Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany.
Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
Chaos. 2019 Dec;29(12):123119. doi: 10.1063/1.5122739.
Networks of phase oscillators are studied in various contexts, in particular, in the modeling of the electric power grid. A functional grid corresponds to a stable steady state such that any bifurcation can have catastrophic consequences up to a blackout. Also, the existence of multiple steady states is undesirable as it can lead to transitions or circulatory flows. Despite the high practical importance there is still no general theory of the existence and uniqueness of steady states in such systems. Analytic results are mostly limited to grids without Ohmic losses. 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 and explicitly compute them for tree and ring networks. We investigate different mechanisms leading to multistability and discuss the impact of Ohmic losses on the existence of solutions.
在不同的背景下研究了相振荡器网络，特别是在电力网格建模中。功能网格对应于稳定的稳态，使得任何分岔都可能产生灾难性的后果，直至停电。此外，多个稳态的存在是不理想的，因为它可能导致过渡或循环流动。尽管具有很高的实际重要性，但在这种系统中仍然没有关于稳态存在性和唯一性的一般理论。分析结果主要限于没有欧姆损耗的电网。在本文中，我们引入了一种方法来系统地构造存在欧姆损耗时的实功率潮流方程的解，并为树状和环状网络显式地计算它们。我们研究了导致多稳定性的不同机制，并讨论了欧姆损耗对解的存在的影响。
