Optimal Pump Scheduling in Water Supply Systems with Maximum Demand Charges

The calculation of optimized pump schedules is sometimes complicated by the inclusion of a maximum demand charge in the electricity tariff. Maximum demand charges can be as much as 35% of energy costs, and in the United Kingdom they usually apply over a calendar month. In this paper, medium term maximum demand policies are assumed to be represented in daily scheduling by constraints on power use or by penalty costs. Derivation of optimal constraints or penalty costs has been formulated as a stochastic dynamic program in which variations in daily demand for water are modeled as a Markov process, and solved for the case where there is a single maximum demand charge for the system under consideration. A hypothetical case is provided to illustrate the process, and cost functions and optimal constraints for this case are presented graphically. The method has considerable advantages over heuristic techniques because it takes full account of uncertainty in the demand for water, and of the recursive nature of the problem.