Efficient Algorithms for Nonlinear Optimization Problems in Power Grid
As an important branch of operation research, nonlinear programming (NLP) has evolved considerably in the last few decades and provides powerful tools in engineering. In this dissertation, we mainly focus on applying optimization techniques on solving the Optimal Power Flow(OPF) problem in the power...
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| Format: | Dissertation |
| Language: | English |
| Published: |
ProQuest Dissertations & Theses
01.01.2022
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| ISBN: | 9798845406934 |
| Online Access: | Get full text |
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| Summary: | As an important branch of operation research, nonlinear programming (NLP) has evolved considerably in the last few decades and provides powerful tools in engineering. In this dissertation, we mainly focus on applying optimization techniques on solving the Optimal Power Flow(OPF) problem in the power grid, which is generally nonlinear, nonconvex, and computational expensive with large system size. We start by addressing the problem of globally solving nonconvex mixed-integer quadratically constrained programming (MIQCP). By using the compact lifted mixed-integer formulation to relax the square function in a piecewise manner, we construct the compact disjunctive approximation (CDA) to approximate the nonconvex MIQCP to arbitrary precision. Further, we refine the state-of-art approaches exploiting semidefiniteness and combine it with the CDA scheme to construct a global solver to approximate the alternating current OPF problem. Considering the uncertainty brought by the widespread usage of renewable energy, we work on solving the quadratically-constrained robust optimization problem. We construct an explicit region based on Brouwer's theorem such that one can compute the next iterate by optimizing over this set. A sequence of the robust convex optimization problem is formulated which can be solved by utilizing the Sequential Robust Convex Optimization Algorithm (SRCOA) with the cutting-plane techniques as a subroutine. We proposed the subroutine with the exact and approximate oracles separately in the pessimization step. By providing the convergence guarantee of the subroutines, we further show the recursive feasibility, infinite descent, and convergence of SRCOA. To deal with the large-scale power distribution system, we present the convergence analysis of a novel distributed real-time approach named Equivalence of Network-based Distributed Controller for Optimization (ENDiCO) to achieve the network-level optimal solutions in fewer time steps by exploring the radial topology of the network based on the equivalence assumption. For the proposed nonlinear model, we show the local convergence guarantees for ENDiCO through the second-order sufficient condition and verify the convergence numerically for specific parameter values that are commonly used in practice. Meanwhile, we model the formulation of the subsystem over time and provide sufficient conditions to guarantee the convergence performance at some specific time step t. |
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| Bibliography: | SourceType-Dissertations & Theses-1 ObjectType-Dissertation/Thesis-1 content type line 12 |
| ISBN: | 9798845406934 |