The photovoltaic (PV) systems are often subject to shading in practical operation. Non-uniform shading for PV array with bypass diodes leads to mismatch in power generation, and thus resulting in multi-peak power-voltage (P-V) characteristics. Most existing maximum power point tracking (MPPT) control strategies are local optimum oreinted, as based on the gradient search or its variations, e.g. perturbation-and-observation (P&O) or extremum seeking control (ESC). The multi-modal P-V characteristics for PV array with variable shading demands for global search for the optimum to avoid the signifiant power loss otherwise. This study investigates both the P-V and the current-voltage (I-V) characteristics of the PV panel under variable shading. Analytical model is established based on an approximate model of the PV device. The stair-case profile of the I-V relationship is shown to have close and consistent correspondence to the shading distribution. The voltage breakpoints for the multipeak curve are also within predictable ranges. With such results, the global search can be achieved with multiple local search within finite number of intervals. Simulation results validate the analytical modeling and the ESC based global ESC for partially shaded PV panels.

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