Stability of Multi-Microgrids: New Certificates, Distributed Control, and Braess's Paradox

TL;DR

This paper develops new stability certificates for multi-microgrid networks that are distributed and account for network topology, revealing that increasing connections can sometimes destabilize the system due to Braess's Paradox.

Contribution

It introduces novel distributed stability conditions for lossy multi-microgrids and uncovers the paradoxical effect of added connections on system stability.

Findings

New stability certificates for lossy networks using local information

Demonstration of Braess's Paradox in multi-microgrid stability

Validation of stability conditions through numerical simulations

Abstract

This paper investigates the theory of resilience and stability in multi-microgrid networks. We derive new sufficient conditions to guarantee small-signal stability of multi-microgrids in both lossless and lossy networks. The new stability certificate for lossy networks only requires local information, thus leads to a fully distributed control scheme. Moreover, we study the impact of network topology, interface parameters (virtual inertia and damping), and local measurements (voltage magnitude and reactive power) on the stability of the system. The proposed stability certificate suggests the existence of Braess's Paradox in the stability of multi-microgrids, i.e. adding more connections between microgrids could worsen the multi-microgrid system stability as a whole. We also extend the presented analysis to structure-preserving network models, and provide a stability certificate as a function of original network parameters, instead of the Kron reduced network parameters. We provide a detailed numerical study of the proposed certificate, the distributed control scheme, and a coordinated control approach with line switching. The simulation shows the effectiveness of the proposed stability conditions and control schemes in a four-microgrid network, IEEE 33-bus system, and several large-scale synthetic grids.