Optimal operation of multi-reservoir systems under uncertainty

The principal purpose of a reservoir system is to provide inertia against variable inflows so as to make more profitable use of the water possible. The principal design factor to bring about this inertia is the storage of the reservoir. A second important factor is the operational management. Both define the inertia a reservoir provides against variable inflows. Traditional optimization models are based on deriving a release policy that optimizes a given objective. Such approaches do not account for the fact that the release, which is a function of random inflow and thus a random variable itself, may have a distribution with different variance measure based on the available forecasts. Work is in progress to develop a mean-variance model within nonlinear optimization framework in desire to minimize variance of the objective to obtain robust (maximum return) operating policy. The parameter iteration method (Gal, 1979) is used to find an approximation for the optimal policy of a dynamic system dependent on stochastic state variables. The solution method is suitable for systems that would otherwise be difficult to solve by stochastic dynamic programming (SDP) approach. The parameter iteration method seeks to determine the correct coefficients of the remaining benefit function of an assumed form. The remaining benefit function defines the expected value (benefit) of the water remaining in the reservoir at the end of a given period, and is analogous to an expected value of the Cost-to-Go or Bellman function of deterministic dynamic programming. The benefit at the end of the operating horizon acts as a boundary condition (Bras et al., 1983) for real-time implementation. This iterative procedure converges to the optimal remaining benefit functions, and the solution from the remaining benefit function is identical to that obtained by stochastic dynamic programming (SDP). Once the optimal remaining benefit functions and forecasted inflows for the next periods are available, optimal releases for the next periods can be determined for deterministic and probabilistic (expected return) scenarios. The influence of forecasts of different lengths and their uncertainty on river system management are under study for three multi-reservoir systems: the Salt River Project (SRP) in Arizona, Lewis River Basin in Washington and the Santa Ynez River Basin in Southern California. Copyright ASCE 2004.