Transmission Line Charging Current

[veritas]

I wish to determine the amount of charging current for a given transmission line. Is it correct for me to say that the total charging current, Ictot, is the sum of the positive and zero sequence charging currents?

I.e. Ictot = I1c + I0c where the positive sequence charging current (I1c) is based on the B1 value and the zero sequence (I0c)on the B0 value.

My reasoning is that I1c represents the capacitance current required to charge the phase-to-phase capacitances whilst I0c represents the capacitance current required to charge each phase w.r.t. ground.

Is this correct?

Thanks in advance.

 

[7anoter4]

First of all I have to know you are not a student as this forum policy is not to assist to student home work.
Second your equation is possible for a single phase line more or less. For a three phase transmission line it is a little more complicate. You don't need to use symmetrical components but equivalent capacitance.
If you would know what could be GMR and GMD you already know the equivalent reactance and you could calculate
the charging current. As the three phase are actually in triangle you have to transform this in a star and then calculate the
equivalent capacitance with respect the ground. So, this is more or less the same way as for inductive reactance calculation. When you have the reactance between phases and against the ground you can use symmetrical components
to calculate the currents.

 

[veritas]

7anoter4

I am not a student. Have been a protection for nearly 20 years. I need to calculate the charging current for a 132kV line as I need to set the charging current compensation for a current diff scheme.

To be honest, I find it hard to follow what you're saying. Why would all three phases be in a triangle? Some lines are vertical and other are horizontal and others are triangular. Why can B1 and B0 not be used directly?

Thanks.

 

[jghrist]

See line charging current calculation examples in Appendix H of the SEL-311L Instruction Manual (can be downloaded from SEL site). These use only the distance between conductors of OH lines to calculate shunt capacitance and charging current.

 

[bacon4life]

Per Bergen & Vittal "Power Systems Analysis"

"The effect [of the earth under the line] is usually quite small for lines of reasonable height operating under normal nonfault conditions."

They reference two books for further information on line to ground capitances:
Anderson "Analysis of Faulted Power Systems"
Grainger and Stevenson "Power System Analysis"

 

[7anoter4]

I'll try to transmit a doc.file.May be helpfull.

 

[veritas]

7anoter4

Thanks for the Word doc. I've actually produced something similar whereby I try to demonstrate how the sequence impedances of the transmission lines are derived by first constructing the phase impedance matrix and then using the analysis trnaformation to obtain the sequence impedance matrix (though I've done it all in SI units). Nevertheless your document is very helpful.

But the fundamental question to me still remains - is it correct to say that for a transposed transmission line that the charging current is the combination of two components. One being the component to charge the capacitances between the phases (which I see as a positive sequence phenomenon) and the other component to charge the line to ground capacitances. I presume these current to be in phase and equal in magnitude thus zero sequence currents.

Further, I expect the zps charging currents to manifest themselves in the neutral of relay circuits.

Am I correct or seriously confused?

By the way, I have a copy of Grainger and Stevenson but failed to be enlightened by it. Most likely due to my lack of insight.

Thanks.

 

[jghrist]

Note that in 7anoter4's paper as well as in the SEL-311L calcs, there is no reference to line-earth or line-shield distances. As noted by bacon4life, the effect of the earth is negligible. In any case, the voltages to earth are not in phase, so the capacitive currents to earth would not be in phase and would not be pure zero-sequence. The distances from each phase to earth might be different, leading to an unbalanced current with a zero-sequence component, but since all the currents are small, the unbalanced portion would be even smaller and could be neglected.

 

[7anoter4]

If you intend to introduce the earth influence an improved equation may be used:
Cn=2*pi()*k/(ln(Deq/r)-ln((H12*H23*H31)^(1/3)/(H1*H2*H3)^(1/3)) F/m [excell language]
r is the conductor radius [instead of GMR]
k=absolute permittivity =eps.0*epsr. For air epsr=1. eps.0=8.85 × 10-12 F/m
where H1,H2,H3 are the vertical distance from the phase conductor A,B,C to the image of phase conductor A,B,C and H12,H23,H31 are the distances from the actual phase conductor A to the image of phase conductor B and so on.
As usually H1~H12 and the second term is 0 so the capacitance to earth may be neglected as jghrist said.
See [for instance]:

 

[7anoter4]

see for instance:

http://www.ee.up.ac.za/main/_media/en/undergrad/subjects/ekk310/chap_5_slides.pdf

 

[bacon4life]

After looking at our transmission line models, I can see where you are coming from. Many of our transmission lines have a zero sequence admittance modeled as 0.25 to 1.0 of the positive sequence capacitance.

I was also surprised that the zero sequence capacitance only went up by about 10% when I added shield wires to one of our line models in Aspen.

Perhaps it is usually neglected due to low zero sequence voltage, rather than the admittance being small? Bergen mentions looking in chapter 5 of Grainger, but I don't have a copy of it.