Measurement units of power and energy

Energy = Power x Time

This means that any indication of an amount of energy must always be related to a certain lapse of time: seconds, or hours or years. Energy and power are two totally different concepts. Wrong use can lead to great misunderstandings.

The basic units are:

• For energy: Joule
• For power: Joule per seconde or Joule/sec. This is also called a Watt
• So 1 Watt is 1 Joule/ seconde or 1 J/sec.

For units which are either greater or much greater, the following prefixes are used:

The suffixes that indicate the duration of power are:

1 hour is 3,600 seconds en 1 year is 8,760 hours

For transforming amounts of energy expressed in Joules it is convenient to know:

1 PJ = 31,7 MW year

When the amounts of energy are expressed in kWh, the numbers are normally very high, and become much easier to imagine by transforming them into kilowatt-years or megawatt-years. The great advantage is that it then becomes apparent at a glance, with what average power this year's-worth of energy was produced. This is why it is always helpful to transform amounts of kWh produced (or consumed) during a year into kW-years by dividing the number of kWh by 8,760. This number, in kW-years or MW-years, shows the average power that is equivalent to the energy that was produced, or consumed, during that year.

I will now give three examples of the convenience of this method:

Example 1:

We are presented with a steam turbine with an electricity yield of 4,818,000,000 kWh (kilowatt-hours) over a certain year. Nobody will be able to conclude from this enormous number what the average power is with which this turbine has produced this amount of energy over that year. This is why one needs to divide this gigantic number by 8,760 (the number of hours contained in a year), coming to an amount of 550,000 kilowatt-years (kWy). That shows immediately that the total amount of energy in that year was produced with an average power of 550,000 kW, or 550 MW. The power of a medium-size steam turbine. And now, suddenly, both the energy produced over the year and the average power at which it was produced have become intelligible numbers.

Example 2:

A wind turbine specified as a "large 3 MW" is reported to have yielded 6,570,000 kWh of electricity during a certain year. That, again, sounds like an impressive amount. But it remains unclear how much it is exactly. So let us transform that number into kilowatt-years again by dividing it by 8,760, working out at 750 kilowatt-years. Now we see immediately that this wind turbine, announced as a "3 MW turbine", or a "3,000 kW wind turbine", produced electricity at an average power of 750 kW, or 0.75 MW.

Example 3 :

It is said that in 2006 and 2007, the Netherlands' electricity consumption expressed in MWh was approximately 113.88 million MWh. No one can get an idea of how much that really is. Therefore, let us transform the information from MWh into megawatt-years, again by dividing by 8,760, the number of hours per year. That makes 13,000 megawatt-years. By omitting the suffix "years" we can see straight away that the total electricity consumption is generated by an overall average power of all supplying power plants over the year of 13,000 MW. An intelligible number from which conclusions can be drawn.

The cumulative increase over a number of years of processes that rise every year at a constant rate like, for example, energy or electricity consumption, or the increase of the population, etc.

Cumulative change in the case of a 2 % yearly increase

After   5 years 1,02 ⁵  = 1,104

After 10 years 1,02 ¹⁰ = 1,219

After 15 years 1,02 ¹⁵ = 1,346

After 25 years 1,02 ²⁵ = 1,64

Cumulative change in the case of a 3 % yearly increase

After   5 years 1,03 ⁵  = 1,16

After 10 years 1,03¹⁰ = 1,34

After 15 years 1,03 ¹⁵ = 1,56

After 25 years 1,03 ²⁵ = 2,09

Cumulative change in the case of a 4 % yearly increase

After   5 years 1,04 ⁵  = 1,22

After 10 years 1,04¹⁰ = 1,48

After 15 years 1,04 ¹⁵ = 1,80

After 25 years 1,04 ²⁵ = 2,66

To take the last line as an example, after 25 years, an annual increase of 4% will result in an increase of 1.66, i,e, 1 changes into 2.66. These numbers make it clear how rash it can be not to take into account such increases, in the case of the future of some processes, such as the rise of energy consumption or population. Definitely in the case of yearly rises of 3 and 4%, that increase grows very fast after a few years. Considerably more than the increase merely being proportionate to the number of years.

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