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Published on February 2nd, 2015 | by Guest Contributor

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The Great “Power vs. Energy” Confusion

February 2nd, 2015 by  

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?

electricityWhile 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:

  1. How much total energy can the system store? (Think watt-hours)
  2. 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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  • This is great, thanks for writing it. Question then comment: Is there a term that covers both power and energy? I.s., power is a property of X and energy is a different property of X? What would X be? (Or, should I say, “Watt would X be” 🙂 )

    Comment: It would be great to see added to this essay a couple more pragmatic examples. For instance, show the numbers for a typical (currently operating BWR style) nuclear reactor, a major PV installation project of X square meters of PV in Iowa, another PV in Nevada, and a N typical large scale wind generators, with their power and energy parameters. This would involve reference to rated average power, peak output, typical output, etc.

  • derekbolton

    Good article, and particularly with regard to energy storage. But the annoying thing there is that most press releases about storage systems only mention the power (or $/power), and most that do mention capacity don’t mention power. Very few state both. This contributes to the confusion in the media.
    And then, there’s the recovery efficiency…

    • yep. i brought this up with the author, who thinks we shouldn’t mention anything if they don’t provide both. i’m on the line about it, but i do intend to push their PR people for both numbers when only one is provided. i have a feeling it is actually the fault of the PR people who want to keep it “simple.” but who knows?

      • derekbolton

        Maybe quote the number they provide, but draw attention to the omission of the other.

  • JamesWimberley

    British journalists have their own system of units (“BSI”).
    Weight: the elephant
    Volume: the London Bus
    some large number of London Buses: 1 Wembley Stadium
    Area: the football pitch
    some large number of football pitches: 1 Wales

    • Ronald Brakels

      Now they know how many holes it takes to fill the Albert Hall.

      • Joseph Dubeau

        In order by to double the size a one foot hole, how much would one have to remove from the hole. 😉

        • Ronald Brakels

          You might need to ask an expert on digging holes to get the answer to that one. Tell you what, Tony Abbott looks like he is about to have a lot of spare time on his hands, so why don’t you drop him a line? It’s right up his alley.

          • vensonata

            Tony Abbot…now there is another hole for the Albert Hall.

    • lol. have to admit that we don’t go down that route too often. however, i sometimes think we should. the constant pull between helping people to visualize & put in context vs helping to educate the masses…

  • Marion Meads

    When California became the number 1 in the dairy industry we prefer the terms: cow-lowatt for power and cow-lowatt hours for energy. For heating value, we measure them in cow-lories. We use cow-culators to count the number of heads of cows by operating remotely the cow-rodrones. So we renamed our state Cow-lifornia. How about that?

    • spec9

      Well . . . Cow-abunga!

    • jeffhre

      Go Ags!

  • jburt56

    P = dE/dt

    • spec9

      I don’t think bringing up Calculus is going to simplify things for most people.

      • jeffhre

        Just a reminder of the sum of the problems that brought us to this point, played out in reverse jburt’s perverse pleasure.

  • A picture tells a thousand words. Explainers are critical when introducing new concepts and things – like renewables. Force – Work – Energy – Power are important to understand, even at a general interest level. You could go back to the early days of mining and start with horsepower. Or assume readers are all on the same page with SI units. SI units are easier.

    • No way

      Hehe, great pic.

    • Marion Meads

      We can easily visualize a horse, but a foot-pound, what the heck is that? Is that a pound of horse’s foot? Foot-pound per minute, is that a contest of eating a pound of a foot of a horse in a minute?

      • This is an opportunity to start RemedialCleantecnica blog, Marion.

        • Marion Meads

          Sarcasm doesn’t become the best of us. I never made any mistake in all of my postings when it comes to units of power and energy. SI units rule instead of furlongs per fortnightly.

          See this for a refresher:

          http://en.wikipedia.org/wiki/FFF_system#Notable_multiples_and_derived_units

          • I don’t think you got the purpose of the post. The figure of horsepower isn’t sarcastic. It’s exactly how “horsepower” was determined. Horses was used in mines for hoisting materials and lowering workers. Showing mass – force – work – energy – power in an illustrative way is important, no matter who the audience is.

          • Marion Meads

            The picture is nothing but about a horse pulling some unknown weight. It failed to convey the meaning of the 33,000 foot-pounds per minute as it is an abstraction of force, distance and time. How is the time illustrated, and how is the distance illustrated in the picture?

            Part of the reason is that English units are archaic and it adds to the confusion and no such illustration will ever suffice. I say, go SI units and leave the ancient units behind.

          • Marion, you have a difficult time with satire. I can’t tell if you’re being fatuous or pedantic. Doing fatuousness well is a sign of intelligence. A pendant is usually someone who utilizes gods gifts as well as expected.

