Neutral Earthing Resistor Formulas
Neutral earthing resistor formulas: the resistance for a ground fault current limit, the power in the resistor during a fault and the energy for a rated time.
The formulas
| To find | Formula |
|---|---|
| Phase voltage | Vp = VL / √3 |
| Resistance for a current limit | R = Vp / Ig |
| Power during a fault | P = Ig² × R = Vp × Ig |
| Energy for the rated time | E = P × t |
VL is the line voltage of the system, Ig the ground fault current that the resistor lets through and t the time rating of the resistor. The formulas take a solid fault from one phase to earth and ignore the impedance of the source and the cable, so the real current is a little lower. The resistor is rated for a short time, such as 10 s, because the protection clears the fault, and it needs a longer rating if the fault can stay. The current limit comes from the protection design, the cable screens and the damage allowed, and the values here are examples.
Worked example: an 11 kV system with a limit of 400 A
- Vp = 11,000 / √3 = 6,351 V
- R = 6,351 / 400 = 15.88 Ω
- P = 400² × 15.88 = 2.54 MW
- For a rating of 10 s, E = 2.54 × 10 = 25.4 MJ
Resistance and power for an 11 kV system by current limit
| Current limit | Resistance | Power in the fault |
|---|---|---|
| 50 A | 127 Ω | 0.3175 MW |
| 100 A | 63.51 Ω | 0.6351 MW |
| 200 A | 31.75 Ω | 1.27 MW |
| 400 A | 15.88 Ω | 2.54 MW |
| 1000 A | 6.351 Ω | 6.351 MW |
Frequently asked questions
Why limit the ground fault current?
A lower fault current means less damage to the machine and the cables, lower step and touch voltages and less stress on the system, while still giving a current that the protection can sense.
What is the trade-off?
A lower current is harder to detect, and it calls for a sensitive earth fault relay. A higher current gives easier protection but more damage.
What other limits does the resistor have?
A continuous rating for a neutral current in service, a voltage rating at the neutral and a temperature rise limit. The maker states them.
What is the difference from a solid earth?
A solidly earthed system lets the full fault current flow and has no neutral resistor. The resistor trades fault current for lower damage.
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