Abstract
In this paper we present in detail how to handle the nonlinear and state-dependent elements in the power consumption function (PCF) of a variable speed pump (VP). The function is formulated by piecewise linear approximations with dynamically specified breakpoints. In the proposed method, the head variation resulting from the change in the water level of the upstream and downstream reservoirs and head loss caused by the friction of water on the penstock wall are both considered. Furthermore, we put forward a heuristic to incorporate the head loss in a penstock shared by multiple VPs in a short-term hydro scheduling tool used for daily operation in the real world. The case study is taken from the Limmern pumped storage hydropower plant with 4×250 MW reversible Francis pump-turbines with variable speed technology. Each penstock is shared by two of the four units. The numerical results demonstrate that the appropriate formulation of the PCF and the accurate representation of the head loss in a shared penstock are crucial for obtaining realistic and optimal scheduling for VPs.