Improving the performance of Stochastic Dual Dynamic Programming

Matos, Vitor Luiz de; Philpott, Andy; Finardi, Erlon Cristian

doi:10.1016/j.cam.2015.04.048

Cited by 84 publications

(55 citation statements)

References 11 publications

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“…(1) -(12) In essence, the algorithm determines the optimal decision set for each by building a piece-wise linear outer approximation of + | [ +1 ( , +1 )] and identifying an approximate future cost function +1 ( , +1 ) of +1 at each stage [26]. Therefore, a set of linear constraints ('Benders' cuts') is gradually built and appended to each master problem and the expectation term in (14) - (15) is replaced by the terms 2 and +1 respectively, which represent the future cost for stages 2 to and + 1 to , respectively.…”

Section: Problem Definitionmentioning

confidence: 99%

“…It is assumed that the terminal cost +1 ( , +1 ) = 0, but it could be any convex function representing future costs after . [26]. Therefore, a set of linear constraints ('Benders' cuts') is gradually built and appended to each master problem and the expectation term in (14) - (15) is replaced by the terms 2 and +1 respectively, which represent the future cost for stages 2 to and + 1 to , respectively.…”

Section: Problem Definitionmentioning

confidence: 99%

“…More specifically, upper and lower bounds of the optimal solution are defined and calculated at each iteration, and the algorithm terminates when the distance between these bounds is within a tolerance value. The upper and lower bounds are given by (22)- (23), and convergence of the two bounds is checked at the end of each forward pass run, according to (25), where , represent the mean value and standard deviation of the forward pass optimal objective function values at iteration [26].…”

Section: Problem Definitionmentioning

confidence: 99%

“…A VAR model depicts the evolution of a multivariate stochastic process , as a linear function of the previous instances of the process. Consequently, a ℎ order VAR model has been adopted to represent the -dimensional stochastic process , as expressed in (26), where corresponds to the random variables at , correspond to time-invariant × matrices, − represents the values of time-periods before and is a ×1 error term matrix. The error matrix should contain zero-mean terms (i.e.…”

Section: Sddp Extension For Capturing Multivariate Dependent Uncermentioning

confidence: 99%

“…The problem formulation for the subsequent stages is illustrated in (15), which constitutes a generalization of (14) and symbols are used in the same context. It is assumed that the terminal cost +1 ( , +1 ) = 0, but it could be any convex function representing future costs after .s.t.(1) -(12) In essence, the algorithm determines the optimal decision set for each by building a piece-wise linear outer approximation of + | [ +1 ( , +1 )] and identifying an approximate future cost function +1 ( , +1 ) of +1 at each stage [26]. Therefore, a set of linear constraints ('Benders' cuts') is gradually built and appended to each master problem and the expectation term in (14) - (15) is replaced by the terms 2 and +1 respectively, which represent the future cost for stages 2 to and + 1 to , respectively.…”

mentioning

confidence: 99%

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Stochastic Dual Dynamic Programming for Operation of DER Aggregators Under Multi-Dimensional Uncertainty

