Question

What are the applications of power series in electrical engineering?

Answer 1

Many applications in ac circuits, but probably in other areas as well.

Explanation:

Many ac voltage waveforms are not perfect sinusoidal waves so we may use the Fourier series theory to approximate them very accurately as an infinite sum of sine and cosine waveforms.
This makes electrical calculations much easier than with non-sinusoidal waveforms.

Recall that any periodic function (voltage or otherwise) of period `T=2L` , which is piecewise continuous over the interval `(-L;L)`may be written in an infinite Fourier series as follows :

`f(x)= a_0/2+sum_(n=1)^oo a_ncos((npix)/L)+b_nsin((npix))/L`,

where `a_0=1/Lint_-L^Lf(x)dx`
`a_n=1/Lint_-L^Lf(x)cos((npix)/L)dx`
`b_n=1/Lint_-L^Lf(x)sin((npix)/l)dx`

And then offcourse, if the interval is more complicated, one may use variations of these formulae to accommodate it etc.