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arXiv · 0910.5673

Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators

Florian Dorfler·Francesco Bullo
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Abstract

Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a non-uniform Kuramoto model. Here, non-uniform Kuramoto oscillators are characterized by multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. Extending methods from transient stability, synchronization theory, and consensus protocols, we establish sufficient conditions for synchronization of non-uniform Kuramoto oscillators. These conditions reduce to and improve upon previously-available tests for the standard Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying system parameters and initial conditions.

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Florian Dorfler, Francesco Bullo. 2009-10-29. Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators. https://arxiv.org/abs/0910.5673

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