Transformers in series 2

[ProJPS]

Hi all,
If I have two step down transformers connected in series, would the overall transformer efficiency of both be:
- The efficiency of the least of most efficient unit
- The average of both the individual efficiencies


Rgards

 

[Compositepro]

The answer to your question is really obvious if you think about it at all. It is neither of your proposals. First, ask yourself what is the definition of transformer efficiency.

 

[waross]

Transformers don't work well in series. The voltage across each is inversely proportional to the transformers share of the load. This is a simplification. In the real world the added factors of possible magnetic saturation, the individual loads current demands with other than proper voltage applied and the power factor of individual loads all act to complicate the issue.

If you mean two transformers in cascade, then you multiply the efficiencies.
Suppose that one transformer has an efficiency of 98% and the other has an efficiency of 95% your overall efficiency will be .98 x .95 = .931 or 93.1%
This is assuming that both transformers are loaded to the conditions at which the efficiencies were calculated.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[prc]

In a way,in the transmission system all transformers are connected in series from generator to residential load! waross,where is the load sharing? When in series, the same power will flow except at the end you will get net power as per multiplied efficiency value as you correctly said.

But if the primaries and secondaries of,say, two identical units are connected in series, then the load per unit will drop to half. The no-load losses will drop less than half as at half flux density in core,core loss will drop much more than half.Net efficiency will be arithmetical average of the individual efficiencies at half load with lower no-load loss.

 

[waross]

First let's define series and cascade.
I would rephrase your statement as;
"In a way,in the transmission system all transformers are connected in cascade from generator to residential load!"
I used to encounter situations where under phase loss conditions the secondaries of two transformers would actually be in series across a healthy transformer and would back feed into the unfed primary lines of the distribution circuit. Given fairly equal loading the back fed voltages would be about 1/2 of normal. This situation would kill a lot of refrigerators and freezers.
After encountering this in the real world I tend to make a distinction between series connections and cascade connections.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[ProJPS]

Thanks Waross! I just needed to confirm my suspicion.

 

[waross]

Efficiency is all about losses. For any combination of applied voltage and given load, there will be losses. This applies to each transformer under consideration.
This raises the question;
"How is the efficiency calculated?" If the efficiency is calculated on the basis of the actual load and losses of the individual transformers, then we may multiply the efficiencies to arrive at the overall efficiency.
If the published efficiency figure is used, it is valid only for one value of applied voltage and connected load. The published efficiency is useful when comparing transformers but may be misleading at times.
The point is that efficiency numbers are a way to express losses and what we are really interested in are the losses, even if we may not always realize this.
If we can add the losses, why must we multiply the efficiencies? This may seem counter intuitive until we remember that the losses on the downstream transformer are part of the load on the upstream transformer.
A much simplified example:
A transformer supplies a 25 Watt load at 50% efficiency. Losses = 25 Watts. Load = 25 Watts
This transformer is supplied by a transformer running at 50 % efficiency. This transformer must supply both the load and the losses of the other transformer so it sees a load of 50 Watts. Losses = 50 Watts. Load = 50 Watts
To supply the total load and losses on the upstream transformer requires 100 Watts (50 Watts load and 50 Watts losses.)
The total losses to feed a 25 Watt load are 50 Watts + 25 Watts = 75 Watts.
100 Watts in and 25 Watts out = 25% efficiency.
50% efficiency x 50% efficiency = 25% efficiency.
Before you declare that transformers with 50% efficiency are unreasonable consider that these transformers may be very lightly loaded to the point that the load is about equal to the excitation losses. These transformers may actually be rated at over 95% efficiency but they are not being loaded anywhere near the load at which the published efficiency is calculated.
Beware of using percentages blindly without understanding what they are actually representing.
This rant is more about the dangers of using derived figures without a full understanding of them than about efficiency.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[stevenal]

"In a way, in the transmission system all transformers are connected in series from generator to residential load..."

These transformers are connected in cascade as Waross indicated. If parallel transformers have their primary windings in parallel, and their secondary windings in parallel; then series connected transformers would have their windings likewise connected in series. Not very practical.

 

[sbkenn]

Series -> average
Cascade -> multiply

 

[bilalk]

ProJPS, do you mean that the primaries of both transformers are connected in series (as LOOP FEED for instance) or is the secondary of the first tx serving as input to the primary of the second tx?
In general, efficiency is always output as it relates to the input. So in the first case above, each transformer's output can be related to each transformer's input independently, however, in the second case, the output of the second transformer will be related to the input of the first transformer.
Would you be able to give more background information about the application?

 

[ProJPS]

Bilalk, the secondary of the first transformer is the primary of the second transformer.