Inverter-Fed Motor Cable Formulas

VFD motor cable formulas: the DC bus voltage, the reflected-wave overshoot at the motor, the critical cable length and the dv/dt of the output pulses.

The formulas

VL is the line voltage of the supply, Zm the surge impedance of the motor (high) and Zc that of the cable (low), tr the rise time of the inverter pulse and v the speed of the wave in the cable, about half the speed of light (150 m/µs) for a typical cable. When the cable is longer than Lc, the pulse reflects at the motor and the voltage at the motor terminals can reach nearly twice the DC bus voltage. The 0.8 factor comes from measuring the rise between 10% and 90% of the pulse. The impedances, the rise time and the speed are examples, and the drive maker and the motor maker give the limits of the cable length, the insulation class and any output filter.

Worked example: a drive on a 400 V supply

Rise time 100 ns, Zm = 500 Ω, Zc = 50 Ω.

1. Vdc = √2 × 400 = 565.7 V, and the upper limit 2 × Vdc = 1,131 V
2. Γ = (500 − 50) / (500 + 50) = 0.8182, so Vpeak = 565.7 × (1 + 0.8182) = 1,029 V
3. Lc = 0.1 × 150 / 2 = 7.5 m
4. dv/dt = 0.8 × 565.7 / 0.1 = 4.525 kV/µs

Critical length and dv/dt by rise time (400 V supply)

Frequently asked questions

Why is the voltage at the motor higher than at the drive?

The fast pulse travels down the cable as a wave and reflects at the motor, which has a much higher impedance than the cable. The reflected wave adds to the pulse.

What does a shorter rise time do?

It makes the critical length shorter, so the overshoot appears on shorter cables, and it raises the dv/dt that stresses the insulation and the bearings.

How is the overshoot reduced?

With a dv/dt or sine filter at the drive, a shorter cable, or a motor with an insulation system for inverter duty. The drive maker lists which one fits.

Does this change the cable choice?

The cable must also stand the peak voltage and the capacitive current of the pulses, so use a type that the drive maker approves, often a screened cable.

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