MC-C5 · Starting & speed control

Starting and Speed Control of the Induction Machine

Frequency is the handle that changes an induction machine’s speed over the widest range. But moving the frequency alone makes the flux move with it, so this lesson works out what the voltage must do as the frequency falls for the flux to stay where it is.

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

The stator flux is proportional to voltage divided by frequency, written Φ ∝ V/f. With the voltage held fixed, predict first where the flux goes as the frequency falls and whether it reaches the saturation zone shaded in red; then move the frequency slider and check.

Frequency ff = 1.00

The slider changes only the frequency, with the voltage fixed. Gold curve = flux, red band = saturation zone; the blue dashed line is the rated flux.

Stator flux Φ ∝ V/f

Φ = V/f = 1.00

For the flux to halve, the voltage would have to come down. Keeping the voltage and lowering only the frequency does not shrink the flux; it grows it, because in Φ ∝ V/f only the denominator got smaller.

V fixed, f halved — Φ is?

Misaligned

The three handles of speed

The rotor speed is N = (1 - s)·120f/P. In this formula the only handles on speed are the slip s, the frequency f and the pole number P. Slip control lowers the stator voltage or adds resistance to a wound rotor; it is simple, but at a given torque the rotor copper loss grows in proportion to slip, so efficiency drops, and the range is narrow. Pole changing reconnects the windings to change the pole number, so it moves only in a few discrete steps such as 2:1. Frequency control is wide and continuous and has become the core of variable-speed drives today, but it comes with one condition.

ObserveN = (1 - s) 120fP

Speed changes through only three handles: slip, frequency and pole number.

Change the frequency and the voltage must follow

The stator voltage is nearly equal to the induced emf, so it can be written V ≈ 4.44 f N1 Φ, and solving for the flux gives Φ ∝ V/f. Holding the voltage and lowering only the frequency grows the flux until the core saturates, and the magnetizing current rises steeply and overheats the machine, so the voltage is lowered in proportion to the frequency to keep V/f constant. The flux then stays constant and the same current gives the same torque, which is why the range below rated frequency is called the constant-torque region. At very low frequency, though, the voltage drop across the stator resistance becomes relatively large and the flux falls short, so a little extra voltage is added there to compensate. Above rated frequency the supply voltage cannot rise any further, so the flux falls in inverse proportion to frequency; the torque falls but the output stays nearly constant, which is the constant-power (field-weakening) region.

ChooseΦ ∝ V / ?

The flux is proportional to voltage divided by frequency.

Fill inΦ const → Vf = ?

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

Hold down the starting current, keep the starting torque

Applying full voltage straight from standstill, where the slip is 1, leaves the rotor-side impedance at its smallest, and the starting current surges to five to seven times rated. Star-delta starting first connects the windings in star (Y), which lowers the voltage across each phase to 1/√3, so the line current and the starting torque both fall to 1/3 of a direct full-voltage start, and once the speed has risen the windings are switched to delta (Δ) for normal running. Because the torque drops along with the current, it suits starting with a light load. Reactor starting or an autotransformer starter lowers the voltage at the stator to cut the current, and the torque falls with the square of that voltage. A wound rotor uses external resistance and proportional shifting to lower the starting current while actually raising the starting torque. An inverter drive brings the speed up smoothly at low frequency while keeping V/f, so the slip is small from the start and the starting current can be held near rated.

On your ownI(Y)I(Δ) = ?

Starting in Y lowers the phase voltage to 1/√3 and cuts the line current to 1/3.

Back to the first screen

Halving the frequency with the voltage held fixed made the flux 2 times larger and pushed it into the saturation zone. The stator voltage is V ≈ 4.44 f N1 Φ, proportional to frequency times flux, so the flux has no choice but to follow Φ ∝ V/f; that is why, when frequency is used to change speed, the voltage is lowered together with it to keep V/f, and so the flux, constant. Done this way, the whole torque-speed curve can be slid sideways, at constant torque below rated frequency and at constant power above it. Starting belongs to the same story: the large current of a direct full-voltage start is cut to 1/3 with Y-Δ, trimmed by lowering the voltage with a reactor, handled by proportional shifting with wound-rotor resistance, or tamed by an inverter that keeps V/f even at low frequency. The induction machine story that began with the rotating field ends here with a machine whose speed and starting are under control.

Starting and speed control: the speed N = (1 - s)·120f/P changes only through slip, frequency and pole number. Frequency is the widest handle, but since the flux is Φ ∝ V/f, V/f must be held constant for the flux to stay constant (constant torque below rated, constant power above). The large starting current is held down by Y-Δ (current and torque 1/3), a reactor or autotransformer starter, wound-rotor external resistance (proportional shifting), or an inverter.

Closing out group C

That completes the induction machine. Three-phase current builds a rotating field (C1), the rotor chases it, lagging by the slip (C2), that slip fits into the equivalent circuit as the single term R2/s (C3), the torque draws a hill against slip (C4), and frequency and voltage move that hill to control starting and speed (C5). The next group, D, is the synchronous machine, whose rotor turns at exactly synchronous speed. It moves on to how a machine with slip 0 produces torque, and why it can even adjust the power factor.