Three-phase power lines are usually represented as self and mutual series impedances and shunt admittances at a given frequency. Carson's equations for calculating self and mutual impedances include an improper integral. To solve the integral, the high-order terms should be calculated. Thus, many studies approximated by ignoring the geometry-dependent higher-order terms. However, estimates using approximation models produce impedance errors when compared to calculations using Carson's original equations. Thus, the objective of this study is to present a model with less error that is suitable for the computer-based calculation of self and mutual series impedances for three-phase overhead transmission and distribution lines. For this purpose, the proposed model selects a knee point that significantly reduces the calculation error as a result of the sensitivity analysis. The impedances calculated with the proposed model are compared to those calculated using Carson's original equations and various approximation models. The proposed model exhibits the least error at a frequency range of 0.01 to 1 kHz when compared with modified Carson's equations and the complex depth earth return model.
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