Identification of PV solar cells and modules parameters using the genetic algorithms: Application to maximum power extraction

doi:10.1016/j.solener.2010.02.012

Solar Energy

Volume 84, Issue 5, May 2010, Pages 860-866

https://doi.org/10.1016/j.solener.2010.02.012 Get rights and content

Abstract

In this paper, we propose to perform a numerical technique based on genetic algorithms (GAs) to identify the electrical parameters (I_s, I_ph, R_s, R_sh, and n) of photovoltaic (PV) solar cells and modules. These parameters were used to determine the corresponding maximum power point (MPP) from the illuminated current–voltage (I–V) characteristic. The one diode type approach is used to model the AM1.5 I–V characteristic of the solar cell. To extract electrical parameters, the approach is formulated as a non convex optimization problem. The GAs approach was used as a numerical technique in order to overcome problems involved in the local minima in the case of non convex optimization criteria. Compared to other methods, we find that the GAs is a very efficient technique to estimate the electrical parameters of PV solar cells and modules. Indeed, the race of the algorithm stopped after five generations in the case of PV solar cells and seven generations in the case of PV modules. The identified parameters are then used to extract the maximum power working points for both cell and module.

Introduction

The algorithms that we use to determine parameters of PV generators (solar cells, modules and arrays) must be efficient and sufficiently accurate for process optimization and photovoltaic systems design tasks. These algorithms are of two types: those that use selected parts of the current–voltage (I–V) characteristic (Charles et al., 1981, Charles et al., 1985, Laplaze and Youm, 1985, Chan and Phang, 1987) and those that exploit the whole characteristic (Easwarakhanthan et al., 1986; Phang and Chan, 1986; Ikegami et al., 2001, Jervase et al., 2001). The first group of algorithms involves the solution of five equations, derived from considering selected points of the I–V characteristic, i.e. the open-circuit and short-circuit points, the maximum power points and the slopes at strategic portions of the characteristic for different level of illumination and temperature. Although, the exact solution of these equations requires iterative techniques, this method is often much faster and simpler in comparison to curve fitting. The disadvantage of this approach is that only selected parts of the I–V characteristic are used to determine the parameters. The second group of algorithms is based on curve fitting and offers the advantage of taking all the experimental data in consideration. Conversely, it has also the disadvantage of artificial solutions. In fact, the fitting techniques with several parameters are, generally, based on non-convex optimization criterion, and using traditional deterministic optimization algorithms leads to several sets of local minima solutions, and none one of them can describe the physical reality.

In this paper, we present a non-linear least-squares optimization algorithm for the identification of the five electrical solar cell and module parameters from experimental data. This fitting is based on the Genetic Algorithms (GAs) strategy. These algorithms are recently applied in several domains, such as in optimization of large solar hot water systems (Loomans and Visser, 2002), in design and control strategies of PV–Diesel systems (Dufo-Lopez and Bernal-Agustin, 2005), in sizing optimization of hybrid solar–wind system (Yang et al., 2008), etc. For the estimation of the electrical parameters of PV generators, we found that GAs increase the probability of obtaining the best minimum value of the cost function in very reasonable time, and more accurate solution in comparison to the approaches reported in the literature (Ikegami et al., 2001). The identified parameters are then used to extract the working maximum power point (MPP).

Section snippets

The one diode model

The theoretical expression of the current crossing a photovoltaic cell versus the applied voltage results from the Schottky diffusion model in a PN junction, and is given by (Charles et al., 1985): $I = I_{ph} - I_{s} [\exp (\frac{V + R_{s} I}{{nV}_{th}}) - 1] - \frac{V + R_{s} I}{R_{sh}}$ where I_ph and I_s are the photocurrent and the saturation current, respectively. R_s is the series resistance, R_sh is the shunt resistance, n is the ideality factor and V_th is the thermal voltage.

The electrical parameters R_s, G_sh = 1/R_sh, I_ph, n and I_s are computed from the I

The genetic algorithms

To numerically treat the I–V curves, we performed a fitting procedure based on the genetic algorithms (GAs). The error criterion which used in the non-linear fitting procedure is based on the sum of the squared difference between the theoretical and experimental current values. Consequently, the cost function to be minimized is given by (Easwarakhanthan et al., 1986, Phang and Chan, 1986): $χ = \sum_{i = 1}^{m} {[I_{i}^{\exp} - I (V_{i}, θ)]}^{2}$ where $I_{i}^{\exp}$ is the measured current at the V_i bias, θ = (I_ph, I_s, R_s, G_sh, n) is the set

Identification of the electrical parameters

We use a homemade GAs program developed on Matlab environment for both PV cell, module and array. For flexibility, we choose to develop this program instead of using Genetic Algorithms and Direct Search Toolbox of Matlab.

Maximum power point extraction

In order to extract the maximum available power from PV cell, it is necessary to operate it (the cell) at its maximum power point (MPP). Several MPP methods, such as perturbation, fuzzy control, power–voltage differentiation and on-line method have been reported (Bahgat et al., 2004, Yu et al., 2004, Enrique et al., 2007). These control methods have drawbacks in stability and response time in the case when solar illumination changes abruptly. A direct MPP method using PV model parameters was

Conclusion

In this work, we applied the genetic algorithms to characterize PV solar cells and modules, particularly for the determination of electrical parameters namely such as the photocurrent, the saturation current, the series resistance, the shunt resistance and the ideality factor. Determination of these parameters starting from the experimental data is formulated in the form of a non convex optimization problem. The resolution of this problem by conventional techniques of non-linear programming,

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Identification of PV solar cells and modules parameters using the genetic algorithms: Application to maximum power extraction

Abstract

Introduction

Section snippets

The one diode model

The genetic algorithms

Identification of the electrical parameters

Maximum power point extraction

Conclusion

Ren. Energy

Solar Cells

Solid-State Electron.

Solar Energy

Solar Energy

Solar Energy Mater. Solar Cells

Solar Cells

Solar Energy

Solar Cells