Challenge: Size a Cable for This 132kW Motor in a 45°C Ambient Tray Installation

Take a moment. Calculate the design current. Identify the derating factors. Select the cable. Then read on.

Step 1: Calculate the design current (I_b).

The motor draws power from the supply. The supply current includes losses in the motor (efficiency) and the reactive component (power factor):

Ib = P / (√3 × V × PF × η)

Ib = 132,000 / (√3 × 415 × 0.87 × 0.95)

Ib = 132,000 / (1.732 × 415 × 0.87 × 0.95)

Ib = 132,000 / 594.0

Ib = 222.2 A

Step 2: Select the protection device rating (I_n).

The MCCB must be rated at or above I_b. Standard MCCB ratings: 200, 225, 250, 315, 400 A. For a motor circuit, also consider starting current — but for cable sizing, we need I_n ≥ I_b:

In = 250 A (next standard rating above 222.2 A)

Step 3: Determine the required tabulated current (I_t).

The cable must carry I_n after derating factors are applied:

It ≥ In / (Ca × Cg)

Where C_a is the ambient temperature correction factor and C_g is the grouping correction factor.

Ambient temperature correction (C_a):

For XLPE insulation (90°C maximum operating temperature) at 45°C ambient, from IEC 60364-5-52, Table B.52.14:

Ca = 0.87

Grouping correction (C_g):

For 5 circuits on a perforated tray (single layer, touching), from IEC 60364-5-52, Table B.52.17:

Cg = 0.73

Required tabulated current:

It ≥ 250 / (0.87 × 0.73)

It ≥ 250 / 0.635

It ≥ 393.7 A

IEC 60364-5-52 selection:

From IEC 60364-5-52, Table B.52.10 (Reference Method E, XLPE, copper, 3-phase), find the cable with tabulated current ≥ 393.7 A:

Selected cable: 185 mm² 4-core XLPE/copper

Note the 150 mm² cable at 391 A is tantalisingly close to the required 393.7 A. This is where shortcuts kill you. A 2.7 A shortfall means the cable is undersized. There is no rounding down in cable sizing.

AS/NZS 3008.1.1:2017 comparison:

Under AS/NZS 3008.1.1:2017, the reference ambient is 40°C. The ambient derating from 40°C to 45°C is less severe (C_a = 0.90 from Table 6), but the base tabulated currents in Table 13 for the same installation method may differ slightly. The grouping factors from Table 22 for 5 circuits on a perforated tray give C_g = 0.73 (same as IEC for this configuration). Working through the AS/NZS calculation typically yields the same 185 mm² result for this scenario, though the margin is more comfortable because the ambient derating is less severe.

Cable sized for current capacity — now verify voltage drop. For 185 mm² copper cable at 45 m:

From IEC 60364-5-52 tables or manufacturer data, the mV/A/m value for 185 mm² 4-core XLPE at 0.87 PF is approximately 0.23 mV/A/m (combining resistive and reactive components).

Vd = (mV/A/m × Ib × L) / 1000

Vd = (0.23 × 222.2 × 45) / 1000

Vd = 2.30 V

As a percentage of supply voltage:

Vd% = (2.30 / 415) × 100 = 0.55%

This is well within the 5% limit (20.75 V). Voltage drop is not the governing factor for this installation — the cable size is determined by current capacity after derating.

If the run were longer — say 200 m (common in mining and industrial plants) — voltage drop would become the controlling factor and might push the cable to 240 mm² or beyond, regardless of current capacity.

What made this challenge tricky:

• The combined derating factor is severe. C_a × C_g = 0.635. The cable must carry 57% more current than the protection device rating to account for the hot, crowded installation environment. Engineers who forget either factor — or who apply them to I_b instead of I_n — will undersize the cable.
• The 150 mm² trap. At 391 A versus 393.7 A required, the 150 mm² cable looks adequate at first glance. It is not. A cable that is 99.3% of the required rating is still undersized. In a real installation, this 2.7 A margin could be consumed by any deviation from assumed conditions.
• Motor efficiency matters. Omitting the 0.95 efficiency factor would give I_b = 211 A instead of 222 A. That 11 A difference would not change the cable size in this case, but in a borderline scenario it is the difference between a cable that passes and one that does not.
• Power factor in the design current. PF = 0.87 means the motor draws more current per kilowatt of mechanical output than a unity PF load. Forgetting PF in the I_b calculation is the most common motor cable sizing error — it undersizes the cable by approximately 15%.