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

Forecast errors of multiple information sources of a cascade hydropower system cause risks of water and energy supply in real-time operation. Mechanisms minimizing multiple risks with budgeted cost under oscillations of multiple forecast uncertainties through robust operation are not yet well-investigated. This study proposed a multiobjective robust optimization (RO) and decision-making framework comprising series of models for risk analysis, robust control, and decision making. The risk analysis model identifies and analyzes dependent risks that stem from forecast errors of supply and demand-side information by Copula functions. A RO model was established for minimizing risk probabilities, vulnerabilities of ecological protection, water and energy supply, as well as revenue loss from energy. Thereafter, a multiattribute decision-making model was incorporated for determining the compromise solution from competing non-dominated solutions. The proposed framework was applied to the cascade hydropower system of the Xiluodu, Xiangjiaba, Three Gorges project and Gezhouba reservoirs on the Yangtze River, China. The principal findings were as follows. (a) Addressing the singular forecast uncertainty of streamflow is inadequate to obtain robust solutions. (b) In a normal year, RO can reduce the average conditional value-at-risk of ecological water shortfall, consumptive water shortfall, and energy shortfall by 25.1%, 35.3%, and 16.5% than that of chance-constrained programming. (c) Multiple risks are dispersed through risk avoidance and hedging that reduces outflow variance and homogenizes mean outflow, lowering down efficiencies of energy production and water usage as a tradeoff. The proposed model framework could be applied to inform operation of cascade hydropower systems.