SUMMARY A highly accurate and robust Marquardt least squares method, which simultaneously solves a set of nonlinear equations, is employed to analyse the accuracy of the Heidler function parameters recommended by IEC 62350–1 Ed. 2. In addition, Heidler function parameters for reproduction of various frequently used standardized waveshapes are provided. The possibility of using the Marquardt least squares method for fitting Heidler function to actual measured data is explored. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, a numerical model is proposed for computing the per-unit-length internal impedance of tubular cylindrical conductors for complex arguments of arbitrary magnitudes. The proposed model either numerically solves the exact formula for internal impedance consisting of modified Bessel functions or utilizes asymptotic approximations of modified Bessel functions when applicable. It is shown that the results obtained by the proposed model are highly accurate and numerically stable. The proposed model is also applicable for solid cylindrical conductors.

Exact formulas for internal impedance per unit length of tubular cylindrical conductors energized by time-harmonic current involve Bessel functions. These functions are defined by infinite series, which yield unstable and often erroneous results for complex arguments of large magnitudes. Although it is well known how to evaluate Bessel functions numerically and many routines are now available to perform the actual computation, the available software routines often fail when computing equations that consist of a product and a quotient of Bessel functions under large complex or real arguments. For such cases, different approximate formulas can be used. In this paper, three types of approximate formulas for internal impedance of tubular cylindrical conductors are compared with respect to numerical stability and accuracy.