# Transformer output connected to another transformer. Measuring 'Real Power' at input of first transformer

I have a watt meter connected to the primary of one transformer to measure power. The output of this transformer is connected to the input of another transformer.

The watt meter is measuring the inductive load of the primary of the second transformer, as 'real power'. I figured I have to add a capacitor in parallel to the primary of the second transformer to filter out the current at the given frequency but I am not sure.

If I connect a load to the secondary of the second transformer, the reactance of the primary of the second transformer will change, in turn changing it's ability to filter out the frequency with the parallel capacitor.

Is what I am describing true? Or does it work differently? How are power lines avoiding experiencing 'real power' dissipation from transformers of appliances in our homes. I know transformers are inductive and give power back to the source. But in the double transformer test I describe the watt meter was measuring the 'apparent power' of the primary of the second transformer, as the the 'real power' in the 'eyes' of the primary of the first transformer. so if I measured voltage and current at the primary of the second transformer, I would multiply them to get an apparent power of 20VA. The watt meter would show 20Watts (real power) at the primary of the first transformer.

I hope that is clear. Thank you.

• If the second transformer was unloaded it should not appear as real power. Was it getting hot? Real power will turn into heat. Were you operating the second transformer within its voltage rating? Commented Jan 27, 2016 at 14:40
• What are your transformers? Can they both be individually connected to the AC power? Data sheets and links to the transformers are really important here. Commented Jan 27, 2016 at 14:41
• Transformer windings have resistance too. This resistance dissipates real power. Only ideal transformers are pure inductors. Commented Jan 27, 2016 at 14:42
• I did this test a while ago. They can be both connected to 120 outlet of the wall. But I only connected one of them to the wall and the other to the output of the one connected to the wall. My wattmeter was one of those kill-watt-meters you plug into the wall with your appliance. I'm not at home right now so I can't post the type of transformers I used. I will post that info when I get home. But based on previous measurements, the transformer I plugged into the wall has roughly a primary inductance of 1H :(maybe a little more) and it steps down by a factor of 8. I think is rated for 2 amps. Commented Jan 27, 2016 at 15:08
• The second transformer is about the same size but I think the step down is something like 5 or 6 times, rather than 8. Commented Jan 27, 2016 at 15:09

## 1 Answer

The real power that you measure when there is no load connected to a transformer is the "iron losses" in the laminations consisting of hysteresis and eddy-current losses. The reactive power is due to the magnetization of the core. There will be a small copper loss in the primary due to the magnetizing and core loss current.

The total losses for one transformer feeding another will include some copper losses in the first transformer due to the total current supplied to the second transformer. The real and reactive power of the second transformer should be reflected unchanged in the measurements made on the primary of the first transformer.

Here is something to compare your results with:

I measured the no-load losses for a 150 VA transformer with a 120 V, 60 Hz primary. At 122.2 V, the input current was 0.13 A, the power was 5.3 watts, the apparent power was 16.6 VA and the power factor was 0.31. The data was taken with a Kill-A-Watt. The transformer weighs about 6.5 lbs and has a 3-3/4 X 3-1/8 X 1-7/8 inch lamination stack.

Data for a transformer rated about 100 VA was 3.1 W and 9.1 VA. A transformer rated 25 or 50 VA measured 3 W and 10.4 VA at no-load. The two larger transformers were for industrial products sold to paper mills and auto manufacturers. I believe the small transformer was used in a consumer product.

Comparison of Kill-A-Watt data with data taken with other meters leads me to believe that it is accurate within 1 to 3 percent.

If the meter indicates "lots" of power with nothing but the transformers connected and they aren't burning up, there must be something wrong with the meter or your use of it. My Kill-A-Watt has a Watt/VA button that toggles the display between Watts (real power) and VA (apparent power).

Here is a Kill-A-Watt meter showing watt and VA readings for a CFL lamp.

• Thank you, this makes sense. I realized when you put an inductive load (i.e primary of another transformer) onto the secondary of a transformer, the inductance will add up in parallel. My second transformer had a very low primary inductance compared to the first transformer so when I measured the total inductance when hooking them up it went from 1.5H to 0.6H without any load on the secondary of the second transformer. I got confused and thought the apparent power was being measured as real power on the primary side of the first transformer but really they impedance was just dropping by a lot. Commented Feb 12, 2016 at 22:59