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Understanding electric and plug-in vehicles requires a slightly different knowledge set than what mechanics and drivers have needed to know for decades. One of the most obvious new concepts is the large battery pack and electric motor added to the car. The capacity values of these devices can be written using kW (kilowatt) and kWh (kilowatt hours), but don't think that a 90 kW motor is anything like a 90 kWh battery pack. That little h makes a big difference. Exactly what is the difference? Well, that's what we investigate in this week's Greenlings. Follow us after the jump to learn more.


[Sources: Idaho National Lab]
Photo by Vince Alongi. Licensed under Creative Commons license 2.0.


Defining kW and kWh

The simplest definitions of kW and kWh are as follows:

  • kW = one thousand watts (and a watt is one joule of energy per second)
  • kWh = using a thousand watts for an hour (3,600,000 joules).

That may make kW and kWh look like they're easily connected, but, as Wolfram Alpha says, "kW (kilowatts) and kWh (kilowatt hours) are not compatible units, so cannot be compared." Kilowatts are a unit of power, while kWh is a unit of energy. Think of it this way: kW defines how much energy a device uses or generates in a given amount of time. Meanwhile kWh defines how much energy that device actually used or generates. So, a 100-watt light bulb that is on for 10 hours needs 1 kWh (1,000 watt-hours). This is the same as ten 100-watt bulbs burning for one hour.

Both kW and kWh are SI (metric) units and can be applied to any type of machine or energy storage system respectively. That means a gas engine or electric motor can both have a kW rating. Similarly since kWh is a measure of energy, you can define the capacity of a tank of liquid fuel or a battery in kWh.

In battery terms, a kWh rating defines how much energy the battery pack has available to provide to the electric motor and, thus, sort of, how far the car can go before needing to be recharged. In order to make batteries last longer (in terms of durability rather than range) they are typically not used to their full capacity. GM engineers have opted to only use half of the capacity of the Chevy Volt's 16 kWh battery pack in order to help it last for 10 years / 150,000 miles. That means it will only provide 8 kWh of usable energy to get a 40-mile nominal electric-only range.

Still, since we don't know the usable capacity of all the battery packs used in plug-in vehicles, we'll use total capacity to compare some of the more popular EVs:


Model

Battery Capacity

EV Range (official estimates)

Miles per kWh

Chevy Volt

16 kWh

40 miles

2.5

Ford Focus BEV

23 kWh

75 miles

3.2

Tesla Model S (base model)

42 kWh

160 miles

3.8

Nissan Leaf

24 kWh

100 miles

4.1

Tesla Roadster

53 kWh

244 miles

4.6

Citroën C-ZERO

16 kWh

80 miles

5

A123 PHEV Prius

5 kWh

30-40 miles (top speed, 35 mph)

6-8

Note that these battery packs are being used in very different types of vehicles, which accounts for some of the difference in miles per kWh.

Be mindful of these numbers since, as we mentioned, the Volt only uses 50 percent of its capacity while the Tesla Roadster can use 100 percent of its 53 kWh. The Tesla battery pack is only expected to retain at best about 70 percent of capacity after 4-5 years while the Volt is being developed to still have 100 percent of its rated capacity after 10 years.

In battery terms, a kWh rating tells us how much energy the pack has to give to the electric motor. So, the 24 kWh pack in the Nissan Leaf could provide 24 kW for one hour, not taking into account what it's actually being asked for by the electric motor or what connectors are in it to regulate the flow. The kWh number is also important in plug-in cars because it's used as a way to talk about how expensive a battery is: the cost per kWh currently sits at around $1,000, but the big automakers are working hard to drop this to $600 or $500 or lower. Just for comparison one gallon of gasoline has a capacity of about 36 kWh and currently costs about $2.65 in southeast Michigan.

Batteries are in a unique position compared to many other devices. While they are primarily energy storage devices measured in kWh, they also have power ratings in kW. The power rating of a battery describes how fast it can release or absorb energy. Think of it in terms of a fuel tank. A high capacity, low power battery would be like a big tank with a pin-hole for the fuel to pour out of. A high power battery would have a larger opening for the fuel to come out of (or go into). We'll have more on this in a future installment of Greenlings.

This brings us to electric motors, which are also given a kW rating. If you're coming to EVs from standard gasoline vehicles, understanding a motor's kW rating is simpler than understanding kWh because a kilowatt is equal to around 1.34 horsepower. Therefore, it is possible (and easy) to translate electric motor strength into hp, more commonly used to define liquid-powered engine power. A 100 kW motor puts out 134 hp.

