A320 Captain reported during single-engine taxi with inoperative APU; the generator failed resulting in loss of cabin lighting and nosewheel steering. Aircraft was towed to the gate.

Narrative

We landed in ZZZ and were taxing to the gate when we were advised by ops that it would be a 30-40 min wait for a gate. We coordinated with ground and parked on a taxi way. Our APU was MEL'D; and we were in a SETWA (Single-Engine Taxi Without APU) aircraft. We shut down engine 2. I told passengers that we will be waiting 30-40 min for a gate; but never stated it was ok to get out of their seats; and I did not turn the seat belt sign off. After 5 min we were informed by ops that a gate opened and we could proceed in. Within moments of receiving the info from ops; the FA called and told me people were out of their seats. I told the FA that we just got a gate; and I would make an announcement. I then made the announcement that we had a gate open for us and we would be proceeding to the gate; and to remain seated. After a few minutes of coordinating with ground and ramp; we started taxing to the gate. Within seconds of starting to taxi our only generator failed; and all the displays went dark in the flight deck including our ECAMs. I also heard engine 1 spool up. I stopped the aircraft rather quickly. I then heard screams from the cabin; which I assumed the lights turning off in the back frightened passengers. I made a 'remain seated announcement and we were dealing with a mechanical issue.' We had no engine gauge instrumentation so I could not tell the status of engine 1. But we had no APU to get another generator online. We told ground control and they asked if we would like a tow in; and I said yes. We consulted the QRH and found a procedure to reset gen 1; we did that and gen 1 came online. But we had no nose wheel steering. We thought the safer option would be to get towed into the gate still; and we were worried the generator would fail again if we tried to crossbleed start engine 2. My assumption was right and the generator failed again while waiting for the tow in. Also the FA called me and told me we would need medics at the gate as one of the passengers was still up when we restarted our taxi to the gate. They fell and hit their head in the fwd galley during the abrupt stop. We called ops to get medics at the gate. Once we were hooked up to a tug; I told the passengers that we would be shutting down engine 1 and we would be towed into the gate. Once hooked up to the tug; I told the ground crew that I could lose them when I shut down engine 1; and to chock-us when they get to the gate and use hand signals. I shut down engine 1; and we were towed to the gate.