Batteries: Power, Energy and Units

Your house likely contains indoor plumbing, a set of pipes, faucets and fixtures for the convenient use of water. When you open a faucet, water flows at some rate into a basin, which can collect it. The rate is determined by how much you open the faucet and by the pressure the water is under. The size of the basin determines how much you can collect without causing a small disaster. So, the important concepts in your indoor plumbing are the water pressure, the flow rate, and the basin size.

Now let's start talking about batteries. To charge a battery is like filling a bathtub - the rate at which you fill the tub is "flow rate", so for instance if your faucet puts out 10 gallons/minute, you can fill a 20 gallon tub in 2 minutes. For a battery, the flow rate is called the "power" and measured in Watts (W). A watt is a joule/second, so you can see already one of the source of confusion: for fluids, we consider volume (gallons) the base unit, whereas for energy, the base unit most people are familiar with measures flow rate. Just remember that a watt measures how fast the energy is flowing, i.e. power. The most common unit used in electric cars for power is the kilo-watt (kW). 1 kW is 1.34 HP, so 1 HP is 0.746 kW. Just remember that a kW is "stronger" than a horse power by about a third, and you'll be good.

Moving on to energy. The "size" of a battery is how much energy it can store. Typically this is expressed in kilo-watt hours (kWh). So for instance if a battery can store 10 kWh, that could be because 1000 watts of power flows into it for 10 hours to make it full (1000W * 10h = 10,000 Wh = 10 kWh). To refer back to our bathtub, it would be like saying that the capacity of our bathtub is 10 gallon/minute * 2 minutes, or 20 G/M*minute. It's a very awkward way of thinking, but for energy, especially electricity, it actually makes some sense. Energy is also measured by a huge variety of different units, check out this table, which lists the energy of 1 kWh expressed in a variety of different units.

You can immediately see several very interesting things from this table of energy equivalences. One of the most interesting, in my opinion, is comparing the Food Calories to the Gallons of Gasoline. A person consumes about 2500 Calories per day, which is about 3 KWh. But 3 kWh is only about 1/10th of a gallon of gasoline - so unless you are a very special person, it's likely that your car consumes vastly more energy than you do. That's why biofuels have become so controversial recently in the food crisis - the same energy that can drive your SUV for a day could feed a human for a month or more.

Another interesting point is that batteries store much less energy than gasoline per pound, or per liter (this called energy density). Even the Tesla Roadster, with almost 1000 pounds of batteries, stores only 56 kWh, which is less than 2 gallons of gasoline energy equivalent. Another way of saying this is that liquid fuels are highly energy dense - that's why they are so convenient. One reason they are so dense is that they rely on the oxygen in our atmosphere for the release of their energy - so actually it isn't just the gasoline you need, it's also all of the air required to burn that gasoline, which is many times heavier and take much more space than the gasoline itself. If we commuted on the moon, gasoline would be a terrible energy storage device because we'd have to carry around huge cylinders of compressed oxygen to make it useful.

An important thing to note before we move on is that many people are in a deep state of confusion about the unit "kWh", and often mistakenly use "kW" or even "kW/h" instead. Fortunately, it's almost always possible to figure out what unit they meant to use by inspecting the context. Are they talking about power (rate of flow) or energy (storage)? In addition, you can sometimes tell by the size of the quantity what they really meant. For EVs/hybrids, battery storage is typically between 1 kWh (Prius) and 60 kWh (Tesla Roadster), whereas power is typically between 20 kW (Prius) and 200 kW (Tesla Roadster). With these two rules, it's almost always possible to figure out what they really meant.

So, energy is storage, measured in kWh. Power is flow rate, measured in kW. That only leave one concept from our indoor plumbing: pressure. Typically, householders don't have to worry about their water pressure, and this is also true for electric cars. The engineers who design the system have to sweat these details, but as long as everything is working, you shouldn't. Nevertheless, you may sometimes see this given, so I'll explain it here as well. Pressure in a water system measures "how hard the water pushes", typically in pounds per square inch (PSI). If your system has 40 PSI, that means that for each square inch of e.g. hot water tank inner surface, the water is pushing out with 40 pounds of force. If you've ever tried to completely stop the flow coming out of a hose with your thumb, you know that this is significant! Remember, pressure is totally different from flow rate - as witnessed by those low-flow shower heads that never-the-less have brutal pinhead streams coming out. But pressure is an important thing in determining what the flow rate will be: for a given opening, the higher the pressure the higher the flow rate. Yet pressure tells you nothing about storage: just because you've got high pressure doesn't mean you have a large bathtub.

In electrical systems, pressure is measured in volts. You can think of it as "how hard the electrons push." As with water, this pressure helps to determine what the flow rates will be, so a higher voltage system is likely to be capable of higher power, all else being equal. As with water, voltage tells you nothing about how much energy the battery can store. One important thing about voltages is that, like with water pressure, they have to be properly matched for the power to flow as you want. If you want to charge a battery, you need to match it's voltage. This is why every battery has it's own charger - specially designed to convert the voltage of the source (e.g. the electricity from your wall plug) to the voltage required by the battery.

Charging a battery is generally well understood, but there are some important things about so-called "quick-charging" which are not well known. It's all about what is a "reasonable" flow rate for electricity. When you charge a battery from the grid (e.g. a plug in your house), power flows down the wires, through the charger, and is stored in the battery. The amount of energy stored is equal to the power times the time, minus a bit for losses. So for instance if you run 1 kW for 12 hours (overnight), you can add about 12 kWh to your batteries state of charge. Now imagine that you've got a Tesla Roadster, with it's 56 kWh of storage. A regular six hour charge will require 56 kWh / 6 h = 9.3 KW, which is a pretty big draw. That's like running 9 toasters side-by-side. You'd have to have a special circuit to make sure you didn't blow a fuse/switch the breaker. And you'd want to be careful with the cables to avoid arcing, etc. Yet everyone complains that a six hour charge time is unreasonable.

What would happen if you wanted to charge it in an hour? 56 kWh / 1h = 56 kW! That's like the power draw from your entire neighborhood - or like that dude at Christmas who has 10,000 christmas lights. Even with a 220V circuit (like for your oven), you'd need a 250+ amp breaker (power = volts * amps, so amps = power / volts = 56,000/220 = 255), which of course IS NOT AVAILABLE. So you're going to have to get fancy and have a multi-circuit charger with big fat cables, and the power company may have to retrofit your house with better service. It would be like piping a water-main into your house instead of a little copper tube.

And the oft-rumoured and much desired 5 minute quick charge? 56 kWh / 5 minutes = 672 kW, about 2/3 of a megawatt. Now you're talking about the power use of half a city. You'd have to have high voltage power towers coming into your house, and your own electric sub-station. The wire going into the car would have to be several inches in diameter to prevent it from melting under it's own resistance. You'd need the Colorado River flowing into your house!

Do I think 5 minute quick charging batteries are possible? Maybe. Do I think they are practical? Not at all - even for specialized charging stations, it's a crazy dream. Far more likely is battery swapping, ala Project Better Place.

I've detailed here a guide for understanding batteries and electric cars, but of course a similar amount of confusion exists at the generating end as well. WattHead has an excellent post up which covers the power-plant end of this confusion: Kilo-who's-its and Mega-what's-its: A Primer on Energy, Power and Capacity. I hope I've managed to explain the difference between power and energy clearly, and I hope you'll be able to sort through the confusion that you will see in many places online.