UC Santa Barbara

A quadratic optimization model is applied to a large‐scale reservoir system to obtain operation schedules. The model has the minimum possible dimensionality, treats spillage and penstock releases as decision variables and takes advantage of system‐dependent features to reduce the size of the decision space. An efficient and stable quadratic programming active set algorithm is used to solve for the optimal release policies. The stability and convergence of the solution algorithm are ensured by the factorization of the reduced Hessian matrix and the accurate computation of the Lagrange multipliers. The quadratic model is compared with a simplified linear model and it is found that optimal release schedules are robust to the choice of model, both yielding an increase of nearly 27% in the total annual energy production with respect to conventional operation procedures, although the quadratic model is more flexible and of general applicability. The adequate fulfillment of other system functions such as flood control and water supply is guaranteed via constraints on storage and spillage variables. Copyright 1985 by the American Geophysical Union.