Current in Delta Winding Phases
Current in Delta Winding Phases
(OP)
If I have line current magnitudes and angles for A, B, and C phase current, how can I calculate the current flowing through the individual windings in a delta winding?
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Current in Delta Winding Phases
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RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
If I connect a three phase transformer or a bank of single phase transformers in a delta winding on the primary (source side), I usually have a set of jumpers to connect it to a distribution line. For these jumpers, I measure the line currents going to the delta winding and can determine the delta winding currents as HamburgerHelper had suggests. I agree with this.
I don't see why you need to concern yourself with zero sequence current. We're just dealing with phase currents and not sequence currents.
I think with David's delta grounded-wye connection, I'm again looking at the delta as the high side connection and the grounded-wye as the low side connection. You normally connect load to the low side connection not across the primary delta side; otherwise, you wouldn't need a transformer. So if I load up the secondary, then the previous argument is the same. I can get the delta winding currents from the line currents. Maybe I'm misunderstanding what you were trying to say, davidbeach, so I hope you can unconfused me.
RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
RE: Current in Delta Winding Phases
The positive and negative components are by definition balanced.
Use the transformer tap ratio and phase shift and convert the positive sequence load currents to the high side.
This gives you IPa1, IPa2, IPa0
Do the same for the negative sequence components but phase shift them the opposite of the positive sequence phase shift.
assuming abc rotation
a = 1<120 deg
IPb1 = a^2*IPa1
IPc1 = a*IPa1
IPb2 = a*IPa2
IPc2 = a^2*IPa2
This gives you high side:
IPa = IPa1+IPa2
IPb = IPb1+IPb2
IPc =IPc1+IPc2
This is what you get when if you measured at the high side.
Total with circulating zero sequence currents =
Winding Iab = (IPa1 + IPa2) - (IPb1 + IPb2) + I0P
Ibc = (IPb1 + IPb2) - (IPc1 + IPc2) + I0P
Ica = (IPc1 + IPc2) - (IPa1 + IPa2) + I0P
IP0 = ISa0*TransformerRatio
So,basically you take what you would see with the positive and negative components in the winding and just add the circulating zero sequence currents to it. Or just do what Stevenal said and not look at the components.
RE: Current in Delta Winding Phases
Consider a grounding bank, a transformer with a grounded wye winding connected to the system and a delta winding not connected to anything. Now apply a ground fault. Current will flow (depending on convention) up the neutral and split equally among the three phases. There will be an equal current (in per unit) within the delta. No current in the phases on the delta side, they aren't even connected.
Several years ago we had a customer that had a 208V service buy a piece of equipment that needed 480V. They (or their electrician) went to the electrical supply house and bought a 480/208 transformer, a pretty common item, without any consideration of the fact that it was delta on the 480 and wye on the 208. They hooked it up and grounded the neutral. For a while all was well. Then there was a primary (distribution voltage) ground fault that blew a primary fuse. Normally that would have been that. But because it was acting as a grounding transformer, the blown fuse didn't clear the fault, it just moved the source of the fault current to the customer's transformer. Significant damage, enough current in the neutral to eventually burn it clear, thus finally clearing the original fault, 30 minutes or so later. Of all of that neutral current, for every amp of 3I0 on the neutral there was an amp of I0 (on a per unit basis) in the delta. Most of that never left the delta winding, just went round and round. What they needed was the less common, but readily orderable, 208 delta to 480 wye transformer.
In a perfect positive sequence balanced load world none of that matters, but that's not where the fun is. The fun all happens when the zero sequence world lifts the veil and pokes into things.
RE: Current in Delta Winding Phases
You could not calculate the delta winding current if all you knew were the line currents (all zero).
RE: Current in Delta Winding Phases
If one phase is lost upstream, the Y:D will back feed and pick up the load downstream of the open circuit.
Often the load is too great and the transformer burns up.
If two phases are lost, the Y:D will back feed about 50% voltage into the lost phases.
After a maintenance outage, (every Sunday) power would be restored by closing fused cut-outs, one phase at a time.
After several hours of no power, all the refrigerators and freezers in the residential areas would be trying to start. At 50% voltage the compressors would stall and overheat. Eventually the thermal trips would open but despite that, somewhere in town a couple of compressors would fail.
There are a couple of mitigating techniques:
The wye point may be floated. You may experience transient overvoltages on energization.
One of the wye lines may be left unconnected. The bank will function as an open delta and should be oversized.
It was common in the country mentioned to see three phase transformer banks with one fused cut-out open. The fuse had blown during a phase loss event and the transformer bank was happily working as an open delta.
If you consider the voltage drop across an open delta, both under load and under short circuit conditions, you will see that the vector sum of the voltage drops is equal to the voltage drop of a single transformer. Thus the open delta may be considered as a virtual transformer equal to the other two transformers.
The current for a single phase load or the unbalanced part of a three phase load will be supplied 50% by the in phase transformer and 50% by the other two transformers. The current through the out of phase transformers will be 50% leading and 50% lagging.
(This may be verified by studying a generator nameplate that gives voltages and currents for both wye connections and double delta connections.)
You may be able to resolve the winding currents if you know both line currents and phase angles. Don't forget that all three transformers contribute to the zero sequence current.
Bill
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