Decentralized Frequency-Domain Conditions for D-Stability with Application to DC Microgrids

TL;DR

This paper introduces a decentralized frequency-domain approach for D-stability in networked systems, enabling regional pole placement without sharing subsystem models, with applications to DC microgrids.

Contribution

It develops a novel decentralized method for D-stability using frequency-domain criteria, applicable to DC microgrids, avoiding the need for communication or proprietary data sharing.

Findings

Method guarantees D-stability via local frequency criteria.

Applicable to DC microgrids with a broadcastable grid code.

Numerical examples confirm effectiveness.

Abstract

This paper proposes a decentralized method for regional pole placement, or $\mathcal{D}$-stability, in linearized networked systems. Existing LMI-based methods are hindered by confidentiality concerns regarding proprietary subsystem models and the absence of communication infrastructures. To overcome these barriers, we map the target region $\mathcal{D}$ of pole placement to an auxiliary left-half plane and introduce positive functions to handle the resulting complex-coefficient dynamics. We prove that $\mathcal{D}$-stability is guaranteed via local frequency-domain criteria without requiring shared subsystem models or inter-subsystem communication. This method is then tailored to DC microgrids, where a loop transformation is utilized to reallocate the burden of stability certification, deriving a broadcastable grid code for decentralized parameter synthesis. Numerical examples verify the efficacy of the proposed method.