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Protection Riddle No. 68 - Calculation of eartfault in distribution feeders
How can I calculate eartfault in distribution feeders?
Author : Tag - From: Iran
Thu, February 18th, 2010 - 11:44
Ground fault current magnitudes depend on the system grounding method. Solidly- and low impedance grounded systems may have high levels of ground fault currents.
Ungrounded systems have no intentional ground. For a single-line-to-ground fault on these systems, the only path for ground current to flow is through the distributed line-to-ground capacitance of the surrounding system and of the two remaining unfaulted phases of the faulted circuit.
In resonant-grounded or compensated distribution networks the system is grounded through a variable impedance reactor connected to the power transformer secondary neutral or the neutral of a grounding bank. This reactor compensates the system phase-to-ground capacitance such that the zero-sequence network becomes a very high impedance path. The reactor, known as the
Petersen coil, permits adjustment of the inductance value to preserve the tuning condition of the system for different network topologies.
Resonant grounding provides self-extinction of the fault arc in overhead lines for about 80 percent of temporary ground faults. Considering that about 80 percent of ground faults are temporary, we conclude that more than 60 percent of overhead line ground faults clear without breaker tripping. High-impedance grounded systems are grounded through a high-impedance resistor or reactor with an impedance equal to or slightly less than the total system capacitive reactance to ground. The neutral resistor is of such a high value that ground faults on such systems have very similar characteristics to those of resonant-grounded systems. Because ground faults in ungrounded, high-impedance grounded, and compensated systems do not affect the phase-to-phase voltage triangle, it is possible to continue operating either system in the faulted condition. However, the system must have a phase-to-phase insulation level and all loads must be connected phase-to-phase.

Formulae for calculating initial earth fault current:

Generally for earth fault current determination, estimation of earth path loop impedance is necessary.
BS7430 (1998), sub-section 3.13, defines the earth fault loop impedance Zloop in relation to the various types of earthing systems, as follows.

For TN systems:

Z loop = Z nez + Z sec + Zc + Za + Z bond + Z mr

For TT and IT systems:

Z loop = Z nez + Z sec + Zc + Za + Z bond + Z er

Where Znez is the impedance of the neutral earthing device at the source winding.
Zsec is the positive sequence impedance of the source. For a transformer this includes both windings and the upstream impedance. For a generator this will be the sub-transient impedance.
Zc is the impedance of one phase conductor of the particular cable.
Za is the impedance of its armouring of the particular cable. This impedance can be taken as purely resistance (Ra).
Zbond is the impedance of the earthing terminals and bonding conductors at the sending end of the cable.
Zmr is the metallic return path impedance of a TN system. This impedance can be taken as purely resistance, but will usually be low enough to ignore. For offshore installations the multiple series and parallel branches of steel work in three dimensions will render such an impedance as almost zero.
Zer is the impedance of the earth return path of the ground for a TT or IT system. It will be approximately the total impedance of the ground rod or grid at the source and the ground rod or grid at the consumer. The impedance will be almost purely resistance, being typically a fraction of an ohm for damp soil conditions to several ohms for dry sandy and rocky soils. See also the international standard IEEE 80,1986, section 12.
Vph is the nominal phase-to-neutral voltage of the source.
If is the fault current at the far end of the feeder cable where the point of fault occurs.

The majority of low voltage networks are solidly earthed and short large cross-section bonding conductors are used. Hence Znez and Zbond can be assumed to be zero. The current ratings of most consumer cables are much lower than the current rating of the source transformer or generator. Hence in most situations Zsec can be taken as zero. As a first approximation the return path is Zmr and Zer could be taken as 1.0 ohm (see also IEC60079 Part 14 (1996) subsection 12.2.4 for hazardous areas).
The approximate expressions for Zloop is therefore:
For TN systems and for TT and IT systems in high conductivity soils

Zloop = Zc + Ra + 1.0

As the cross-sectional area of the cable phase conductors reduces, its impedance increases.
Similarly the resistance of the cable armouring also increases. In practice it is usually found that
minimising Zloop becomes difficult for small sizes of cables when their route lengths exceed more than about 100 m. The critical length depends upon the type of armouring i.e. wires or braid, and the material used i.e. steel, aluminium, copper, and phosphor bronze. When the critical length is exceeded the circuit should be fitted with an earth leakage current relay, because the overcurrent fuses or circuit breakers will not respond quickly enough to satisfy the recommended international practices.
Also an arcing fault, in general, results in much lower levels of current. It is often suggested that the available arcing ground fault current can be estimated by multiplying the bolted 3-phase fault current by some multiplier. Multipliers between 0.19 and 0.38 are often suggested for a 480V systems. 
Author : Hamid - From: Iran
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