UBC Theses and Dissertations

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UBC Theses and Dissertations

Dynamic power system modelling and linear optimal stabilization design using a canonical form Habibullah, Bavadeen S.


The linear optimal stabilization of power systems has become a very active area of research in recent years. Implementation of an optimal control scheme usually requires the measurement of all state variables, some of which are not accessible. Dynamic estimators may be used to estimate immeasurable states. But the addition of dynamic estimator makes the overall control scheme more complex and unduly sensitive to disturbances and changes in parameters. There is another problem with the optimal control design, i.e. the choice of the performance index matrices Q and R. In this thesis a fairly accurate synchronous machine model in terms of easily measurable state variables is developed. By neglecting the short lived armature transients, the best dynamic model of a synchronous machine with torque angle, speed, electric output power, terminal voltage or current and field voltage or current as the state variables is derived. The model is used for supplemental excitation control and linear optimal control designs. For the former not only the mechanical mode but also the electrical mode oscillations are considered. For the latter the system equations are transformed into a canonical form and the optimal control thus designed is a function of the weighing matrices Q and R of the cost function. Chapter 2 is devoted to the dynamic modelling of a synchronous machine, Chapter 3 to the supplemental excitation control and Chapter 4 to the development of design techniques for the linear optimal control. Numerical examples are given in Chapters 5 and 6 for both single machine and multi-machine power systems. The nonlinear test results of power systems indicate that transient responses can be greatly improved by the linear optimal control schemes developed in this thesis.

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