Abstract
Water utilities can achieve significant savings in operating costs by optimising pump scheduling to improve efficiency and shift electricity consumption to low-tariff periods. Due to the complexity of the optimal scheduling problem, heuristic methods that cannot guarantee global optimality are often applied. This paper investigates formulations of the pump scheduling problem solved using a branch and bound method. Piecewise linear component approximations outperform non-linear approximations within application driven accuracy bounds and demand uncertainties. It is shown that the reduction of symmetry through the grouping of pumps significantly reduces the computational effort, whereas loops in the network have the opposite effect. The computational effort of including convex, non-linear pump operating, and maintenance cost functions is investigated. Using case studies, it is shown that linear and fixed-cost functions can be used to find schedules which, when simulated in a full hydraulic simulation, have performances that are within the solver optimality gap and the uncertainty of demand forecasts.
Highlights
In the US up to 4 % of all energy demand is consumed by water distribution and treatment works (Pasha and Lansey 2014)
The changes in computational performance are investigated when taking into account maintenance constraints on pumps, grouping pumps to reduce the symmetry of the model and changing the problem size by varying the number of time steps and the size of the network
This is known as symmetry and it is considered good practice to remove it from the model (Sherali and Smith 2001)
Summary
In the US up to 4 % of all energy demand is consumed by water distribution and treatment works (Pasha and Lansey 2014). Optimal pump scheduling has been shown to reduce the energy cost of a water distribution system (WDS) by 10–20 %, this by shifting consumption to time periods with lower electricity cost or improving operational efficiency (Boulos et al 2001). The changes in computational performance are investigated when taking into account maintenance constraints on pumps, grouping pumps to reduce the symmetry of the model and changing the problem size by varying the number of time steps and the size of the network.
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