Symmetrical Components Question

[jd5191]

In question below, can someone explain why Vpos does not equal Ipos x Zpos bur rather Ipos x (Zneg + Zzero)?

Also are Vb and Vc switched, per the standard symmetrical component matrix?

 

[Ampera18 PE]

yes I think VB and VC are switched. Also I'm using Electrical PE Review notation where Vp = V fault

The confusion lies in that Vpos = Vp - (Ipos * Zpos), not Ipos*Zpos

And Vp = Ipos* (Zpos+ Zneg + Z0)

So, distribute: Ipos* Zpos + Ipos * Zneg + Ipos * Z0 - Ipos*Zpos = Ipos *Zneg + Ipos *Z0 = Ipos (Zneg+ Z0)

 

[jd5191]

Thanks @Ampera18, I'm constantly screwing up Symmetrical Components

 

[PEExam123]

"i" is missing in the denominator for the currents (I pos, I neg and Izero). This would have an impact on the calculations. 

 

[Art]

I would approach this analytically:

-you know it can't be 0 (that is the grounded phase)

-you know since you have some pos/neg Z it can't be 100

That leaves 114 and 173. If you understand the fault scenarios you know the phase V will rise 173 if no pos/neg Z

If we assume no pos/neg:

If = 0.577/0.1 = 5.77, so N rise is 0.577, add that vectorially to the phase and ph-g is now 1.73 x ph, but it affects both un- faulted phases equally, so no change in ph-ph V.

I would pick 114, but confirm it with algebra.

If = V(sum of seq Z) = 5 V = 5 pu

each ph contributes 1/3 (Z2) of If of opposite seq

Vdrop = 1.667 x 0.05 = 0.0833, rise in this case

0.0833 + ph V 0.577 = 0.66

0.66 x sqrt 3 = 1.144

114 kV