This dissertation proposes a power management and control strategy for islanded microgrids, which consist of multiple electronically-interfaced distributed energy resource (DER) units, to achieve a prescribed load sharing scheme. This strategy provides i) a power management system to specify voltage set points based on a classical power flow analysis; 2) DER local controllers, designed based on a robust, decentralized, servomechanism approach, to track the set points; and 3) a frequency control and synchronization scheme. This strategy is then generalized to incorporate both power-controlled and voltage-controlled DER units. Since the voltage-controlled DER units do not use inner current control loops, they are vulnerable to overcurrent/overload transients subsequent to system severe disturbances, e.g., faults and overloading conditions. To prevent DER unit trip-out or damage under these conditions, an overcurrent/overload protection scheme is proposed that detects microgrid abnormal conditions, modifies the terminal voltage of the corresponding VSC to limit DER unit output current/power within the permissible range, and restores voltage controllers subsequently. Under certain circumstances, e.g., microgrid islanding and communication failure, there is a need to switch from an active to a latent microgrid controller. To minimize the resultant transients, control transition should be performed smoothly. For the aforementioned two circumstances, two smooth control transition techniques, based on 1) an observer and 2) an auxiliary tracking controller, are proposed to achieve a smooth control transition. A typical microgrid system that adopts the proposed strategy is investigated. The microgrid dynamics are investigated based on eigenvalue sensitivity and robust analysis studies to evaluate the performance of the closed-loop linearized microgrid. Extensive case studies, based on time-domain simulations in the PSCAD/EMTDC platform, are performed to evaluate performance of the proposed controllers when the microgrid is subject to various disturbances, e.g., load change, DER abrupt outage, configuration change, faults, and overloading conditions. Real-time hardware-in-the-loop case studies, using an RTDS system and NI-cRIO industrial controllers, are also conducted to demonstrate ease of hardware implementation, validate controller performance, and demonstrate its insensitivity to hardware implementation issues, e.g., noise, PWM nonidealities, A/D and D/A conversion errors and delays.

We introduce methods for dealing with linear programming (LP) problems with uncertain data, using the notion of weighted analytic centers. Our methods are based on high interaction with the decision maker (DM) and try to find solutions which satisfy most of his/her important criteria/goals. Starting with the drawbacks of different methods for dealing with uncertainty in LP, we explain how our methods improve most of them. We prove that, besides many practical advantages, our approach is theoretically as strong as robust optimization. Interactive cutting-plane algorithms are developed for concave and quasi-concave utility functions. We present some probabilistic bounds for feasibility and evaluate our approach by means of computational experiments.

This thesis provides a novel approach to the problem of state estimation for discrete-time nonlinear systems in the presence of large model uncertainties. Though classical nonlinear Kalman filters such as the extended Kalman filter (EKF) can handle uncertainties by increasing the value of noise covariances, this is only applicable to systems with small uncertainties. To this end, a discretetime robust extended Kalman filter (REKF) is formulated and applied to examples from the fields of aerospace engineering and signal processing with an emphasis on attitude estimation for small unmanned aerial vehicles (UAVs) and image processing under the influence of atmospheric turbulence. The robust filter is an approximate set-valued state estimator where the Riccati and filter equations are obtained as an approximate solution to a reverse-time optimal control problem defining the set-valued state estimator. The advantages of the REKF over the classical EKF are investigated for examples from the fields aerospace engineering and signal processing where large model uncertainties are introduced. In the case of small UAVs, an alternative attitude estimation algorithm based on the REKF is proposed in the event of gyroscopic failure and the inability of the vehicle to carry redundant sensors due to limited payload capabilities. In the case of image reconstruction under atmospheric turbulence, a robust pixel-wandering (random shifts) scheme is proposed to aid the process of image reconstruction. Also, problems pertaining to platform vibration analysis for aerospace vehicles and a frequency demodulation process in the presence of channel-induced uncertainties is also discussed.

The European Commission 6th Framework Project COCOMAT (Improved MATerial Exploitation at Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse) was a four and a half year project (2004 to mid-2008) aimed at exploiting the large reserve of strength in composite structures through more accurate prediction of collapse. In the experimental work packages, significant statistical variation in buckling behaviour and ultimate loading were encountered. The variations observed in the experimental results were not predicted in the finite element analyses that were done in the early stages of the project. The work undertaken in this thesis to support the COCOMAT project was initiated when it was recognised that there was a gap in knowledge about the effect of initial defects and variations in the input variables of both the experimental and simulated panels. The work involved the development of stochastic algorithms to relate variations in boundary conditions, material properties and geometries to the variation in buckling modes and loads up to first failure. It was proposed in this thesis that any future design had to focus on the dominant parameters affecting the statistical scatter in the results to achieve lower sensitivity to variation. A methodology was developed for designing stiffened composite panels with improved robustness. Several panels tested in the COCOMAT project were redesigned using this approach to demonstrate its applicability. The original contributions from this thesis are therefore the development of a stochastic methodology to identify the impact of variation in input parameters on the response of stiffened composite panels and the development of Robust Indices to support the design of new panels. The stochastic analysis included the generation of metamodels that allow quantification of the impact that the inputs have on the response using two first order variables, Influence and Sensitivity. These variables are then used to derive the Robust Indices. A significant outcome of this thesis was the recognition in the final report for COCOMAT that the development of a validated robust index should be a focus of any future design of postbuckling stiffened panels.

The European Commission 6th Framework Project COCOMAT (Improved MATerial Exploitation at Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse) was a four and a half year project (2004 to mid-2008) aimed at exploiting the large reserve of strength in composite structures through more accurate prediction of collapse. In the experimental work packages, significant statistical variation in buckling behaviour and ultimate loading were encountered. The variations observed in the experimental results were not predicted in the finite element analyses that were done in the early stages of the project. The work undertaken in this thesis to support the COCOMAT project was initiated when it was recognised that there was a gap in knowledge about the effect of initial defects and variations in the input variables of both the experimental and simulated panels. The work involved the development of stochastic algorithms to relate variations in boundary conditions, material properties and geometries to the variation in buckling modes and loads up to first failure. It was proposed in this thesis that any future design had to focus on the dominant parameters affecting the statistical scatter in the results to achieve lower sensitivity to variation. A methodology was developed for designing stiffened composite panels with improved robustness. Several panels tested in the COCOMAT project were redesigned using this approach to demonstrate its applicability. The original contributions from this thesis are therefore the development of a stochastic methodology to identify the impact of variation in input parameters on the response of stiffened composite panels and the development of Robust Indices to support the design of new panels. The stochastic analysis included the generation of metamodels that allow quantification of the impact that the inputs have on the response using two first order variables, Influence and Sensitivity. These variables are then used to derive the Robust Indices. A significant outcome of this thesis was the recognition in the final report for COCOMAT that the development of a validated robust index should be a focus of any future design of postbuckling stiffened panels.

Thesis (M.S.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed March 27, 2008) Includes bibliographical references (p. 86-89).

Thesis (Ph.D.)--McMaster University (Canada), 1991. / Source: Dissertation Abstracts International, Volume: 53-11, Section: B, page: 5750. Supervisor: N. Balakrishnan.

Thesis (Ph.D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 57-10, Section: B, page: 6347. Adviser: N. Balakrishnan.

Thesis (Ph.D.)--McMaster University (Canada), 1990. / Source: Dissertation Abstracts International, Volume: 62-13, Section: A, page: 0000.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.