Modelling overflow using mixed integer programming in short-term hydropower scheduling

Short-term hydropower scheduling seeks to find a production schedule that maximizes profit, but must also consider the hydrological balance and risk of overflow. Overflow is by nature a non-linear and non-convex phenomenon. Common approximations and relaxations may cause non-physical results such as overflow from reservoirs that are not full. This paper presents a mixed-integer linear programming formulation that can be used to prevent non-physical overflow behaviour, but that comes at a cost of significant higher solving time. To achieve an acceptable solving time, we propose a heuristic to provide tight upper bounds on the overflow variables in each time step. When applied on the model of the Fossdal watercourse in Norway, the proposed method reduces the solving time with more than 90% compared to using a conservative fixed coefficient for all time steps.