A stochastic model for the unit commitment problem

Takriti, Samer; Birge, John R.; Long, Erping

doi:10.1109/59.535691

Cited by 471 publications

(278 citation statements)

References 7 publications

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“…. , t end b , constraints (27) are implied by (26) together with (10). Thus, to avoid redundancy we only include them for the time periods …”

Section: Transmission Boundary Limits For Allmentioning

confidence: 99%

“…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%

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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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“…. , t end b , constraints (27) are implied by (26) together with (10). Thus, to avoid redundancy we only include them for the time periods …”

Section: Transmission Boundary Limits For Allmentioning

confidence: 99%

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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“…3 surplus (cost in case of inelastic demands) in intra-day operations. Examples include the works of Takriti et al (1996), Wang et al (2008), Constantinescu et al (2011), Jin et al (2014), Ruiz et al (2009), Bouffard et al (2005), Papavasiliou and Oren (2013). These studies have demonstrated significant improvements in reliability over deterministic formulations.…”

Section: Previous Workmentioning

confidence: 99%

A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

Zavala

Kim

Anitescu

et al. 2017

Operations Research

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We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversification. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation yields price distortions that are bounded by the bid prices, and we show that adding a similar penalty term to transmission flows and phase angles ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities converge to the quantile of real-time counterparts. The undesired effects of price distortions suggest that stochastic settings provide significant benefits over deterministic ones that go beyond social surplus improvements. We propose additional metrics to evaluate these benefits.

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“…In contrast, stochastic unit commitment procedures [16,24,25] assume the availability of a number of forecast scenarios, each representing a distinct potential time series of the forecasted quantities. Throughout, we use the term scenario in a narrow sense, representing a full specification of all random data required to instantiate a unit commitment problem, with associated probability of occurrence.…”

Section: Introductionmentioning

confidence: 99%

“…For investigations into stochastic unit commitment, several approaches for generating multiple trajectories have been used. An ad hoc procedure was used in an early study to create scenarios of large increasing or decreasing load ramps [25]. A common approach is to perturb a single forecast with some stochastic error terms.…”

Section: Introductionmentioning

confidence: 99%

Toward scalable stochastic unit commitment. Part 1: load scenario generation

et al. 2015

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Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Tra-ditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load sce-narios, with associated probabilities, that in aggregate capture the range of likely load time-series. The shift from point-based to scenario-based forecasting necessi-tates a shift in forecasting technologies, to provide accurate inputs to stochastic unit commitment. In this paper, we discuss a novel scenario generation method-ology for load forecasting in stochastic unit commitment, with application to real data associated with the Independent System Operator for New England (ISO-NE). The accuracy of the expected scenario generated using our methodology is consistent with that of point forecasting methods. The resulting sets of realistic scenarios serve as input to rigorously test the scalability of stochastic unit com-mitment solvers, as described in the companion paper. The scenarios generated by our method are available as an online supplement to this paper, as part of a novel, publicly available large-scale stochastic unit commitment benchmark. Abstract Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Traditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load scenarios, with associated probabilities, that in aggregate capture the range of likely load time-series. The shift from point-based to scenario-based forecasting necessitates a shift in forecasting technologies, to provide accurate inputs to stochastic unit commitment. In this paper, we discuss a novel scenario generation methodology for load forecasting in stochastic unit commitment, with application to real data associated with the Independent System Operator for New England (ISO-NE). The accuracy of the expected scenario generated using our methodology is consistent with that of point forecasting methods. The resulting sets of realistic scenarios serve as input to rigorously test the scalability of stochastic unit commitment solvers, as described in the companion paper. The scenarios generated Disciplines Industrial Engineering | Systems Engineering

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A stochastic model for the unit commitment problem

Cited by 471 publications

References 7 publications

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

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

A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

Toward scalable stochastic unit commitment. Part 1: load scenario generation

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