Turning on any high-power device trips my RCD
Somewhere in your electrical system you have leakage between neutral and ground.  

All neutrals are connectd without fusing, so the very small voltage on neutral reaches all points in the neutral system. Current follows all paths in proportion to their conductivity (1/resistance) - the regular wired neutral is the dominant path, but some small amount of current uses the leakage between neutral and earth, and when your load is high, that current exceeds 30ma and SNAP!