Author(s): M. M. Vaseti; M. Tabesh
Linked Author(s):
Keywords: Water distribution network; Hydraulic equations; Newton-RaphsonMethod; Initial Guess; Head
Abstract: To analyze water distribution networks the hydraulic equations of a group of components should be solved. Different unknown variables such as H, Q, ∆Q may be considered to obtain the set of hydraulic equations. Newton-Raphson method is one of the popular iterative procedures and is widely used for hydraulic analysis of water distribution systems. Usually it is recommended to use H-equations by the NewtonRaphson method. However, this method is so sensitive to the initial guess values and if these values are not close to the final solution the procedure may not be converged. For H-equations the problem is more highlighted when pressure reducing valve or pump is introduced to the network. This paper presents a methodology to improve the above-mentioned weaknesses of the Newton-Raphson method and remove the effects of initial guess on the convergence of the method. At this approach the components of the Jacobean Matrix are revised somehow that the problem of singularity in the inverse matrix is removed. Then by considering two mixed loops the matrix is refreshed at each iteration. On the other hand, to solve the oscillation problem around the final solution some modifications are made on the variable coefficient to reduce the variable difference between two iterations. To evaluate the proposed methodology one well known network from literature is analyzed. It is shown that using this method the convergence problem is resolved and water distribution networks can be analyzed by any initial guess value.
Year: 2009