Cost Per Mile

One reason it's important to understand all of this is that it will help to determine how much it will cost you to drive your plug-in vehicle. Right now, knowing your mpg and the cost of gasoline will do the trick. Determining the cost per mile of an EV requires knowing your utility's rates and how much juice your car will require to fill up. For example, a charger that uses two kW and takes eight hours draws 16 kWh of electricity. If your utility charges a dime per kWh, then to "fill up" costs you $1.60. Then, you take this number and divide it by how far you can go on to determine your cost per mile.

The Idaho National Lab has also provided a handy chart for this (download the PDF). It's slightly out of date because it can only help us calculate costs for an EV that get 2, 3, or 4 miles per kWh, but if gives you can idea. Here's how to read the chart:

The fuel cost of driving an electric vehicle depends on the cost of electricity per kilowatt-hour (kWh) and the energy efficiency of the vehicle. For example, to determine the energy cost per mile of an electric vehicle, select the location on the left axis (Electricity Cost per kWh) at 9 cents in the graph below. Draw a horizontal line to the right until you bisect the EV 3 mi/kWh line. Now draw a vertical line down until you bisect the bottom axis (Energy Cost per Mile). This tells you that the fuel for an electric vehicle with an energy efficiency of 3 miles per kWh costs about 3.0 cents per mile when electricity costs 9 cents per kWh.



kW and Hydrogen Fuel Cells

Just as with any other machine, kilowatts are also used to explain the output of a fuel cell stack. Unlike a battery, the stack does not store energy, it simply transforms it from chemical to electrical. Therefore the power rating describes the rate at which it can produce electrical energy. The power output range varies tremendously depending on what kind of fuel cell we're talking about. Proton Exchange Membrane (PEM) fuel cells are often used in hydrogen cars, and generally range from 50 to 250 kW. Since fuel cells send their electricity to the electric motor, the kW rating of the motor defines how much of this energy is actually required at any given moment. And, instead of being limited by the kWh in the battery pack, the range of a hydrogen car is limited by the amount of fuel in the storage tank which can also be defined in terms of kWh (1 kg of compressed hydrogen gas has a capacity of about 39.7 kWh), but that's a different subject.






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  • 14 Comments
      • 5 Years Ago
      It's also worth pointing out that a kWh in the tank isn't a kWh at the wheels, you need to take into account the tank - wheels efficiency of the drive train which is roughly.

      25% petrol
      33% diesel
      40-50% fuel cell
      80-90% electric motor

      Electricity is very high value energy as is typically 'worth' (financially & thermodynamically) 3-5 times as much as a kWh of liquid or gas chemical energy.
      Due to conversions as above you need 2-5 kWh of fuel to make 1kWh of electricity.

      This is one of the reasons that converting electricity into hydrogen or any other liquid fuel is a silly idea.


      Also an electric motor can perform much better (low end tourque, no gears etc) than an ICE so 50kW electric motor could perform like a 100kW ICE

        • 5 Years Ago
        quote: ( This is one of the reasons that converting electricity into hydrogen or any other liquid fuel is a silly idea )

        I said some days ago that you don't convert electricity into liquid fuels. You use electricity to convert mass of something into a different mass, ex¨water into hydrogen, or water and co2 into methanol.

        Quote: ( Electricity is very high value energy as is typically 'worth' (financially & thermodynamically) 3-5 times as much as a kWh of liquid or gas chemical energy.
        Due to conversions as above you need 2-5 kWh of fuel to make 1kWh of electricity. )

        Ahh Ahh you are a trader of electricity . Gas worth 2.60$ , electricity worth 2-5 times as much as a kw/h of liquid or gas chemical energy, then what ?? raise the price of a kw/h of electricity to 2.60$ multiplied by 5 = 13 $ / kw/h.

        I told you that this site is for the traders. Many folks just negate all easy technologies and propose mandated suffocation and ruin and no energy and increase in price. That's why we have to pay money for each and every moves we make like gasoline with no alternative but gasoline is the worst polluter, there isn't enouph except where the richs put there money safelly out of sight of income tax in private kingdom. named saudi-arabia and swiss banks. Endless energy for them and bankrupcy for the u.s.a workers and taxpayers and air breathers.
      • 5 Years Ago
      "translate electric motor strength into hp, more commonly used to define liquid-powered engine power" - in the US maybe, most countries have progressed to using kilowatts

      Interesting the difference in ideas towards battery longevity between GM and
      Tesla
      • 5 Years Ago
      "a kilowatt is equal to around 1.34 horsepower. Therefore, it is possible (and easy) to translate electric motor strength into hp, more commonly used to define liquid-powered engine power. A 100 kW motor puts out 134 hp."

