Systems and methods for anisotropic vector hysteresis analysis

1. A method for analyzing magnetic hysteresis of an anisotropic magnetic material implemented by one or more data processors, the method comprising:

determining, by at least one data processor, a plurality of magnetic hysteresis loops associated with a local coordinate of a coordinate system based on a magnetic field successively applied to each principal axis of the anisotropic magnetic material;

determining, by at least one data processor, a relaxation factor associated with convergence behavior of a plurality of estimated solution points;

generating, by at least one data processor, a plurality of target points on the plurality of magnetic hysteresis loops by applying a first correction and the relaxation factor, wherein the first correction is a flux density correction or a magnetic field correction, wherein the first correction is applied using a first correction scheme;

determining, by at least one data processor, an error between the plurality of magnetic hysteresis loops and the plurality of estimated solution points;

repeating, by at least one data processor, the generating and determining the error up to a preset number of iterations;

applying, by at least one data processor, wherein the error is greater than an error threshold after the preset number of iterations, a second correction to the plurality of target points on the plurality of magnetic hysteresis loops, wherein the second correction is applied using a second correction scheme different from the first correction scheme; and

determining, by at least one data processor, a second error between the plurality of target points on the plurality of magnetic hysteresis loops with the second correction and the plurality of estimated solution points.

2. The method according to claim 1 , wherein the first correction scheme is an H-correction scheme based on applied field intensity and the second correction scheme is a B-correction scheme based on applied flux density.

3. The method according to claim 1 , further comprising:

repeating, by at least one data processor, the applying and determining until the second error is below the error threshold.

4. The method according to claim 1 , wherein the relaxation factor is an under relaxation factor based on an unstable convergence behavior of the plurality of estimated solution points.

5. The method according to claim 4 , wherein the relaxation factor is an over relaxation factor for stable convergence behaviors of the plurality of estimated solution points.

6. The method according to claim 1 , wherein determining the plurality of magnetic hysteresis loops comprises:

applying an isotropic vector play model to each principal axis of the anisotropic magnetic material based on the magnetic field;

determining a flux density as a function of the magnetic field; or

determining the magnetic field as a function of the flux density; and

determining a permeability tensor and intercept corresponding to the anisotropic magnetic material.

7. The method according to claim 1 , wherein the flux density correction is based on a minimum differential permeability.

8. The method according to claim 1 , wherein the magnetic field correction is based on a maximum differential permeability.

9. The method according to claim 2 , wherein the first correction is the flux density correction and the second correction is the magnetic field correction.

10. The method according to claim 2 , wherein the first correction is the magnetic field correction and the second correction is the flux density correction.

11. The method according to claim 1 , wherein the coordinate system is 2-dimensional or 3-dimensional.

12. The method according to claim 1 , wherein the plurality of magnetic hysteresis loops are determined based on an analysis of a physical examination of an exemplary anistropic magnetic material and wherein a system incorporating the anistropic magnetic material is built or modified based on the analyzing.

13. The method according to claim 1 , wherein the analyzing occurs in a simulation environment.

14. The method according to claim 1 , wherein the plurality of magnetic hysteresis loops are determined based on a physical electrical system being modeled.

15. The method according to claim 1 , further comprising providing, by at least one data processor, the error to a user via a graphical user interface for design modifications to a physical electrical system being modeled.

16. A system for analyzing magnetic hysteresis of a magnetic material, the system comprising:

at least one data processor;

memory storing instructions, which when executed by the at least one data processor, result in operations comprising:

determining a plurality of magnetic hysteresis loops associated with a local coordinate of a coordinate system based on a magnetic field successively applied to each principal axis of the anisotropic magnetic material;

determining a relaxation factor associated with convergence behavior of a plurality of estimated solution points;

generating a plurality of target points on the plurality of magnetic hysteresis loops by applying a first correction and the relaxation factor, wherein the first correction is a flux density correction or a magnetic field correction;

determining an error between the plurality of magnetic hysteresis loops and the plurality of estimated solution points;

repeating the generating and determining the error up to a preset number of iterations;

applying, wherein the error is greater than an error threshold after the preset number of iterations, a second correction to the plurality of target points on the plurality of magnetic hysteresis loops, wherein the second correction is applied using a second correction scheme different from the first correction scheme; and

determining, by at least one data processor, a second error between the plurality of target points on the plurality of magnetic hysteresis loops with the second correction and the plurality of estimated solution points; and

a non-transitory computer-readable storage medium configured to store data related to the plurality of target points and the plurality of estimation of solution points.

17. The system according to claim 16 , wherein the first correction scheme is an H-correction scheme based on applied field intensity and the second correction scheme is a B-correction scheme based on applied flux density.

18. The system according to claim 16 , wherein execution of the memory storing instructions results in operations further comprising:

repeating the applying and determining until the second error is below the error threshold.

