Bifurcation subsystem method and its applications in analysis and control design for power systems

A bifurcation subsystem method, a novel model reduction method, is able to identify a small order subsystem that (1) experiences, produces, causes, and provides the cures for power system instability problems; (2) captures the critical dynamics (the center manifold) and preserves the dynamic behaviors of the full system; (3) does not utilize a nonlinear or linear transformation that requires significant computation; (4) retains the physically meaningful state variables and parameter structure of the full system due to the fact that no linear or nonlinear transformation is needed; (5) makes the classification of the power system bifurcations possible by noting that states of the generator or load devices in the bifurcation subsystem model; and (6) can be used to design stabilizing control to be applied to the full system bifurcation. The complete theoretical framework for the bifurcation subsystem method is established in the first part of this thesis.; The second part of this thesis is dedicated to the design of robust control based on the bifurcation subsystem method using a methodology that can provide and clearly demonstrate advantages over classical control design methods. The first component of this methodology is the use of the RGA analysis to show that the robust control design produced by this methodology (1) breaks the external system into subsystems that are decoupled from one another and from the bifurcation subsystem and (2) shows the effectiveness of the control in each subsystem. The second component is to use a structured uncertainty that captures the nonlinear change in linear model due to the bifurcation parameter change from the nominal value to the bifurcation value. The third component is the use of the bifurcation subsystem model for design of the controller rather than the full system model. The fourth component is the selection of the performance index, weighting matrix, measurements and control that are based on the bifurcation and the bifurcation subsystem being stabilized.; H_∞ control attempts to find the control that minimize the performance index for the possible uncertainty that occurs at the frequency where the system is most vulnerable. The design methodology preselects and coordinates the frequency uncertainty and subsystem at which the robust controller should have effect. (Abstract shortened by UMI.)...