# balanced 3 phase example



## kduff70 (Nov 9, 2014)

I'm have trouble getting my understand down pack of how to use the abc and the acb sequence in a three phase circuit only when it come to having the angles associated with the magnitudes. I have attached the example from Grainger Power System analysis but I just keep getting stuck on the phase angle for Line to Line . can some point me to more example of how to use the abc and acb sequences ? Or will somebody be willing to explain it to me . I just cant seem to get this one part thank you in advance for any help.


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## J-Dubbs (Nov 9, 2014)

Think of the line to line voltages as a delta connection. When you go from a delta to a wye connection, your phase angle shifts by -30 degrees. The reason for this can easily be calculated when you show the addition of the A-N and B-N vectors to give you the A-B vector. I won't do it here, but do a search for "delta-wye phase shift" and you should find all the info you need. So that explains the phase angle shift, and the magnitude is of course the line voltage over the square root of 3.

Now, the key to the sequence is that you must remember that voltage/current vectors ALWAYS ROTATE COUNTER-CLOCKWISE. So use zero degrees as your reference. If the rotation is ABC, you'll see A come around first, then B, then C. If you freeze them when A is at zero, then B will be the next one to come around, and so it must be at -120 degrees (240 degrees). C will come around last, so it's sitting at 120 degrees.

So in the problem, AB is given to be at 0 degrees. For ABC rotation, this means BC is next and will be at -120, then CA at 120. If the rotation is changed to ACB, then you'll have AC at 0, CB at -120, and BA at 120.

Once you've got this figured out, you just perform your phase shifting as noted above and you can get your L-N voltages pretty easily. The current angles are simply their respective L-N voltage angles minus the impedance angle. In this case, the Cosine of the impedance angle will also give you your power factor.

Hope that helps, or at least didn't make things more confusing.


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## KatyLied P.E. (Nov 10, 2014)

In wye connections the line currents equal the phase currents. The line to line voltages are square root of 3 greater than the phase voltages and lead the phase voltages by 30 degrees. Hence the answer above. In delta connections the line voltages equal the phase voltages. The line currents are square root of 3 times the phase currents and lag the phase currents by 30 degrees. Just the opposite of wye.


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## kduff70 (Nov 10, 2014)

Thank you both J-Dubbs and KatyLied

I understand exactly what you both are saying but I think the thing that get me confused is when B is next to rotate I get a little confuse becuse it -120 but you really use 240 . Is this because 240 is the postive angle for a negative 120?


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## J-Dubbs (Nov 10, 2014)

In terms of angles, 240 and -120 are the same thing and can be used interchangeably. It's just a matter of preference which one you use. Some people like to use only positive angles, and others prefer to use positive up to 180 and negative the other way to 180. But if you enter Cos(240) and Cos(-120) in your calculator, you'll get the exact same answer.

So in ABC rotation, A=0, B=-120, and C=120. In CBA rotation, you just reverse the angles for B and C.


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## kduff70 (Nov 10, 2014)

I get it now thank you for your help


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