Worked Example: Industrial Motor Feeder — 75 kW DOL Motor, 150 m Run

This example calculates cable size under AS/NZS 3008.1.1:2017, BS 7671:2018+A2, IEC 60364-5-52, and NEC/NFPA 70:2023. The 150 m route length makes this a borderline case where voltage drop during motor starting — not steady-state current capacity — may govern cable selection.

For a three-phase induction motor:

I_FL = P / (√3 × V × PF × η) — (Eq. 1)

Under AS/NZS (415 V):

I_FL = 75,000 / (√3 × 415 × 0.86 × 0.935)

I_FL = 75,000 / (1.732 × 415 × 0.86 × 0.935)

I_FL = 75,000 / 578.0

I_FL = 129.8 A

Under BS 7671 / IEC / NEC (400 V):

I_FL = 75,000 / (√3 × 400 × 0.86 × 0.935)

I_FL = 75,000 / 557.0

I_FL = 134.6 A

For DOL starting with I_st/I_FL = 7.5:

I_start = 7.5 × I_FL — (Eq. 2)

The starting current of approximately 1,000 A persists for 12 seconds as the high-inertia fan load accelerates to full speed. During this period, the cable must deliver the starting current without excessive voltage drop at the motor terminals.

Each standard has different reference conditions and derating tables.

Ambient temperature correction (k₁):

Reference ambient = 40°C. Actual = 45°C.

From AS/NZS 3008.1.1:2017, Table 22, Row 45°C, Column 90°C XLPE:

k₁ = 0.95

Grouping correction (k₂):

6 circuits on perforated cable tray, touching.

From AS/NZS 3008.1.1:2017, Table 24, Row: 6 multicore cables on tray:

k₂ = 0.73

Combined derating:

k_total = k₁ × k₂ = 0.95 × 0.73 = 0.694 — (Eq. 3a)

Ambient temperature correction (C_a):

Reference ambient = 30°C. Actual = 45°C.

From BS 7671, Table C.1, Row 45°C, Column 90°C XLPE:

C_a = 0.87

Grouping correction (C_g):

6 circuits on perforated cable tray (Reference Method E).

From BS 7671, Table C.3, Row: 6 multicore on tray, touching:

C_g = 0.73

Combined derating:

C_total = C_a × C_g = 0.87 × 0.73 = 0.635 — (Eq. 3b)

Ambient temperature correction:

Reference ambient = 30°C (same as BS 7671).

From IEC 60364-5-52, Table B.52.14, Row 45°C, Column 90°C XLPE:

C_a = 0.87

Grouping correction:

From IEC 60364-5-52, Table B.52.17, 6 multicore on tray:

C_g = 0.73

Combined derating:

C_total = 0.87 × 0.73 = 0.635 — (Eq. 3c)

Temperature correction:

From NEC Table 310.15(B)(1), 90°C column, 45°C ambient:

C_a = 0.87

Adjustment for conduit/raceway grouping:

From NEC 310.15(C)(1), Table 310.15(C)(1), 6 current-carrying conductors. For cable tray per NEC 392.80(A)(1)(a), cables rated 2,000 V or less, 6 multiconductor cables on a single-layer tray:

C_g = 0.80 (NEC 392 is more generous for open cable tray)

Continuous load factor: NEC 430.22 requires motor branch circuit conductors to have ampacity not less than 125% of the motor full-load current:

F_cont = 1.25

Combined effective derating:

C_total = C_a × C_g / F_cont = 0.87 × 0.80 / 1.25 = 0.557 — (Eq. 3d)

The cable must have a tabulated current-carrying capacity (before derating) that satisfies:

I_z ≥ I_FL / k_total — (Eq. 4)

For NEC, the requirement is:

I_z ≥ (1.25 × I_FL) / (C_a × C_g)

Cable selection from each standard’s tables:

First surprise: Based on current capacity alone, AS/NZS selects 70 mm², BS/IEC select 95 mm², and NEC selects 4/0 AWG (107 mm²). The NEC result is 53% more copper than AS/NZS. But we have not checked voltage drop yet.

For a three-phase circuit, voltage drop is calculated using the impedance method:

ΔV = √3 × I_FL × L × (r × cos(φ) + x × sin(φ)) / 1000 — (Eq. 5)

Where r and x are the resistance and reactance per unit length (mΩ/m), and φ is the load power factor angle (cos(φ) = 0.86, sin(φ) = 0.51).

70 mm² (AS/NZS selection):

From AS/NZS 3008.1.1:2017, Table 35, 70 mm², XLPE copper, three-phase:

r = 0.321 mΩ/m, x = 0.110 mΩ/m

ΔV = 1.732 × 129.8 × 150 × (0.321 × 0.86 + 0.110 × 0.51) / 1000

ΔV = 33,730 × 0.332 / 1000

ΔV = 11.20 V = 2.70% (of 415 V)

95 mm² (BS 7671 / IEC selection):

From BS 7671, Table 4E2B, 95 mm²:

r = 0.236 mΩ/m, x = 0.110 mΩ/m

ΔV = 1.732 × 134.6 × 150 × (0.236 × 0.86 + 0.110 × 0.51) / 1000

ΔV = 34,979 × 0.259 / 1000

ΔV = 9.06 V = 2.27% (of 400 V)

4/0 AWG / 107 mm² (NEC selection):

From NEC Chapter 9, Table 9, 4/0 AWG copper:

r = 0.203 mΩ/m, x = 0.110 mΩ/m

ΔV = 1.732 × 134.6 × 150 × (0.203 × 0.86 + 0.110 × 0.51) / 1000

ΔV = 34,979 × 0.231 / 1000

ΔV = 8.08 V = 2.02% (of 400 V)

All selections pass the running voltage drop limits (AS/NZS 3000 Cl. 3.6.2: 5%, BS 7671 Appendix 12: 5%, IEC 60364-5-52 Cl. 525: 5%, NEC 215.2 Informational Note: 5%).

