Title: Fractional-order modular multilevel converter for high voltage supply

Authors: Vivek Patel; Ashok Mankani; Kumar Saurabh; Aritra Chakraborty

Addresses: Institute for Plasma Research, Gandhinagar, 382428, India ' Institute for Plasma Research, Gandhinagar, 382428, India ' Institute for Plasma Research, Gandhinagar, 382428, India ' Institute for Plasma Research, Gandhinagar, 382428, India; Homi Bhabha National Institute (HBNI), Anushaktinagar, Mumbai 400094, Maharashtra, India

Abstract: The modular multilevel converter (MMC) is a multilevel converter topology mainly used for medium/high-power applications, specifically for high-voltage direct current transmission systems. This paper proposes a mathematical fractional order (FO) modelling of MMC. Fractional behaviour helps to model and describe a real object more accurately than the integer order model. State-space equations of MMC are obtained and solved using fractional calculus. The application of FO elements, such as capacitors and inductors in power electronic systems, is explored for potential advantages in transient response, stability, and control. An approximation of the fractional-order capacitor (FOC) and fractional-order inductor (FOI) was done using minimax approximation in MATLAB. Utilise fractional-order differential solver (fde12) in MATLAB to analyse the steady state and transient response of the three-phase FO-MMC under various conditions. The simulation outcomes confirm the efficacy of the FO-MMC model, and the comparative performance analysis illustrates its superior transient response compared to integer-order MMC.

Keywords: modular multilevel converter; MMC; fractional calculus; fractional-order capacitor; FOC; fractional-order inductor; FOI.

DOI: 10.1504/IJPELEC.2025.144696

International Journal of Power Electronics, 2025 Vol.21 No.2, pp.170 - 194

Received: 27 May 2024
Accepted: 05 Nov 2024
Published online: 27 Feb 2025 *

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