An accurate representation of water delay times for cascaded reservoirs in hydro scheduling problems

Representation of cascaded reservoirs is an important feature in hydrothermal scheduling problems. In particular, consideration of water delay times may be a challenging aspect, due to the large time lags involved into the spatial and time-coupling water conservation constraints. In the literature, such water delay times are usually considered as constant values or even neglected. In this paper, we propose a linear model for the consideration of streamflow routing along the river channels, so that different water delay times may be considered simultaneously between each pair of hydro plants, one for each portion of the total outflow of the upstream plant. In the proposed approach, additional terms for a set of previous time steps are included in the water conservation constraints, whose participation factors are obtained based on streamflow routing curves and on the time discretization considered in the problem. Results are presented for a short term planning problem with a 1 week horizon.