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      수요의 불확실성을 고려한 확률적 발전계획문제에 대한 발전원 분해기법 = A Unit Decomposition Approach for the Stochastic Unit Commitment Problem under Demand Uncertainty

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      https://www.riss.kr/link?id=A108707115

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      다국어 초록 (Multilingual Abstract) kakao i 다국어 번역

      This paper addresses the unit commitment problem, where a system operator decides the on-off status and the amount of generation of each generator for each time period during a given planning horizon to meet the electricity demand at minimum cost. Especially, to deal with uncertain demand, we consider the stochastic unit commitment problem, where the expected cost is minimized under the pre-determined set of scenarios. To mitigate the increasing computational burden of the problem as the number of scenarios increases, we propose a unit decomposition approach to solve the problem. It is a specialized Lagrangian relaxation-based solution approach that relaxes coupling constraints among generators and thus decomposes the remaining problem into single-unit commitment problems. We also propose an efficient dynamic programming algorithm for the subproblem to enhance the proposed solution approach. Through the numerical experiments, we show the efficiency of the proposed dynamic programming algorithm for the subproblem. In addition, we demonstrate the efficiency of the proposed unit decomposition approach for the stochastic unit commitment problem.
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      This paper addresses the unit commitment problem, where a system operator decides the on-off status and the amount of generation of each generator for each time period during a given planning horizon to meet the electricity demand at minimum cost. Esp...

      This paper addresses the unit commitment problem, where a system operator decides the on-off status and the amount of generation of each generator for each time period during a given planning horizon to meet the electricity demand at minimum cost. Especially, to deal with uncertain demand, we consider the stochastic unit commitment problem, where the expected cost is minimized under the pre-determined set of scenarios. To mitigate the increasing computational burden of the problem as the number of scenarios increases, we propose a unit decomposition approach to solve the problem. It is a specialized Lagrangian relaxation-based solution approach that relaxes coupling constraints among generators and thus decomposes the remaining problem into single-unit commitment problems. We also propose an efficient dynamic programming algorithm for the subproblem to enhance the proposed solution approach. Through the numerical experiments, we show the efficiency of the proposed dynamic programming algorithm for the subproblem. In addition, we demonstrate the efficiency of the proposed unit decomposition approach for the stochastic unit commitment problem.

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      참고문헌 (Reference)

      1 Ostrowski, J., "Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem" 27 (27): 39-46, 2011

      2 Knueven, B., "The Ramping Polytope and cut Generation for the Unit Commitment Problem" 30 (30): 739-749, 2018

      3 Pan, K., "Strong Formulations for Multistage Stochastic Self-scheduling Unit Commitment" 64 (64): 1482-1498, 2016

      4 Shiina, T., "Stochastic Unit Commitment Problem" 11 (11): 19-32, 2004

      5 Carpentier, P., "Stochastic Optimization of Unit Commitment: A New Decomposition Framework" 11 (11): 1067-1073, 1996

      6 Nowak, M. P., "Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-thermal System Under Uncertainty" 100 : 251-272, 2000

      7 Frangioni, A., "Solving Unit Commitment Problems with General Ramp Constraints" 30 (30): 316-326, 2008

      8 Frangioni, A., "Solving Nonlinear Single-unit Commitment Problems with Ramping Constraints" 54 (54): 767-775, 2006

      9 Guan, Y., "Polynomial Time Algorithms and Extended Formulations for Unit Commitment Problems" 50 (50): 735-751, 2018

      10 Frangioni, A., "New MIP Formulations for the Single-unit Commitment Problems with Ramping Constraints" IASI 2015

      1 Ostrowski, J., "Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem" 27 (27): 39-46, 2011

      2 Knueven, B., "The Ramping Polytope and cut Generation for the Unit Commitment Problem" 30 (30): 739-749, 2018

      3 Pan, K., "Strong Formulations for Multistage Stochastic Self-scheduling Unit Commitment" 64 (64): 1482-1498, 2016

      4 Shiina, T., "Stochastic Unit Commitment Problem" 11 (11): 19-32, 2004

      5 Carpentier, P., "Stochastic Optimization of Unit Commitment: A New Decomposition Framework" 11 (11): 1067-1073, 1996

      6 Nowak, M. P., "Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-thermal System Under Uncertainty" 100 : 251-272, 2000

      7 Frangioni, A., "Solving Unit Commitment Problems with General Ramp Constraints" 30 (30): 316-326, 2008

      8 Frangioni, A., "Solving Nonlinear Single-unit Commitment Problems with Ramping Constraints" 54 (54): 767-775, 2006

      9 Guan, Y., "Polynomial Time Algorithms and Extended Formulations for Unit Commitment Problems" 50 (50): 735-751, 2018

      10 Frangioni, A., "New MIP Formulations for the Single-unit Commitment Problems with Ramping Constraints" IASI 2015

      11 Rajan, D., "Minimum Up/down Polytopes of the Unit Commitment Problem with Start-up costs" 1-14, 2005

      12 Lee, J., "Min-up/min-down Polytopes" 1 (1): 77-85, 2004

      13 Zimmerman, R. D., "MATPOWER: Steady-state Operations, Planning, and Analysis Tools for Power Systems Research and Education" 26 (26): 12-19, 2010

      14 Van Ackooij, W., "Large-scale Unit Commitment Under Uncertainty: An Updated Literature Survey" 271 (271): 11-85, 2018

      15 Wolsey, L. A., "Integer Programming" John Wiley & Sons 2020

      16 Wuijts, R. H., "An Improved Algorithm for Single-unit Commitment with Ramping Limits" 190 : 106720-, 2021

      17 Damcı-Kurt, P., "A polyhedral study of production ramping" 158 : 175-205, 2016

      18 Fan, W., "A new Method for Unit Commitment with Ramping Constraints" 62 (62): 215-224, 2002

      19 Kazarlis, S. A., "A Genetic Algorithm Solution to the Unit Commitment Problem" 11 (11): 83-92, 1996

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