Stabilization of structure-preserving power networks with market dynamics

TL;DR

This paper develops a distributed dynamic pricing algorithm for power networks that maximizes social welfare and ensures stability of both the physical grid and market dynamics using a port-Hamiltonian framework.

Contribution

It introduces a novel primal-dual gradient method applied to a third-order structure-preserving model, linking market and physical dynamics for stability.

Findings

Proves local asymptotic stability of the combined system.

Derives a port-Hamiltonian form for the interconnected system.

Provides a distributed algorithm for market stabilization.

Abstract

This paper studies the problem of maximizing the social welfare while stabilizing both the physical power network as well as the market dynamics. For the physical power grid a third-order structure-preserving model is considered involving both frequency and voltage dynamics. By applying the primal-dual gradient method to the social welfare problem, a distributed dynamic pricing algorithm in port-Hamiltonian form is obtained. After interconnection with the physical system a closed-loop port-Hamiltonian system of differential-algebraic equations is obtained, whose properties are exploited to prove local asymptotic stability of the optimal points.