This looks like a question in Harmonic Analysis but I have no idea where you're starting. Can you give more details. D. Booth

Dear Hamed, It may be better to ask clearly, weather you are studding continuity and existence and uniqueness of some harmonic equations., any way I would suggest to read through the following links for initial concepts about some monophonic analysis of order/generation first and second : https://en.wikipedia.org/wiki/Second-harmonic_generation

A good Functional Analysis Book cover this topic for mathematicians, for Engineers and applied scientists there is series of books here, https://books.google.com.au/books/about/Harmonic_Analysis_for_Engineers_and_Appl.html?id=EO1lDAAAQBAJ&redir_esc=y

David Eugene Booth

Thank you for your attention.

I have an algorithm that uses the second harmonic of current to detect fault during power swing. The simulation results in Matlab Simulink confirm this.

But in addition to the simulation results I need to prove this idea mathematically.

Muhammad Ali

Thanks a lot.

My field of work is power systems on this question. Thank you for helping me with this.

Some of the answers and references here may be helpful. Beat, D. Booth

https://www.researchgate.net/post/In_most_of_the_systems_we_eliminate_even_order_harmonics_saying_that_their_effect_is_negligible_How_can_this_be_physically_interpreted

David Eugene Booth

Thank you so much for sending the link

But I need to prove the existence of the second harmonic in the transient of fault by the formula.

Yes. Did you at the links and articles provided at my other link? I thought some of them might be helpful. Best, David BTW I have no experience at this beyond advanced Calculus. I apologize.