# 3 Phase Systems Theory and Procedure -- Determining Average Power

#### lavaswormdan

Joined Dec 7, 2016
1
1. The problem statement, all variables and given/known data
Consider the 3 following Scenarios:
1. 2. rms value of line voltage is 208 V

Three equal impedances, 60 +j30 W each, are delta-connected to a 230-V rms, three-phase circuit. Another three equal impedances, 40 +j10 W are wye-connected across the same circuit at the same points.

2. Relevant equations
S = 3|Ia|^2(Zy)
P = Real Component (S)

3. The attempt at a solution
How come when analyzing circuit one the procedure for determining the average power is to
1. find the line current Ia which is simply 110<0 divided by the impedance (Z(delta)/3 + 2)
2. calculate S = 3|Ia|^2(Zy) where Zy =(Z(delta)/3 + 2)
3. take the real component of S and that is your average power.

But when analyzing circuit 2 the procedure is:
1. Convert Van = 208 to Vp = 208/ root(3)
2. compute S by using S = (3 * Vp^2)/ (Zpcomplex conjugate)
3. take the real component of S and that is your average power.

And when analyzing circuit 3 the procedure is:
1. Find the line current
2. compute S by using S = (3 * Vs * (complex conjugate of line current)
3. take the real component of S and that is your average power.

Essentially I am kind of confused about what this Vp, Zp are that is used in the second consideration. Also why for every one of these scenarios the procedure for getting average power is different and the previous methods do not work. All of these examples seem the exact same is what really confuses me. What makes these 3 analyses different? How do I know what procedure to follow? I am doing self study so any help that can be provided is greatly appreciated.