      That can't be true, can it? I thought a "100kW motor" was a motor that *consumed* 100 kW of power, and its mechanical power output was somewhat less than 100 kW.
        • 5 Years Ago
        Good question. NEMA electric motor ratings in horsepower are their ability to do useful work, but you could sneak in a kW figure measuring electric power consumption. Electric motor efficiency ranges from 75%-90+%, so the difference is appreciable but not huge. If motor power is given as DIN PS (Pferdestärke, love it) or SAE net then it must be kW measured at the engine's crankshaft. E.g. the Tesla Roadster's 288 bhp 215 kW net electric motor.

        For performance what really counts is effective, true, or wheel horsepower measured at the road on a chassis dynamometer.
      • 5 Years Ago
      There is energetic efficiency, and cost to obtain it.

      I would focus on influencing consumer behaviour and low cost CO2 efficiency improvements for stationary processes (electricity production and consumption, HVAC, etc) first.

      Just the added weight of the expensive accu pack already decreases overall efficiency of an EV to maybe 50%, so for mobility focus on frugal ICE's.

      Overall, more bang for the buck.
        • 5 Years Ago
        Obviously in the short term, consumer behavior and lower cost measures like cfls are much more cost effective, but in the long term you have to have some kind of solution that moves off fossil fuels. Biofuels, EVs, renewable hydrogen are all working toward that goal.

        What do you mean by efficiency of 50% (plug to wheel, well to wheel) ? What are you comparing it to? The figure is relatively meaningless without a comparison. Are you saying there is a halving of efficiency just by weight? I don't think that is accurate given most cars in the compact to mid-size category (most popular) weight ~2500-3000lbs today and a 100 mile BEV adds about a 500lb battery while having lighter motor and transmission (also don't forget optimizations that can be done in incorporating a battery pack into as a structural component). That's only a 20% increase in weight. Have a 1000lb pack (like the Roadster) and that's still only a 40% increase in weight. EVs aren't even close to doubling the weight of the typical vehicle.

        And efficiency doesn't scale exactly inversely with weight either, so the effect is even smaller. From a previous discussion, weight directly affects efficiency for rolling resistance and during acceleration. Additional rolling resistance losses from battery weight can be completely eliminated by low rolling resistance tires (which can more than halve rolling resistance forces by reducing the rolling resistance coefficient, ranges from .01 to .006 which is close to halving). Even then, rolling resistance doesn't seem to play that big of an efficiency role, about 5-15%. Acceleration losses are balanced out by stronger regen, and acceleration itself isn't the biggest component to typical driving (maintaining speed is the biggest component).

        The biggest factor in EV range (and by extension efficiency too), air resistance, doesn't depend on mass.
      • 5 Years Ago
      I hope the bloggers at ABG study this article carefully.
        • 5 Years Ago
        Indeed...

        ABG is what, about 3 years old? The irony of this being posted _now_ is beautiful.
      • 5 Years Ago
      "Both kW and kWh are SI (metric) units"

      Actually kWh is not SI. The SI unit for energy is the Joule. The kWh is kind of a mixed unit since people don't like to think in kilo seconds. The movement to have decimal time (back when the metric system was proposed) didn't quite work so this is what we're stuck with. I'd rather we just spoke in terms of megaJoules, but I'll take kWh over BTU any day.

      Personally I think we should have just converted to a base 12 number system (which is much more natural for counting things), but that's neither here nor there.
        • 5 Years Ago
        "Base 8 is just like base 10... (if you're missing both thumbs!)"
        Tom Lehrer
      • 5 Years Ago
      What happen to the battery in russia, u.s.a, canadian, swedish winter ?

      I said to install a small gasoline or diesel inboard electric generator to help the battery when it get below 50% and to enhance performance when the driver wants, and all the time in bad winter conditions. It can give 100 mpg because a serial generator is more efficient then a ice only or battery only. An ice working with a generator is more efficient and way less costly because it's cheaper and easier to tailor the torque and power figure to the simple generator compare with a 4-5 speeds costly and inneficient transmission+ gears differential set bolted to the entire weight of the car.

      Actually wall-mart sell a 150$ small chinese gasoline recharger. I guess a good one fitted to an electric car will cost 1000$ to 3 000$ max for a big bad one. I want in my life
      to experience more then stupid, old fashion, limp, polluting, underpowered ice engines bolted to a complex power rubbing cost and weight adder transmission.
      • 5 Years Ago
      simple - kW tells you how FAST you can go, and kWh tells you how FAR you will go. One tells you the size (displacement) of the engine, the other tells you the size of the gas tank!!
      • 11 Months Ago
      Very inaccurate for the Tesla. With the advance battery pack management the battery of a Tesla will retain 80% of the charge after 10 years, at least is what Tesla guarantees, may be the author knows something that Tesla don't
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