Ndtyhij

I haven't really seen an answer yet so I'll take a crack at it. There is no answer directly in any episode or movie. Several people have mentioned the following quote from the movie Insurrection

<ARTIM> Don't you ever get tired?

<DATA> My power cells continually re-charge themselves.

The original question was, "How is data powered?" then a further explanation of the question, "What powers Data from Star Trek The Next Generation? Did he generate his own internal power or did he have to plug into the Enterprise periodically to recharge? Or perhaps a combination of the two?"

The second part or explanation is sort of answered above and in some other answers. What powers him are power cells. Based on the quote from the movie they recharge themselves.

However nobody fully answered the broad and more interesting question of how data is powered. I wanted to ask this question myself, but it would have been deemed a duplicate question by the overseers of the site.

I would like to posit, that when we view sci fi or Star Trek we accept that whatever is true in our universe is true in the Star Trek Universe as well unless there is a conflict. So what we call a chair, in the STU is also a chair. If we use a term scientific or otherwise it holds true that it has the same meaning in the STU. There are some conflicts since the STU is more technologically and scientifically advanced than us so of course there would be new discoveries that might conflict with our own understanding of physics, chemistry, etc.

In this case there is no STU explanation for what is powering data. What is a power cell? How does it work? How does it recharge itself? Some others above gave answers that tried to deal with some of these issues.

Since there's no conflicting science and no direct answer ever given, my answer is that it's either fission or fusion. I would doubt that it's fission since the amount of nuclear waste that's created would have to be dealt with and one would think that it would have surfaced in an episode somewhere. So based on current physics, and that the STU gives no answer or any conflicting theory, that it's fusion. This would give data an almost unlimited power supply in a small area with relatively little nuclear waste material to deal with.

Data does mention in Deja Q that he drinks an organic compound that is "good for me." He further explains that it does lubricate his systems. So data does need or can benefit at least from some forms of maintenance. Something like minor waste disposal, for lack of a better term "android excrement" would be something I would not expect to necessarily be dealt with in an episode.

The only other possible source in Universe that I can think of would be some sort of anti-matter generator, antimatter fuel cell, or whatever you want to call it. Again, I'm not sure how that would work since we don't have technology like that. But we do know in universe that at least the federation does need dilithium or other crystals and that they have to be maintained in some way or replaced from time to time. If it's something that simply keeps going on in perpetuity or at least for a really long time without complication, it has to be fusion.