Voltage drop on a distribution feeder

Reference notes

Use Next → on the narrator above to walk through feeder voltage drop: the picture, the single-phase and three-phase approximations, the percentage-drop convention, the surprising effect of leading power factor, and the conductor-sizing trade-off between NEC ampacity and voltage drop.

The picture

Every feeder has resistance R and reactance X. When line current I flows, an IR drop and an IX drop subtract from the source voltage along the way. The voltage at the customer's panel is therefore lower than the substation's bus voltage. Designers size conductors so this drop stays within an acceptable percentage of nominal voltage — typically 3 % on a branch circuit, 5 % combined from service to the farthest outlet (NEC informational notes).

The standard approximations

For a short feeder where the angle of the receiving-end voltage is close to the sending-end voltage:

where I is the line current, R is the per-phase line resistance (ohms), X is the per-phase line reactance (ohms), and θ is the power-factor angle of the load (positive for lagging, negative for leading).

Note the role of each term: R sees the in-phase current (the I cos θ component); X sees the quadrature current (the I sin θ component). At unity PF only R contributes. At lagging PF, X adds to the drop. At leading PF, X subtracts from it.

Worked example

A balanced 3-phase 480 V (V_LL), 200 A load served by 500 ft of 4/0 Cu in PVC conduit:

• 4/0 Cu in PVC ≈ R = 0.063 Ω/1000 ft, X = 0.039 Ω/1000 ft (from NEC Chapter 9 Table 9 or manufacturer data).
• For 500 ft: R = 0.0315 Ω, X = 0.0195 Ω.

At 0.85 PF lagging: cos θ = 0.85, sin θ = √(1 − 0.85²) ≈ 0.527.

Power factor and the Ferranti effect

The X·sin θ term has a sign that depends on the PF direction. For lagging PF (positive θ) it adds to the drop. For leading PF (negative θ) it subtracts. Push the leading PF far enough on a reactance-dominant line and the voltage at the receiving end can be higher than at the sending end:

This is the Ferranti effect, classically observed on long lightly-loaded transmission lines where the line charging current dominates. Operators must manage it with shunt reactors or by avoiding light-load operation of long EHV circuits.

Conductor sizing — two independent constraints

1. Ampacity (NEC 310.16 for the cable type and ambient temperature). Sets a minimum size so the insulation does not overheat under the design current. For 200 A continuous in 75 °C-rated insulation, the typical pick is 4/0 Cu or 250 kcmil Al.
2. Voltage drop. Sets a minimum size to stay within the target percentage. Scales as 1/R, which for stranded Cu scales roughly with conductor area.

Pick the larger size that satisfies both. On short feeders ampacity wins easily. On long feeders (typically > 150 ft for branch circuits, > 300 ft for feeders) voltage drop frequently sets the size larger than ampacity would. The design current I_max — the largest expected steady-state load current — must stay below both the ampacity limit and the voltage-drop budget at that current.

Rule of thumb for 600 V circuits: voltage-drop-driven upsizing kicks in around 50 ft per ampere for a typical PF — so a 200 A circuit longer than ~100 ft warrants a voltage-drop calculation alongside the ampacity check.

Per-unit form

In a per-unit power-system study, voltage drop is approximately:

For small angles and resistive-dominant lines: ΔV_pu ≈ |Z_pu| · |I_pu|. The full form is the same trigonometry we just did in volts and amperes.

Keyboard shortcuts

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• R replay narration  ·  M mute / unmute  ·  F fullscreen
• On step 5, click the Toggle PF button to flip lagging ↔ leading and watch ΔV change sign on reactance-heavy lines.