Considering complex nonlinear relationships of hydropower dispatch

this paper proposes a mixed-integer nonlinear programming(MINLP)model for optimizing load distribution of hydropower plant. A polynomial fitting technology is used to deal with nonlinear functions involving at least two variables of water level

storage

discharge

and generation in the MINLP. The order and formulation of each function are analyzed and determined. Two fourth-order polynomial formulations are developed to express the fore-bay and tailrace water levels in terms of storage volume and total outflow of the reservoir

respectively. Considering the effect of water head on power generation

a quadratic function of water head and turbine discharge is proposed to accurately describe the power generation of the unit. Thus

a three-dimensional surface which can represent the relationship among water head

discharge

and generation is obtained

which can satisfy the requirement of calculating power generation under different net heads. Finally

the MINLP model is worked out by a mathematical solver and verified by solving the actual load distribution problem of Xiluodu hydropower plant with 18 generating units. A comparison between MINLP model and mixed-integer linear programming(MILP)model is presented in terms of application complexity and result accuracy. The results show that the MINLP model is easy to use and capable of producing higher-accuracy optimization results. Furthermore

the error of total turbine water consumption through the actual curve reverse interpolation is 91% less than that from MILP

better representing the actual unit operation.