In a delta-wye transformer, or in a delta-wye bank of single-phase transformers, with unbalanced loading of the secondary, there will be zero-sequence currents in the secondary windings. The zero-sequence currents in the secondary also result in zero-sequence currents in the primary windings. Because the zero-sequence currents are equal in each phase (both magnitude and phase angle, by definition of the symmetrical components), they will sum to zero at the corners of the delta primary and there will be no zero-sequence current in the lines.
Just because there is zero-sequence current in a primary winding, this does not mean that there is any total current in the primary winding. If there is no current in a secondary phase-neutral winding, there will be no current in the corresponding primary phase-phase winding. There will still be zero-sequence current flowing in the primary winding. The zero-sequence current will be offset by positive- and negative-sequence current.
Say you have a delta-wye transformer with no connection at all to one end of ØB and ØC of the secondary windings. The other ends are connected to ground. On the third phase there is a load connected to ground with 300A. There will be 100A of zero-sequence current flowing in the ØB and ØC secondary windings, even though there is no connection to them.
Remember, the sequence currents are only a mathematical construct to enable using three sets of equal three-phase currents in situations where the phase currents are not balanced. Each of the sequence currents has an equal current magnitude in each phase, by definition.
Thank you for your patience with me, friends.
Can you take a look at your signs in the last post please?
With the ends of the windings open, there will be no current flowing in the windings. If a proven mathematical construct indicates a current where there is none, possibly the sign is reversed so the current in phase B and phase C equal and cancel in the delta. Possibly your currents cancel and sum to zero so that there is no circulating current.
I have been responsible for systems with a combination of wye:delta and delta:wye transformers banks. We had many issues and failures with wye:delta banks but we never had any indication of circulating currents on our delta:wye banks. Due to a mixed load of commercial, industrial and residential, and a large part of our system running on two phases due to a failed undersea cable, we were never able to keep our system balanced over the course of the day.
We had transformer burnouts but mostly due to failed ventilation and/or overloads. Never an indication of circulating currents.
I regret that I am not able to make direct measurements at this time. The next time that I get back to the island I will do so.
PS; If the secondary of the wye:delta bank has any regenerative loads such as three phase induction motors, then I would expect to see some circulating currents in the delta.
Thanks again. I will be doing some further research on my own. I am becoming uncomfortable with this discussion. It's not good for the forum and I may find myself to be embarrassingly in the wrong.
Thanks again.
Yours Bill
Bill
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"Why not the best?"
Jimmy Carter
100A of zero sequence current in one direction. A total of 100A of positive and negative sequence current in the other direction. Zero total current. Mathematically very useful.
"A transformer bank with full load on the secondaries and no contribution from the primary lines?? Is this patentable?"
At last the solution to unlimited energy. Unfortunately zero sequence secondary energy comes from positive sequence primary energy, and conservation of energy still rules.
Transformer heating and possible burnout would be the result of total phase current exceeding the transformer capacity, and not the zero sequence component alone.
In Jghrist's example, I agree the sequence current in the unloaded phases sums to zero.
I've been thinking about your "mathematical construct" comment, and I agree. But isn't some sort of mathematical construct needed to define delta circulating current? Assuming the three winding currents are different and non-zero, we would need some sort of manipulation to find the common component that makes up the circulating current. I had thought the zero sequence component would be the correct mathematical construct to use. How else should we define circulating current?
May I make a suggestion.
In the transformer feeding the bank in question the following condition may prevail.
First, consider that one transformer is missing and the three phase line is fed open delta. B-C is open and there is a single phase load on B-C. This load is fed from the open delta. The current is in phase with B-C but is leading in one of the open delta transformers and lagging in the other.
Now if the missing transformer is installed the cirrent will split, 50% will be supplied by what was the open delta and 50% will be supplied by the B-C phase transformer. This is a current split and not a circulating current. (Check the signs), but the zero sequence component will show up in three phases.
I suggest that when a phase to neutral load is applied to one phase of a delta wye transformer bank, there is no resulting current in two phases, but the zero sequence current will show up in three phases of a delta transformer feeding the system. This zero sequence current will be a current split rather than a circulating current.
This makes me happy and follows field experience. Does it satisfy the zero sequence constructions?
Yours
Bill
Bill
--------------------
"Why not the best?"
Jimmy Carter
Consider this scenario: The grounded wye side is networked with another grounded wye transformer winding located at the other end of a line. For simplicity, there is no load on or through this network. The joining line is mutually coupled with another unrelated line that experiences a line to ground fault. As in Jghrists example, I0 will flow in each phase while 3I0 will return through neutral/ground. On the delta side, I0 will circulate around the delta connected windings. Unlike Jghrist's example, there is no positive or negative sequence current to sum to the zero sequence cuurent to find phase currents. Ia = Ib = Ic = I0. Can we agree that in this case we have a delta circulating current equal to I0?
Open the delta, and this circulating current is blocked. I'm not finding a difference between the circulating current here and the "split current" above.
We're getting pretty far from the OP situation. In the OP, there are not two banks in parallel. The concern is one three-phase bank with different impedances. You don't have circulating currents in the sense of parallel transformers with different ratios where you can have current circulating between the two transformers.
If you have unbalanced loads on a delta-wye transformer, then you have current in each primary winding proportional to the current in the secondary winding. Considering the currents to be "circulating" is unnecessarily confusing. Whatever winding current that doesn't add up to zero at the delta corner goes out the line as line current.
