under normal conditions
A formal, written expression used to state that something holds true or is done under ordinary circumstances.
Under normal conditions, this machine operates without problems.
通常 is a noun/adverb meaning 'usual' or 'normally'; 通常条件下で is a set phrase meaning 'under normal conditions'.
条件下 means 'under conditions of'; it is a compound used in formal contexts, often preceded by a modifier.
Compound of 通常 (normal) + 条件 (conditions) + 下 (under) + で (particle). A straightforward formal phrase.