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UBC Theses and Dissertations

Stabilization and optimization of a power system with sensitivity considerations. Wedman, Leonard Nickolaus


An investigation is made into some aspects of the analysis and design of high order systems. The problems treated are system stabilization, parameter optimization, computation of an optimal controller and parameter sensitivity. The methods developed for solving these problems are applied to a 9ᵗʰ order linearized power system. To stabilize the system, an eigenvalue shift technique is used. Eigensystem sensitivity analysis is applied to determine both the parameter change required and the new eigensystem after the change has been made. A correction method is applied to the new eigensystem for improving accuracy in order that large steps in parameter change may be taken. This method is subsequently used in an optimization procedure for parameter setting to minimize a cost functional of quadratic form. For the computation of an optimal controller, Puri and Gruver's successive approximation method is used in conjunction with a fast recursive method developed for solving each approximation of the Ricatti matrix. The calculation can be initiated by the eigenvalue shifting method to ensure that the system is initially stable. Finally, a time response sensitivity study is made using a method developed for simultaneous sensitivity function determination. This method reduces computation time significantly over the conventional method ⁽⁹⁾ thus enabling the investigation of time response sensitivity to a large number of parameters. The results of the sensitivity study are then applied to the design of a suboptimal controller.

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