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An Analytical Method for Fast Optimization of Multireservoir Hydropower Systems Operations Considering Risk-Return Tradeoffs

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Water Resources Research 2025年第6期61卷

作者： S. Jamshid Mousavi Kumaraswamy Ponnambalam Department of Civil and Environmental Engineering Amirkabir University of Technology Tehran Iran Department of Systems Design Engineering University of Waterloo Waterloo ON Canada

Long-term multireservoir operations optimization is challenging for existing optimization methods such as stochastic dynamic programming (SDP) and implicit stochastic programming (ISP) suffering from excessive computing time requirements. More difficult is to tackle a risk-based optimization problem and provide an efficient frontier of the objective function for multireservoir systems. The Fletcher–Ponnambalam (FP) method is an explicit stochastic optimization method suitable for multireservoir operations optimization which faces no curse of dimensionality of SDP and has no need for scenario generations of ISP, thus is extremely fast. Earlier implementations have developed expressions for mean and variance of storages and releases, including deficits and surpluses, to estimate fairly accurate values of the linear and quadratic objective functions when compared with other well-known methods. This paper introduces analytical derivations of hydropower equations to be used in the recent extension of the FP method and applies it to a long-term operations optimization problem of a three-reservoir system in Iran. The objective function is to maximize the expected value of the annual energy, which is a multiplicative nonlinear function of both releases and storage levels. The computational results from simulations for the 60 years of available inflow data for the chosen multireservoir system using the policies derived by the FP, ISP, and SDP methods were compared. The solution qualities were nearly the same, but the FP method has tremendous speedups over the other methods. Secondly, expressions for the variances of monthly energy productions were derived to compute efficient frontier for risk-return tradeoffs of annual energy to guide decision makers. Analytic expressions are derived for the moments of energy function to be used in hydropower multireservoir operations optimization, not considered before The derived expressions for the second moment of the generated energy i

关键词： multireservoir hydropower operations stochastic dynamic programming implicit stochastic programming risk and efficient frontier

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