Stability Assessment of PMSM based Solar Water Pumping System in Partially Shaded Conditions Using an Analytical Equivalent Model

Solar-powered water pumping systems offer a sustainable and off-grid solution for agricultural irrigation. However, the performance of photovoltaic (PV) arrays deteriorates significantly under partial shading, reducing the overall power yield. To mitigate this, Maximum Power Point Tracking (MPPT) algorithms are employed to maximize energy extraction. These algorithms require thorough validation through simulation before hardware implementation. Most conventional simulations assume resistive loading, which fails to capture the electromechanical characteristics of motor-driven pumps. This paper presents an analytically derived simplified model of a PMSM-driven solar water pumping system that captures essential dynamic behavior while significantly reducing simulation complexity and computational time. The model is validated under both uniform irradiance and partial shading conditions, demonstrating its robustness and accuracy. By simplifying the inverter-motor system with an analytically equivalent model, the simulation becomes significantly more efficient, enabling quicker iterations during MPPT algorithm development and validation. Moreover, this model facilitates rapid and efficient controller design by providing a tractable framework for analyzing closed-loop system behavior. A structured methodology for MPPT controller design is introduced, including stability analysis under varying solar conditions. Simulation results highlight how MPPT convergence time affect system dynamics such as overshoot and settling time. Overall, the proposed analytical model proves to be a powerful tool for developing, verifying, and optimizing MPPT and control strategies in PMSM-based solar pumping systems, particularly under varying shading scenarios.