Short-term hydropower optimal scheduling considering the optimization of water time delay

• We propose a model of short-term hydropower optimal scheduling considering the optimization of water time delay.
• We formulate water time delay as a nonlinear function of the outflow from upstream reservoir.
• The problem is converted into a mixed integer linear programming problem by integer algebra techniques.
• The optimization of water time delay can improve the operability and economic benefits of scheduling.

This paper is proposed to develop a novel mixed-integer model to solve the short-term hydropower optimal scheduling problem. The model is designed with consideration of the optimization of water time delay. The water time delay is the time required for discharging water from upstream reservoir to its downstream reservoir. It is always in change, which makes a real challenge to handle the corresponding mathematical models. In order to develop the model, we formulate water time delay as a nonlinear function of the outflow from upstream reservoir, which can describe the coupling of hydraulic and electric among cascaded hydropower stations accurately. Meanwhile, the complicated head-sensitive water-to-power conversion and piecewise output limits are also taken into account. To overcome the difficulty of solving the mixed-integer nonlinear optimization problem, the formulation above is converted into a mixed integer linear programming (MILP) problem in terms of integer algebra techniques. The applied commercial software is called CPLEX, which can solve the related MILP problem successfully. Based on a case study with 13 reservoirs and 44 hydropower units, the study shows that the proposed model with water-time-delay can improve the operability and economic benefits of scheduling.