Calculating transformer size for zig-zag configurations (artificial neutral for HRG)

[MechEdetour]

Hello folks.

I am trying to make sense of a pretty common industry practice for HRGs... the use of a zig-zag transformer to produce an artificial neutral.

For some context, existing ungrounded systems that would like to upgrade to high resistance grounded but lack a system neutral need an additional means to measure the fault current. One way to go about this is by deploying a zig-zag transformer that provides the required neutral, and therefore a means for the fault current to be measured through the grounding resistor.

Typically this is done with an individual 3-phase zig-zag transformer with no secondary winding (err, autotransformer?). With that being said, three single-phase transformers can also be wired to yield the same zig-zag setup, also resulting in an artificial neutral... some HRG vendors go about it this way. I am trying to better understand the setup and the individual transformers sizing + fault current magnitude at different parts of the circuit.

Please forgive the crude sketch, but assuming a fault current of 5A, is my logic correct in that each CPT only carries 1/3 the fault current?



Each CPT is 480V Primary/240V Secondary, so doing a transformer sizing calc, my 1.67A "load" @ 240V would require at a minimum a 240V*1.67A = 400VA transformer. Since pulsing current is usually another 5A (for a total of 10A), let's say 800VA. Am I going about this the right way?

My questions:
1) Even though these are single-phase CPTs, they are wired in a 3-ph setup. Do I need to treat my calcs that same as a 3-ph setup and consider the 1.73 multiplier in my calcs?
2) Is the primary current on my CPTs actually 1.67A per primary? I do have a 2:1 transformer ratio between the primary and secondary of the CPTs so it could be that it's only .83A on the primary? I don't think so since this isn't a conventional use of a transformer, but I am having my reservations.

 

[jim dungar]

In my experience it is rare to use 3 'off the shelf' transformers to build your own zig-zag configuration. I have always just ordered what I needed.

For off the shelf I have used wye-delta configurations instead of zig-zag.

 

[MechEdetour]

In my experience it is rare to use 3 'off the shelf' transformers to build your own zig-zag configuration. I have always just ordered what I needed.

For off the shelf I have used wye-delta configurations instead of zig-zag.

I will say that it is atypical, but some vendors do provide the 3 individual CPTs as their zig-zag solution. Some do it with a single 3-phase transformer, others do it the way I have shown in my sketch.

Coincidentally, and not sure how I missed it previously, but I just came across this blurb in Post Glover's application guide:

The KVA rating of each of the transformers should be equal to one-third the rated line-to-line voltage times rated ground current for continuous duty.

This is more or less in line with my calculation, but they say to use L-L voltage to determine transformer KVA. In my case I guess it would be 480V * (1/3) * 5A = 800VA. I would still like to understand why this is the case. From my sketch it seems that the primary and secondary of each CPT would see the same current.

 

[winnie]

I've done _one_ self built zig-zag transformer. The coils all need to be the same voltage. You can't use 480:240 transformers, though you could use 480/240 : 240/120 transformers wired for 240 : 240V.

Jonathan

 

[MechEdetour]

I've done _one_ self built zig-zag transformer. The coils all need to be the same voltage. You can't use 480:240 transformers, though you could use 480/240 : 240/120 transformers wired for 240 : 240V.

Jonathan

How does that work? So in that case it wouldn't matter if the system voltage is 600V delta or 480V delta? I understand that these CPTs would not be used in a conventional way, and maybe that's why it works the way you describe.

 

[jim dungar]

How does that work? So in that case it wouldn't matter if the system voltage is 600V delta or 480V delta? I understand that these CPTs would not be used in a conventional way, and maybe that's why it works the way you describe.

The secondary winding voltage needs to be the same voltage as the primary winding in order to be used as a zig-zag.

 

[winnie]

How does that work? So in that case it wouldn't matter if the system voltage is 600V delta or 480V delta? I understand that these CPTs would not be used in a conventional way, and maybe that's why it works the way you describe.

The secondary winding voltage needs to be the same voltage as the primary winding in order to be used as a zig-zag.

You need three transformers, each with two of the same voltage coils on the same core, wired in the zig-zag configuration.

The coil voltage rating needs to be high enough that the coils are not saturated during normal operation. If the individual coil voltage is X, then the L-L voltage rating of the zig-zag connection is 3X. So 240V coils should be more than fine for a 480V system.

Jonathan

 

[MechEdetour]

If the individual coil voltage is X, then the L-L voltage rating of the zig-zag connection is 3X. So 240V coils should be more than fine for a 480V system.

