Elsevier

Renewable Energy

Volume 78, June 2015, Pages 105-113
Renewable Energy

A three diode model for industrial solar cells and estimation of solar cell parameters using PSO algorithm

https://doi.org/10.1016/j.renene.2014.12.072Get rights and content

Highlights

  • A three diode model using three diodes better explains the I–V characteristics of large size industrial silicon solar cells.

  • PSO algorithms can estimate the various parameters of the three diode model of such industrial silicon solar cells.

  • Increase of series resistance with current through such industrial silicon solar cells is within 10%.

Abstract

A new lumped-parameter equivalent circuit model using three-diodes is presented in this work for large area (∼154.8 cm2) industrial silicon solar cells. The estimation of values of ideality factors n1 (>1) and n2 (>2) using a Particle Swarm Optimization (PSO) algorithm for the two-diode model of the industrial samples has been found not to be in conformity with the theoretical values (n1 = 1 and n2 = 2 in the literature). The two diodes of the two-diode model are not able to define the different current components of the solar cells clearly. A model with three-diodes has been proposed to better explain the experimental data. In the proposed model, we considered the series resistance, Rs, of the solar cell to vary with the current flowing through the solar cell device. All the parameters of the proposed model have been estimated using a PSO algorithm and they were compared with the parameters of the two-diode model. The new model has been found to be a better model to define clearly the different current components of the large size industrial silicon solar cells.

Introduction

Modeling of a solar cell is required to predict the behaviour of a real solar cell under various environmental conditions and thereafter to generate its current–voltage (I–V) and power-voltage (P–V) characteristic curves. The common approach is to utilize the electrical equivalent circuit, which is primarily based on a light generated current source connected in parallel to a p–n junction diode. Many models have been proposed for the simulation of a single solar cell or for a complete photovoltaic (PV) system at various solar intensities and temperature conditions [1], [2], [3], [4], [5]. Different models have also been used to study the shading effect on PV systems [6], [7], [8]. Two most commonly used equivalent circuit models of the solar cell in the literature are one-diode and two-diode models [1], [2], [3], [4], [5], [6], [7], [8].

An ideal solar cell is represented by a light generated current source, Iph, where Iph is proportional to the solar radiation falling on it. Practical light generated current behaviour deviates from the ideal behaviour due to optical and electrical losses inside the solar cell. In the one-diode model, one diode is connected in parallel to a light generated current source as shown in Fig. 1(a). Diode current, Id, represents the current due to diffusion and recombination in the Quasi Neutral Regions (QNRs) of the emitter and bulk regions of the P–N junction. The series resistance, Rs, represents the resistance in the path of the current, due to contact resistances and resistance in the emitter and bulk regions. Shunt resistance, Rsh, represents the current leakage across the P–N junction of the solar cell and so it is connected in parallel to the diode in the equivalent circuit model. On the other hand, the two-diode model shown in Fig. 1(b) considers two-diodes connected in parallel to the current source. The current through the first diode, Id1, is the current component, which is the same as Id in the one-diode model. The current due to recombination in the Space Charge Regions (SCRs) is also considered in the two-diode model and is represented by the diode current, Id2 through a second diode. Series resistance, Rs, and shunt resistance, Rsh, are the same resistance components as defined for the one-diode model.

The load current (I) and the load voltage (V) are related through Eqs. (1a), (2a) for the one-diode and the two-diode models respectively.I=IphI0{exp[q(V+IRS)nkT]1}V+IRSRsh=I(V,I,parameters1)whereparameters1={Iph,I0,n,RS,Rsh}I=IphI01{exp[q(V+IRS)n1kT]1}I02{exp[q(V+IRS)n2kT]1}V+IRSRsh=I(V,I,parameters2)whereparameters2={Iph,I01,n1,I02,n2,RS,Rsh}

For one-diode model, the value of ideality factor, n, is between 1 and 2. For two-diode model, two ideality factors, n1 and n2 should be 1 and 2 respectively.

