In this thesis the eigenstructure (eigenvalues and eigenvectors) assignment technique based algorithm has been developed for the design of controllers for power system applications. The application of the algorithm is demonstrated by designing power system stabilizers (PSSs) that are extensively used to address the small-signal rotor angle stability problems in power systems. In the eigenstructure assignment technique, the critical eigenvalues can be relocated as well as their associated eigenvectors can be modified. This method is superior and yield better dynamical performance compared to the widely used frequency domain design method, in which only the critical eigenvalues are relocated and no attempt is made to modify the eigenvectors. The reviewed published research has demonstrated successful application of the eigenstructure assignment technique in the design of controllers for small control systems. However, the application of this technique in the design of controllers for power systems has not been investigated rigorously. In contrast to a small system, a power system has a very large number state variables compared to the combined number of system inputs and outputs. Therefore, the eigenstructure assignment technique that has been successfully applied in the design of controllers for small systems could not be applied as is in the design of power system controllers. This thesis proposes a novel approach to the application of the eigenstructure assignment technique in the design of power system controllers. In this new approach, a multi-objective nonlinear optimization problem (MONLOP) is formulated by quantifying different design objectives as a function of free parametric vectors. Then the MONLOP is solved for the free parametric vectors using a nonlinear optimization technique. Finally, the solution of the controller parameters is obtained using the solved free parametric vectors. The superiority of the proposed method over the conventional frequency domain method is demonstrated by designing controllers for three different systems and validating the controllers through nonlinear transient simulations. One of the cases includes design of a PSS for the Manitoba Hydro system having about 29,000 states variables, which demonstrates the applicability of the proposed algorithm for a practical real-world system.

In this thesis the eigenstructure (eigenvalues and eigenvectors) assignment technique based algorithm has been developed for the design of controllers for power system applications. The application of the algorithm is demonstrated by designing power system stabilizers (PSSs) that are extensively used to address the small-signal rotor angle stability problems in power systems. In the eigenstructure assignment technique, the critical eigenvalues can be relocated as well as their associated eigenvectors can be modified. This method is superior and yield better dynamical performance compared to the widely used frequency domain design method, in which only the critical eigenvalues are relocated and no attempt is made to modify the eigenvectors. The reviewed published research has demonstrated successful application of the eigenstructure assignment technique in the design of controllers for small control systems. However, the application of this technique in the design of controllers for power systems has not been investigated rigorously. In contrast to a small system, a power system has a very large number state variables compared to the combined number of system inputs and outputs. Therefore, the eigenstructure assignment technique that has been successfully applied in the design of controllers for small systems could not be applied as is in the design of power system controllers. This thesis proposes a novel approach to the application of the eigenstructure assignment technique in the design of power system controllers. In this new approach, a multi-objective nonlinear optimization problem (MONLOP) is formulated by quantifying different design objectives as a function of free parametric vectors. Then the MONLOP is solved for the free parametric vectors using a nonlinear optimization technique. Finally, the solution of the controller parameters is obtained using the solved free parametric vectors. The superiority of the proposed method over the conventional frequency domain method is demonstrated by designing controllers for three different systems and validating the controllers through nonlinear transient simulations. One of the cases includes design of a PSS for the Manitoba Hydro system having about 29,000 states variables, which demonstrates the applicability of the proposed algorithm for a practical real-world system.

Design optimization involving complex structures can be a very resource-intensive task. Convex optimization problems could be solved using gradient-based approaches, whereas non-convex problems require heuristic methods. Over the past few decades, many optimization techniques have been presented in the literature to improve the efficiency of both these approaches. The present work focuses on the non-convex optimization problem involving eigenvalues that arises in structural design optimization. Parametric Model Order Reduction (PMOR) was identified as a potential tool for improving the efficiency of the optimization process. Its suitability was investigated by applying it to different eigenvalue optimization techniques. First, a truss topology optimization study was conducted that reformulated the weight minimization problem with a non-convex lower-bound constraint on the fundamental frequency into the standard convex optimization form of semidefinite programming. Applying PMOR to this, it was found the reduced system was able to converge to the correct final designs, given a reduced basis vector of suitable size was chosen. At the same time, it was shown that preserving the sparse nature of the mass and stiffness matrices was crucial to achieving reduced solution times. In addition, the reformulation to convex optimization form, while possible with the discretized form of vibrational governing equations, is not straightforward with the buckling problem. This is due to the non-linear dependence of the geometric stiffness matrix on the design variables. Hence, we turned to a metaheuristic approach as an alternative and explored the applicability of PMOR in improving its performance. A two-step optimization procedure was developed. In the first step, a set of projection vectors that can be used to project the solutions of the governing higher-order partial differential equations to a lower manifold was assembled. Invariant components of the system matrices that do not depend on the design variables were identified and reduced using the projection vectors. In the second (online) step, the buckling analysis problem was assembled and solved directly in the reduced form. This approach was applied to the design of variable angle tow (VAT) fiber composite structures. Affine matrix decompositions were derived for the linear and geometric stiffness matrices of VAT composites. The resulting optimization framework can rapidly assemble the reduced order matrices related to new designs encountered by the optimizer, perform the physics analysis efficiently in the reduced space, evaluate heuristics related to the objective function, and determine the search direction and convergence based on these evaluations. It was shown that the design space can be traversed efficiently by the developed PMOR-based approach by ensuring a uniform error distribution in objective values throughout the design space. / Doctor of Philosophy / When designing complex structures, designers often have specific performance criteria based on which they improve their preliminary conceptual designs. This could be done by varying some features of the initial designs in a way that these performance criteria are improved. However, it is not always intuitive or efficient to do this manually. Design optimization techniques provide efficient mathematical algorithms that can extract useful information from the governing partial differential equations of the structure and use it to identify the optimal combination of values for a certain set of features, called the design variables, to achieve the optimal performance criteria, referred to as the objective function. As the complexity and size of the structural design problem further increases, typical optimization techniques become slow and resource-intensive. In this work, we propose an optimization framework that uses parametric model order reduction (PMOR) to address this bottleneck. In essence, PMOR filters the large order matrices that arise in these structural analysis problems and provides the optimizer with smaller order matrices that retain the most important features of the original system. This was applied to a truss topology optimization and fiber-composite plate optimization study, both conducted with different types of optimization solvers. It was shown that PMOR resulted in significant efficiency improvements in the design optimization process when paired with an appropriate optimization algorithm.

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.