A Lyapunov-based approach to power systems stability and control
File(s)
Author(s)
Gao, Jianli
Type
Thesis
Abstract
The thesis investigates a problem largely unsolved for more than half a century, namely constructing a rigorous Lyapunov function for transient stability analysis (TSA) of the multi-machine power systems with transfer conductances (TCs). The model of power systems with TCs is termed as the ``lossy" model. This problem dates from a technical note by Pai and Murthy in 1973, which proposed a rigorous solution for a lossy two-machine case and conjectured that this solution could be generalized to the lossy multi-machine power systems. However, follow-up attempts to construct a rigorous Lyapunov function for the lossy multi-machine power systems have either been incomplete or based on strict assumptions. To address this problem, the thesis proposes an explicit solution focusing on two key aspects. First, an explicit control Lyapunov function (CLF) for the lossy multi-machine power systems is constructed. This is achieved by the design of an auxiliary dynamic state which allows for explicit computation of the ``cross-term" candidate in the CLF. On this basis, an explicit dynamic excitation control law is derived. Therefore, the closed-loop equilibrium is rendered as a locally asymptotically stable equilibrium. Second, an optimization-based approach to calculate the ``critical" level set of the CLF is proposed, whereby the region of attraction (ROA) of the stable equilibrium is evaluated. Therefore, the transient stability property of a post-fault initial state can be directly assessed. Case studies on several benchmark power systems to demonstrate the effectiveness of the proposed solution are presented.
Version
Open Access
Date Issued
2023-12
Date Awarded
2024-06
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Chaudhuri, Balarko
Astolfi, Alessandro
Publisher Department
Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)