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Simulation-and Discretization-Free Explicit Stochastic Reservoir Operation Optimization Method
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  • Kumaraswamy Ponnambalam,
  • S Jamshid Mousavi,
  • Alcigeimes B Celeste,
  • Ximing Cai
Kumaraswamy Ponnambalam
University of Waterloo

Corresponding Author:ponnu@uwaterloo.ca

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S Jamshid Mousavi
Amirkabir University of Technology
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Alcigeimes B Celeste
Federal University of Sergipe
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Ximing Cai
University of Illinois at Urbana
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The Fletcher-Ponnambalam (FP) method is an explicit stochastic optimization method for design and operations management of storage systems. It has been applied successfully in many real-world operations optimization problems (for example, the Great Lakes system and the Parambikulam-Aliyar project) and groundwater management problems. The FP method faces no curse of dimensionality unlike stochastic dynamic programming (SDP) and no need for scenarios generation as in implicit stochastic programming (ISP) methods. The paper introduces a novel implementation for the FP method by removing the need for nonlinear constraints and by decreasing the number of decision variables to just one third of its original value, significantly reducing solving time (~27 times faster than the original formulation). Additionally, new expressions derived for first and second moments of both reservoir release deficit and spill terms and the already-derived expression for second moments of reservoir storage are incorporated into the new formulation enabling the FP method to reach an improved optimality for a nonlinear objective function. The enhanced procedure is applied to solving a water reservoir operation optimization problem for a major dam in Brazil. The result comparisons made with SDP, two-stage stochastic programming and ISP along with a thorough analysis of release operation policies for both non-Gaussian correlated and Gaussian independent inflows prove the optimality of this highly numerically efficient and convenient-to-use FP method.