d-q Small-Signal Model for Grid-Forming MMC and Its Application in Electromagnetic-Transient Simulations

Cleiton M. Freitas (), Edson H. Watanabe and Luís F. C. Monteiro
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Cleiton M. Freitas: Electrical Engineering Department, Rio de Janeiro State University, 524 São Francisco Xavier, Rio de Janeiro 20550-900, Brazil
Edson H. Watanabe: Electrical Engineering Program, COPPE/Federal University of Rio de Janeiro, 149 Athos da Silveira Ramos Ave, Rio de Janeiro 21941-909, Brazil
Luís F. C. Monteiro: Electronic Engineering Graduate Program, Rio de Janeiro State University, 524 São Francisco Xavier, Rio de Janeiro 20550-900, Brazil

Energies, 2023, vol. 16, issue 5, 1-22

Abstract: The modular multilevel converter (MMC) is a keystone of modern energy transmission systems. Consequently, there is an ongoing pursue for mathematical models to represent it under different configurations and control approaches. In short, this paper introduces an analytical Thévenin-equivalent model for representing the MMC when it is controlled with inner current- and an outer voltage-loop altogether. The model is based on a linearized representation of the converter and conveys the dynamics of passive components, such as submodule capacitors and arm reactors, as well as both control loops. Besides that, the proposed model is divided into a close-loop transfer matrix and the equivalent impedance matrix, both of which represent the relationships between the ac-side dq voltages and currents. We also propose a framework for implementing electromagnetic–transient simulations using the impedance model of this power electronic converter. The framework reduces a multi-bus power grid to a multi-input multi-output (MIMO) feedback system where impedance/admittance matrices of the MMC and other grid elements compose its loops. For validation purposes, it is considered a three-bus power grid comprising one MMC and another two grid-connected VSC. The proposed model was validated by comparing its results with a switching-level PSCAD model of the system.

Keywords: MMC model; impedance modeling; MMC transfer function; grid-forming; inverter-based power grid (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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