Customers really want to be dealt with in a way that makes them feel special. You'll find that most customers don't expect you to perform miracles for them. They want only for you to do your very best to get them the services they need, when they want them. When you show that you're doing your very best, often the nasty, festering, BIG problems melt down to just little problems that can be quickly and easily resolved. Understand that you will be getting a lot of complaints and gripes and don't take them personally.
People like to complain, and the utility company is often a good target.
Let them know you sympathize. Take a step to the left and get on their side. Become an ally. Often they won't be able to tell you, or they'll ask for less than you expected. Just be blunt about it.