So in that case it should be adequate for the 600V as well, correct?

Since only coil voltages seem to be relevant here, how does the kVA size come into the picture? For my example above where there would be 5A of fault current and even 10A flowing @ a pulsing rate (for locating fault with a pulsing circuit), how does this translate into calculating kVA size? Is it the same as if I had 5A-10A of load current?

 

[winnie]

During a fault, 1/3 current flows in each leg of the system. So if you have a 10A fault current, you have 3.33A in each coil.

Take the current * the coil voltage rating to get the VA rating of the coil. In your case 240V * 3.33 = 800. In general a 1 kVA transformer can carry 1 kVA on the primary _and_ 1 kVA on the secondary, so in your case you would need 3 pieces of 0.8 kVA 240V:240V transformers to carry 10A of fault current on a continuous basis.

Given your 5A continuous, 10A pulsed, you could get away with smaller transformers, on the other hand it doesn't pay too much to try to exact size these transformers; they are so small that the cost of installation will vastly exceed the difference between 500VA or 750VA or 1kVA units.

-Jonathan

 

[MechEdetour]

During a fault, 1/3 current flows in each leg of the system. So if you have a 10A fault current, you have 3.33A in each coil.

Take the current * the coil voltage rating to get the VA rating of the coil. In your case 240V * 3.33 = 800. In general a 1 kVA transformer can carry 1 kVA on the primary _and_ 1 kVA on the secondary, so in your case you would need 3 pieces of 0.8 kVA 240V:240V transformers to carry 10A of fault current on a continuous basis.

Given your 5A continuous, 10A pulsed, you could get away with smaller transformers, on the other hand it doesn't pay too much to try to exact size these transformers; they are so small that the cost of installation will vastly exceed the difference between 500VA or 750VA or 1kVA units.

-Jonathan

Thank you @winnie for the explanation.

May I ask another question?

Referring to the post you made previously,

I've done _one_ self built zig-zag transformer. The coils all need to be the same voltage. You can't use 480:240 transformers, though you could use 480/240 : 240/120 transformers wired for 240 : 240V.

Jonathan

A 480/240 : 240/120 CPT would be wired such that it's used in it's 240 : 240 form. The primary however would still be physically connected to a 480V delta system (as shown in my initial sketch), wouldn't it?. Is it fair to say that the only reason that would be allowed is because the primary is suitable up to 480V (ie. insulation, etc. is rated for it)? Or would this particular CPT wired for 240 : 240 only be suitable for a system that is rated 240V?

These CPTs are only being used to produce a neutral so I am trying to make sense of all the nuances.

 

[jim dungar]

The primary however would still be physically connected to a 480V delta system (as shown in my initial sketch), wouldn't it?

Technically there is no primary or secondary when you are dealing with autotransformer configurations. Instead, they have High and Low voltage sides, although factory built units may list primary and secondary on their nameplates. Typically a zig-zag transformer would have maximum voltage rating.

A DIY transformer configuration will require a DIY label.

 

[winnie]

Thank you @winnie for the explanation.

May I ask another question?

Referring to the post you made previously,


A 480/240 : 240/120 CPT would be wired such that it's used in it's 240 : 240 form. The primary however would still be physically connected to a 480V delta system (as shown in my initial sketch), wouldn't it?. Is it fair to say that the only reason that would be allowed is because the primary is suitable up to 480V (ie. insulation, etc. is rated for it)? Or would this particular CPT wired for 240 : 240 only be suitable for a system that is rated 240V?

These CPTs are only being used to produce a neutral so I am trying to make sense of all the nuances.

You are correct, the transformer will need a voltage to ground insulation rating suitable for 480V. Most small transformers use 600V insulation systems, but it certainly pays to check.

This same issue is seen with buck/ boost transformers where a 24V coil might be electrically in series with a 208V coil.

Jonathan

 

[MechEdetour]

Side question - what is the phase to artificial neutral voltage when a zig-zag setup is deployed. Does the same 1.73 factor apply? So 277V from line to artificial neutral for the 480V sketch I have above?

 

[jim dungar]

Does the same 1.73 factor apply?

Yes.

 

[MechEdetour]

Yes.

Thanks for the quick reply! I was a bit premature in asking my question as well. I noticed that it's pretty much answered in post# 3 above.

