A Port-Hamiltonian Approach to Optimal Frequency Regulation in Power Grids

Abstract

This paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. Two price-based controllers are proposed; the first one an internal-model-based controller and the second one based on a continuous gradient method for optimization. Both controllers can be implemented in a fully distributed fashion, with freedom in choosing a controller communication network. As a result, two real-time dynamic pricing models described by port- Hamiltonian systems are obtained. By coupling with the port- Hamiltonian description of the physical network we obtain a closed-loop port-Hamiltonian system, whose properties are ex- ploited to prove asymptotic stability of the set of optimal points. Numerical results show the performance of both controllers in a simple case study.