On Stability Analysis Methods of Power Electronics Integrated Power Grids

Abstract

The use of power electronics in power grids has become crucial in the transition toward a sustainable and resilient energy future due to their provision of efficient and flexible power flow control. However, power grids with substantial power electronics integration pose critical stability challenges, including small-signal instability and large-signal instability. First of all, the negative impedance characteristic of constant power loads (CPLs) may cause the Jacobian matrix of the system to exhibit a positive real part in the characteristic roots, leading to small-signal instability. Furthermore, large disturbances such as fluctuations of load power and short circuit faults can lead to transient voltage instability or synchronization instability. The challenge in addressing these issues lies in the difficulty of efficiently and accurately assessing system stability and designing a safe power electronics integrated power grids, especially when the system is of high order, with complex operation, and having significant uncertainties due to the use of renewable energy and load fluctuations. This thesis focuses on exploring effective stability analysis methods to overcome these challenges and offers guidance for designing safely operating power grids.

First, to address the issues that the order of a DC microgrid is high and its stability analysis is complex, we propose a small-signal stability analysis method based on singular perturbation theory and Karush-Kuhn-Tucker (KKT) matrices. The proposed method applies singular perturbation theory to decompose the original system into a boundary-layer subsystem and a reduced-order subsystem. It is found that the Jacobian matrix of the boundary-layer subsystem has the same eigenvalues as the KKT matrix's. Based on the sufficient condition that the stability of the reduced-order subsystem is equivalent to the Hurwitz stability of both the boundary-layer and reduced-order Jacobian matrices, an analytical stability criterion for the equilibrium is derived. This method effectively establishes the analytical stability criteria for equilibrium points in closed-loop DC microgrid systems, accounting for controller dynamics, thereby providing a reliable theoretical foundation for the stable design of controller parameters. Moreover, the proposed method reduces computational complexity of small-signal stability analysis for large-scale DC microgrids.

Then, to address the issue that existing large-signal stability analysis methods incur high computational cost and are not applicable to large-scale power grids, we propose a large-signal stability analysis framework based on Brayton-Moser’s mixed potential function and comparison principle. Within this framework, we first introduce an improved algorithm for the closest unstable equilibrium point (UEP) method for estimation of the region of attraction (ROA) of the stable equilibrium. This algorithm constructs a decoupled auxiliary energy function based on the comparison principle, allowing the critical energy values to be calculated from known unstable equilibrium points of the corresponding decoupled subsystems. This approach avoids the need to find all solutions of the power flow equations, thereby reducing the computational cost of the ROA estimation. Furthermore, to address the issues of low critical energy values and high conservativeness in ROA estimation associated with the previous algorithm, we further propose an ROA estimation method based on a quadratic auxiliary energy function. By integrating the comparison principle and optimizing the critical energy value through a quadratic function, this method reduces the computational load while also decreasing the conservativeness of ROA estimation.

Finally, we investigate the stability of AC power grids with power electronics equipment based on impedance-based and data-driven methods. First of all, to address the issue that voltage source rectifiers (VSRs) are prone to instability when connected to a weak grid, we propose a resistance-emulating control (REC) for VSRs which eliminates phase-locked loops (PLLs) and improves the stability margin of weak-grid-connected VSRs. The small-signal $dq$-admittance model of the grid-connected VSR with REC is built and the admittance characteristics of the grid-connected VSR with REC and conventional dual-loop control (DCC) are analyzed and compared. The influence of short circuit ratio (SCR), voltage-loop bandwidth, and the output power on the stability of the VSR with REC and DCC is analyzed based on the generalized Nyquist criterion. The comparison results indicate that the VSR with REC has better adaptability to a weak grid and can achieve a higher bandwidth for the voltage loop. Besides, it is found that the DCC controlled VSR is more suitable for light-load operation than the REC controlled VSR. Secondly, to address the problems that conventional transient stability methods (including Lyapunov energy function method) are over-conservative and bifurcation-based manifold analysis methods are computationally intensive, we propose an online transient stability prediction framework for inverter-based power grids based on a data-driven method. The proposed framework offers a machine learning model for a fast and accurate transient stability prediction in early post-fault stages. This overcomes the limitations of conventional transient stability assessment methods with high conservativeness and computations.

Date of Award	28 Nov 2025
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Hua HAN (External Supervisor) & Chi Kong TSE (Supervisor)