Lyapunov functions for power systems with transfer conductances

This thesis is mainly concerned with constructing Lyapunov functions for power systems with transfer conductances. The first two chapters of this thesis are devoted to the problem statement and a survey of the existing solutions. The remainder of the thesis is organized in two parts. The first part develops a theory which may be used to construct Lyapunov functions for general interconnected systems. This theory is an extension of the existing dissipative systems theory for interconnected systems. The extension is to "localize" the known results so that the dissipative systems theory for interconnected systems is applicable to the power system transient stability problem. The second part gives various procedures to construct Lyapunov functions for power systems using the theory developed in the first part. The procedures for constructing Lyapunov functions for power systems with transfer conductances are numerical in nature. (However we have analytical results for some very simple cases). Convergence of these numerical procedures is guaranteed for uniformly damped power systems. In the case of nonuniform damping, although we cannot guarantee convergence, the procedures have been observed to give good results in all the examples that have been tried.