An efficient analytical approach for obtaining a five parameters model of photovoltaic modules using only reference data

Abstract

Exploiting the equivalent one-diode circuit of a photovoltaic (PV) module, this paper proposes a novel and fully analytical model to predict the electrical performance upon solar-irradiance intensity and PV module temperature. The model refers essentially to an equivalent circuit governed by five parameters and the extraction of them permits to describe the current-voltage curve of the PV panel and consequently permits to assess the energy output of PV modules. The proposed model extracts the five characteristic parameters using only exact analytical relationship and tabular data always available such as short-circuit current, open circuit voltage and the Maximum Power Point (MPP). The difference with other models consists in the complete absence of mathematical simplifications or other physical assumptions. All used equations were obtained with a transparent analytical procedure. A new resolution procedure for solving the equation that describe the equivalent one diode circuit system is also described. The procedure is based upon the Generalized Reduced Gradient (GRG) algorithm and transforms the extraction of the five parameters into a constrained nonlinear optimization problem. The purely analytical model, the absence of data to be obtained from graphic methods or not always available in datasheets, and a new optimised procedure to solve the system of equations lead to obtain values of the five parameters that perfectly fit the official tabular data. The suggested procedure of numerical solution of a local minimum problem allows converging towards the solution with the desired accuracy in a fast and effective way. Although in scientific literature there are several models able to determine the value of these five parameters, these procedures are always affected by inevitable inaccuracies linked to various simplifications or due to the use of non-tabular data such as some graphic characteristics of the experimental I-V curve (moreover not always available). The model, as opposed to those already known in the literature, is exclusively based on analytical relationships and is free of any simplifications that may affect the reliability of the results. The proposed model allows a more accurate modelling of the PV modules based solely on reference data and the availability of decision support tools that may reliably predict the energy produced by a photovoltaic panel is essential in the design phase of the plant to avoid future problems related to incorrect sizing. Furthermore, reliable energy predictions lead to more correct economic analyses that can stimulate the diffusion of the PV technology.