Pump Scheduling for Uncertain Electricity Prices

Water utilities have optimized pump schedules to take advantage of day/night electricity pricing plans for several decades. As intermittent renewable energy sources such as solar and wind power provide an increasingly large share of the available electricity, energy providers are moving to dynamic pricing schemes where the electricity price is forecast 24 hours in advance on 30-minute time steps. The customer only knows the actual price several days after the electricity is used. Water utilities are uniquely positioned to take advantage of these dynamic prices by using their existing infrastructure for pumping and storage to respond to changing costs for power. This work develops an operational technique for generating pump schedules and quantifying the uncertainty in the cost of these schedules. With information about the pumping schedules and the distribution of possible costs, a system operator can pump according to her desired level of risk. To develop this information, a representative sample of electricity price forecasts covering nearly the full range of possible price curves must be created. Forecasts from the energy supplier and historical data on actual prices are used to condition stochastic sampling of daily energy price trajectories using covariance decomposition methods. From this ensemble of realizations, electricity price profiles are classified into a handful of scenario classes. The optimal pumping schedule for each price class is then computed. Once the pumping schedule is known, the price of that schedule is evaluated against all other price classes to determine the robustness of the schedule. The method is applied on a simple real-world network in Ireland. In this application, electricity prices vary every half hour and range from 5 to 262 €/mWh. Optimizing the pumping schedule proved to be the slowest step in the process so selection of proper price scenarios on which to generate the schedule was critical to obtaining results in an operational time-frame.