Parallel transformers - checking my models

In summary, the equations model the flux through the transformer with the mutual inductance between the coils.
  • #1
fahraynk
186
6
upload_2017-1-23_22-39-52.png

So on the left is a circuit which shows a voltage source and 2 coupled inductors in a parallel magnetic circuit shown on the right (transformer with a parallel core).
Can someone tell me if I am modelling it correctly with the following equations?
Rc1,Rc2,Rc3 are the reluctance of each branch of the transformer core
M = mutual inductance between the coils.
φ1 and φ2 are the flux on left loop and right loop of the magnetic circuit.
φ10 and φ20 are the total flux from L1 and L2 alone
$$M=k\sqrt{L1*L2}\\k=\frac{\phi_{12}}{\phi{1_0}}=\frac{\phi_{21}}{\phi{2_0}}$$

Here are the equations I came up with :

$$
MI_2'+L_1I_1'+R_1I_1+V_0cos(wt)=0\\
MI_1'+L_2I_2'+R_2I_2=0\\
\phi_1R_{c1}+R_{c2}(\phi_1-\phi_2)=N1I1\\
\phi_2R_{c3}+R_{c2}(\phi2-\phi1)+N1I1-N2I2=0\\$$
so the total flux through path 2 (φ2)- the total flux produced by the 2nd inductor (φ20)= φ12

$$L_2I_2=N2\phi2_0\\k=\frac{\phi_{12}}{\phi1_0} \hspace{10 mm}\phi_{12}=\phi_2-L_2\frac{I_2}{N2}\\
k=\frac{(N2\phi_2-L_2I_2)N1}{N2L_1I_1}$$

Is this enough equations to solve... or am I missing an equation? If so... what equation am I missing? I think there needs to be something relating I2 to I1 without the derivatives... ?
 

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  • #2
Tried to pay a tutor to answer but they said I don't have to pay because their answer might be wrong -_-
 
  • #3
This man isn't serious, he got his answer, never tried to pay the tutor...
 
  • #4
valentin bogatu said:
This man isn't serious, he got his answer, never tried to pay the tutor...
I tried to pay for an answer, meaning If I got an answer for the current I1, I2. But after like 48 hours I went through like 5 people and did not get the answer? I pretty much got my own work shown back to me with no current.
 

FAQ: Parallel transformers - checking my models

What is a parallel transformer?

A parallel transformer is a type of transformer where the primary and secondary windings are connected in parallel, rather than in series. This means that the voltage across the primary and secondary windings is the same, and the currents are additive.

Why would I need to check my parallel transformer model?

It is important to check your parallel transformer model to ensure that it accurately represents the behavior of the actual transformer. This can help identify potential issues or errors in the model that could affect the performance of the transformer.

How do I check my parallel transformer model?

There are several methods for checking a parallel transformer model, including using simulation software, performing tests on the actual transformer, and comparing the results of the model with known theoretical values. It is important to use multiple methods to validate the accuracy of the model.

What are some common issues that can arise with parallel transformer models?

Some common issues that can arise with parallel transformer models include incorrect winding ratios, incorrect turns ratios, and improper modeling of the core losses. These issues can lead to inaccurate results and affect the performance of the transformer.

Are there any resources or tools available for checking parallel transformer models?

Yes, there are many resources and tools available for checking parallel transformer models, including simulation software, online calculators, and industry standards and guidelines. It is important to use reliable and validated resources to ensure the accuracy of the model.

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