Is there a wire configuration where its line to line voltage is more then sqrt3 times its ground voltage?

Question

Is there a type of wire configuration for malti-phase electricity were it’s line to line voltage is more then the square root of three times it’s ground voltage? If there is, what is it, and how so? There are no restrictions to this question; consider any number of phases and frequencies.

This doesn't include simply stepping the voltage up or down with transformers

Answer 1

In the early days of electrical power there were many multi-phase systems, but 3 phase was the one standardized on .

Yes a four phase. The sqrt of 3 only applies to 120 degree phase separation. for a 4 phase setup the phase to phase voltage would be a 90 degree phase separation (a to b phase and a to d phase would be A^2 +B^2 = C^2) (a to c would be A+C) .
The opposite phase would be 180 degrees and therefore add up to more than a three phase system.

In a six phase system the phase angle between 1 and 4 ,1 and 5 etc will be same as a 3 phase system.
http://www.iavalley.cc.ia.us/~thatcher/
http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=5766261
http://www.ieee.org/organizations/pes/public/2004/mar/peshistory.html
also I believe high number phases would allow a higher phase to phase value than 3 phases, as in 12 phases, there are several vector sums in a 12 phase system that would allow a higher voltage than 3 phase. As long as the phase separation exceeds 120 degrees the multiplier gets bigger until 180 degrees.

my $0.02.....Why?
Yours: Grumpy

Answer 2

I didn't want to dig it up but the configuration you are looking for is as Dan explained an "Open Delta configuration". I believe Dan had the voltages incorrect. You do have a "wild leg" . All three phases would be 120V to ground, but between the two directly connected phases the voltage would be 208. But across the open end of the Delta the voltage would be 240 volt. Utility companies used to use this configuration for residential services because it only requires two windings.

Answer 3

There is a rather weird setup used in the states to give 120 - 0 -120 and 240V delta from one transformer which might count...
It puts the so called 'wild leg' 277V above ground.

What it does is center tap one of the transformer secondaries (which are wired delta) and ground this point (which also provides the neutral), single phase 120-0-120 is available from the ends of this winding, with 277V being present between the neutral and the junction of the other two windings.

Not sure if this counts.

In fact another option is a transformer wired "delta" and having more then 3 phases, with one corner grounded, as the number of phases increases the longest available chord length must increase as the area within the windings increases and so the maximum voltage between a correctly chosen pair of terminals increases.... Deck one of them and their you are.

Regards, Dan.

Answer 4

First a slight correction in the phrasing of the question:
"... more than sqrt3 times its ground voltage?"

That should read like line to ground voltage or more commonly "phase voltage". The term phase voltage is equally applicable to both delta and wye configurations.

Anyway, the frequency of transmission would not have any bearing on the voltage magnitude ratio between line to line and phase voltage, so that option can be discarded. It can be shown that a two phase "wye" connected system would have its line to line voltage as twice its phase voltage. Also, it can be shown that beyond three phases, this relationship gets smaller than sqrt(3) for side-by-side phases. Then again as Grumpy mentions you also have more line-to-line options when you get to four phases or more so... you could have multiple line-to-line voltages that are greater than sqrt3 times the phase voltage depending on which lines you are measuring the voltage between.

If you think of it pictorially, you would subtract the phasor arrows similar to vector subtraction. In a two phase system you have two arrows exactly opposite one another. Taking the vector subtraction of those two you would have a phasor that is twice the length (the line to line voltage). Subsequently, with more phases, we have phasors that are more closely spaced and thus produce a smaller line to line voltage when subtracting side by side phasors.

The above is applicable to a wye connected system, but I am sure you could also think of some weird asymmetrical configuration that would be totally impractical for power systems but still fulfill your requirement in the question.

Answer 5

Sure. Your standard electric range or dryer service plug has a line to line voltage [North America] of 240 volts, while line to ground is 120 volts. 240 > 120*sqrt(3).

Answer 6

hi Brandonh, extreme voltage skill is many times disbursed as 3-section, because of the fact it quite is a greater helpful thank you to distribute skill. So there are 3 lively wires (one for each section) and one independent cord (return). on your place, there is many times basically one section, one independent (return) and earth (for risk-free practices).

Answer 7

use a 3 phase step up transformer.