A unifying energy-based approach to stability of power grids with market dynamics

TL;DR

This paper introduces a unified energy-based framework for analyzing the stability of power grids with integrated market dynamics, employing port-Hamiltonian systems and distributed algorithms to ensure stability and optimality.

Contribution

It develops a novel unifying energy-based approach using port-Hamiltonian systems for power grid stability analysis with market dynamics, including constraints and congestion.

Findings

Proves asymptotic stability of the closed-loop system at optimal points.

Extends stability results to include nodal power constraints.

Proposes a dynamic pricing algorithm without demand or supply knowledge.

Abstract

In this paper a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous generators involving voltage dynamics. By applying the primal-dual gradient method to a social welfare optimization, a distributed dynamic pricing algorithm is obtained, which can be naturally formulated in port-Hamiltonian form. By interconnection with the physical model a closed-loop port-Hamiltonian system is obtained, whose properties are exploited to prove asymptotic stability to the set of optimal points. This result is extended to the case that also general nodal power constraints are included into the social welfare problem. Additionally, the case of line congestion and power transmission costs in acyclic networks is covered. Finally, a dynamic pricing algorithm is proposed that does not require knowledge about the power supply and demand.