Generalized uncertainty sets for adaptive robust unit commitment problems조정 가능 강건 기동 정지 계획 문제에 대한 일반화된 불확실성 집합

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Unit commitment (UC) problem has played an important role in determining the short-term production and distribution plans within power systems over the last decade. However, recent changes in the power system operation, such as high penetration of renewable energy and the electricity consumption increases, cause uncertainty to the UC problem and threaten the reliability of the power system. In recent years, many researchers have extensively studied the UC problem with uncertainty, but more accurate and efficient UC model is required to operate the power system in the sense of reliability and economic efficiency. The goals of this thesis are to identify the cost-efficient robust UC models which provide less conservative operation schedules and to find efficient solution methods for those models. First, we consider a two-stage robust contingency-constrained unit commitment (CCUC) problem with a generalized N-k security criterion, the so-called N-$\alpha$k security criterion. We only consider the contingency of the generator outages and do not consider the load uncertainty here. Since previous security criteria, such as N-1 and N-k security criteria, may not be reliable enough or may be over-conservative, we generalize the previous N-k security criterion to an N-$\alpha$k security criterion to overcome the aforementioned drawbacks. The operational information is used to construct an uncertainty set of the N-$\alpha$k security criterion, where some extreme contingency scenarios with the low probability of realization may be excluded. A Benders decomposition (BD) type cutting plane algorithm is used to solve the proposed model, and the maximum feasible subsystem cuts are additionally generated at each BD iteration to improve the performance of the BD type cutting plane algorithm. Numerical case studies illustrate the effectiveness of the CCUC problem with the proposed security criterion and provide some guidelines for designing the N-$\alpha$k security criterion. Second, we consider a multistage adaptive robust unit commitment problem where the ellipsoidal uncertainty set is used to express the uncertainty of the load. Previous robust UC models have two well-known drawbacks. One is that they are formulated as the two-stage adaptive robust models that do not respect the nonanticipativity of the dispatch decisions. The other is that they consider the budget uncertainty set, which is known to be a conservative one. Contrary to the previous works, we here consider the multistage adaptive robust UC model and the ellipsoidal uncertainty set. Multistage adaptive robust UC model is a state of the art UC model discussed in the recent literature. But it has more computational difficulty than the two-stage adaptive robust UC model. Ellipsoidal uncertainty set is a well-constructed uncertainty set, which reflects the correlation between uncertain parameters. The robust optimization model considering the ellipsoidal uncertainty set can be less conservative than the one considering the budget uncertainty set in some cases. However, since the ellipsoidal uncertainty set contains nonlinear constraints, the robust optimization model considering it is also computationally challenging. To overcome the computational difficulties of these approaches, we reformulate the multistage adaptive robust UC model as a computationally tractable model. We then solve the reformulated model using the constraint generation (CG) algorithm. We consider the discretized ellipsoidal uncertainty set and solve the separation problem of the CG algorithm using the KKT conditions. We call this separation procedure as a pseudo-exact separation procedure. Computational results show the efficacy of the proposed reformulation techniques and the CG algorithm with the pseudo-exact separation procedure. Lastly, we study a multistage adaptive robust unit commitment problem considering continuous and discrete uncertainties. The uncertainty of load and renewable energy output, and the contingency of the generators are treated as continuous and discrete parameters, respectively. Thus, considering these uncertainties in a single multistage adaptive robust model can be computationally challenging. The goal is to formulate a multistage adaptive robust UC model that provides a UC schedule robust against various uncertainties. The solution methods for the multistage adaptive robust UC model are presented. We implement the proposed model to the IEEE 118-bus system and show the efficacy of the proposed model and solution methods.
Advisors
Park, Sungsooresearcher박성수researcher
Description
한국과학기술원 :산업및시스템공학과,
Publisher
한국과학기술원
Issue Date
2020
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 산업및시스템공학과, 2020.2,[vi, 113 p. :]

Keywords

unit commitment▼asecurity constrained unit commitment▼acontingency-constrained unit commitment▼aadaptive robust optimization▼amultistage robust optimization▼aN-k security criterion▼aellipsoidal uncertainty set; 기동 정지 계획▼a보안 제약 기동 정지 계획▼a우발성 제약 기동 정지 계획▼a조정 가능 강건 최적화▼a다단 강건 최적화▼aN-k 보안 제약▼a타원형 불확도 집합

URI
http://hdl.handle.net/10203/283606
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=908362&flag=dissertation
Appears in Collection
IE-Theses_Ph.D.(박사논문)
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