How can I increase my base power without increasing my consumption more than production?

Upgrade buildings and do research. Your power usage may increase a little but the food / fuel consumption won't. As you do this you will be able to increase your food / fuel production as well. Some heroes (if you are lucky enough to get them) also help with the production.

Eventually you will be able to get good rewards from events that let you store a lot of resource items and your production will be far less important.