Kilowatts kW vs Kilowatt Hours kWh

Being careful and consistent when dealing with kilowatts kW and kilowatt-hours kWh is a basic for all energy professionals. Someone who misuses these shows either a lack of care or a lack of understanding - both of which can be fatal.

Understanding the difference between kilowatts kW and kilowatt-hours kWh is therefore a basic for energy industry professionals. The key to understanding the difference is understanding the how they relate to time.

An analogy with distance and speed can is helpful to grasp the concepts of kW and kWh. We measure distance in fixed amounts – such as 50 kilometers. Energy is measured in the same way using the unit kWh. 50 kWh is a fixed amount of energy.

Speed is the rate at which we are covering distance – such as 50 km/h. The rate of energy generation or consumption is measured using units of kW. This rate is known as power. The kW is a measurement of kJ/s (kJ is a different unit to measure energy. For reference 3,600 kJ = 1 kWh).

Table 1 – Analogy with speed and distance
Amount		Rate
Distance	km	Speed	km/hr
Energy	kWh	Power	kW

If you ever see kW/hr – this is almost certainly an error. Technically this is equivalent to acceleration – the rate at which we are changing our power. People often mistakenly use kW/hr when they should be using kWh – don’t be one of these people!

How then to relate kW to kWh? We need one more piece of information – the length of time over which we are producing or consuming energy.

If we were driving a car at a certain speed, to know how far we had driven we need to know how long we had been driving. Likewise if we are consuming energy at a certain rate, to know how much energy we had consumed we need to know how long we had been operating.

For example, if we had been consuming at 50 kW for 1 hour, we would have consumed 50 kWh. Two hours would lead to a consumption of 100 kWh, half an hour 25 kWh.

Table 2 – Relationship between rate, length of time and consumption

How varying the rate (speed or power) affects consumption

Time	Speed	Distance	Rate	Amount
1 hour	50 km/hr	50 km	0.5 kW	0.5 kWh
1 hour	75 km/hr	75 km	1 kW	1 kWh
1 hour	100 km/hr	100 km	2 kW	2 kWh

How varying the length of time affects consumption

Time	Speed	Distance	Rate	Amount
0.5 hour	100 km/hr	50 km	1 kW	0.5 kWh
1 hour	100 km/hr	100 km	1 kW	1 kWh
2 hour	100 km/hr	200 km	1 kW	2 kWh

These concepts need to be grasped forwards, backwards and side to side. You must be comfortable with moving from:

kW * hr = kWh
kWh / hr = kW
kWh / kW = hr

We can now use these concepts to analyze energy data.

Suppose you have the following data for a CHP scheme. This is a CHP scheme with the facility to dump heat (not all heat generated is necessarily recovered).

Table 3 – Sample data
Engine electric size	kWe	400
Engine thermal size	kW	400
Annual heat recovered	kWh	1,809,798
Annual power generated	MWh	2,571
Annual operating hours	hr	5,638

What insights can we gain from this? I would look at the following:

Annual heat recovered

Calculate the maximum amount of heat our engine could generate in a year (i.e. assuming full load operation for the entire year).

maximum heat generation = engine thermal size * annual operating hours
22,55,200 kWh of heat = 400 kW * 5,638 hours

This validates the annual heat recovery as reasonable at 80% of the maximum available heat.

Calculate the average heat recovery

average heat recovery = annual heat recovery / annual operating hours
321 kW = 1,809,798 kWh / 5,638 hr

We do not why this number is low. It could be due to part load operation of the CHP or due to heat dumping.

Annual power generated

Again we dimension the power generation using the operating hours. Note the division to convert from kWh to MWh.

maximum power generated = engine electric size * annual operating hours
2,255 MWh = 400 kW * 5,638 hours / 1000

This flags up an error with the annual power generated value of 2,571 MWh as it is greater than our maximum!

We could also spot this error by calculating

average electric output = annual power generated / annual operating hours
456 kWe = 2,571 MWh / 5638 hr * 1000

This gives us an average engine electric output of 456 kWe - which is greater than the size of our engine.

Summary

The two concepts of an amount of energy (kWh) and the rate of energy consumption/generation (kW) are related to each other by a length of time.

Understanding this allows energy industry professionals to check the validity of data, as well as calculate new data to evaluate performance. Both skills are valuable to engineers and non-engineers alike.

Thanks for reading!