A Study on Modeling and Simulation of Water Distribution Systems Based on Loop Corrective Flows and Containing Controlling Hydraulics Elements

In the context of water networks, in order to supply water to consumers without any disruption in service, the state of the system has to be monitored. One way to achieve this is by using simulators algorithms that provide means of combining the water consumptions called also pseudo-measurements by relating them to the mathematical model of the system. Therefore a comprehensive description of the water distribution system should be used to attain a true picture of the state of the system. This implies that all hydraulics elements including non-linear controlling elements such as pumps and valves should be included in the description of the water distribution system. This paper addresses the problem of simulation of water networks containing controlling hydraulics elements by using simulator algorithms constructed with the loop corrective flows equations. It is well known that these controlling hydraulics elements may cause numerical difficulties in the simulations due to their discontinuous properties. It is shown that using the loop equations can provide an adequate mean for handling the discontinuous nature of the controlling hydraulics elements. This is in spite of having to deal with the loop structure of the water network in the simulator algorithm which implies the use of graph theory. The case of non-linear elements check valves, pumps and pressure reducing valves is presented. The main contribution of the paper is that it proposes a partial rebuilding of the spanning tree obtained with the Depth First (DF) search, which partial rebuilding results from the changing of the status of the non-linear controlling hydraulics elements during the convergence of the Newton-Raphson numerical optimization method used by the simulator algorithm. The numerical results are verified with the EPANET software which is an established computer program used in the simulation of water networks.