Ipf : 3ph simultaneous fault

Question

Hello, can anyone explain what's going on here with 3 phase fault currents... 
 From BS7671 Appendix 14 it states, in a 3ph system, the highest prospective fault current occurs with a simultaneous fault across all 3 phases and that an 'approximation' of this is determined by measurement between live and neutral multiplied by 2... i am presuming the measurement between live and neutral being what we'd normally measure with an earth loop impedance meter eg Zs. I do appreciate this factor of 2 is a simplification and over approximation because fault currents (particular 3phase systems) are really quite a complicated beast! 
 but my query relates from the IET 5th edition Electrical installation design guide [page 81]. The design guide appears to agree that " A fault across the three phases is considered the worst case etc. ." but then goes on to give the formula [Ipf] approximately equalling Cmax Uo / Zx + ZD 
 No mention of the multiplication of 2 or am i getting my wires crossed. 
 Note 1 from design guide [page 84] gives an example whereby a circuits total line impedence Zpf = sqrt(r^2 + x^2) = 0.0204 ohms ... in simple terms is this the same as Zs? 
 the design guide goes on to give 
 Ipf = 1.1 * 230/0.0204 =12.4kA 
 but from BS7671 appendix 14's version of events, wouldn't Ipf approximate as 
 Ipf = (1.1 * 230/0.0204) *2 = 28.8kA ? 
 Thanks

mapj1 · Accepted Answer

The approximation only works if you are at the end of a cable run and the impedance is largely the same resistance in the loop for all 3 phases and neutral, and magnetic effects are small. Thenn you can say if there is a 1 phase PSSC of "X" amps, that is set by the series resistance of one live path and one neutral path, and at the point of fault the voltage rises to approx half the single phase voltage. A well balanced L-L-L fault (ignoring the detail that this is about as likely as a flying unicorn) has a voltage at fault of approx zero, as all 3 phases sum to zero, so the current is now set by the full phase voltage dropped over just the impedance of the live path, as the return path voltage drop has been cancelled. Aha, same resistance, twice the voltage, twice X is the PSSC I hear you say.... 
 Hmm. With the assumptions clearly laid out like that, and they almost never are in the textbooks, let's shoot a few holes in them. 
 1) the outbound and return impedance may well not be the same, neutral or earth may be either a higher, or a lower resistance than the live path, and so the 'double it' assumption is generally not great. 
 2) It assumes the 3 phases are independent - but close to the transformer, which may be a star secondary delta primary winding, a load on one phase affects the voltages on the other two to some degree as the primary, and magnetic fields in the core, are shared. 
 3) I challenge anyone to create 3-way a balanced fault - in reality one pair of phases connect first, and given the sort of currents in consideration, quite quickly things will be heating, and hot metal vapour on the move - it will not be a simple loss-less contact with no voltage drop. If it was, there would be no arc and no heat. 
 
 But as a tester only has 2 wires, making a 2 wire reading and double it, is as good as it gets. 
 
 Mike.

AJJewsbury · Answer

Note 1 from design guide [page 84] gives an example whereby a circuits total line impedence Zpf = sqrt(r^2 + x^2) = 0.0204 ohms ... in simple terms is this the same as Zs? 
 
 Sort of. Calculating Z from R and X is a general thing for a.c. circuits (overall impedance (Z) has contributions from both the simple resistance (R) and the reactance (X) of the conductors). In general Z could represent any sort of loop - L-L, L-N, L-PE or indeed L-L-L, or just some small part of it. Resistance is nice and simple - what you'd measure with a d.c. Ohmmeter for example, but reactance takes into account all the funny effects you get due to capacitance and/or inductance when the current is a.c.. As a result Impedance is an odd two-dimensional value - you can't just add two Z values together as if they were simple linear values - it's vector addition - you need to split Z into it component parts, add the individual parts separately, then combine them back into an overall Z value. SQRT(R&sup2;+X&sup2;) doing the combining them back together bit - it's literally just Pythagoras - R and X form two sides of a triangle and using sum of squares of the other two sides is used to calculate the hypotenuse (Z). The other way of calculating things with triangles is using trig functions - sin, cos, tan etc - conventionally we use cos - otherwise know as the power factor. 
 Zs (with the s subscript) is specifically the impedance of the earth fault loop (L-PE) - as it's to Earth (the worst case when ADS is considered) it's similar to a single phase L-N fault and unlike a bolted L-L-L fault so no 2x to worry about. If you did get a L-L-L-PE fault then in theory it all balances from the L-L-L part and no current flows along the PE - so really it reduces back to a simple L-L-L fault. 
 - Andy.

Ipf : 3ph simultaneous fault

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