2 Answers
From this page: https://azure.microsoft.com/en-ca/global-infrastructure/availability-zones/, official documentation says "Availability Zones are tolerant to data centre failures through redundancy and logical isolation of services." Therefore I believe that the DCs within an AZ are independent and will have separate power, network and other systems. The reason for this is to ensure that services are still available if one or more DCs go down.
Each Availability Zone is designed to be fault isolated from each other, so each AZ would have independent power. Multiple data centres within a single AZ may share power, but in practice, they would still be kept as separate as possible, as part of good engineering design.
So whilst a localized power outage may impact multiple data centres within an AZ, it may not necessarily affect the entire AZ.
I would imagine that within an AZ (likely in a lot of locations) there could be only a single power company available and each datacenter has its own power circuit but the same supplier and that Azure would use different suppliers between AZ within a region.