Can someone explain this graphic

[topgone]

It is the easiest, but the values require vector addition.
Keeping track of transformer phase shifts is a common issue when paralleling secondaries as Don pointed out in post #9. I had a similar issue when I had to explain to a customer that they wired their underground primary wrong and there was nothing we could do to our transformer to fix the problem. It was going to be another three years before they could take the required outage so they would have their backup and be able to commission their ATO scheme.

I did the vector addition as mentioned. But using 277 and 120V as the input, I didn't come near the 381V figure. Can somebody show me the math for that?

 

[wwhitney]

I did the vector addition as mentioned. But using 277 and 120V as the input, I didn't come near the 381V figure. Can somebody show me the math for that?

Post #14 (the correction of a typo in post #4). Or if you prefer cartesian coordinates, using the diagram in post #7:

Brown vector = (277,0)
-1 * Blue vector = (120 * cos(-30 deg), 120 * sin(-30 deg)) = (104, -60)
Brown - Blue = (381, -60)
| Brown - Blue | = sqrt (381² + 60²) = 386V

Cheers, Wayne

 

[electrofelon]

I did the vector addition as mentioned. But using 277 and 120V as the input, I didn't come near the 381V figure. Can somebody show me the math for that?

Based on the 30 degree phase shift as Don described, the law of cosines gives the voltage via this calculation:

sqrt(120² + 277² + 2*120*127*cosine(30 degrees)) = 386V

Cheers, Wayne

For a fun little math exercise, compute the value without using the law of cosines

 

[topgone]

Post #14 (the correction of a typo in post #4). Or if you prefer cartesian coordinates, using the diagram in post #7:

Brown vector = (277,0)
-1 * Blue vector = (120 * cos(-30 deg), 120 * sin(-30 deg)) = (104, -60)
Brown - Blue = (381, -60)
| Brown - Blue | = sqrt (381² + 60²) = 386V

Cheers, Wayne

Thanks. Where can we find the missing 5 V?

 

[wwhitney]

Thanks. Where can we find the missing 5 V?

Error in the original illustration, or the system voltages are 1.5% below nominal. : - )

Cheers, Wayne

 

[jaggedben]

Error in the original illustration, or the system voltages are 1.5% below nominal. : - )

Cheers, Wayne

Or what zbang said in post #5.