Unbalanced load on serially connected core type transfomer

[chaseadam]

I have a beefy 24V to 120V core type transformer that I would like to convert to a center tapped 240v transformer. Since there are two balanced sets of windings around each side of the core, I thought I may be able to connect the 120v windings in series instead of parallel to get a center tapped 240v (120v/120v 180°phase). Is this a legitimate connection option?

The goal with this transformer would be to power a small off grid house, so the load between the 120v taps will likely be unbalanced (potentially severely). From what I have read, this can cause extra "currents" in the core which cause heating. Is this a serious concern? Can someone explain or point me in the right direction of understanding the implications of an unbalanced load between the center tapped windings in my scenario?

[T3sl4co1l]

How many VAs is that..?

If it's laid out as you say, then I'd suggest connecting the 24V windings in parallel: this will help balance the flux, which I suppose might help with core heating, but mainly it's because it will reduce leakage between the two windings, keeping them better balanced.

Also, whatever the nominal VA capacity is, expect no more than half that.  Because you're drawing primary-to-primary current, not primary-to-secondary, so you're only using half the wire on the transformer.  It's also probably designed for a 10% regulation at nominal ratings, which means voltage drops by 10% at that level; again you lose half that because of using both primaries (so you get 10% regulation at only half nominal VAs to begin with), and you probably half again so the regulation is better (you don't want a soft 10%-regulation mains).

That's somewhat made back by the autoformer effect: if your load is 240V, then it gets nom VA/2 again, because half is supplied from the mains directly, the other half through the transformer.

Tim

[chaseadam]

The UPS it is in currently is rated at 3000VA, so I imagine it is at least that if not higher to address the 10% nominal issue you mentioned. I was incorrect and found it is a 48V system. When in inverting mode, the 48V is applied to the primary in parallel arrangement between the two sets of windings around the core.

I understand that if I am only using half of the windings I will be limited to half the VA of the transformer based on my understanding of how VA is calculated (RMSVxRMSA). In the arrangement I propose (secondaries in series) with the 3000VA nominal capacity I guess, each 120V leg can support up to 1500VA individually or 3000VA combined?

Can you provide more details around "balancing flux" and "leakage between the windings"?

I did not follow the primary->primary and primary->secondary comment. I believe I will be pulling power from the secondary only as the power is applied to the 48V primary windings.

I didn't follow the comment about the autoformer effect, can you point me to a specific page or search term which I can use to learn more?

[T3sl4co1l]

Just think about the transformer and winding resistances:

Apply 120V to the "near" primary (denoting the primaries as the 120V windings).  You get 48V on the near (same-side) secondary, and slightly less than 120V and 48V on the opposite windings (the loss is due to leakage flux, which acts to slightly reduce the voltage ratio, among other things).

Apply a load to the near 48V.  Voltage drops across its resistance, and the primary's resistance.  (The voltage on the opposite windings drops slightly further, due to the primary IR losses only.)

Apply a load to the far 120V winding instead.  Voltage drops across its resistance, and the primary's resistance, and the leakage flux (which manifests as a series inductance).  The near 48V winding is slightly lower in voltage (due to primary IR loss only), and the far 48V winding is lower still (due to leakage and primary IR loss).

Leakage between windings on opposite sides of a core / magnetic loop will be fairly high, enough to be noticeable (affecting regulation) even at line frequency.  But the windings within each core leg will be pretty well coupled.  So you can treat each side as a sub-transformer of its own.  By wiring the 48V secondaries in parallel, you are shorting out that leakage path between those sub-transformers.  It's like using a pair of 120:48V transformers back-to-back to get 120 again.  Except it's better, because the primaries are already mostly coupled (>90%, I would guess), so the 48V coupling only has to mop up the excess (the leakage, <10%).

With the 48V windings in parallel, apply a load to the far 120V winding.  The voltage doesn't drop as far, because most of the leakage is shorted out.  Now only the IR losses of each 120V winding remain.  A small current flows between the 48V windings, due to flux balancing; I doubt this will be more than 10% of their rating, even when the far 120V winding is heavily loaded.

How much IR loss are we talking?

When the transformer is operating as designed, both 48V windings are powered, and the 120V windings are loaded (in parallel, I assume, unless they were used for 240VCT; in which case, I'll assume parallel equivalent anyway, for convenience).  Which works the same as what we're doing, powering the 120V and (maybe) loading the 48V.

With all four windings active, each primary gets one unit of I*R, and each secondary gets one unit of I*R.  The pairs of primary and secondary windings are wired in parallel, halving each pair's total resistance.  The primary and secondary act in series, bringing the total back to one unit of I*R.

Likely, it was designed so that I*R is 5 or 10% of nominal output, i.e., for a 120V output (in the step-up configuration), it drops 6-12V at full load current (3kVA --> 25A).  That's 12.5A per 120V winding.

