The key question in hydropower production is the time pattern of the use of the water in the reservoir. The water used to produce electricity today can alternatively be used tomorrow. The analysis of the operation of hydropower is therefore essentially a dynamic one. The paper introduces some basic models for social allocation of stored water over discrete time periods using non-linear programming assuming capacities of generation and transmission as given. Implications of constraints such as limited storage capacity and limited connector capacity for (international) trade are studied. Results are derived for water allocation and development of the electricity price over time. Graphical illustrations are provided in the two- period case and successive pairs of periods in a multi-period setting by means of the bathtub diagram. Thermal capacity is added to hydro and the optimal mix is studied. The walls of the hydro bathtub are extended endogenously by thermal capacities. Finally, the case of monopoly is studied.Different from standard monopoly behaviour of contracting output, if total available water is to be used, the strategy of a monopolist is to redistribute the use of water for electricity production over periods compared with the social optimal distribution.
