Industrial Motor Feeder in Northern Germany

Scenario

A food processing plant in Hamburg is installing a new 3-phase induction motor (15 kW, 400 V) for a conveyor system. The cable must run 72 m from the MCC panel to the motor across a factory floor with ambient temperature of 45°C and shared conduit with four other power cables. Local DIN VDE 0298-4 mandates ≤3% voltage drop and requires copper conductors with PVC insulation (PVC-CU). Space constraints limit conduit diameter, favouring compact cable sizing — but derating cannot be ignored.

Given Data

• Voltage: 400 V
• Power: 15,000 W
• Power Factor: 0.85 (nameplate value for IE3 motor)
• Cable Length: 72 m
• Acceptable Voltage Drop: 3%

Calculation

Using the Cable Size Calculator’s underlying formula for 3-phase AC:

1. Full-load current:
   ( I = \frac{P}{\sqrt{3} \times V \times \text{pf}} = \frac{15{,}000}{1.732 \times 400 \times 0.85} \approx 25.6 , \text{A} )

2. Minimum cross-section for voltage drop (copper, ρ = 0.0172 Ω·mm²/m):
   ( A = \frac{\sqrt{3} \times \rho \times L \times I \times 100}{V \times %\text{drop}} = \frac{1.732 \times 0.0172 \times 72 \times 25.6 \times 100}{400 \times 3} \approx 5.7 , \text{mm}^2 )

3. Tool input & output:
   Inputs → voltage=400, power=15000, power_factor=0.85, length=72, acceptable_voltage_drop=3
   Output → cable_size=6.0 mm², calculated_voltage_drop=2.87%

Note: While 6 mm² meets voltage drop, derating applies — 5 cables in one conduit at 45°C yields ~65% derating factor (DIN VDE 0298-4 Table 12). Base ampacity of 6 mm² PVC-CU is 41 A → derated capacity = 41 × 0.65 ≈ 26.7 A > 25.6 A. Marginally acceptable, but tight.

Result and Decision

The calculator recommends 6.0 mm², and thermal verification confirms it satisfies both voltage drop (2.87% < 3%) and derated current capacity. However, due to zero margin for future load increase or temporary overloads, engineers selected 10 mm² PVC-CU cable, which provides 35 A base rating → derated 22.8 A still sufficient? Wait — no: 10 mm² base = 57 A → 57 × 0.65 = 37.1 A, ample margin. Voltage drop recalculates to 1.72%, well below 3%. Final selection: 10 mm², balancing safety, compliance, and maintainability.

Lesson

Voltage drop compliance alone is insufficient — always validate against derated current-carrying capacity using local standards; undersized margin invites nuisance tripping and premature aging. When derating pushes design close to limits, stepping up one standard size (e.g., 6 → 10 mm²) costs <12% more but delivers >40% thermal headroom.