Short Term Security Constrained Hydrothermal Scheduling Considering Transmission Losses

This paper proposes a Dual Dynamic Programming (DDP) approach to solve a network constrained short term hydrothermal scheduling problem with transmission losses. The DDP methodology, contrary to traditional dynamic programming approaches, approximates the cost-to-go function for each stage by a multistage Benders decomposition. In order to consider the electrical network in detail, an inner loop is performed to solve every stage, where the (quadratic) DC model losses for each line are approximated by a piecewise linear function. Line capacities are also considered. The hydro system is represented in high detail. It includes cascaded reservoirs, several hydraulic constraints and an accurate representation of hydro generation as a multi-dimensional piecewise linear function of storage, turbine and spillage. To assess the approach, a study case based on an IEEE 118 bus system is performed. Convergence properties and the optimal dispatch are compared whether the transmission losses are taken or not into account. The accuracy of the approach proposed is verified. Preliminary studies with the whole Brazilian System is also presented.