The variable-frequency drive

A variable-frequency drive (VFD, also called an inverter or frequency converter) makes a new three-phase supply for the motor, with whatever frequency and voltage the control asks for. Since the synchronous speed is $120 f / p$, controlling the frequency controls the speed.

Inside the drive

Three stages, in order:

1. Rectifier. A six-diode bridge turns the 400 V, 50 Hz supply into DC. The DC voltage is close to the peak of the line voltage: $400\sqrt{2} \approx 565$ V.
2. DC link. Capacitors smooth that voltage and store a little energy. When the motor brakes, energy flows back into them (Chapter 3 deals with where it goes).
3. Inverter. Six IGBTs switch the DC link onto the motor phases thousands of times a second. Pulse-width modulation varies the width of the pulses so that their average follows a sine wave of the chosen frequency; the motor's inductance smooths the current (lesson A5).

Modulation index m

0.80

Carrier frequency

15 × f

Output frequency

50 Hz

Fundamental peak

226 V

Switching frequency

750 Hz

V/Hz command

400 V @ 50 Hz

V / f = 400 V / 50 Hz = 8 V/Hz → 50 Hz : 400 V

V/f control

The flux in the motor is set by the ratio of voltage to frequency: $\Phi \propto E / f \approx V / f$. Keep $V/f$ constant, 400 V / 50 Hz = 8 V/Hz, and the flux stays at its rated value at every speed. Then the torque-speed curve keeps its shape and simply slides along the speed axis.

Drive output frequency

30 Hz

FanConstant torque

Low-speed voltage boost (5 %)

• Motor at 30 Hz
• Motor at 50 Hz (line)
• Load

The curve slides along the speed axis with the same shape: the motor runs at any speed with a small, constant slip.

Output voltage

240 V

Synchronous speed

900 rpm

Operating speed

887 rpm

Slip speed

13 rpm

Maximum torque

168 N·m

Three things to see on the widget:

• Constant slip. With a constant-torque load of 60 N·m, the motor runs about 39 rpm below synchronous speed at 50 Hz, and still about 41 rpm below at 25 Hz. The slip in rpm, not in per cent, stays the same. That is why a VFD gives a stiff speed at any frequency.
• Low speed. Below about 10 Hz the stator resistance $R_1$ takes a large share of the small voltage, and the flux (and torque) fall. At 5 Hz the maximum torque drops from 197 to 49 N·m. A voltage boost of 5 % at 0 Hz restores it to 102 N·m. Switch it on and watch the curve.
• Field weakening. Above 50 Hz the drive cannot raise the voltage beyond the supply. $V/f$ falls, so the flux falls, and the maximum torque drops roughly as $(50/f)^2$: at 75 Hz it is 95 N·m, less than half. The motor can run faster, but only at reduced torque: a constant-power region.

Predict first

A constant-torque conveyor runs at 60 N·m. You lower the drive from 50 Hz to 25 Hz. What happens to the slip speed (n_s − n, in rpm)?

It halvesIt stays about the sameIt doubles

Beyond V/f

• Vector (field-oriented) control measures or estimates the rotor flux and controls the flux and torque components of the stator current separately, just like field and armature current in a DC motor (Chapter 1, lesson 3). It gives full torque at zero speed and a fast torque response: cranes, hoists, winders.
• Direct torque control reaches the same goal by switching the inverter directly from torque and flux estimates.

Side effects to plan for

• Motor cooling. A self-cooled motor (IC411) loses most of its cooling at low speed. Long running at low speed and full torque needs a derated motor or a separate fan.
• Supply harmonics. The diode rectifier draws current in pulses, rich in 5th and 7th harmonics (Chapter 6: reactors, 12-pulse, active front ends).
• Voltage stress. Fast PWM edges travelling down a long cable can double at the motor terminals (Chapter 6: cable reflections). Inverter-duty insulation, filters and short cables help.
• Bearing currents. Common-mode voltage can discharge through the bearings; insulated bearings or shaft grounding on larger motors.
• Braking. A diode rectifier cannot return energy to the grid; the DC link voltage rises when the motor brakes (Chapter 3: braking resistor, regenerative drives).

ExplorerGo deeper: derivations and open questions

Why the slip speed is constant. With $R_1 = 0$, show that $T$ depends on $s\,\omega_s$ only when $V/f$ and $X/f$ are fixed. Start from the torque formula of Chapter 1, lesson 2, and write $R_2'/s = R_2' \omega_s / (s\,\omega_s)$.

DC link ripple. A six-pulse rectifier gives a DC voltage with a 300 Hz ripple. Why 300 Hz? What happens to it when the capacitor ages?

Field weakening for a fan. A fan needs torque that rises as $n^2$. Can a fan run at 60 Hz on a motor sized for 50 Hz? Compare the torque it needs with the maximum the motor can give at 60 Hz on the widget.