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.

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In September 2000, the Brazilian system dispatch and spot prices were calculated twice, using different inflow forecasts for that month, as in the last 5 days of August the inflows to the reservoirs in the South and Southeast regions changed 200%. The first run used a smaller forecasted energy inflow and the second used a higher energy inflow. Contrary to expectations, the spot price in the second run, with the higher energy inflow, was higher than the one found in the first run. This paper describes the problem, presents the special features of the PAR(p) model that allow the described behavior, and shows the solution taken to avoid the problem.

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