Inductance and Transformer Modeling
Deadline 28/03 23:59
Grading and Procedure
See the Evaluation sheet for details.
Q1) Inductor Design
In this assignment you are required to design and analyze an inductor wrapped around a toroidal core. You are free to choose any type of material, but at least find a decent manufacturer, so you have a detailed data-sheet of the toroid core.
Choose a number of turns, and current so that the core operates in the linear region, but just close to saturation with DC excitation. Again you are free to choose any combinations, but choose reasonable values. Do NOT copy from each other.
Part A - Analytical Calculations
1- Calculate the inductance of the coil assuming the flux is homogeneously distributed, and there is no leakage flux, and the core is linear (i.e. constant permeability).
2- Calculate the inductance when the flux is NOT homogeneously distributed, and there is no leakage flux, and the core is linear.(Hint: You can divide the core in discretized cylindrical sections)
3- Repeat parts 1 and 2 by assuming the core is non-linear and the DC current is increased by 50%.
Now assume you opened a 2mm air-gap in the toroid as shown below:
4- Repeat part 1 by assuming there is NO fringing flux.
5- Repeat part 1, but this time propose a method to estimate the effect of the fringing flux and calculate the inductance.
Part B - Finite Element Analysis
In this part you will repeat the calculations you did in part A using a FEA software.
Here are a few suggestions:
You can use any software you want, please have a look at the course page
If you haven't used any FEA software before, I advise you to start with FEMM, which is free and a simple program. If you are planning to use FEA simulations in your professional life, then it makes sense to learn a more capable program (e.g. Maxwell)
2D simulations will be enough for assignments in this course, but if you feel comfortable you can proceed with 3D simulations (but you have been warned).
You can approximate the coils by solid copper regions (i.e. you don't have to model each number of turns), but if you want you can model each coil as a bonus.
There are a few expert users in the class, if you feel stuck, please ask for help. The solution is usually very simple.
1- Analyze to core in magneto-static (DC current, steady-state) using linear magnetic magnetic properties (i.e constant permeability). Show the flux density distribution in the core. Don't forget to include air-region around the core.
2- Calculate total inductance, and leakage inductance (you can use the magnetic energy stored in the core and in the air region to estimate these values).
3- Repeat parts 1 and 2 with non-linear material properties.
4- Now, with non-linear material properties, include the airgap and show the effect of the fringing flux, and also calculate the inductance for this geometry.
Part C- Discussion
In this part, compare all the analytical and FEA inductance calculations in a table and discuss the differences.
Also discuss the differences between 2D and 3D FEA simulations (you don't have to make 3D simulations, just discuss which effects are ignored in 2D simulations).
Q2) Transformer Design
In this question you are going to repeat the analytical transformer design you did in the class. The specs are:
- 500 kVA, Single Phase
- 34.5kV/25 kV
- 50 Hz
- Ambient Temp: -30C-50C
However this time, you are required to do a more detailed analysis regarding the material, core geometry, number of turns, equivalent circuit parameters etc.
I want you to come with an optimum design, but also discuss the effect of a few design parameters (i.e. different lamination types, varying number of turns etc.)
Please present all relevant parameters of your design, values of the equivalent circuit parameters, cost, efficiency etc.