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In a photovoltaic permanent magnet synchronous motor pumping system (PVPMSM), both photovoltaic modules and switching-mode converters present nonlinear and time-variant characteristics, which result in a difficult control problem. This paper presents an in-depth analysis of the operating point dynamics. A potential trade-off exists between maximum power and stability of the system operating point. Analysis of parametric singularities based on bifurcation theory permits to optimize the maximum power-stability trade-off. Tracing the bifurcation structures related to the parameter set (T, G), we can determine the maximum power point(MPP) in midway and far enough from the bifurcation points from these structures. An algorithm aiming to determine the MPP within the range of stability through power bifurcation analysis is proposed in this paper. Our methodology was validated with the simulation that was carried out on MATCONT/MATLAB, and the results are demonstrated.

Nonlinear dynamic control of a photovoltaic pumping PMSM at MPP: Low-Frequency instability induced by Hopf bifurcation