Partial Shading Analysis of Multistring PV Arrays and Derivation of Simplified MPP Expressions

In this paper, the electrical response of a partially shaded photovoltaic (PV) array, comprising several strings connected in parallel, is investigated. The PV array is simulated by employing an enhanced version of the widely used single-diode model, reformulated in an explicit manner employing the Lambert W function. The multiple maximum power points (MPPs) that appear on the P-V characteristic of the array in partial shading conditions are analyzed, in terms of their number and properties. Simplified empirical expressions are then derived to calculate the voltage, current, and power for each local MPP, at any irradiance level and temperature, using only datasheet information, in a most simple and straightforward manner, without resorting to detailed modeling and simulations. The derived formulae are validated using both simulation and experimental results.