calculation of transformer primary current 2

[Mondy]

Dear All

Can anyone help me in calculating the total primary current of a transformer. The magnetizing current lags the secondary load current referred to the primary, and the total primary current is the vector sum of the two components. How do I find the mag current angle of lag and also once I know the angle, how do I calculate the vector sum mathematically? (assuming a load of unity P.F and no leakage in the transformer). I know how to do it graphically by forming a parallelogram and measuring the diagonal, but have no idea how to do it using a calculator (trig?)

Can anyone help?

 

[dpc]

What level of accuracy are you hoping for? The magnetizing current is insignificant compared to the load current for nearly any kind of analysis.

If you really need to know the magnetizing current to a high accuracy, you have to take into account that it is fairly rich in harmonics and will not be a pure sine wave.

Open circuit exciting current measurements can give you the power factor and hence phase angle of the current in theory, but the angle is very close to 90 deg and difficult to accurately measure.

 

[Mondy]

Thanks for your help dpc

Normally the mag current is too small to be significance, but recently I have been working with transformers where, due to design peculiarities, the mag current is disproportionately large and needs to be accounted for in the primary current. Although the mag current is high, the waveform is not that badly distorted, as the magnitude is not down to core saturation (or even nearing saturation).

I can calculate the mag current quite accurately (both the watts component and the magnetizing VA component), but ignoring harmonics and assuming sine wave, how is the lag angle calculated? And once I’ve got it roughly calculated, where do I go from there?

Many thanks
Mondy

 

[jbartos]

Suggestion: Sometimes, the manufacturer provides data sheet that includes the transformer test data.
Secondary current Is lag angle alfa for the known secondary side Watts and VA is:
alfa=arccos(Watts/VAs)
Rated transformer secondary current is:
Is=Re[Is] + jIm[Is] = VA/(sqrt3 x Vs)=(Watts + jVars)/[sqrt3 x (Vs + j0)]
Shift the Is to the transformer stator side by multiplying it the transformer turns ratio (Ns/Np), i.e.
Is'=(Ns/Np)xIs
Assumed that Vs is on a real axis.
Magnetizing current Im:
Im=Re[Im] + jIm[Im]=|Im| x [cos(beta) + jsin(beta)]
where beta is normally high. It should be available from measurements via calculations or from the transformer data sheet.
Angle gama for the primary current Ip=Is'+Im is:
gama=atan{[(Im[Is'] + Im[Im]]/[Re[Is'] + Re[Im]}
Ip=Im+Is'= Re[Im] + jIm[Im] + Re[Is'] + jIm[Is'] =
= sqrt{[Re[Im]+Re[Is']]**2 + [Im[Im]+Im[Is']]**2} x exp[-j x gama]

 

[Mondy]

Thanks Jbartos

Wow I certainly got what I asked for! I am afraid you are way above me here, is there any way you could put this a little more in layman's terms for me. I am thinking just single phase simple model of just resistive drops with unity PF load. Does the total mag current always lag the Pri current by the same angle and if so how is this angle calculated? and then how do you add this to the primary current? This should give me more than adequate accuracy.

Once again thanks for your reply, I envy your understanding and wish I had paid more attention in maths class!!

Cheers
Mondy

 

[jbartos]

Suggestion: Reference:
1. Donald G. Fink, H. Wayne Beaty "Standard Handbook for Electrical Engineers," 14th Ed., McGraw-Hill, 2000,
page 10-5
Figure 10-5 Loaded Transformer: a) Flux Distribution Single Phase, b) Phasor Diagram, 1:1 Ratio
Figure 10-6 Equivalent Circuit for a Two-Winding Transformer Considering Exciting Current
The above reference gives a very simple and informative description of the excitation current, IE, and is approximate relationship to other current. IE will lag the primary voltage Ep by almost 90deg. Its magnitude is very small and tends to be neglected in most cases except yours. The complex variable approach or phasor approach is necessary to calculate the IE from the transformer equivalent circuit accurately. Else, the manufacturer tech support should be contacted for its value.
Also, you may like to visit a technical library. It usually has several books that cover transformers reasonably good and comprehensibly.

 

[jbartos]

Suggestion: Visit

http://pemclab.cn.nctu.edu.tw/W3elemac/W3slide/ch2.xformer/

etc. for more info

 

[Mondy]

Thanks for your help jbartos, I'ts very much appreciated