Parameter extraction of two diode solar PV model using Fireworks algorithm

doi:10.1016/j.solener.2016.10.044

Solar Energy

Volume 140, 15 December 2016, Pages 265-276

https://doi.org/10.1016/j.solener.2016.10.044 Get rights and content

Highlights

•
Fireworks based solar PV parameter extraction is proposed for two diode model.
•
Simulations are carried out in MATLAB/SIMULINK environment.
•
Statistical error analysis such as IAE MAE, RE are performed and compared.
•
Simulated values of FWA are compared with experimental datasheet values to know the validity of the proposed method.

Abstract

The double diode model for photovoltaic (PV) modules is currently less adopted than one-diode model because of the difficulty in the extraction of its seven unknown parameters $I_{PV}, I_{01}, I_{02}$ , $R_{s}$ , $R_{p}$ , $a_{1}$ and $a_{2}$ , which is a serious inverse problem. This paper proposes application of the Fireworks Algorithm (FWA) for the accurate identification of these unknown parameters in such a way to solve effectively this modeling problem. In particular, firstly, the FWA has been comprehensively tested with two different technologies of Mono-Crystalline (SM55 & SP70) and Multi-Crystalline (Kyocera200GT) PV modules. In addition, further statistical and error analysis for three different panels are exclusively carried out to validate the suitability of proposed methodology. The results of proposed algorithm are benchmarked with popular Genetic Algorithm and Particle Swarm Optimization (PSO) methods. Fitness convergence curves or FWA method for SM55, SP70 and Kyocera200GT produce very less objective function as 2.2498E−07, 2.85765E−08 and 4.0075E−08 respectively. This illustrates the wise and accurate validation of FWA method. Calculated curve-fit via FWA in agreement to datasheet curve strongly suggest the FWA can constitute the core of suitable optimization code for two diode PV parameter extraction.

Introduction

Energy scarcity motivated researchers around the globe to think for pollution free, and cost effective energy alternative. Presently 40.4% of world’s energy demand is met by coal, however, its continuous depletion, hazardous effluent emission and limited stock availability turned world’s attention towards renewable energy resources. Among the various types, Solar Photovoltaic (PV) is the most promising one, due to its significant advantages such as zero emission, zero noise and easy maintenance (Sudhakar Babu et al., 2015). Further it is an excellent choice for remote area electrification since extension of existing power grid can be too expensive.

One of the major hurdles faced by the PV researchers is solar PV cell modeling. This occur due to (i) non-linear current-voltage characteristic of PV (Mohammed Azharuddin et al., 2014), (ii) complex parameter identification and (iii) generating PV array characteristics under partial shaded condition is tedious. Therefore PV cell modeling is given higher importance. Moreover, an accurate solar PV cell model is always helpful in predicting the system performance precisely. Among many ways, the most common and the convenient form are via electrical equivalent circuit where two main modeling methods exist: (i) One-diode model and (ii) Two diode model. One diode model also called 5 parameter model (De Soto et al., 2006, Laudani et al., 2014a) require 5 unknown parameters and is widely accepted for its simplicity. However, the one diode model fails to include the recombination loss occur in the depletion region. Thus, for precise PV cell modeling two diode models is preferred. Though it requires 7 parameters to model, the complexity can be easily justified in view of high accuracy. In addition, it is true that, the closeness of the predicted PV characteristics depend on accuracy of cell model parameter values. However, the non-linearity present impose difficulty towards the extraction of model parameters that cannot be overtaken as done for one diode model by means of reduced forms (Laudani et al., 2014a, Laudani et al., 2014b). Therefore, identification of double diode model parameters of PV module is a fundamental topic for researchers and various researchers worked on different methods to provide solution.

Owing to problem solving capability, many researchers followed optimization technique in literature for solar PV parameter extraction. Genetic Algorithm (GA) method is first proposed in (Jervase et al., 2001) for PV parameter extraction problem; however the results produced show relatively high percentage of errors. Alternatively authors in (Ye et al., 2009, Wei and Deyun, 2011) used Particle Swarm Optimization (PSO) method but similar to GA, this method also suffers from premature convergence problem. Avoiding the above problem Simulated Annealing (SA) method intended for extraction of solar PV parameters is implemented in (El-Naggar et al., 2012). Since the performance of SA is highly dependent on cooling schedule it is extremely difficult to obtain better results without proper tuning. In (AlHajri et al., 2012) a new pattern search heuristic algorithm is used. Even though obtained results are comparatively good, the method exhibit large complexity in exploration of search space. Authors Oliva et al. (2014) proposed Artificial Bee Colony (ABC) optimization technique. The bee behavior based on hunt for food is derived and implemented for solar PV parameter estimation. However, due to its slower convergence the algorithm is less chosen. Artificial Bee Swarm Optimization (ABSO) a class ABC method yields better convergence in comparison to the ABC however, it show sluggish performance when applied for PV parameter extraction (Askarzadeh and Rezazadeh, 2013). The method of tuning music based on the available memory is used for the PV parameter extraction process in (Askarzadeh and Rezazadeh, 2012). This harmony based optimization uses three important parameters, such as pitch adjusting rate, bandwidth and harmony memory to find global optimum. The selection of initial parameters and requirement of large memory space impose constraints on computational time. Bird Mating Optimization (BMO) technique, a recently devised metaheuristic algorithm, imitating metaphorically the mating strategies of bird species is proposed in (Alireza and Alireza, 2013). Though, BMO method seems to be simple, the complexity arises when perceptive different species are used. The authors in (Alireza and Alireza, 2013) implemented chaos optimization technique for PV parameter estimation; but this method suffers from parameter selection. In paper (Rajasekar et al., 2013), Bacterial Foraging Algorithm (BFA) is implemented for extracting solar PV characteristics from datasheet value but, high computational burden limits its usage. The Differential Evolution (DE) method is another heuristic algorithm adopt the characteristics of GA is applied for PV parameter extraction in (Ishaque et al., 2011b). The method show very good convergence however involvement of more parameters makes DE less preferred (Ishaque et al., 2011c).

