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I am having a little bit of confusion for some reason understanding how the phase and line voltage can be the same for a delta connected system, i understand why the current is different for the phase and line current (since there are 2 paths for the line current to go through etc and hence it is larger then the phase currents).

All i have found is pages, youtube videos etc mainly just saying it is equal to the phase voltage, nothing specifically saying why. I understand why no neutral connection is needed as well (since the sum of the voltages etc is 0).

enter image description here

Essentially what i am asking is how/why are the line voltages and phase voltages the same?

Is it due to the fact that they are 120 degrees out of phase? Hence say a 3 phase balanced source of 120 V was connected to a delta system, how is VRY=120V when Y is at 120V peak? If Y = +120 V peak, then wouldn't R be 0V? However it is not is it?

To get VYR to be a difference of 120 V, what does VR and VY equal?

I guess i do not get how say point R can be essentially 2 different voltages for YR and then RB.

enter image description here

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  • \$\begingroup\$ Try drawing where you think a line voltage is and ask yourself if that isn’t the exact same place as the phase voltage. \$\endgroup\$ – Andy aka Mar 3 at 14:14
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Voltage, by definition, is the potential difference in charge between two points.

In your image, Point R, by itself, does not have a voltage because it is only one point. Point R with respect to Y (RY = two points) does. Point R with respect to B (RB = two points) does as well. Point R itself can be apart of more than one voltage simply because you require two points to determine a voltage. In a delta system, the two points required to measure a line voltage also happen to be the same two points connected across the phase.

I think your confusion may come from being familiar with wye systems. Don't let the architecture fool you though! In the image below, Point A has no voltage on its own. The phase voltage is still from Point A to Neutral (AN). In the case of the wye, the line voltage is between points A and B (AB).

Wye vs. Delta

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The phase voltage is the voltage across the transformer winding or load element associated with a phase. The diagram posted in the question shows three coils that can be assumed to be transformer windings. The RY coil is connected to lines R and Y therefore the voltage across that coil is the R-to-Y line voltage. It is as simple as that and obvious, so it is rarely spelled out as I have done.

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  • \$\begingroup\$ Yes i understand that thanks but then how can VRY be 120 V when the difference of VYR was 120V? Is it due to the phase difference? As in isnt essentially the point R acting as 2 different voltages, possibly 0 V when Y is 120V and 120V when B is 0 volts? \$\endgroup\$ – Student Mar 3 at 13:38
  • \$\begingroup\$ When I look at the diagram, should i just look at it as if one thing is happening at a time? I am getting confused how a single point can be due different voltages but i assume its due to the phase shift \$\endgroup\$ – Student Mar 3 at 13:45
  • \$\begingroup\$ I am not quite sure what you are asking. Individual points do not have a specific voltage unless you define one point as a zero voltage reference point. With a Y system, the neutral is usually grounded and used as a reference. One point on a delta system is sometimes grounded, but not often. If you want to have a reference point you might create a Y circuit connected to the delta in order to have a neutral. \$\endgroup\$ – Charles Cowie Mar 3 at 13:51
  • \$\begingroup\$ With AC systems, you usually forget about peak voltage and voltage at specific times and just deal with RMS values unless you need to be concerned about zero crossing points and timing. In that case a created or phantom Y neutral may be needed. \$\endgroup\$ – Charles Cowie Mar 3 at 13:58
  • \$\begingroup\$ Ok thanks, so can i look at it since the voltage is only going through one phase i.e. phase voltage VRY, teh line voltage must be the same since (only one component is there). Also is phase voltage the voltage just across the component say the inductor in that case? As in it isnt teh voltage at one point say 120 volts at Y then 0 V at R to get teh 120 V phase voltage? \$\endgroup\$ – Student Mar 3 at 14:03

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