An induction motor has two main parts, a stationary stator on the outside and a rotor that turns inside it. The stator carries three sets of windings, one for each phase, spaced around the core. When three-phase current flows through them, the windings produce a magnetic field that rotates around the inside of the stator at the supply frequency. That rotating field crosses the air gap and induces currents in the rotor bars, and those induced currents produce a field of their own. The two fields pull against each other and drag the rotor round. The rotor always turns a little slower than the field, and that small difference, called slip, is what allows the induction to happen in the first place. Figure 1.Inside a three-phase induction motor. The stator windings set up a rotating field that crosses the air gap and drives the rotor.
Figure 1.Inside a three-phase induction motor. The stator windings set up a rotating field that crosses the air gap and drives the rotor.
Three ways of measuring the same supply
A, the base, is the real power in kW. This is the actual work, turning the pump, driving the fan, lifting the load, plus the losses. It is the part of the current that lines up with the voltage.
O, the vertical, is the reactive power in kVAr. This is the magnetising component. It sits ninety degrees out of phase with the voltage, which is exactly why it does no work but still has to be supplied.
H, the hypotenuse, is the apparent power in kVA. This is what the grid actually has to deliver, the full current at the full voltage, regardless of how much of it ends up doing useful work.
Power factor is the ratio of the useful part to the total, cos θ, which is A divided by H, or kW divided by kVA. A power factor of 1 means everything the grid sends you is doing work. A power factor of 0.5 means half of what the grid sends you is just magnetising iron and moving back and forth.
What happens as the motor loads up
Now watch what happens to each side of the triangle as the motor takes on load.
The vertical side, the magnetising kVAr, barely moves. It is roughly the same at light load as it is at full load, because the magnetic field is roughly the same. So, picture that vertical line as a fixed height.
The horizontal side, the real power in kW, is the part that grows with load. At light load the motor is doing very little work, so A is short. The triangle is tall and thin, the angle θ₂ is wide, and cos θ₂ is small. Poor power factor. At full load the motor is doing a lot of work, so A is long. With the same height and a much longer base, the triangle flattens out, the angle θ₁ closes up, and cos θ₁ is large. Good power factor.
So loading the motor does not reduce the reactive power. The reactive power is still there, roughly unchanged. What changes is that the real power has grown enough for that fixed reactive component to be a smaller share of the total. Same height, different width.
This is why an oversized or lightly loaded motor is a classic power factor problem. Fit a 30 kW motor to a duty that only needs 8 kW and the motor still draws close to its full magnetising kVAr while delivering 8 kW of real work, so the power factor on that circuit will always read poorly.
The shape of it
Plot power factor against load and you get a curve that climbs steeply at first and then levels off near the motor's rated value.
At no load, power factor can sit as low as 0.1 to 0.2. By half load it is usually up around 0.7. By full load it is up at the motor's nameplate figure, typically somewhere between 0.8 and 0.9 depending on the design. The steep part of that curve, down in the bottom left, is where a lot of real installations actually live, motors running part loaded because they were sized for a worst case, or for a duty that rarely turns up.
