Voltage drop and conductor sizing on the PE Power exam

A conductor has to carry the load current under its installed conditions and deliver acceptable voltage at the far end. The PE Power exam asks for either check, or for the conductor that satisfies both. The NCEES handbook holds the voltage drop relations under Voltage Drop. Ampacity comes from NEC Article 310: the ampacity table and its correction and adjustment tables. Conductor resistance and reactance come from NEC Chapter 9, Tables 8 and 9.

What you actually need to own

• The resistance-only relation. For unity power factor and negligible reactance, the handbook gives VD = 2 × L × R × I / (K × 1,000). L is the one-way length in feet, R is in ohms per 1,000 ft, and K is 1.0 for single-phase or dc and 2/√3 for three-phase. The three-phase case reduces to √3 × I × R × L/1,000. With round numbers, 200 A over 300 ft at 0.05 Ω per 1,000 ft drops 5.2 V on a three-phase circuit.
• The relation with reactance. Otherwise the line-to-neutral drop is approximately I × (R × PF + X × sin Φ), with Φ the inverse cosine of the power factor. R and X are the per-phase ohms of the actual run. Multiply by √3 for the line-to-line drop.
• Where R and X come from. Chapter 9, Table 8 gives dc resistance. Table 9 gives ac resistance and reactance by conductor material and conduit type, and an effective impedance to neutral already evaluated at 0.85 power factor. That column is R × PF + X × sin Φ per 1,000 ft. For a load near 0.85, the current times that value times the length in thousands of feet gives the line-to-neutral drop directly.
• Ampacity under installed conditions. Start from Table 310.16. Multiply by the ambient correction factor from Table 310.15(B)(1) and by the adjustment factor for the number of current-carrying conductors from Table 310.15(C)(1). Read the ampacity and the correction factor in the same insulation temperature column. Section 110.14(C) adds a termination limit.
• Counting conductors. Spares in the raceway count. A neutral that carries only unbalanced current does not count. A neutral on a wye circuit serving mostly nonlinear load does.
• Sizing in the right direction. Divide the load current by the combined factors and find the smallest conductor whose table ampacity meets that number.
• Both limits. Ampacity and voltage drop are separate checks. The permissible current is the smaller of the two results, and the chosen size is the larger.
• Circuits that are not one plain run. Parallel conductors divide the resistance by the number per phase. On a tapped feeder each segment carries the sum of the loads downstream of it.

Where people lose points

• K = √3 in the handbook relation. The three-phase constant is 2/√3.
• Doubling the length when the 2 in the relation already covers out and back.
• Per-1,000-ft values used as the ohms of the run. Scale by length first.
• Tangent for sine, or dropping the reactance term at a lagging power factor.
• A line-to-neutral drop against a line-to-line nominal. Match the two before taking percent.
• Table 9 slips. The wrong conduit column, or ac resistance in place of effective impedance.
• One factor applied, the other skipped. A hot, crowded raceway needs both.
• Mixed temperature columns between the ampacity and its correction factor.
• Drop computed at the table ampacity or the breaker rating. Use the current the load draws.
• The wrong limit. A stated project limit governs over the code's recommended figures.

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. The voltage drop figures candidates quote come from informational notes to 210.19(A) and 215.2(A)(1). They are recommendations, not requirements. Each holds its own circuit to 3 percent at the farthest outlet, with a somewhat larger combined figure for feeder plus branch circuit. Both apply together. See the PE Power handbook and code books.

How to study it

Take one three-phase feeder and work it four ways: resistance only, with reactance at a lagging power factor, from the Table 9 effective impedance, and backwards from an allowed percent to the largest permitted impedance per 1,000 ft. Then put it in a hot, crowded raceway and find which limit governs. Next, work motor circuits, and see how power factor correction lowers the current that causes the drop.

Part of the Transmission and Distribution Analysis area of the PE Power exam. → Practice it on CastorPrep