It sounds like you have a situation similair to mine. I also have a zero-lot-line house (5ft between houses). I got HOA approval to put pool equipment on the side of the house (like EVERY other pool in the neighborhood). Then the pool company sees my survey and says "sorry that's an easment on the side of the house - no permenant structures - we cannot submit this for permitting - we are calling the city". Then come to find out - they state that I have to put it at the end of my lot - but the HOA won't allow it.

I call the city - the place that okay's permits doesn't look at whether equipment is on an easment - so they will permit it even though it violates local zoning codes (that's how the 25 other pools got away with it).

Anyway - you may have a zoning regulation stating you cannot place the equipment on the side of the house - the HOA cannot force you to violate zoning laws - call the city & the county that governs your area to confirm.