Study On Voltage Stability Of Power Systems Based On Bifurcation Theory

With the implementation of the stratagem of "power transmission from west China to east China, interchange from North China to South China, Nation-wide interconnection" and power market, the complexity of the power network structure and operation have been enhanced increasingly, the uncertainty of operating conditions is increased greatly, the operation point of power system is pushed closer and closer to its stability limits, the voltage collapse occurs more easily than ever. Voltage instability is widely recognized as one of significant reasons treating the security and stability operation of power system. Therefore, Great concerns over voltage stability have been growing.Power system is a large, complicated nonlinear dynamic system. It has been proved that bifurcation theory is one of effective tools for studying the structure stability of nonlinear dynamic system. Bifurcation theory has been widely applied in many engineering fields, and a great of results have been obtained, however it has in the initial stage for the application of voltage stability in power system. Based on the bifurcation theory and numerical methods, several critical topics on the voltage stability of power system are studied in the thesis, and some significative results are obtained. Main research works and contributions are summarized as follows.1,Based on the differential algebraic equations(DAEs) of power system, an effective algorithm is presented for locating and identifying the singularity induced bifurcation (SIB) points by using the SIB theorem, the method indicates that when the singularity point under a given parameter value has been searched and the corresponding mismatch is calculated, in that case the singularity induced bifurcation point under another parameter value can be accurately traced through only changing the input powers at the generator buses but the input powers at load buses keep unchanging. Due to the combination of the Newton-Raphson(NR) method and the Newton-Raphson-Seydel(NRS) method, there is no the initial value problem, and the ill phenomena of the Jacobian matrix in the vicinity of a bifurcation point can be avoided.2,Based on the bifurcation theory, a systematic and adaptive method for tracing the static bifurcation points of the DAEs is presented in the analysis of power system voltage stability. The two main types of static bifurcations, a common saddle node bifurcation(SNB) and a new type of bifurcation --limit induced bifurcation(LIB), are studied simultaneously and all kinds of device limits are considered. Compared with the existing static analysis methods of voltage stability, the proposed method takes account into the dynamics of devices by using the DAEs model in voltage stability, and overcomes the unreasonable assumptions for practical power system such as equilibrium bus, pv bus and so on. The step size control considers the curvature of equilibrium manifold, the SNB point is traced in terms of the adaptive stratagem of the step size control. The LIB point is traced in terms of the location of device limit points, an additional calculation is unnecessary. The recognition criterion of LIB in the practical engineering application is given.3,The reactive power limit of a generator is thought as constrain, based on the bifurcation theory and numerical methods, by the definitions of a series of correlative concepts such as maximum loading point, bifurcation subtype, transition of bifurcation subtype, and subsurface and so on, the voltage stability region of power system is analyzed, a new methodology for investigating the smoothness of the transfer limit surface of voltage stability is presented by characterizing the state of a generator using a maximum loading point, and the accelerate stratagem of algorithm convergence is also discussed. The transfer limit surface is smooth without constraint, with single constraint and two constrains without a duplicate-switching. The transfer limit surface is nonsmooth when two constraints with a duplicate-switching or more constrains are considered. The smoothness of the transfer limit surface is very useful for calculations of preventive controls and stability indices related to voltage stability.4,Based on the bifurcation theory, on the bases of the analysis of On-load tap changer on the effect of voltage stability, a new method for improving voltage stability and preventing voltage instability is presented by optimizing the modification of the On-load tap changers, the proposed method increase also the loadability. The study has shown that the modification effect of the proposed method is closely related to the model of load. In high voltage circumstances, the voltage stability can be improved by adjusting taps for the voltage-sensitive load. The loadability increase obtained using tap optimization is relatively small in this case. Thus, it appears that tap modification by itself should be used only for minor security limit violations. For more serious security problem, tap adjustment could be combined with other preventive control measurements such as capacitor Switching, generation rescheduling, and so on.To sum up, based on the bifurcation theory, a series of topics on the voltage stability of power system such as tracing of the equilibrium manifold, locating and identifying of bifurcation points, smoothness of transfer limit surface of voltage stability, optimizing modification of On-load tap changers, and so on are studied thoroughly, and many results are obtained.At the end of this dissertation, a systematical summary and future study are given...