Problems in Selective Modal Analysis and Control
Saad, Mohamed Shawky
Abed, Eyad H
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In this dissertation, we develop monitoring and control systems for improving the performance of systems that are required to operate at the edge of their stability envelopes. The concept of modal participation factors, which is an essential construct in the theory of Selective Modal Analysis, is used extensively in this work. The basic definition of modal participation factors that was originally given for unforced linear time-invariant systems is revisited, and related notions of output participation factors and input-to-output participation factors are introduced, studied and applied to models of electrical power systems. A signal-based approach for real-time detection of impending instability in nonlinear systems is considered. The main idea pursued involves using a small additive white Gaussian noise as a probe signal and monitoring the spectral density of one or more measured states or outputs for certain signatures of impending instability. Input-to-state and input-to-output participation factors are used as tools to aid in selection of locations for probe inputs and states or outputs to be monitored, respectively. Since these participation factors are model-based, the work presented combines signal-based and model-based ideas toward achieving a robust methodology for instability monitoring. Case studies from power systems are used to illustrate the developed monitoring system, one of which involves the WSCC 3-generator, 9-bus network. Feedback algorithms are developed for assigning modal participation factors in general linear time-invariant systems using eigenvector assignment-based techniques. The goal is to reduce the interaction between a selected group of states (the high-value group) and an undesirable mode (for example a critical mode, i.e., one corresponding to an eigenvalue or pair of eigenvalues approaching the imaginary axis in the complex plane). In particular, we address two cases, one in which the mode of interest corresponds to a real eigenvalue approaching zero, and the other in which the mode involves a complex conjugate pair of eigenvalues that may be approaching the imaginary axis. A novel procedure for computing the desired closed-loop right eigenvector(s) associated with the critical mode (based on given constraints on the desired closed-loop participation factors) is presented. An example from power systems is presented to demonstrate the effectiveness of the controller. The example used is the WSCC 3-generator, 9-bus network.