is the electricity tariff, in Euro per kWh, during time interval t;
• 1 is the efficiency of the pump’s motor พ, which we take to be constant for each pump; and
• At is the length of a time-step.
In order to satisfy the required water demand, several constraints have to be implemented. Firstly, the pressure in the network depends both on the topology and the flows. Indeed, for each pipe, the downward
pressure is equal to the sum of the upward pressure, a hydrostatic component resulting from the height
difference between the two points and a dynamic component due to pressure losses. It thus follows