Solar PV parameter estimation using multi-objective optimisation

Solar PV parameter estimation using multi-objective optimisation

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  Bulletin of ElectricalEngineering and Informatics Vol. 8, No. 4, December 2019, pp. 1198~1205 ISSN: 2302-9285, DOI: 10.11591/eei.v8i4.1312  1198 Journal homepage: http://beei.org/index.php/EEI Solar PV parameter estimation using multi-objective optimisation Nikita Rawat, Padmanabh Thakur, Utkarsh Jadli Department of Electrical Engineering, Graphic Era Deemed to be University, India Article Info ABSTRACT Article history: Received Aug 20, 2018 Revised Jan 7, 2019 Accepted May 28, 2019 The estimation of the electrical model parameters of solar PV, such as light-induced current, diode dark saturation current, thermal voltage, series resistance, and shunt resistance, is indispensable to predict the actual electrical performance of solar photovoltaic (PV) under changing environmental conditions. Therefore, this paper first considers the various methods of parameter estimation of solar PV to highlight their shortfalls. Thereafter, a new parameter estimation method, based on multi-objective optimisation, namely, Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is proposed. Furthermore, to check the effectiveness and accuracy of the proposed method, conventional methods, such as, ‘Newton-Raphson’, ‘Particle Swarm Optimisation, Search Algorithm, was tested on four solar PV modules of polycrystalline and monocrystalline materials. Finally, a solar PV module photowatt PWP201 has been considered and compared with six different state of art methods. The estimated performance indices such as current absolute error matrics, absolute relative power error, mean absolute error, and P-V characteristics curve were compared. The results depict the close proximity of the characteristic curve obtained with the proposed NSGA-II method to the curve obtained by the manufacturer’s datasheet. Keywords: Multi-objective optimisation, Solar PV Particle swarm optimisation Newton-Raphson NSGA-II Copyright © 2019 Institute of Advanced Engineering and Science. All rights reserved. Corresponding Author: Nikita Rawat, Department of Electrical Engineering, Graphic Era Deemed to be University, 566/6 Bell Road, Society Area, Clement Town Dehradun, Uttarakhand, India. Email: nikitarwt8@gmail.com 1. INTRODUCTION Among all the available inexhaustible energy sources, solar PV systems have received utmost attention throughout the world because of their abundance, lack of pollution, zero noise, and less maintenance characteristics and their wide acceptance in integration with modern power grids [1]. Though, solar energy is being considered as the most accessible renewable energy resources with huge potential of electricity generation, unfortunately, it is often characterized by low power density, low conversion efficiency and high installation costs [2]. Therefore, there is need to explore the research in the area that could be supportive in enhancement of optimal capturing capacity of available solar energy. Over the years, myriad of works have been carried out to ensure improved performance of the solar PV. Among all of the existing research areas the parameter estimations and modeling of solar PV have received utmost attentions by the researchers. The accurate estimation of electrical model parameters, such as, light-induced current (IPh), diode dark saturation current (Io), thermal voltage (VT), series resistance (Rs), and shunt resistance (Rp), of solar PV is necessary for accomplishing the following motives: a. To improve the overall efficiency of PV systems [3]. b. To predict expected power output in varying environmental condition [4].
