The dynamic control of flood limited water level (DC-FLWL) belongs to the research field of risk operation.The risk source mainly comes from the uncertainty of inflows,including the risk from the forecasting error in real-time operation and the potential risk in the design phases from insufficient consideration about the uncertainty of design flood.A new model considering capacity compensation and the uncertainty of design flood for cascade reservoirs was developed to calculate the bound of DC-FLWL.Firstly,the probable maximum FLWL was defined by analyzing the principle of capacity compensation and an explicit expression of flood control risk was given.The joint distribution of the upstream and interval floods was established by a Copula function.When the downstream reservoir encountered a certain design flood,the possible range of upstream flood could be obtained,thus the uncertain design floods could be obtained.By simulating the operation of the cascade reservoirs under a risk constraint,the DC-FLWL could be calculated.The proposed method was applied to Pankou-Huanglongtan cascade reservoirs in Du River basin,and the results were compared with homogeneous frequency and typical year methods.It showed that:1) By employing empirical information from the historical flood data, the proposed method can provide reference information to the simulation of the design floods of cascade reservoirs;2) The bound of DC-FLWL obtained by the proposed method was much safer than the homogeneous frequency and typical year methods;3) The bound of DC-FLWL for HLT could be widened from[240.00,247.00] m to[240.00,248.21] m,which would increase 13 and 11 million kW·h extra hydropower generation during a wet year in 2000 and a dry year in 1994,respectively.The proposed method could give a sufficient consideration about the capacity compensation regulation and design flood uncertainty of cascade reservoirs, and the bound of DC-FLWL could be calculated while no flood control risk was increased.
