# calculating voltage drop in a transformer

Discussion in 'General Electronics Chat' started by ben22, Sep 2, 2014.

1. ### ben22 Thread Starter New Member

Jul 10, 2013
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I'm trying to figure out how to calculate the voltage loss on an AC transformer.

AC transformers all come with two ratings for power loss (in watts): no-load loss and full-load loss.

No-load loss is a constant and will be there no matter how many volt-amps are flowing through the transformer. I understand that full-load loss goes from 0 at 0 volt-amps, to the full amount at the rated maximum of the transformer in roughly linear fashion - so if you have a 10 kVA transformer with a 100 watt full-load loss rating, then at 5 kVA you get 50 watts loss, at 10 kVA you get 100 watts loss (plus the no-load loss).

So power loss is pretty easy to calculate. But what about voltage drop? Is there an easy way to derive that from power loss? Or do I need to get inductance and resistance values for a particular transformer to calculate that?

Thanks!

Ben

2. ### crutschow Expert

Mar 14, 2008
13,505
3,376
For an accurate voltage drop you need the resistance of the primary and secondary windings. The inductance is not a factor.

You could make an approximate estimate by assuming the difference between the no-load and full-load loss is all due to the winding resistance. Then divide that power difference by the maximum secondary output full load current to get the voltage drop due to this loss.

3. ### ben22 Thread Starter New Member

Jul 10, 2013
25
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Yes that makes sense. Thank you!

I should have said power loss increases along a x-squared curve, not linearly. but the voltage drop will be linear as current increases.

Ben

4. ### ben22 Thread Starter New Member

Jul 10, 2013
25
0
While I can now do the approximate voltage drop calculation, I am still struggling a bit with how to conceptually think about the power and voltage loss in a transformer, especially how utilizing a tap on the secondary (lets say the 2.5% high tap in case voltage drop has become a problem) would affect this.

Overall, I am trying to understand how to model a circuit with a step-up and step-down transformer. The most basic example I can think of that illustrates the issue is as follows:

assume a load of 1,200 watts @120 V with perfect power factor, so 10 amps (this quantity of amps would not diminish if the voltage was less (i.e. 110 V) due to voltage drop - the load only wants 10 amps no matter the voltage), and a generator that produces at 120 V and is capable of meeting this load easily (all at 60 Hz). In between the generator and the load are a step-up transformer that goes from 120 V to 12,000 V, and then an identical step-down transformer that goes from 12,000 V back to 120 V. Let's assume that the wires connecting the generator, transformers and load have no resistance.

How can I model the voltage drop that these transformers produce and the current flowing through this circuit? I am not sure why (as mentioned above) the inductance of the transformer plays no part in voltage drop - within one transformer, does one coil's inductance somehow "cancel" another coils inductance? How to determine how much current passes between the generator and the step-up transformer, and between the step-up and step-down transformers? And how would a non-unity power factor affect this?

I found an "equivalent circuit" for a transformer here: http://en.wikipedia.org/wiki/Transformer#Equivalent_circuit
but I'm not sure if its ever possible to get all the values they reference for a real-world transformer, so not sure how useful this is....or is this it? I just need to do circuit analysis on this to get the answers I'm looking for?

If anyone can help, please invent values for the variables for the transformers that are needed (and hopefully normally available in the real world...) to make these calculations (winding resistances, L values and required magnetizing current, power loss ratings...)

5. ### BR-549 Well-Known Member

Sep 22, 2013
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Why? I have never needed to know the voltage drop of a transformer. Why do you? Are you trying to make a transformer?

6. ### wayneh Expert

Sep 9, 2010
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The unloaded voltage is easy, right? Just the turns ratio. The secondary voltage will sag from that as the RMS current in the secondary is drawn across the DC resistance of the secondary. This give an approximation of the voltage drop but is probably close enough for most folks.

What more do you need?

