A Case Study of Electric Vehicles

Over at National Semiconductor, we've been working on metrics for measuring and improving the performance to power ratios of our devices.  During some recent meetings I was talking to a colleague about electric vehicles.  The question came up, "if your car doesn't have a fuel tank, how do you measure the MPG (KPL) of the vehicle?" Does the efficiency of the charger affect your mileage? Does the battery replacement cost get included into the cost of the fuel or the cost of ownership?  Here's my take on this - and it makes me think I want a fully electric car - but maybe not yet...

So you are the proud owner of a new "Zolt" (a fictitious car company) "Wunderwatt" (a fictitious automobile) fully electric 4-door sedan.  It came complete with regenerative braking.  You found this "feature" is a bit strange -  when you take your foot off the accelerator pedal, the car immediately starts to slow down - much sooner than a conventional car.  This is due to the motor now running as a generator to charge the battery.  This feature really improves the "time between charges" - a measure of how efficient the automobile is with the energy it stores.  Here are Zolt's specifications for the Wunderwatt:

Battery Capacity: 75 kW-hr (Lithium Ion)
Mileage on a single charge: 400 miles (643 kilometers) - based on non-stop
Time to recharge: 9 hours (110VAC), 4.5 hours (220VAC)
Battery Life: approximately 4 years (degrading from age due to temperature)
Battery Replacement Cost: approximately $5000 US (hopefully less)

To figure out how the charge relates to mileage, we must first calculate the equivalent of the MPG rating - in this case Miles (or Kilometers) per kW-hr of stored energy.  This will be an average based on the car manufacturer's rated distance on a charge, but might actually be lower (or higher due to regenerative braking).  The mileage on a single charge could be calculated by running the motor on a dynamometer at some fixed speed until the battery goes dead.  This is not a real world method, so there needs to be some standard for measuring this value.  To calculate the MPkW-hr you simply divide the total mileage on a single charge by the battery capacity.  In the case of the Wunderwatt, it is 400 / 75 = 5.34 MPkW-hr or 644 / 75 = 8.59 KPkW-hr.  So for each kilowatt-hour of storage you can drive approximately 5.34 miles (8.59 kilometers).

Next, we need to estimate the annual usage of the vehicle.  Most families will average about 15000 miles (24140 kilometers) per year.  This may vary, but it's a number used by many automobile leasing companies for annual usage, so it's probably pretty accurate.  To calculate annual power consumption we simply divide this number by the MPkW-hr (KPkW-hr) number which yields kilowatt-hours consumed by the vehicle.  In our case we get 15000 / 5.34 = 2810 kilowatt-hours which are also the same for metric.  The average US household uses roughly 900 kilowatt-hours per month - so the car uses roughly the same power over a year that an average US household does in 3 months, but there are several other factors we need to consider.

The car does not have a 400 mile long extension cord, it has batteries.  Batteries are not 100% efficient at charging or discharging, so we need to introduce a battery efficiency loss factor - for Lithium Ion, we'll use 0.998 which is negligible and we'll ignore it.  Additionally, the charger is converting line power to charge current.  This process can be anywhere from 70% to 90% efficient (and possibly higher), so let's split the difference at 80% and introduce a charge efficiency loss factor of 0.8.  We now divide the total power used by the vehicle by our loss factor: 2810 / 0.8 = 3513 kilowatt-hours of input energy into the car. 

Now that we have an energy consumption number, the annual "fuel" cost can be calculated.  We simply take the energy consumed and multiply by the cost per unit energy.  For an electricity cost of $0.15 US per kW-hr, we get 3513 kW-hr * 0.15 = $527 annual electricity cost.  Now, your amount may be higher or lower depending on the local cost of electricity.  But there is still another factor, the replacement cost of the batteries - they have a finite lifespan.  The question is whether to include that in the devaluation of the vehicle, the maintenance cost, or the fuel cost. 

If we include cost of replacing the batteries with the fuel cost, then we need to amortize the cost of the battery over the lifespan.  Lithium Ion batteries age - the aging process has been slowed down on modern cells, but due to elevated temperatures in a vehicle (e.g. sitting in a hot parking lot every day), it may only last 2-3 years.  For our Wunderwatt model, the lifespan is specified at 4 years with a replacement cost of $5000 US.  That amortizes out to $1250 per year.  So the total cost of fuel for the vehicle is roughly $1777 annually. 

To compare that with an average gasoline powered sedan that gets 25 MPG (10.6 KPL) we'll need to calculate the fuel cost. Using an average cost per gallon of regular (87 octane) gasoline of $4.00 US (as of June 15th, 2008), the cost of driving the same 15000 miles would be (15000 / 25) * 4.00 = $2400 per year.  This was quite a surprise to me!  Even including the battery replacement cost on an annual basis, driving this mythical electric car is still cheaper than a conventional gasoline powered vehicle.  The overall costs should also be cheaper since there are really no oil changes, fewer moving parts in the electric car and regenerative braking (which was not considered in the mileage of the electric car).

