Delta-Star or Star-Delta Transformation

[powersys]

For balanced 3-ph ac circuit analysis, a delta-connected-load can be converted to be a star-connected-load. Is the theory applied to a delta-connected-source? Can we convert a delta-connected-source to a star-connected-source in circuit analysis? Thanks.

Do we need to adjust the "phases"? What is the values of θ1, θ2, and θ3 in the equivalent star-connected configuration as shown in the figure below?

**broken link removed**

 

[R.G.]

Yes, you may compute an equivalent star connected source for every delta, and an equivalent delta for every star. The voltages and phase angles get changed a bit. It's been 34 years since I did that so I don't remember the conversion factor.

Delta/star/delta conversion is at least on chapter in every motors textbook ever printed for the last 75 years.

 

[powersys]

Yes, you may compute an equivalent star connected source for every delta, and an equivalent delta for every star. The voltages and phase angles get changed a bit. It's been 34 years since I did that so I don't remember the conversion factor.

Delta/star/delta conversion is at least on chapter in every motors textbook ever printed for the last 75 years.

Yes... We can find it almost in every textbook on electrical engineering. However, the textbooks I read so far do not mention about delta-star conversion applied on 3-ph voltage source. Therefore, I'm not sure, after the conversion, θ1 is still 0 degree, or shifted some degree... Pls advise. Thanks.

 

[R.G.]

Do you mean the relative phase between the three or the absolute phase of the hypthetical coverted sources compared to the original source?

Imagine drawing the star sources into the delta arrangement in a different color, with the star point in the middle so the output leads are the same. Imagine that the V(an) leg of the star comes out on the lead that connects Vvab and Vbc, that V(bn) comes out on the lead that connects Vbc and Vca, and that V(cn) comes out on the lead that connects Vca and Vab.

Let's work backwards. Assign Van a phase of 0 degrees. That makes Vbn be +120 degrees and Vcn be -120 degrees. From there, by inspection the phase of Vab must be zero degrees minus -120degees or +120; Vbc must be 0 degrees minus 120 degrees or -120 degrees, and Vca must be 120-(-120) or zero.

You now have the differences in phase between the two. Work it forwards now.

 

[powersys]

Let's work backwards. Assign Van a phase of 0 degrees. That makes Vbn be +120 degrees and Vcn be -120 degrees. From there, by inspection the phase of Vab must be zero degrees minus -120degees or +120; Vbc must be 0 degrees minus 120 degrees or -120 degrees, and Vca must be 120-(-120) or zero.

I still could not visualize how to relate the phase of star circuit to that of delta circut... Would u pls advise? Thanks.

 

[R.G.]

Imagine that you have only the star circuit.

The delta voltages must be simply the differences in the voltages at each output line of the star circuit. This is true for instantaneous as well as RMS voltage.

Therefore, if you assume that you know the phases of the star circuit, the phase of each leg of the delta must be the difference in phase from leg to leg of the star.