Multistability in lossy power grids and oscillator networks
arXiv:1908.10054 · doi:10.1063/1.5122739
Abstract
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows throughout the grid. Whether such a steady state exists for a given network is of eminent practical importance. The loss of a steady state typically leads to power outages up to a complete blackout. But also the existence of multiple steady states is undesirable, as it can lead to sudden transitions, circulating flows and eventually also to power outages. Steady states are typically calculated numerically, but this approach gives only limited insight into the existence and (non-)uniqueness of steady states. Analytic results are available only for special network configuration, in particular for grids with negligible Ohmic losses or radial networks without any loops. In this article, we introduce a method to systematically construct the solutions of the real power load-flow equations in the presence of Ohmic losses. We calculate the steady states explicitly for elementary networks demonstrating different mechanisms leading to multistability. Our results also apply to models of coupled oscillators which are widely used in theoretical physics and mathematical biology.
arXiv commentThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Chaos 29, 123119 (2019) and may be found at https://doi.org/10.1063/1.5122739
References in corpus (22)
- Synchronization in complex networks
- Synchronization in Complex Oscillator Networks and Smart Grids
- Solvable model for chimera states of coupled oscillators
- Analysis of a power grid using the Kuramoto-like model
- On the existence and linear approximation of the power flow solution in power distribution networks
- Comparative analysis of existing models for power-grid synchronization
- Linear Optimal Power Flow Using Cycle Flows
- Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis
- A Dual Method for Computing Power Transfer Distribution Factors
- Cycle flows and multistabilty in oscillatory networks: an overview
- Transdisciplinary electric power grid science
- Nonlocal failures in complex supply networks by single link additions
- There are no non-zero Stable Fixed Points for dense networks in the homogeneous Kuramoto model
- Dual theory of transmission line outages
- Kuramoto dynamics in Hamiltonian systems
- Multistability of Phase-Locking and Topological Winding Numbers in Locally Coupled Kuramoto Models on Single-Loop Networks
- A Theory of Solvability for Lossless Power Flow Equations -- Part I: Fixed-Point Power Flow
- A Theory of Solvability for Lossless Power Flow Equations -- Part II: Conditions for Radial Networks
- Multistability of Phase-Locking in Equal-Frequency Kuramoto Models on Planar Graphs
- Topologically Protected Loop Flows in High Voltage AC Power Grids
- Synchronization of Coupled Oscillators in a Local One-Dimensional Kuramoto Model
- Solvability of Power Flow Equations Through Existence and Uniqueness of Complex Fixed Point