Protection
Neutral earthing resistor value and rating
- where
- resistance (Ω)
- system line-to-line voltage (V, entered in kV)
- earth-fault current limit (A)
- power during a fault (W, shown in MW)
- energy over the rated time (J, shown in MJ)
- rated time (s)
Explain this equation
Sizes a neutral earthing resistor to limit an earth fault to a chosen current and gives the power and energy it must absorb over its short-time rating. Use it when specifying an NER or checking an existing one.
U/√3 is the phase-to-neutral voltage that appears across the resistor during a solid earth fault. I is the current you want to allow. P is the heating rate during the fault and E the total heat over the rated time t.
With the transformer and fault impedances neglected, the resistor alone limits the current, so Ohm’s law gives R. Heat is I²R, and for a short-time rating nearly all of it is stored in the element mass, so energy is simply P × t.
Sense check: 1000 A at 11 kV needs about 6.35 Ω and dissipates about 6.4 MW, or 64 MJ over 10 s.
Watch out: the voltage is entered in kV and multiplied by 1000. Using the line-to-line voltage without √3 gives too much resistance and only 58 % of the intended current.
Resistance needed to limit an earth fault to a chosen current on a resistance-earthed system, with the power and energy the resistor must absorb for its short-time rating.
Enter your values to see the result.
Good to know
The resistor sees the full phase-to-neutral voltage during a solid earth fault. Common UK 11 kV values limit the current to around 1000 A (or to the transformer full-load current) for 10 s or 30 s. IEEE C57.32 sets standard time ratings (10 s, 1 min, 10 min, extended) and the temperature-rise limits for each. The energy figure lets you check the element mass against its temperature rise.
Common mistake
Using the line-to-line voltage directly in R = U/I, which gives √3 too much resistance and limits the current to 58 % of the intended value.
Limits
Neglects transformer zero-sequence and fault impedance, which slightly reduce the actual current. Resistance change with temperature (typically +10 to +20 % for stainless steel over the rating) is not included; specify the resistance at ambient.
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.