The Great “Power vs. Energy” Confusion

February 2nd, 2015 by Guest Contributor

By Rob Lewis

“I went on a diet and lost 15 horsepower.”

“I filled up my car’s gas tank. It took 20 volts.”

Most people would recognize these statements as nonsense. After all, it seems obvious that weight isn’t measured in horsepower, and a quantity of liquid isn’t measured in volts. In both cases, the speaker got the units of measure wrong.

While these mistakes may be absurd, in the field of energy generation and storage, similar errors are made all the time, and hardly anybody seems to notice. The core problem is confusion of two related, but different, physical quantities: energy and power. They’re not the same thing! If you read and understand this article, you’ll know more about the difference than a lot of reporters, and when you hear that a new wind farm will generate “250 megawatts per year,” you’ll know that something is wrong!

So what is energy, anyway?

While we all have a vague sense of what energy is, it helps to know the precise definition. Stated as simply as possible, energy is the capacity to do work. In physics, work is the act of exerting a force over a distance. Pushing a sofa across a room, or lifting your carry-on into a plane’s overhead compartment are both work. (On the other hand, just standing there with your suitcase held over your head might tire you out, but it’s technically not work because you’re not actually moving the luggage.)

So we might say that energy is what makes it possible to push things around. The “thing” might be a car moving down a highway, a lump of bread dough on your kneading board, or an electron in the filament of a light bulb. Pushing these things around is work, and it takes energy to do it. If we know the strength of the force we need in order to move an object, and the distance we’re going to move it, we can calculate the amount of energy we’ll need.

There are several different units used to measure energy: joules, BTUs, newton-meters, and even calories. When we’re talking about electrical energy, the most common unit is the watt-hour. One watt of electrical power, maintained for one hour, equals one watt-hour of energy. A thousand of these is a kilowatt-hour (kWh), and note that a thousand watts for one hour, or one watt for a thousand hours, both equal one kWh. They’re the same amount of energy.

Working Faster = More Power

Did you see how I snuck the term “power” into that last paragraph? Here’s the critical difference between it and energy: while energy measures the total quantity of work done, it doesn’t say how fast you can get the work done. You could move a loaded semi-trailer across the country with a lawnmower engine if you didn’t care how long it took. Other things being equal, the tiny engine would do the same amount of work as the truck’s big one. And it would produce the same amount of energy and burn the same amount of fuel. But the bigger engine has more power, so it can get the job done faster. Power is defined as the rate of producing or consuming energy. Say this ten times: “Power and energy are not the same thing! Power is energy per unit of time.”

The standard unit of electrical power is the watt, which is defined as a current of one ampere, pushed by a voltage of one volt. More simply, volts x amps = watts (there is a complication if we’re talking about alternating current, but we’ll ignore it for now). In the USA, the standard wall socket delivers 120 volts. If you plug in a light bulb and find that a current of ½ amp is flowing through it, you know that the power used by the bulb is (120) x (½), or 60 watts.

So much for power. How much energy is the bulb using? That depends on how long we leave it burning. A 60-watt bulb burning for one hour will consume 60 watt-hours of energy. Ten bulbs burning for ten hours would consume 10 x 60 x 10, or 6,000 watt-hours, which we can write more conveniently as 6 kWh. A thousand households all doing this would consume 6,000 kWh, which equals 6 megawatt-hours, or 6 MWh (since 1,000,000 watts = 1,000 kilowatts = 1 megawatt).

So the thing to remember about measurements of electrical energy is to always look for the “hours.” It simply makes no sense to say that a power plant can generate so many “megawatts per year.” What they probably mean is “megawatt-hours per year.”

Well, wait a minute. Doesn’t “megawatt-hours per year” fit our definition of power? It’s energy (megawatt-hours) per unit of time (years). Exactly right! So instead of spelling out “megawatt-hours per year,” wouldn’t it be simpler to just rate the power plant in watts? Indeed it would. And since there are 8,766 hours in an average year, we can convert “MWh/year” into just “MW” by dividing by this number. This tells us that our hypothetical wind farm producing 250 MWh/year is generating power at an average rate of 250 ÷ 8766, or 0.0285 MW, which is the same as 28.5 kW.

Notice I said “average rate.” When the wind’s not blowing, the rate of production is of course zero kW. So in order to average 28.5 kW, the wind farm would have to produce considerably more than that some of the time. This leads to another important spec called “peak power output”: the maximum that the wind turbines can produce under ideal conditions. For our 28.5 (average) kW plant, the peak output could be 50 kW or more.

Solar plants of course have similar considerations: zero output at night, and peak output typically at high noon in summertime. But if you average this out over a year, you get an average output rating in kilowatts or megawatts.

Energy Storage: Both Watts and Watt-Hours

Much of the discussion about clean energy concerns ways of storing it for those times when the wind isn’t blowing or the sun isn’t shining. Without effective storage, we’re forced to rely on conventional power plants during these periods.

Energy storage usually means batteries, but there are other ways, like pumped hydro and molten salt. But whatever the technology, there are two performance parameters of interest:

How much total energy can the system store? (Think watt-hours) How much power can it deliver at any moment? (Think watts)

The usefulness of a storage system depends on both of these quantities. A system that stored an enormous amount of energy wouldn’t be very useful if it could only return that energy a few watts at a time. And a system powerful enough to light up a whole city wouldn’t be good for much if its batteries died after a few minutes.

The moral of this story: storage systems have to be able to store enough energy to last through the “blackout” periods, and they have to be able to deliver that energy fast enough to meet the electrical load. Once you know both the energy storage capacity (say, in megawatt-hours) and the output power (say, megawatts), you can simply divide these numbers to find how long the backup power will last. For example, a 20 megawatt-hour storage facility delivering power at the rate of 2 megawatts will last for 20 ÷ 2, or 10 hours on a full charge.

Conclusion

It’s common for people to use the words “power” and “energy” interchangeably. But now you know the difference: energy is the total amount of work done, and power is how fast you can do it. In other words, power is energy per unit of time. Power is watts. Energy is watt-hours.

Image: electricity, via Shutterstock











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