Thesis (M.S. in Civil Engineering)--Vanderbilt University, 2004. / Title from PDF title screen. Includes bibliographical references.

In this thesis, we develop scalable frameworks to (re)design a class of large-scale network systems with built-in control mechanisms, including electric power systems and the Internet, in order to improve their economic efficiency and performance while guaranteeing their stability and robustness. After a detailed introduction relating to power system control and optimization, as well as network congestion control, we turn our attention to merging primary and secondary frequency control for the power grid. We present modifications in the conventional generation control using a consensus design approach while considering the participation of controllable loads. The optimality, stability and delay robustness of the redesigned system are studied. Moreover, we extend the proposed control scheme to (i) networks with more complexity and (ii) the case where controllable loads are involved in the optimization. As a result, our controllers can balance power flow and drive the system to an economically optimal operating point in the steady state. We then study a real-time control framework that merges primary, secondary and tertiary frequency control in power systems. In particular, we consider a transmission level network with tree topology. A distributed dynamic feedback controller is designed via a primal-dual decomposition approach and the stability of the overall system is studied. In addition, we introduce extra dynamics to improve system performance and emphasize the trade-off when choosing the gains of the extra dynamics. As a result, the proposed controller can balance supply and demand in the presence of disturbances, and achieve optimal power flow in the steady state. Furthermore, after introducing the extra dynamics, the transient performance of the system significantly improves. A redesign framework for network congestion control is developed next. Motivated by the augmented Lagrangian method, we introduce extra terms to the Lagrangian, which is used to redesign the primal-dual, primal and dual algorithms. We investigate how the gains resulting from the extra dynamics influence the stability and robustness of the system. Moreover, we show that the overall system can achieve added robustness to communication delays by appropriately tuning these gains. Also, the meaning of these extra dynamics is investigated and a distributed proportional-integral-derivative controller for solving network congestion control problems is further developed. Finally, we concentrate on a reverse- and forward-engineering framework for distributed control of a class of linear network systems to achieve optimal steady-state performance. As a typical illustration, we use the proposed framework to solve the real-time economic dispatch problem in the power grid. On the other hand, we provide a general procedure to modify control schemes for a special class of dynamic systems. In order to investigate how general the reverse- and forward-engineering framework is, we develop necessary and sufficient conditions under which an linear time-invariant system can be reverse-engineered as a gradient algorithm to solve an optimization problem. These conditions are characterized using properties of system matrices and relevant linear matrix inequalities. We conclude this thesis with an account for future research.

(i) The thesis sets out to address the problematic phenomenon of Systems of Congestion via Basic Queueing Theory. The theory, and its application in practice, appears to be a field of study which is the common domain of “theorists” and “practitioners”. (ii) This professional dichotomy has come about due to diverging interests in that one group is mainly interested in the purity of mathematical modelling, and the other group is motivated to use modelling, which conveniently employs applications oriented solutions. (iii) The schism between the groups has been accentuated by the “practitioners” who in addition to having an interest in steady state system behaviour make use of methods of modelling of the transient operation of complex Systems of Congestion. (iv) At the outset the thesis demonstrates how closed form solutions are obtained for steady state and transient state operation of a selection of Systems of Congestion. The attendant mathematical derivations are elegant and intricate. (v) Having revealed the limited utility of closed-form solutions the thesis proceeds to investigate the feasibility of using dynamical systems theory to study the transient behaviour of complex Systems of Congestion. (vi) The creation of Chaos Theory in recent decades suggests that it may be employed as a useful tool in analysing Systems of Congestion. Iterative Chaos Theory methods of orbit generation for complete Systems of Congestion are therefore examined. The use of such orbit generation methods is found to be satisfactory for simple Systems of Congestion. More than a perfunctory knowledge of chaos mapping is however required. The simplicity of modelling is emphasized. (vii) Based on the results of benchmarking the creation of dynamic system orbits against an existing simulation method, the research advances to modelling of the transient operation of complex systems. Once again the iterative method of orbit generation displays the ease of modelling while simultaneously unfolding system dynamics graphically. (viii) One may hopefully contend that a tool of eminent utility has been developed to aid practitioners in studying and optimizing Systems of Congestion. / Thesis (PhD (Industrial Engineering))--University of Pretoria, 2006. / Industrial and Systems Engineering / Unrestricted