This paper develops a novel four-stage power flow solver for ill-conditioned systems. Although the developed solver could be considered efficient, it is not competitive with the Newton-Raphson method in well-conditioned cases. With the aim of being fully competitive in a wide range of cases and scenarios, the developed algorithm is integrated within a novel efficient solution paradigm. As a result, a robust and efficient solution framework, competitive in both well and ill-conditioned cases, is obtained. The new proposals are tested in various well and ill-conditioned cases from 30-, to 13,659-buses. Results obtained with the developed solvers are promising.
