What is the optimal software package (free software is recommended) to design the ferrite core inductors, which can be used in the power converters, especially for the highly frequency operation?
To my knowlhege there is no such universal Software. However, there are diverse Excel spreadsheets. Also some manufactures have their own tools.
However i ususally do the Design by the air gap Design Software for frequescies blow 500kHz. We are doing transformers for 2.5Mhz in the kW range, there i would use the well know Al. Method.
I would like to second Michael that the design of ferrite cored inductors is semieprical where one one uses a mixed appraoch of analysis and experminets. The companies producing coils and transformers have their own design packages.
However there is is also computer aided design tools that you can yourself apply them and verify how far they are accurate. There is for example SDT from EPCOS:https://www.electronicproducts.com/Software/Development_Tools_and_Software/Free_software_aids_ferrite_magnetic_design.aspx
I would also advice you to use the design formulas and procedure in the link: https://coefs.uncc.edu/mnoras/files/2013/03/Transformer-and-Inductor-Design-Handbook_Chapter_10.pdf