Under partial shading conditions (e.g., due to buildings, trees, and clouds), multiple peaks may exist on the power-voltage (P-V) characteristic curve of photovoltaic (PV) array, leading to the conventional maximum power point tracking methods fail to extract the global maximum power point (GMPP). In this paper, a mathematical model of PV array under partial shading conditions with a voltage calculated principle is established. The presented model is implemented with an m-file in MATLAB software, which is used as a tool to study the non-linear characteristics of current-voltage (I-V) and P-V curves of PV array, as well as quickly develop the GMPP tracking controllers. Besides, an adaptive random particle swarm optimization (ARPSO) algorithm is presented to accurately extract the GMPP under partial shading conditions. Five simulation cases with different partial shading patterns are used to evaluate the performance of the presented approach by comparing with the conventional PSO, perturbation and observation (P&O), incremental conductance (INC), and genetic algorithm (GA) methods. Simulation results show that the ARPSO algorithm can rapidly find the GMPP under different shading conditions compared with the conventional PSO algorithm. Furthermore, the presented algorithm can accurately extract the GMPP when the shading condition sharply changes, while the P&O and INC algorithms fail to track the GMPP, but only detect the rightmost MPP encountered either local or global and regardless of the course. Besides, the ARPSO can rapidly and accurately converge to the GMPP with smaller population size and higher convergence speed compared with the GA.
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