An efficient power-flow approach based on Heun and King-Werner's methods for solving both well and ill-conditioned cases

Solving the Power-Flow in ill-conditioned cases is still challenging as most of the available robust methodologies are not efficient enough to be widespread used in industry applications. This paper addresses this issue by developing a novel approach suitable for both ill and well-conditioned power cases. Since the developed approach arises from the combination of the King-Werner and Heun's methods, it is called Heun-King-Werner method. The developed approach naturally performs as a robust method in ill-conditioned cases and as a high order Newton-like method in well-conditioned systems, which makes it very suitable for solving both cases. The developed approach is tested using various realistic well and ill-conditioned cases under different demanding scenarios. Its performance is compared with other well-known Power-Flow methods. Results show that the developed approach is robust, reliable and computationally much more efficient than other well-known methods. In well-conditioned systems, it performs similar to the standard NR method but improving its convergence features in some cases. Based on the results, the developed approach may be widespread used in industry tools.