AbstractThis paper describes an efficient and reliable algorithm that modifies the Fast Decoupled Load Flow (FDLF) in order to overcome non‐convergence troubles in solving strongly stressed power systems. The Hartkopf's algorithm for improving the Newton‐Raphson method's convergence features in ill‐conditioned cases is taken as a basis. The proposed changes to FDLF consist fundamentally in minimizing the squared power mismatches with a second order interpolation technique. The simple modification makes it possible to establish for sure whether a case of non‐convergence is owing to numerical or to physical problems, and lets the operator evaluate the system condition correctly. Several numerical examples show the remarkable behaviour of the algorithm proposed.