FDM simulation of an electrical transformer?

In summary, the conversation discusses the goal of programming a FDM simulation of a transformer and the challenges that arise when trying to simulate a model using SPICE. The model produces the right differential equations but it becomes problematic when trying to solve for i1' and i2' due to the perfect coupling. Additionally, the output signal is affected by the ratio between L1 and L2, leading to unexpected results. The conversation suggests that FDM may not be the best method for simulating transformers due to truncation error and recommends adding internal resistance to mitigate its effects.
  • #1
Will Flannery
114
34
My goal is to program a FDM simulation of a transformer. So, we have the coupled inductor model to start with ...
SIsGV.jpg


However, if L1 = 1, L2 = 9, and coupling is perfect then M = sqrt(1*9) = 3 and L1 - M = -2.

So, this seems problematical to me. Also, if I try to simulate this model using SPICE, just for fun you understand, my goal is to program the sim myself, SPICE chokes on the negative inductor value and no output signal is generated.

I note that the model above does produce the right differential equations, that is, v1 = L1*i1' + M*i2' v2 = L2*i2' + M*i1'

However, if you try to simulate these differential equations directly, and the coupling is perfect, the the ratio L1 / M = M / L2 = sqrt(L1) / sqrt(L2) and you cannot solve them for i1' and i2'. So, I'm stuck starting with these differential equations too.

One more thing - running the SPICE transformer model, i.e. specifying L1 = 1, L2 = 9, and k = 1, with a 1 v. 60 Hz input produces the expected 3 v. output. However, changing k to .9 reduces the output to a few mv. Even .99 and its still a few mv. That seems very peculiar to me (I'm not an EE).
 
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  • #2
This is not the kind of thing you want to simulate with FDM. The main drawback of FDM is the truncation error you get in the derivatives. Transformers are super-sensitive to the derivative of the currents. Where's the input coming from? If you really want to do FDM, you should add some internal resistance to mitigate the effects of truncation error.
 

1. What is FDM simulation and how does it apply to electrical transformers?

FDM (Finite Difference Method) simulation is a computational technique used to approximate solutions to partial differential equations. In the case of electrical transformers, FDM simulation is used to model the behavior of electric and magnetic fields within the transformer, allowing for analysis and optimization of its design and performance.

2. How does FDM simulation differ from other simulation methods, such as FEM or BEM?

FDM simulation discretizes the domain into small cells and approximates the derivatives of the field variables at each cell, while FEM (Finite Element Method) and BEM (Boundary Element Method) use different mathematical approaches to discretize the domain. FDM is typically used for complex geometries and dynamic problems, while FEM and BEM are better suited for simpler geometries and static problems.

3. What are the key factors to consider when setting up an FDM simulation for an electrical transformer?

The key factors to consider include the material properties and geometry of the transformer, the boundary conditions, and the desired accuracy and computational resources. Properly defining these parameters is crucial for obtaining accurate results and optimizing the simulation process.

4. What are some common challenges faced when using FDM simulation for electrical transformers?

Some common challenges include accurately modeling the non-linear behavior of materials, dealing with high-frequency effects, and managing the large computational resources required for complex geometries and dynamic simulations. It is also important to validate the simulation results with experimental data to ensure accuracy.

5. How can FDM simulation of electrical transformers contribute to the development of new technologies?

FDM simulation allows for detailed analysis and optimization of transformer designs, leading to improved efficiency, reliability, and performance. It also enables the exploration of new materials and geometries, paving the way for the development of innovative transformer technologies. Additionally, FDM simulation can reduce the time and cost of physical prototyping, accelerating the development process.

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