Dynamic generation of scenario trees

Pflug, Georg Ch.; Pichler, Alois

doi:10.1007/s10589-015-9758-0

Cited by 68 publications

(55 citation statements)

References 30 publications

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“…Starting from a known initial state x 0 the system states evolve according to (5) as illustrated in Figure 2(a) giving rise to a structure known as a scenario tree. There have been proposed several methodologies to generate scenario trees from data [20], [21]. The nodes of the tree are assigned a unique index i with i = 0 being the root node which corresponds to the initial state x 0 .…”

Section: Stochastic Systems and Multistage Riskmentioning

confidence: 99%

Risk-averse risk-constrained optimal control

Sopasakis

Schuurmans

Patrinos

2019

2019 18th European Control Conference (ECC)

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Multistage risk-averse optimal control problems with nested conditional risk mappings are gaining popularity in various application domains. Risk-averse formulations interpolate between the classical expectation-based stochastic and minimax optimal control. This way, risk-averse problems aim at hedging against extreme low-probability events without being overly conservative. At the same time, risk-based constraints may be employed either as surrogates for chance (probabilistic) constraints or as a robustification of expectationbased constraints. Such multistage problems, however, have been identified as particularly hard to solve. We propose a decomposition method for such nested problems that allows us to solve them via efficient numerical optimization methods. Alongside, we propose a new form of risk constraints which accounts for the propagation of uncertainty in time. † P. Sopasakis is with Queen's University Belfast,

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Section: Stochastic Systems and Multistage Riskmentioning

confidence: 99%

Risk-averse risk-constrained optimal control

Sopasakis

Schuurmans

Patrinos

2019

2019 18th European Control Conference (ECC)

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“…In the conventional construction of a tree (cf. [9]), each node of the tree has an associated discrete time net-load sample, and the representation of the statistics is nodal, that is: each node v ∈ V of the tree has a certain probability π v that is the marginal probability of that particular sample for the quantized process at that stage. A better interpretation of the approximate scenario tree for a continuous time process is that realizations are mapped into piece-wise constant sample paths.…”

Section: General Polynomial Interpolation Of Electric Net-load Prmentioning

confidence: 99%

Continuous Time Multi-Stage Stochastic Reserve and Unit Commitment

Hreinsson

Analui

Scaglione

2018

2018 Power Systems Computation Conference (PSCC)

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In this paper we introduce a continuous time multi stage stochastic optimization for scheduling generating units, their commitment, reserve capacities and their continuous time generation profiles in the day-ahead wholesale electricity market. Our formulation approximates the solution of a variational problem, in which the balance, generation capacity and ramping constraints are in continuous time. Due to the greater accuracy of our representation of ramping events this approach improves the system reliability and lowers the real-time cost.

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“…Many methods have been developed to generate scenario trees. Some of the most popular methods are moment-matching (Høyland et al, 2003), scenario reduction (Heitsch and Römisch, 2009), copulas (Kaut, 2014), or minimization of the nested distance (Pflug and Pichler, 2015), for example. In this paper, the authors specifically use the minimization of the nested distance to build the inflow scenario trees.…”

Section: Introductionmentioning

confidence: 99%

Scenario-Tree Modeling for Stochastic Short-Term Hydropower Operations Planning

Séguin

Audet

Côté

2017

J. Water Resour. Plann. Manage.

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The authors investigate the complexity needed in the structure of the scenario trees to maximize energy production in a rolling-horizon framework. Three comparisons, applied to the stochastic short-term unit commitment and loading problem are conducted. The first one involves generating a set of scenario trees built from inflow forecast data over a rolling-horizon. The second replaces the entire set of scenario trees by the median scenario. The third replaces the set of trees by scenario fans. The method used to build scenario trees, based on minimization of the nested distance, requires three parameters: number of stages, number of child nodes at each stage, and aggregation of the period covered by each stage. The authors formulate the question of finding the best values of these parameters as a blackbox optimization problem that maximizes the energy production over the rolling-horizon. Numerical experiments on three hydropower plants in series suggest that using a set of scenario trees is preferable to using the median scenario, but using a fan of scenarios yields a comparable solution with less computational effort.

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Dynamic generation of scenario trees

Cited by 68 publications

References 30 publications

Risk-averse risk-constrained optimal control

Risk-averse risk-constrained optimal control

Continuous Time Multi-Stage Stochastic Reserve and Unit Commitment

Scenario-Tree Modeling for Stochastic Short-Term Hydropower Operations Planning

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