Electric energy is sold by the kilowatt hour (kWh). A kilowatt is a unit of power. A kilowatt hour is a unit of energy. It's the sum of power consumption over a given period in hours.
As in example, saying a motor consumes 100 kW and runs for 20 hours or 2000 kWh
A kilowatt per hour (kW/h) I think it gives the average power.
For the same above example it would be 5 kW/h.
What do you think?