Scenario tree reduction in stochastic programming with recourse for hydropower operations

Xu, Bin; Zhong, Ping‐an; Zambon, Renato C.; Zhao, Yong; Yeh, William W.‐G.

doi:10.1002/2014wr016828

Cited by 64 publications

(28 citation statements)

References 44 publications

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“…The established approach to incorporating information from the spread of the ensemble is multi-stage stochastic optimisation, which applies a reduced form of the ensemble known as a scenario tree to guide corrective decisions as new forecast data are revealed (Shapiro et al, 2014). Whilst this approach has been applied in a handful of water-related studies, including short-horizon problems (Raso et al, 2014) as well as using seasonal streamflow forecasts (Housh et al, 2013;Xu et al, 2015), it relies on arbitrary decisions (such as the preferred scenario tree nodal structure), and it is computationally demanding and highly complex, making experimentation laborious and results hard to diagnose. For these rea- Simulations use the rolling horizon model with a perfect 12-month (observed) inflow forecast, applied to 95 % reliability reservoirs with draft ratio of 0.5.…”

Section: Forecast-informed Scheme: Rolling Horizon Adaptive Controlmentioning

confidence: 99%

Complex relationship between seasonal streamflow forecast skill and value in reservoir operations

Turner

Bennett

Robertson

et al. 2017

Hydrol. Earth Syst. Sci.

110

105

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Abstract. Considerable research effort has recently been directed at improving and operationalising ensemble seasonal streamflow forecasts. Whilst this creates new opportunities for improving the performance of water resources systems, there may also be associated risks. Here, we explore these potential risks by examining the sensitivity of forecast value (improvement in system performance brought about by adopting forecasts) to changes in the forecast skill for a range of hypothetical reservoir designs with contrasting operating objectives. Forecast-informed operations are simulated using rolling horizon, adaptive control and then benchmarked against optimised control rules to assess performance improvements. Results show that there exists a strong relationship between forecast skill and value for systems operated to maintain a target water level. But this relationship breaks down when the reservoir is operated to satisfy a target demand for water; good forecast accuracy does not necessarily translate into performance improvement. We show that the primary cause of this behaviour is the buffering role played by storage in water supply reservoirs, which renders the forecast superfluous for long periods of the operation. System performance depends primarily on forecast accuracy when critical decisions are made -namely during severe drought. As it is not possible to know in advance if a forecast will perform well at such moments, we advocate measuring the consistency of forecast performance, through bootstrap resampling, to indicate potential usefulness in storage operations. Our results highlight the need for sensitivity assessment in value-of-forecast studies involving reservoirs with supply objectives.

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Section: Forecast-informed Scheme: Rolling Horizon Adaptive Controlmentioning

confidence: 99%

Complex relationship between seasonal streamflow forecast skill and value in reservoir operations

Turner

Bennett

Robertson

et al. 2017

Hydrol. Earth Syst. Sci.

110

105

View full text Add to dashboard Cite

show abstract

“…The random variables are often described by a known probability distribution, a set of statistical moments, or likelihood scenarios. Given that the description of the continuous stochastic process would intensify the modeling effort of the problem, a set of discretized scenarios [17,18] is employed as an alternative and the model is discretized and solved accordingly. Stochastic programming that uses scenario-tree as the uncertainty descriptions [19] have been verified to outperform Stochastic Dynamic Programming (SDP) [20] and Sampling Stochastic Dynamic Programming (SSDP) models [21] that use Markov processes or historical realization samples.…”

Section: Simulation Modelsmentioning

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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“…In the field of mathematical optimization, stochastic optimization is a framework for modeling optimization problems that involve uncertainties. Stochastic optimization has applications in a broad range of areas, ranging from finance to transportation to energy optimization [27][28][29][30][31]. Stochastic optimization has been found to be an effective tool to address uncertainties within the model and provide a better understanding of optimization results.…”

Section: Introductionmentioning

confidence: 99%

Risk Analysis for Reservoir Real-Time Optimal Operation Using the Scenario Tree-Based Stochastic Optimization Method

Sun

Zhu

Chen

et al. 2018

Water

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The inherent uncertainty of inflow forecasts hinders the reservoir real-time optimal operation. This paper proposes a risk analysis model for reservoir real-time optimal operation using the scenario tree-based stochastic optimization method. We quantify the probability distribution of inflow forecast uncertainty by developing the relationship between two forecast accuracy metrics and the standard deviation of relative forecast error. An inflow scenario tree is generated via Monte Carlo simulation to represent the uncertain inflow forecasts. We establish a scenario tree-based stochastic optimization model to explicitly incorporate inflow forecast uncertainty into the stochastic optimization process. We develop a risk analysis model based on the principle of maximum entropy (POME) to evaluate the uncertainty propagation process from flood forecasts to optimal operation. We apply the proposed methodology to a flood control system in the Daduhe River Basin, China. In addition, numerical experiments are carried out to investigate the effect of two different forecast accuracy metrics and different forecast accuracy levels on reservoir optimal flood control operation as well as risk analysis. The results indicate that the proposed methods can provide decision-makers with valuable risk information for guiding reservoir real-time optimal operation and enable risk-informed decisions to be made with higher reliabilities.

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Scenario tree reduction in stochastic programming with recourse for hydropower operations

Cited by 64 publications

References 44 publications

Complex relationship between seasonal streamflow forecast skill and value in reservoir operations

Complex relationship between seasonal streamflow forecast skill and value in reservoir operations

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

Risk Analysis for Reservoir Real-Time Optimal Operation Using the Scenario Tree-Based Stochastic Optimization Method

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