Linear programming of headloss, leakage, and variable pump energy consumption for optimal operation of water distribution systems

The field of optimal water system operation is well explored. Minimal cost system operation depends upon several factors, mainly the following: consumer water balance constraints, minimal or maximum water head constraints at system nodes, and minimizing leakage and pump station energy consumption, which is dependent on the pump stations varying total head. The above factors have a nonlinear relation to the flow variable and are commonly solved using timely nonlinear techniques such as MIP, NLP, or heuristics. This study utilizes an iterative linearization technique to iteratively linearize the problem and solve each step using linear programming. The methodology is demonstrated on an illustrative example.