MMC Impedance Modeling and Interaction of Converters in Close Proximity

Abstract

This paper develops a small-signal impedance model of modular multilevel converters (MMCs) using harmonic statespace (HSS) method and studies the stability in a multiple converter scenario. In order to simplify analysis on the coupling characteristics between different frequencies in MMCs, the proposed model is developed in the positive-negative-zero (PN0) sequence-frame, where the zero-sequence current in three-phase three-wire system is directly set to zero without introducing complicated method. A simple 2 by 2 admittance matrix in PN0frame is extracted from the MMC small-signal model for ease of system stability analysis. Using the developed impedance model, the multi-infeed interaction factor (MIIF) measure is adopted to analyze the most significant interactions for multi-infeed converter systems to be prioritized. Different outer-loop controllers are adopted and compared in the analysis to illustrate the effect of different control modes on converter impedance and system stability. Analytical studies and time-domain simulation results are provided to validate the proposed model and stability analysis.

Block Diagonal Dominance-Based Model Reduction Method Applied to MMC Asymmetric Stability Analysis

“…For symmetric conditions, it can be seen from Fig. 2(a) that only one pair of frequency couplings (25 Hz & 75 Hz) appears, the coupling mechanism of which has been studied well in [15]- [17]. Refs [15]- [17] also explain why a 2×2 impedance matrix is adequately accurate for reflecting the MMC AC-side dynamics.…”

“…2(a) that only one pair of frequency couplings (25 Hz & 75 Hz) appears, the coupling mechanism of which has been studied well in [15]- [17]. Refs [15]- [17] also explain why a 2×2 impedance matrix is adequately accurate for reflecting the MMC AC-side dynamics. For asymmetric conditions (Larmb=Larmc=0.36H, L arma =3×0.36H), it can be seen from Fig.…”

“…Compared with the diagonal dominance theory [21], the robustness of the Definition 1 is greatly improved due to its ability of partitioning the Z(s) with flexible dimensions. From the experience of symmetric cases [15]- [17], the dimension of the submatrix z ii (s) can be set as 2 (n ii =2), the simplest form containing at least one pair of coupling terms. It is noted that if Definition 1 cannot be complied with the 2×2 dimension, then the n ii needs to be increased.…”

“…At first, the BDD characteristics of the derived MIMO impedance is analyzed in α-β domain. The grid impedance Z αβ± grid (s) in α-β domain can be transformed from the three-phase grid impedance Z x grid (s) (e.g., Z a grid (s) = R ga +sL ga ) using (17).…”

“…To the best knowledge of the authors, the impedance-based asymmetric stability analysis of the MMC has so far been missing, where the main difficulty may lie in the applicability of the resulting high-dimensional impedance to practical analysis. Specifically, for symmetric cases, as demonstrated in [15]- [17], a 2×2 impedance matrix can accurately depict the MMC AC-side dynamics, because there mainly exists one pair of frequency couplings. However, for asymmetric cases, multiple frequency couplings will appear, especially those at the same frequency (denoted by the sequence coupling [8]).…”