Multiple transformers in series

[gar]

221024-2124 EDT

TwoBlocked:

If you are still watching this thread, then my question to you is how you would study ( calculate ) the voltage across a load resistor at the end of several transformers cascaded in series?

By cascaded in series I mean the following ---
1. Each transformer consists one single primary two terminal winding magnetically coupled to a single two terminal secondary winding with high resistance isolation between the two windings.
2. We assume that each transformer can be approximated by an ideal transformer with an internal impedance of some series resistance, and some series inductance.
3. By cascaded in series I mean the secondary of one transformer is connected to the primary of a next transformer, and so on.

So how would you calculate the change in voltage across the load resistor as resistance changes?

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[Opie11]

Gar:

Yes, I think that is the question I was originally trying to ask, in addition to a few other concerns, but was unable to state it the way you did. Thank you.

 

[gar]

221025-0827 EDT

Opie11:

If you want to determine the series source impedance of your circuit at the load end, then make an open circuit voltage measurement and its phase angle at the load end. Then place a known resistive load as a test load on the circuit, and measure the voltage and current values at the resistive load including phase angle. Calculate the source impedance.

The assumption is that the first measurement gives you the open circuit source voltage, and the second measurement allows you to calculate the equivalent internal impedance of the series impedance.

Depending upon the magnitude of the series inductance you may be able to just assume the source is a series resistance.

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[ggunn]

Ancillary question: Transformer impedance is shown as %Z. Percent of what? I know how to use the number in an available fault current calculation for a transformer but I confess that I don't know what it means.

 

[winnie]

Transformer impedance is measured by shorting the secondary and then adjusting primary voltage until full load current flows. The % of full voltage to get full current with the shorted secondary is the % impedance.

If you  assume linearity then you can treat this as the % magnitude voltage drop under full load. This voltage drop has a significant reactive component and isn't in phase with the transformer output voltage.

Jon

 

[ggunn]

Transformer impedance is measured by shorting the secondary and then adjusting primary voltage until full load current flows. The % of full voltage to get full current with the shorted secondary is the % impedance.

Thanks. I figured it had to be something like that since it is dimensionless in the calculation.

 

[TwoBlocked]

221024-2124 EDT

TwoBlocked:

If you are still watching this thread, then my question to you is how you would study ( calculate ) the voltage across a load resistor at the end of several transformers cascaded in series?

By cascaded in series I mean the following ---
1. Each transformer consists one single primary two terminal winding magnetically coupled to a single two terminal secondary winding with high resistance isolation between the two windings.
2. We assume that each transformer can be approximated by an ideal transformer with an internal impedance of some series resistance, and some series inductance.
3. By cascaded in series I mean the secondary of one transformer is connected to the primary of a next transformer, and so on.

So how would you calculate the change in voltage across the load resistor as resistance changes?

.

Hey Gar, Reading other's posts and doing a little research I find I do not have as good an understanding as I thought I had. Even some references I looked at had a simple, incorrect explanation. Here's an online calculator, but as other's mentioned, you need to know the X/R ratio:

https://voltage-disturbance.com/engineering-calculators/transformer-calculator

If I were in your shoes, I'd contact the vendor or manufacturer for help. Playing with the numbers in the calculator, It looks like a reasonable approximation of voltage drop in % would be half the impedance %.

 

[Fred B]

As stated each transformer will have a percentage drop related to internal resistance. Then each set of conductors will have an amount of drop. Then if loads are applied in between any pairing of transformers the loads would add to drop of voltage available to the next transformer.
What is your bottom line to achieve? Is it a specific kVA at the end? It seems a bit odd to go up the down then back up again in a series of transformers. Could a simple buck or boost by a single transformer run from the initial transformer be easier to get to the bottom line?

 

[gar]

221026-1202 EDT

Opie11:

Your first post seemed to imply a simple series circuit starting with an ideal voltage source, and ending in a single load.

This kind of circuit can be replaced for simplicity for an adequate analysis by an equivalent circuit consisting of an ideal voltage source, a single resistance and inductance in series as internal impedance, all in series with a single load.

Later posts indicated a more complex circuit consisting of serial-parallel combinations of various internal impedances and parallel loads. If all these parallel loads are constant, then you can still reduce the problem to a single voltage source, internal series inductance and resistance, and a single load.

From a protection perspective you treat each transformer on its own. Ideally each transformer requires an input fuse and output fuse. However, the output fuse of one transformer may be smaller than the input fuse of the next transformer. In this case the smaller fuse can be used to replace the larger fuse. However, this is going to cause fuse blowing problems. So you can not really have a larger transformer be a load on a smaller transformer. Also note: in general the input fuse to a transformer does not adequately protect the load side of the transformer.

In general when you have series connected transformers the transformers must decrease in size as you progress thru the series sequence. With special circuitry this rule might not be a limitation.

.

 

[Opie11]

Gar:
There are simple setups, 2 transformers, with a single load. We are obviously union in my line of work and the load is controlled by a different union which is protective of its area of responsibility, no access. We will protect these transformers individually.

Most scenarios are more complex with transformers in close proximity to each other. Also, there is typically a load at each voltage to include an additional transformer. Going forward I will put forth the suggestion to individually protect the transformers.

We usually use 25KVa transformers and less. Not always decreasing in size but used per what's available. Will put forth the suggestion to keep the sizes in consideration during design.

Thanks for the input!

 

[gar]

221026-1929 edT

Opie11:

I have two scope plots of transformer inrush current at
https://beta-a2.com/EE-photos.html
photos P6 and P7.

This is a small transformer at 120 V 60 Hz input with a full load rating of about 1.5 A RMS. Note: that I recorded a peak inrush of 40 A for this plot. Even calculating an RMS value for this peak the value isi about 28 A. Instaneous trip on a Sq-D QO is about 6 times its rating or 9 A for a breaker to protect this transformer. Thus, an input breaker that will hold on this inrush is at least a 28 A unit. And this will not protect a full load on the transformer.

This illustrates the kind of problem that can result from cascaded breakers and protective devices.

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[Jerry Solar]

Any help would be appreciated in understanding how to calculate voltage drop, amps, and over current protection when having multiple transformers, up to 5 , connected in series.
In doing research I am not finding anything that clearly addresses this.

Do you have a wiring diagram? I think you meant for the transformers to be connected in tandem. In series it means something else.

 

[gar]

22103-1500 EDT

Jerry Solar:

Can you define what you mean by tandem vs your meaning of series?

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[ggunn]

22103-1500 EDT

Jerry Solar:

Can you define what you mean by tandem vs your meaning of series?

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I assume that he means sharing a common bus on the primary side, i.e., what I would think of as a parallel connection.

 

[Canton]

Holly ! I just read through all the posts, but half way had to go back to the OP. I get the confusion on “series” transformer (cascading in my opinion), but did the OP every get addressed? ……

 

[gar]

221112-1534 EST

Canton:

It seems to me the original post has been addressed.

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[ggunn]

221112-1534 EST

Canton:

It seems to me the original post has been addressed.

And as usual for this forum used as a jumping off point for myriad diversions.