MC-C5 · Starting & speed control

Starting and Speed Control of the Induction Machine

Frequency gives the widest way to change an induction machine’s speed. But touching frequency alone shakes the flux. Pin down what the voltage must do as the frequency falls so the flux stays constant.

If you lower only the frequency at fixed voltage, the flux…

The stator flux is proportional to voltage over frequency: Φ ∝ V/f. Lower the frequency slider. With the voltage held fixed, predict first where the flux goes and whether it reaches the saturation limit (the red zone).

Frequency ff = 1.00

Slide for continuous frequency (voltage fixed). Gold curve is flux, red is saturation.

Stator flux Φ ∝ V/f

Φ = V/f = 1.00

For the flux to halve you would have to lower the voltage. Holding the voltage and lowering only the frequency does not shrink the flux — it grows it, because in Φ ∝ V/f you only cut the denominator.

V fixed, f halved — Φ is?

Misaligned

The three handles of speed

The rotor speed is N = (1 - s)·120f/P. The only ways to change speed are slip s, frequency f and pole number P. Slip control (lowering the stator voltage or adding resistance to a wound rotor) is simple but raises slip loss and has a narrow range. Pole control swaps windings and only gives discrete steps like 2:1. Frequency control is wide and continuous, the mainstay of variable speed today, but it comes with one condition.

ObserveN = (1 - s) 120fP

Speed changes only through slip, frequency and pole number.

Change the frequency and the voltage must follow

The stator voltage is nearly the induced EMF, V ≈ 4.44 f N1 Φ. Solving for flux gives Φ ∝ V/f. Lowering only the frequency while holding the voltage grows the flux, saturates the core, and the magnetizing current runs away and overheats. So the voltage is lowered in proportion to frequency to keep V/f constant. Then the flux is constant and the torque capability is kept — the constant-torque region. Above the rated frequency the voltage can rise no further (the voltage ceiling), so the flux drops; the torque falls but the power is held — the constant-power (field-weakening) region.

ChooseΦ ∝ V / ?

Flux is proportional to voltage over frequency.

Fill inΦ const → Vf = ?

To keep the flux constant, keep V/f constant.

Hold down the starting current, keep the starting torque

Applying full voltage straight from standstill, where the slip is one, makes the starting current surge to five or six times rated. Star-delta starting first connects the windings in star to lower the phase voltage to 1/√3, cutting both starting current and starting torque to one third, then switches to delta as the speed rises (for light loads). A reactor or autotransformer lowers the voltage at the stator to cut the current. A wound rotor uses external resistance and the proportional shift to lower the starting current while actually raising the starting torque. An inverter drive starts smoothly at low frequency keeping V/f, holding down the starting current at the root.

On your ownI(Y)I(Δ) = ?

Star starting lowers phase voltage to 1/√3 and current to one third.

Back to the first screen

Halving the frequency at fixed voltage doubled the flux and drove it to saturation, because the stator voltage is V ≈ 4.44 f N1 Φ, so the flux is Φ ∝ V/f. So when changing speed by frequency, the voltage is lowered with it to keep V/f constant, that is, the flux constant. Then the whole torque-speed curve can be shifted in parallel: constant torque below rated, constant power above. Starting is the same thread. The large full-voltage starting current is tamed by star-delta to a third, by a reactor lowering the voltage, by wound-rotor resistance using the proportional shift, and by an inverter holding V/f at low frequency. The induction story that began with the rotating field closes here as a machine we know how to command.

Starting and speed control: the speed N = (1 - s)·120f/P changes only through slip, frequency and poles. Frequency control is the widest, but since flux is Φ ∝ V/f, V/f must be kept constant to keep the flux constant (constant torque below rated, constant power above). The large starting current is held down by star-delta (current and torque to 1/3), a reactor or autotransformer, wound-rotor resistance (proportional shift), and an inverter.

Closing out group C

That completes the induction machine. Three phases weave the rotating field (C1), the rotor chases it with a slip (C2), that slip folds into the equivalent circuit as the single term R2/s (C3), torque draws a hill of slip (C4), and frequency and voltage shift that hill to command starting and speed (C5). The next group D is the synchronous machine, whose rotor runs at exactly synchronous speed. We turn to how that zero-slip machine makes torque and why it even controls power factor.