And total winding loss was I^2*R.  To leave the 48V windings unused, you drop half the loss, which is helpful, but you can't double the 120V windings' currents to compensate: that would quadruple their losses, and the transformer would run way too hot.  At best, sqrt(2) more current can be drawn, but this has two problems: one, the winding internal (hotspot) temperature will be ~41% higher; and two, more current simply drops more I*R voltage, worsening regulation.

It's also slightly worse due to the flux balancing current.  If the load is 120V and 12.5A, and the flux imbalance is ~10% like I worst-casetimated earlier, then the 48V windings will be carrying about 10% of their rating, i.e., 3A (out of 31A each).  Which dissipates a little heat, so the best case will actually be like 10% below sqrt(2).  But still, probably limited by regulation (how low can your line voltage drop, before it's really too bothersome to use on heavy loads?).

In any case, that's still 1.5kVA or so worth of capacity, which is not bad at all.

Tim

[chaseadam]

Thank you for the additional details. I followed everything up until the total winding loss at the end. I plan on wiring the 48V side in parallel and the 120v in series (or for this scenario using the 120v independently in an unbalanced way).

I understand I need to take into account the loading related to flux balancing if there is an unbalanced load, but still not sure how to properly model it. If I have an unbalanced load I cannot use the full 1.5KVA on a single side of the transformer, but can you walk through how to model the impact of an unbalanced load again/differently?

Is the 10% flux imbalance sufficient for modeling? If so, please verify the following scenario with 48V parallel and 120V loaded unbalanced. I am assuming no losses inside a side of the windings for simplicity.

overloaded example because side A will exceed 1500VA due to flux compensation

	48v	120v
side A	31.25	12.5
side B	0	0

properly loaded worst case example because side A has ~10% VA reserved for flux compensation for difference in loads. This would give each side approximately 1350VA to work with (90% of 1500VA)

	48v	120v
side A	28	11.25
side B	0	0

properly loaded real world example where the unbalanced sides must have 10% VA reserved for flux caused by *difference* in loading (12A-8A=4A, 4A*120V=480VA, 10%*480VA=48VA). Side A is 1440VA loaded and 48VA for flux which is less than 1500VA.

	48v	120v
side A	30	12
side B	20	8

[johansen]

To measure the impedance of your transformer, find a 10 amp (minimum) variac. short the two 48 volt windings together, connect the 120v windings in series for 240, put an amp meter in series and turn up the variac till 12.5 amps flow and record the voltage. multiply the two together, as the power factor of this experiment will probably be 90% or better.. and you get copper losses. if you want to, let the transformer sit for a while and measure its temperature.. watch the amps decrease as well, as the resistance of the windings increase.

Open one of the secondary coils, keep the other shorted and you should be able to calculate the impedance by comparing the difference in voltage between the two 120vac coils.

you can reconfigure this test many different ways to get all the information you need.


anyhow, your statement:
" If I have an unbalanced load I cannot use the full 1.5KVA on a single side of the transformer"

This is not true, in fact you can draw 141% of 1.5kva power from one winding, and zero from the other winding. your total power loss in watts will be the same as 1.5 kva from each 120vac winding. however, whatever temperature rise you had will be about doubled in just that one coil.
or you can draw 130% from one coil and 55% from the other. in this case, the power loss will still be 1.69 in one coil and .31 in the other, for a sum of exactly 2.
another example is 120% from one coil and 74% from the other is still equivalent to 100% from both. however, in these examples there will be more current in one of the 48 volt coils than the other.. this is probably not a big deal, the difference in current will compound temperature rise limitations but that compounded effect should be less than 10% of the total power lost in the windings. (you will need to measure the various impedances to solve this problem)

When the two coils are wound over the top of each other, such as a generator or motor, the different temperature rises isn't a problem because thermally they have very good coupling. this is why most 5kw generators has a 120/240v 20 amp breaker and plug.. but they also have a 120vac 30 amp plug and breaker. pull power from both though, and you can burn out the coils.


honestly i can't see a problem with forgetting about this matter. you may want to put two thermocouples inside the two coils however and set up a warning system if you do run into reasonable temperature rise limits.

[Ian.M]

Lets consider the best case scenario of feeding it 240V across both windings and drawing 120V from one end and the center tap.   In that configuration, the current in the two primary halves is equal and opposite, so there is no uneven heating and it should be able to handle its full VA rating.  It will actually have some extra margin as the only secondary current is from the imbalance due to flux leakage, so it will run cooler than it would in the UPS.  OTOH the UPS almost certainly isn't rated for continuous full power operation.

For a step-up configuration from 120V to 240V, half the primary can only handle half the VA, so the worst case scenario is an unbalanced 120V load of 1/2 its nominal VA on the half of the primary that's not being driven.  For 240V loads you get its full VA rating, or mix the two proportionately.