19. The system according to claim 16 , wherein the relaxation factor is an under relaxation factor based on an unstable convergence behavior of the plurality of estimated solution points.

20. The system according to claim 19 , wherein the relaxation factor is an over relaxation factor for stable convergence behaviors of the plurality of estimated solution points.

21. The system according to claim 16 , wherein determining the plurality of magnetic hysteresis loops comprises:

applying an isotropic vector play model to each principal axis of the anisotropic magnetic material based on the magnetic field;

determining a flux density as a function of the magnetic field; or

determining the magnetic field as a function of the flux density; and

determining a permeability tensor and intercept corresponding to the anisotropic magnetic material.

22. The system according to claim 16 , wherein the flux density correction is based on a minimum differential permeability.

23. The system according to claim 16 , wherein the magnetic field correction is based on a maximum differential permeability.

24. The system according to claim 17 , wherein the first correction is the flux density correction and the second correction is the magnetic field correction.

25. The system according to claim 17 , wherein the first correction is the magnetic field correction and the second correction is the flux density correction.

26. The system according to claim 16 , wherein the coordinate system is 2-dimensional or 3-dimensional.

27. The system according to claim 16 , wherein the plurality of magnetic hysteresis loops are determined based on an analysis of a physical examination of an exemplary anistropic magnetic material and wherein a system incorporating the anistropic magnetic material is built or modified based on the analyzing.

28. The system according to claim 16 , wherein the analyzing occurs in a simulation environment.

29. The system according to claim 16 , wherein the plurality of magnetic hysteresis loops are determined based on a physical electrical system being modeled.

30. The system according to claim 16 , wherein the operations further comprise providing, by at least one data processor, the error to a user via a graphical user interface for design modifications to a physical electrical system being modeled.

31. A non-transitory computer readable medium containing program instructions which, when executed by at least one data processor, result in operations comprising:

determining a plurality of magnetic hysteresis loops associated with a local coordinate of a coordinate system based on a magnetic field successively applied to each principal axis of the anisotropic magnetic material;

determining a relaxation factor associated with convergence behavior of a plurality of estimated solution points;

generating a plurality of target points on the plurality of magnetic hysteresis loops by applying a first correction and the relaxation factor, wherein the first correction is a flux density correction or a magnetic field correction;

determining an error between the plurality of magnetic hysteresis loops and the plurality of estimated solution points;

repeating the generating and determining the error up to a preset number of iterations;

applying, wherein the error is greater than an error threshold after the preset number of iterations, a second correction to the plurality of target points on the plurality of magnetic hysteresis loops, wherein the second correction is applied using a second correction scheme different from the first correction scheme; and

determining a second error between the plurality of target points on the plurality of magnetic hysteresis loops with second correction and the plurality of estimated solution points.

32. The non-transitory computer readable medium according to claim 31 , wherein the first correction scheme is an H-correction scheme based on applied field intensity and the second correction scheme is a B-correction scheme based on applied flux density.

33. The non-transitory computer readable medium according to claim 31 , wherein execution of the computer instructions results in operations further comprising:

repeating the applying and determining until the second error is below the error threshold.

34. The non-transitory computer readable medium according to claim 32 , wherein the relaxation factor is an under relaxation factor based on an unstable convergence behavior of the plurality of estimated solution points.

35. The non-transitory computer readable medium according to claim 34 , wherein the relaxation factor is an over relaxation factor for stable convergence behaviors of the plurality of estimated solution points.

36. The non-transitory computer readable medium according to claim 31 , wherein determining the plurality of magnetic hysteresis loops comprises:

applying an isotropic vector play model to each principal axis of the anisotropic magnetic material based on the magnetic field;

determining a flux density as a function of the magnetic field; or

determining the magnetic field as a function of the flux density; and

determining a permeability tensor and intercept corresponding to the anisotropic magnetic material.

37. The non-transitory computer readable medium according to claim 31 , wherein the flux density correction is based on a minimum differential permeability.

38. The non-transitory computer readable medium according to claim 31 , wherein the magnetic field correction is based on a maximum differential permeability.

39. The non-transitory computer readable medium according to claim 32 , wherein the first correction is the flux density correction and the second correction is the magnetic field correction.

40. The non-transitory computer readable medium according to claim 32 , wherein the first correction is the magnetic field correction and the second correction is the flux density correction.

41. The non-transitory computer readable medium according to claim 31 , wherein the coordinate system is 2-dimensional or 3-dimensional.

42. The non-transitory computer readable medium according to claim 31 , wherein the plurality of magnetic hysteresis loops are determined based on an analysis of a physical examination of an exemplary anistropic magnetic material and wherein a system incorporating the anistropic magnetic material is built or modified based on the analyzing.

43. The non-transitory computer readable medium according to claim 31 , wherein the analyzing occurs in a simulation environment.