Soft Starter and VFD Sizing Formulas

Soft starter and VFD formulas: start current and torque at a reduced voltage, drive input power, kVA and current, and synchronous speed from frequency.

The formulas

k is the ratio of the locked-rotor current to the full-load current In (from the motor data), f the voltage as a fraction of the supply voltage during the ramp, η the efficiencies as fractions, p the number of poles and ns the speed in rpm. The motor current is proportional to the voltage and the torque to its square, so a soft starter cuts the torque quickly and the load must still be able to start at that torque. A drive limits the current itself, so its input current is close to the load current, but its output current rating must cover the motor full-load current and the overload the load needs. The efficiencies and the input power factor are examples, so use the data sheets.

Worked example: soft starter at 50% voltage

A motor with In = 95 A and k = 6.

1. Ist = 6 × 95 = 570 A direct-on-line
2. At 50% voltage: I = 0.5 × 570 = 285 A
3. Torque = 0.5² = 25% of the direct-on-line start torque

Worked example: VFD input for a 55 kW shaft load

Motor efficiency 0.94, drive efficiency 0.97, input power factor 0.95, 415 V.

1. Pin = 55 / (0.94 × 0.97) = 60.32 kW
2. S = 60.32 / 0.95 = 63.49 kVA
3. I = 63.49 × 1000 / (√3 × 415) = 88.33 A

Soft starter ramp (In = 95 A, k = 6)

Synchronous speed of a 4-pole motor

Frequently asked questions

Why does a soft starter cut the torque so much?

The torque goes with the square of the voltage, so 50% voltage gives only 25% of the torque. Check that this is above the load torque or the motor will not accelerate.

Does a VFD reduce the start current?

Yes. The drive raises the voltage and frequency together and limits the current, so the motor starts with close to full-load current and good torque.

Is the rated speed the same as the synchronous speed?

No. The rated speed is lower by the slip, for example 1,480 rpm against 1,500 rpm for a 4-pole motor at 50 Hz.

How do I choose the drive rating?

Pick a drive whose output current is at least the motor full-load current and covers any overload the load needs. Use the maker's rating tables, which also give the ambient and altitude derating.

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