A decomposition approach to the two-stage stochastic unit commitment problem

Zheng, Qipeng P.; Wang, Jianhui; Pardalos, Pãnos M.; Guan, Yongpei

doi:10.1007/s10479-012-1092-7

Cited by 108 publications

(80 citation statements)

References 38 publications

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“…Our formulation is based on the mixed-integer linear programming UC formulations introduced by [5,31,34]. We extend these formulations to capture network transmission constraints, in the form of a DC power flow model.…”

Section: The Baseline Unit Commitment Modelmentioning

confidence: 99%

Contingency-constrained unit commitment with post-contingency corrective recourse

et al. 2014

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We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-ε reliability criterion. This reliability criterion is a generalization of the wellknown N-k criterion, and dictates that at least (1 − ε j ) fraction of the total system demand must be met following the failures of k or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art.

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Section: The Baseline Unit Commitment Modelmentioning

confidence: 99%

Contingency-constrained unit commitment with post-contingency corrective recourse

et al. 2014

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“…Many popular algorithms for stochastic unit commitment (SUC) problems are based on decomposition techniques. They can be divided into three groups: Benders decomposition [9], Progressive Hedging [10], and Lagrangian relaxation [11] or Dantzig-Wolfe decomposition [12]. All three approaches are applicable to two-stage or multi-stage models and can be used to decompose the problem by stages, scenarios, or generation units.…”

Section: Introductionmentioning

confidence: 99%

The value of stochastic programming in day-ahead and intra-day generation unit commitment

Schulze

McKinnon

2016

Energy

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The recent expansion of renewable energy supplies has prompted the development of a variety of efficient stochastic optimization models and solution techniques for hydro-thermal scheduling. However, little has been published about the added value of stochastic models over deterministic ones. In the context of day-ahead and intra-day unit commitment under wind uncertainty, we compare two-stage and multi-stage stochastic models to deterministic ones and quantify their added value. We present a modification of the WILMAR scenario generation technique designed to match the properties of the errors in our wind forecasts, and show that this is needed to make the stochastic approach worthwhile. Our evaluation is done in a rolling horizon fashion over the course of two years, using a 2020 central scheduling model based on the British power system, with transmission constraints and a detailed model of pump storage operation and system-wide reserve and response provision. We show that in day-ahead scheduling the stochastic approach saves 0.3% of generation costs compared to the best deterministic approach, but the savings are less in intra-day scheduling.

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“…The computation time strongly depends on the number of scenarios even if a decomposition method, such as Benders decomposition [15], Lagrangian relaxation [16,17], or a progressive hedging algorithm [1] is applied. The size of the Benders master problem will increase dramatically if many scenarios are included.…”

Section: Literature Reviewmentioning

confidence: 99%

Solution sensitivity-based scenario reduction for stochastic unit commitment

Feng

Ryan

2014

Comput Manag Sci

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A two-stage stochastic program is formulated for day-ahead commitment of thermal generating units to minimize total expected cost considering uncertainties in the day-ahead load and the availability of variable generation resources. Commitments of thermal units in the stochastic reliability unit commitment are viewed as first-stage decisions, and dispatch is relegated to the second stage. It is challenging to solve such a stochastic program if many scenarios are incorporated. A heuristic scenario reduction method termed forward selection in recourse clusters (FSRC), which selects scenarios based on their cost and reliability impacts, is presented to alleviate the computational burden. In instances down-sampled from data for an Independent System Operator in the US, FSRC results in more reliable commitment schedules having similar costs, compared to those from a scenario reduction method based on probability metrics. Moreover, in a rolling horizon study, FSRC preserves solution quality even if the reduction is substantial. Abstract A two-stage stochastic program is formulated for day-ahead commitment of thermal generating units to minimize total expected cost considering uncertainties in the day-ahead load and the availability of variable generation resources. Commitments of thermal units in the stochastic reliability unit commitment (SRUC) are viewed as first-stage decisions, and dispatch is relegated to the second stage. It is challenging to solve such a stochastic program if a lot of scenarios are incorporated. A heuristic scenario reduction method termed forward selection in recourse clusters (FSRC), which selects scenarios based on their cost and reliability impacts, is presented to alleviate the computational burden. In instances down-sampled from data for an Independent System Operator in the U.S., FSRC results in more reliable commitment schedules having similar costs, compared to those from a scenario reduction method based on probability metrics. Moreover, in a rolling horizon study, FSRC preserves solution quality even if the reduction is substantial.

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A decomposition approach to the two-stage stochastic unit commitment problem

Cited by 108 publications

References 38 publications

Contingency-constrained unit commitment with post-contingency corrective recourse

Contingency-constrained unit commitment with post-contingency corrective recourse

The value of stochastic programming in day-ahead and intra-day generation unit commitment

Solution sensitivity-based scenario reduction for stochastic unit commitment

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