Iterative LP water system optimal operation including headloss, leakage, total head and source cost

Linear water balance optimal operation models are common with relative short solution times but suffer from a lack of certainty whether the given solution is at all hydraulically feasible. Introducing hydraulic headloss, water leakage and changing pump energy consumption, effect the resulting system optimal operation but also create a non-linear problem due to the convex relation between flow, headloss, water leakage and total head. This study utilizes a methodology published by the authors for linearization of convex or concave equations. An iterative linear programming (LP) minimal cost optimal operation supply model is solved including the Hazen–Williams headloss equation, pressure related water leakage equation, changing pump energy consumption and source cost. The model is demonstrated using an example application. ‘Greater than’ or ‘less than’ water head constraints at nodes may force the system to maintain certain water levels in water tanks reducing the available operating volume forcing pumping stations to operate in peak tariff periods as less storage is available in low tariff periods. Operationally, reducing water leakage may be achieved by reducing water heads along the system by means of shifting pump operation periods and maintaining low water levels in water tanks. Source costs may serve as penalties or rewards discouraging or encouraging the use of certain water sources.