Grainger's Power System Analysis

[Rei]

I'm trying to understand the concept of phase sequence and came across two similar examples in Grainger's Power System Analysis but solved differently. One example add in the 30 deg angle when go from line voltage to phase voltage and a another example not.

example 1.2

In a balanced three-phase circuit, the voltage Vab is 173.2<0deg. Determine all the voltages and currents in the Y-connected load having Z=10<20 ohm. Assume that the phase sequence is abc.

solution: Vab = 173.2<0 Van = 100<-30

Vbc = 173.2<240 Van = 100<210

Vab = 173.2<120 Van = 100<90

example 1.3

The terminal voltage of a Y-connected load consisting of three equal impedances of 20<30 ohm is 4.4kV line to line. The impedance of each of the three lines connecting the load to a bus at a substation is Z=1.4<75. Find the line-to-line voltage at the substation bus.

solution: Van = 2540<0 and Ian = (2540<0)/(20<30) = 127<-30

Why example 1.3 doesn't use the 30 deg angle when go from line voltage to phase voltage, but example 1.2 does?

 

[Flyer_PE]

In the first example, they are explicitly setting the reference voltage as the line voltage. The angle is 0 and all other values are determined based on that reference.

In the second example, they don't state which voltage is the reference. They chose to set the phase voltage to an angle of 0 degrees. The line voltage will be at +30o from that reference.