An optimization model for the integrated operation of the multiple reservoirs in the Upper Yellow River

The Yellow River is the second largest river in China. There are seven reservoirs and hydropower stations in the mainstream of the Upper Yellow River. This paper presents an optimal mathematical model for the integrated operation of the seven reservoirs and hydropower stations. The objective of this model is to maximize the sum of electricity generated by all the hydropower stations with the constraint of firm power, and the Discrete Differential Dynamic Programming (DDDP) is employed to find the optimal solution of this model. The decision variables of DDDP are chosen as the reservoir discharge, while the state variables are reservoir storages, and the backward recursive equation is derived to find the reservoir optimal operation policies stage by stage. This model is used to find the integrated optimal operation policies of the past 33 years with observed hydrological data, the results show that there has been a 5.89% increase in the average annual electricity generated by all the seven hydropower stations. This implies that the model presented in this paper is good and can be used to derive the integrated operating rules of the reservoirs in the Yellow River.