Synchronized States of Power Grids and Oscillator Networks by Convex Optimization

Abstract

Synchronization is essential for the operation of ac power systems: all generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of synchronization is of utmost practical importance. In this article, we propose a novel approach to computing and analyzing the stable stationary states of a power grid or a network of Kuramoto oscillators in terms of a convex optimization problem. This approach allows us to systematically compute all stable states where the phase difference across an edge does not exceed π/2. Furthermore, the optimization formulation allows us to rigorously establish certain properties of synchronized states and to bound the error in the widely used linear power flow approximation.