Kilo-who's-its and Mega-what's-its: A Primer on Energy, Power and Capacity

Cross-posted from ItsGettingHotInHere.org

Gentle reader,

In the course of your readings in the blogosphere, your academic research, or your energy-related activism, you will likely see a number of similar and often confusing terms bandied about to describe how much power a power plant can produce (MW vs MWa), how much it generates (KWh vs MWh), how much an appliance consumes (watts vs amps), etc., etc. etc. Furthermore, these units and terms apply to two related but very different concepts - energy and power - which while often used interchangeably in common parlance, have very different technical meanings.

The end result is that all this can all be very confusing as you can often find yourself accidentally comparing apples and oranges, kilowatt-hours and horse power or nameplate capacity and average capacity, etc. Confusing these terms is easy and common and mix-ups can have major consequences for your conclusions (this post was prompted by this one, for example, which confuses energy and capacity, leading to very different conclusions...)

The following is an primer on some of the different units of power and energy and descriptions of power plant generation you may encounter and what they mean. There is a lot here and you may not encounter a need for all of it immediately. However, if you don't have a strong physics background (and that means most of us!), or you (like me) get your kilo-whats-its and mega-whos-its confused sometimes, you may find what follows a useful summary of many of the concepts and units you need to know (and some you probably don't). Use this as reference if you want, for times when you get confused later (and you probably will):

Power vs. Energy - What's the Big Diff?

When trying to explain electricity, power and energy, I invariable fall back on analogies to water flows. You see, electricity flows a lot like water, following a path of least resistance, from source to sink, spring to sea. So to understand the difference between power and energy, let's start by taking a bath. Ok, you don't really need to get into the tub (although you can if you want... just keep that laptop dry!), but I think we can all visualize one...

Power, is a measure of the rate at which work can be done, or in our bathtub analogy, the rate at which water can flow out of your faucet. To visualize what power means, think about the size of your faucet. How high can you turn up the water? Bigger faucet = more water flow is possible = more power.

Energy is a measure of the amount of work actually done. In our bathtub analogy, energy is a measure of the water actually in the tub. How many gallons are in their after five minutes?

Power and energy are clearly related. Power x time = energy in fact. Or to put it another way, if your faucet can put out one gallon per minute, and you leave it on for ten minutes, you'll have ten gallons in your tub.

But notice that a quantity of energy doesn't necessarily translate to a certain quantity of power. You could have left your faucet on at a rate of half a gallon per minute for 20 minutes, or a rate of 5 gallons a minute for 2 minutes, and still ended up with the same quantity of water (or energy in our analogy), ten gallons. To convert from energy to power, you'd need to know the length of time over which you sustain that amount of power output. Energy / time = power.

OK, time to get out of the bath and turn on a light (you can dry off first if you want). To understand how power and energy relate to the light bulb, take a look at the top of the light bulb if it's an old incandescent one (before you turn it on or you'll blind yourself silly! And what are you doing with an incan in your house anyway!) or on the base of a compact fluorescent. It probably says something like 100 W for an incan, or 15 W for a fluorescent. W stands for "watt," the basic unit of power (for electricity anyway). The wattage of the light bulb is the rate at which energy needs to be applied to light the bulb to keep it lit, or the rate of energy consumption when the bulb is on.

Now leave your bulb on for an hour. How much energy has it consumed? Well, if it's a 100 watt incandescent, it uses 100 watts x 1 hour = 100 watt-hours. The watt-hour, or Wh is the basic unit of energy (at least when talking about electricity... there are other units to confuse you for other kinds of energy, but we'll get to those later).

Note that energy is actually something tangible - in the case of the bath tub example, its the water in the tub; in the case of the light bulb example, it's the room being lit for an amount of time (it's work that's been done). Power is something instantaneous - how much output is it giving right now, how much electricity is it using at this moment - and sometimes a unit of potential (or capacity as we'll get to later) - i.e. what's the maximum rate of flow your faucet will allow, or the maximum amount of power your microwave can use to zap your lunch.


Kilo-who's-its and Mega-what's-its: Units of Power and Energy

Like most units, you can use your latin prefixes to denote different quantities of the unit. For example: 1,000 watts = 1 kilowatt (or 1 kW). 1,000,000 W = 1,000 kW = 1 megawatt (1 MW). 1,000 MW = 1 gigawatt (GW) and so on...

Here's some things units of power are used to describe: what's needed to turn on a lightbulb, a microwave, a stereo or any other electric appliance (usually in watts, or W); the instantaneous output or maximum output of a power plant (i.e. one of the various capacities used to describe a power plant, see below, usually in MW); the power of a car's engine (in the US, usually in horsepower, another unit of power, or in the UK, in familiar kilowatts or KW)...

