Localization and Reshaping of Non-Minimum-Phase Zeros in Multi-Converter Systems

TL;DR

This paper introduces a Jacobian-based method to identify and reshape non-minimum-phase zeros in multi-converter systems, improving stability margins by strategic zero placement without needing internal converter models.

Contribution

It develops a novel framework for quantifying and reshaping NMP zeros in multi-converter power systems using only system-level data, enabling better control design.

Findings

Zeros are strictly real and can be expressed via singular values of a system matrix.

As zeros approach the origin, the system's stability margin inevitably degrades.

Zero reshaping effectively moves the dominant zero away from the origin, enhancing stability.

Abstract

Non-minimum-phase (NMP) zeros in multi-converter power systems impose bandwidth ceilings on feedback control, yet quantifying them at the system level has been impractical because commercial converters withhold their internal controller models. This paper develops a Jacobian-based framework that decouples the NMP zeros from individual converter dynamics, proves them to be strictly real, and expresses their values as the singular values of a matrix constructed solely from the grid admittance matrix and steady-state power injections. Because these zeros govern the peak magnitude of the complementary sensitivity function, an exponential lower bound on this peak is derived as a function of the dominant zero, establishing that as the zero approaches the origin the stability margin degrades unavoidably. To counteract this degradation, a zero reshaping strategy is proposed that ranks converter nodes by their real participation factors and identifies the optimal site for voltage droop deployment without iterative search, steering the dominant zero away from the origin and thereby suppressing the sensitivity peak.