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  Bulletin of ElectrEng and Inf ISSN: 2302-9285  Solar PV parameter estimation using multi-objective optimisation (Nikita Rawat) 1199 c. To obtain accurate design specification of the power conditioning equipment connected with the solar PV, and [5]. d. To simulate maximum power tracking algorithm, precisely. Generally, existing methods were divided into three categories in the research, such as: Analytical methods, Numerical methods, and Metaheuristics methods. Usually, the manufacturer provides the remarkable points, such as, ‘voltage at the maximum power point (VMP)’, ‘current at the maximum power point (IMP)’, ‘short-circuit current (ISC), and ‘open-circuit voltage (VOC)’ in their data sheet [6]. The accuracy of parameter estimation through analytical methods relies heavily on the accurate emplacement of these remarkable points or known parameters on solar PV output characteristics [3, 7]. Among the various existing numerical methods, Newton-Raphson (NR) method [8], Lambert W function [9], and Gauss-Seidel (GS) method [10], were frequently considered in estimation of accurate electrical parameters of solar PV. Though these numerical methods have a higher level of accuracy than the analytical methods, these methods suffer from extensive computation time for the convergence also they converge to local maxima instead of global in case of wrong selection of initial values especially in NR and GS methods [8, 11]. Although Metaheuristics Algorithms based approaches play a vital role in the extraction of electrical model parameters of solar PV, unfortunately, the speed of convergence is found to be low in genetic algorithm (GA) [3]. Also, the GA based approach is found to be unsuitable for highly interactive fitness function [3]. The swap between the initial temperature and cooling schedule is a major issue in simulating annealing (SA) [12]. Though particle swarm optimization (PSO) outperforms SA and GA [13], at the same time it is found inept to track accurate characteristics as provided in manufacturer’s datasheet. Also, the uniformity of estimated electrical model parameter cannot be assured through PSO [3, 13-15]. Besides the shortfalls as discussed above, most of the aforementioned methods consider the task of parameter estimations as a single objective optimisation i.e., the error between the real and estimated or predicted current at a known voltage is considered as the objective function. Indeed, parameter estimation of solar PV is a multi-objective optimisation (MOO) task, wherein, accurate values of all five parameters, such as IPh, Io, VT, Rs, and Rp are highly desirable to achieve characteristics exactly in tune with the real characteristics of solar PV. Unfortunately, in most of the research works, all of these five unknown parameters were not considered to reduce computational complexities. Therefore, to rectify the inconsistencies prevailing in these methods, the present study proposes an accurate method of parameters extraction based on MOO [16], to accurately describe the solar PV output characteristics. 2. THE SOLAR PV CELL MODEL The single diode model or Rp-model of solar PV is shown in Figure 1 which has been used in the present work to investigate the performance of solar PV. Although, there are two and three diode models of solar PV but these models have simultaneously increased the computational complexity due to a large number of unknown parameters. Also, a significant trade-off between accuracy and computational simplicity is achieved in Rp-model [11]. Figure 1. Single-diode solar PV model The characteristic equation of Rp-model, as given in (1), provides the relation between the output voltage (V) and current (I) in terms of unknown parameters. (1) exp 1 s s Ph o T p V R I V R I I I I V R                  
