Long-term optimal operation of cascade hydropower stations based on the utility function of the carryover potential energy

Challenge remains to find the optimal carryover storage to balance the immediate and carryover utilities for long-term hydropower reservoir operation due to low forecast accuracy, limited foresight, and complex hydrologic, hydraulic and electric connections between cascade hydropower reservoirs. Thus, this paper proposes a long-term optimal operation model to dynamically control the optimal carryover storages for cascade hydropower reservoirs. First, the carryover utility of cascade hydropower stations is expressed as a function of the carryover potential energy rather than the carryover storage, thus decreasing the function parameters and using the limited prior knowledge. Then, the utility function of the carryover potential energy (UFCPE) is fitted by a quadratic function based on a successive iteration method, based on which a two-stage optimal operation model (TSOOM) is developed to guide the long-term optimal operation of cascade hydropower stations. The case study with five cascade hydropower stations in the Yalong River Basin shows that: 1) UFCPE can be well fitted by a quadratic function, and it increases linearly in the dry season, but monotonically at a decreasing rate in the flood season resulting from a large quantity of surplus water; and 2) The performance of UFCPE-based TSOOM is much superior to those of conventional rules and conventional optimization methods and quite close to that of dynamic programming successive approximation in guiding the long-term cascade hydropower reservoirs operation.