Explicit Expressions for Solar Panel Equivalent Circuit Parameters Based on Analytical Formulation and the Lambert W-Function

Abstract

Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation...), it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze commercial solar panel performance (i.e., the current-voltage-I-V-curve) at different levels OPEN ACCESSEnergies 2014, 7 4099 of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer's datasheet.

A Novel High Accuracy PV Cell Model Including Selfheating and Parameter Variation

“…One of the difficulties is the implicit nature of equation (1) regarding . This has been addressed by various techniques, ranging from pure mathematical approaches (including Lambertian W-Function, [31]) to pure numerical solutions, mainly in MATLAB [5,6,16,35]. Later models [40 -52] take into account the parameters variation with temperature and irradiance.…”

“…is 0 by default and when modified has to be positive. Cubas et al [31] and Cuce et al [47] results were scaled, and equation 19…”

“…Some authors consider the ideality factor as being constant over the operating temperature range and with a generic value for in the interval [1, 1.5] for every kind of cell [22], [31]. Cuce et al [29] propose = 1.2 for monocrystalline silicon cells, and = 1.3 for polycrystalline ones.…”

“…Some studies indicate a linear decreasing with temperature [18]. Cubas et al [31] say that "the lack of accuracy produced when considering the ideality factor as constant is generally reduced, given that variations of this parameter only affects the curvature of the I-V curve." This is arguable, as interferes in an exponential dependency and small variations of lead to significant changes in , and finally in .…”

Silicon PV module fitting equations based on experimental measurements

“…There is a general need for all those PV users to get a better knowledge about their PV systems so as to gain the best efficient energy as compared with cost. In contrast, PV power is highly related to the weather conditions such as; temperature and sun irradiance, which complicates the measurement optimizations, therefore, a modeling for such systems is an essential need . A PV cell has a nonlinear current‐voltage (I‐V) characteristic that can be modeled using a current source, one or more diodes, and resistors.…”