Whale optimization-based fractional order control for high-performance grid-connected photovoltaic multilevel inverters: diode-clamped versus T-type MLIs

This work presents a new integration of the Whale Optimization Algorithm (WOA) with Finite Control Set Model Predictive Control (FCS‑MPC) to optimise Fractional‑Order Proportional-Integral (FOPI) controllers for Multilevel Inverters (MLIs)-a combination hitherto unexplored in the literature. In the proposed hierarchical scheme, the WOA‑tuned FOPI operates in the outer loop to generate highly accurate and adaptive current reference signals, while FCS‑MPC forms the inner loop, predicting the inverter's behaviour for all possible switching states and selecting the one that minimises a defined cost function. This coordinated outer-inner control design enhances reference tracking accuracy and reduces steady‑state error, leading directly to improved harmonic suppression, voltage regulation, and dynamic stability. The proposed WOA‑FOPI‑FCS‑MPC control achieves a 12-15% reduction in Total Harmonic Distortion (THD) and a 22% improvement in dynamic stability compared to conventional PI‑based predictive control. Additionally, a systematic comparison between diode‑clamped and T‑type MLIs in a 1 MW PV‑grid system reveals that the T‑type inverter reaches 98.5% efficiency and 1.48% voltage THD at 7‑level operation, offering an optimal trade‑off between switching device count, power quality, and efficiency. Statistical analysis-including mean, minimum, maximum, standard deviation, and computational time-confirms the robustness and consistency of the proposed optimisation, while benchmark function evaluations validate the global search capability of WOA. The results, validated through MATLAB/Simulink simulations and preliminary experimental tests, demonstrate the method's strong potential for high performance industrial PV grid integration.