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   ISSN: 2302-9285 Bulletinof Electr Eng and Inf, Vol. 8, No. 4, December 2019 : 1198 – 1205 1200 Where, VT=(αKTNs)/e is in terms of diode ideality factor (α), electron charge (e), Boltzmann’s constant (K), number of solar PV cell in series (Ns), and temperature (T). 3. PROPOSED OBJECTIVE FUNCTION The output characteristic of a PV cell relies on five parameters, namely, IPh, Io, VT, Rs, and Rp, as given in (1). To estimate these unknown parameters, five equations, as given in (2), (3), (4), (6), and (8), can be derived from (1) as [17]: a. Under short circuit condition, i.e., when V=0, I=ISC, the relation, as given in (1), can be written as: (2) b. Under open circuit condition, i.e., when I=0, V=VOC, the relation as given in (1), can be derived as: (3) c. At maximum power point (MPP), i.e., when I=IMP, V=VMP, the relation, as given in (1), can be written as: (4) d. The slope at MPP on P-V curve will be parallel to the voltage axis and hence it is found that (5) On solving (5) the forth equation can be derived as: (6) e. The final equation is derived by calculating the slope of the I-V characteristic curve. The slope of the I-V characteristic curve is derived by differentiating the output current with respect to the output voltage under short circuit condition. (7) On solving (7) the fifth equation can be derived as: (8) The (2), (3), (4), (6), and (8), have been combined to define objective function, f(x), as: (9) Now, the MOO problem is formulated as: (10) 1( ) exp 1 SC S SC S SC Ph o T P I R I R f x I I I V R                    2 ( ) exp 1 OC OC Ph o T p V V f x I I V R                   3 ( ) ( ) exp 1 MP MP s MP MP S MP Ph o T P V I R V I R f x I I I V R                      MP MPP MP I dI dV V   4 1 ( ) ( ) exp o MP MP s MP MP MP s T T P I V I R f x I V I R V V R                    1 SC I I p dI dV R      5 ( ) exp s o SC s p s p T T R I I R f x R R R V V            1 2 3 4 5 ( ) ( ), ( ), ( ), ( ), ( ) f x f x f x f x f x f x  1 2 3 4 5 ( ( ), ( ), ( ), ( ), ( )) min f x f x f x f x f x
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  Bulletin of ElectrEng and Inf ISSN: 2302-9285  Solar PV parameter estimation using multi-objective optimisation (Nikita Rawat) 1201 Here, x is the array of decision variables {x1, x2, x3, x4, x5}. In the proposed work x1, x2, x3, x4, and x5 represents IPh, Io, Rs, Rp and VT, respectively. 3.1. Proposed parameter estimation method Various MOO methods generated from GA, such as the Vector-Evaluated Genetic Algorithm, Strength Pareto Metaheuristics Algorithm, Pareto Archived Evolution Strategy, classical non-dominated sorting-based multi-objective evolutionary algorithm, and NSGA-II, were tested and verified. Among these Methods, NSGA-II is considered to be one of the best methods due to its lower computation time and non-elitism approach. Therefore the present work considers NSGA-II, to evaluate the electrical model parameters of solar PV [16]. The following steps have been used in the proposed NSGA-II: a. Initialisation: objective function f (x), as given in (9), main population D, and the input variable and their ranges are initialized. b. Non-Domination Sort: NSGA-II uses non-domination sort to sort the initialized main population D. Each individual p in the main population D has two sets. The set Sp contains the individuals which are dominated by p whereas set np contains those individuals which are dominated to p. If the individual p has zero individuals in its set np, then p is assigned to front one (F1) and