*Energy Basics is a series covering fundamental energy concepts.*

*Posts in this series include HHV vs LHV and Average vs Marginal Carbon Emissions.*

Understanding the difference between kilowatts (kW) and kilowatt-hours (kWh) is a basic for energy industry professionals. The key is understanding they are related to time.

An analogy with distance and speed can illuminate 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 per second (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

Time | Speed | Distance | Rate | Amount | |||||

How varying the rate (speed or power) affects consumption | |||||||||

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 | |||||||||

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

- We can calculate the
**Maximum heat generation****=****Engine thermal size * Annual operating hours**(This is assuming full load operation for each hour). - This gives us 22,55,200 kWh of heat.
- This validates the annual heat recovery as reasonable at 80% of the maximum available heat.
- We can calculate the
**Average Heat Recovery****=****Annual heat recovery / Annual operating hours**. This gives us an average of 321 kW. - We do not know whether or not this number is low because of part load operation of the CHP or due to heat dumping.

Annual power generated

- The
**Maximum power generated**=**Engine electric size * Annual operating hours.** - This gives us a maximum generation of 2,255 MWh (note I have divided by 1,000 to convert from kWh to MWh).
- 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**. This gives us an average engine electric output of 456 kWe (greater than the size of our engine).

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.