Yes, BoPi can control a variable speed pool pump if its control box (VFD) has inputs avaliable to control the pump’s operation and speed. As BoPi only has 4 avaliable relays, it will limit the number of things that can be controlled by BoPi but with 2 relays, the pump can be turned on and off and control one speed beyond the default one that can be permanently enabled if the pump is on.
Such wiring will give you 2 speeds and the ability to turn it off while still allowing BoPi to control the pool lights and either a heat pump or electrolysis if needed.
