Comparison between Closed-Loop and Partial Open-Loop Feedback Control Policies in Long-Term Hydrothermal Scheduling

Stochastic dynamic programming has been extensively used in the optimization of long-term hydrothermal scheduling problems due to its ability to cope with the nonlinear and stochastic characteristics of such problems and the fact that it provides a closed-loop feedback control policy. Its computational requirements, however, tend to be heavy even for systems with a small number of hydro plants, requiring some sort of modeling manipulation in order to be able to handle real systems. An alternative to closed-loop optimization is an approach that combines a deterministic optimization model with an inflow forecasting model in a partial open-loop feedback control framework. At each stage in this control policy, a forecast of the inflows during the period of planning is made, and an operational decision for the following stage is obtained by a deterministic optimization model. The present paper compares such closed-loop and partial open-loop feedback control policies in long term hydrothermal scheduling, using a single hydro plant system as a case study to focus the comparison on the feedback control performance. The comparison is made by simulation using data from historical and synthetical inflow sequences in the consideration of three different Brazilian hydro plants located in different river basins. Results have demonstrated that the performance of the partial open-loop feedback control policy is similar to that of the closed-loop control policy, and is even superior in dry streamfiow periods.