Phase and line voltage and current question for 3-phase AC circuits.

Stanislav Mitrovic

Joined Mar 30, 2016
2
In any 3 phase delta and/or wye load balanced configuration pair, is it true that when all phase currents/voltages are added(using complex arithmetic of course)then the sum of them is equal to 0?
If it is, then is this also true for all line currents/voltages when they are added as well?

MrAl

Joined Jun 17, 2014
11,489
In any 3 phase delta and/or wye load balanced configuration pair, is it true that when all phase currents/voltages are added(using complex arithmetic of course)then the sum of them is equal to 0?
If it is, then is this also true for all line currents/voltages when they are added as well?
Hi,

Did you mean to ask about the line-to-line voltages and currents rather than the 'line' voltages and currents?
I ask because it is common to call the phase voltage the line voltage but I do realize there are variations on this.

If that is true, to find the answer simply write out the complex forms for all three phase voltages. Then, subtract one from the other following the same orientation for all the subtractions. You then have the three line-to-line voltages in complex form. You can then assume equal resistances across all lines, and then you can then calculate what you want to know.

Stanislav Mitrovic

Joined Mar 30, 2016
2
Hi,

Did you mean to ask about the line-to-line voltages and currents rather than the 'line' voltages and currents?
I ask because it is common to call the phase voltage the line voltage but I do realize there are variations on this.

If that is true, to find the answer simply write out the complex forms for all three phase voltages. Then, subtract one from the other following the same orientation for all the subtractions. You then have the three line-to-line voltages in complex form. You can then assume equal resistances across all lines, and then you can then calculate what you want to know.
Thank-You for your response.

Phase voltage I was referring to the potential between one of the legs from a 3-phase circuit and a common neutral in a wye connection or some kind of ground connection in a delta to serve as a reference point(I don't really know what delta configurations use as a common reference point since there is no "neutral" in a delta but I have heard, from an educational video, that there is some kind of ground connection that emulates a neutral. In a wye, a point is used in the center to measure the potential to or from any one of the legs.)

Line voltage is the potential between any one of the legs that are active current carriers in a 3 phase circuit. They are greater in magnitude by the multiple of square_root of 3 and are ahead by 30 degrees from the phase voltage.

Phase currents are the currents that are measured across the impedance points in a delta or wye destination area that are using power.

Line currents are currents that are being carried to the destination area from the source. Like the relationship between phase and line voltages, they are also greater in magnitude from the phase currents by the multiple of square_root of 3. However, unlike the phase and line voltages, line currents lag behind the phase currents by 30 degrees.

MrAl

Joined Jun 17, 2014
11,489
Thank-You for your response.

Phase voltage I was referring to the potential between one of the legs from a 3-phase circuit and a common neutral in a wye connection or some kind of ground connection in a delta to serve as a reference point(I don't really know what delta configurations use as a common reference point since there is no "neutral" in a delta but I have heard, from an educational video, that there is some kind of ground connection that emulates a neutral. In a wye, a point is used in the center to measure the potential to or from any one of the legs.)

Line voltage is the potential between any one of the legs that are active current carriers in a 3 phase circuit. They are greater in magnitude by the multiple of square_root of 3 and are ahead by 30 degrees from the phase voltage.

Phase currents are the currents that are measured across the impedance points in a delta or wye destination area that are using power.

Line currents are currents that are being carried to the destination area from the source. Like the relationship between phase and line voltages, they are also greater in magnitude from the phase currents by the multiple of square_root of 3. However, unlike the phase and line voltages, line currents lag behind the phase currents by 30 degrees.
Hi,

Ok then it was correct to presume you meant that "line voltage" was synonymous with "line-to-line voltage" so what I told you previously should work out OK. You just subtract one phase voltage from the other, maintaining the same orientation throughout.