Synchronized States of Power Grids and Oscillator Networks by Convex Optimization

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 stable states where the phase difference across an edge does not exceed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>π</a:mi><a:mo>/</a:mo><a:mn>2</a:mn></a:math>. 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. Published by the American Physical Society 2024