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Induced voltage earth potential rise between substations
2

Induced voltage earth potential rise between substations

Induced voltage earth potential rise between substations

(OP)
Hi there.

In Cigré report TB347 p. 26 there is a modelling of EPR (Earth Potential Rise) in case of a single phase fault.
Refer to attached page 26: Can anyone explain me in detail how the formula for EPRr is derived. In the text it is mentioned that the expression can "easily" be derived !.

Best Regards
Hans-Henrik Hansen.

RE: Induced voltage earth potential rise between substations

Reminds me of my college days where professors would always say "it is intuitively obvious' or "it can be shown that" about concepts that they could not adequately explain.

It appears that the formula is a simplification of the impedance of two parallel paths for the fault current, one through Rr and Rl, and one through the earth conductor. The problem is not that simple because:
1. The same current does not flow through the phase conductor and the earth conductor, so you can't just subtract Zm from Ze.
2. There is also mutual inductance between the earth and the phase conductor and between the earth and the earth conductor.

RE: Induced voltage earth potential rise between substations

I agree with jghrist,of course.Usually this demonstration will be in symmetrical components-that means per phase.I’ll try to explain using total short-circuit Isc.
It is not so simply but may be if we suppose Z'm between faulted phase and the grounded wire will be the same as Zm between the grounded wire and the Ground [since the equivalent ground conductor depth is very large compared with distance between conductors].
If Isc+I'e+Ig=0 then I'e=-(Isc+Ig)
DV=I'e*Z'e+Isc*Zm+Ig*Zm=I'e*Z'e-I'e*Zm=I'e*(Z'e-Zm)
DV=Ig*(Rl+Rr)+Ig*Zm=Ig*(Rl+Rr+Zm)
The equivalent impedance of grounding wire parallel with the Ground will be:
Zeq=(Z'e-Zm)*(Rl+Rr+Zm)/(Z'e-Zm+Rl+Rr+Zm)
DV=Isc*Req Ig=DV/(Rl+Rr+Zm)=Isc*(Z'e-Zm)/(Z'e+Rl+Rr)

RE: Induced voltage earth potential rise between substations

(OP)
Hi 7another4
Could you possible attach a circuit diagram to explain the formulas. Thank you.
Best Regards
Hans-Henrik

RE: Induced voltage earth potential rise between substations

RE: Induced voltage earth potential rise between substations

I admire the work that you put behind this, 7a4! I tried to do the same thing - because this is something we have encountered as a practical problem in a refinery recently - but it seemed to be such a complex (no pun at all) situation that I gave it up.

I guess that I was too ambitious when I tried to add phase angles to the situation. In the Cigré report TB347, figure 5.3, the R:s and Z:s are added without regard to if they are purely resistive or not. It looked so simple.

Am I supposed to substitute R+jwL for Z in this equation? I guess that I have to, but it would, of course, be much simpler if the reactive parts were neglible. But then Z would also be neglible, I guess. I also guess that this is self-evident to you linemen and generation guys. But for someone that mostly sees drives and motors, it is not. Not at all.

Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

RE: Induced voltage earth potential rise between substations

Thank you, Gunnar. Actually I was graduate in Electrical Machines and Apparatus- design and engineering- but, since the energetic domain was more attractive- 30 years ago- I left the workshop for power station –and substation-design.blush
Zm=3*reE+j*0.435*log10(De/Dmed)
De=658*sqrt(roE/f)[m] equivalent Ground depth [according to Carson] where roE =earth resistivity [ohm.m] f=frequency Dmed=(dAE*dBE*dCE)^(1/3) dAE,dBE,dCE are the distances between the phase A,B,C to grounding wire[E].
re=~0.768*rc [equivalent grounding wire diameter for 37 strands copper conductor]
reE= earth resistance [it does not depends on resistivity but only on frequency]
reE=~PI()^2*f/10^4 ohm/km. For f=60 Hz reE=~0.06 ohm/km.

RE: Induced voltage earth potential rise between substations

That didn't make much simpler! bigsmile

Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

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