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Algorithms for Stochastic Mixed-Inte...

Li, Can.

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Algorithms for Stochastic Mixed-Integer Nonlinear Programming and Long Term Optimization of Electric Power Systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algorithms for Stochastic Mixed-Integer Nonlinear Programming and Long Term Optimization of Electric Power Systems./
作者:	Li, Can.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	367 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-01, Section: B.
Contained By:	Dissertations Abstracts International83-01B.
標題:	Chemical engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28498705
ISBN:	9798516959332

Algorithms for Stochastic Mixed-Integer Nonlinear Programming and Long Term Optimization of Electric Power Systems.
Li, Can.

Algorithms for Stochastic Mixed-Integer Nonlinear Programming and Long Term Optimization of Electric Power Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 367 p.

Source: Dissertations Abstracts International, Volume: 83-01, Section: B.

Thesis (Ph.D.)--Carnegie Mellon University, 2021.

This item must not be sold to any third party vendors.

This thesis addresses two challenging problems. The first part is focused on developing algorithms and software for two-stage stochastic mixed-integer nonlinear programming problems (SMINLPs). The second part is on the long-term planning of power systems.Stochastic programming, also known as stochastic optimization, is a mathematical framework to model decision-making under uncertainty that has been widely applied in process systems engineering (PSE). Two-stage stochastic mixed-integer programming (SMIPs) is a special case of stochastic programming that considers first and second stage decisions made sequentially with both discrete and continuous variables. Although there have been algorithmic advances in linear SMIPs, the decomposition algorithms to address the nonlinear counterpart, stochastic mixed-integer nonlinear programs (SMINLPs), are few. In Part I of this thesis, we propose four decomposition algorithms for different classes of SMINLPs. For SMINLPs with convex nonlinear constraints, mixed-binary first and second variables, and discrete probability distributions, we propose an improved L-shaped algorithm that combines strengthened Benders cuts and Lagrangean cuts. This algorithm has no guarantee of global optimality. To close the optimality gap, we propose a generalized Benders decomposition-based branch-and-bound algorithm where the stage two problems are convexified sequentially by performing basic steps. For SMINLPs with nonconvex constraints, mixed-binary first and second variables, and discrete probability distributions, we propose a generalized Benders decomposition-based branch-and-cut algorithm where we combine the Benders cuts derived from convexification of the stage two problems and the Lagrangean cuts. A spatial branch-and-cut algorithm is performed to guarantee convergence to global optimality. Last but not least, a sample-average approximation-based outer approximation algorithm is proposed for nonconvex SMINLPs with continuous probability distributions. This algorithm does internal sampling within an outer approximation framework using confidence interval estimates.Part II addresses generation expansion planning of power systems under high penetration of renewables. We propose a mixed-integer linear programming(MILP) model that incorporates both the investment decisions on the generating units, storage units, and transmission lines, and short-term unit commitment decisions to capture the variations of the renewables. To make the large-scale MILP model tractable, we propose several spatial and temporal aggregation schemes and adapt the Benders decomposition algorithm and the nested Benders decomposition algorithm to solve the problem efficiently. We also investigate several different algorithms to select the representative days. Case studies of the ERCOT region are provided to demonstrate the capabilities of our approaches.

ISBN: 9798516959332Subjects--Topical Terms:

560457
Chemical engineering.
Subjects--Index Terms:

Stochastic programming

Algorithms for Stochastic Mixed-Integer Nonlinear Programming and Long Term Optimization of Electric Power Systems.
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500 $a Source: Dissertations Abstracts International, Volume: 83-01, Section: B.
500 $a Advisor: Grossmann, Ignacio.
502 $a Thesis (Ph.D.)--Carnegie Mellon University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a This thesis addresses two challenging problems. The first part is focused on developing algorithms and software for two-stage stochastic mixed-integer nonlinear programming problems (SMINLPs). The second part is on the long-term planning of power systems.Stochastic programming, also known as stochastic optimization, is a mathematical framework to model decision-making under uncertainty that has been widely applied in process systems engineering (PSE). Two-stage stochastic mixed-integer programming (SMIPs) is a special case of stochastic programming that considers first and second stage decisions made sequentially with both discrete and continuous variables. Although there have been algorithmic advances in linear SMIPs, the decomposition algorithms to address the nonlinear counterpart, stochastic mixed-integer nonlinear programs (SMINLPs), are few. In Part I of this thesis, we propose four decomposition algorithms for different classes of SMINLPs. For SMINLPs with convex nonlinear constraints, mixed-binary first and second variables, and discrete probability distributions, we propose an improved L-shaped algorithm that combines strengthened Benders cuts and Lagrangean cuts. This algorithm has no guarantee of global optimality. To close the optimality gap, we propose a generalized Benders decomposition-based branch-and-bound algorithm where the stage two problems are convexified sequentially by performing basic steps. For SMINLPs with nonconvex constraints, mixed-binary first and second variables, and discrete probability distributions, we propose a generalized Benders decomposition-based branch-and-cut algorithm where we combine the Benders cuts derived from convexification of the stage two problems and the Lagrangean cuts. A spatial branch-and-cut algorithm is performed to guarantee convergence to global optimality. Last but not least, a sample-average approximation-based outer approximation algorithm is proposed for nonconvex SMINLPs with continuous probability distributions. This algorithm does internal sampling within an outer approximation framework using confidence interval estimates.Part II addresses generation expansion planning of power systems under high penetration of renewables. We propose a mixed-integer linear programming(MILP) model that incorporates both the investment decisions on the generating units, storage units, and transmission lines, and short-term unit commitment decisions to capture the variations of the renewables. To make the large-scale MILP model tractable, we propose several spatial and temporal aggregation schemes and adapt the Benders decomposition algorithm and the nested Benders decomposition algorithm to solve the problem efficiently. We also investigate several different algorithms to select the representative days. Case studies of the ERCOT region are provided to demonstrate the capabilities of our approaches.
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650 4 $a Operations research. $3 547123
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650 4 $a Sensitivity analysis. $3 3560752
650 4 $a Optimization. $3 891104
650 4 $a Electric power. $3 2143306
650 4 $a Decomposition. $3 3561186
650 4 $a Approximation. $3 3560410
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650 4 $a Algorithms. $3 536374
650 4 $a Clustering. $3 3559215
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