 

[MechEdetour]

I am full of questions today. Assuming typical 240x480 primary and 120x240 secondary CPTs:

Can someone tell me what would happen if I had my primary wired for 480 and secondary for 120 in both normal and faulted scenarios?

When both primary and secondary are wired for 240, I can see how the current would be equal on both the primary and secondary side (1.67A per leg). If the windings are wired such that there is a 4:1 primary to secondary ratio, I want to assume that I would see 4x the current on one side. However the way it's wired (ie. primary winding of CPT1 wired in series with secondary winding of CPT2) does not jive with ohms law... the current must be equal through both windings.

I don't know enough about the physics to understand what would happen. I did a bunch of digging and came across a lot of helpful information, but this is pretty specific...

 

[jim dungar]

I am not sure what your CPT abbreviation is short hand for?
You should not be using control power transformers to create your zig-zag transformer.

If the coil voltages are not the same the zig-zag will not perform as intended. You will have some type of auto transformer. I would not bother trying to figure it out, unless i was still in school and it was a homework problem.

 

[winnie]

I needed some LTspice practice, so I build a delta voltage source grounded via a zig-zag transformer simulation.


When the transformers weren't '1:1' then the neutral impedance simply went up. This intuitively makes sense to me; the assymetric zig-zag transformer is sort of a normal wye added to the zig-zag, and wye coil arrangements create a high impedance neutral.

The turns ratio of the coils in the zig-zag must be 1:1 for proper operation.

-Jonathan

 

[MechEdetour]

I am not sure what your CPT abbreviation is short hand for?
You should not be using control power transformers to create your zig-zag transformer.

If the coil voltages are not the same the zig-zag will not perform as intended. You will have some type of auto transformer. I would not bother trying to figure it out, unless i was still in school and it was a homework problem.

CPT is Control Power Transformer in this case.

While not ideal, I think you'd be surprised to learn how often this is done (using qty 3 single phase CPTs and wiring them into a zig-zag config). I think for HRG applications, a single 3-phase zig-zag transformer is probably pretty rare. Especially considering how small they tend to be since they only carry the ground-fault current.

I don't miss homework. However, I do need fuel to let people know when they're wrong.

I needed some LTspice practice, so I build a delta voltage source grounded via a zig-zag transformer simulation.
View attachment 2578211

When the transformers weren't '1:1' then the neutral impedance simply went up. This intuitively makes sense to me; the assymetric zig-zag transformer is sort of a normal wye added to the zig-zag, and wye coil arrangements create a high impedance neutral.

The turns ratio of the coils in the zig-zag must be 1:1 for proper operation.

-Jonathan

Great info!

Since the neutral impedance increases, would it increase enough to prevent ground-fault current from flowing? Maybe put a better way, does the added impedance greatly exceed the 56 ohm resistance. I imagine if the impedance due to this "mis-wiring" is substantial ground fault current would be too low to trigger alarms.

 

[winnie]

CPT is Control Power Transformer in this case.

While not ideal, I think you'd be surprised to learn how often this is done (using qty 3 single phase CPTs and wiring them into a zig-zag config). I think for HRG applications, a single 3-phase zig-zag transformer is probably pretty rare. Especially considering how small they tend to be since they only carry the ground-fault current.

I don't miss homework. However, I do need fuel to let people know when they're wrong.

Great info!

Since the neutral impedance increases, would it increase enough to prevent ground-fault current from flowing? Maybe put a better way, does the added impedance greatly exceed the 56 ohm resistance. I imagine if the impedance due to this "mis-wiring" is substantial ground fault current would be too low to trigger alarms.

I don't trust my simulation to give you a solid answer. I don't have proper numbers for 480V source impedance, zig-zag transformer coil inductance or leakage inductance, or transformer iron saturation. If you want to do a full engineering analysis, I'm happy to share what I did to give you a starting point.

In my model, if I have a 56 ohm connection between 1 phase and the derived neutral, I get about 4.9A RMS through the 56 ohm resistance. If I change the transformers to 4:1 turns ratio, I get 3A of current through the same 56 ohm resistance. A smaller change than I expected, but the 56 ohm grounding resistance is pretty big.

If I use a 5.6 ohm grounding resistance, the corresponding numbers are 48.2A and 3.9A. So the impedance of the balanced zig-zag is below 1 ohm, and the impedance of the one built with 4:1 transformers is in the realm of 50 ohms. I've not calculated the values precisely, because as I said the parameters of the transformers themselves are all wrong. This is just to give you an idea of the magnitude of the effect.