Journal Article

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

Mousavi, S. Jamshid, Ponnambalam, Kumaraswamy

2025

Overview

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. Plain Language Summary Optimizing long‐term operations for multiple reservoirs is difficult with traditional methods like stochastic dynamic programming (SDP) and implicit stochastic programming (ISP) because they require a lot of computing time. It's even harder to address risk‐based optimization and to create an efficient frontier, which shows the best trade‐offs between different goals. The Fletcher–Ponnambalam (FP) method is a fast and effective solution that doesn't suffer from the complexity issues of SDP and doesn't need scenario generations like ISP. Previous versions of the FP method could accurately estimate values using mean and variance of storage and releases. This paper improves the FP method by introducing new hydropower equations and applies it to optimize a three‐reservoir system in Iran over 60 years of inflow data. The goal is to maximize annual energy, a complex function of water releases and storage levels. The FP method produced solutions comparable in quality to SDP and ISP but was much faster. Additionally, new calculations for monthly energy variance were developed to help make better risk‐return decisions for annual energy production. Key Points 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 is used to produce efficient frontier easily for annual hydroenergy production function The Fletcher–Ponnambalam (FP) results are better than stochastic dynamic programming and comparable to implicit stochastic programming but much faster than these methods

• Publisher: John Wiley & Sons, Inc,Wiley
• Subject: and efficient frontier / Computing time / Dynamic programming / Energy / Hydroelectric power / implicit stochastic programming / Inflow / Methods / multireservoir hydropower operations / Objective function / Optimization / Risk / stochastic dynamic programming / Stochastic programming / Stochasticity / Tradeoffs