CVaR-based factorial stochastic optimization of water resources systems with correlated uncertainties

Wang, Y. Y.; Huang, Guohe; Wang, Shuo

doi:10.1007/s00477-016-1276-9

Cited by 16 publications

(5 citation statements)

References 39 publications

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“…The revenue from energy production and cost of energy purchase can be determined once the monetary value of energy purchase can be quantified using spot price λ . As discussed by Wang et al [32], λ also represents the decision makers' risk preference toward uncertain real-time markets besides the economic interpretation. The sensitivity tests on the influence of λ on the model results are essential for informed decision-making when forecasting λ becomes difficult for either economic reasons or risk preference reasons.…”

Section: Net Revenue Resultsmentioning

confidence: 99%

Analysis of a Stochastic Programming Model for Optimal Hydropower System Operation under a Deregulated Electricity Market by Considering Forecasting Uncertainty

Zhong

Du³

et al. 2018

Water

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In a deregulated electricity market, optimal hydropower operation should be achieved through informed decisions to facilitate the delivery of energy production in forward markets and energy purchase level from other power producers within real-time markets. This study develops a stochastic programming model that considers the influence of uncertain streamflow on hydropower energy production and the effect of variable spot energy prices on the cost of energy purchase (energy shortfall). The proposed model is able to handle uncertainties expressed by both a probability distribution and discretized scenarios. Conflicting decisions are resolved by maximizing the expected value of net revenue, which jointly considers benefit and cost terms under uncertainty. Methodologies are verified using a case study of the Three Gorges cascade hydropower system. The results demonstrate that optimal operation policies are derived based upon systematic evaluations on the benefit and cost terms that are affected by multiple uncertainties. Moreover, near-optimal operation policy under the case of inaccurate spot price forecasts is also analyzed. The results also show that a proper policy for guiding hydropower operation seeks the best compromise between energy production and energy purchase levels, which explores their nonlinear tradeoffs over different time periods.

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Section: Net Revenue Resultsmentioning

confidence: 99%

Analysis of a Stochastic Programming Model for Optimal Hydropower System Operation under a Deregulated Electricity Market by Considering Forecasting Uncertainty

Zhong

Du³

et al. 2018

Water

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“…The CVaR (Wang et al., 2016) or expected shortfall, which is a criterion suitable for assessing the mean value of an outcome from undesirable cases, was used originally in the field of finance to measure expected losses above a certain loss threshold (Value‐at‐Risk, VaR):

CVa{R}_{\alpha }(L)=E\left\{L\vert L\ge Va{R}_{\alpha }(L)\right\},

Va{R}_{\alpha }(L)=\mathrm{max}\left\{l\vert P(L\ge l)\ge \alpha \right\},

where

L

is the random variable of loss,

\alpha

is the confidence level (

\alpha \in [0,1]

E\left\{\cdot \right\}

is the expected value function, and

Va{R}_{\alpha }(L)

is the VaR that evaluates the maximum loss such that the probability of exceeding the loss is

\alpha

. A schematic of the relationship between

\mathrm{E}(L)

Va{R}_{\alpha }(L)

, and

CVa{R}_{\alpha }(L)

is shown in Figure 2.…”

Section: Methodsmentioning

confidence: 99%

“…The CVaR (Wang et al, 2016) or expected shortfall, which is a criterion suitable for assessing the mean value of an outcome from undesirable cases, was used originally in the field of finance to measure expected losses above a certain loss threshold (Value-at-Risk, VaR):…”

Section: Robustness Metrics and General Model Formulationmentioning

confidence: 99%

Scenario‐Based Multiobjective Robust Optimization and Decision‐Making Framework for Optimal Operation of a Cascade Hydropower System Under Multiple Uncertainties