If you want to analyze the circuit with equal three-phase quantities, you can do it by breaking the current into three separate components (symmetrical components) that each have equal magnitudes in each phase but add together to get the unbalanced total current. One of these components, the zero-sequence component has equal phase angles as well as equal magnitudes for the three phases. Each winding has the same zero-sequence current, so they add to zero at the corners of the delta. This is how they get to be considered to be "circulating". But this is only one of the three symmetrical components of the current.
You don't need to use symmetrical components to analyze the winding currents. It is a method that can make analysis easier. You don't need to consider any current "circulating" around the windings. Just because the winding currents are not equal does not mean that you have to consider part of the current circulating around the windings.
Thank you jqrist. I think that that is what I have been trying to say.
One possible proof may be to "break" the delta. If there is a small voltage across the broken delta, (open delta in IEC land) then there will be circulating currents when the delta is closed.
If there is a large voltage across the break you have probably interrupted a legitimate load current with the break and there may not be cause for circulating currents.
A circulating current may be a zero sequence current but I don't accept the corollary. I have seen and cured a lot of circulating issues when the delta winding is the secondary or tertiary or when there is a phantom delta formed by a three legged core.
A wye:wye bank with a single phase load on the secondary will have a corresponding load on one phase of the primary. A delta wye with a load on one phase of the secondary will supply half the load from the corresponding primary winding and half the load from the resultant of the vectors of the two other phases.
The secondary currents will all be reflected in the primary line currents and primary winding currents and there will be no current left to circulate. Every amp will be accounted for by the primary line currents. The currents in two of the phases will be out of phase with the phase voltages but this will be accounted for by the current in the third phase line.
Zero sequence yes, circulating, no.
That is not to say that an unbalance will not cause a circulating current somewhere upstream in the system, but not in this bank.
Bill
--------------------
"Why not the best?"
Jimmy Carter
Waross,
If you break the delta in my example, full line to line primary voltage will appear across the break and all secondary current goes to zero. No circulating current then?
Jghrist,
The OP never said what what was downstream of his bank. We can only speculate on this point.
My example was not intended to throw in the concept of circulating currents between unmatched three phase transformers, but to provide an example of circulating delta current that I thought we could agree on. I guess we don't. Perhaps another example would work better?
All,
I remain troubled by the use of a phrase that apparently has no definition. On this point Jghrist has provided the only reasonable alternative; reject the use of the phrase. Waross has provided a method to determine if it is present or not, but no means to quantify it. Mgtrp introduced the phrase here. Mgtrp, please tell us what you meant.
In the case of a delta-wye transformer where there is a source on the grounded wye side, you have a grounding bank. If there is a Ø-grd fault (or unbalanced load) on the wye side, and no load connected to the delta side, you will have current truly circulating in the delta. There is no positive- or negative-sequence current. Only zero-sequence current. There will be equal current (magnitude and phase angle) in all three phases both on the wye and delta side.
This is an extreme example of currents observed by waross in wye-delta banks.
I must learn to think before typing. Breaking the delta in my example will not result in full line to line voltage because of the second source.
Jghrist,
Good example, much simpler than mine. So circulating current is equal to I0 in this case. So what is the general rule for quantifying circulating current when sources and loads may exist on either side?
Sorry about the comment on the "Break the delta". The effect is very evident on the secondary of a four wire wye:delta. Breaking a primary delta will defeat the purpose.
I have always considered "Circulating currents" to be unwanted and possibly destructive currents, whether in a delta winding, core laminations, bus bars or whatever.
A circulating current, just like a load current, has a corresponding current in the companion winding.
Circulating currents that I have encountered and corrected are I believe, zero sequence currents, in that the problem current has the same phase angle in all three phase windings of the delta, both primary and secondary.
This circulating current will combine vectorily to the load current in the windings. The resultant current may be much greater than the expected load current in at least one phase and often less than the load current in the other phases.
A delta wye transformer bank is basically three independent single phase transformers. Connect a single phase transformer line to line on a three phase supply and the load current will still be accurately reflected in the primary winding, just as if the transformer were connected to a single phase supply. Other loads on the three phase system will not affect the currents in the transformer windings and the ratio between primary and secondary will still be accurate.
Anyone who has worked with the larger single phase generators that have been converted from three phase to single phase will be familiar with the current split when a single phase load is applied to a delta transformer winding or a delta connected generator stator. The connection does not create circulating currents at the fundamental frequency.
We may have a misunderstanding concerning terms.
Three phase transformers with three legged cores may have issues with circulating currents caused by the phantom delta but three single phase transformers with a delta primary and a wye secondary have no mechanism to create circulating currents in the delta primary, even if they are different impedances.
And the real, destructive, transformer destroying circulating currents that I have encountered do not cancel. Often line conditions on one phase will cause the current and determine the phase angle of the circulating current. The total current in each phase will be the vector sum of the circulating current and the load and exciting currents. I have seen the circulating current exceed rated full load current of a transformer.
But you don't get that type of current with a delta primary and a wye secondary on a three transformer bank.
Bill
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"Why not the best?"
Jimmy Carter
I agree we have a misunderstanding of terms; exactly why I'm asking for a quantifiable definition. It's beginning to look like there is none that is accepted here, just a non-quantifiable "unwanted" zero sequence current.
I hear you on the magnetic circuit, and agree that three single phase transformers will have a different zero sequence impedance than a similar size three legged core three phase. This different impedance should be evident whether the zero sequence current is wanted or not.
