12 Questions
What type of conditions are applied to a conducting plate excited on both sides by the same magnetic field intensity H?
Neumann conditions
In which type of cases can eddy current losses be calculated using the formula H^2 / (2 * sigma * delta)?
Semi-infinite cases for thick conductors
What does the imaginary part of the complex permeability in transformer core joints represent?
Magnetic losses in the material
How are core structures like joints between legs and yokes modeled for frequency response analysis?
By integrating expressions for magnetic field components over the domain
What is considered to be electrically thick in the context of conductors?
Conductors where magnetic field intensity H reduces to 0 before reaching the midpoint
Which type of potential varies with respect to y when analyzing the change in magnetic field intensity inside a conductor?
Magnetic vector potential A
What is the primary factor considered when calculating eddy current losses in a coil?
The alternating magnetic field
For a thin conductor with thickness less than or equal to the skin depth, the eddy current loss per unit volume is calculated using which parameters?
Resistivity, peak flux density, and conductor thickness
How are the losses due to axial and radial fields in a winding treated?
They are calculated separately and then summed up
What assumption is made when using magnetostatic FEM simulation for eddy current loss analysis?
The conductors are electrically thin and eddy currents do not influence the leakage field
How are the FEM results verified in the described approach?
By considering only the axial field and using analytical formulas
What is the primary advantage of using finite element analysis (FEM) for eddy current loss calculations?
FEM is independent of geometrical complications
Study Notes
- Lecture 29 discusses the application of non-homogenous Neumann conditions, specifically focusing on eddy current losses in power transformer windings using FE analysis.
- Neumann conditions are applied to a conducting plate excited on both sides by the same magnetic field intensity H, commonly found in rotating machines or transformers.
- By analyzing the change in magnetic field intensity H from the surface to inside the conductor, one can observe variations in the magnetic vector potential A with respect to y.
- For thick conductors (electrically thick), the magnetic field intensity H reduces to 0 before reaching the midpoint, representing semi-infinite cases where eddy current losses can be calculated using H^2 / (2 * sigma * delta).
- Modeling transformer core joints for frequency response analysis involves considering complex permeability due to losses in the magnetic material, with the imaginary part representing losses.
- Complex permeability is calculated for core structures like joints between legs and yokes by imposing boundary conditions for the x component of the magnetic field Hx.
- The calculation involves integrating expressions for Hx and Hy over the domain, with contributions from boundary edges canceling out for accurate analysis.
- Eddy current losses in a coil, such as a high voltage winding of a power transformer, are calculated by considering the alternating magnetic field, leakage field direction, and conductor geometry.- Eddy current loss formula is discussed for a thin conductor of thickness t less than or equal to skin depth, excited by B0 on both sides.
- Eddy current loss per unit volume is calculated using resistivity (rho), peak flux density (B0), and conductor thickness (t).
- Losses due to axial and radial fields are calculated separately and then summed up for the entire winding.
- Magnetostatic FEM simulation is used to find eddy current losses, assuming conductors are electrically thin and eddy currents do not significantly influence the leakage field.
- Field values are calculated using static FEM simulation and classical eddy current theory for loss analysis.
- Verification of FEM results is done using analytical formulas, considering only the axial field.
- Eddy current loss per unit volume for each conductor is calculated individually and summed up for all conductors in the winding.
- Comparison between analytical and FEM results shows close agreement, validating the FEM analysis procedure.
- Finite element analysis procedures can be validated by simplifying flux distribution, making approximations, and comparing values to gain confidence for solving complex problems.
- FEM provides an advantage of being independent of geometrical complications, making it a valuable numerical technique.
Explore the application of non-homogenous Neumann conditions and FEM analysis to calculate eddy current losses in power transformer windings. Learn about magnetic field intensity, conductor properties, complex permeability, and comparison between analytical and FEM results.
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