Crculating currents in a neutral 1

[bfuchs]

Hi guys,

I have a case of circulating currents in a Neutral circuit.
The neutral circuit is made up of 4x500 single core cable on a 3 phase 4 wire TNC supply from a generator to a switchboard (Phase are 4x400sqmm per phase).

The 'combined' neutral curent on the N circuit was measured at 20A or so. The current on the 4 individual conductors of the neutral were (approx) 130A, 30A, 50A, 40A.
Oscilloscope reading show that the 130A is in phase opposition (aprox.) to the other 3, indicating that there is a circulating current on the cables in addition to the actual 'total' neutral current of 20A.

No harmonicw were measured (THD curent = 1% or so)

Have you guys ever witnessed this ?

The cable run is aprox 100m long, cables are on cable trays in a cable trench run out of the building to the external generator sets.

Is this common ? Unusual ?

We suspect an inducted current caused by a "back-EMF" induced by a magnetic field over the surface of the cables (closed loop). One of Maxwell equations shows this.

Would love to hear from you !

 

[bfuchs]

Thanks for that !

I tried searching for the document mentionned above (EPRI-Power Plant Electrical ref. series VOL.4-WIRE AND CABLES), and have not been successful in locating it. Is downloadable from their website ?
Where can I access it (free ? what price ?)

Cheers

 

[7anoter4]

1) My EPRI handbook is dated 1982 .I'll try to find it using the link:

https://login.epri.com/login.asp

without any success. I think you have to contact EPRI at this address:
EPRI 3420 Hillview Avenue, Palo Alto, California 94304 USA
2) I think I exaggerated when I said "I'll develop a software". I am not a programmer. I am only an engineer using VisualBasic6 [or .NET] to write a modest program for my personal use [at my work place they are truly programmers [working with assembler or UNIX or else] and I never employ the Society software or other document outside.
3) I think that IEC 60287 vol.1- 3 is treating the parallel cable imbalance load case:

http://www.standardsdirect.org/standards/standards3/StandardsCatalogue24_view_20879.html

and also : "Calculation of current division in parallel single-conductor powercables for generating station applications"
IEEE Transactions on Power Delivery,
Volume 6, Issue 2, Apr 1991 Page(s):479 – 487
See:

http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel3/61/3636/00131101.pdf?arnumber=131101

Regards

 

[bfuchs]

Thanks for the detail.
Reviewing it I have one question (at this stage).

The formula refer to "ln(1/Da1-a2)"

I do not understand this...

I assume we are talking about the N log function, and Da1-a2 is the distance between conductors..

But in what unit ?
millimeters ? Meters ? Inches ? feet ?

If Da1-a2 = 1 (m? mm?) .. then ln (1/1) = 0...
If Da1-a2 < 1 (m?, mm), then ln (1/Da1-a2) < 0...

I checked the IEEE document, and the formula you have written is there as well...Da1-a2 is given in inches.. so if the conductors are 1 inch apart (25.4 mm for us SI engineers), then there is ZERO mutual capacitve reactance... that does not sound right...

There is something 'obvious'I am missing.

I would never take the logarithmic of a distance... as it does not have a unit anymore... I don't mind taking the log of a ratio (for example r / D ).

In fact "Elements of power system analysis" by William D. Stevenson, Jr (the favourite book of our senior resident elec engineer) states that Xc = 2.862/f * 10e9 * ln (D/r) (and that gives a linear reactance value .. ie per meter)

I am sure you have the answer to this question,

Boris

 

[7anoter4]

I hate xls but I have not any other possibility. So, if I did some mistake tell me pls. and I will fix it as soon as possible.
The EPRI is not the first specification dealing with parallel single phase cables imbalance. The first was F.Buller in 1946 but is impossible to find this book. His premise was:
IA1+IB1+IC1+IN1+IA2+IB2+IC2+IN2=0
That means: IN1=-(IA1+IB1+IC1+IA2+IB2+IC2+IN2)
He stated the formula for British Units, of course, but now I use SI as more convenient.
Magnetic Flux between A1 and N1 is: F[A1-N1]=miuo*IA/2/pi()*ln(DA1-1/kcd/rc)*La
where miuo=4*pi()/10^7 H/m air permeability [in SI or as we say MKSA-meter, kilogram[mass],second and ampere].
kcd=.778 [instead to add 0.25 I prefer to multiply by kcd]
XA1-N1=-w*FA1-N1=-2*PI()*frq*4*pi()/10^7/2/pi()*ln(DA1-N1/kcd/rc) that means:
XA1-N1=-4*frq*pi()/10^7*ln(DA1-N1/kcd/rc)
XB1-N1=-4*frq*pi()/10^7*ln(DB1-N1/kcd/rc) and so on.
EN1=IN1*RN1+j*(IA1*XA1-N1)+...+j*IN2*(XN2-N1)+INconsumer*(Rcons+j*Xcons)
Where IN1,IA1...IN2 are vectors[I should say "phasors" instead "vectors" as they are not actually vectors as E [Electric Field Intensity] for instance].
IA1*XA1-N1=4*frq*pi()/10^7*La*(IA1*ln(DA1-N1/kcd/rc)= 4*frq*pi()/10^7*La*(IA1*LN(DA1-N1)-IA1*LN(kcd*rc))
IB1*XB1-N1=4*frq*pi()/10^7*IB1*La*ln(DB1-N1/kcd/rc)= 4*frq*pi()/10^7*IB1*La*LN(DB1-N1)-IB1*LN(kcd*rc)
IC1*XC1-N1=4*frq*pi()/10^7*IC1*La*ln(DC1-N1/kcd/rc)=4*frq*pi()/10^7*La*( IC1*LN(DC1-N1)-IC1*LN(kcd*rc))
IN2*XN2-N1=IN2*La*ln(DN2-N1/kcd/rc)= IN2*4*frq*pi()/10^7*La*LN(DN2-N1)-IN2*LN(kcd*rc)
IN1*RN1+j*(IA1*XA1-N1)+...+j*IN2*(XN2-N1)=*4*frq*pi()/10^7*La*(IA1*LN(DA1-N1)+IB1*LN(DB1-N1)+....+IN2*LN(DN2-N1)-(IA1+IB1+IC1+IA2+IB2+IC2+IN2)*LN(kcd*rc))
but IN1=-(IA1+IB1+IC1+IA2+IB2+IC2+IN2) then:
IN1*RN1+j*(IA1*XA1-N1)+...+j*IN2*(XN2-N1)=*4*frq*pi()/10^7*La*(IA1*LN(DA1-N1)+IB1*LN(DB1-N1)+....+IN2*LN(DN2-N1)+IN1*LN(kcd*rc))
EN1=IN1*(RN1+4*frq*pi()/10^7*LN(kcd*rc)+4*frq*pi()/10^7*(IA1*LN(DA1-N1)+IB1*LN(DB1-N1)+....+IN2*LN(DN2-N1))+INconsumer*(Rcons+j*Xcons)
Notes:
1) Self-reactance does not exist without reference to the other conductors. This formula presented by you in the above post does not represent the self-reactance but the reactance from conductor to its shield[if it does exist] or to earth if the shield is grounded or a partial reactance used to be combined in order to find the reactance between phases or to earth.
2) As you may see, the measuring units are not important, but they have to be the same for all conductor.
Regards