Short Circuit 1.5 Multiplier

[Flapjack]

In the Cooper Bussmann Short Circuit Current Calculations document, for single phase, center tapped transformers they recommend a 1.5 multiplier for L-N faults. It goes onto say "The 1.5 multiplier is an approximation and will theoretically vary from 1.33 to 1.67. These figures are based on change in turns ratio between primary and secondary, infinite source available, zero feet from terminals of transformer, and 1.2 x %X and 1.5 x %R for L-N vs. L-L resistance and reactance values."

Does anybody know how they get the 1.33 and 1.67 values?

The document has an "Impedance Data for Single Phase Transformers" table with impedance multipliers. For 25-100kVA transformers, the impedance multipliers are the 1.2 x %X and 1.5 x %R (full winding), but for 167kVA to 500kVA, that changes to 2 x %X and 1.5 x %R.

Wasn't sure how the increase in the reactance multiplier impacted the 1.5 approximation...




 

[G._S._Ohm]

In the Cooper Bussmann Short Circuit Current Calculations document, for single phase, center tapped transformers they recommend a 1.5 multiplier for L-N faults. It goes onto say "The 1.5 multiplier is an approximation and will theoretically vary from 1.33 to 1.67. These figures are based on change in turns ratio between primary and secondary, infinite source available, zero feet from terminals of transformer, and 1.2 x %X and 1.5 x %R for L-N vs. L-L resistance and reactance values."

Does anybody know how they get the 1.33 and 1.67 values?

The document has an "Impedance Data for Single Phase Transformers" table with impedance multipliers. For 25-100kVA transformers, the impedance multipliers are the 1.2 x %X and 1.5 x %R (full winding), but for 167kVA to 500kVA, that changes to 2 x %X and 1.5 x %R.

Wasn't sure how the increase in the reactance multiplier impacted the 1.5 approximation...




My two cents:
1 and 1/3, 1 and 1/2, 1 and 2/3.
This sounds like a rough guesstimate that 90% or 95% or 99% of the multipliers that are out there will be contained in the interval 1.3 to 1.7, with mean value 1.5.

 

[mivey]

Does anybody know how they get the 1.33 and 1.67 values?

Off-hand: not exactly but it will vary because the half-to-full winding impedance ratio can vary. At the terminals, it is based on comparing I_240 = 240 / sqrt(R_ohm-full-winding^2 + X_ohm-full-winding^2) with I_120 = 120 / sqrt(R_ohm-half-winding^2 + X_ohm-half-winding^2). Further from the terminals, you add the 240 volt or 120 volt circuit resistance and reactance in ohms to the terms in the denominator.

For ABB utility distribution transformers, they estimate the half-wind impedance as 0.375 R_ohms-full and 0.50 X_ohms-full for a typical design. They state an approximation as %R_120 = 1.5 * %R_240 and %X_120 = 2.0 * %X_240 for percent impedance.

Wasn't sure how the increase in the reactance multiplier impacted the 1.5 approximation...

Well, the X/R is increasing so it does not move up as much as you might think.

 

[G._S._Ohm]

1.5 +/- 0.17 is +/-11%.
I've heard +/-10% for this kind of variation.

 

[Phil Corso]

MyBeardAndMe...

The R and X multipliers are Vendor-Specific!

Regards, Phil Corso

 

[mivey]

The R and X multipliers are Vendor-Specific!

And design specific. Many references use the approximations from Kersting's ?Modeling and Analysis of Unsymmetrical Transformer Banks Serving Unbalanced Loads?:

Interlaced secondary:
Z_half% = 1.5 * R_full% + j 1.2 * X_full%

Non-Interlaced secondary:
Z_half% = 1.75 * R_full% + j 2.5 * X_full%



but the impedances on the non-interlaced are not really the same for both halves as the impedance is higher for the outer winding. Kersting uses data Hopkinson derived while at GE. The formulas using for Z_half% = Z_primary% + Z_secondary_half% are:

Interlaced secondary winding:
Z_primary% = 0.5 * R_full% + j 0.8 * X_full%
Z_secondary_half% = R_full% + j 0.4 * X_full%

Non-interlaced secondary winding:
Z_primary% = 0.25 * R_full% - j 0.6 * X_full%
Z_secondary_outer_half% = 1.5 * R_full% + j 3.3 * X_full%
Z_secondary_inner_half% = 1.5 * R_full% + j 3.1 * X_full%

which is about the same as the general approximation above. These show up as a footnote to the transformer impedance table in GE's "Distrbution Data Book" noting that the half-winding impedance varies with a 1.5 multiplier for R and a 1.2 to 2.5 multiplier for X which obviously came from Hopkinson while he was there.