The number of parameters as given in Eq. (1b) for modeling in case of the one-diode model is five. These parameters are light generated current, Iph, diode parameters: reverse saturation current, I0, and ideality factor, n, series resistance, Rs, and shunt resistance, Rsh. In the two-diode model, the number of parameters becomes seven as given in Eq. (2b). The parameters are the reverse saturation currents I01 and I02 and ideality factors n1 and n2 for the two diodes, along with other parameters - Iph, Rs and Rsh. Estimation of all parameters of a solar cell model is required for modeling the performance of any photovoltaic system. Many analytical and numerical methods [9], [10], [11], [12], [13], [14] have been suggested in the literature to estimate some or all parameters of the one-diode model or the two-diode model from measured I–V characteristics. Heuristic methods such as genetic algorithms, pattern search algorithm, differential evolution and particle swarm optimization have been suggested by others [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26] for the same purpose. Heuristic methods have shown better precision and computational efficiency for estimation of solar cell parameters as compared to analytical and numerical methods. Recently, a swarm intelligence based method called Particle Swarm Optimization (PSO) has been successfully applied to various fields of power system. Phuangpornpitak et al. [19] have presented a survey on the application of PSO in solving optimization problems in electric power systems. Kongnam and Nuchprayoon [20] have applied PSO to a wind energy control problem. PSO algorithm has been used to solve for optimum rotor speed under fixed-speed operation and optimum tip-speed ratio under variable-speed operation. Qin and Kimball [21] presented an approach to extract parameters of a PV cell using PSO. PSO was applied only on single diode model and some parameters were predicted beforehand. Only n, Rs and Rsh were estimated using PSO. Sandrolini et al. [22] used a PSO algorithm for the extraction of the double-diode model parameters of photovoltaic (PV) modules. Authors used PSO algorithm to fit the calculated current–voltage characteristic of a PV module to the experimental one.

In this paper, a new lumped-parameter equivalent circuit model using three diodes, has been proposed for large area crystalline silicon solar cells. In addition, in the proposed model, the parameter, Rs has been considered to vary linearly with the load current through the device and thus the variation of Rs with the load current has been studied on the same large area solar cell samples in this work. The aim of this work is to suggest a better model for the bigger size industrial solar cells and to estimate the parameters of the model by fitting the calculated I–V curves to the measured I–V curves, through an iterative process using the PSO algorithm.

This paper is organized as follows. Section 2 discusses the theory of the proposed model followed by an overview of the PSO algorithm. Section 3 describes the experimental methods used for the fabrication of the solar cell samples and measurement of the current–voltage characteristics. The procedure used for parameter extraction is discussed in Section 4. Results are discussed in Section 5. The comparison of two models, existing and new, is highlighted in Section 6 and finally the paper is concluded in Section 7.

Section snippets

Proposed model: three-diode model with variable Rs

For the two-diode model, the ideal values of n1 and n2 would be 1 and 2 respectively; but for industrial samples of size as big as about 154.8 cm2 and efficiency about 16%, n1 was estimated between 1 and 1.5 and n2 was estimated between 2 and 5. These values indicated that the two diodes were not sufficient to represent the different current components of the experimental solar cells clearly.

In this work, a three-diode model has been proposed, as illustrated in Fig. 2. In the model, the first

Experimental methods

In the present study, an I–V measurement system (M/s Newport Corporation, Model: J80036) with adjustable 3 bus bar nest assembly (26 pin each) was used. It consisted of a solar simulator, electrical measurement system interfaced with a LabVIEW based software. The solar simulator (Model: Oriel Sol3A, M/s Oriel Instrument USA, meeting IEC 60904-9 (2007); ASTM E 927-05 (2005) and JIS C 8912-1998 standards) used a CW Xenon arc lamp (1600 W and had an output beam sizes of 20 × 20 cm2) with an AM1.5G

Procedure

Particle Swarm Optimization technique as described in Section 2.2 was applied to fit the calculated I–V curves for the two-diode model (Eq. (2a)) and for proposed three-diode model (Eq. (3a)) to the measured I–V curves of the solar cell samples mentioned in Section 3.

2-Diode model

Comparison of calculated and measured I–V plots for 12 industrial samples was carried out for the two-diode model using the PSO algorithm. The parameters of the model were estimated by fitting of the calculated I–V curve to the measured I–V curve with the least achievable MAE. The calculated and measured I–V curves for two solar cells have been shown in Fig. 4, illustrating the good match obtained between the two curves. For Sample V1, the MAE obtained was 0.00626A, which in percentage term was

MAE values in the two models

MAE values were compared for different silicon solar cell samples for the two models. General observation is that, MAE was a little higher for the three-diode model in most cases, as compared to the two-diode model as shown in Fig. 7. In some cases, the MAE was lower for the three-diode model. A little higher values of MAE (still up to third decimal place) did not have observable effect on the fitting of the calculated curve to the measured curve (Fig. 6).

Estimated parameter values in two models

Comparison of solar cell parameters

Conclusions

A new equivalent circuit model using three diodes has been proposed in this work, to model industrial crystalline silicon solar cells of large area. This would be a better model to describe the I–V characteristics of large size solar cells as compared to the one-diode or two-diode models existing in the literature. Series resistance of these solar cell samples has been found to increase with increase in load current from open-circuit to short-circuit conditions. This variation was found to be

Acknowledgement

We like to acknowledge the NWP-55 Grant from CSIR, India, as some measurements were carried using the facility created under this grant (TAPSUN initiative of CSIR).

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