The actual instantaneous amount of energy being consumed by the machine is measured in Joules. And that's what the electric company charges you for: energy, not power.
Now, 1 Watt is equal to an energy consumption (or production) of 1 Joule per second. So if your machine consumes 1 Joule of energy every second, and you run it for 1 minute, the electric company will bill you for 60 Joules. Of course as with some other measurements (like Farads) the basic unit is often hopelessly impractical for everyday use. Billing you for Joules would require very wide paper for the big numbers you would need. So the convention was adopted many years ago of expressing energy as power x time. After all, the definition of power is energy / time. So rather than talk about so many Joules, we use kiloWattHours to scale the measurement up to something useful. In other words 1 kWh is 3,600,000 Joules. So your machine, rated at a power of 2.7kW consumes 2700 Joules every second (alright assuming 100% efficiency!) After 1 hour you've consumed 3600 x 2700 Joules and will be billed for them, or as you would recognise it, 2.7kWh. If your machine was only on for 30 minutes you get billed for 1800 x 2700 Joules or 1.35kWh. It doesn't mean your machine has lost power (the 2700 factor is the same), it means it was on for a shorter period of time.
Regards
Ken