Why Your Cable Sizing Is Wrong: The Reactive Component Most Engineers Ignore

There is a voltage drop calculation error that I see repeatedly in design reviews — from junior engineers and experienced practitioners alike. It's subtle enough to pass a cursory check, but significant enough to cause real problems on long cable runs with motor loads.

The error: calculating voltage drop using only the resistive component of cable impedance, ignoring the reactive (inductive) component entirely.

For small cables on short runs, this doesn't matter much. But for cables 50mm² and above feeding motor loads at power factors of 0.75–0.85, the reactive component can add 15–30% more voltage drop than a resistance-only calculation predicts. I've seen cables that "passed" a simplified voltage drop check fail commissioning tests because the actual voltage at the motor terminals was significantly lower than calculated.

The Two Components of Cable Impedance

Every cable has two impedance components:

• Resistance (R) — opposition to current flow due to the conductor material. Dominant in small cables.
• Reactance (X) — opposition to current flow due to the magnetic field created by the conductor. Increases with cable size and spacing.

The total impedance per unit length is:

The voltage drop in a cable depends on both components and the power factor of the load:

The simplified formula that many engineers use:

The difference between Equation 2 and Equation 3 is the reactive term X sinφ. When power factor is 1.0 (purely resistive load), sinφ = 0 and the reactive term vanishes — the simplified formula is exact. But for motor loads with PF = 0.80, sinφ = 0.6, and the reactive term becomes significant.

Why This Matters More for Large Cables

Here's the key insight that many engineers miss: as cable cross-sectional area increases, resistance decreases but reactance stays approximately constant.

For a 4 mm² cable, the X/R ratio is 0.017 — reactance is negligible, and the simplified formula is perfectly adequate. For a 185 mm² cable, the X/R ratio is 0.583 — reactance is more than half the resistance. For a 400 mm² cable, reactance actually exceeds resistance.

A Worked Example That Exposes the Error

Scenario: 185 mm² 4-core XLPE/SWA cable, 200 m route length, feeding a 200 kW motor at 415 V, 3-phase, PF = 0.80.

Design current:

Cable impedance data (from BS 7671 Table 4E4B at 90°C): R = 0.127 Ω/km, X = 0.074 Ω/km

Resistance-only voltage drop (the common mistake):

Full impedance voltage drop (the correct calculation):

The difference: 4.87% vs 3.69% — the full calculation gives a voltage drop that is 32% higher than the resistance-only result. The resistance-only calculation says "3.69%, well within 5% — pass." The full calculation says "4.87%, marginal and may fail when cable is warm." If the allowable limit is 5%, the engineer using the simplified formula has almost no margin, and any increase in ambient temperature or load would push the circuit over the limit.

What the Standards Actually Say

BS 7671

BS 7671, Appendix 12, Note 7 — Voltage drop in consumers' installations

The mV/A/m values in BS 7671 Appendix 4 tables (e.g., Table 4E4B) are given in two forms:

• Two-column format: separate R and X columns for 3-phase circuits, requiring the engineer to combine them using the full formula
• Three-column format: combined value at a specific power factor (typically 0.8 or 1.0)

If you use the combined column, the reactive component is already included — but only at the stated power factor. If your load's power factor differs from the table assumption, you must use the R and X columns with the full formula.

AS/NZS 3008

AS/NZS 3008.1.1, Clause 4.5.2 — Voltage drop calculation

AS/NZS 3008 Tables 35–42 provide voltage drop values in mV/A/m. The standard explicitly requires the use of the full impedance formula for circuits where the power factor differs from 0.8. Table 35 Note 2 states that the tabulated values assume PF = 0.8, and for other power factors, the R and X components must be used separately.

NEC

NEC, Chapter 9, Table 9 — AC Resistance and Reactance for 600-Volt Cables

The NEC takes the most explicit approach: Chapter 9, Table 9 provides separate R and X columns for every conductor size and conduit type. There is no combined mV/A/m value — the engineer is forced to use both components. The NEC effectively prevents the resistance-only error by table design.

When the Simplified Formula Is Acceptable

The resistance-only approach is adequate when:

1. Cable size ≤ 16 mm² — reactance is negligible regardless of power factor
2. Power factor ≥ 0.95 — sinφ ≤ 0.31, so the reactive term is small even for large cables
3. The voltage drop margin is large — if the calculated voltage drop is well below the limit (e.g., 1.5% against a 5% limit), the reactive component won't change the result

For any other situation — particularly motor feeders on long runs with cables 50 mm² and above — use the full impedance formula.

A Rule of Thumb

For cables 50 mm² and above at power factor 0.80:

• Add approximately 15% to the resistance-only voltage drop for 50–95 mm² cables
• Add approximately 25% for 120–185 mm² cables
• Add approximately 35% for 240–400 mm² cables

These are rough corrections, not substitutes for the proper calculation. But they're useful as a quick sanity check on existing calculations.

The Real-World Consequence

At a large-scale mining operation, I reviewed a cable schedule for a concentrator plant upgrade where 12 motor feeders had been sized using resistance-only voltage drop calculations. The cables were 95 mm² to 300 mm², with route lengths of 150–400 m. When we recalculated using full impedance, three circuits exceeded the 5% voltage drop limit and two were above 7%. The motors on those circuits had a history of "difficulty starting" and "intermittent undervoltage trips" that the operations team had been living with for years. Resizing those three cables resolved the issue completely.

The takeaway: if you have motor circuits that start reluctantly or trip intermittently, recalculate the voltage drop using the full impedance formula. The answer may be in the cable, not the motor.

Related Resources

• Northeast Blackout: Long Feeder Voltage Drop — How reactive impedance on a 200m feeder contributed to a grid collapse
• Cable Sizing: The 50m Office Feeder — 4 Standards Compared — See how impedance values differ between AS/NZS, BS, IEC, and NEC
• Voltage Drop: The 100m Workshop Cable — NEC's 3% rule vs the world on long cable runs
• View all worked examples →