            Mass versus weight is a heady phenomena. SI units for mass is easy. Mass is mass. US units for weight take into account that we humans live on earth under a gravitational pull of 32.17 foot times pound (mass) per second per second. However, here on earth we tend to interchange the two. For instance, a horse hoisting up 33,000 pounds (weight) of tin ore from a mine shaft is pretty self explanatory. The mine shaft is so many feet deep. Also, the mine is on earth.

            The illustration is excellent actually. It pretty much shows power necessary to hoist up a thing over a certain period of time. Now assume the horse worked a total of 8 hours that day, the energy spent would be 8 horsepower hours.

            On the other hand, I did suggest that SI units should be used, but for some reason you chose to be pedantic.

          • jeffhre

            A pendant? How illuminating!

      • Joseph Dubeau

        foot–pound – a unit of work equal to the work done by a force of one pound acting through a distance of one foot in the direction of the force.

        For moving objects, the quantity of work/time (power) is calculated.
        Therefore, the work done by a force F on an object that travels along a curve C is given by the line integral:

  • RobMF

    Battery killed the gas tank 😉

    • Marion Meads

      And the Americans should let go of their English units. They still lived in archaic system of units. Along with the success of renewable energy, the Americans should go full scale with the SI Units.

      • Burnerjack

        But I’m still 12 and 1/2 stone…

    • Burnerjack

      Like video killed the radio star?

  • I don’t like the analogy of the suitcase over the head. If you put it on an elastic steel frame, then there would be no energy. But there is energy expended if you are holding it because of micro movements, and the mechanism of the muscles. It would be like holding it up with a jet of water.

  • JamesWimberley

    “Power is watts. Energy is watt-hours.” Absolutely. Let’s leave joules, ergs, foot-pounds, BTUs, barrels of oil etc to the specialists who need them. It’s an electrical age, so electrical units are best. A kilowatt is the power of a pony.

    And a reminder to everyone that renewables’ share of energy is not the same as their share of electricity.

    • vensonata

      Yes, this electricity vs energy confusion comes up often. That calls for another article. While our electricity use in Canada is alarming, our energy use is obscene!

      • s F YOU University

        Only because it’s much harder/takes more energy to HEAT a home than it is to COOL it. Heat would be insane to do electrically in most average homes, but to have an air conditioner is easy to do with pure electricity (due to less energy).

    • No way

      Well, I’d keep the joules since it’s the international standard. But the rest should be thrown in the garbage can. Along with other crazy obsolete units like miles, gallons, ounces, stones, pounds, feet, hands, tooths (or whatever other body parts might there might be ;). No inches, pinches or ponchos when measuring.
      Not to mention new made up units made by ones that should be gone like MPGe

      There is one unit I personally would make an exception for among these irrelevant units and that is the pint. And that is for the sole reason that you would get slightly more beer than a half liter would give you otherwise.

      • Hugo Ferreira

        That depends if it is a Imperial Pint or a US Pint, as if the measurements aren’t inconsistent enough, you have different values with the same name depending in what non metric place you are 😛

        • No way

          Or even different depending on the content being wet or dry. 😛

        • Michael G

          That difference is because the newly independent American colonies tried to go decimal with gallons (as they had with money) by making them 10 pints. Didn’t work – couldn’t legislate people to stop thinking 8 pints to a gallon.

      • Michael G

        Actually, the US is waiting for the rest of the world to get totally scientific and give up this crazy km/hr and deg. C for meters/sec and deg. Kelvin. No half-way measures before we join in! Speed limits on the freeway of 28 m/s, and weather reporters saying “getting cold tonight – could go down to 270 degrees!” – or “Scorcher today! 310 degrees at noon!”

        • nakedChimp

          well, that’s funny at least 😉

      • JonathanMaddox

        A pint is rather less than half a litre in the USA. Seriously.

        George Orwell had his characters rail against the indignity of metrication, a half-litre being insufficient and a litre being excessive.

        But some of us never used *any* round number for our beer glass standards, so have been completely unaffected by the move from traditional to metric units.

        http://www.smithsonianmag.com/arts-culture/pints-liters-pots-and-schooners-beer-size-matters-28912334/?no-ist

      • s F YOU University

        lol

    • spec9

      Watt-hours is kind of a clumsy term but I guess it works. It is basically signifying watts times hours (watts*hours). But it works well for the amounts of electricity we consume. Joules is way too small . . . 1 kilowatt-hour = 3.6×106 J

      • Shane 2

        Joules too small? Well then bytes are too small. That’s why we have kilo, mega, giga, and tera to help us out. When I see that a thumb drive is 32 GB, I know what is implied. I have no problem with 3.6 MJ to designate the energy for 1 kilowatt-hour.

      • Ulenspiegel

        kWh is actually a very nice energy unit when discussing fossil energy and electric energy:

        1 liter oil = 10 kWh heat

        1 m^3 NG at normal pressure = 10 kWh heat

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