Power System Voltage Stability Study Based On Bifurcation Theory

Voltage stability has been of great concern to the power industry. It is of great sgnificance for the effective control to prevent voltage collapse to reveal the mechanism of voltage instability phenomena to ensure the safe operation of the system. The current academe has not yet formed a complete theoretical system on the mechanism of voltage instability. As a powerful tool for the study of nonlinear dynamic system stability mechanism, bifurcation theory has been applied to the study of power system voltage stability. This paper takes bifurcation theory as a tool to study voltage stability mechanism and its control.Multi-parameter bifurcation in power system is studied in this paper based on the single parameter bifurcations. The existence of several kinds of more complicated bifurcations are verified, which are called codimension-2 bifurcation, including Bogdanov-Takens bifurcation, Generalized Hopf bifurcation and Zero-Hopf bifurcation. The voltage instability modes of them are also studied. Finally, the paper points out that the small disturbance voltage stability region should be considered the complement of the union of saddle node bifurcation, Hopf bifurcation, singularity induced bifurcation, limit induced bifurcation, homoclinic bifurcation, Bogdanov-Takens bifurcation, Generalized Hopf bifurcation and Zero-Hopf bifurcation. The results of these studies contribute to a more comprehensive study and analysis of the mechanism of voltage instability.The system load margin is characterized by the sub-critical Hopf bifurcation values. It is of great significance to improve the system load margin by delaying or even eliminating Hopf bifurcation. The optimization model of Hopf bifurcation control of voltage stability is established according to a new Hopf bifurcation of voltage stability indicator in this paper. The model considers the more realistic constraints, including the system damping limits, generator reactive power out limits, excitation voltage limits and node voltage limits. A two-stage kindred-protected genetic algorithm is presented by this paper to solve the optimization model effectively. The algorithm takes advantage of the ergodicity of chaotic variables to generate the initial population, and it completes the choice inside the kindred during the first stage so that each kindred member is a fine individual. The second stage of the algorithm completes the choice between the different kindreds, which is a kind of 'excellent - excellent' choice, making the algorithm can be much faster convergence to the global opimal solution. Simulation results of the test function, the WSCC 9-bus system and New England 39-bus system proved the effectiveness and feasibility of the model and algorithm.