First things first. The kilowatt-hour (kWh) is not a unit of power. It is a unit of energy. Here's why:
The kW is a unit of power. It is 1000 W or 1000 J/s.
Rearranging this we get energy = power × time
If we choose to measure power in kW and time in hours, we have:
energy (kWh) = power (kW) × time (h)