An Exact Solution Method for the Hydrothermal Unit Commitment Under Wind Power Uncertainty With Joint Probability Constraints

Ackooij, Wim van; Finardi, Erlon Cristian; Ramalho, Guilherme

doi:10.1109/tpwrs.2018.2848594

Cited by 27 publications

(16 citation statements)

References 36 publications

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“…Two approaches are possible: either the safety level is set for each constraint (e.g., time step) individually, giving an Individual CCO program, or for the system as a whole, resulting in a Joint CCO program. While the ICCO is obviously less robust than the JCCO (see the discussion in [521,528] in the context of UUC), the latter is in general significantly more difficult to solve, especially if one wishes to do this exactly (i.e., without artificially discretizing the underlying random vectors or approximating the probabilistic constraint). This explains why CCO (either Individual or Joint) models are the least employed in the literature on UC.…”

Section: Chance-constrained Optimization Approachesmentioning

confidence: 99%

“…In the recent [521], classic methods are developed and adapted from CCO to handle integer variables for a UC problem under uncertainty on wind generation, while accounting for a DC network. The method differs from the one considered in [26], where a cutting-plane based methodology (for the convex continuous part) is inserted in a Branch & Bound solver directly, i.e., in each node of the B&B tree a convex optimization problem has to be solved.…”

Section: Chance-constrained Optimization Approachesmentioning

confidence: 99%

“…The method differs from the one considered in [26], where a cutting-plane based methodology (for the convex continuous part) is inserted in a Branch & Bound solver directly, i.e., in each node of the B&B tree a convex optimization problem has to be solved. In contrast, in [521] the approach is inverted: in each iteration of a cutting-plane-like method, two MILPs are solved, one of which defines the next iterate and a lower bound, while the other provides a feasible solution and thus an upper-bound. The methodology is shown to scale up to a 46-bus system in a HUC problem.…”

Section: Chance-constrained Optimization Approachesmentioning

confidence: 99%

See 2 more Smart Citations

Large-scale unit commitment under uncertainty: an updated literature survey

Ackooij¹,

et al. 2018

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The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chanceconstrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115-171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject.

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Section: Chance-constrained Optimization Approachesmentioning

confidence: 99%

Section: Chance-constrained Optimization Approachesmentioning

confidence: 99%

Section: Chance-constrained Optimization Approachesmentioning

confidence: 99%

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Large-scale unit commitment under uncertainty: an updated literature survey

Ackooij¹,

et al. 2018

Self Cite

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“…In this paper, assume the closed-form expression of the logarithmic moment generating function is not available, thus (36) is a typical stochastic optimization problem with a fixed probability distribution P 0 [2]. Standard stochastic optimization technique can be used to solve (36) such as the sample average approximation [13] and stochastic approximation.…”

Section: Solution Strategymentioning

confidence: 99%

“…During the past decades, the issues of fossil fuel depletion and climate change are becoming more and more grievous. To cope with these questions, renewable energy such as wind energy generation and photovoltaic (PV) generation has been integrated into power systems in large scale [1,2]. However, renewable energy has the nature of being intermittent and unpredictable, which leads to changes in power system operation, such as unit commitment (UC) problems, economic dispatch (ED) problems, energy and reserve (ER) dispatch problems [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Distributionally Robust Model of Energy and Reserve Dispatch Based on Kullback–Leibler Divergence

et al. 2019

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This paper proposes a distance-based distributionally robust energy and reserve (DB-DRER) dispatch model via Kullback-Leibler (KL) divergence, considering the volatile of renewable energy generation. Firstly, a two-stage optimization model is formulated to minimize the expected total cost of energy and reserve (ER) dispatch. Then, KL divergence is adopted to establish the ambiguity set. Distinguished from conventional robust optimization methodology, the volatile output of renewable power generation is assumed to follow the unknown probability distribution that is restricted in the ambiguity set. DB-DRER aims at minimizing the expected total cost in the worst-case probability distributions of renewables. Combining with the designed empirical distribution function, the proposed DB-DRER model can be reformulated into a mixed integer nonlinear programming (MINLP) problem. Furthermore, using the generalized Benders decomposition, a decomposition method is proposed and sample average approximation (SAA) method is applied to solve this problem. Finally, simulation result of the proposed method is compared with those of stochastic optimization and conventional robust optimization methods on the 6-bus system and IEEE 118-bus system, which demonstrates the effectiveness and advantages of the method proposed.

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2021

Mathematical Programming for Power Systems Operation With Applications in Python

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An Exact Solution Method for the Hydrothermal Unit Commitment Under Wind Power Uncertainty With Joint Probability Constraints

Cited by 27 publications

References 36 publications

Large-scale unit commitment under uncertainty: an updated literature survey

Large-scale unit commitment under uncertainty: an updated literature survey

Distributionally Robust Model of Energy and Reserve Dispatch Based on Kullback–Leibler Divergence

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