# Dissimilar Vector Group Transformers fed from 2 dissimilar phased sources of power

A bit of a debate among'st my peers about utilizing paralleling generators with dissimilar vector group transformers.

The theory goes as such: Generator A will be energizing the LV side of a Yd11 4160:600Vac transformer. Generator B will be energizing the LV side of a Yd1 4160:600Vac transformer. Both transformers have identical impedance % values. Both generators have sync scopes that match gen voltage to the bus voltage on 600Vac LV side before closing their respective breakers.

The common point of connection is on the HV side.

Generator A closes to dead-bus first energizing both transformer A and subsequently transformer B in a rather series orientation. Phase shift from LV to HV of transformer A will lead by 30 degrees which will energize Transformer B and subsequently be leading again by another 30 to the LV side. Generator B will now see a reference voltage 60 degrees leading of Generator A but it should not care: it'll sync to that voltage and close to the live bus.

The debate now is: will circulating-current (or cross-current) still be an issue, many of my peers say it will but refuse to explain and I cannot see how; as the difference in potential has now been neutralized by phase-shifting Generator B to match. thoughts?

Edited to eliminate vagueness: Both generators are identical in pitch windings (.6667 or 2/3rds), both have methods of KVAR sharing and both excitation systems are externally-powered PMG type and are tuned identically to produce exactly 600Vac L-L. Simply: is the vector group dissimilarity enough to produce circulating-current?

• Simulate it and be done. – Andy aka Jun 19 '20 at 8:51
• Could you point me in the direction of a simulator then? I have big iron and my version of simulate is energize and cross my fingers – Jesse Joy Jun 19 '20 at 18:21

You are correct. It does not matter that the two generator's transformers are phased differently because the generators will simply operate at a different relative phase position when synchronized to the system.

Circulating current is always a possibility between two voltage sources paralleled. It has nothing to do with your particular configuration. You can estimate the circulating current by taking the voltage difference between the sources divided by the total loop impedance (ZT1 + ZT2 + ZG1 + ZG2) but make sure to put all on same voltage base. Easiest approach would probably be to do it in per unit.

For example, assume the transformers are both 5%, 50MVA transformers. That impedance on a 600V base is 0.05 x $$\\frac{0.6^2}{50}\$$ = 0.36mΩ. Assume each generator Xd = 100% at 45MVA, which is 1.0 x $$\\frac{0.6^2}{45}\$$ = 8mΩ on 600V base. The total loop impedance is then 16.72mΩ. Now, when both machines have the exact same voltage magnitude and relative phase position then ∆V = 0. As such, no circulating current will flow. However, if one generator is 10% higher in voltage and has a 10° phase separation (from relative 0°) then |∆V| = |1.1@10° - 1@0| = 0.208 per unit. Since our impedances where calculated on a 600V base our ∆V will be 0.208 x 600V ≈ 125V ph-ph. Divide by $$\\sqrt3\$$ to get 72V as driving voltage across our loop. So, our circulating current in each phase would be 4,306A. At 600V that is about 4.5MVA. Compared to generator full load current (43.3kA) the circulating current is only about 10%.

Circulating current can be tolerated if you don't exceed the ratings of generator and transformers. Note that the circulating current is producing a var loss in the transformers ($$\I^2\$$X) of 40kVAR (total).

EDIT: I modeled this in ATPDraw (graphical interface for ATP) to show the circulating current when the lower generator is running 10% higher voltage and 10° above relative 0°.

The current waveforms below are the phase currents in generator 1 (ABC rotation).

Below is image of the circuit in ATPDraw:

This analysis I describe above is fundamental frequency (60Hz in this case) balanced currents. The 2/3rd pitch design suppresses 3rd harmonic. Even if the machines had significant 3rd harmonic content the delta transformer winding will block it from flowing into the 4160V since it is zero-sequence. Third harmonic, when generated symmetrically across the phases as in a generator, behaves as a zero-sequence quantity (3rd, 6th, 9th etc. are all zero-sequence).

• Thank you! This helps a lot! – Jesse Joy Jun 19 '20 at 18:06
• @JesseJoy You are very welcome. – relayman357 Jun 20 '20 at 2:51