Synchronization of Power Systems under Stochastic Disturbances

TL;DR

This paper models stochastic disturbances in power systems using Brownian motion, deriving formulas for fluctuations in frequency and phase differences, and analyzes how network modifications affect synchronization stability.

Contribution

It introduces a method to calculate variances of frequency and phase differences under stochastic disturbances, including explicit formulas for uniform ratios and bounds for non-uniform cases.

Findings

Frequency fluctuation depends on disturbance-damping ratio and inertia.

Phase angle difference fluctuations are independent of inertia.

Network modifications influence phase difference fluctuations and stability.

Abstract

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.