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09 — Calculators

Capacitance and charging current of a cable

A cable is also a capacitor. Over twenty metres nobody notices. On a long screened motor cable fed from an inverter it becomes a current that flows although nothing is connected — and the residual current device upstream sees it.

Input

From the cable data sheet. Screened cables are markedly higher than unscreened ones.

Use 50 Hz for mains. Under inverter supply the governing frequency is that of the switching edges, not the output frequency.

Result

Charging current per line conductorFlows even with no load connected. A residual current device sees the share returning through the screen.
—mA
Cable capacitance
—nF
Capacitive reactive power
—var
Capacitive reactance
—Ω

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

Operating capacitance per kilometre
250 nF/km
Cable length
150 m
System voltage (line to line)
400 V
System
Three-phase (3~)
Frequency
50 Hz

Result

Charging current per line conductor
2.72 mA
Cable capacitance
37.5 nF
Capacitive reactive power
1.88 var
Capacitive reactance
84,883 Ω

Formula

  • C = C′ · L
  • Three-phase: U_conductor = U / √3
  • I_c = 2π · f · C · U_conductor
  • X_c = 1 / (2π · f · C)

Assumptions and standards

  • The operating capacitance comes from the cable data sheet and is entered here. It depends on construction and screen, not on cross-section alone.
  • The calculation uses a single frequency. On an inverter the actual leakage current is considerably higher, because the steep switching edges contain high-frequency components.
  • The charging current is reactive: it loads the cable and the protective device but transfers no active power.

Frequently asked

Why does the residual current device trip with no fault present?

Because part of the capacitive current flows to earth through the screen and is therefore a differential current. On long screened cables fed from an inverter this quickly adds up to tens of milliamperes. Remedies: a shorter cable, a device with a higher rated residual current, or a type sensitive to all current forms.

From what length does this matter?

On a 50 Hz supply usually only from several hundred metres. On an inverter far sooner — effects are measurable from roughly 50 metres of screened motor cable, because the switching frequency is orders of magnitude above the mains frequency.

Do I add the charging current to the operating current?

Not arithmetically. The charging current is at right angles to the active current, so the sum is geometric. At the usual magnitudes the contribution to the total is small — normally negligible for cable sizing, but not for differential current or the reactive power balance.

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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