Power-grid modelling via gradual improvement of parameters

Bálint Hartmann, Géza Ódor, Kristóf Benedek, István Papp
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Abstract

The dynamics of electric power systems are widely studied through the phase synchronization of oscillators, typically with the use of the Kuramoto equation. While there are numerous well-known order parameters to characterize these dynamics, shortcoming of these metrics are also recognized. To capture all transitions from phase disordered states over phase locking to fully synchronized systems, new metrics were proposed and demonstrated on homogeneous models. In this paper we aim to address a gap in the literature, namely, to examine how gradual improvement of power grid models affect the goodness of certain metrics. To study how the details of models are perceived by the different metrics, 12 variations of a power grid model were created, introducing varying level of heterogeneity through the coupling strength, the nodal powers and the moment of inertia. The grid models were compared using a second-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the values of the phase, the frequency and the universal order parameters. Finally, frequency results of the models were compared to grid measurements. We found that the universal order parameter was able to capture more details of the grid models, especially in cases of decreasing moment of inertia. The most heterogeneous models showed very low synchronization and thus suggest a limitation of the second-order Kuramoto equation. Finally, we show local frequency results related to the multi-peaks of static models, which implies that spatial heterogeneity can also induce such multi-peak behavior.
通过逐步改进参数建立电网模型
人们通过振荡器的相位同步来广泛研究电力系统的动力学,通常使用 Kuramotoequation。虽然有许多众所周知的阶次参数来描述这些动力学特性,但人们也认识到了这些指标的不足之处。为了捕捉从相位无序状态到相位锁定再到完全同步系统的所有转变,人们提出了新的度量方法,并在同质模型上进行了演示。本文旨在填补文献空白,即研究电网模型的逐步完善如何影响某些指标的优劣。为了研究不同指标如何感知模型的细节,我们创建了 12 种电网模型,通过耦合强度、节点功率和惯性矩引入不同程度的异质性。使用二阶仓本方程和自适应 Runge-Kutta 求解器对电网模型进行比较,测量相位、频率和普阶参数值。最后,将模型的频率结果与网格测量结果进行比较。我们发现,普遍阶参数能够捕捉网格模型的更多细节,尤其是在惯性矩减小的情况下。最不均匀的模型显示出非常低的同步性,因此建议对二阶仓本方程进行限制。最后,我们展示了与静态模型多峰值相关的局部频率结果,这意味着空间异质性也能诱发这种多峰值行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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