Electric Power Devices

The hardware of a power system: transformers, capacitor banks, batteries and ultracapacitors, photovoltaic and wind sources, and the tests that characterize a transformer. Electric Power Devices carries 8–12 of 80 questions across five subtopics, level with General Applications and Transmission and Distribution Analysis and just behind the three largest areas.

What the problems look like

Short calculations from a nameplate, a test report or a one-line, plus code lookups. Recurring shapes — transformer referral, regulation, efficiency, parallel load sharing, autotransformer ratings and tap selection; capacitor bank output, unit voltage, discharge, stored energy and NEC Article 460 sizing; storage runtime, C-rates and ultracapacitor ride-through; PV and wind string voltage, annual energy, inverter limits and rotor power; and testing: open-circuit and short-circuit data reduced to equivalent-circuit values, and what each acceptance test can detect.

By exam day you should be able to —

• refer impedances across a transformer: Z′₂ = a²Z₂, R_eq = R₁ + a²R₂;
• compute regulation and efficiency: %VR = (I_op/I_ra)(%R cos θ + %X sin θ), η = P_out/(P_out + P_cu + P_core), with peak efficiency at a load fraction of √(P_core/P_cu,rated);
• divide load between paralleled units in proportion to S_rated/%Z, and rate an autotransformer from S_IO/S_W = (N_SE + N_C)/N_SE;
• reduce test data: open-circuit R_c = V_o²/P_o, X_m = V_o/I_m; short-circuit R_eq = P_sc/I_sc², |Z_eq| = V_sc/I_sc, X_eq = √(|Z_eq|² − R_eq²);
• work a capacitor: Q = 2πfCV², so Q = Q_rated(V/V_rated)²; energy between two voltages ½C(V₁² − V₂²); Δt = C·ΔV/I at constant current;
• size storage: Wh = V × Ah, I = M·C for a C-rate, and Peukert's t = H(C/(I·H))^k for lead-acid;
• handle PV and wind: V = V_STC[1 + (T_cell − 25°C)β/100], E = A·r·H·PR, and P = ½ρAv³ times the conversion fraction.

Where people lose points

• Referral: an impedance moves by a², not a, and is larger on the higher-voltage winding. Refer first, then add.
• Which loss scales: winding loss goes with the square of the load fraction; core loss stays constant while the unit is energized. Efficiency is built on kW, so apply the power factor to the kVA.
• Regulation: %R pairs with cos θ and %X with sin θ. Split %Z by its own X/R ratio, in quadrature, and scale by I_op/I_ra at any load other than rated; sin θ is negative for a leading load.
• Test recipes: the open-circuit test, at rated voltage, gives the shunt branch (V²/P); the short-circuit test, at reduced voltage, gives the series branch (P/I²). Confirm the test current equals rated current before reading the wattmeter as full-load winding loss; otherwise scale it by (I_rated/I_test)².
• Parallel transformers: percent impedances sit on each unit's own kVA base. The bank's limit is the load at which the first unit reaches its nameplate.
• Read the drawing: wye or delta sets the voltage on each capacitor unit, and the same units deliver three times the vars in delta. Switch positions decide what is connected. Series battery blocks add voltage; parallel strings add ampere-hours.
• Capacitor rules and windows: under NFPA 70-2020 (NEC) 460.8(A), capacitor circuit conductors need ampacity of at least 135% of rated current, not the 125% used for continuous loads. For ride-through, use only the voltage window above drop-out.
• PV and storage limits: module voltage falls as cells heat, so the longest string is set by V_oc at the lowest expected temperature, rounded down. An inverter's ac rating caps its output whatever the array's dc rating. A battery must satisfy both the duty's ampere-hours and its discharge-rate limit.

Have these at your fingertips

The referral rule, both test recipes, Q ∝ V² and ½CV². In the Handbook the transformer material sits under Single-Phase Transformer Equivalent Circuits, Transformer Losses, Transformer's Percentage Voltage Regulation, Transformer's Efficiency, Condition for Maximum Efficiency, Single-Phase Transformers in Parallel and Autotransformers, with Open-Circuit Testing and Short-Circuit Test alongside. Capacitors has the bank and energy relations; Theoretical Energy, Discharge Rates and Peukert's Relation for Lead-Acid Batteries cover storage; Photovoltaic (PV) Systems holds the PV relations. Capacitor, PV, wind, storage and interconnection rules come from NEC Articles 460, 690, 694, 480/706 and 705, and the exam opens one chapter of a standard at a time.

Going deeper

• Power factor correction and capacitor sizing on the PE Power exam — sizing a bank and Article 460
• The per-unit system on the PE Power exam — percent impedance and base changes
• Power Electronic Circuits and Control Devices — the inverters behind PV and storage
• The PE Power handbook and code books — working with one chapter open

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.