Generalized equal-area criterion: a method for on-line transient stability analysis

The wide application of WAMS (Wide Area Measurement System) provided a new thinking for transient stability analysis of power system. Based on real-time measurement information from WAMS, a method to quickly analysis power system transient stability that does not depend on network structure, model and parameters of power system is proposed in this paper. Firstly, the parameters of system are identified online by improved least squares method on basis of that the multi-machine power system is equivalently reduction to one machine infinity bus system. The equilibrium point and stability margin of equivalent system are rapidly computed, and then the stability of system is quickly judged. The simulation results show that the algorithm can accurately judge transient stability of system and has better antidisturbance ability and robustness. The issue of dependence of transient stability analysis on system model and parameter is solved. The adverse influences of data lose and measurement errors in actual measurement of the WAMS on analysis results are avoided effectively. Keywords-power system; wide-area measurement system; parameter identification; energy function; transient stability analysis

This article presents the Lyapunov functions based on the artificial intelligence (AI) method for transient stability assessment and the determination of stability region (SR). First, Lyapunov stability theory and the definition of SR are introduced. Then, the characteristics of neural networks as a general function approximator are employed as the Lyapunov function learner, and the Lyapunov function is constructed combined with stochastic gradient descent (SGD). Then, the falsifier's task is to find the state vectors that violate Lyapunov stability conditions, and the counterexamples would be added to the training set for the function learner to accelerate convergence. After obtaining the Lyapunov function of power system, the estimation of SR boundary can be represented by the maximum level set of Lyapunov function. Finally, the IEEE 9-bus 3-machine system is used as test system to demonstrate the validity and effectiveness of the proposed construction method of Lyapunov functions for power system transient stability analysis.

Renewable energy generation equipment exhibits rapid control characteristics at millisecond or even microsecond timescales, which significantly differs from the electromechanical transient characteristics of traditional synchronous generators. When these two types of sources interact in a power system, they can substantially alter the system's dynamic response, posing serious challenges to power system stability. This paper focuses on transient stability analysis in power systems. Based on the equal-area criterion, the influence mechanism of high-penetration renewable energy integration on power system transient stability is investigated by analyzing the impact of renewable energy penetration levels and spatial distribution on system power characteristics. Finally, simulation tests on the New England 10-machine 39-bus system are conducted to validate the theoretical analysis.

Large-scale AC-DC hybrid power systems have become a basic pattern for power transmission in China. Currently, time-domain simulation is widely used for transient stability analysis, which has the disadvantages of high computational burdens and lack of system stability margin information. An alternative method for transient stability analysis is the direct method, which assesses transient stability from the energy point of view. Direct method requires much less computation efforts. In addition, the stability margin of the system can be obtained. Due to the challenges in system modelling, energy function construction, and determination of critical energy value, it is challenging to apply direct method for transient stability analysis of AC-DC hybrid power systems. This paper is a step in exploring the application of direct method in AC-DC hybrid power systems.

Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances.Important conclusions and decisions are made based on the results of stability studies.The conventional method of analyzing stability is to calculate the transient behaviour of generators due to a given disturbance.Direct methods of stability analysis identify whether or not the system will remain stable once the disturbance is removed by comparing it with a calculated threshold value.Direct methods not only avoid the time consuming solutions required in the conventional method, but also provide a quantitative measure of the degree of system stability.This additional information makes direct methods very attractive when the relative stability of different plans must be compared or when stability limits must be calculated quickly.Direct methods of transient stability analysis of a multi machine power system, using a function describing the system's transient energy, are discussed.By examining the trajectory of the disturbed system, the following fundamental questions are dealt with: the concept of a controlling unstable equilibrium point (U.E.P), the manner in which some generators tend to lose synchronism, and identifying the energy directly responsible for system separation.Resolving this issue will substantially improve transient stability analysis by direct method.

Parallel time domain simulation is one of the reliable and potential methods that might realize the real-time online transient stability analysis of power system. In the paper, a new parallel calculation method, based on waveform relaxation method, is proposed for power system transient stability analysis. In the method, the entire transmission network is first divided into several subsystems by the geographical location; for each subsystem, its neighboring systems are represented as equivalent voltage sources at the boundary buses; the tie line flows are considered as the communication waveform among the subsystems; then, time domain simulation for each subsystem is performed in parallel. The test result of the practical system indicates that the new parallel algorithm completely achieves the on-line real-time or even over-real-time calculation speed and could be applied to the on-line transient stability analysis of practical system.

