A Common Framework for Developing Robust Power-Flow Methods with High Convergence Rate

This paper presents a novel Power-Flow solution paradigm based on the structure of the members of the Runge–Kutta family. Solution approaches based on the introduced solution paradigm are intrinsically robust and can achieve high-order convergences rates. It is demonstrated that some well-known Power-Flow solution methods are in fact special cases of the developed framework. Explicit and embedded formulations are discussed, and two novel solution methodologies based on the Explicit Heun and Embedded Heun–Euler’s methods are developed. The introduced solution techniques are validated in the EU PEGASE systems, considering different starting points and loading levels. Results show that the developed methods are quite reliable and efficient, outperforming other robust and standard methodologies. On the basis of the results obtained, we can affirm that the introduced solution paradigm constitutes a promising framework for developing novel Power-Flow solution techniques