Optimization of hydropower systems operation with a quadratic model

Abstract This paper is devoted to the development and application of a reservoir optimization model that yields monthly release policies. The generalization consists of the capability to handle nonlinear energy generation rates in the objective function (maximization of system annual energy generation). A quadratic model for the elevation-storage (average storage) curve is used. The optimization problem is described and formulated as the optimal control of a multivariable state-space model in which the state and control vectors are constrained by sets of equality and inequality relations. Lagrange and Kuhn-Tucker multipliers are used to adjoin these equality and inequality constraints to the objective functions. The resulting cost functional is maximized by using the minimum norm formulation of the functional analysis. Numerical results are reported for a real system in operation consisting of three rivers; each river has two series reservoirs.