Modeling of photovoltaic fields in mismatching conditions by means of inflection voltages

This paper presents a suitable algorithm for modeling photovoltaic fields operating under mismatching conditions. It is based on the detailed non-linear model (including series and parallel resistors) of all PV modules composing the PV field. The main advantage is in the possibility to express each PV module voltage as an explicit function of the current by using the Lambert-W function, thus the PV field is analyzed string-by-string and one equation is constructed by equalizing the string voltage with the voltages of all active modules and the blocking diode. Then the field current is calculated by adding the currents of all strings for a same string voltage. The computational burden and accuracy of the proposed algorithm was tested experimentally and compared with previous approach proposed in literature. A string of 4 PV panels has been used as test bench and the maximum power has been evaluated by considering and by neglecting the series and parallel resistors in the PV models. The power and current relative mean errors between the experimental and estimated values were 1.80 % (0.57 W) and 4.23 % (1.02 W), respectively, demonstrating that the relative error in the estimation of the maximum power can be improved by almost 50% adopting the complete PV model.