Fatouros

Konstantelos

Papadaskalopoulos

et al. 2019

IEEE Trans. Sustain. Energy

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Abstract--The operation of aggregators of distributed energy resources (DER) is highly complex, since it entails the optimal coordination of a diverse portfolio of DER under multiple sources of uncertainty. The large number of possible stochastic realizations that arise, can lead to complex operational models that become problematic in real-time market environments. Previous stochastic programming approaches resort to two-stage uncertainty models and scenario reduction techniques to preserve the tractability of the problem. However, two-stage models cannot fully capture the evolution of uncertain processes and the a priori scenario selection can lead to suboptimal decisions. In this context, this paper develops a novel stochastic dual dynamic programming (SDDP) approach which does not require discretization of either the state space or the uncertain variables and can be efficiently applied to a multi-stage uncertainty model. Temporal dependencies of the uncertain variables as well as dependencies among different uncertain variables can be captured through the integration of any linear multidimensional stochastic model, and it is showcased for a porder vector autoregressive (VAR) model. The proposed approach is compared against a traditional scenario-tree-based approach through a Monte-Carlo validation process, and is demonstrated to achieve a better trade-off between solution efficiency and computational effort.Index Terms--Aggregator, distributed energy resources, multidimensional uncertainty, stochastic dual dynamic programming, vector autoregressive modeling. I. NOMENCLATURE A. IndexesIndex of time periods, running from 1 to . Index of energy storage (ES) units, running from 1 to . Index of flexible loads (FL), running from 1 to . Index of wind turbines (WT), running from 1 to . Index of micro-generators, running from 1 to . B. ParametersEnergy market price at period . Operating cost of micro-generator . Cost of demand shedding. C. VariablesPower sold to (positive)/bought from (negative) the market at period . ,Power output of micro-generator at period . Demand shed at period ., Energy level of ES unit at period . ,Power input (positive) / output (negative) of ES unit at period . , ℎChange of demand of FL at period due to load shifting. ,Demand of FL at period after load shifting., Dispatched wind power output of WT at period . II. INTRODUCTIONA. Background FUNDAMENTAL feature of the emerging Smart Grid paradigm involves the integration of a large number of distributed energy resources (DER) storage units, in order to support the economic operation of the future low-carbon power system [1]- [2]. However, the large number, small individual size and inherent stochasticity characterizing these DER have complicated system scheduling and market coordination. Furthermore, driven by the wide integration of renewable generation in power systems, there is a general consensus to move energy trading as close as possible to real-time [3]- [4], which intensifies the complexity of DER coordination. These challenges have...

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Section: Problem Definitionmentioning

confidence: 99%

Section: Problem Definitionmentioning

confidence: 99%

Section: Problem Definitionmentioning

confidence: 99%

Section: Sddp Extension For Capturing Multivariate Dependent Uncermentioning

confidence: 99%

mentioning

confidence: 99%

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Stochastic Dual Dynamic Programming for Operation of DER Aggregators Under Multi-Dimensional Uncertainty

Fatouros

Konstantelos

Papadaskalopoulos

et al. 2019

IEEE Trans. Sustain. Energy

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Optimizing vaccine distribution in developing countries under natural disaster risk

Seranilla,

Löhndorf

2023

Naval Research Logistics

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For many developing countries, COVID‐19 vaccination roll‐out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy‐makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run smoothly and without delays. We propose a stochastic‐dynamic facility location model that allows policy‐makers to choose vaccination facilities while accounting for possible facility failure. The model is a multi‐stage stochastic variant of the classic facility location problem where disruption risk is modelled as a binary multivariate random process–a problem class that has not yet been studied in the extant literature. To solve the problem, we propose a novel approximate dynamic programming algorithm which trains the shadow price of opening a flood‐prone facility on historical data, thereby alleviating the need to fit a stochastic model. We trained the model using rainfall data provided by the local government of several major cities in the Philippines which are exposed to multiple flooding events per year. Numerical results demonstrate that the solution approach yields approximately 30%–40% lower cost than a baseline approach that does not consider the risk of flooding. Recommendations based on this model were implemented following a collaboration with two large cities in the Philippines which are exposed to multiple flooding events per year.

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Stochastic Dual Dynamic Programming

Füllner

Rebennack

2022

Encyclopedia of Optimization

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Improving the performance of Stochastic Dual Dynamic Programming

Cited by 84 publications

References 11 publications

Stochastic Dual Dynamic Programming for Operation of DER Aggregators Under Multi-Dimensional Uncertainty

Stochastic Dual Dynamic Programming for Operation of DER Aggregators Under Multi-Dimensional Uncertainty

Optimizing vaccine distribution in developing countries under natural disaster risk

Stochastic Dual Dynamic Programming

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