Title: Whale Optimization Algorithm-based Fractional Order Fuzzy Type-II PI Control for Modular Multilevel Converters

Abstract: Designing a robust controller for Modular Multilevel Converters (MMCs) is crucial to ensure stability and optimal dynamic performance under various operating conditions, including faulty and disturbed scenarios. The primary objective of controlling grid-connected MMCs (GC-MMCs) is to accurately track real and reactive power references while maintaining excellent harmonic performance in the output response. This paper proposes a novel model-free control strategy for GC-MMCs, employing a Fractional Order Proportional-Integral (FOPI) controller and a Fractional Order Fuzzy type-II Proportional-Integral (FOFPI) controller. The FOFPI controller utilizes a type-II Fuzzy Inference System (FIS) to adaptively adjust the proportional and derivative gains during the control process, enabling effective control of the MMC under diverse operating conditions. The type-II FIS, which leverages type-II fuzzy sets, can mitigate uncertainty and nonlinearity in the system. Furthermore, the incorporation of fractional-order mathematics enhances the flexibility of the proposed controllers. To optimize the initial parameters of the proposed controllers, the Whale Optimization Algorithm (WOA), a meta-heuristic algorithm, is employed. The results demonstrate that the proposed controllers exhibit superior performance under voltage disturbance conditions, varying input voltage, and can ensure the stability of the MMC.