A four-dimensional model of hydro generation for the short-term hydrothermal dispatch problem considering head and spillage effects

The generation of a hydroelectric plant is a nonlinear function of the turbined outflow, storage and sometimes also of the spillage. Other aspects, such as forbidden operating zones and individual turbine efficiency curves, are also important. Although for the self-scheduling of a hydro plant a precise integer modeling of the hydro power production function (HPF) is convenient, in the security constrained short-term hydrothermal dispatch problem for large-scale systems a strategy which best balances an accurate representation with an acceptable computational burden is required. In this paper, a detailed review of different approaches to model the HPF is presented, and a new four-dimensional piecewise linear model is proposed. This model takes into account the water head as a function of forebay and tailrace levels and considers spillage effects. Nonconcave regions of the HPF are approximated by using convexification and regression techniques. A major advantage of this approach is to consider the influence of storage, turbined outflow and spillage in a single function that can be used in a straightforward way, instead of deriving several curves for different heads. Numerical results show the applicability of this approach to the day-ahead network constrained short-term hydrothermal dispatch problem of the large Brazilian system.