R and L from Z1, Z2 and Z0
R and L from Z1, Z2 and Z0
(OP)
Hi,
I have a cable:
Z1=Z2=0.9 + 2j
Z0 = 19.+11j
how do I go by and calculate R and L?
I have a cable:
Z1=Z2=0.9 + 2j
Z0 = 19.+11j
how do I go by and calculate R and L?
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R and L from Z1, Z2 and Z0
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RE: R and L from Z1, Z2 and Z0
Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.
RE: R and L from Z1, Z2 and Z0
RE: R and L from Z1, Z2 and Z0
So with the fomulas from deltawhy, and for the particular case where Z1=Z2, the "real" values are:
Za = Z0 + 2 x Z1
Zb = Z0 - Z1
Zc = Z0 - Z1 = Zb
So for the particualr case:
Za = 20.8 + 15j
Zb = Zc = 18.9 + 9j
how do you go from Za, Zb, Zc to just Z = R + jLw per phase (which should be the same for all phases, right?)
RE: R and L from Z1, Z2 and Z0
Also Gunnar told you about getting L from X. His w term is 2 * pi * f.
RE: R and L from Z1, Z2 and Z0
ok i got the part where i go from L to X, but I need to get to either L or X first, so far I have only Za, Zb and Zc. How do these 3 figures relate to a one value, Z?
RE: R and L from Z1, Z2 and Z0
If you are trying to find a ground fault, you need Z1, Z2 and Z0 (usually can assume Z1=Z2). If you are trying to find the maximum 3 phase fault you only need Z1.
You kind of need to answer what you are trying to achieve before we can distill it down into a simple Z = R + jX format.
RE: R and L from Z1, Z2 and Z0
The reverse calculation of Zaa, Zab, Zan, Znn from Z1, Z2, Z0 is obviously possible only when one additional condition for the parameters is given.
When Zaa etc are known, then R is the real part of Z, and 2*pi*L is the imaginary part of Z, as already stated by others.
RE: R and L from Z1, Z2 and Z0
Cheers.
RE: R and L from Z1, Z2 and Z0
However, if you are after the original phase impedances then it gets much trickier. In actual fact you cannot work back from Z1, Z2 and Z0 to the original Z11, Z12, etc. unless there are no earth conductors AND the line is transposed. Once you have earth conductors the best you can hope for is getting the values of the equivalent phase impedance matrix where the diagonal elements are Zaa-eq and the off-diagonal elements are Zab-eq.
With say two neutral conductors the 3x3 phase impedance matrix ZP is derived from something like ZP = ZA – ZB*ZD-1*ZC. The original self-impedances and mutual impedances between the phases itself are contained in the ZA matrix.
ZP-eq is derived from ZP by averaging out the diagonal and off-diagonal entries since transpositioning is always assumed.
Zaa-eq = (Zaa + Zbb + Zcc)/3 = all the diagonal entries of ZP-eq
Zab-eq = (Zab + Zbc + Zac)/3 = all the off-diagonal entries of ZP-eq
This ensures that the sequence matrix is a decoupled one. The averaging out means your original information is lost unless you have no earth conductors and the line is transposed as mentioned before.
Hope this helps or as clear as mud?
RE: R and L from Z1, Z2 and Z0
Also, I never quite answered your original question. The sequence impedance matrix is derived from the phase impedance equivalent matrix, [ZS] = [A]^-1*[ZPeq]*[A] where [A] = (1 1 1, 1 a a^2, 1 a^2 a).
Working backwards get, [ZP] = [A]*[ZS]*[A]^-1.