Maximum power point tracking in PV arrays exposed to partial shading condition irrespective of the array configuration

A method is proposed for calculating the I-V and P–V curves of a PV array composed of series-, parallel- and series–parallel connected-cells or modules or strings exposed to uniform and non-uniform radiation with and without bypass diodes (BpDs). The P–V curve of the array exposed to uniform radiation has one power peak irrespective of the presence or absence of BpDs. In non-uniform radiation, the curve has a number of power peaks equal to that of the radiation levels in presence of BpDs irrespective of the number of diodes against one peak in absence of BpDs. The proposed method is based on combining Lambert-based simultaneous-solutions of the describing-equations V = g (I) and I = f (V) to obtain a global voltage equation V in terms of current I over all current range. The method is extended to locate the global maximum power point (GMPP) of the array by locating a point close to the GMPP on the calculated P–V curve of the array where it interests with a parabolic equation proposed -for the first time- to relate the output power to the corresponding output voltage of the array. To pinpoint the location of local maximum power points (LMPPs) and GMPP for the array, the “islocalmax” Matlab function is used along with the calculated P–V curve of the array. The calculated I-V and P–V curves by the proposed method as well as the locations of the GMPP and LMPPs agree reasonably with the present experimental-measurements and those reported in the literature.