these three algorithms. Each and every characteristics graph shows HPSOGWO outperformed than others. Table 1 Parameters Setting for Each Algorithm PSO GWO HPSOGWO Inertia weight Number of c1 = c2 = c3 = 0.5 may be between wolves is 5 0.9 and 0.4 C1 = C2 = 2 Search domain w = 0.5+ rand s ()/2; is 36 and I =∈ [2,0] 218 Table 2 Comparative Study based on Different Level of Fitness
  16. [17] Maximum Minimum Mean Standard Deviation Average Case Method RMSE RMSE RMSE of RMSE Computational Time RTC Single Diode GWO 0.01663624 0.001434366 0.003536 0.0078453 98.8936 Sec HPSOGWO 0.00151312 0.00095276 0.002012 0.00751123 42.1381 Sec PSO 0.00244805 0.001022083 0.002057 0.02896407 169.462 Sec RTC Double Diode GWO 0.04214202 0.001993715 0.004019175 0.00768977 167.89 Sec HPSOGWO 0.03338124 0.0009842015 0.0037681456 0.00736789 54.3914 Sec PSO 0.036029972 0.001184587 0.023682121 0.02646232 294.37 Sec Table 3 Optimal Parameters for SDM and DDM Optimal Parameters for SDM Optimal Parameters for DDM Parameters PSO GWO PSO-GWO Parameters PSO GWO PSO-GWO Iph 0.6025 0.76112 0.7632 Iph 0.73 0.7627 0.7664 Isd 0.24419 0.44851 0.3287 Isd1 0.928 0.7427 0.8627 Rs 0.002757 0.03485 0.0363 Rs 0.0039 0.0313 0.03329 Rsh 75.4366 55.2308 56.1813 Rsh 85.32 51.3139 54.828 η 1.74815 1.5158 1.5322 η1 1.7 1.5775 1.7078 Isd2 0.00026 0.6142 1.497 η2 1.8 1.9649 1.482 Table 4 Comparative Study Based on Total Absolute Error and Accuracy
  17. [18] Case Method Total Absolute Error RMSE Accuracy RTC Single Diode GWO 0.027807 1.7861 98.214 HPSOGWO 0.0209817 0.7182 99.2818 PSO 0.021422 2.896 97.103 RTC Double Diode GWO 0.022134 1.7689 98.2311 HPSOGWO 0.020150 0.7312 99.2688 PSO 0.02431 2.646 97.354 6. Conclusion This paper presents optimal parameters of solar cells from the experimental data sets of single diode and double diode RTC cells for the control and design of a PV system. The estimated current, as well as power rating of a solar, depends upon several input parameters like photo-generated current, reverse saturation current, series resistance, shunt resistance, and ideality factor which are described in Section 2. Due to the complexity of the optimization problem, a new multi-objective hybrid optimization method involving both PSO and GWO is applied. Moreover, a comparison between the PSO–GWO hybrid on the one hand, and PSO and GWO each used in isolation on the other, is performed for both the single and double diode objective function. Due to its capability of searching global optimum, the convergence speed proposed PSO–GWO hybrid algorithm is a fruitful algorithm that can serve as an alternative method for finding the modelling parameters of PV modules. As mentioned in Section 5, the proposed hybrid algorithm PSO–GWO is efficient other than PSO and GWO using convergence speed, computational efficiency, rootmean-square error, and accuracy. In this key study, pro219 Figure 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 extract the parameters precisely and proficiently of PV modules (S75) verified in Figures 5 and 6. However, one of the significant weaknesses of HPSOGWO is a relative error and standard deviation. The reliability and accuracy of the proposed optimization ought to be additionally improved in the future. Presenting distinctive statement systems and adjustments or hybridizations of the optimization might be a potential methodology easing these shortcomings. Conflict of Interest The authors declare that they have no conflict of interests. References [1] M.S. Ismail, M. Moghavvemi, and T.M.I., Mahlia characterization of PV panel and global optimization of its model parameters using genetic algorithm, Energy Conversion and Management, 73, 2013, 10–25. [2] L.L. Jiang, D.L. Maskell, and J.C. Patra, Parameter estimation of solar cells and modules using an improved adaptive Figure 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. Peréz-Cisneros, A chaotic improved artificial bee colony for parameter estimation of photovoltaic cells, Energies, 10, 2017, 865. [4] H.M. Hasanien, Shuffled frog leaping algorithm for photovoltaic model identification, IEEE Transactions on Sustainable Energy, 6, 2015, 509–515. [5] D.F. Alam, D.A. Yousri, and M.B. Eteiba, Flower pollination 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, Parameters extraction of a single diode solar cell model using bat 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, Parameter estimation of PEM fuel cells employing the hybrid grey 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 swarm optimization and grey wolf optimizer for improving convergence performance, Journal of Applied Mathematics, 2017, 2017, e2030489. https://doi.org/10.1155/2017/2030489. [9] F.A. S¸enel, F. Gök¸ce, A.S. Yüksel, T. Yi˘git, A novel hybrid PSO–GWO algorithm for optimization problems, 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 a hybrid PSO and Grey wolf optimization algorithm, 2019 2nd International Conference on Power Energy, Environment 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 Algorithm for Solving Convex Economic Load Dispatch Problem, 2016, 4. [12] U. Jain, R. Tiwari, and W.W. Godfrey, Odor source localization by concatenating particle swarm optimization and grey wolf optimizer, in S. Bhattacharyya, N. Chaki, D. Konar, U.K.r. Chakraborty, C.T. Singh (eds), Advanced computational and communication 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 design of a grid-connected desalination plant powered by renewable 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 photovoltaic modules using a hybrid flower pollination algorithm, Energy Conversion and Management, 144, 2017, 53–68. [15] E.-G. Talbi, A taxonomy of hybrid metaheuristics, Journal of Heuristics, 8, 2002, 541–564. https://doi.org/10.1023/ A:1016540724870. [16] P. Dutta and A. Kumar, Modeling and optimization of a liquid flow process using an artificial neural network-based flower pollination 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 control 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 model to optimize the liquid flow rate of a process control system, Chemical Engineering Transactions, 71, 2018, 991–996. https://doi.org/10.3303/CET1871166.

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