Frequency-domain modeling of unshielded multiconductor power cables for periodic excitation with new experimental protocol for wide band parameter identification

Abstract

A complete modeling technique for unshielded power cables is proposed. The focus is on applications where the resonance phenomena take place in electrically long cables and is originated from periodic excitation, such as power converters. The resonance problems caused by switching converters tend to become more common with the advent of wide band gap semiconductors. This paper includes a new experimental protocol specific for unshielded power cable parameter identification in a wide frequency band, from DC up to medium frequencies (tens of MHz), with an impedance analyzer. It also introduces a frequency-domain simulation tool with conversion to the time domain, via the Fourier series. This frequency-domain modeling is straightforward, and its accuracy depends only on the accuracy of the cable parameter identification.

Appendix

The estimation of the stray capacitance between the cable conductors and a concrete plane (floor, walls) can be done using the PEEC technique described in [5, 6]. This method was applied to calculate the capacitance of a wire of radius $r_0$ and length $\ell$ parallel to a concrete ground, placed at a distance h above the ground, as shown in Fig. 19. In the figure, $\sigma _1$ is the complex conductivity of the air and $\sigma _2$ is the complex conductivity of the concrete. The capacitance between the wire and the concrete surface can be calculated with Eqs. (15) to (18).

Fig. 19

Schematic for the capacitance calculation

$$\begin{aligned} C_\mathrm{CM}&=-\frac{1}{{{\mathbf {I}}}{{\mathbf {m}}}(Z_\mathrm{CM})\omega } \end{aligned}$$

(15)

$$\begin{aligned} Z_\mathrm{CM}&=Z_1+Z_2 \end{aligned}$$

(16)

$$\begin{aligned} Z_1&= \frac{1}{2\pi \ell \sigma _1}\left[ \ln \left( \frac{\ell +\sqrt{\ell ^2+r_0^2}}{r_0}\right) \right. +\nonumber \\&\quad \left. -\,\sqrt{1+\left( \frac{r_0}{\ell }\right) ^2}+\frac{r_0}{\ell } \right] \end{aligned}$$

(17)

$$\begin{aligned} Z_2&= \frac{1}{2\pi \ell \sigma _1}\frac{\sigma _1-\sigma _2}{\sigma _1+\sigma _2}\left[ \ln \left( \frac{\ell +\sqrt{\ell ^2+r_0^2}}{r_0+2h}\right) +\right. \nonumber \\&\quad \left. -\,\sqrt{1+\left( \frac{r_0+2h}{\ell }\right) ^2}+\frac{r_0+2h}{\ell } \right] \end{aligned}$$

(18)

As an example, suppose the section of the wire is $2.5\,\mathrm{mm}^2$, its length $\ell =1$ m, and it is placed at $h=1$ m. In this case, the stray capacitance between the wire and the concrete floor ($\sigma _2=2.5$ mS/m) would be:

$$\begin{aligned} C_{CM}=8.6\, pF \end{aligned}$$

Based on this example, the stray capacitances in the impedance measurement set were estimated to be of the order of 10 pF along the document.