A Simultaneous Dynamic Optimization Approach to Address Restoration Policies in Reservoirs

Abstract

In this work, we develop a dynamic optimization model for a Paso de las Piedras reservoir, which supplies drinking water for more than 400,000 inhabitants and for industrial purposes, to determine restoration policies for algal growth control. A biogeochemical model has been formulated within a simultaneous dynamic optmization framework to solve the optimal control problem whose solution provides limiting nutrient inflow profiles to the lake and in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space. Spatial discretization has been performed in two layers. Simultaneous approaches proceed by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with a successive quadratic programming algorithm. Numerical results provide profiles for both tributary derivation through a wetland and zooplanktivorous fish removal rate.