Study Of Several Problems In Power System Transient Stability Analysis

Power systems depend heavily on results of transient stability analysis in planning, operating and recovering in case of the contingencies. The exactness of analysis is most important for dynamic security assessment. The thesis analyzes some important methods in power system transient stability analysis, and proposes a new criterion for transient instability. The effectiveness of the new criterion is studied. The main results are listed below.(1) Restrictions on the power system by theory of the PEBS method are proposed. The PEBS theory is based on the stability boundary theorem. The one-parameter-transversality conditions for two system families, as well as the converging condition for a perturbed system are theoretical requisitions in theory of the PEBS method. PEBS theory demonstrates the reliability of this method when these conditions are satisfied. The limitation of this theory is revealed by the fact that these conditions require the power system containing an infinite bus, neglecting transfer conductance and being complete stable.(2) Restriction on the power system by BCU theory is demonstrated. The BCU theory demands a system family satisfying the one-parameter-transversality condition. This condition requires that, for a not-complete stable power system, the corresponding general gradient system must be not complete stable.(3) A necessary and sufficient condition for the complete stability of the general gradient system is proved, i.e. the general gradient system has both the sink point and the source point. This condition is only relevant to the type of the equilibrium points and is easy to be verified.(4) The integration path of the transient energy function including non-integrable term is clarified. The initial point of the integration path in literatures is modified. Prevailing approximation methods are evaluated. The linear path method take a virtual linear path connecting endpoints of the true path as the integration path, while trapezoidal approximation method integrates along the fault-on trajectory, which is conceptually different from the correct path. We cannot expect the latter method to improve the accuracy in getting the transient energy value. These two methods get the energy values that are neither sufficient nor necessary for stability analysis. This reduces the reliability of the methods employing on the energy functions. Based on the correct integration path, the positive semi-definiteness of the energy function in the stability region is demonstrated, and the conjecture of the positive semi-definiteness of the individual machine transient energy function is proved true.(5) An energy expression for the transient energy of the equivalent non-autonomous one-machine-infinite-bus system in theory of the EEAC method is proposed. It is proved that, the dynamical saddle point (DSP) corresponds to the potential energy maximal point where the kinetic energy is not zero. A path-dependant term is present in this energy expression. The integration path for this term is identical to the integration path of the transient energy constructed by first integral. In this sense, EEAC method has inner relationship with other methods based on the transient energy function, such as the PEBS method, BCU method, individual machine energy function method, and the Hybrid method.(6) The DSP-Vp criterion and the successive slipping criterion of transient instability are put forth, which improve the reliability of the DSP criterion taken by the EEAC method. The effectiveness of the new criterion on a point unit with one degree of freedom is verified. Through the analysis on the point unit, it is not necessary to determine the critical group, which is essential in analyzing the power system by the EEAC method.(7) The length of the trajectory is proposed as a function for the employment of the sensitivity analysis. Its sensitivity to the fault-clearing time is higher than the energy function or the distance function. This allows less integrating time while the accuracy is maintained.(8) The ISD phenomenon is discussed in view of the stability region. When the dampingcoefficient is small enough, the boundary of the stability region of the post-fault system becomes less flat, the gap can appear in the stability region of some power systems. Such a gap is not a hole in the stability region, but it is not clear whether a gap can goes through the stability region. If the fault-on trajectory goes across the gap, then ISD will appear.2...