transformer Z% in parallel

[arc101]

Say you have two step down transformers (240v/120v, Z=5%) wired in series. Will this make total Z=10%? Then actual Z would vary by a factor of 4 (due to the different voltages)?

 

[davidbeach]

In essence you would have a transformer twice the size (kVA) with Z=5%.

 

[arc101]

Why isn't Z% additive? I thought it was a per unit value, so it would add?

 

[jghrist]

The total impedance would be 10% on the single transformer kVA base. If the base voltage of the different parts of your system changes with the transformer ratio, then the transformer percent or per unit impedance does change.

 

[davidbeach]

I'm sorry, I missed that they were in series, I read too fast and thought parallel.

 

[dk101010]

am I missing something here? Connecting two transformers in series will limit the kVA rating of the transformer to the smaller one. Also, the impedance is 10% if they have the same bases.

 

[arc101]

I was visualizing 480v into the primary with two connected in series. This would mean 240v across the secondary and 120 across each of the secondary windings. Wouldn't the total z be 10%?

 

[jghrist]

I was visualizing something different:

-------    ---------    ------
       >  <         >  <
 240   >  <  120    >  < 60
       >  <         >  <
-------    ---------    ------

instead of

-------    --------- 
       >  < 
 240   >  <  120
       >  < 
       |  |
    ---+  +---
       |  |
       >  < 
 240   >  <  120 
       >  < 
-------    ---------

 

[arc101]

So I'm confused. What would the KVA and total Z% be?

 

[dpc]

So which one of jghrist's two connections are you talking about?

 

[arc101]

------- ---------
> <
240 > < 120
> <
| |
---+ +---
| |
> <
240 > < 120
> <
------- ---------

 

[BJC]

If your hook them up in parallel - 480 volt high side and 240 /120 on the low the Z is still 5%.
If you calculate the fault current on the secondary side it's transformer full load current divided by impedance. It's the same if you the short is 240 L-L or 120 L-N.

 

[arc101]

are you calling this parallel?

H1----- ---------
> <
240 > < 120
> <
| |
---+ +---
| |
> <
240 > < 120
> <
H2----- ---------

I would call this series, since H1 and H2 are 180 deg out of phase? So why don't the impedances add?

 

[dpc]

OK, I still don't know what connection you are interested in.

 

[davidbeach]

For this discussion please use the following definitions:

Transformers in parallel -> The high side windings are in series, the cores in parallel, and the low side windings in series.

Transformers in series -> The high side of one transformer is connected to the source, the low side of this transformer is connected in series to the the high side of the second transformer and the circuit continuing through the low side of the second transformer.

Based on the above, are you asking about a parallel or a series connection?

 

[arc101]

i guess neither,

H1-----+ +--------- Load
> <
240 > < 120 transformer 1
> <
H2-----| |
| |
| |
H1-----| |
> <
240 > < 120 transformer 2

> <
H2----- --------- Load

480V connected to H1 of transformer 1 and H2 of transformer 2. H2 of transformer 1 tied to H1 of transformer 2.

It is my understanding (from all of this) that the Total Z% would be 1/2 of the original. Any thoughts?

(Thanks for all of the replies)

 

[davidbeach]

That is exactly what I was describing as a parallel connection.

For future reference when doing ASCII art, use the [ignore]

 and

[/ignore]tags around your art to produce this:

H1-----+  +--------- Load
       >  < 
 240   >  <  120       transformer 1
       >  < 
H2-----|  |
       |  |
       |  |
H1-----|  |
       >  < 
 240   >  <  120       transformer 2
       >  < 
H2-----    --------- Load

That is much more readable. Yes, in ohms you have half the impedance. In % or per unit you have half the impedance if you don't change the base, but if you consider the combination as a single transformer with twice the kVA base you have half the impedance when comparing that base to the original transformer base.

 

[stevenal]

DavidBeach:

The connection you are describing as series is properly termed a cascade or tandem connection by IEEE. Note that the secondary winding is actually in parallel (not series) with the primary winding of the downstream transformer. The term series is not defined in a way that can apply to four terminal devices. To further complicate matters, the thread title references "parallel", while the question asks about "series."

 

[arc101]

Thanks, that clears things up.

 

[JensenDrive]

This is strange. Depending on how I examine the last figure, I can talk myself into the xfmr arrangement gives 1/2 Z or 2x Z, on an ohms basis:

Case for 1/2 Z:
Start with one xfmr, and reflect all the transformer impedance to the 240V side. Now add the 2nd xfmr and you have 2 impedances in parallel, so half the Z.

Case for 2x Z:
Start with one xfmr, and transfer all the tranformer impedance to the 120V side. Now add the 2nd xfmr and you have 2 impedances in series, so 2x the Z.

Seems to show me that you cannot really transfer impedances across the xfmr for this case. I think you need to know leakage impedance on a per winding basis to determine the net effective impedance of this xfmr arrangment.