Modeling and Analysis of Fractional-Order Modular Multilevel Converters State-Space Time-Invariant Model

Abstract

This paper investigates the fractional-order properties of real inductance and capacitance, and proposes a fractional-order model for Modular Multilevel Converters (MMC) and analyzes it. The Caputo fractional calculus operator is employed to characterize the fractional-order behavior of inductance and capacitance. The Generalized State-Space Model (GSSM) of MMC is derived by considering the sum and difference of variables from the upper and lower arms. Fractional-order Park transformation matrix at different frequencies is applied to the integer-order model of MMC in the three-phase stationary coordinate system to obtain a fractional-order State-Space Time-Invariant Model (FSSTI). The model introduces the influence of the orders of capacitance and inductance into the coupling components among the three-phase MMC state variables. This enhances the model's precision while eliminating the time-varying components in the integer-order model, simplifying the complexity of the model. This study investigates the impact of capacitor and inductor orders on the steady-state characteristics of MMC through time-domain simulations. From the results, optimal orders are selected for hardware-in-the-loop simulations. The findings indicate that the proposed model accurately describes the operational characteristics of the MMC. By appropriately choosing the orders of inductors and capacitors, the MMC can effectively optimize its performance under the same conditions.