Abstract: Aimed at flow propagation in short-term optimal operation of cascade reservoirs, a flow hysteresis problem is considered using a black box model by the theory of functional analysis and a new thought of big data analysis. A relevant linear mapping relationship between the reservoir inflow and outflow is constructed by the space mapping principle, using the measured data of inflow and outflow discharges of the cascade hydropower plant reservoirs. Then, a short-term optimal operation model considering flow delay time is developed and a method of its calculation is given. Finally, an analysis is presented comparing our calculations with the method of fixed hysteresis time and the real operation case. Results show that this model is simple and practical for a wide range of application to short-term optimal operation of cascade reservoirs.