Iterative linearization scheme for optimal operation of water distribution systems including leakage and cost at source

Following the least cost design problem of water distribution systems, optimal operation is probably the most explored topic in water distribution systems management. This study presents a methodology for linearization of increasing or decreasing convex non-linear equations and their incorporation into LP optimization models, building on a recently published paper methodology of the authors. The algorithm is demonstrated on the Hazen-Williams head loss equation, pressure related water leakage equation and source cost combined with an LP optimal operation water supply model. The non-linear nature of the relation between flow and head loss and leakage create a model with convex equations, thus forming a non-linear optimization model. An overall iterative linear programming scheme for dealing with these difficulties and creating an iterative linear optimization problem is suggested. The algorithm potential is briefly demonstrated on a hypothetical regional water supply system example application.