ranked one. c. Crowding Distance: As the fitness value or rank is achieved, the next step is to assign the crowding distance Fi(dj), where Fi is the ith front counter and dj is the crowding distance of the jth individual in front Fi. The crowding distance is the distance between two individuals. d. Tournament Selection: The selection of the individual is dependent on its individual rank and crowding distance. The rank of the individual has been checked and the individual with the smallest rank is selected. In case of similar rank of two individuals, the crowding distance is considered for the selection. In this case, the individual with larger values of crowding distance, i.e., Fi(dj) , is selected. e. Genetic Operators: Offspring population is created using the genetic operator’s binary crossover and mutation. f. Recombination: The parent population is united with the offspring population and sorted again using non-domination sorting. The unfit individuals are replaced by the fit one and the original size of the population is maintained. 4. RESULTS AND DISCUSSION 4.1. Estimation of performance indices for polycrystalline and monocrystalline PV modules Three polycrystalline and monocrystalline PV module with specifications as given in Tong NT et al [18] were considered. For proposed method and PSO, similar lower and upper bound values were taken, while for the NR method, different initial values were used. The electrical model parameters value for the PV modules found by the proposed method, NR, PSO, and search algorithm is summarised in Table 1. Figure 2-5 shows the P-V characteristic of the PV modules. It is evident that the P-V curve obtained by the proposed method for both type of PV cell modules were closest to the MPP. Also, it was observed that NR was the second best among the other methods but the accuracy of NR method is very much subjected to the selection of initial values which is evident from Table 1. Table 2 summarises the ARPE calculated for PV modules. The ARPE for all the PV modules using the proposed method were calculated to be very less. Thus, from the analysis of all the results it is evident that proposed method outperforms NR, PSO, and search algorithm in the case of polycrystalline as well as monocrystalline PV modules. Figure 2. P-V characteristics for WW energy, AS240-6P30 module Figure 3. P-V characteristics for Solarworld, Pro. SW255 module
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   ISSN: 2302-9285 Bulletinof Electr Eng and Inf, Vol. 8, No. 4, December 2019 : 1198 – 1205 1202 Figure 4. P-V characteristics for Nemy, JP270M60 module Figure 5. P-V characteristics for Solarworld, Plus SW280 module Table 1. Extracted parameters for polycrystalline and monocrystalline PV modules by the proposed and existing methods PV modules ParameterE xtracted Search algorithm [18] NR Lower Bound Upper Boun d PSO Proposed method Initial value Estimated value Polycrystalline WW Energy AS240-6P30 IPh (A) 8.5705 8.5 8.5707 8 8.6 8.5568 8.5108 Io (A) 0.0074E-6 1E-8 6.83E-9 7E-10 1E-7 3.488E-8 1E-8 Rs (Ω) 5.79E-3 0.3 0.3490 0.1 0.5 0.3450 0.343 Rp (Ω) 94.87 2000 4175.46 50 5000 2047.8 3500.6 VT α=1.1725 1.6 1.7997 0.1 2 1.9489 1.8509 Solarworld, Pro. SW255 IPh (A) 8.8805 8 8.8807 8 9 8.8565 8.8814 Io (A) 0.026E-6 1E-6 2.317E-8 10E-10 1E-6 2.311E-8 0.1E-7 Rs (Ω) 3.457E-3 0.1 0.21 0.1 0.5 0.2093 0.2277 Rp (Ω) 57.40 2000 2570.3 50 5000 2579.5 3735.8 VT α=1.2554 1 1.9228 0.1 2 1.9237 1.8422 Monocrystalline Solarworld, Plus SW280 IPh (A) 9.7109 9.7 9.7112 9 10 9.6748 9.6945 Io (A) 0.019E-6 1E-8 1.735E-8 1E-10 1E-7 1.844E-8 0.9E-8 Rs (Ω) 5.357E-3 0.2 0.3235 0 0.5 0.3447 0.3371 Rp (Ω) 61.07 2000 2714.3 50 1000 2591.2 3563.3 VT α=1.2793 1.8 