Stability of Multimicrogrids: New Certificates, Distributed Control, and Braess’s Paradox

This article investigates the theory of resilience and stability in multimicrogrid (multi-
$\mu$
G) networks. We derive new sufficient conditions to guarantee small-signal stability of multi-
$\mu$
Gs in both lossless and lossy networks. The new stability certificate for lossy networks only requires local information, thus leading to a fully distributed control scheme. Moreover, we study the impact of the 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-
$\mu$
Gs, i.e., adding more connections between microgrids could worsen the multi-
$\mu$
G 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-
$\mu$
G network, the IEEE 33-bus system, and several large-scale synthetic grids.