# Parametric local stability condition of a multi-converter system

## TL;DR

This paper develops a parametric local stability condition for a network of identical DC/AC converters, providing a decentralized, explicit criterion that depends on system parameters and aligns with practical insights.

## Contribution

It introduces a novel stability theory for partitioned linear systems with symmetries, deriving explicit, decentralized stability conditions for multi-converter systems.

## Key findings

- Stability conditions depend on reactive power support and resistive damping.
- Conditions are explicit and can be evaluated in a decentralized manner.
- The theory generalizes to other systems like synchronous machines.

## Abstract

We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom. We develop a stability theory for a class of partitioned linear systems with symmetries that has natural links to classical stability theories of interconnected systems. We find stability conditions descending from a particular Lyapunov function involving an oblique projection onto the complement of the synchronous steady state set and enjoying insightful structural properties. Our sufficient and explicit stability conditions can be evaluated in a fully decentralized fashion, reflect a parametric dependence on the converter's steady-state variables, and can be one-to-one generalized to other types of systems exhibiting the same behavior, such as synchronous machines. Our conditions demand for sufficient reactive power support and resistive damping. These requirements are well aligned with practitioners' insights.

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Source: https://tomesphere.com/paper/1904.11288