First of, your understanding of a Side Channel Attack is wrong: Generally attackers already know what algorithms are running on hardware, it's mentioned in the datasheet of the chip or product. SCAs are meant to extract pre-encoding data by exploiting an implementation specific data-dependency feature.
There's quite a lot of literature regarding SCA protection and more specifically protection against power profiling. The most effective accepted solution generally comes down to making sure that each bitflip is compensated by a closely positioned bitflip in the opposite direction.
It's not 100% foolproof, but it's as close as we get today (unless some company somewhere solved it better and didn't publish yet, although I'd be skeptical of unpublished cryptographic insurance).
Issues with your solution
Why your solution won't work: You're basically inserting predictable and even known noise. Since you should assume that the attacker knows your exact implementation, it'd be trivial to filter out your inserted power frequency and just continue on as if you'd never put in the protection.
Issues with any self-designed solution
Schneier's Law, let me repeat that, with feeling: Schneier's Law
If this is for an actual product, drop this idea and consult an expert.
If this is for a hobby project or school assignment, do go on, have some fun daydreaming, but keep the problems in mind.