Calculating Per Unit Fault Impedance: Finding Errors in Given Relationships

[acw260]

Homework Statement

Given the relationships:

Xpu = MVAbase / MVAfault

Xpu = ( MVAbase / MVArated ) * ( X% / 100 )

MVAfault = sqrt(3) * V * Ifault

Xohms = [ V / sqrt(3) ] * Ifault

Homework Equations

Show that:

Xpu = [ MVAbase / V^2 ] * Xohms

The Attempt at a Solution

No matter how I approach this problem I keep finding that one of the given relationships must be incorrect. Could someone with better algebra skills then me please take a look and confirm whether (a) there is an error in the set problem or (b) I'm just being dense?

Thanks

 

[Svein]

I have no idea of what you are trying to ask - but "Xohms = [ V / sqrt(3) ] * Ifault" seems very wrong. Resistance (ohms) is always Voltage divided by current.

 

[acw260]

Please see the attachment for the problem in its original format, which should make things clearer.

I have solved the derivation of equation 5(a).

I can solve the derivation of equation 5(b) no problem using "V=IX" (ignoring the resistance of the cables for the purposes of the fault calculation, as instructed in the problem).

What I can't see is how the given equation "Xohms = [ V / sqrt(3) ] * Ifault" fits into the derivation of equation 5(b). This equation seems wrong.

 

[Svein]

What I can't see is how the given equation "Xohms = [ V / sqrt(3) ] * Ifault" fits into the derivation of equation 5(b). This equation seems wrong.

A typo. It should be "Xohms = V /[sqrt(3) * Ifault]".

 

[NascentOxygen]

Xohms = [ V / sqrt(3) ] * Ifault

A typo. It should be "Xohms = V /[sqrt(3) * Ifault]".

Or, equivalently, Xohms = [ V / sqrt(3) ] / Ifault