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.

In recent years, the widespread adoption of phase-locked loop type grid-connected converters has presented new challenges for transient stability and small-signal stability analysis of power systems. Therefore, it is crucial to develop effective methods for analyzing the stability of converters-interfaced power systems. In this paper, a generalized swing equation model of a single converter connected to an infinite bus is derived. Then, approximate analytical solutions for the model are obtained. The accuracy of the analytical solutions is verified through simulation analysis. Based on the analytical solution, a parameter stability analysis is performed to gain further insights on both transient and small-signal stability. Finally, the proposed results are verified using several examples, demonstrating the accuracy and effectiveness of the suggested methods.

Obtaining the solution of Kuramoto oscillator model is an effective way to understand the mechanism behind the dynamical behaviors it represents. However, it is not an easy work to get, even the approximation solution for the second order Kuramoto oscillator network because of its complex coupling interaction and strong nonlinearity. Hence, this paper first establishes a new polynomial mathematical model for the second order Kuramoto oscillator network, which is partly decoupled in a polynomial fashion. Then, a quadratic harmonic balance method (HBM) is developed to get the approximate solution for quadratic differential algebraic equation (QDAE) system. An equivalent quadratic technique is introduced to convert the polynomial Kuramoto oscillator model into a QDAE system aiming to obtain its harmonic solution. Finally, the suggested harmonic solution is utilized to explain the morphological characteristics of the stable motion of oscillators, and the relative motions for the oscillators in Kuramoto network is concluded by a set of nonlinear state output equations. It is also found that the distance between the maximum phase angle and the controlling unstable equilibrium point (UEP) can be used as a stability margin for the oscillator network. A single-machine infinite bus (SMIB) power system, an IEEE 3-machine 9-bus power system and an IEEE 10-machine 39-bus power system are employed as different dimension second order Kuramoto oscillator network cases to demonstrate the validation and accuracy of the proposed method and analysis.

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.

The static-voltage-stability region (SVSR) is an effective tool for monitoring the safe operation of grid voltage. Rapidly obtaining the static-voltage-stability-region boundary (SVSRB) of a power system is crucial for the application of SVSR technology. First, this paper reveals the mechanisms underlying the failure scenarios that may occur with conventional boundary tracking methods. Then, an improved method incorporating curve extrapolation and correction conversion strategies is proposed, which enhances the efficiency of constructing the SVSRB. Furthermore, the analytical expression of the SVSRB is derived from the intermediate information obtained during the predictor stage. Finally, simulation examples based on a simple power system, the IEEE 3-machine, 9-bus power system and IEEE 300-bus power system were developed to verify the accuracy and efficiency of the proposed method.