Synchronization of power systems under stochastic disturbances

Synchronization of power systems under stochastic disturbances

Wang, Zhen (Shandong University)
Xi, Kaihua (Shandong University)
Cheng, Aijie (Shandong University)
Lin, H.X. (TU Delft Mathematical Physics; Universiteit Leiden)
Ran, André C.M. (Vrije Universiteit Amsterdam; North-West University)
van Schuppen, J.H. (TU Delft Mathematical Physics)
Zhang, Chenghui (Shandong University)

2023

The synchronization of power generators is an important condition for the proper functioning of a power system, in which the fluctuations in frequency and the phase angle differences between the generators are sufficiently small when subjected to stochastic disturbances. Serious fluctuations can prompt desynchronization, which may lead to widespread power outages. Here, we model the stochastic disturbance by a Brownian motion process in the linearized system of the non-linear power systems and characterize the fluctuations by the variances of the frequency and the phase angle differences in the invariant probability distribution. We propose a method to calculate the variances of the frequency and the phase angle differences. For the system with uniform disturbance-damping ratio, we derive explicit formulas for the variance matrices of the frequency and the phase angle differences. It is shown that the fluctuation of the frequency at a node depends on the disturbance-damping ratio and the inertia at this node only, and the fluctuations of the phase angle differences in the lines are independent of the inertia. In particular, the synchronization stability is related to the cycle space of the network. We reveal the influences of constructing new lines and increasing capacities of lines on the fluctuations in the phase angle differences in the existing lines. The results are illustrated for the transmission system of Shandong Province of China. For the system with non-uniform disturbance-damping ratio, we further obtain bounds of the variance matrices.

Invariant probability distribution
Variances
Network topology
Graph theory
System stability
Cycle space

http://resolver.tudelft.nl/uuid:31864b30-7708-4aec-8ef8-17814c10b38f

https://doi.org/10.1016/j.automatica.2023.110884

2023-08-21

0005-1098

Automatica, 151

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2023 Zhen Wang, Kaihua Xi, Aijie Cheng, H.X. Lin, André C.M. Ran, J.H. van Schuppen, Chenghui Zhang