Short Circuit Analysis - X/R ratio given in symmetrical components

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joshtrevino

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Beaumont, TX
I currently do not have access to short circuit software, but have built a spreadsheet from a class that I recently took on short circuit analysis. The utility has provided me available fault current and X/R ratio broken into symmetrical components (X1/R1, X0/R0). My calculator is not built for symetrical components, but a single system X/R ratio from the source.

Is there a way to calculate source X/R from the symmetrical components? Can I use one of the symmetrical component X/R's for a "close enough" calculation?

Am I completely missing the boat here? Please help. Its been too long since I had this stuff in college...
 
charlie b

charlie b

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araffs said:
Try to use complete analysis software like SKM-POWER.
Click to expand...
He already said he did not have access to that sort of thing. As to my response, you have had the class far more recently than me. I don't remember if there is a simple way to combine the positive, negative, and zero sequence values that you have into a combined value. Sorry.

 
P

Phil Corso

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Boca Raton, Fl, USA
Josh,

No! As a rule, it is not possible to derive Xo/Ro values from pos-seq values! You can, however, readily find them for generators. And for transformers there are Rules-of-Thumb (RoT) available! But, if your calc really needs more than 3 significant-figure accuracy you have to ask the manufacturer!

Regards, Phil Corso ( cepsicon@aol.com )
 
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AZElectrical

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X1/R1 is the positive sequence reactance to resistance value available from the utility, X0/R0 is the zero sequence. A utility can source different fault currents based on the type of fault being analyzed (due to differences in positive and zero sequence impedance of transmission lines and similar components). A balanced three phase fault will have only positive sequence current and is typically the worst case in terms of short circuit current. If your spreadsheet is calculating three-phase fault current, use X1/R1. If you have a choice for the type of fault to simulate, X0/R0 would apply for single-line to ground and double-line to ground.
 
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joshtrevino

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Beaumont, TX
AZElectrical said:
X1/R1 is the positive sequence reactance to resistance value available from the utility, X0/R0 is the zero sequence. A utility can source different fault currents based on the type of fault being analyzed (due to differences in positive and zero sequence impedance of transmission lines and similar components). A balanced three phase fault will have only positive sequence current and is typically the worst case in terms of short circuit current. If your spreadsheet is calculating three-phase fault current, use X1/R1. If you have a choice for the type of fault to simulate, X0/R0 would apply for single-line to ground and double-line to ground.
Click to expand...


Thank you.
 
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Phil Corso

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GentlePeople,

The term Symmetrical Components, need not be feared, although on this forum some "partcipants" seem to be. Come on fellas... it?s only a mathematical tool!
Early in the history of Electrical Engineering, fault-currents for "balanced", 3-ph short-circuits were easily determined with classical mathematics: Kirchhoff's laws; D-Y and Y-D impedance equivalency; complex numbers; superimposed currents; and 3-phase circuit "transformation" into single-phase circuits.

As circuit complexity grew, both in size and interconnection, the classical approach became tedious and often unwieldy. In 1918 C.L. Fortescue (he was with the Westinghouse Electric and Mfg. Co.) introduced the "Method of Symmetrical Components!? It is a solution, preferable to those mentioned above, for solving problems having "unbalanced" conditions! Examples are: line-to-line; line-to-ground (earth); double-line-to-ground, open-circuits; unbalanced sources; unbalanced loads; unbalance impedances connecting source and load; etc!

Avoiding deep technical discussion, it is simply a means to "transform" a seemingly unwieldy, complicated system of voltages or currents or impedances, into symmetrical ones. For example, the method changes unequal-voltages, displaced by unequal-angles into a set of 3 sets of equal-voltages:, as follows:
o The 1st set of three equal voltages, referred to as the positive-sequence component, are separated by 120?, having a phase- rotation, say A-B-C!
o The 2nd set of three equal voltages, referred to as the negative-phase component, and whose magnitude is different than those in a) but having a phase-rotation in a direction opposite to a), that is, C-B-A.
o The 3rd set of three equal voltages, referred to as the zero-sequence component, having equal magnitudes, in phase
with one another
This method is used to solve unsymmetrical faults listed above, as well for operating generators, and motors under unbalanced electrical conditions. A key mathematical element for its success was the introduction of an operator, 'a', to rotate vectors 120?. Of course, it is analogous to the complex-number operator, 'j', used to rotate a vector 90?!

