Study Of Bifurcation Control For Nonlinear Power Systems

As an emerging new research field, bifurcation control of power systems is very challenging. Bifurcation is a qualitative change due to the variation of parameter, which generally leads to the oscillation and collapse of the voltage of power systems. Consequently, it is an effective way for bifurcation control to investigate the stability of voltage of power systems. It is the main aim of bifurcation control to change dynamic characteristic of different bifurcation phenomenon in power systems; the ideal state is achieved, which may avoid the destructive phenomenon such as oscillation, instability and collapse of voltage. So far, the research results on the bifurcation control have been extensively applied, especially mechanics, electronic, aerospace and biological medicine, etc..The main work of this dissertation is as follows:the relationship between bifurcation and stability of voltage of power system is analyzed; the solution for model reduction of bifurcation point is investigated; the method for calculating the furthest saddle-node is discussed; the controller associated washout-filter feedback control and static var compensator is designed; by virtue of subsystems and center manifold, the stability of voltage is studied; the practical bifurcation theory and way is proposed, which enriches and extends the technology of bifurcation control in power system. The main innovation is as follows:(1) An effective matrix reduced technique is proposed. The key of this algorithm is introducing an auxiliary variable and an auxiliary equation to form an extended Moore-Spence system, and decomposing the high order Jacobi matrix into two low order matrices. The method enables the high dimensionality of Jacobi matrix be reduced and the complexity matrix factorization be simplified.(2) A new method which maximizes the distance to the critical point is proposed. By calculating directly the parameters, the distance to the saddle-node points is maximized, which is uniformed with the sensitivity of loading margin. This method needs to solve linear equations of systems with extended Jacobi matrix. Since the iteration step to compute the left eigenvector is avoided, this method is simpler and quicker than computation sensitivity directly.(3) A nonlinear static var compensator (SVC) controller with washout-filter feedback is designed to improve voltage stability. The advantage and disadvantage of some compensators are compared. In order to increase the stability margin and improve dynamic performances of power systems, the washout-filter feedback for SVC controller is developed. Bifurcation analysis proves that the controller can eliminate the unstable bifurcations associated with voltage oscillation. Moreover, voltage stability is improved significantly by SVC with washout-filter feedback controller.(4) Center manifold is utilized to analyze the voltage stability. The center manifold method enables us to obtain a lower dimensional and topological equivalent system of the large power system in the neighborhood of the bifurcation point. This dissertation extends the center manifold from quadratic to cubic of Taylor power. Furthermore, the conditions of local asymptotical stability in systems with saddle-node and Hopf bifurcations are deduced.(5) Linear feedback, washout-filter and normal form methods are used to design controller to stabilize the voltage stability. For power systems with saddle-node bifurcation, an output tracking controller is designed based on differential-geometry linearization. Moreover, the expected output state of the controlled system is obtained. By virtue of washout-filter, a state feedback controller is designed for the nonlinear systems with Hopf bifurcation. The controller makes the subcritical Hopf bifurcation transform into supercritical one. In the meanwhile, the equilibrium points are remained unchanged. On the basis of normal form theory, the center manifold equations are further reduced to the simplest normal form which is only composed of the 3rd and 5th order terms.By using center manifold, matrix reduction technique and Matlab tool, simulation examples are presented to show the effectiveness of the proposed methods. The relation of bifurcation and voltage stability is studied and summarized. The bifurcation theory is investigated generally.The controller is designed to stabilize the voltage of power systems in this dissertation. The studies have more profound theoretical significances and important engineering application values, which contribute to the development and application of the bifurcation control to the nonlinear power systems.