Modern projector headlights require an inverter and transformer because the bulbs run off of an A/C 70 volt system. So just because the bulbs have two prongs they do not necessarily work on a 12 volt DC system. These cars are often the target of head light thefts as they cost $2,600 to replace them and your insurance company will only do it once: telling you to park your car some place besides where thieves can find it.
Any halogen or other resistance bulb relies upon high amperage (30 amps per set of bulbs which is why there is usually only two elements lit at a time), and a steady 13.6 volt power supply which a stock SI-10 alternator (what came stock in your car) can not provide. You need to change out your alternator to a newer "one wire" CS alternator (it bolts on after you change the serpentine belt pulley over to a V-belt pulley). That way you get the full rated 105 AMPS of power of the alternator at just above idle unlike the SI which only provided full rated power above 3,600 RPM (which was infrequent at best).
The SI alternator was nothing more than an on board battery charger. All power had to come from the battery and if you added a lot of accessories the alternator frequently could not keep up, so voltage dropped and your lights dimmed. Keep in mind at full power the alternator out put enough power to run the lights and the ignition, but not the lights, ignition, and windshield wipers (or the lights, ignition, windshield wipers, and the defroster blower motor). So in a way Ralph was right, many Chevys were unsafe at any speed.