Power Electronic Circuits and Control Devices

Rectifiers, dc-dc converters, inverter-based resources and variable-frequency drives, plus relay, Boolean and ladder logic. At 5–8 of 80 it sits level with Rotating Machines as the smallest area on the PE Power exam, with two subtopics.

What the problems look like

Short calculations and circuit reading. Recurring shapes — the average dc output of a diode or thyristor bridge; ripple and output harmonics; the duty ratio of a buck, boost or buck-boost stage read from a drawing; a drive's terminal voltage at a commanded frequency or its true-rms input current; an inverter's current and reactive capability. On the control side: complement or simplify a Boolean expression, pick the gate or contact network that realizes it, predict what a ladder rung does, time on-delay and off-delay timers, and an occasional motor control-circuit question from NFPA 70-2020 (NEC).

By exam day you should be able to —

• find rectifier averages: V_o = 2V_m/π (single-phase full-wave), V_o = (V_m/π)(1 + cos α) (single-phase thyristor bridge, resistive load), V_o = 3V_m,L-L/π (six-pulse), each on V_m = √2·V_rms;
• solve dc-dc converters for D = t_on/T: buck V_o = D·V_s, boost V_o = V_s/(1 − D), buck-boost V_o = −V_s·D/(1 − D);
• apply scalar V/f control: voltage linear in frequency up to rated speed, held constant above it, with flux ∝ V/f;
• combine harmonics: I_rms = √(ΣI_n²) = I_1·√(1 + THD²), and total power factor = distortion factor × displacement factor; ac line-current orders h = p·k ± 1 for a p-pulse converter (dc side: p·k);
• size an inverter: I_L = |S|/(√3·V_L) and Q_max = √(S_rated² − P²);
• reduce logic with De Morgan: (A + B)′ = A′·B′ and (A·B)′ = A′ + B′; A ⊕ B = A·B′ + A′·B;
• trace a ladder rung: series is AND, parallel is OR, a normally closed contact is the complement.

Where people lose points

• rms where a peak belongs. Rectifier relations are written on V_m. Convert the stated rms voltage first, and on a three-phase bridge use the peak line-to-line value. Check: a six-pulse average is about 1.35 × the rms line-to-line voltage.
• Topology before formula. Settle half-wave or full-wave, filtered or unfiltered, resistive or inductive load first. A large filter capacitor holds the output near the peak; a filtered half-wave rectifier ripples ΔV ≈ V_m/(fRC), a full-wave one half that. A fully controlled six-pulse bridge with smooth dc current follows V_dc = V_do·cos α, with V_do the diode-bridge average, not (1 + cos α).
• Duty ratio. D is the on-fraction. Identify the converter from where the inductor, switch and diode sit, then substitute D back to confirm the output.
• Harmonics add in quadrature. Square each component before summing. Line current follows apparent power, so reactive output or distortion raises current at the same kW.
• Volts per hertz. Scale the line-to-line nameplate voltage linearly with frequency; the affinity laws describe the fan, not the inverter. Above base frequency voltage stays at nameplate and torque capability falls with flux. Read a plotted V/f profile, including any offset at zero.
• De Morgan in full. Complement every term and exchange the operator; a double complement cancels. Confirm with a truth table.
• Read the rung drawn, not the rung you expect. A seal-in contact bypasses only the elements its branch spans; every series element outside it can still drop the coil. A stop that must act on a broken wire is a normally closed contact in series.
• Timers. An on-delay contact changes state at time-out and resets the instant its coil drops; an off-delay contact outlasts its coil by the preset. A non-retentive timer restarts from zero; a retentive one keeps its count until reset.

Have these at your fingertips

The rectifier averages, the three duty-ratio relations, De Morgan's theorems and the quadrature sum. In the Reference Handbook they sit under AC-DC Converters, DC-DC Converters, Variable-Speed Drives and De Morgan's Theorems; peak, rms and quadrature-sum relations are in AC Circuits, THD in Power Quality. The Handbook prints the uncontrolled three-phase average but not the controlled cos α form, so know that one by heart. Motor control-circuit rules come from the NEC; the exam opens one chapter of a standard at a time.

Going deeper

• Motor starting and motor circuits on the PE Power exam — the starters these rungs control
• Three-phase circuits, delta-wye and the 30° shift on the PE Power exam — the shift behind twelve-pulse front ends
• Rotating Machines — the motor on the other side of the drive
• The PE Power handbook and code books — what you get, and how to be fast in them

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.