X/R Calculation Confusion

[ThePunisher]

Hi all. I am doing PER-UNIT calculation using P.U. (R + jX) as per ANSI standards. In calculating the X/R ratio at the fault point, I used equivalent (P.U. jX)/ (P.U. R).

However, I read a book that states that calculating X/R ratio using complex form (P.U. jX)/ (P.U. R) is not conservative and not recommended for ANSI calculations. It stated that an Rseparate/Xseparate should be used.

I am bit confused as to what and how to calculate separate R and separate X. Are they different from (P.U. jX)/ (P.U. R)?

regards

 

[davidbeach]

When a ANSI standard mentions X/R, the X/R is assumed to be calculated by evaluating an R-only network and an X-only network. Probably goes back to days when two sets of real number calculations were far easier than one calculation using complex numbers.

 

[ThePunisher]

Thanks David, but what is the difference between the two (Real vs. Complex). If both are in Per-Unit, is there a difference in terms of equivalent Z?

 

[davidbeach]

Some difference, but I can't say for sure what it is. I've never hand calc'ed a large enough system for it to matter. For big systems I generally rely on the analysis software.

 

[PHovnanian]

For the case of a linear system, I'd say that the network R and X values are independent. They can be added separately and either the answer should be the same as carrying complex values through the network and figuring X/R at the end. But for the nonlinear case (saturating magnetics and the like), X will change as the voltage magnitude at the non linear components change. In this case, just handling the real and reactive components as two separate networks and combining them at the end won't give the correct figure.

 

[ThePunisher]

Phovnanian, I would normally calculate the P.U.R and P.U. X of each element on an MVA and voltage base. Then I draw an impedance diagram separately for P.U.R and P.U.jX and combine all Rs and Xs up to the fault point and get P.U.Req and P.U.jXeq. I calculate P.U. Zeq = P.U.Req + P.U.jXeq and use it to calculate the symmetrical three phase fault.

The X/R at the fault point will be (equivalentP.U.R)/(equivalent P.U.X) Will this approach going to be adequate in determining the X/R at the fault point?

David, would you agree?

 

[waross]

A suggestion:
R and X in Omic values may be combined as resistances in parallel.
To combine R and X in PU values you must also consider the base MVA that each value is based on. Something like an average weighted by the inverse MVA bases.


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

 

[ThePunisher]

Hi Waross,

What do you mean by "To combine R and X in PU values you must also consider the base MVA that each value is based on. Something like an average weighted by the inverse MVA bases".

I understand that each P.U. R and X are based on a common and equipment MVA base, however, most of them actual impedances are also in P.U. of their own MVA rating. Converting each one of them to ohms will defeat the purpose of using per-unit for simplicity. Can you give me a simple sample?

 

[PHovnanian]

If you have some per Z given in per unit at one MVA base, it can be converted to the per unit value for another MVA base using the following formula:

MVA_b1 = MVA Base 1
Z_1 = impedance of some actual Z at Base 1

MVA_b2 = MVA Base 2
Z_2 = impedance of the same actual Z at Base 2

Z_2 = Z_1 * ( MVA_b2 / MVA_b1 )

It isn't necessary to convert to ohms and back to a new base. Although if you do so and cancel out terms, the above equation is what you'll get.

 

[ThePunisher]

Hi PHovnanian, I am using a common MVA base on all my per-unit calculation of all the elements. The KV base depends on the nominal voltage of the bus where these elements are connected. I use the X/R ratio of each of the elements (i.e. transformers, generators, motors) and I get the equivalent P.U. R and P.U. jX of each element based on a common MVA base using

P.U. Z2 = Z1 * (MVAbase/MVAequip)*(kVequip/kVbase)^2 P.U.

For cables, since the actual R and X values in ohms are calculated:

P.U. Z2 = Z1*(MVAbase)/(kVbase)^2 P.U.

From here I calculate the P.U. Rs and P.U. jXs separately and then get the equivalent X/R at the fault point using these values.

I always came into the belief that this the way to go, till I read some article saying that this is not conservative enough. My question would be, what is then the right way to go to be conservative enough using the same P.U. values I calculated?

Your assistance is greatly appreciated.

 

[juleselec]

As David said, ANSI expects you to calculate the X/R ratio using separate R and X networks. This is actually pretty straightforward - the R network is simply the impedance network without all the reactances, and vice versa for the X network (i.e. they are networks of scalar impedances).

You would then calculate the thevenin equivalent circuit for both the R and X networks at the fault location. These values are now your R_separate and X_separate.

It should be pretty clear that the X/R values you would get from simplifying separate R and X (scalar) networks would be different to the values you'd get from the network reduction of complex phasors,

i.e. reducing two parallel complex impedances, say Z1 || Z2 = Z1 * Z2 / (Z1 + Z2), involves complex division, which in turn involves multiplying complex conjugates. Contrast this to network simplification with scalar quantities, which is just straightforward arithmetic. You should probably prove it for yourself with a simple example

 

[dpc]

ANSI allows the separate R and X reduction or a separate R and Z reduction, IIRC. This is spelled out in ANSI C37. The differences between these two are fairly small.

I'd refer to Conrad St. Pierre's book on Short Circuit calculations for an explanation of the logic behind the separate R and X reduction.





David Castor

http://www.cvoes.com

 

[DannyZucko]

Hi Guys,

I did a power system analysis project recently and came across this acticle with made power calculations very quick and simple.
It may not be directly linked to the above question but may be of interest.

Danny

http://s.pangonilo.com/index.php/tutorials/mva-method/mva-method-short-circuit-calculation

 

[shalhoob109]

Please read this file about "The Importance of the X/R Ratio in Low-Voltage Short Circuit Studies"

http://www.powerstudies.com/articles/ImportanceofX-over-RRatios.pdf

Shalhoob