I am an electrical engineering undergraduate student and entering my final year of study. I plan on applying to doctoral programs in the field of power engineering. Specific advice from the field would be appreciated, but I welcome professors and students from other backgrounds to comment.
I say power engineering because I'm interested in studying problems related to the electrical grid. However, there are a lot of problems out there: multi-agent systems, smart grid technologies, distributed grid technologies, power electronics, and many, many more. It's such an overwhelming list that I don't know how to choose, or even how to educate myself enough to make a choice. I'm sure other fields have this problem of "too many subjects, too little time".
I know in a general sense that I want to enter this field and do research in it, and that I would enjoy the challenge of a PhD program. At this point, though, I don't know which specific aspect I want to study.
My questions are these: how much should I know before applying to a program? Upon entrance to a doctoral program, how much time do I have to pick a certain area of research? I've heard of students being co-advised by more than one professor; does this mean my study can be somewhat multifaceted?
Edit: Answers specific to doctoral study in the United States would be appreciated.