Is there a word for wanting, or craving, power

Thirst for power is an idiomatic expression that is often used to convey the idea.

Usages:

Thirst for power is also a book by Leon Trotsky

Hitler's Thirst For Power Essay Examples

From Invisible Power:

• Pigott was described as "an iron-fisted decision-maker who cannot satisfy a thirst for power."The NCC chief reacted like a bemused parent, retorting that Ottawa is not a playground merely for the residents, ......

You may use powermad. Here's an example from The Empowered Leader by C Miller:

I suspect that most powermad leaders never define themselves that way. Their erosion to the abusive use of power was so gradual that they may not have seen it.

and one from a biography of Theodore Roosevelt by L L Gould:

To a significant portion of his party, moreover, [Theodore] Roosevelt seemed a powermad radical lusting for a return to the highest office in the land.

megalomaniac

Obsession with the exercise of power.

If you describe someone as a megalomaniac, you are criticizing them because they enjoy being powerful, or because they believe that they are more powerful or important than they really are.

You can describe someone as being power-hungry:

adjective: Having a strong desire for power.

‘the power-hungry and evil dictator’

^{Oxford dictionaries}

If you want a noun, change Marcello's suggestion into ' megalomania'

David McLelland, an American psychologist, studied human needs and motivations. One human need he identified was the need for power, which he abbreviated nPow.

McClelland defines nPow as a desire for power either to control other people (for [one's] own goals) or to achieve higher goals (for the greater good), and describes people high in this trait as seeking neither recognition nor approval from others, but only agreement and compliance. Prsons with a high nPow score are likely to seek power over others.

So someone who desires power can be said to have a high nPow score.