We once had one of those servo controlled variac systems. Three phase, three variacs, all on a common vertical shaft. Each variac was large, about 50cm diameter. The whole system was in a six foot tall, 19-inch rack. I seem to recall it was rated at 15 amps per phase, but that's a vague memory. It was a monster.
These days UPS systems seem to be default solution. In spite of the fact that they're a pain and seem to fail almost as often as the power.