Stability and Scenario Trees for Multistage Stochastic Programs

Heitsch, Holger; Römisch, Werner

doi:10.1007/978-1-4419-1642-6_7

Cited by 14 publications

(17 citation statements)

References 39 publications

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“…These methods were further extended to chance constrained and mixed-integer two-stage stochastic programs in [29], which are stated with respected to cell discrepancy (or the Kolmogorov metric), while [30] extended the work in [29] with a certain polyhedral discrepancy. Further extensions to multi-stage stochastic programs were made in [31][32][33][34]. Because of the encouraging numerical results reported in [3,4], these methods have been applied widely in power systems studies such as [11,[35][36][37][38][39].…”

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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Section: Literature Reviewmentioning

confidence: 99%

Solution sensitivity-based scenario reduction for stochastic unit commitment

Feng

Ryan

2014

Comput Manag Sci

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“…Reference [15] extends the earlier work by relying directly on the probability metrics. Based on stability behavior of multi-stage stochastic programming models, reference [16] argues that scenario tree reduction in a multi-stage model should not only rely on L r -norms, and [17] derives a new scenario reduction method motivated by the idea mentioned in [16].…”

Section: Relation To the Literaturementioning

confidence: 99%

“…<Fig.2 here> on the realizations in the final year of the predecessor period which is defined as the reference year, and calculated according to (14)- (16). For example, given the annual electricity demand and natural gas price in the reference year, then the specifications S VAL of those variables in target year t ranging from year s +1 to s + l (where l is the length of the subperiod) can be found by using t − s in equations (14)- (16).…”

Section: Division Of the Planning Horizon And Scenario Tree Generationmentioning

confidence: 99%

Scenario construction and reduction applied to stochastic power generation expansion planning

Feng

Ryan

2013

Computers & Operations Research

133

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A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone. Abstract:A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone.

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“…[HR09a,HR10]). In contrast to D f the distance D * f is a metric as it satisfies the triangle inequality.…”

Section: Stability Of Multi-stage Stochastic Programsmentioning

confidence: 99%

“…The branching structure of the tree is not predetermined, but automatically detected by the algorithms such that a good approximation of P measured in terms of the closeness of optimal values is obtained. The whole approach is based on a quantitative stability analysis of (linear) multi-stage stochastic programs (see [HRS06,HR10]). The algorithms rely on applying scenario reduction sequentially over time and are first analyzed in [HR09a].…”

Section: Introductionmentioning

confidence: 99%