Two-stage Stochastic Optimal Operation Model for Hydropower Station Based on the Approximate Utility Function of the Carryover Stage

Challenge remains to find the optimal carryover storage to balance the immediate and carryover utilities for long-term hydropower reservoir operation due to high uncertainties of long-term forecasts. In this study, a two-stage stochastic optimal operation model (TSSOOM) is developed to dynamically decide the optimal carryover storage. First, a two-stage decision framework is developed by dividing the entire operation horizon into current and carryover stages. Then, a successive iteration method based on periodic Markov characteristics of reservoir operation is proposed to obtain the approximate utility function of the carryover stage (AUFCS). Finally, three TSSOOMs based on different forecast accuracy are developed to guide the long-term hydropower reservoir operation, including TSSOOM with no forecasts (TSSOOM_NF), TSSOOM with perfect forecasts (TSSOOM_PF), and Bayes TSSOOM (TSSOOM_B) that consider both inflows and their forecast uncertainties. The case study in the Ertan station of China shows that: (1) the back propagation neural network (BPNN) can approximate the UFCS with a high accuracy and avoid the need to predetermine the function type of the UFCS; (2) the AUFCS increases with the carryover storage and current inflow, and it changes gradually from a nearly linear surface to an approximate concave surface with the shift from the dry season to the flood season; (3) TSSOOM can convert the complex multi-period decision problem into a two-stage optimization decision problem and obtain the optimal carryover storage that can strike a balance between immediate and carryover utilities.