The upstream side is drilling and gathering oil and natural gas. Motors up to 1500 or more HP are used to drill the wells. Lots of smaller motors and actuators are used thoughout. Pumps and compressors (pumps for natural gas) are generally driven by electric motors. Valves can be electrically actuated, either by motors or for smaller valves, solenoids. Lots of heaters.
Refineries also have lots of pumps, valves, heaters. Also, transformers/switchgear, especially at refineries, which use a lot of power.
Downstream side, after the refineries, lots of pumps (or compressors), valves, motors. Once you get to the retail level these are small and computer controlled.
Impossible to say one type or a few types of power electronics are used, because the industry is so vast it uses almost everything available. From 40 year old contactors and starter relays, to the latest in solid state DCS's.