MVA Method Phase to Ground Question 1

[haze10]

Studying the MVA method for its simplicity. Understand its limitations, but for quick calc to determine min AIC of equipment seems like a good approach.
I can follow and comprehend the method for 3 phase faults. But I am having some difficulty with phase to phase, and phase to ground.

Phase to ground fault:
MVAsc=3/(1/MVA1 + 1/MVA2 + 1/MVA0)
I understand where positive, negative, zero MVA is derived. But, I don't understand why it is multipled by 3. Is it looking at each of the 3 phases going to ground at the same time, so its 3 cables in parallel? Or is it just one phase to ground? If latter, is it normal to have higher phase to ground Isc than three phase Isc?

If the ground fault is on a wye system, say 480/277, and I'm looking for one phase to ground, after arriving to the MVA do I use Vll (480) or Vln(277) to calc Isc?

For phase to phase fault:
MVAsc= (Sqrt 3 x MVA1)/2

I assume the Sqrt 3 is reference to 3 phase, and the 2 is the two phases, but don't comprehend how this is derived. Anyone have a good explanation?

thanks, all comments appreciated.

 

[prc]

Yes; the 3 in the formula comes from short circuit MVA from the three phases in parallel. Please refer to the well known IEEE paper " Short Circuit ABC-Learn it in an hour, use it anywhere, memorize No Formula" by Moon H Yuen, in IEEE Transactions on Industry Applications Vol1 A-10 No.2 March-April ,1974 Pages 261-272 for more details

 

[HamburgerHelper]

Just a fun tidbit, Moon H Yuen worked for Bechtel for 27 years and he was held down from advancing in the company due to him being "too useful" in his current position. When Moon got wind of this as to why they weren't promoting him even after all his contributions, he quit and went to start his own company, YEI Engineering.

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If you can't explain it to a six year old, you don't understand it yourself.

 

[haze10]

The Moon paper is my primary reference. But its a bit vague on my questions. For instance, phase to ground. If you have a wye system, do you use the phase to phase voltage, or the phase to ground voltage? Thanks for explaining the 3 multiplier, the Moon paper didn't quite detail that it was all three phases to ground simultaneously. My first assumption there would be a single phase to ground fault.

 

[cuky2000]

For SLG fault, the total fault current is the sum of each individual sequence current, that happen to be all equal for SLG. The MVA method like the ohmic or the pu method, calculate initially the sequence impedance current. The total phase SLG fault current is 3 times any of the equals sequence currents. For additional details, see below:
For LL fault the boundary conditions the positive sequence component of voltage equals the negative sequence component of voltage. This also means that the two sequence networks are connected in opposition. Now making use of the sequence network relationship:
V[sub]a1[/sub] = V[sub]a2[/sub] ; V[sub]a[/sub] - I[sub]a1[/sub] Z1 = -I[sub]a2[/sub] Z2 & I[sub]a1[/sub] = V[sub]a[/sub]/(Z1+Z2)= V[sub]a[/sub]/2.Z1 (for Z1 =Z2)
I[sub]f[/sub] = Ib=-Ic = a[sub]2[/sub]I[sub]a1[/sub] + aI[sub]a2[/sub] + I[sub]a0[/sub] & (I[sub]a2[/sub] = - I[sub]a1[/sub], I[sub]a0[/sub] =0)
I[sub]f[/sub] = (a[sup]2[/sup]-a)Ia1 = j(1.73).Ia1= j(1.73). V[sub]a[/sub]/2.Z
I[sub]f[/sub] .V[sub]a[/sub] = j(1.73).V[sub]a[/sub][sup]2[/sup]/2Z
∴ [highlight #FCE94F] MVAsc = j(1.73).MVA1/2[/highlight]

Use the line-to-line voltage (V[sub]LL[/sub]). Notice that to obtain the fault current, the resultant equivalent MVA[sub]sc[/sub] is also divided by the V[sub]LL[/sub].