Impedance modeling of modular multilevel converter based on harmonic state space

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, which take into account the internal dynamics of MMC, are developed according to the harmonic linearization principle. 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. Index Terms-Modular multilevel converter (MMC), impedance modeling, impedance measurement, harmonic state-space (HSS), harmonic coupling. especially for renewable energy integration applications [5]-[7].The impedance-based stability analysis method is one of the preferred methods for stability analysis of power electronics systems, especially for multi-converter interconnected systems [8]- [11]. The impedance modeling of power converters is the prerequisite for applying the impedance-based analytical approach. Most of the research has so far focused on the impedance modeling of 2-level converters [9]- [14]. Sequence impedance models of 2-level grid-connected VSCs with current control and phase-locked loop (PLL) dynamics were developed in [9], [14]. DQ small-signal impedance of 2-level VSCs with closed-loop control was derived in [10]- [13]. However, very few authors have by far reported the impedance modeling of an MMC. The dc-side impedance of an MMC was derived for dc voltage ripple prediction in [15], but there is no mention of ac-side impedances. In the beginning of our previous work [6], [16], the ac-side impedance models of the MMC were developed, where, however, the capacitor voltage harmonics and high-order circulating current harmonics were ignored in the impedance modeling, resulting in imprecise impedance models. Later, the harmonic linearization method and harmonic state-space (HSS) method were introduced by the authors to develop the MMC impedance models in [17], [18], which are able to include all the steady-state harmonics of the state variables. In addition, a similar method to the HSS, so called multi-harmonic linearization method, was also proposed to model the MMC impedance in [19].MMC is a converter system with a typical multi-frequency response due to its significant steady-state harmonic components in the arm currents, capacitor volt...

Sub‐synchronous oscillation mechanism and its suppression in MMC‐based HVDC connected wind farms

“…It is assumed that the equivalent switching frequency is high enough and the capacitor voltages are balanced at all times [6][7][8]. Hence, the averaged equivalent circuit of MMC can be obtained, as presented in Fig.…”

“…Hence, according to (21)~(25), the small perturbation HSS model of the MMC can be obtained as (26) by applying the HSS modelling procedure that is introduced in (1)~ (8).…”

“…However, compared with conventional VSCs, MMCs have much more complex internal dynamics [6][7][8], such as harmonic circulating currents and capacitor voltage fluctuations, which might have detrimental effects on the operation stability of the interconnected system, especially for renewable energy integration applications [9][10][11]. For instance, a subsynchronous oscillation (SSO) phenomenon was observed in a real MMC-HVDC project for wind farm integration in China [10], where the oscillation frequency is approximately 21 Hz in the ac phase currents (as shown in Fig.…”

Recent contributions and future prospects of the modular multilevel converters: A comprehensive review

“…Impedance model, which is derived using various methods in the literature, is required for stability analysis of MMC based application …”

“…Impedance model, which is derived using various methods in the literature, is required for stability analysis of MMC based application. [69][70][71][72][73] Lyu et al 74 investigate the stability analysis of MMC-based HVDC with wind farm integration in frequency domain. In this review paper, impedance model is derived only for compensated modulation case as expressed in Lyu et al 74 Thereby, the impedance model of direct modulation case with/without circulating current control will not be repeated in this paper.…”