To sum up, the methods implemented solar PV for parameter estimation have the following drawbacks: (1) large convergence time (2) prone to errors and (3) complexity. Therefore as an alternative method in this paper, a new optimization technique named FireWork Algorithm (FWA) is proposed for solving solar PV parameter extraction problem. FW algorithm (Tan and Zhu, 2010, Fireworks Algorithm, 2015) is relatively a new global optimization method inspired by the phenomenon of fireworks explosion, where fireworks and sparks are analogous to solutions to a given problem, and an explosion can be viewed as a search in the solution space around the firework. With proper balance between exploration and exploitation process, the FW algorithm finds better solution for the given optimization problem. Further numerical experiments on various set of benchmark functions showed that, the FWA method converge to a global optimum at a much faster rate than conventional algorithm (Fireworks Algorithm, 2015). To know the suitability of FWA for PV parameter extraction problem, numerical simulations are performed with FWA method and other optimized model parameter. To know the veracity, FireWork (FW) results are compared with timeworn GA and PSO method. In addition, a comprehensive analysis is made between methods employing two diode models. Moreover to demonstrate the superiority of FW method error between actual and simulated values is plotted.

The remaining section of the paper is organized as follows: Section 2 expounds the modeling of the solar PV. Section 3 describes the steps involved in application of FW method for PV parameters estimation problem. Discussions on results obtained are elaborated in Section 4. In addition, comparative studies of FW method with three different PV panels are analyzed in Section 5. Conclusions are presented at last.

Section snippets

Modeling of PV module

It is advisable to model a solar PV system before proceeding into the installation part of it; since it is helpful to better understand the behavior of solar panel under varying atmospheric conditions. Therefore for accuracy reasons two diode models is preferred. Moreover, actually it brings out the exact behavior of PV cell characteristics. It comprises of a current source $I_{pv}$ in parallel with two diodes $D_{1}$ and $D_{2}$ connected to series ( $R_{S}$ ) and shunt resistances ( $R_{P}$ ). Diode $D_{1}$ indicates

Optimization technique

Fireworks algorithm (FWA) developed by Tan Y and Zhu Y is a recent arrival in the field of optimization technique that falls under the class of global optimization algorithms. This stochastic optimization technique is capable of solving non-linear, complex numerical computation with high accuracy. Further various works on solving practical optimization problems with FWA method can be found in literature (Sangeetha et al., 2016, Srikanth Reddy et al., 2016, Zhang et al., 2016, Goswami and

Results and discussions

In order to test the effectiveness of Fireworks based solar PV parameter extraction three panels such as KC200GT, SM55, SP70 of various make with entirely different characteristics having different materials Multi crystalline, mono crystalline are considered for the study. The usage of different panel types and its current market share is presented in Fig. 5. Since the efficiency and market share of multi crystalline and mono crystalline type panels are comparatively high, the authors validated

Comparative study

To further emphasize the importance of FWA method a quantitative comparison is made with GA and PSO methods on six different parameters: (a) Root Mean Square Error, (b) Individual Absolute Error (c) Relative Error, (d) Convergence speed, (e) Occurrence of local convergence and (f) Parameter dependency. Wheel chart portraying the performance of the methods based on the above performance criteria is presented in Fig. 11. The chart can be understood in the following way, the method occupying lower

Conclusion

In this paper a new Fireworks algorithm for solar PV parameter estimation is proposed and the following conclusions are arrived.

(i)
It is seen that the exploration and exploitation ability in Fireworks algorithm have a strong impact in reducing the probabilities of premature convergence.
(ii)
To reduce computational complexity only four parameters ( $a_{1}, a_{2}, R_{s}, R_{P}$ ) are obtained iteration wise and the other values are calculated manually.
(iii)
The generated code via FWA method applied to KC200GT, SM55 and SP70

Acknowledgements

The authors would like to thank the Management, VIT University, Vellore, India for providing the support to carryout research work. This work is carriedout at Solar Energy Research Cell (SERC), School of Electrical Engineering, VIT University, Vellore. Further, the authors also would like to thank the reviewers for their valuable comments and recommendations to improve the quality of the paper.

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Parameter extraction of two diode solar PV model using Fireworks algorithm

Highlights

Abstract

Introduction

Section snippets

Modeling of PV module

Optimization technique

Results and discussions

Comparative study

Conclusion

Acknowledgements

Energy Convers. Manage.

Renew. Energy

Sol. Energy

Appl. Energy

Sol. Energy

Sol. Energy

Ain Shams Eng. J.

Sol. Energy Mater. Sol. Cells

Sol. Energy

Simul. Model. Pract. Theory

Sol. Energy

Sol. Energy

Energy