Motor starting and motor circuits on the PE Power exam

Motor questions on the PE Power exam come in two kinds. The first is the machine during a start: how much current it draws, how much torque it develops, and how far the bus voltage sags. The NCEES handbook covers it under Induction Machines, in Motor Starting and Electrical Machine Theory, and under Synchronous Machines for synchronous motors. It names the four induction starting methods but prints no starter ratios, so you carry those in. The second is the motor branch circuit: which current sizes which device. That is NEC Article 430, with the standard ampere ratings in 240.6.

What you actually need to own

• Locked-rotor current. A stalled motor is a fixed impedance, so its current is proportional to its terminal voltage. When the start is given as locked-rotor kVA, or as a nameplate code letter (kVA per horsepower, NEC Table 430.7(B)), convert with S = √3 · V_L · I_L.
• Torque follows voltage squared. At a fraction a of rated voltage, the motor develops a² times its full-voltage torque at the same speed. Apply a² to the motor's own locked-rotor torque.
• Each starter has its own ratios. Autotransformer on tap a: motor voltage a, motor current a · I_LR, line current a² · I_LR, torque a². Series reactor or resistor that leaves the motor at voltage fraction a: line current equals motor current, a · I_LR, and torque is a². Wye-delta: each winding sees V_LL/√3 during the start, and both line current and torque are one third of the across-the-line delta values.
• Whether it starts. Motor torque must exceed load torque at zero speed and at every speed on the way up. Run-up time is t = J · ω / (T_motor − T_load), with ω in rad/s, average torques over the run-up, and J the total inertia at the motor shaft. Through a speed reducer with motor speed n times load speed, load inertia refers to the motor shaft as J/n² and load torque as T/n.
• Starting voltage dip. In per unit on one base, V_bus = 1 / (1 + Z_S · S_LR), where Z_S is the source impedance and S_LR the locked-rotor apparent power at rated voltage. A 0.05 pu source feeding a 2 pu start holds 1/1.10 = 0.91 pu, a 9% dip.
• Synchronous motors. A synchronous motor is not self-starting on a fixed-frequency supply. It is brought up by an external drive, or as an induction motor on its damper windings and shorted field, and the dc field is applied near synchronous speed.
• The motor branch circuit. Section 430.6(A)(1) sends you to the full-load current tables (Table 430.250 for three-phase motors) for conductors, switches, and the branch-circuit short-circuit and ground-fault device. Separate overload protection under 430.32 uses the nameplate current, at a percentage set by the marked service factor and temperature rise. Table 430.52 gives the short-circuit device percentage by motor type and device type. Section 430.62(A) builds the feeder device from the largest branch device plus the other motors' full-load currents. Table 430.251(B) holds locked-rotor currents for choosing controllers and disconnects.

Where people lose points

• Using a where a² belongs. An autotransformer reduces line current twice. A series reactor reduces it once.
• An extra √3 in wye-delta. In wye, line current is winding current. The ratio to the delta locked-rotor line current is 1/3.
• Scaling torque linearly with voltage, or applying the reduction to full-load torque when the motor's locked-rotor torque is a different figure.
• Working a dip from full-load current. A start is a locked-rotor event.
• Swapping the two full-load currents. Table current for conductors and short-circuit protection. Nameplate current for overloads.
• Reading the wrong device column in Table 430.52. Time-delay fuses, non-time-delay fuses, inverse-time breakers and instantaneous-trip breakers each have their own.
• Rounding the wrong way. The branch device may go up to the next standard rating under 430.52(C)(1). The feeder value under 430.62(A) is a ceiling, so it rounds down.
• Ignoring a capacitor below the overload relay. Section 460.9 bases the overload setting on the corrected current the relay carries.

A note on the codes

The exam supplies its codes, including the 2020 NEC and the 2017 NESC, and scores code answers against those editions. Article 430 is long, so know where its tables sit before exam day. See the PE Power handbook and code books.

How to study it

Take one motor and one locked-rotor current. Work the line current and starting torque across the line, on an autotransformer tap, through a reactor and in wye-delta, side by side. Then size that motor's branch circuit from Article 430 end to end, writing the section or table number beside each figure. The dip calculation is the per-unit system in miniature.

Part of the Rotating Machines area of the PE Power exam. → Practice it on CastorPrep