Customers in the Tekapo and Albury areas are affected after two of the lines company's conductors were severed yesterday.
The pilot was safe and no one else was reported injured.
Transpower estimated power would be restored this afternoon.
Its executive general manager of grid delivery, Mark Ryall, told RNZ's Morning Report programme today the helicopter pilot was very lucky.
He took out two conductors - one with the rotor and one with beam of the helicopter.
"He's managed to land safely in an emergency landing, so he's very lucky," Ryall said.
It was an unusual, but not unheard of, accident with five or six incidents involving helicopters or aircraft in the last 20 years, he said.
Crews worked on restoring the lines until dark yesterday and were due to resume at first light today. The goal remained to restore power by late this afternoon.
"If they can do it any quicker they will," Ryall said.
Things had gone smoothly so far and crews were working hard, he said.
"We feel for consumers."
Compensation was only available under the Consumer Guarantees Act or their business insurance, Ryall said.
'Lesson in resilience'
Tekapo community board chair and local real estate agent Steve Howes told Morning Report there were a number of Chinese and Japanese visitors staying in town during national holidays in their countries.
They were struggling to understand what was going on, he said.
"It's really the management of guest management, they just don't understand how a small town can be without power."
The outage was also causing "really massive issues" for businesses in town, particularly restaurants and hospitality, he said.
Kerr himself was powering his house from his electric vehicle and said he had been driving round to help others.
He acknowledged such outages were not common and the cause was unexpected, but it was "a lesson in resilience," he said.
Alpine Energy chief customer and strategy officer Andrew Kerr told Morning Report about 1750 households in Tekapo were without power.
Workers had managed to reconfigure the network to get most people restored in the Fairlie area yesterday.
Although people were being asked to conserve power there so as many households as possible could be kept on, he said.
"We're working with Transpower... essentially we're waiting for them to fix the lines (that were) affected by the helicopter."
The system serving Tekapo was separate and "most people in Tekapo will be without power".
Generators were being used to supply some public services, such as the fire station, public toilets and community centre, he said.
The community centre would be open today for anyone need to charge their phone or get a cup of tea.
