A subgradient-based optimization for reservoirs system management

The problem of determining the optimal operating policy for a system of reservoirs equipped with hydroelectric power plants is a nonlinear programming problem. In general, practitioners have found it hard to solve even a problem for a system with a small number of planning periods and hydroelectric plants using current nonlinear programming techniques. This is due, in large measure, to complex nonlinearities of the power generating functions and a large number of linear equality constraints involved in the model. Furthermore, most reservoirs systems in arid regions have periods of low water level which often results in an empty feasible region adding considerable difficulties to the operational feasibilities of the solutions. In this paper, we provide a general formulation of the water resource allocation problem with explicit engineering details generally omitted or oversimplified in the published literature, and investigate several solution procedures for their applicabilities, and we develop an efficient algorithmic framework exploiting the general water resource system special network structure to solve the linear equality constraints. Practical feasibility of this approach is demonstrated in several applications with a real water resource system.