[Paper Review] Impedance Analysis of Modular Multilevel Converter Based on Harmonic State-Space Modeling Method

Jing Lyu, Qiang Chen+2 more|arXiv (Cornell University)|May 2, 2017

HVDC Systems and Fault Protection26 references3 citations

TL;DR

This paper proposes a harmonic state-space (HSS) modeling approach to accurately derive small-signal impedance models for modular multilevel converters (MMCs), addressing the limitations of traditional methods that fail to capture multi-frequency dynamics. By incorporating harmonic linearization, the method enables precise impedance characterization under open-loop, ac voltage closed-loop, and circulating current closed-loop controls, validated through simulation and experiments.

ABSTRACT

The small-signal impedance modeling of modular multilevel converter (MMC) is the key for analyzing resonance and stability of MMC-based ac power electronics systems. MMC is a converter system with a typical multi-frequency response due to its significant steady-state harmonic components in the arm currents, capacitor voltages, and control signals. Therefore, traditional small-signal modeling methods for 2-level voltage-source converters (VSCs) cannot be directly applied to the MMC. In this paper, the harmonic state-space (HSS) modeling approach is introduced to characterize the harmonic coupling behavior of the MMC. On this basis, the small-signal impedance models of the MMC are developed according to the harmonic linearization principle, which can include all the steady-state harmonic effects of the state variables, leading to the accurate impedance models. Furthermore, in order to reveal the impact of the internal dynamics and closed-loop control on the small-signal impedance of the MMC, three cases are considered in this paper, i.e., open-loop control, ac voltage closed-loop control, and circulating current closed-loop control. Finally, the analytical impedance models are verified by both simulation and experimental results.

Motivation & Objective

• Address the challenge of small-signal impedance modeling in MMCs due to their inherent multi-frequency harmonic components.
• Overcome the limitations of conventional small-signal modeling techniques used for 2-level VSCs, which are inadequate for MMCs.
• Develop an accurate impedance model that captures harmonic coupling effects in arm currents, capacitor voltages, and control signals.
• Investigate the impact of internal dynamics and different control strategies—open-loop, ac voltage closed-loop, and circulating current closed-loop—on MMC impedance.
• Verify the analytical impedance model through both simulation and experimental validation.

Proposed method

• Adopt the harmonic state-space (HSS) modeling framework to represent the time-varying, multi-frequency behavior of MMCs.
• Apply harmonic linearization to derive small-signal impedance models that include all steady-state harmonic components of state variables.
• Formulate the impedance model based on the HSS representation, enabling analysis of harmonic coupling across multiple frequency components.
• Construct three distinct impedance models corresponding to different control configurations: open-loop, ac voltage regulation, and circulating current suppression.
• Utilize the HSS approach to systematically analyze how control loops influence the overall impedance characteristics of the MMC.
• Validate the analytical model using both electromagnetic transient simulations and experimental hardware tests on an MMC prototype.

Experimental results

Research questions

• RQ1 How can the harmonic coupling effects in MMCs be accurately captured in small-signal impedance modeling?
• RQ2 What are the differences in impedance behavior between open-loop, ac voltage closed-loop, and circulating current closed-loop control strategies in MMCs?
• RQ3 To what extent does the HSS-based modeling approach improve the accuracy of impedance models compared to conventional methods?
• RQ4 How do steady-state harmonic components in arm currents, capacitor voltages, and control signals affect the small-signal stability of MMC-based systems?
• RQ5 Can the proposed HSS-based impedance model be effectively validated through both simulation and experimental results?

Key findings

• The HSS-based impedance model successfully captures the multi-frequency dynamics of the MMC, including harmonic coupling effects from steady-state components.
• The impedance model under ac voltage closed-loop control exhibits improved stability margins compared to open-loop and circulating current control cases.
• The inclusion of harmonic linearization significantly enhances model accuracy, particularly in predicting resonance behavior in MMC systems.
• Experimental results confirm the analytical predictions of the impedance model, demonstrating good agreement between simulation and measurement.
• The model reveals that circulating current control has a notable influence on the positive-sequence impedance, especially at higher harmonic frequencies.
• The proposed method enables reliable stability assessment of MMC-based power electronic systems, supporting design and control optimization.