Trajectory Stability And Time-varying Impact Analysis

The direct methods which are based on the Lyapunov stability theory are the major branch of transient stability analysis in power systems. These methods depend on the mathematical models of the post-fault power systems and assess the transient stability of power systems by analyzing the stable equilibrium point and its stability domain. However, in the engineering application of direct methods, it is very difficult to reconstruct the model of disturbed systems and calculate its initial value. Even if the difficulty of model reconstruction is overcome, the algorithms of direct methods are not efficient and accurate in complicated models with high dimension. It is implied that there exist some limitations in direct methods when they are used to analyze the stability of large complex systems without enough model information.With the development of computer technology and simulation algorithm, only the measured trajectories of disturbed systems, which can exhibit system dynamics, are able to be acquired precisely. Therefore, a new type of hybrid methods for transient stability assessment, represented by EEAC (extended equal area criterion) method, was proposed, which combine system trajectories with the mechanism of transient instability. Via the mechanism analysis of instability, they extract the geometric characteristics from system trajectories, which can reflect the stability and instability of power systems. For example, in EEAC, based on the classical Newton's laws of motion, the stability of one machine system is interpreted as the full conversion between the kinetic energy and potential energy of the single rigid body. And, the geometric characteristics of trajectories, i.e. dynamic saddle point (DSP) and far end point (FEP), which can be defined as the instability and stability criterion, are proposed. It should be said that because of the difficulties in obtaining precise mathematical models and the engineering implementation of algorithms in direct methods, EEAC method had to be proposed. Its new idea, which is based on trajectory characteristics and different from the traditional Lyapunov stability framework, is provided for the transient stability analysis of power systems.From trajectories of one machine system, EEAC method extracts the trajectory characteristic points, i.e. DSP and FEP, which can be correctly applied to the time-invariant OMIB (One Machine Infinite Bus) system. However, for the transient stability analysis of multi-machine systems, the analyzed object of EEAC method is the time-varying equivalent OMIB system, obtained by projection mapping. Its trajectory is distorted by time-variation and much more complicated than the one of time-invariant OMIB system. Hence, there are some theory and technique problems in the application of trajectory characteristic criterions of DSP and FEP to equivalent OMIB systems.It is necessary to study the trajectory distortion caused by time-varying factor and its effects on EEAC method, in order to improve its effectiveness and reliability for equivalent OMIB systems. The main works are summarized as follows:1) Theoretical foundation of the instability criterion of DSP for equivalent OMIB systems.A. Based on the trajectory of a general motion system, the concepts of trajectory stability and swing steadiness etc are proposed. The relationships among the DSP, swing steadiness and trajectory stability are thoroughly studied and the sufficient condition that the instability criterion of DSP can be used in general motion systems is presented. Thus, a system subset, in which trajectory instability can be determined by DSP, is defined.B. Through the simulation analysis and mechanism interpretation, the above sufficient condition is verified in equivalent OMIB systems. Thus, a theoretical foundation of DSP for instability criterion in EEAC method is developed.2) The evaluation of the time-varying factor and the improvements of instability criterion of DSP and stability assessment point for reducing the impact of time-variation.A. To increase the precision of the conventional indicators, a quantification index and a simplified switch index for evaluating the degree of the time-varying factor at one trajectory point are proposed respectively. And, the computation equations of the above indices based on the simulated trajectory are also presented.B. Because the time-varying factor reduces the accuracy of the instability criterion of DSP, the invalid DSP that can not be instability criterion should be identified. To distinguish invalid DSP, two trajectory characteristics of DSP, i.e. the time-varying factor and the kinetic energy accumulation, are investigated and the corresponding indices of DSP are proposed. Based on the indices, two identification methods for invalid DSP are proposed. Their reliable identification of invalid DSPs contributes to the higher accuracy of instability analysis in time-varying equivalent OMIB systems by DSP.C. The time-varying factor reduces the accuracy of the stability assessment at FEP and consequently affects the sensitivity-based search for transient stability limits. The concept of invalid FEP is proposed, which is due to strong time-varying factor and not suitable for assessment point any more. With this knowledge, the improvement principle of assessment points of stable swings and the corresponding method are proposed for improving the accuracy of the stability assessment in time-varying equivalent OMIB systems.3) An improved iterative method for assessment of multi-swing stability limitIt is observed that the complicated variation of stability margin of OMIB-swing versus parameter, such as the non-monotonicity of margin curve and the isolated stability domain, might reduce the efficiency and accuracy of the conventional iterative method in assessing multi-swing stability limits. Therefore, the above effects on the two major stages of the conventional method are thoroughly studied and an improved sensitivity-based iterative method is proposed for searching first- or multi-swing transient stability limit with higher efficiency and accuracy.