The Dynamic Voltage Stability Based On Hopf Bifurcation Theory In Power System

The intensive research on voltage stability of bulk connected power system plays a significant role in the safe, reliable and efficient operation of the power system. Generally, the feasibility boundar of dynamic voltage stability is constructed by three bifurcation space: Saddle, Hopf and singularity induced bifurcation. Hopf bifurcation is a kind of typical dynamic bifurcation which can server as a bridge between the determinate solutions and the periodic ones. The dynamic voltage stability based on Hopf bifurcation theory is studied in this thesis, the main content was shown as below.The direct method was an effective way to determine the Hopf bifurcation points in power system dynamic voltage stability. However, for an n-dimensional power system a (2n+2)-dimensional augmented system was required in classic direct methods and the computation to solve the augmented system was expensive. A novel approach to calculate the Hopf bifurcation points is presented. In this method, a simple (n+2)-dimensional augmented system is founded which includes the differential-algebraic equations set to describe the dynamic characteristics of the power system and 2 scalar equations. The Hopf bifurcation points can be ascertained by solving the new augmented system.A restarted-refined Arnoldi method is introduced into the dynamic voltage stability analysis to calculate the critical eigenvalues of bulk power system. The refined Ritz vectors are used as the approximations based on the refined projection theory in order to enrich the information of the eigenvectors in the projective subspace. The method can be combined with the continuous arithmetic which was used to trace the equilibrium manifold. The key eigenvalue can be ascertained by the application of restarted-refined Arnoldi method at each equilibrium point of the power system DAE models. The Hopf bifurcation appears if there is a pair of conjugate eigenvalues with zero real-part.A step adaptive-adjustion continuous method with consideration of second-order sensitivity of eigenvalue real-part to load increase is put forward. The forecast step is adjusted adaptive by the application of the first and second sensitivity of eigenvalue real-part to load increase. The biggish step is applied to trace the equilibrium manifold at initial point, the step will be decreased automatically when the operation point is close to the Hopf bifurcation in order to avoid jumping over the Hopf bifurcation.A hybrid method to calculate Hopf bifurcation by the tracing of the key eigenvalue is presented. The equilibrium manifold is traced by the continuous method at beginning. The key eigenvalue is ascertained based on the sensitivity of eigenvalue real-part to load increase. The key eigenvalue is traced when it is closed to the imaginary coordinate-axis until the Hopf bifurcation appeares.The feasibility boundary based on the selected control parameters is depicted by the application of the continuous method presented. The efficiently control parameters are selected according to the sensitivity of load margin to control parameter.To sum up the above arguments, the direct method to determine the Hopf bifurcation points of power system is studied at first. Then the step adaptive-adjustion continuous method and the hybrid method to trace the key eigenvalue are presented respectively which are integrated with eigenvalues-analysis. Lastly, the feasibility boundary based on the selected control parameters is depicted by the application of the continuous method presented and the sensitivity of load margin to control parameter.