Transient stability analysis is critical for maintaining the reliability and security of power systems. This paper provides a comprehensive review of research methods for transient stability analysis under large disturbances, detailing the modeling concepts and implementation approaches. The research methods for large disturbance transient stability analysis are categorized into five main types: simulation methods, direct methods, data-driven methods, analytical methods, and other methods. Within the analytical method category, several common analytical strategies are introduced, including the asymptotic expansion method, intrusive approximation method, and other analytical methods. The fundamental principles, characteristics, and recent research advancements of these methods are detailed, with particular attention to their performance in various aspects such as computational efficiency, accuracy, applicability to different system models, and stability region estimation. The advantages and disadvantages of each method are compared, offering insights to support further research into transient stability analysis for hybrid power grids under large disturbances.

Estimation of the region of attraction of the power system using sum of squares (SOS) programming theory is investigated in this paper. Firstly, the Taylor expansion formula is applied to explore the inherent polynomial structure of the swing equation. The single machine projection equation for a multi-machine system is proposed based on the amplitude characteristic of the rotor angle response in decoupled space. Secondly, the theory of SOS programming originating from the polynomial system is derived, and the theory about estimation of the region of attraction for the differential algebraic system is summarized. Thirdly, the method for estimating the region of attraction for the polynomial swing equation based on a V-S two-stage iterative procedure is proposed. Finally, a single machine infinite bus power system, an IEEE 3-machine power system, and an IEEE 4-machine power system are employed to validate the effectiveness and accuracy of the proposed method and analysis.

Modern power systems are high-dimensional, strongly coupled nonlinear systems with complex and diverse dynamic characteristics. The polynomial model of the power system is a key focus in stability research. Therefore, this paper presents a study on the approximate transient stability solution targeting the fault process in power systems. Firstly, based on the inherent sinusoidal coupling characteristics of the power system swing equations, a generalized polynomial matrix description in perturbation form is presented using the Taylor expansion formula. Secondly, considering the staged characteristics of the stability process in power systems, the approximate solutions of the polynomial model during and after the fault are provided using coordinate transformation and regular perturbation techniques. Then, the structural characteristics of the approximate solutions are analyzed, revealing the mathematical basis of the stable motion patterns of the power grid, and a monotonicity rule of the system’s power angle oscillation amplitude is discovered. Finally, the effectiveness of the proposed methods and analyses is further validated by numerical examples of the IEEE 3-machine 9-bus system and IEEE 10-machine 39-bus system.