Artículos en revistas This paper presents a continuation and optimization based algorithm to detect power flow unsolvability. In addition, the algorithm obtains the power flow solution, if it exists, no matter how ill-conditioned the power system is. The proposed algorithm is based on the parameterization of the distance from the starting point to the real power flow to be solved, using a convergence margin. The performance of the algorithm is illustrated considering an highly loaded scenario of the operation of the Spanish power system. info:eu-repo/semantics/publishedVersion