- #1

oscarrod5

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https://en.wikipedia.org/wiki/Mathe...ric_power#/media/File:3_phase_AC_waveform.svg

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- #1

oscarrod5

- 1

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https://en.wikipedia.org/wiki/Mathe...ric_power#/media/File:3_phase_AC_waveform.svg

- #2

anorlunda

Staff Emeritus

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Line-to-neutral voltages are in blue and line-to-line voltages in red. Note that the magnitude of the line-to-line is ##\sqrt{3}## times larger, and ±30 degrees different in phase compared to line-to-neutral.

- #3

Borek

Mentor

- 29,167

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at that instantaneous point, the potential difference looks to be 0.

Yes. Have you taken into account it actually is not different from the case of a single phase and neutral: you can also find the instantaneous point at which potential difference is zero?

- #4

Tom.G

Science Advisor

Gold Member

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Here in the U.S. the 3-phase to residential areas is often 16kV between phases (DELTA connected). One phase of this is then stepped down to the usual 240V centertapped for residential use.what exactly the potential difference is between any 2 phases in 3 phase power.

For larger apartment buildings with an elevator and air conditioning (and for larger restaurants) the 16kV 3-phase is stepped down to 120/208 3-phase/4-wire (WYE connected). This causes some complaints about electric stoves not heating as fast as they 'should.' Of course this is because of the 208V feeding a 240V stove. Try explaining

Medium size industrial plants are often fed with 416/240 3-phase/4-wire with a 240/120V transformer on the customer site. This has its own quirk in that the transformer often has a fuse mounted right on the transformer, which is behind a blank panel on the circuit breaker box. If the maintenance guy hasn't run across this before, the lights may be out for quite a while during troubleshooting.

There is/was a nominal 440V feed and a 480V feed, but I have no details on those.

Cheers,

Tom

- #5

Baluncore

Science Advisor

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The peak single phase voltage is 230 * √2 = 325 Vpk.

See the plot of the 'Y', single phase voltagess a, b, and c, relative to the neutral.

The Δ difference voltages between phases are also shown. V(a)-V(b), V(b)-V(c), V(c)-V(a).

The difference voltages are 400 Vrms. The peak difference voltage is 400 * √2 = 563 Vpk.

The three phase voltage is root 3 times the single phase voltage.

230 Vrms * √3 = 400 Vrms.

325 Vpk * √3 = 563 Vpk.

- #6

DaveE

Science Advisor

Gold Member

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277/480 Wye is quite common in US industrial settings. My last company sold Lasers that used this feed and it was seldom a problem in any sort of place that would want a big laser. Everyone overseas had to buy an autotransformer though. The cooling water, OTOH, was always a PITA for everyone.There is/was a nominal 440V feed and a 480V feed, but I have no details on those.

- #7

Windadct

- 1,449

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While the vector diagram are helpful - I think they are best as the second or final step to looking at this. The 3 Phase waveform is the good first step - a vertical line on this diagram shoes the REAL TIME potential difference for each connection.

- #8

dlgoff

Science Advisor

Gold Member

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I don't know if this is helpful or not:I think it is easiest to visualize using a vector diagram. Does the following help?

View attachment 285782

Line-to-neutral voltages are in blue and line-to-line voltages in red. Note that the magnitude of the line-to-line is ##\sqrt{3}## times larger, and ±30 degrees different in phase compared to line-to-neutral.

http://www.faqs.org/docs/electric/AC/AC_10.html

from:

http://www.faqs.org/docs/electric/AC/index.html

- #9

PeterO

Homework Helper

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- 62

You can use the standard Mathematics expression to find the Potential Difference. notably, the difference between the two Sine functions. Sin A - Sin B = 2 x Cos [(A+B)/2] x Sin [(A-B)/2]

https://en.wikipedia.org/wiki/Mathe...ric_power#/media/File:3_phase_AC_waveform.svg

We used to recite that as " sine minus sine equals two cos a half sum, sine a half difference." (With similar expressions for sin plus sin, cos plus cos and cos minus cos)*

The phases in -phase electricity are 120 degrees difference, so you are looking at two expressions like Sin(A) and Sin(A+120). (if I could type pi I could do that in radians rather than degrees)

"a half sum" equals (A +60), but cos(A+60) is just a phase shifted Sin(A)

"a half difference" equals 120, but sin(120) = √3 / 2

so 2 x {cos half sum) x (sin half difference) effectively means √3 sin(A), so the 3-phase PD is √3 times the single phase PD.

*

sin plus sin equals two sine a half sum, cos a half difference

sin(A) + sin(B) = 2 . sin[(A+B)/2] . cos[(A-B)]/2

cos plus cos equals two cos a half sum cos a half difference

cos(A) + cos(B) = 2 . cos[(A+B)/2] , cos[(A-B)/2]

cos minus cos equals two sine a half sum sine a half difference reversed.

cos(A) - cos(B) = 2 . sin[(A+B)/2] . sin[(B-A)/2]

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