A variant of Newton–Raphson method with third‐order convergence for energy flow calculation of the integrated electric power and natural gas system

Abstract

The energy flow calculation of the integrated electric power and natural gas system (IEGS) is generally tackled by the classical Newton–Raphson (NR) method with second-order convergence. However, this method may fail to converge or incur oscillating iterations leading to heavy computation burden if the initial point is not selected properly, especially in heterogenous integrated energy systems containing the natural gas system. To handle this problem, a variant of Newton–Raphson method with third-order convergence is proposed, which needs one function and two derivative evaluations per iteration without increasing the number of derivative evaluations. In order to verify the effectiveness of the proposed method, simulation studies are carried out on several different cases for the energy flow calculation of IEGS. Experiment results reveal that the proposed method is superior to the classical Newton–Raphson method and its other variants in terms of computational efficiency.