Transformer Power Analysis.

Factual Questions
1

I am trying to do some power analysis to review for an exam. I am having some problems though figuring out what my next step should be.

Imagine a transformer with a 1:10 ratio. On the secondary side there are 3 loads, each tapped off a different spot on teh transformer. One is at 100%, one is tapped at 50% and the last is tapped at 25%. They share a common ground.

I am trying to find the total power generated in the circuit. I can calculate the reflected impedence but am unsure how to calculate the total power. Do I divide the Vs^2 by the sum of the reflected impedance and the source impedance? Or since power in=power out can I just calculate the individual power of each load and add them and that will = the ppower being put into the system?

Transformers have always been confusing to me. Any help would be appreciated.

2

Can you clear a few things up for me? Are you trying to find the total power draw of just the loads or of the entire system, including the transformer? Are the loads resistive, reactive, or both?

3

Sorry. The loads each have reactive and resistive components. I am trying to find the power draw of the whole system. This is an ideal transformer as well.

4

Ok, so we’re assuming zero power loss, and zero percent regulation (load voltage equals no load voltage) in the transformer. You need to first calculate the impedances of each of the loads, I assume you know the input voltage and the turns ratio of the transformer, so you can then calculate the secondary output voltages. Apparent power can then be calculated using P = V[sup]2[/sup]/Z with P in units of VA. From this and the impedance vectors you can then calculate true power in watts. Fun, huh?

5

Ok. I have the load impedances. I guess my question is is the total power on the secondary side equal to the total power on the primary side? The reason I ask is because I am trying to calculate the power usage of the ENTIRE circuit, to include the primary side.

6

Well, it is in an ideal transformer, which assumes no losses. Real transformers have more power going in than out, with the balance being divided up between iron losses and copper losses. Unless you know information about the winding geometry, iron characteristics, winding wire gauges, and other factors, there’s no way to calculate transformer power losses. If you’re assuming an ideal transformer, you’re assuming zero losses.

7

For resistive loads,

P[sub] primary[/sub] = V[sub] primary[/sub] [sup]2[/sup]/R[sub] primary[/sub]

Load 1: P[sub]1[/sub] = V[sub]1[/sub] [sup]2[/sup]/R[sub]1[/sub]
Load 2: P[sub]2[/sub] = V[sub]2[/sub] [sup]2[/sup]/R[sub]2[/sub]
Load 3: P[sub]3[/sub] = V[sub]3[/sub] [sup]2[/sup]/R[sub]3[/sub]
Etc.

For an ideal transformer, the power delivered to the primary is equal to the power dissipated by the load(s). Thus

P[sub]primary[/sub] = P[sub]1[/sub] + P[sub]2[/sub] + P[sub]3[/sub] + …

V[sub]1[/sub] = (N[sub]1[/sub]/ N[sub]primary[/sub])*V[sub] primary[/sub]
V[sub]2[/sub] = (N[sub]2[/sub]/ N[sub]primary[/sub])*V[sub] primary[/sub]
V[sub]3[/sub] = (N[sub]3[/sub]/ N[sub]primary[/sub])*V[sub] primary[/sub]