7. ### BR-549 Well-Known Member

Sep 22, 2013
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Sorry Ben, I re-read your original post. That #4 post confused me.
That's why they rate transformers with power lose, not voltage lose. The secondary of the transformer can be higher than the primary, thus you have a voltage increase, not a voltage drop. The power loss in a transformer has two components. Voltage and current. The input V and I is power in. The output V and I is power out. If the transformer is perfect, input V and I will equal output V and I. Do you get the idea?

8. ### crutschow Expert

Mar 14, 2008
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There is only one main inductance, the magnetizing inductance, which determines the magnetizing current due to the applied primary voltage. It may appear to be a different value when measured at the primary and secondary due to the turns ratio but a transformer is just a number of coils wound on the same core and all share the same magnetizing inductance flux. This inductance does not significantly vary with current and has no effect on the load current or voltage (see the next paragraph). The leakage inductance would have an effect on the output voltage but it is usually so small as to be negligible.

The magnetic flux generated by the primary load current is cancelled by the secondary load current. If you look at the primary and secondary voltages and consequent current directions through the transformer due to the voltages you will see why this is so. The primary current flows into the (+) winding terminal but the secondary current flows out of the (+) terminal, leaving no net added flux. Thus the magnetizing inductance is not seen by the primary or load current.
The current passing between the primary and secondaries of all the transformers in a chain is determined by the turns ratios of all the transformers. The loss factors have no significant effect on these current values, just the voltages.
The power factor has no significant effect. It's the transformer current going through the winding resistance that causes most of the loses, which is independent of the load voltage/current phase angle.

9. ### studiot AAC Fanatic!

Nov 9, 2007
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10. ### MrAl Distinguished Member

Jun 17, 2014
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Hi,

The main idea with the primary and secondary resistance is you can 'reflect' the primary resistance to the secondary or reflect the secondary resistance to the primary so you end up with only one resistance in series with either the primary or secondary and that absorbs the power due to winding resistance. There will also be core loss, which you would have to look up in the data sheet of the core laminations being used.
There is also leakage inductance designed into some transformers and that would act to reduce the output voltage as well. There are several factors that are involved in the leakage inductance such as gap (if any) and lamination stacking factor which comes partly from how the laminations are placed on top of each other when forming the stack ('interleaving', such as 1x1, 2x2, 3x3 etc).

The primary resistance reflects to the secondary as the square of the turns ratio, and the secondary resistance reflects to the primary as the inverse square of the turns ratio. For example if the secondary resistance is 1 ohm and the turns ratio is 0.1 (10 to 1 step down where 100vac in equals 10vac out) then the reflected primary resistance is 1*(1/0.1^2)=1*100=100 ohms. If the physical primary resistance was 20 ohms then the total primary resistance now is 100+20=120 ohms, and the secondary resistance is now assumed to be zero. Thus we end up with one resistor and one ideal transformer. If there is leakage inductance that can be represented as an inductor of an appropriate value in series with one of the windings, so then we end up with a single resistor, a single inductor, and an ideal transformer.

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11. ### ben22 Thread Starter New Member

Jul 10, 2013
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Even a 1 or 2 volt loss coming out of the 240 V secondary is important to me, is leakage inductance so small in, for example, a typical 10 kVA step-down pole-mounted transformer that we are talking 0.1 V or 0.001 V or less of a loss?

Also the wikipedia entry on the equivalent circuit of a transformer seems to indicate that the magnetizing current comes from core resistance and core reactance components, and is a separate from the current drawn by the inductance of the primary and secondary coils of the transformer. I know its possible, as MrAl and wikipedia point out, to add all the reactances and resistances together to get a simplifed series circuit. But this would seem to negate that component.

AAC's intro section on transformers seems to differ - see the SPICE examples at the bottom.

Although this now has me a bit confused...it seems that the difference in current between primary and secondary windings decreases in absolute value as overall current increases (in the second to last SPICE example with high resistance the different is 0.0012 A, while in the last SPICE example with low resistance the difference is 0.01845 A, and the resistance is the only thing that differs) and I'm not sure why. Any help on this?

