Transmission and Distribution Analysis

Moving power from source to load: voltage drop, voltage regulation and support, power factor correction, power quality, fault current, transformer connections, power flow and stability, at high, medium and low voltage. It carries 8–12 of 80 questions, and its eight subtopics are the most of any area on the exam.

What the problems look like

Short calculations, many read from a one-line whose switch positions decide the answer. Recurring shapes — a feeder voltage drop, or the smallest conductor that holds a stated limit; percent regulation and regulator tap or compensator settings; a capacitor bank sized to a target power factor, and its effect on current and loss; THD, unbalance and resonance; fault duty at a bus and sequence-network connections; winding voltages and currents, vector groups, open-delta and paralleled banks; transfer across a reactance and line constants; and swing-equation and equal-area questions.

By exam day you should be able to —

• compute voltage drop two ways (the first at unity PF, negligible X): VD = 2·L·R·I/(K·1,000), with K = 1.0 single-phase or dc and 2/√3 three-phase, and VD_ln ≈ I·[R·PF + X·sin(cos⁻¹ PF)];
• find regulation, (V_NL − V_FL)/V_FL, with V_NL = V_s/A for a line with known constants;
• size correction with ΔQ = P(tan Φ₁ − tan Φ₂), and the loss reduction 100[1 − (PF₁/PF₂)²];
• quantify power quality: THD = √(ΣVₙ²)/V₁ for n ≥ 2, unbalance = maximum deviation ÷ average, and the parallel resonant order h = √(S_sc/Q_c);
• convert fault duty, S_sc = √3·V_nom·I_sc, and connect the sequence networks: series for a single line-to-ground fault, I = 3E/(Z₁ + Z₂ + Z₀); positive and negative only for line-to-line, I = √3·E/(Z₁ + Z₂); all three in parallel for double line-to-ground;
• read a transformer connection: winding voltage, phase shift, and its zero-sequence path;
• work power flow and stability in per unit or line-to-line kV: P = (V₁V₂/X)·sin δ, SIL = V²/Z_s, and (2H/ω_s)·d²δ/dt² = P_m − P_e.

Where people lose points

• √3, 3 or neither: pair a line-to-line voltage with √3 and line current, or with three-phase MVA; pair a line-to-neutral voltage with per-phase quantities. Three-phase loss is 3I²R.
• Read the one-line first: an open breaker or tie removes its branch entirely. Check tap points and the faulted bus.
• Voltage drop: L is the one-way routed length; keep the X·sin term at lagging power factor. Ampacity and voltage drop are separate checks, and a stated project limit governs over the NEC's recommended figures.
• Regulation: divide by the full-load voltage, and use the actual no-load voltage (V_s/A on a line), not the nominal. A regulator range of ±10 percent in 32 steps is 0.625 percent per step.
• Capacitors: the tangent relation runs on real power. Kvar added is not kVA released; loss falls with the square of current. A bank relieves only the conductors between itself and the source, and a fixed bank at light load can drive the bus leading.
• Harmonics: combine orders as a root-sum-square without the fundamental. Inductive reactance scales by h, capacitive by 1/h. Triplen currents add in the neutral.
• Faults: fault MVA and fault current rank buses differently across voltage levels. Include the source impedance and every series element, and count motors as sources. A delta or ungrounded-wye winding leaves its terminal open in the zero-sequence network, and a ground fault's impedance enters as 3Z_F.
• Transformers and stability: an open-delta bank carries 57.7 percent of the three-unit rating. Clock hour × 30° is low-voltage lag, so hour 11 is a 30° lead. In stability work ω_s = 2πf, angles are in radians, and X spans the whole path; the swing equation carries 2H, the clearing-time relation 4H.

Have these at your fingertips

The voltage-drop relations, the tangent correction, S_sc = √3·V_nom·I_sc, the fault interconnections and the power-angle and swing equations. The Handbook has them under Voltage Drop, Voltage Regulation, Power Factor Correction and Voltage Support, Power Quality, Fault Current Analysis, Transmission Line Models, Power Flow, and Power System Stability, plus 3-Phase Circuits and Per Unit System. Some problems also draw on the NEC (NFPA 70-2020): ampacity at Table 310.16, motor full-load current at Table 430.250, the motor overload setting with a load-side capacitor at 460.9. The exam opens one chapter of a standard at a time.

Going deeper

• Voltage drop and conductor sizing on the PE Power exam — both relations
• Power factor correction and capacitor sizing on the PE Power exam — the tangent relation
• Fault current analysis on the PE Power exam — duty at a bus
• Symmetrical components and unbalanced faults on the PE Power exam — the sequence networks

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.