Convergence of Newton method in nonlinear network analysis

The convergence of Newton method in nonlinear network analysis is discussed. It is shown that formulating the nonlinear edge flow resistances in terms of edge flow rates (Flow method) or corrected loop flow rates (Loop method) gives better convergence than the nodal head or pressure formulation (Node method). This evaluation is based on the estimation of the magnitude of the radius of attraction for the Newton method. Our result applies to both water and low pressure gas networks.