Transformer Ohms from %Impedance (Reflected)

[mesutphen]

I am recalculating the reach of a dev. 21 generator protection relay. Included in the previous reach of the device was the step-up transformer and 90% of the transmission line. The transformer is a 22.8/345KV 258/430MVA transformer. From the transformer test report, the impedance is 0.1026+4.416j ohms on a 258MVA base.
Looking at the original calculations of the transformer impedance, I am confused by their method. The following is written:

"%Z = 0.1026% + j4.416%(on 258MVA base)
at the 22.8KV terminals:
Zohms=(10*22.8^2 / 258,000)[0.1026 + j4.416]"

I would think that the 22.8KV per unit impedance would be calculated by taking the 345KV impedance, multiplied by (22.8/345)^2 and divided by 258MVA.

Based on my thinking, the Zohms equation above doesn't make sense. If someone understands how that equation works, please let me know. Or is my thinking wrong?

When they calculate the impedance from the transmission line, they do use my thinking. "Ztrans=5.3+j44.5, Z at 22.8KV terminals = (22.8/345)^2*Ztrans = 0.0231+j0.1944"

 

[jghrist]

Percent or per unit impedance is the same on both sides of a transformer. You get ohms by multiplying by the base impedance times the per unit impedance. Base impedance in pu Zb = kV²/MVA. Zohm = Zb·Zpu = (kV²/MVA)·Zpu = (kV²/MVA)·(Z%/100) = [kV²/(kVA/1000)]·(Z%/100) = 10·(kV²/kVA)·Z%

 

[waross]

%Z² = %R² + $X²
OR
Z = R + jX

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[PHovnanian]

From the transformer test report, the impedance is 0.1026+4.416j ohms on a 258MVA base.

Is that actual ohms? Percent (most likely)? Or per unit (doubtful)?

"%Z = 0.1026% + j4.416%(on 258MVA base)
at the 22.8KV terminals:

Zohms = Zbase * Zpu

Zbase = KV^2/MVA (for 3 phase systems)
= (22.8)^2/258
= 2.015 ohms

so:

Zohms = (0.001026 + j0.04416) * 2.015
= 2.067 + j 88.98 milliohms

Note the conversion from percent to per unit.

It looks like someone labeled the test data impedance unclearly and made a few other real/percent/per-unit conversion errors.

I would think that the 22.8KV per unit impedance would be calculated by taking the 345KV impedance, multiplied by (22.8/345)^2 and divided by 258MVA.

Like jghrist said, the per-unit or percent impedance of the transformer are the same on both sides.

The Ztrans impedances given aren't clear about what base they have been specified at. Or are they actual ohms?

 

[rbulsara]

There is an apparent mix up of units; ohms vs. % vs. per unit. The OP needs to start afresh with the actual nameplate data, which typically states the impedance in %Z not ohms. Zpu will be %Z/100.

The formulas stated by jgshrist are correct, so take it from there.

The ohms value in this case is not "actual" ohms per say but a convenience for calculation, if you choose to use voltage and ohms for the calculation.

Transformer nameplate %Z uses its own rating (kVA and kV) as the base. Zbase and hence Zohms will change based on which voltage you use as your base. If you do the short circuit calc for either voltage, the eventual fault MVA will be the same.

OP may also need to convert the values to a correct base if he is using the base other than transformer ratings.


Rafiq Bulsara

http://www.srengineersct.com

 

[7anoter4]

I suppose the xt%=11.4% and the copper losses [in Smva=258 MVA basis] are pcu=683 kw.
From HV side:
xtrf=xt%/100*kv^2/Smva=52.6 ohm [kv=345 Smva=258]
pcu/1000=3*Irated^2*Res=3*(Smva/sqrt(3)/kv)^2*Res Res=pcu/1000*(kv/Smva)^2=1.22 ohm
Let's take Sbase=10,000 MVA zbase=kv^2/Sbase=11.9 ohm
xpu=xt%/100*(Sbase/Smva)=11.4/100*(10000/258)= 4.4186 or xpu=xtrf/zbase = =52.6/11.9 = 4.42
rpu=Res/zbase =1.22/11.9=0.1025
Now from the MV side:
ResMV=ResHV*(KVMV/KVHV)^2
XtrfMV=XtrfHV*(KVMV/KVHV)^2
ResMV=1.22*(22.8/345)^2= 0.005328 ohm
XtrfMV=52.6*(22.8/345)^2=0.22973 ohm
ZMVbase=22.8^2/10000= 0.051984 ohm
Recalculating xpu and rpu :
Xpu==0.22973/0.051984= 4.41924
Rpu= =0.005328/0.051984= 0.102499
The same impedance values from MV side can be calculated in this way:
XtrfMV=xpu*ZMVbase XtrfMV=4.42*0.051984=0.22977 ohm
ResMV=rpu*ZMVbase ResMV=0.1025*0.051984=0.005328 ohm
ZMV=ZMVbase*(rpu+j*xpu)
ZMV=22.8^2/10000*(0.1026+j*4.42)
That is what jghrist said.
The transmission line impedance calculated for 22.8 kV is correct formulated.