Transformers

[otm]

Hello Everyone,

I'm going to try and be brief, but there's no assurances.

I've been given some transformer work to do, and have made some headway, but have become stuck.

I've been given a transformer equivalent circuit (where R2 and X2) are on the secondary side of the transformer, with values for r1, x1, rm and xm, plus the turns ratio,

I've then converted this into it's further equivalent form by using the referred values for R2 and X2

(I hope your with me so far)

with the transformer operating in no-load and at 415V, I've worked out the primary current, the primary real power, the primary power factor, and the Secondary voltage.

My problem now comes with the transformer supplying a load impedance of (24.16 + j36.69)Ω and again running at 415V...

I need to find the following:

the Primary Current, the Primary Power Factor, the Secondary Current, the Secondary voltage, the secondary apparent power, the secondary real power, the secondary reactive power, the secondary power factor, the efficiency and the voltage regulation.

I'm a little stuck with where to start, and with some of the method.

Any help would be amazing,

Cheers,

Owen.

PS. I've tried to be vague enough so as not to make you guys think I'm asking you to do it for me, but if I've been too vague, please let me know.

 

[Grossel]

HI. It is a while since I worked with transformer theory, so I can't imagine the equivalent model in my head right now (you should draw them and upload graphic).

Anyway, the key here is to reduce the transformer equivalent into as few components as possible. It doesn't matter if you put the simplified impedances on primary or secondary side.

 

[otm]

Hello Grossel,

I've attached a quick graphic of the work I've done, I hope it helps.

I can understand referring the load impedance across, but then in my head at the moment don't get how you would use that.

I will need to sleep on it I think.

Cheers,

Owen

 

[Grossel]

Hi. The values you get is wrong. You shall find r1' and x1'.

I upload a copy of your drawing where I have added some text and the values for r1' and x1' that I think is right.

When that is done, you should also set up a help circuit where you also refer to a Zl' to get the primary current.

 

[RCinFLA]

You should add the primary leakage inductance and primary series resistance.

Primary leakage inductance is measured by shorting secondary.
Secondary leakage inductance is measured by shorting primary.

Primary and series resistance can be measured with a four point ohm meter.

Primary magnetizing inductance is measured with secondary unloaded (open circuit).

 

[otm]

Hello Grossel and RCinFLA,

I've uploaded a clearer image (I hope) showing what I've done. I've now referred the load impedance Zl and I think I've done this correct, and I know (I think) that the voltage across the load in this configuration relates to the secondary voltage via the turns ratio squared??

so I need to use a bit of circuit theory to find the V2 voltage, once I know this, put it back to the secondary side via the turns ratio, then use ohms law across the impedance to find the secondary current.

does that sound right??

Any help is most appreciated.

Cheers,

Owen.

 

[RCinFLA]

Yes, with the assumption that Lmag and Rmag are insignificant to load.

 

[otm]

Hello,

Last night I think I had a break through, but I feel my method still might need to be checked..

I took the referred Load impedance, and added it the impedances of r1 and x1 ( (0.0611 +J0.1769) + (1.169 +J1.776) = (1.2301 +J1.9529) )

I found the current going through this new combined impedance using ohms law, with V1 = (415 + J0)

This makes I2' = (415 + J0) / (1.2301 + J1.9529) which is equal to (95.8324 -J152.1428)

I then found the magnitude of this, then using the turns ratio found the current I2 = 39.558 amps, then ohms law to get V1 (V = 39.558 ×(√24.16² + √36.69²) = 1737.79 Volts) This number is less than my no-load voltage, but in the same region so I feel confident with that, but I'm not 100% confident with that.......


I think I've managed to get the Primary Current, and Power factor as well.

I1 = I0 + I2'

(I0 comes from the no load test from finding I0a and I0r)

(4.970 - J10.122) + (95.8324 - J152.1428) = (100.8024 - J162.2648)

finding the magnitude of this gives 191.02 Amps, (which feels like a concern, thats a lot!!)

Putting the I1 phasor into polar gives 191.0262< -58.1506

Cos(-58.1506) gives a power factor of 0.528 lagging.



Sorry for so much maths, I need reassurance I've done the right thing... and if there are any mistakes along the way, showing the steps I've done someone can pinpoint the issue quicker.


Thank You for all your help so far.

Owen.

 

[otm]

Hello

I'm guessing by the lack of replies, I've not done anything wrong!!

I've been looking through lecture notes, and am struggling to see the difference between the secondary apparent power, the secondary real power, the secondary reactive power?

Sounds stupid I know, I appreciate the difference of transformer Power in W and VA, but don't know if that applies to the three types of secondary power listed above.

Owen.