Hydropower unit commitment with nonlinearity decoupled from mixed integer nonlinear problem

Abstract

This paper formulates a nonlinear and discrete hydropower unit commitment (UC) problem, which is particular useful to coordinate with the higher level operation of cascaded hydropower reservoirs. Given the outflow process, this UC problem maximizes energy production during a planning horizon, to determine the unit operating zones and allocate the release among units in one hydroplant. This work shows how the constraints on the start-up number and up/down hours can be transformed into linear equations. The objective is equivalently interpreted to sequentially minimize spillages, maximize generation efficiency, and maximize energy production, which makes it possible to handle the nonlinearity in a low-dimensional space due to the lowest priority of the third sub-objective where the nonlinearity comes. The UC problem is skillfully decomposed into a zone commitment (ZC) that determines the optimal operating zones using the mixed integer linear programming, and one-stage sub-problems that allocate the outflow among units using the hill-climbing method. The case studies that deal with quarter-hourly hydropower unit commitments during a day show that the present model and procedure turn out to be efficient for a UC problem with up to four units, becoming volatile then on, but still acceptable for up to nine units.