Same prefix thing applies for energy units: 1,000 watt-hours (Wh) = 1 kilowatt-hour (kWh). 1,000,000 Wh = 1,000 kWh = 1 megawatt-hour (MWh). 1,000 MWh = 1 gigawatt-hour (GWh) and so on...

Here's some things units of energy are used to describe: the amount of energy you consumed in your last month (i.e. on your energy bill, usually in kWh); the yearly output of a power plant (usually in MWh or GWh); the stored energy in a battery or a quantity of fuel like gasoline or hydrogen (usually in kWh or MWh for batteries or in the case of fuel, in another unit of energy like BTUs or jules); the potential energy stored in an object (i.e. the amount of energy that could be released by dropping a brick from the top of a building or the energy that could be released by letting a reservoir of water fall through a dam's turbines); the energy of a moving object over time (i.e. the amount of energy that could be captured by a wind turbine from the moving wind or from crashing waves) ...

Yes, But How Big is That Power Plant?

Good question. By now, I hope you see that that depends on what you mean by "how big?" How much power can it produce? How much power does it produce on average? Each question has a different answer, and each answer uses different units (Head heart yet? Mine does!). Let's take one at a time...

Capacity - or how much power can it produce? When you ask about how much power a power plant can produce, you are asking about capacity. If you are talking about the maximum amount of power it can produce, that's a term called "nameplate" capacity (or the maximum engineering rated capacity, so named because it's usually printed on a nameplate plaque at the facility).

Average output or average capacity - how much power does that plant normally produce? You often also see reference to a plant's average capacity, or the average power output of the facility over a given period of time (i.e. over a year or month). While it's not a strict rule, to clarify between nameplate capacity and average capacity, you sometimes see people use the units aMW to refer to average MW. If you see aMW (or sometimes MWa just to be confusing!), that usually denotes average capacity and not nameplate capacity. If you don't see that, you've usually got to rely on context to figure out if someone is talking about nameplate or average capacity (which are often mistakenly interchanged!).

At any given time, the power output of a plant can very between zero and the maximum nameplate capacity of the plant, just like the flow from your bath tub's faucet can vary depending on how far you turn the nob to open the flow. The instantaneous output of a plant is described in units of power, usually as MW.


Nameplate vs average capacity, "capacity factors," and energy, or How much energy does that power plant actually produce?


The ratio between the average capacity of a plant and its nameplate capacity is referred to as the plant's capacity factor. For example, a wind farm usually has a capacity factor of around 30-35%, which means over a given year, it runs on average at 30-35% of it's maximum nameplate capacity. That doesn't mean that the wind only blows 1/3rd of the time, or that the plant always operates at 1/3rd of it's maximum capacity, just that on average, the plant puts out 30-35% of it's maximum capacity. So a wind farm with a maximum, or nameplate capacity of 100 MW would usually operate at 30-35 average MW or aMW over a given year. A "baseload" coal or nuclear plant, that runs full-out most of the year (except for outages for repairs) could have a capacity factor of 80-90%. So a 1,000 MW coal plant would operate at an average capacity of 800-900 aMW.

Average capacity / nameplate capacity = capacity factor. Or, using simply algebra: nameplate capacity * capacity factor = average capacity.

Average output relates more closely to energy than nameplate capacity, and either knowing a plant's average capacity or it's capacity factor is critical to determining the real energy generation - and therefor real fuel use, environmental impact, etc - of a power plant. Average capacity * time = the energy consumed in that period of time. In contrast, nameplate capacity * time = the maximum amount of energy a plant could have theoretically produced over that time, had it run full-out the whole time. Since no plant ever runs at full capacity 100% of the time, that later figure is pretty much useless.

For example, a common mistake is to assume that a 1,000 MW wind farm is equivalent to a 1,000 MW coal plant. But as I hope is now clear, if the capacity factor of a coal plant is 80%, it will have an average capacity of 800 aMW and over a year, for example, produce 7,008,000 MWh in a year (800 aMW*8760 hrs in a year). In contrast, a 1,000 MW wind farm with a 33% capacity factor (which is typical) will have an average capacity of
333 aMW and produce only 2,917,000 MWh in a year. (For quick math, you can simply assume it takes 3 times as much wind power capacity to equate to a coal plant's capacity, so 3,000 MW of wind = 1,000 MW of coal).

I'll try to get into more practical applications of all this stuff in a subsequent post (as I try to explain the fatal - and very common - error in this recent post).