Variable frequency drives and constant V/f speed control

Inside a VFD

Almost all drives have three stages:

• Rectifier: a diode bridge converts the three-phase AC mains to DC.
• DC bus: capacitors (and sometimes a choke) smooth the DC. The voltage is about √2 × V_line, so around 565 V from a 400 V supply.
• Inverter: six IGBTs switch the DC bus on and off at several kHz, producing three-phase pulse-width-modulated (PWM) voltage. The width of the pulses sets the effective voltage and the order of switching sets the frequency.

The motor's inductance smooths the current, which is nearly sinusoidal even though the voltage is a train of pulses. Because the output is generated electronically, frequency and voltage are set independently of the mains.

Speed follows frequency

The speed of an AC machine is set by the frequency of the stator field:

N_s = 120 × f / p

For a four-pole induction motor, 50 Hz gives 1500 rpm, 25 Hz gives 750 rpm and 100 Hz gives 3000 rpm. The rotor runs slightly below this, and the slip remains small if the drive keeps the motor flux and load within limits. A permanent magnet synchronous motor (PMSM) follows the synchronous speed exactly, so its speed is f-controlled with no slip, and a standard (non line-start) PMSM needs a drive to start and run.

Constant V/f and why

The air-gap flux of a motor is proportional to the voltage divided by the frequency:

Φ ∝ V / f

If you lower the frequency but keep the voltage, the flux and current rise, the iron saturates and the motor overheats. If you lower the voltage too far, the flux drops and so does the torque. A scalar V/f drive therefore keeps the ratio constant. For a 400 V, 50 Hz motor that means 8 V per hertz.

• 50 Hz: 400 V, N_s = 1500 rpm
• 25 Hz: 200 V, N_s = 750 rpm
• 10 Hz: 80 V, N_s = 300 rpm

With constant flux the motor can produce its rated torque at any speed up to base speed, which suits conveyors, hoists and pumps.

Low-speed boost

At low frequency the stator resistance drop (I × R) is no longer small compared with the applied voltage. With a strict V/f ratio the voltage left to magnetize the motor is too low, and the flux and torque fall. Drives add a voltage boost at low frequency, often with a setting of a few percent of rated voltage. It restores flux and starting torque, but too much boost overheats the motor at low speed. A motor with a shaft-mounted fan also loses cooling at low speed, so continuous low-speed operation at full torque may need a separate cooling fan.

Field weakening above base speed

The drive cannot output more voltage than the DC bus allows, so above the base frequency (50 Hz here) the voltage stays at its rated value while the frequency keeps rising. V/f falls, so the flux weakens. The motor can run faster, but the available torque falls roughly as 1/f, so the power stays about constant. This is the constant-power region. Further above it, the pull-out torque falls roughly as 1/f².

Example: a 4 kW, four-pole motor with a rated torque of 26.5 N·m at 1440 rpm and 50 Hz is run at 75 Hz. The synchronous speed is 2250 rpm, so with a somewhat larger slip it runs at about 2150 rpm. The available continuous torque is about 26.5 × 50 / 75 ≈ 17.7 N·m, which gives P = 17.7 × 2π × 2150 / 60 ≈ 4.0 kW, about the rated power. Speed above the base speed is limited by the mechanical design of the rotor and bearings.

Vector control

Scalar V/f control is simple but regulates torque only indirectly. Vector (field-oriented) control measures the stator currents, converts them to a rotating reference frame aligned with the rotor flux and regulates two components separately: one that sets the flux and one that sets the torque. This is how a DC machine behaves. It gives fast torque response and accurate speed down to nearly zero, with full torque at standstill when an encoder is used (sensorless vector control is good at low speed but less so near zero). Direct torque control is a related technique. For PMSMs, vector control is standard, and the current angle is also used for field weakening.

Try it in the simulators

Neither simulator models the drive's rectifier or inverter, but both show the effect of frequency and voltage on the motor.

In the three-phase induction motor simulator, set Starting method to Variable frequency drive (VFD). During the Ramp time (default 5 s) frequency and voltage ramp up together, with a small voltage boost at low frequency, and the simulator shows the Peak starting current (× In) and Start time. Use Supply frequency and Applied line voltage to compare 50 Hz and 25 Hz. The Synchronous speed readout follows the frequency in the way N_s = 120 × f / p predicts.

In the permanent magnet synchronous motor simulator (default 2.2 kW, 400 V, four poles, 50 Hz), the Synchronous speed readout follows Supply frequency exactly. The Load angle readout there is shown as a percentage of the pull-out torque, which follows V/f up to the rated flux (pull-out torque is 1.8 times rated at rated flux):

• Set Supply frequency to 25 Hz and Applied line voltage to 200 V. The synchronous speed is 750 rpm and the load angle readout stays at about 31% for the default 55% load.
• Keep 400 V and raise the frequency to 75 Hz. This is field weakening: the flux is 2/3 of rated, and the Load angle reading rises to about 46%.
• At 100 Hz and 400 V the Load angle reaches about 61%, and at 100% Mechanical load the motor goes out of step.

Try it in the simulator