Power Flow Solutions by Newton-Raphson Method with Approximated Second-Order Term of Taylor Series

Abstract

This paper presents a Newton-Raphson method with an approximated second-order term of the Taylor series for solving the power flow problem where the power flow equations are in polar form. The proposed method is to include the second-order derivative term of the Taylor series in the Newton-Raphson method and subsequently approximate it using the first-order differentiation of the central finite difference. To compare the proposed method’s capability of finding a solution, it is compared with the Newton-Raphson method both in the polar form and rectangular form of power flow equations. The proposed method and the comparative methods are applied to the ill-conditioned 13 bus, IEEE 14 bus and IEEE 30 bus systems. The results demonstrate that the proposed method is the only method that can satisfy in all systems and the ill-conditioned 13 bus systems with a high and highly reactive load at bus 11. While the Newton-Raphson method both in polar form and rectangular form can identify the solution in all systems, it cannot identify the solution in the ill-conditioned 13 bus with a highly reactive load at bus 11.
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