Multi-stage stochastic optimization applied to energy planning

Pereira, M.V.F.; Pinto, L.M.V.G.

doi:10.1007/bf01582895

Cited by 1,111 publications

(737 citation statements)

References 3 publications

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“…This method was firstly introduced in [18]- [19] for the optimal scheduling of hydrothermal generation systems, driven by the need to model the reservoir interconnections for the future inflow sequences. SDDP has been used to model a variety of operational problems [20].…”

Section: Contributionsmentioning

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: Contributionsmentioning

confidence: 99%

“…see [18], [19], [25]-[28]). The temporal independence assumption implies that the future cost function at each do not depend on the evolution of , which allows cut-sharing among all / belonging at the same time-period at the cost of ignoring timedependence of .…”

Section: Sddp Extension For Capturing Multivariate Dependent Uncermentioning

confidence: 99%

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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“…The latter was introduced in [10] for the optimal scheduling of a hydrothermal generation system, driven by the need to model the reservoir interconnections for the future inflow sequences. The ability of SDDP to refine the solution quality around areas of the state space most likely to occur ('areas of interest') facilitates the solution of high dimensional problems.…”

Section: B Contributionsmentioning

confidence: 99%

A stochastic dual dynamic programming approach for optimal operation of DER aggregators

Fatouros

Konstantelos

Papadaskalopoulos

et al. 2017

2017 IEEE Manchester PowerTech

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Abstract-The operation of aggregators of distributed energy resources (DER) is a highly complex task that is affected by numerous factors of uncertainty such as renewables injections, load levels and market conditions. However, traditional stochastic programming approaches neglect information around temporal dependency of the uncertain variables due to computational tractability limitations. This paper proposes a novel stochastic dual dynamic programming (SDDP) approach for the optimal operation of a DER aggregator. The traditional SDDP framework is extended to capture temporal dependency of the uncertain wind power output, through the integration of an n-order autoregressive (AR) model. This method is demonstrated to achieve a better trade-off between solution efficiency and computational time requirements compared to traditional stochastic programming approaches based on the use of scenario trees.

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“…Such approaches are, for example, stochastic decomposition methods for multistage models (see [20]), approximate dynamic programming (see [17]), and Stochastic Dual Dynamic Programming (SDDP), initiated in [13], revisited in [16,22], and also studied in the present paper.…”

Section: Introductionmentioning

confidence: 99%

SDDP for multistage stochastic linear programs based on spectral risk measures

Guigues

Römisch

2012

Operations Research Letters

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a b s t r a c tWe consider risk-averse formulations of multistage stochastic linear programs. For these formulations, based on convex combinations of spectral risk measures, risk-averse dynamic programming equations can be written. As a result, the Stochastic Dual Dynamic Programming (SDDP) algorithm can be used to obtain approximations of the corresponding risk-averse recourse functions. This allows us to define a risk-averse nonanticipative feasible policy for the stochastic linear program. Formulas for the cuts that approximate the recourse functions are given. In particular, we show that some cut coefficients have analytic formulas.

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Multi-stage stochastic optimization applied to energy planning

Cited by 1,111 publications

References 3 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

A stochastic dual dynamic programming approach for optimal operation of DER aggregators

SDDP for multistage stochastic linear programs based on spectral risk measures

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