Theory/Power and Energy:

Power and Energy come up quite often in the discussion of Photovoltaic systems and renewable energy in general and are often misused due to the common misconception that they are one and the same. I would like to clear this little issue up. To begin I will demonstrate the most common misuse of the two in a simple quiz. Which one is correct?

1. Last month my PV array generated 8 kilowatts of energy.
2. Last month my PV array generated 8 kilowatt-hours of energy.

To some this may seem obvious; to others it may not. Anyway, the correct answer is number 2 and I will now explain the difference.

Definitions of Energy and Power

The two basic units of energy and power in the standard SI unit system are the Joule and the Watt. The formal definition of the Joule is:

'the amount of Energy expended when applying 1 Newton of force over a distance of 1 meter or passing a current of one amp through a resistance of one ohm'.

The Watt is a rate of energy use: Power is Energy per unit of Time. 1 Watt equals 1 Joule per second [J/s]. The official definition of the Joule may still leave some uneasy. To clarify the magnitude of one Joule I will use the example of a conventional 100 Watt incandescent light bulb. A light bulb rated at a Power of 100 Watts will use 100 Joules of Energy per second that it is operating. Another way to demonstrate the quantity of energy in one Joule is to think of how much energy is required to bring one liter [think of a Nalgene bottle] of water from room temperature (20 degrees Celsius) to a boil (100 degrees Celsius). This would require 334,640 Joules. So as you can see, one Joule is actually a fairly small amount of energy.

Why is it confusing?

Now that we have an understanding of energy and power we can address the basic misconception between the two. Power is a rate of energy use, and is usually expressed in Watts [W]. Note: a thousand Watts is equal to one kilowatt (kW). Where the confusion comes in is when we use the term kilowatt-hour to express units of energy, which is however correct. One kilowatt-hour is equivalent to the amount of Energy consumed when a device using energy at a rate of 1 kW is operated for one hour, in other words, 1000 Joules per second being used for 3600 seconds, resulting in a total energy use of 3,600,000 Joules.

Here are two examples:

 In your electricity bill, you pay for the amount of energy (kWh) you used per month, not for power (kW). A typical price for electrical energy is \$0.15 per kWh. Imagine if you take 2 hours to clean your room with a vacuum cleaner that says: ‘1.6 kW’, how much will it cost? – We go from power to energy by multiplying power with the amount of time: 1.6 kW * 2 = 3.2 kWh. Since you pay \$0.15/ kWh, you pay a total of 3.2 kWh * \$0.15/kWh = \$0.48.

 Look at the beautiful solar array in the figure. In full sun conditions, the array receives about 1000 Joules per second (or: Watts) of power. About 10% of that power is converted into electricity and stored in the battery. How much energy is stored in the battery after a day of 5 full sun hours? – 10% of 1000 Watts is 100 Watts. Again, Energy = Power * Time so 100 Watts * 5 hours is 500 Wh (or: 0.5 kWh) of energy. This is equal to 1.8 million Joules. So to summarize: a kWh is a unit of energy and a kW is a unit of power, when discussing a solar array the capacity of the array is usually described in kW’s, meaning the rate at which it can make electricity from solar irradiation, while the amount of energy harvested over a given time period is expressed in kWh’s. Now, test yourself to ensure that you understand this concept:

How much energy is consumed in kWh when you leave your 100 W incandescent light bulb on for 8 hours overnight while you’re sleeping?

Extra: How much CO2 do you emit by doing this (assuming 1.5 lbs per kWh)?

Those weren't too difficult, were they?

More about storing energy and efficiencies next week.

Regards,

Garrett