A co-tree flows formulation for steady state in water distribution networks

This article describes a co-tree flows formulation for steady state simulation in water distribution networks, which reduces the original governing system of equations into a smaller set, expressed in terms of the co-tree chord flows. The formulation is derived from graph theory and matrix partitioning. The reduction in the size of the set of equations does not require any new conditions on the initial solution estimate, unlike the loop flow correction method. The proposed formulation is numerically equivalent to the link flow method. However, it requires, about 5% for the Jacobian memory storage requirements of the link flow method, thereby also drastically reducing the time of execution for solving the resulting nonlinear system, as well. Furthermore, the Jacobian matrix of the new method is symmetrical, which can reduce the memory storage by half. Thus, even for large distribution systems, there is no need for sparse matrix solvers, which trade off the storage memory with time of execution in order to manage the data requirements.