Under the plans, Distribution Network Operators (DNOs) would have to increase payments to £70 if they fail to meet the minimum levels of service during severe weather.
The cap for payments would increase from the current £216 to £700, and payments would be made automatically wherever possible.
The regulator also wants the claims process by which customers receive payment to be simplified.
Ofgem said the proposed changes, which follow increased payments for customers cut off during normal weather conditions, would strengthen incentives for companies to act quickly and reconnect customers as soon as possible.
Ofgem's senior partner for distribution, Hannah Nixon said: "Many parts of Britain have seen some extreme weather conditions over the last few months and Ofgem has been proactively looking at ways to help consumers who face disruption to their energy supply in these situations.
"Increasing the financial payments would send a strong message to the network companies that they need to do all that they can to reconnect all customers as fast as possible."