Rotating Machines

Induction and synchronous machines, with some dc and single-phase machines, running and starting: speed and slip, torque, power flow, excitation, and what each starter does to current and torque. The area carries 5–8 of 80 questions across two subtopics, machine types and applications, and motor starting. It shares the exam's smallest range with Power Electronic Circuits and Control Devices.

What the problems look like

Short calculations, curve reading and concept questions. Recurring shapes — speed, slip and pole count from a nameplate or a rotor frequency; induction motor power flow to air-gap, converted or shaft power; wound-rotor resistance moving the torque-speed curve; synchronous machine excitation, pull-out power, test-curve reactance, V-curves and governor droop; choosing a machine for a duty; dc motor speed after a voltage or resistance change; starter ratios (autotransformer, series reactor, wye-delta, part-winding); a motor curve read against a load curve; starting voltage dip; and run-up time. A few go to the code for a locked-rotor current.

By exam day you should be able to —

• find speed and slip: n_s = 120f/p with p in poles, s = (n_s − n)/n_s, f_rotor = s·f_line;
• convert power to torque: T (N·m) = 9549·P (kW)/n (rpm), or T (lb-ft) = 5252·P (hp)/n (rpm);
• walk the induction power flow: P_AG = P_in − P_SCL − P_core, P_RCL = s·P_AG, P_conv = (1 − s)·P_AG;
• use the round-rotor power-angle relation P = (3·E₀·E/X_s)·sin δ, with pull-out at δ = 90°, and X_ds = V_oc/I_sc from the test curves;
• apply starter ratios: torque follows voltage squared; an autotransformer on tap a draws a²·I_LR from the line, a series reactor a·I_LR, a wye-delta starter I_LR/3;
• estimate a starting dip, V_bus = 1/(1 + Z_S·S_LR) in per unit on one base;
• compute run-up time, t = J·ω/(T_motor − T_load) with average torques, ω in rad/s.

Where people lose points

• Poles and slip direction: p in n_s = 120f/p counts poles, not pole pairs. An induction motor runs below synchronous speed, an induction generator above it.
• Power-flow stages: s and (1 − s) multiply the air-gap power, not the input. Core loss comes out on the stator side.
• Rotor resistance: at constant torque, slip scales with total rotor-circuit resistance, winding plus bank. Breakdown torque keeps its value and moves to a higher slip.
• Synchronous per-phase quantities: put every voltage on a line-to-neutral basis and multiply by 3, not √3. A motor at leading power factor is over-excited and supplies reactive power. A salient-pole machine adds a reluctance term in sin 2δ. Unsaturated reactance uses the air-gap line and the measured short-circuit current.
• Governor droop: percent droop divides by full-load speed, not no-load speed; no-load speed sits above full-load. Paralleled units share one frequency.
• Starter ratios: an autotransformer reduces line current twice (a²), a series reactor once (a). Wye-delta gives one third of the delta line current and torque, with no further √3. Apply the voltage-squared factor to the motor's locked-rotor torque, not its full-load torque.
• Reading a start off curves: check standstill, the pull-up dip and the crossing point. After a transition, read the full-voltage curve at the speed already reached.
• Dip, run-up and dc inputs: a start is a locked-rotor event, so use locked-rotor current. Through a speed reducer of ratio n, load inertia refers to the motor shaft as J/n² and load torque as T/n. For a dc motor, read the field connection from the drawing: speed scales with E/Φ, where E = V − I_a·R_a, not with terminal voltage.

Have these at your fingertips

n_s = 120f/p, the power-flow chain, the power-angle relation and the three starter ratios. In the Handbook, both machine types have a Motor Starting and an Electrical Machine Theory section, which hold the induced-torque, power-angle and test-reactance relations. Droop is under Governor Control for Synchronous Generators; the loss chain is under 3-Phase Induction Motor Power Flow. The Handbook prints the power-torque relation in SI form and names four induction starting methods, without series reactor, part-winding or any starter ratio, so carry those and the 5252 form in. Locked-rotor kVA per horsepower comes from the code-letter table, Table 430.7(B) of the 2020 NEC; a wye-delta motor's letter is for the wye connection. The exam opens one chapter of a standard at a time.

Going deeper

• Motor starting and motor circuits — one motor through every starter, then its branch circuit
• The per-unit system — the arithmetic behind a starting dip
• Three-phase circuits and delta-wye — the relations inside the wye-delta ratio
• Power Electronic Circuits and Control Devices — drives and starter control logic
• The PE Power handbook and code books — the supplied editions

Part of the PE Electrical: Power exam. Practice with exam-real problems — Castor, the AI tutor, walks any one you miss. → Start practicing Or take the free PE Power practice exam first.