Synchronized States of Power Grids and Oscillator Networks by Convex Optimization

Hartmann, Carsten; Witthaut, Dirk; Gross, David; Böttcher, Philipp C.

doi:10.1103/PRXEnergy.3.043004

Journal Article

FZJ-2024-07305

Synchronized States of Power Grids and Oscillator Networks by Convex Optimization

Hartmann, C.FZJ* ; Böttcher, P. C.FZJ* ; Gross, D. ; Witthaut, D. (Corresponding author)FZJ*

2024
American Physical Society College Park, MD

PRX energy 3(4), 043004 (2024) [10.1103/PRXEnergy.3.043004]

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Please use a persistent id in citations: doi:10.1103/PRXEnergy.3.043004 doi:10.34734/FZJ-2024-07305

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.

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