A new decomposition-aggregation approach is developed to perform transient stability analysis of an N-machine power system with a speed governor. The system decomposition is performed so that every subsystem includes four machines, instead of only two or three machines as considered in other work. The system model is derived and decomposed into (N − 1)/3 11th-order interconnected subsystems considering transfer conductances, nonuniform mechanical damping, electromagnetic damping and speed governor action. Each of these subsystems is decomposed into a free subsystem containing 12 nonlinearities and interconnections. A square aggregation matrix of order (N − 1)/3 is obtained instead of orders N and (N + 1)/2 for the pair-wise and triple-wise decompositions, respectively. The approach is applied to a 10-machine power system and an estimate for the system asymptotic stability domain is determined. System transient stability computations are carried out considering a three-phase short circuit fault, with successful reclosure, near a system bus or a sudden loss of one of the system loads. The approach is used to determine a reclosure time for the faulted line and a reconnection time for the lost load required for the system to regain its prefault (normal) conditions. The approach developed is suitable and can be easily used for stability analysis of power systems (the number of machines may be more than 10). The developed approach can also reduce the conservativeness of the decomposition-aggregation method.

This paper presents an overview about the main advances which occurred in the application of a direct method for transient stability analysis. The text is mainly focused on the potential energy boundary surface (PEBS) and boundary controlling unstable (BCU) method. The author's opinion about future perspectives and research areas of interest are given at the end of the text.

An optimized algorithm for optimal power flow based on deep learning

The transient stability analysis of power systems can be described by differential and algebraic equations, and due to the increased speed with parallel computing techniques, use of the waveform relaxation method to solve these equations has attracted much attention. In order to enhance the calculation speed of the waveform relaxation method, it is of prime importance to reduce the required number of iterations for each time window. To this end, an initialization and preconditioning techniques have been proposed to improve convergence of the iterative procedure. In this paper, in order to enhance convergence, we developed a new global initialization technique that consists of linear analysis and a preconditioning technique. Specifically, global initialization is the result of the repeated application of conventional initialization and preconditioning techniques before each of the nonlinear iterative procedures, and then using linear analysis to determine the interaction between the CPUs. By calculating the initial waveforms more accurately, it is expected that additional speedup can be achieved by reducing the required number of iterations necessary for convergence of the nonlinear analysis.

The Virtual Power Plant (VPP) has been proposed to aggregate Distributed Generations (DGs) to act like a single power plant, thus, also has functions on the frequency and voltage support. The previous models of the VPP are static and focus on the energy trading and management. For the system transient response analysis, a dynamic VPP model must be needed. The paper proposes a reduced-order yet accurate aggregated model to represent VPP transients for the stability analysis of power systems. The goal is to provide a model that is adequate for system studies and can serve to the Transmission System Operator (TSO) to evaluate the impact of VPPs on the overall grid. The proposed model can accommodate the transient response of the most relevant controllers included in the distributed generators that compose the VPP. Using a comparison with a real-time detailed Electro-Magnetic Transients (EMT) models of the VPP confirms the validity of the proposed aggregated model. The case studies based on the IEEE 39-bus system verifies the accuracy of the proposed aggregated model on the system stability analysis.

Transient stability domain estimation of AC/DC systems considering HVDC switching characteristics based on the polynomial Lyapunov function method

This paper proposes a decoupling based direct method to analyze the post-contingency transient stability for a general multi-machine power system. A linear decoupling transformation is used to construct the same number of independent single machine infinite bus (SMIB) power systems as oscillation modes. Each SMIB system carries stability information regarding one oscillation mode of the original system at the equilibrium. Then, the transient energy function method is applied on all decoupled SMIB systems to calculate stability margins, the smallest of which indicates the stability margin of the original system. Case studies on an IEEE 9-bus power system and a WECC 179-bus power system demonstrate the validity of the proposed method.

Hydropower is the largest renewable energy source in China. Transient stability is of great significance to the hydropower system. The extended equal area criterion (EEAC) theory is an effective method to analyze the system transient stability. The accuracy of the transient stability analysis is affected by the generator models. However, there is little research on the EEAC-based transient stability analysis of hydropower system considering different practical hydroelectric generator models. To fill this gap, this paper firstly introduces the characteristic of the second-order and fifth-order model of hydroelectric generators. Subsequently, the transient stability of the hydropower system considering generator models with different orders is analyzed based on EEAC theory and validated by time-domain simulation. Finally, the applicability of the second-order and fifth-order model is compared under different parameters of super-transient/ transient reactance, different fault locations and different super-transient time constants.

Chapter 18 - Power System Stability