Stochastic optimization for long term operation of multiple reservoirs. A new approach

The study emphasis of optimal scheduling of reservoir system operations has shifted to stochastic mathematical programming since future reservoir inflows are uncertain and recent advances in stochastic programming. Two techniques have been used extensively in this area. The first approach is chance constraint programming. Chance constraints incorporate the uncertainty of streamflows and insure that the reliability of system output and/or state variables is above a prescribed value. The optimal policy is one which optimizes the objectives while satisfying the reliability levels and other deterministic constraints. The stochastic dynamic programming (SDP) is the second technique used in stochastic programming for reservoirs. It is widely used for small reservoir systems. Unfortunately when the number of reservoirs in the system increases to four or greater the computation time increases dramatically. Foufoula-Georgiou and Kitanidis developed stochastic Gradient DP (GDP)which has promise to solve for optimal controls of systems with more than four reservoirs. Within a DP algorithm, continuous functions are fit to probabilistic return functions at each time period. Optimal operations at each subperiod are then determined by a constrained Newton-type procedure. The dynamic programming methodology is then used to determine the best operations over the entire time domain.