1.9612 0.1 2 1.9746 1.8991 Nemy, JP270M60 IPh (A) 9.2002 9 9.2003 9 10 9.3243 9.2035 Io (A) 0.001E-6 1E-9 1.197E-9 1E-10 1E-7 1.069E-9 1E-9 Rs (Ω) 5.01E-3 0.3 0.3015 0.1 0.5 0.2981 0.3061 Rp (Ω) 207.73 9000 9120.8 1000 10000 9393.7 9838.8 VT α=1.1027 1.6 1.6958 0.1 2 1.6826 1.6827 Table 2. Absolute relative power error for polycrystalline modules PV module Extraction methods Actual Maximum Power Pactual (W) Calculated maximum power Pcal (W) Absolute Relative Power Error ARPE 100(%) actual cal actual P P P    WW Energy AS240-6P30 NR 240.097 239.8 1.2370×10-1 PSO 240.097 235.64 0.0185×102 Search algorithm 240.097 243.3 0.0133×102 Proposed Method 240.097 240.15 2.2074×10-2 Solarworld, Pro. SW255 NR 257.088 256.76 1.2758×10-1 PSO 257.088 256.280 3.1428×10-1 Search algorithm 257.088 250.68 0.0249×102 Proposed Method 257.088 257.15 2.4116×10-2 Solarworld, Plus SW280 NR 282.984 282.99 2.1202×10-3 PSO 282.984 281.24 6.1628×10-1 Search Algorithm 282.984 282.52 1.6396×10-1 Proposed Method 282.984 282.980 1.4135×10-3 Nemy, JP270M60 NR 269.948 269.793 5.7418×10-2 PSO 269.948 272.94 0.0110×102 Search Algorithm 269.948 277.8 0.029×102 Proposed Method 269.948 269.913 1.2965×10-2
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  Bulletin of ElectrEng and Inf ISSN: 2302-9285  Solar PV parameter estimation using multi-objective optimisation (Nikita Rawat) 1203 4.2. Estimation of performance indices for photowatt PWP201 module The unknown parameters of Photowatt PWP201 comprising of 36 polycrystalline silicon series connected cells at T=45˚C [18], is calculated with the proposed method (NSGA-II), NR, GA, PS, SA, (MPCOA), and (GOFPANM) are outlined in Table 3. Figure 6 shows the P-V curve of the PV module. The P-V curve obtained by the proposed method is close to the experimental data, in particular at the MPP point. Further, the values of MPP and ARPE, as estimated with these existing and the proposed method, have been summarised in Table 4. The ARPE is smaller for the proposed method. Table 5 shows the IAE matrics for each experimentally measured I-V points. The MAE calculated for the proposed method is 0.1875%, which is the lowest followed by the MAE calculated by the MPCOA and GOFPANM methods. The convergence process of the proposed method is shown in Figure 7. The proposed method is incomplex and does not have parameters that need to be tuned as in the case of PSO, SA, PS, MPCOA, and GOFPANM methods. Table 3. Photowatt PWP201 module parameters extracted by the proposed method and compared with various methods Parameters Extracted SA [12] NR [8] PS [19] GA [20] MPCOA [21] GOFPANM [22] Proposed method IPh(A) 1.0331 1.0318 1.0313 1.0441 1.03188 1.0305143 1.0301 Io(µA) 3.6642 3.2875 3.1756 3.436 3.3737 3.4822631 0.79851 Rs(Ω) 1.1989 1.2057 1.2053 1.1968 1.20295 1.2012710 1.4944 Rp(Ω) 8333.333 555.56 714.29 555.556 849.693 981.98232 785.1624 Nsα 48.8211 48.45 48.289 48.5862 48.5065 48.6428351 43.583919 (VT=1.1949) Figure 6. The P-V curve of the reference module Photowatt PWP201 by the proposed method and eight other existing method Figure 7. The convergence curve of Photowatt PWP201 by the proposed method (f(x)=0.0373 at 50 generation and 5000 population)
