Fast textured algorithms for large convex optimization : theory and applications to power systems /
In my master's thesis, a textured decomposition method/algorithm was presented for optimal power flow analysis. In this dissertation, we will generalize the methodology and develop fast textured decomposition methods/algorithms (TDM) for large-scale convex optimization problems and investigate...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1996.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=739364291&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | In my master's thesis, a textured decomposition method/algorithm was presented for optimal power flow analysis. In this dissertation, we will generalize the methodology and develop fast textured decomposition methods/algorithms (TDM) for large-scale convex optimization problems and investigate two applications in power systems. We first establish the theoretical foundations of the TDM for problems with constraints in either staircase or angular-block structure. We then generalize our TDM into multi-intersected models for more general structure. We also propose a recursive version of the TDM to further decompose subproblems to smaller sub-subproblems in the textured form. The necessary and sufficient conditz'ons for exact convergence are investigated and proven. The time complexities, insights, and speedup advantage of the proposed algorithms are also analyzed and demonstrated. It is shown that even when we execute the proposed algorithm sequentially, we still can reduce the overall solution time. We also show the trade-off among the number of recursion levels, the number of sequential computing steps, and problem size reduction. To make our TDM more practically applicable, we also develop a heuristic levelization algorithm to systematically levelize those decomposed subsystems. The levelization problem is first mapped into a new and more challenging vertex-coloring problem with a undirected vertex-weighted graph and some extra considerations. We then adopt and propose some heuristic coloring schemes to solve the problem. We incorporate the Hierarchical Aggregation/Disaggregation concept into the TDM and solve the Constrained Economic Dispatch Control Problems in two stages. At the first stage, the initial near-optimal solution is obtained by solving an aggregated formulation of the problem and followed by an AC power flow. Then, at the second stage, the solution is fine-tuned to reach the true optimal solution via the TDM. Computer runs demonstrate the speedup advantage of the algorithm and insights. Finally, we apply the TDM to solve the Optimal Power Delivery Problems in open access environments, which is formulated in terms of transmitted line flows and some device parameters of Flexible AC Transmission Systems. Two versions of the TDM are tested. Some implementation insights and the speedup advantage of the algorithm are illustrated. |
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| Item Description: | Vita. "Major Subject: Electrical Engineering". |
| Physical Description: | xiii, 245 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 189-200. |