Is there a word for wanting, or craving, power

The title is self-explanatory. Is there a word for the desire to have power, or should I just use the phrase?

You can describe someone as being power-hungry:

adjective: Having a strong desire for power.

‘the power-hungry and evil dictator’

^{Oxford dictionaries}

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 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.