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.
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
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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.
The grey values are an example. Simply enter your own.
Matching services
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.
Method and questions
Cable capacitance
The charging current and reactive power a long cable draws with no load at all.
Discuss a projectWorked 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 and standards
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.
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. A shorter cable, a device with a higher rated residual current or a type sensitive to all current forms will help.
From what length does this matter?
On a 50 Hz supply usually only from several hundred metres. On an inverter far sooner, where 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. It is normally negligible for cable sizing, but not for differential current or the reactive power balance.
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