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26 — Calculators

Size a motor feeder

Motor cables are usually sized for the operating current — and then people wonder why the motor starts sluggishly on a long run. The starting current drops across the same cable, and a multiple of the current means a multiple of the voltage drop.

Input

For the motor feeder alone, not for the whole installation.

Result

Required cross-section, standard size
—mm²
Rated motor current
—A
Calculated cross-section
—mm²
Voltage drop in operation at this size
—%
Voltage drop on the cable at startAdds to the dip in the network.
—%

A guide, not a design to standard. We give no warranty for the correctness of the results, the applicable standards and case-by-case verification govern.

Worked example

The default case the calculator starts with, worked through once. Change the values above and it recalculates immediately.

Inputs

Rated motor power
30 kW
System voltage
400 V
Efficiency
92 %
Power factor cos φ
0.86
Length of the feeder
80 m
Permissible voltage drop in operation
3 %
Starting current ratio I_A / I_N
7
Conductor material
Copper (κ = 56 m/Ω·mm²)

Result

Required cross-section, standard size
10 mm²
Rated motor current
54.7 A
Calculated cross-section
9.7 mm²
Voltage drop in operation at this size
2.91 %
Voltage drop on the cable at start
7.11 %

Formula

  • P_in = P_out / η
  • I_N = P_in / (√3 · U · cos φ)
  • A = (√3 · L · I_N · cos φ) / (κ · Δu)
  • Starting: Δu_A ≈ (√3 · L · I_A · cos φ_A) / (κ · A)

Assumptions and standards

  • The cross-section here follows from the operating voltage drop alone. Current-carrying capacity, short-circuit protection and the disconnection condition are separate proofs.
  • For starting, a power factor of 0.3 is used — at start the motor is strongly inductive.
  • For inverter-fed motors, additional requirements on screening and length apply that are not covered here.

Frequently asked

What voltage drop is still acceptable at start?

It adds to the dip in the supplying network. Together they determine what reaches the motor — and starting torque falls with the square of that. If less than eighty percent of nominal voltage remains, starting heavy loads becomes unreliable.

Why is the operating current not enough for sizing?

It is enough for heating, not for starting behaviour. A cable with three percent drop in operation reaches a multiple of that at seven times the current — and that is exactly the moment the motor needs the voltage most.

Does this apply with a variable frequency drive?

The starting part does not: a drive limits the current and ramps up the frequency, so there is no inrush. Other topics arrive instead — screening, leakage currents, permissible cable length per the drive manufacturer.

Calculating is the easy part.

A formula gives you a number. Designing a plant also demands installation method, grouping, discrimination, the standards in force and a look at the installed base. That is what we take on.

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