Integrated transformer is designed with shunt core. Primary of transformer is wounded on main core+ shunt core so as to get required leakage inductance in the transformer itself. I am trying to simulate the transformer in FEMM. Since this software can be only used for 2-D geometry I am not able to simulate the model. Neither I am able to calculate the flux density by transformer flux equation, due to air-gap. While in operation my transformer shunt core is saturated (I guessed from the high noise from transformer). So I am looking to validate the transformer design magnetically or to calculate calculate the flux density in core.
The flux density in each limb of the core determined by division of flux(Webers) by the area of that limb.
First, sketch a diagram of the transformer core showing the directions of the flux path, in order to calculate the total flux, then the density will depend on each core sections. Can you share a figure or a diagram representing the transformer core geometry, in order to more clarify the problem?
R. Rebbah Hello. I have attached the sketch for transformer. Outermost winding is primary winding, so flux path can be predicted now. I need to validate or calculate the flux density in shunt core if the value is within limit or not. I have seen many times failure or saturation of this part . Is it possible to have some generalized calculation?
I guess the shunt core was added to increase the reactive power rating using the flux storage process by means of the air gap, and I presume you are using a FEM 3D software to analyze the local flux density of your model.
if that is the case, set the relative permeability of the ferromagnetic material of the core to a constant value (ex 4000 or 5000) in order to avoid the saturation phenomenon. then, the density can be locally measured on the shunt core, avoiding edges and corners of its geometry.
The flux calculation:
please look at this link (https://www.researchgate.net/publication/260073834_An_Integrated_Transformer-Shunt_Reactor_Operation_Device_for_The_Connection_of_Off-Shore_Wind-Farms ), it proposes a simplified representation of the magnetic circuit of the single-phase transformer with the shunt configuration. An equivalent circuit is also proposed.
you can found an answer to your problem by beginning the modelization using first a single phase of your model to analyze the flux then convert it for the three-phase case.
Here is a screenshot of the magnetic and equivalent circuits.
R. Rebbah Thankyou for the reply, this article is very informative, but my confusion is till the same. The photos attached is signifying gapped core reactor / transformer. Here the air gap is in path of flux direction. So because of air gap there is magnetic energy storage and hence reactance of winding is high.
But if you observe in the picture of integrated transformer (which I have attached above), the gap is not in path of flux direction. This air gap will look similar to the air gap which manufacturer provide as cooling duct. So the reluctance equation as you mentioned above (reluctance of air gap + reluctance of core) is not valid here. But as it has shunt core and primary of winding is passing through this core , so this will act as a shunt inductor in series with winding inductance.
Hence the saturation characteristics for this is little complicated for me to understand.
I found one picture of integrated winding transformer in google. Attached is for reference with electrical equivalent. This type of transformer is usually used in PWM application.
P.S : outer winding is generally primary winding.
In this model, the shunt core Increases the natural leakage flux for filtering purposes. This avoids additional inductors in PWM circuit.
Due to the axial and perpendicular leakage flux components, the 3D FEM is the most commonly used technique and the most accurate for the leakage reactance calculation, especially of non-standard configurations.
however, in order to calculate the leakage flux using classical analytic methods please check this link below. It provides examples of calculating the leakage reactances for different transformers configuration.
For instance, you can calculate the percentage of the leakage reactance of this model without the shunt core, then take the half value of the corresponding reactance and then simulate only the shunt core structure for this inductance value using a 2D FEM model.
Link: https://books.google.dz/books?id=1kzWPb4ok2EC&pg=PA224&dq=transformer+leakage+flux+image+method&hl=fr&sa=X&ved=0ahUKEwjlvIq86cLoAhXwShUIHWm8D3YQ6AEIOzAC#v=onepage&q=transformer%20leakage%20flux%20image%20method&f=true
R. Rebbah Thanks for the explanation and suggesting this book, it seems the problem can be solved now. I will post the result of the investigation after finding the answer. Thank you and stay safe !! :)