A two stage Bayesian stochastic optimization model for cascaded hydropower systems considering varying uncertainty of flow forecasts

Copyright © 2014 American Geophysical UnionThis paper presents a new Two Stage Bayesian Stochastic Dynamic Programming (TS-BSDP) model for real time operation of cascaded hydropower systems to handle varying uncertainty of inflow forecasts from Quantitative Precipitation Forecasts. In this model, the inflow forecasts are considered as having increasing uncertainty with extending lead time, thus the forecast horizon is divided into two periods: the inflows in the first period are assumed to be accurate, and the inflows in the second period assumed to be of high uncertainty. Two operation strategies are developed to derive hydropower operation policies for the first and the entire forecast horizon using TS-BSDP. In this paper, the newly developed model is tested on China's Hun River cascade hydropower system and is compared with three popular stochastic dynamic programming models. Comparative results show that the TS-BSDP model exhibits significantly improved system performance in terms of power generation and system reliability due to its explicit and effective utilization of varying degrees of inflow forecast uncertainty. The results also show that the decision strategies should be determined considering the magnitude of uncertainty in inflow forecasts. Further, this study confirms the previous finding that the benefit in hydropower generation gained from the use of a longer horizon of inflow forecasts is diminished due to higher uncertainty and further reveals that the benefit reduction can be substantially mitigated through explicit consideration of varying magnitudes of forecast uncertainties in the decision-making process.National Natural Science Foundation of ChinaHun River cascade hydropower reservoirs development company, Ltd.UK Royal Academy of Engineerin

Using stochastic dual dynamic programming in problems with multiple near-optimal solutions

Stochastic dual dynamic programming (SDDP) is one of the few algorithmic solutions available to optimize large‐scale water resources systems while explicitly considering uncertainty. This paper explores the consequences of, and proposes a solution to, the existence of multiple near‐optimal solutions (MNOS) when using SDDP for mid or long‐term river basin management. These issues arise when the optimization problem cannot be properly parametrized due to poorly defined and/or unavailable data sets. This work shows that when MNOS exists, (1) SDDP explores more than one solution trajectory in the same run, suggesting different decisions in distinct simulation years even for the same point in the state‐space, and (2) SDDP is shown to be very sensitive to even minimal variations of the problem setting, e.g., initial conditions—we call this “algorithmic chaos.” Results that exhibit such sensitivity are difficult to interpret. This work proposes a reoptimization method, which simulates system decisions by periodically applying cuts from one given year from the SDDP run. Simulation results obtained through this reoptimization approach are steady state solutions, meaning that their probability distributions are stable from year to year

Delta-hedging a hydropower plant using stochastic programming

An important challenge for hydropower producers is to optimize reservoir discharges, which is subject to uncertainty in inflow and electricity prices. Furthermore, the producers want to hedge the risk in the operating profit. This article demonstrates how stochastic programming can be used to solve a multireser-voir hydro scheduling case for a price-taking producer, and how such a model can be employed in subsequent delta-hedging of the electricity portfolio

A game theory–reinforcement learning (GT–RL) method to develop optimal operation policies for multi-operator reservoir systems

Reservoir systems with multiple operators can benefit from coordination of operation policies. To maximize the total benefit of these systems the literature has normally used the social planner\u27s approach. Based on this approach operation decisions are optimized using a multi-objective optimization model with a compound system\u27s objective. While the utility of the system can be increased this way, fair allocation of benefits among the operators remains challenging for the social planner who has to assign controversial weights to the system\u27s beneficiaries and their objectives. Cooperative game theory provides an alternative framework for fair and efficient allocation of the incremental benefits of cooperation. To determine the fair and efficient utility shares of the beneficiaries, cooperative game theory solution methods consider the gains of each party in the status quo (non-cooperation) as well as what can be gained through the grand coalition (social planner\u27s solution or full cooperation) and partial coalitions. Nevertheless, estimation of the benefits of different coalitions can be challenging in complex multi-beneficiary systems. Reinforcement learning can be used to address this challenge and determine the gains of the beneficiaries for different levels of cooperation, i.e., non-cooperation, partial cooperation, and full cooperation, providing the essential input for allocation based on cooperative game theory. This paper develops a game theory-reinforcement learning (GT-RL) method for determining the optimal operation policies in multi-operator multi-reservoir systems with respect to fairness and efficiency criteria. As the first step to underline the utility of the GT-RL method in solving complex multi-agent multi-reservoir problems without a need for developing compound objectives and weight assignment, the proposed method is applied to a hypothetical three-agent three-reservoir system

Valuing year-to-go hydrologic forecast improvements for a peaking hydropower system in the Sierra Nevada

We assessed the potential value of hydrologic forecasting improvements for a snow-dominated high-elevation hydropower system in the Sierra Nevada of California, using a hydropower optimization model. To mimic different forecasting skill levels for inflow time series, rest-of-year inflows from regression-based forecasts were blended in different proportions with representative inflows from a spatially distributed hydrologic model. The statistical approach mimics the simpler, historical forecasting approach that is still widely used. Revenue was calculated using historical electricity prices, with perfect price foresight assumed. With current infrastructure and operations, perfect hydrologic forecasts increased annual hydropower revenue by $0.14 to$1.6 million, with lower values in dry years and higher values in wet years, or about $0.8 million (1.2%) on average, representing overall willingness-to-pay for perfect information. A second sensitivity analysis found a wider range of annual revenue gain or loss using different skill levels in snow measurement in the regression-based forecast, mimicking expected declines in skill as the climate warms and historical snow measurements no longer represent current conditions. The value of perfect forecasts was insensitive to storage capacity for small and large reservoirs, relative to average inflow, and modestly sensitive to storage capacity with medium (current) reservoir storage. The value of forecasts was highly sensitive to powerhouse capacity, particularly for the range of capacities in the northern Sierra Nevada. The approach can be extended to multireservoir, multipurpose systems to help guide investments in forecasting