Date: 202008
Local time of day: 0001-0600
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Night
Aircraft: B767-200
Operator: Air Carrier
Operating under: Part 121
Mission: Cargo / Freight / Delivery
Flight phase: Taxi
Aircraft component: APU
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Confusion; Communication Breakdown; Workload; Time Pressure
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Loss Of Aircraft Control
Detector: Person Flight Crew
When detected: Taxi
Result: Flight Crew Regained Aircraft Control; Flight Crew Took Evasive Action; General Flight Cancelled / Delayed
Contributing factors: Aircraft; Procedure; Human Factors
Primary problem: Human Factors

Narrative: Landed in ZZZ. FO (First Officer) started APU for tow-in; it shut down. I started it; being careful not to let the start switch spring back to Run. It ran fine but we advised Maintenance of a possible problem. Went to the hotel for the four-hour layover. Returning to the aircraft; Maintenance said the APU had shut down on them and they deferred it. This aircraft had APU problems in the past. The plan was to tow the aircraft under battery power only and have the huffer and ground power waiting on Taxiway XX. Starting an engine in the blocks was not an option because of construction on Taxiway XY. We did the Before Start Checklist before ground power was disconnected. I did not request the Engine Start Checklist because there was no point in turning on the fuel and hydraulic pumps if we were on battery power only. We were pushed back and then we were asked to set brakes so the tug could reposition to pull the aircraft instead of push it. Setting the brakes at this point may have depleted the hydraulic pressure in the brake system. The brake pressure gauge was unpowered and reading zero. We were towed from Taxiway XY to Taxiway XX. I closed my window as I could see the huffer on my side of the aircraft and knew it would get noisy during the start. The FO still had his window open for ventilation. Once stopped at the designated spot; I was asked to set the parking brake. External power had not been connected yet and the brake pressure gauge was still unpowered. I set the brake and responded 'brakes set.' I did not give permission to disconnect the tow bar. External power came on and the cockpit flood lights came on. The taxiway is not illuminated and the cockpits lights reflecting off my closed window made it difficult for me to see outside. The FO's window was open and he noticed a separation developing between the aircraft and the ground power cart on his side and also the tug. He called out that we were rolling about the same time Ground called out a warning. He stomped on the brakes and I followed but there was no effect. He called out to put on the hydraulic pumps as I was reaching for them. The ground power cord stayed connected for just a few seconds but it was enough to power the hydraulic pumps and get the aircraft stopped. Taxiway XX is steeply sloped for a taxiway and it didn't take long for the aircraft to get moving. If external power had not come on for those few seconds; we would have rolled a long way backward with no nosewheel steering; no brakes; and quickly moving.The ground power cord had pulled free from the aircraft as well as the pneumatic connections. I kept a steady pressure on the brake pedals while Ground sorted things out. I don't know if they had any chocks available. The FO volunteered to take over the brakes for me. I said I could set the parking brake but after discussion decided not to and I released the parking brake without ever having taken pressure off the pedals. Maintenance said [another Company] had to tow this aircraft a couple of days ago with the same situation. I asked why this didn't happen to that aircraft. They said the tow bar had not been disconnected before ground power was plugged in. The chain of events leading up to this started with a deferred APU; not being able to start an engine in the blocks; having to set the parking brake so the tug could turn around; parking on a steep slope; and disconnecting the tow bar too soon and without permission. Looking back; I wish I had foreseen this possibility and told Ground not to disconnect the tow bar yet and had not said; 'Parking brake set.'


Second narrative: Report narrative contained no additional information.


Synopsis: B767 Flight Crew reported that an inoperative APU and lack of electrical power for hydraulic pumps along with improper ground handling procedures resulted in the aircraft rolling down a taxiway.