This is where the 150 m route length becomes decisive. At starting, the power factor drops to 0.25 (cos(φ) = 0.25, sin(φ) = 0.968), and the current increases to 7.5× full load:

ΔV_start = √3 × I_start × L × (r × cos(φ_start) + x × sin(φ_start)) / 1000 — (Eq. 6)

70 mm² at 973 A starting current (AS/NZS):

ΔV_start = 1.732 × 973 × 150 × (0.321 × 0.25 + 0.110 × 0.968) / 1000

ΔV_start = 252,801 × 0.186 / 1000

ΔV_start = 47.0 V = 11.3% (of 415 V)

Motor terminal voltage = 415 − 47.0 = 368 V

Starting torque retention (torque is proportional to V²):

T_start / T_rated = (368 / 415)² = 0.786 = 78.6% — (Eq. 7)

This is borderline. IEEE 141 (Red Book) recommends a minimum of 80% terminal voltage (64% starting torque) for reliable starting. At 78.6% torque, this motor may fail to accelerate the high-inertia fan load within acceptable time. For a steel mill environment with voltage fluctuations, this is unacceptable.

95 mm² at 1,010 A starting current (BS 7671 / IEC):

ΔV_start = 1.732 × 1,010 × 150 × (0.236 × 0.25 + 0.110 × 0.968) / 1000

ΔV_start = 262,414 × 0.165 / 1000

ΔV_start = 43.3 V = 10.8% (of 400 V)

Motor terminal voltage = 400 − 43.3 = 356.7 V. Starting torque retention = (356.7 / 400)² = 79.5%.

Still below 80% terminal voltage. The motor will likely start but with marginal torque and extended acceleration time. For a high-inertia fan in a steel mill, this is a design risk.

4/0 AWG / 107 mm² at 1,010 A starting current (NEC):

ΔV_start = 1.732 × 1,010 × 150 × (0.203 × 0.25 + 0.110 × 0.968) / 1000

ΔV_start = 262,414 × 0.157 / 1000

ΔV_start = 41.2 V = 10.3% (of 400 V)

Motor terminal voltage = 400 − 41.2 = 358.8 V. Starting torque retention = (358.8 / 400)² = 80.5%.

The NEC selection just barely passes the 80% terminal voltage threshold — by only 0.5%.

All four selections need review. The motor starting voltage drop at 150 m pushes every selection to the boundary. The next cable size up for each standard:

AS/NZS 3008: Upsize from 70 mm² to 120 mm²

From Table 35, 120 mm²: r = 0.188 mΩ/m, x = 0.100 mΩ/m

ΔV_start = 1.732 × 973 × 150 × (0.188 × 0.25 + 0.100 × 0.968) / 1000

ΔV_start = 252,801 × 0.144 / 1000

ΔV_start = 36.4 V = 8.8%

Motor terminal voltage = 415 − 36.4 = 378.6 V. Torque retention = (378.6/415)² = 83.2%. PASS.

BS 7671 / IEC: Upsize from 95 mm² to 120 mm²

From Table 4E2B, 120 mm²: r = 0.188 mΩ/m, x = 0.100 mΩ/m

ΔV_start = 1.732 × 1,010 × 150 × (0.188 × 0.25 + 0.100 × 0.968) / 1000

ΔV_start = 262,414 × 0.144 / 1000

ΔV_start = 37.8 V = 9.4%

Motor terminal voltage = 400 − 37.8 = 362.2 V. Torque retention = (362.2/400)² = 82.0%. PASS.

NEC: Upsize from 4/0 AWG to 250 kcmil (127 mm²)

From NEC Table 9, 250 kcmil: r = 0.171 mΩ/m, x = 0.105 mΩ/m

ΔV_start = 1.732 × 1,010 × 150 × (0.171 × 0.25 + 0.105 × 0.968) / 1000

ΔV_start = 262,414 × 0.145 / 1000

ΔV_start = 38.1 V = 9.5%

Motor terminal voltage = 400 − 38.1 = 361.9 V. Torque retention = (361.9/400)² = 81.9%. PASS.

Motor branch circuit protection varies significantly across standards:

NEC key difference (NEC 430.52): NEC explicitly limits motor branch circuit short-circuit and ground-fault protection to specific multiples of FLC — 250% for inverse-time breakers, 175% for dual-element fuses, 800% for instantaneous-trip breakers. This interacts with cable sizing because the protection device rating determines the minimum cable ampacity.

The key finding in this example is that motor starting voltage drop — not steady-state current capacity — governs cable selection for all four standards when the route exceeds approximately 100 m for a 75 kW DOL motor. The cable sizes selected purely on current capacity (70 mm² to 107 mm²) all had to be upsized to 120–127 mm² once starting voltage drop was checked.

What makes this counterintuitive is the convergence: despite AS/NZS starting with a 70 mm² cable and NEC starting with 107 mm² (a 53% difference in copper), the final cable selections after voltage drop analysis are nearly identical at 120–127 mm². The standards diverge on current capacity but converge on starting voltage drop because the physics of impedance at 150 m are independent of the administrative differences between standards.

This has profound cost implications: an engineer who sizes a motor feeder cable only for steady-state current capacity under AS/NZS 3008 would specify 70 mm², using only 58% of the copper actually required. The motor would either fail to start, take dangerously long to accelerate, or draw excessive starting current from a reduced-voltage terminal — any of which can cause protection trips, voltage sags affecting other equipment, or motor winding damage from extended locked-rotor conditions.