If I am trying to be able to calculate current and voltage all along a circuit that contain a lot of wire and step-up and step-down transformers, I believe it would be useful to know the value of this magnetizing current...So would there then be a way to calculate the value of this current, just given the no-load loss value? Is it as simple as solving for I in P=I·V given the rated primary voltage? Or does no-load loss include losses other than from magnetizing current...perhaps to get the no-load loss I would just take the circuit (using the wikipedia diagram) from Io and leftwards?

on a side note, so this means that the current and voltage on the primary side are in phase with the current and voltage on the secondary, not flipped (180 degrees out of phase), right?

On another side note, does this mean that in a distribution system with step-up and step-down transformers, that the current and voltage are almost 90 degrees out of phase in the medium/high voltage section of the circuit (between the step-up and step-down transformers)?

And MrAl, do you know if typical pole-mounted distribution transformers come with data sheets that give the core losses and the leakage inductances to make those calculations?

12. ### crutschow Expert

Mar 14, 2008
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3,376
I believe the difference is due to the 0.99 coupling factor they use between primary and secondary. So i should say it's the effective turns-ratio that determines the primary and secondary currents, not the actual turns ratio.
Both the primary and secondary currents are in phase with the voltage for a resistive load. The difference is that current is going into the primary on the positive peak while it is coming out of the secondary on the positive peak.

I don't understand why you think there's a 90 degree shift in step up or step down transformers. The turns ratio has no effect on the phase between current and voltage.

13. ### MrAl Distinguished Member

Jun 17, 2014
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518
Hello again,

Sorry i dont have that information. I could check around, but maybe the best bet is to call the power company and see if you can get data from them. If you are buying a transformer from some company i would think they would have some data on it.

14. ### ben22 Thread Starter New Member

Jul 10, 2013
25
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But what about the magnetizing current? in the last SPICE example, the secondary current is what you would expect given the load, but the primary current is 3x as much as the secondary current, because of the "magnetizing current" required. Does this not mean the primary current will always be a bit larger than the secondary current, especially for relatively low loads (relative to the inductance of the transformer)?

I thought that primary current would lag primary voltage because the primary coil is an inductor being "fed" by a voltage source, and thats the effect that inductors have. I understand why secondary current and voltage are in phase - the secondary inductor acts like a generator (voltage source).

15. ### ben22 Thread Starter New Member

Jul 10, 2013
25
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So I got some data from the transformer company but I am not sure how to interpret it...can anyone help? I am not sure why they give impedance, X and R in percentages...Do you know how I can use this to calculate voltage drop across the primary and secondary winding and the current through the primary winding, given a particular load on the secondary?

Data for a 10 kVA single phase distribution transformer copied here:
total losses: 115 watts
% impedance: 1.46
%R: 0.016
%X: 0.020
%R/X: 1.310
% regulation @ PF: 0.8: 2.460
% regulation @ PF: 1.0: 1.570
% EFFICIENCY @ UNITY POWER FACTOR

16. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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What are the nominal primary and secondary voltages?

17. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,047
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Indeed, that is a good approximation at power line frequencies.

18. ### crutschow Expert

Mar 14, 2008
13,505
3,376
The magnetizing current is determined by the primary inductance and is usually large enough so it is negligible compared to the load current but it can obviously be significant compared to small loads.
The primary and secondary load current are coupled by the core flux and are not affected by the magnetizing inductance. The magnetizing inductance only affects the magnetizing current which indeed causes the magnetizing current to lag the voltage. There really is no separate primary and secondary inductor since a transformer is just two or more windings on the same core.

19. ### #12 Expert

Nov 30, 2010
16,704
7,354
Dumbing it down: The primary winding doesn't act like an inductor because it is so tightly coupled to the load resistance that it acts more like a resistor.

(Please don't throw rocks at me if I just insulted your intelligence.)

20. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,301
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What they call no load losses, I would call core loss. What they call full load losses, I would call copper loss, or I squared R loss.

You might find these useful:

http://www.eaton.com/EGDRCUS/US/Lea...Released&Rendition=Primary&dDocName=CT_154545