Motor cable impedance is a required parameter for accurate simulation of the voltage ringing and overshoot at the motor terminals. There are methods to calculate the cable inductance and capacitance based on the cable material properties and geometries. However, perhaps the easiest method is to measure the cable impedance directly.

##### Motor Cable Impedance Measurement

Two impedance measurements are required, the short circuit impedance and the open circuit impedance. The short circuit impedance gives the cable series inductance and resistance. The open circuit impedance gives the cable capacitance and leakage resistance. If an impedance analyzer is not available, use an LCR meter to measure these values at several frequencies. Figure 1 shows the open circuit and short circuit line-line measurements for a three-phase cable. Two of the phase cables are tied together to replicate the standard switching configuration of a 3-phase VSI drive.

##### Cable Parameter Calculation

Figure 2 shows the cable short-circuit impedance versus frequency plot with the associated circuit parameters. The low-frequency impedance gives the cable series resistance *Rs*, and the higher frequencies give the cable series inductance *Ls*. Suggested calculations are given in [1].

Next, Figure 3 shows the cable open-circuit impedance versus frequency plot with the associated circuit parameters. The impedance at lower frequencies gives the cable capacitance *Cp* and leakage resistance *Rp*. If required, the impedance above resonance gives the high-frequency capacitance and resistance. Suggested calculations are given in [1].

This method yields parameters for the measured cable. Adjusting for the cable length gives per-unit-length measurements. This allows simulation of the system with any cable length for that cable type. Also, note that the measurements shown here are line-line and require adjustment to match the line-neutral cable model shown.

Finally, note that this simple cable model only works up to the resonant frequencies shown in the impedance plots. For more accurate simulation at higher frequencies (typically multi-megahertz), use a more detailed model to capture the high-frequency effects. In addition, the per-unit-length modeling approach breaks down at very long cable lengths. At these lengths, the cable length is of the same magnitude as the wavelength of the relevant frequency component. However, this cable modeling approach works for the simulation of voltage overshoot and ringing in many VFD systems installed today.

###### References

[1] A. F. Moreira, T. A. Lipo, G. Venkataramanan, and S. Bernet, “High-frequency modeling for cable and induction motor overvoltage studies in long cable drives,” *IEEE Transactions on Industry Applications*, vol. 38, no. 5, pp. 1297–1306, Sep. 2002. (IEEE Xplore Link)

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