Well, the airport here does have it's own power station. Don't know what it can supply but it's something for an emergency and you power up the essentials, not everything, in emergencies.
It never fails, when there is a major problem at airports, on roads, railroads etc., the contingency planners, emergency teams, back-up protocols all fail miserably. In fact that is the one thing that can be counted on. It seems that every emergency is like it's the first emergency in history for the amount of competency that is demonstrated in handling the situation. Every single time the main complaint is that the customers were not told anything and staff disappeared. Every single time.