If X is a stand-in for an actual, named algorithm, then X Algorithm is usually the correct construction. For example:
The A* algorithm
The DFS shortest path algorithm
The wikipedia page you cite isn't using "Algorithm A" to mean the same thing as "A* algorithm." It's using "Algorithm A" as shorthand for "Any algorithm, which we will ...
'Often' is an adverb, and while a few say adverbs should go before the verb, the order doesn't usually matter.
Or, the order doesn't matter, usually.
Or even, the order usually doesn't matter!
There are three common positions for adverbs in a sentence:
before the subject
between the subject and the verb, or immediately after 'be' as a main verb
This is not a good idiom to use. It's incorrect diction here and hard to understand.
Instead, use "for the purpose of":
The purpose of the component would not be to store electricity until needed for the purpose of energy recovery.
Additionally, in technical writing, it is better to say what the purpose /is/, rather than what it is /not/, or to clearly ...
Have had is the past perfect form of had.
The English past perfect tense is complicated to explain, but a simple heuristic that applies here can be used.
If you are going to say We've X Y, where Y is one of these words/phrases or something similar:
before, previously, recently, "that I can remember", "since X", "until X"
you use past perfect. You ...