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   ISSN: 2302-9285 Bulletinof Electr Eng and Inf, Vol. 8, No. 4, December 2019 : 1198 – 1205 1204 Table 4. Absolute relative power error for Photowatt PWP201 module Methods *Pactual **Pcal ARPE SA 11.5403 11.6958 0.01347×102 NR 11.5403 11.4441 8.60462×10-1 PS 11.5403 11.5025 3.27547×10-1 GA 11.5403 11.5752 3.02418×10-1 MPCOA 11.5403 11.5293 9.53181×10-2 GOFPANM 11.5403 11.5374 2.51293×10-2 Proposed method 11.5403 11.5375 2.42628×10-2 *Actual Maximum Power, Pactual (W) **Calculated maximum power, Pcal (W) Table 5. The error matrics measurement by the proposed method and other existing methods for Photowatt PWP201 module Measured value Calculate d I(A) Current Absolute Error (IAE%) matrics V (V) I (A) Proposed Method Proposed method GOFPANM [20] MPCO A [18] GA [22] PS [19] NR [8] SA [12] 1 0.1248 1.0315 1.028 0.340467 0.233213488 0.119 0.988 0.207 0.213 0.006 2 1.8093 1.03 1.0269 0.301879 0.253065992 0.168 0.845 0.294 0.367 0.062 3 3.3511 1.026 1.0258 0.019497 0.029248318 0.037 0.966 0.123 0.258 0.137 4 4.7622 1.022 1.0219 0.009786 0.2050581 0.247 1.099 0.055 0.138 0.341 5 6.0538 1.018 1.02 0.196078 0.42062017 0.443 1.224 0.222 0.023 0.531 6 7.2364 1.0155 1.0177 0.216174 0.431414845 0.440 1.155 0.196 0.099 0.521 7 8.3189 1.014 1.0142 0.01972 0.226311129 0.223 0.876 0.041 0.383 0.292 8 9.3097 1.01 1.0099 0.009902 0.049480455 0.029 0.626 0.250 0.636 0.082 9 10.2163 1.0035 1.0006 0.289826 0.289826104 0.307 0.237 0.600 1.028 0.281 10 11.0449 0.988 0.9855 0.253678 0.345317896 0.368 0.135 0.668 1.139 0.374 11 11.8018 0.963 0.9609 0.218545 0.354314298 0.371 0.102 0.675 1.189 0.418 12 12.4929 0.9255 0.9237 0.194868 0.249133449 0.288 0.174 0.587 1.144 0.378 13 13.1231 0.8725 0.8712 0.149219 0.068720651 0.008 0.495 0.269 0.867 0.115 14 13.6983 0.8075 0.8023 0.648137 0.061881188 0.035 0.505 0.286 0.919 0.188 15 14.2221 0.7265 0.7227 0.525806 0.137457045 0.194 0.868 0.016 0.648 0.061 16 14.6995 0.6345 0.6339 0.094652 0.188768287 0.309 1.154 0.198 0.487 0.192 17 15.1346 0.5345 0.5342 0.056159 0.037404152 0.226 1.240 0.115 0.575 0.067 18 15.5311 0.4275 0.427 0.117096 0.11682243 0.311 1.666 0.270 0.405 0.187 19 15.8929 0.3185 0.3184 0.031407 -0.031407035 0.057 1.738 0.122 0.735 0.232 20 16.2229 0.2085 0.2083 0.096015 0.143678161 0.302 2.030 0.775 1.222 0.906 21 16.5241 0.101 0.1009 0.099108 0.296150049 0.990 0.520 5.153 5.002 5.287 Total IAE% 3.888021 4.10647917 5.481 18.648 11.13 21.63 5.775 MAE (%) 0.185144 0.195546 0.261 0.888 0.530 1.030 0.275 MAE of 3 points near MPP (%) 0.1875 0.22405 0.2223 0.257 0.510 1.0666 0.3036 5. CONCLUSION The present investigation has considered MOO algorithm NSGA-II for estimating the electrical model parameters of solar PV modules. In comparison to the existing methods such as NR, GA, PSO, PS, SA, MPCOA, and GOFPANM, the proposed NSGA-II method outperformed and provided a better P-V and I-V curve, as well as a lesser value of ARPE and MAE. Henceforth, it is inferred that the MOO-based approach can be recommended as one of the most accurate tools for the parameters estimation of solar PV. REFERENCE [1] M. A. Jusoh, M. F. Tajuddin, S. M. Ayob & M. A. Roslan., "Maximum Power Point Tracking RCharge Controller for Standalone PV System," Telkomnika (Telecommunication, Computing, Electronics and Control), vol. 16(4), pp. 1413-26, 2018. [2] M. Mardlijah and Z. Zuhri. "Solar Panel Control System Using an Intelligent Control: T2FSMC and Firefly Algorithm," Telkomnika (Telecommunication Computing Electronics and Control), vol. 16(6), pp. 2988-2998, 2018. [3] K. Ishaque, Z. Salam, S. Mekhilef & A. Shamsudin., "Parameter extraction of solar photovoltaic modules using penalty-based differential evolution," Applied Energy, vol. 99, pp. 297-308, 2012. [4] S. Shongwe and M. Hanif, "Comparative Analysis of Different Single-Diode PV Modeling Methods," in IEEE Journal of Photovoltaics, vol. 5, no. 3, pp. 938-946, May 2015. [5] F. Attivissimo, A. Di Nisio, M. Savino and M. Spadavecchia, "Uncertainty Analysis in Photovoltaic Cell Parameter Estimation," in IEEE Transactions on Instrumentation and Measurement, vol. 61, no. 5, pp. 1334-1342, May 2012.
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