Although details can be found in Electrical Engineering (power) text books used by power engineering students, if examples are sought, perhaps others, like, KingPB can oblige!
Regards, Phil Corso
 
mbrooke

mbrooke

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AZElectrical said:
X1/R1 is the positive sequence reactance to resistance value available from the utility, X0/R0 is the zero sequence. A utility can source different fault currents based on the type of fault being analyzed (due to differences in positive and zero sequence impedance of transmission lines and similar components). A balanced three phase fault will have only positive sequence current and is typically the worst case in terms of short circuit current. If your spreadsheet is calculating three-phase fault current, use X1/R1. If you have a choice for the type of fault to simulate, X0/R0 would apply for single-line to ground and double-line to ground.
Click to expand...


I could be wrong, but don't single phase to ground faults produce the most current? I always assumed it was around 1.25 times the 3 phase value?
 
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Phil Corso

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Boca Raton, Fl, USA
MBrooke,

It is case-specific! 3-ph fault-current is dependent on only Pos-seq! L-G fault is dependent on the sum of pos, neg and zero-seq's. And since pos and neg seq's are equal (in most cases) then, L-G fault magnitude depends on zero-seq because (in most cases) it is less than pos-seq !

Do you want a more detailed explanation?

Regards, Phil
 
mbrooke

mbrooke

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United States
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Phil Corso said:
MBrooke,

It is case-specific! 3-ph fault-current is dependent on only Pos-seq! L-G fault is dependent on the sum of pos, neg and zero-seq's. And since pos and neg seq's are equal (in most cases) then, L-G fault magnitude depends on zero-seq because (in most cases) it is less than pos-seq !

Do you want a more detailed explanation?

Regards, Phil
Click to expand...



Of course I do! :D:)
 
P

Phil Corso

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Location
Boca Raton, Fl, USA
There are many types of electrical failures in a 3-phase system. Some of the well-known types are: SLG (single-line to ground); LLG (double-line to ground); LLS (line-to-line short); and LLL, (3-phase short or the bolted-fault). Of course most members and posters of this forum are familiar with the first and last.

The current in a 3-phase short is essentially determined by the source phase-to-ground voltage divided by the sum of the circuit element impedances between the source and the point of failure. This is called a 'symmetrical' fault. All of the others are considered 'asymmetrical' faults, and their determination is not as simple as the LLL. Thus electrical engineers resort to the mathematical ?method? called symmetrical components, which was discussed earlier.

The ?method? assigns to each cable, generator, transformer, etc, three impedances: Z1 (the positive-sequence); Z2 (the negative-sequence); and Z0 (the zero-sequence). By judiciously combining these three impedances, any of the faults described above can be solved. Let the system Ph-neutral Voltage = Ey, then fault-current, If, equals:

o For the LLL case, the current If(3) = Ey/Z1.

o For the LLS case, the current If(2) = SQRT (3) x Ey/ (Z1+Z2).

o For the SLG case, the current If(1) = 3 x Ey / (Z1+Z2+Z0), when the neutral is solidly-grounded.

Note, for the case where Z0 = Z1, then, If(1) = If(3). But, if Z0 < Z1, then, If(1) > If(3) !

Phil
 
mbrooke

mbrooke

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Technician
Thanks, this makes it a lot more sense than the web and book resources that drag it on for pages without learning anything significant.


Now impedances can be restive, but how would reactive impedances be included?
 
mbrooke

mbrooke

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Phil Corso said:
Mrooke,

The impedances would be treated as complex numbers, having both real and imaginary components in quadature, i.e., A+jB !

Phil
Click to expand...


But for a simple 600 volt and under circuit is factoring in resistive ohms while excluding reactive impedance enough to yield acceptable numbers most of the time?


Out of curiosity you wouldn't happen to have any examples of A+jB?

I will see if I can dig up an awesome sequence JIF.
 
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