Sun

Huang

et al. 2022

Water Resources Research

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Hydropower, which has long been recognized as an effective and reliable source of renewable energy, accounted for 70% of total renewable energy production in 2016. In addition to provision of clean renewable energy, large hydropower systems are often operated on a long-term schedule with multiobjective requirements such as maintaining flood control, water supply, navigation, and ecological protection (Liu et al., 2020;Xu et al., 2015Xu et al., , 2020. In recent years, following the rapid development globally of intermittent renewable energy sources (e.g., wind and solar energy) to address degraded environmental quality and problems associated with climate change, operation of hydropower systems must now incorporate new tasks associated with integration and stabilization of the uncertain energy production by these intermittent renewable sources (Liu et al., 2019). To enhance comprehensive benefit through delivery of water and energy to the multiobjective demand side, joint operation of reservoir systems with capability to coordinate spatiotemporal water release and water head is essential to resolve conflicts regarding the allocation of water and energy resources to competing demands. In practical application of realtime hydropower operation based on forecasts, one of the most critical challenges in informing multiobjective and joint reservoir operation is how best to make efficient and robust decisions under the condition of uncertainty owing to incomplete knowledge and inaccurate forecasts, such that negative consequences of imbalanced demand and supply are manageable and expected returns or costs are acceptable (Roach et al., 2016).Forecast errors are widely recognized as the primary factors affecting the reliability of hydropower operation strategies (Xu, Liu, et al., 2021), especially in the long-term planning horizon, because forecast models have inherent uncertainties attributable to their input, structure, and parameters in addition to errors associated with human-induced impression or fuzziness (Li et al., 2011;Mo et al., 2021). Under the perturbation of error sources,

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“…Zhang et al (2017) proposed historical and future operating methods for deriving adaptive operating rules considering both historical information and future projections of a WMS. The varied availability of surface water could be obtained by Monte Carlo 6 sampling in a numerical model (Liu et al, 2017); and 3) Correlated uncertainties could also be determined using statistical methods (e.g., relevance analysis and copula functions) (Wang et al, 2017). As flexible statistical approaches, Bayesian and copula methods can capture the joint distributions of correlated parameters at different time scales (Ren et al, 2020;Xu and Valocchi, 2015;Yang et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Coupling ecological water requirement to optimize water resources under changing climatic conditions

Yue

Liu

et al. 2021

Preprint

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Meeting ecological water requirements (EWR) is important for guaranteeing watershed system stability in many arid and semi-arid lands. Rainfall–runoff relationships under the effects of climate change may induce many adverse changes for EWR. Inherent uncertainties in water resources management and potential variations in EWR should both be considered to obtain desired water allocation strategies under changing climatic conditions. In this research, an integrated approach was proposed through incorporation of copula functions and a Markov Chain Monte Carlo (MCMC) simulation into a general chance-constrained programming (CCP) modeling framework. The proposed method was found effective for water resource management with respect to the following: (a) tackling correlated features in watershed rainfall and inflow under climate change based on copula–MCMC simulations, (b) obtaining runoff distributions using the copula sampling method under multiple climate change scenarios, (c) analyzing fluctuations of EWR based on varied monthly flows with consideration of diverse runoff distributions, and (d) obtaining desired water allocation strategies through the developed CCP model with consideration of EWR and water shortage risks. Application of the developed method to water resources management in the city of Dalian (China) indicated that the EWR in the watersheds of Dalian would suffer large variations under changing climatic conditions. Moreover, in comparison with the supply in 2025, the increase of water supply from transferring water from the Dahuofang Reservoir (Hun River) would be 6942–33,772, 6942–25,472, and 2849–14,259 Mt with risk tolerance levels of 20%, 50%, and 80%, respectively.

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CVaR-based factorial stochastic optimization of water resources systems with correlated uncertainties

Cited by 16 publications

References 39 publications

Analysis of a Stochastic Programming Model for Optimal Hydropower System Operation under a Deregulated Electricity Market by Considering Forecasting Uncertainty

Analysis of a Stochastic Programming Model for Optimal Hydropower System Operation under a Deregulated Electricity Market by Considering Forecasting Uncertainty

Scenario‐Based Multiobjective Robust Optimization and Decision‐Making Framework for Optimal Operation of a Cascade Hydropower System Under Multiple Uncertainties

Coupling ecological water requirement to optimize water resources under changing climatic conditions

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