Rotating Machines study guide

What this area covers

Rotating Machines covers the three families you meet in power work: induction motors, which drive most industrial load; synchronous machines, which generate most grid power and sometimes correct power factor as motors; and DC machines, which still appear in drives and as a teaching model for speed control. This area accounts for 5–8 questions on the exam. The area is compact, but its calculations chain several steps, from nameplate to current to voltage dip, so a missed step early carries through to the end.

The ideas everything else rests on

Synchronous speed and slip tie everything together. The stator field of an AC machine rotates at

$$n_s = \frac{120 f}{P}$$

in revolutions per minute, with f in hertz and P the number of poles. An induction motor's rotor always turns a little slower. Slip is that shortfall as a fraction of synchronous speed, and it sets rotor frequency, rotor copper loss and the share of air-gap power that becomes mechanical output.

The torque–speed curve has a shape worth knowing by heart. Starting from standstill, torque rises to a breakdown peak and then falls steeply to zero at synchronous speed. Normal operation sits on the steep, nearly straight part near synchronous speed, where torque is roughly proportional to slip. Torque at any slip scales with the square of applied voltage, which is why a voltage sag during starting can stall a heavily loaded drive.

Starting draws locked-rotor current. At standstill an induction motor looks like a low impedance and draws several times its full-load current. That inrush causes the voltage dip seen by other loads on the same bus. Reduced-voltage starters trade starting torque for lower inrush: an autotransformer starter cuts line current and torque by the square of its tap, a wye–delta starter cuts both to one third, and soft starters and drives control the ramp directly. Motor nameplates express locked-rotor kVA per horsepower through a code letter; the letter definitions live in NEMA MG 1, and the motor's own data sheet is the better source when you have it.

A synchronous machine trades angle for power and excitation for reactive power. With the field producing internal voltage E behind synchronous reactance, three-phase power to or from a round-rotor machine is

$$P = \frac{3 E V}{X_s} \sin\delta$$

using per-phase values. Raising field current while holding real power constant moves the machine from absorbing reactive power to supplying it; the V-curves plot armature current against field current at fixed load and show the minimum at unity power factor.

DC speed control has two regions. Back-EMF is proportional to flux times speed. Below base speed, adjust armature voltage at full field for constant-torque operation. Above base speed, weaken the field, which raises speed at reduced torque and roughly constant power.

How to study it

1. Start from nameplates: compute input kVA, full-load current and efficiency, and check current from power and power factor with the Three-phase power calculator.
2. Work induction motor slip problems: speed from slip, rotor frequency, and the split of air-gap power into rotor copper loss and mechanical power.
3. Draw the per-phase equivalent circuit and find starting current and torque, then repeat at reduced voltage to see the square law.
4. Estimate the voltage dip when a large motor starts on a transformer, then check it with the Motor-starting voltage dip calculator. Compare across-the-line with reduced-voltage starting.
5. Solve synchronous machine phasor diagrams for a given power and power factor, find the internal voltage and power angle, and sketch a V-curve.
6. Finish with DC machines: back-EMF, speed under load, and the effect of field weakening.

Mistakes that cost points

• Using pole pairs instead of poles. The 120 in the synchronous speed formula assumes P is the number of poles.
• Treating output horsepower as input power. Nameplate horsepower is shaft output. Divide by efficiency and power factor before computing line current.
• Applying the tap linearly. An autotransformer starter reduces line current and torque by the square of the tap, not the tap itself.
• Mixing per-phase and three-phase power in the power-angle equation. Use per-phase voltages with the factor of three, or line voltages without it, never one of each.

References worth having

• NEMA MG 1 (motors and generators)
• NFPA 70 (NEC) Article 430
• Chapman, Electric Machinery Fundamentals