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Economic and Computational Methods for the Control of Uncertain Systems
Title
Economic and Computational Methods for the Control of Uncertain Systems
Creator
Zhang, Jin
Date
2019
Description
The Economic Linear Optimal Control (ELOC) can improve the effective use of economic and dynamic information throughout the traditional...
Show moreThe Economic Linear Optimal Control (ELOC) can improve the effective use of economic and dynamic information throughout the traditional optimization and control hierarchy. This dissertation investigates the computational procedures used to obtain a global solution to the ELOC problem. The proposed method employs the Generalized Benders Decomposition (GBD) algorithm. Compared to the previous branch and bound approach, the application of GBD to the ELOC problem will greatly improve computational performance. A technological benefit of decomposing the problem into steady-state and dynamic parts is the ability to utilize nonlinear steady-state models, since the relaxed master problem is free of SDP type constraints and can be solved using any global nonlinear programming algorithm.In order to address the issue of model/plant mismatch, the dissertation will also investigate how to handle box-type uncertainties in ELOC. We consider two methods, a robust formulation for when the uncertainty is completely unknown and a Linear Parameter Varying formulation for when uncertainty can be measured in real time. In both cases, the infinite number of conditions that need to be satisfied are reduced to a finite set of constraints. The resulting problem formulations have a similar structure to the ELOC and can be solved globally by employing the generalized Benders decomposition.Despite a high-quality control law, the ultimate performance of closed-loop systems will be dictated by the quality and limitation of hardware element. Thus, hardware selection is also investigated in the dissertation. The cost-optimal hardware selection problem has been shown to be of the Mixed Integer Convex Programming (MICP) class. While such a formulation provides a route to global optimality, use of the branch and bound search procedure has limited application to fairly small systems. In this dissertation, we illustrate that a simple reformulation of the MICP and subsequent application of the GBD algorithm will result in massive reductions in computational effort.Finally, the problems of value-optimal sensor network design (SND) for steady-state and closed-loop systems are investigated. The value-optimal SND problem has been shown to be of the nonconvex mixed integer programming class. In the dissertation, it is demonstrated after transforming into an equivalent reformation, the application of GBD algorithm will significantly reduce the computational effort.
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ECONOMIC MPC-BASED DESIGN AND OPERATION OF GRID SCALE ENERGY STORAGE SYSTEMS
Title
ECONOMIC MPC-BASED DESIGN AND OPERATION OF GRID SCALE ENERGY STORAGE SYSTEMS
Creator
Adeodu, Oluwasanmi
Date
2019
Description
It is generally recognized that a higher penetration of renewable power on the electric grid, along with the attendant environmental benefits,...
Show moreIt is generally recognized that a higher penetration of renewable power on the electric grid, along with the attendant environmental benefits, is limited by its inherent high variability and intermittency. An approach to alleviating this issue is to install grid scale energy storage as buffer. However, the economic viability of such an endeavor is dependent on the optimal sizing and placement (OSP) of storage units, which in turn requires the specification of an appropriate storage management policy. While stochastic programming with recourse is recognized as the standard approach to stage-wise optimal decision-making under uncertainty, Economic Model Predictive Control (EMPC) is put forward as a deterministic simplification of the former and demonstrated to be a viable economic dispatch strategy for networks with a high proportion of renewable energy and storage. Then, a numerical, EMPC-based gradient search strategy is proposed to address the OSP problem. Since both the operating policy and OSP questions are invariably massive optimization problems in real systems, strong emphasis is laid on computational tractability. Therefore, the analytical nature of a surrogate stochastic control policy, Economic Linear Optimal Control (ELOC), is exploited to develop innovative modifications to both algorithms. The end products are (1), an Approximate Infinite Horizon EMPC (AIH-EMPC) strategy, a relatively low computational cost variant of EMPC and (2), a hybrid EMPC-ELOC OSP strategy that essentially sidesteps the inherent combinatorial complexity of the unit location problem.
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