On convexity issues of short-term hydrothermal scheduling

This paper introduces a convex and normally constrained hydrothermal scheduling method. Convexity is achieved by using a hydro water loss term and a piece-wise linear representation of the relationship between water head and volume. A basic technique is developed for obtaining normal constraints, developed for the first time in this paper, by converting the conditional constraints into unconditional constraints. An example of the conditional constraints is the hydrothermal unit on/off status being expressed as a function of the unit minimum up/down times. Unit start-up and shut-down variables are summed over the minimum-up time and the minimum-down time and the summations are being limited to one. In each case this is to prevent immature unit start-up or shut-down. This allows the hydrothermal scheduling problem to become an ordinary mixed integer problem that can be solved by using standard commercial mixed integer programming solvers. These solvers can be purchased on the market for a few thousand dollars, far below the prices of the specially designed hydrothermal scheduling software products from consulting firms. The algorithm developed in this paper is tested for different cases with good results, especially for small hydrothermal systems.