Induction Motor Simulator & AC Motor Virtual Lab

Understanding the Induction Motor — a Free Interactive AC Motor Simulator

The three-phase induction motor turns roughly half the electrical energy generated on earth into mechanical work. It has no brushes, no commutator and no electrical connection to its rotor at all: the rotor current is induced, exactly as it is in the secondary of a transformer, which is why the machine is sometimes called a rotating transformer. This induction motor simulator solves the per-phase equivalent circuit in your browser, so every number on the screen — speed, slip, current, power factor, efficiency, torque — comes from one consistent solution rather than from a set of formulas that disagree at the edges.

Slip: why an induction motor can never reach synchronous speed

Three windings spaced 120° apart, carrying currents 120° apart in time, produce a magnetic field that rotates at the synchronous speed

Ns = 120 × f / P

where f is the supply frequency in hertz and P the number of poles. At 50 Hz a 2-pole machine gives 3000 rev/min, a 4-pole 1500, a 6-pole 1000 and an 8-pole 750. At 60 Hz those become 3600, 1800, 1200 and 900.

The rotor cannot turn at that speed. If it did, it would be moving with the field, no flux would cut the rotor bars, no EMF would be induced, no current would flow and no torque would be produced — the machine would immediately slow down. So the rotor always runs slightly behind, and the fractional lag is the slip:

s = (Ns − N) / Ns

Full-load slip is not a constant of nature; it falls steadily with machine size, because larger machines have proportionally lower rotor resistance. In the simulator's own catalogue:

Two trends are worth pausing on. Efficiency climbs with size, from 82.6 per cent to over 95. And the 8-pole machine has a distinctly worse power factor than the 2-pole one at similar power, because a slow machine needs more magnetising current for the same output — a real design penalty that catches people out when they specify low-speed drives.

The torque-slip characteristic

Applying Thevenin's theorem to the equivalent circuit gives the torque at any slip:

T = (3 / ωs) × Vth² × (R₂/s) / [ (Rth + R₂/s)² + (Xth + X₂)² ]

The shape that falls out of this has three landmarks. Starting torque at s = 1. Breakdown torque, the maximum the machine can ever produce, at the slip

smaxT = R₂ / √(Rth² + (Xth + X₂)²)

and the near-straight working region between breakdown and synchronous speed, where the machine actually operates and where speed falls almost linearly with load.

Notice what is missing from the breakdown-torque expression: rotor resistance appears in the slip at which the peak occurs, but not in its height. Adding resistance to the rotor slides the peak towards standstill without changing how large it is. That single fact is the entire basis of wound-rotor starting, and you can watch it happen on the slip-ring machine in the simulator — the peak marches from 17 per cent slip out to 92 per cent while its height stays at 684 N·m.

Torque also follows the square of the applied voltage. A supply sagging to 90 per cent delivers only 81 per cent of the torque, which is why a heavily loaded motor on a weak supply can stall on a voltage dip that the lights barely register.

Why deep rotor bars exist: the skin effect that makes motors start

Here is a puzzle that a constant-parameter model cannot solve. Full-load slip on a 75 kW motor is about 1.3 per cent, which demands a very low rotor resistance. But low rotor resistance puts the breakdown torque close to synchronous speed and leaves almost nothing at standstill — on paper such a machine develops well under half its rated torque at start, and could not accelerate its own fan.

Real machines escape this by making the rotor resistance depend on speed. Rotor current frequency is s × f, so at standstill the bars carry full line frequency and the current crowds into the top of each bar; once the machine is up to speed the rotor frequency is only a hertz or two and the current spreads over the whole bar. For a rectangular bar the classical result gives the AC/DC resistance ratio as

kR = ξ (sinh 2ξ + sin 2ξ) / (cosh 2ξ − cos 2ξ), with ξ = h / δ

where h is the bar height and δ the skin depth. Because ξ scales with √(s f), a deep-bar rotor is high-resistance while starting and low-resistance while running — which is exactly what is wanted. This simulator models that effect explicitly, which is why its large machines start properly instead of collapsing at standstill, and it is also what the NEMA design letters physically describe.

No-load and blocked-rotor tests: finding the equivalent circuit

The equivalent circuit is not something you can measure directly. It is reconstructed from three terminal tests, and the no load and blocked rotor test pair is a standard laboratory exercise in every machines course.

