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This paper presents approaches to the calculation of the solution of the load flow problem in ill-conditioned systems based on Newton’s Continuous philosophy. Two approaches to the Heun-King-Werner method are proposed with the objective of obtaining a better computational cost from the reduction of the number of calculations and factorizations of the Jacobian matrices. The methods performance were compared in terms of convergence with the standard Newton-Raphson and the original Heun-King-Werner method. Experiments carried out in ill-conditioned power system models demonstrated that the proposed approaches can significantly reduce the computational cost employed by the original Heun-King-Werner method.