Scenario reduction and scenario tree construction for power management problems

Gröwe-Kuska, Nicole; Heitsch, Holger; Römisch, Werner

doi:10.1109/ptc.2003.1304379

Cited by 546 publications

(454 citation statements)

References 12 publications

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Section: B 6h Operating Horizon Case Studymentioning

confidence: 99%

“…Regarding the latter approach, a multivariate copula model [16] has been fit to the available data, and 5,000 scenarios have been sampled from this model. In order to comprehensively investigate the performance of this approach, six scenario trees of varying complexity have been formed based on the initial set of 5,000 scenarios (Table II), by employing a standard scenario reduction process based on Kantorovich distance [33].Regarding the proposed SDDP approach, the dependencies of the multidimensional uncertainty set are captured through a VAR(1) model, which has been fit to the same set of 5,000 scenarios. Autoregressive models require that the fitted data are stationary i.e.…”

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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: B 6h Operating Horizon Case Studymentioning

confidence: 99%

mentioning

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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“…This study uses the same set of 50 scenarios generated in [12] for the random day-ahead market spot prices λ D , which resulted from applying a scenario reduction algorithm [18] to the complete set of historic data available from June 2007 to May 2010 that are available at the website of the Independent Iberian Market Operator OMIE [27]. As we will see, the imposition of emissions constraints could change the optimal bid of the market participant and, consequently, the series of clearing prices.…”

Section: Data Setmentioning

confidence: 99%

Stochastic optimal generation bid to electricity markets with emissions risk constraints

Heredia

Cifuentes-Rubiano

Corchero

2018

Journal of Environmental Management

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There are many factors that influence the day-ahead market bidding strategies of a generation company (GenCo) within the framework of the current energy market. Environmental policy issues are giving rise to emission limitation that are becoming more and more important for fossil-fueled power plants, and these must be considered in their management. This work investigates the influence of the emissions reduction plan and the incorporation of the medium-term derivative commitments in the optimal generation bidding strategy for the day-ahead electricity market. Two different technologies have been considered: the high-emission technology of thermal coal units and the low-emission technology of combined cycle gas turbine units. The Iberian Electricity Market (MIBEL) and the Spanish National Emissions Reduction Plan (NERP) defines the environmental framework for dealing with the day-ahead market bidding strategies. To address emission limitations, we have extended some of the standard risk management methodologies developed for financial markets, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), thus leading to the new concept of Conditional Emission at Risk (CEaR). This study offers electricity generation utilities a mathematical model for determining the unit's optimal generation bid to the wholesale electricity market such that it maximizes the long-term profits of the utility while allowing it to abide by the Iberian Electricity Market rules as well as the environmental restrictions set by the Spanish National Emissions Reduction Plan. We analyze the economic implications for a GenCo that includes the environmental restrictions of this National Plan as well as the NERP's effects on the expected profits and the optimal generation bid.

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“…An ARIMA(5,1,2) model has been fit to the historical wind power output data and then a sufficient number of scenarios have been sampled and used both for fitting the AR(1) model and constructing scenario tree representations of varying degrees of complexity. As presented at Table II, six scenario trees were constructed according to a scenario reduction process based on Kantorovich distance [13]. In order to compare the solution efficiency and quantify the expected benefit of the seven models, out-of-sample Monte Carlo validation is used.…”

Section: A Case Study Descriptionmentioning

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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Scenario reduction and scenario tree construction for power management problems

Cited by 546 publications

References 12 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

Stochastic optimal generation bid to electricity markets with emissions risk constraints

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

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