The DC test gives stator resistance. Take care with the connection: applying DC across two terminals of a star winding puts two phases in series, so R₁ = V/2I, while on a delta winding it puts one phase in parallel with two in series, so R₁ = 1.5 V/I. Getting that factor wrong scales every copper-loss figure that follows.

The no-load test runs the machine uncoupled at rated voltage. Slip is almost zero, so R₂/s is enormous and the rotor branch is effectively open; what remains is the magnetising branch, the core loss, and friction and windage. Repeating the test at falling voltage and extrapolating the input power back to zero volts separates the last two, because core loss falls as V² while friction and windage does not change. In the simulator that extrapolation recovers the true friction-and-windage figure to within about two per cent.

The blocked-rotor test locks the shaft and raises the voltage until rated current flows. With s = 1 the rotor branch dominates and the magnetising branch can be neglected, giving rotor resistance and total leakage reactance. IEEE 112 specifies about 25 per cent of rated frequency for this test, and the reason is the skin effect described above: run it at full frequency on a deep-bar rotor and the rotor resistance reads far higher than its running value, describing a machine that does not exist above standstill. Run both versions in the simulator and compare the error — the standard exists for a measurable reason.

One caveat the textbooks are honest about and worth repeating: the split of leakage reactance between stator and rotor is not measurable. It is assigned from the design class, and that assumption is the largest single source of error in the whole procedure.

Starting an induction motor: why the inrush matters

At standstill the machine is a short-circuited transformer, and it draws five to seven times full-load current. On a small motor nobody notices. On a large one the volt-drop dims every light on the feeder, so supply authorities set limits and reduced-voltage starting becomes compulsory. Every reduced-voltage method obeys the same square law, because both torque and current scale with the square of the winding voltage.

Star-delta deserves its own sentence, because the factor of three surprises people who expect √3. Reconnecting a delta winding into star drops each winding's voltage by √3, so winding current falls by √3. But in delta the line current was √3 times the winding current, whereas in star they are equal. The two factors multiply and the line current falls to a third. Torque, following voltage squared, also falls to a third. You can verify both on screen: the simulator computes them from the circuit rather than applying a rule of thumb.

Single-phase induction motors: the machine that cannot start itself

A single-phase winding does not produce a rotating field. It produces a pulsating one, which by simple trigonometry is identical to two fields of half amplitude rotating in opposite directions. The rotor sees slip s against the forward field and 2 − s against the backward one, and the net torque is the difference between what the two produce.

At standstill s = 1, so both fields present the rotor with exactly the same slip, the two torques are identical, and they cancel. A single-phase induction motor has precisely zero starting torque. Give the shaft a spin in either direction and it will run up in that direction, which is the classic lecture demonstration. In this simulator that zero is not a special case written into the code — it emerges from the algebra, and the verification suite asserts it.

Every practical single-phase motor therefore carries a second winding, displaced in space and fed with a current displaced in time. The rotating component of the field goes as Imain × Iaux × sinα, where α is the phase angle between the two currents, and the different ways of producing that angle define the motor types:

The permanent split capacitor is the instructive case. Its starting torque is feeble not because its phase split is poor — the capacitor gives an excellent angle — but because a small run capacitor passes very little current. Keeping that capacitor in circuit while running is what gives the PSC its good power factor, around 0.80 against 0.60 for a split-phase machine of similar size.

Who uses this simulator?

• Electrical engineering students preparing an AC machines laboratory, or checking a torque-slip calculation before the viva.
• Technical and vocational trainees who need to see why a motor draws six times its rated current at switch-on before they wire a star-delta starter.
• Lecturers and lab instructors demonstrating no-load and blocked-rotor tests when the laboratory machine is in use, or showing a stall without damaging hardware.
• Maintenance and plant technicians reasoning about why a motor runs hot, starts slowly, or trips on a voltage dip.
• Design and application engineers comparing NEMA design classes, or checking whether star-delta starting will actually accelerate a given load.

Explore Related Simulators

Induction machines sit inside a family. The AC Generator Simulator covers the same rotating field from the generating side, with the EMF equation and alternator characteristics. The Star-Delta Connection Simulator works through the line and phase relationships that make star-delta starting give exactly one third. The Transformer Simulator shares this machine's equivalent circuit almost element for element — an induction motor really is a rotating transformer with a short-circuited secondary. And the DC Motor Simulator & Load Test Lab runs the same style of laboratory procedure on a DC machine, where speed control is easy and starting is the hard part — the mirror image of the trade-off here.