Minimization of Raw Water Pumping Costs Using MILP

Abstract

With increasing demands for water, increasing costs for electrical energy, and often stagnant budgets, water utilities must begin to investigate alternative pumping policies that achieve cost savings while not sacrificing system performance. A study was performed for the city of Raleigh, North Carolina, to determine efficient raw water pumping policies to take advantage of existing storage and newly available time‐of‐use power rates. The problem was formulated as a mixed‐integer linear‐programming (MILP) model. Binary integer variables are used to model commercial demand charges, which are once‐per‐billing period assessments on the maximum on‐ and off‐peak electrical demands. Other costs to be minimized include commercial energy charges, as well as standby generator costs to avoid on‐peak commercial power use. Constraints include satisfaction of water demands, minimum and maximum reservoir levels, minimum and maximum pump run times, and other constraints necessary to ensure feasibility. The model is now being used by the city to achieve substantial savings.