But would I buy this car if it came out tomorrow - the answer is maybe... My perfect electric car would have the performance of a gasoline powered sedan, but use a battery system that does not degrade with time and outlasts the vehicle. There is on-going research in the area of double-layer carbon nanotube supercapacitors.  See this article from Science Daily:
http://www.sciencedaily.com/releases/2005/02/050217224708.htm

The ability to densely pack carbon nanotubes inside these capacitors provides much more surface area to store charge.  They effectively will never wear out and have endless charge-discharge cycles.  Initially these capacitors may find their way into the regenerative braking system to reabsorb as much of the vehicle's kinetic energy and use that for acceleration reducing the size and weight of the on-board batteries. 

The complete equation is shown below in case you want to enter your own values.  If you can think of any additional terms or you have an improved equation, drop me an email or comment here on the blog.  Till next time...

Equation 1 - Electric Vehicle Cost of Ownership 

Where:
- CoO is Annual Cost of Ownership
- Sc is Distance traveled on a charge
- Sa is Distance traveled annually (varies by user)
- Ec is the energy capacity of the battery (usually in kW-hr)
- eff is the charger conversion efficiency
- Ce is the cost of energy (usually in $/kW-hr)

Comments

[Leisa Dreps]

As much as I like to jump for joy about electric cars, I do however feel that saving money should not only be the factor to be considered in this. Yes an electric car could possibly save you a lot of money, versus the gasoline powered engines, but how long does it take to charge their batteries? A good 6 hours or more? That time could have taken you from point A to B, and B to A a couple of times. It is really a good alternative, but making it reliable (like charging locations across the country) could prove to be a challenge.

[Bill]

At last some real facts regarding KWh, charging rates, etc. The real issue is not CO2 emissions but eliminating the ghastly hemorrhaging of the nation's wealth to foreign countries. The constant Amperes needed to recharge an electric car's power plant is significant and I rarely see that addressed, so nice job here. Solar panels available to the public are about 16% efficient so anyone planning to magically charge their car with "clean solar" needs to work night shift and be home during the day, and also have a rooftop of solar panels (NASA's on spacecraft are about 27% efficient, if we ever hit 42% solar panel efficiency in an affordable product THEN we'll be on to something truly significant). One 110W solar panel may provide 12V (17VDC really) at current up to 6 Amps in good sun. Figure the capacity of the auto's power plant, the number of solar panels that would be needed, how expensive they are for the average person and the bottom line is that virtually all the recharging of electric cars will be done from the power grid, requiring significant expansion and consumption of fuels. But! If we replace burning foreign oil in the cars with increased generation of electricity domestically then that will be an immeasurably HUGE boost to the nation's economy.

[Robert LaRue]

The real issue, however, in determining whether to subsidize, promote, or advance EV technology over IC technology, is total greenhouse gas emissions per mile driven.

I have seen no reliable, un-biased data to compare internal combustion vehicles with electric ones. Moreover, such data must compare the hypothetical electric car--not with the average car on the road--but the least CO2 emitting car--whether it be a small diesel engine vehicle, such as are common in Europe, or the hybrid, being touted as the best solution.

I have heard many advocates of EVs talk about how solar or wind electrical generation would make EVs truly ZEVs: however the reality is that--at least here in the US--most of our electricity comes from dirty coal and dirty coal plants. We need reliable figures for how much CO2 is released per kilowatt at the point of fueling the electric car.

My guess is that if we suddenly replaced our most efficient cars with EV's today, the total CO2 emissions would go up, not down.

I'd love someone provide evidence to the contrary. But I suspect it is not forthcoming.

[Jon]

Rick,

Not sure I agree on the global warming issue, but ultimately yes, we need to move on to longer term sources.

The battery is the weak link and the reference you provide is encouraging.

I don't want to limit us to the performance of petrol engines! A 100HP electric motor at all 4 wheels would give me supercar performance with less total HP. 100% torque at 0 RPM.

We do need to start building the nuclear plants and distribution systems necessary to power this. Maybe your SolarMagic boost regulators would do the trick.

[Thiong'o]

Good ideal.
Am so happy to reason from your point of view.
For over ten years I've had this dream of an electrical car.
The main problems I have fore seen are;
-Energy sources and storage.
-Development of an optimum motor that will match the torque of the petro engine.
-Power control and management. etc
My idea was of an electrical car that will be charged via the mains while at rest. It will convert solar energy into electrical, and will use the regenerative braking system in a very smart inteligent way.
Supposing the batteries could be unpluggable such
that we could remove them
at "refilling stations"
With the kind of the nano batteries you mentioned in your articles, then the cost might be unbelievably reduced.
Main challeges for me, have been developing circuits that cordinates the three sources of energy in harmony in order to harness all energy at disposal......
Many ideas I've seen but veiw people to share with.
Opps!!! the worlds petroleum wells are running out, and the ecosystem is yearning for new, nonpolutant livelyhood. Let us work hard to see the electrical car rolling its wheels on the modern roads.....
Too much we can share..

Matthew - Electronics engineering student.

[EnergyZarr]

In response to Darian Smith's comment posted July 5th, I watched both videos on YouTube... very interesting. The only problem I can see with the salt water fuel is that Kanzius doesn't comment on the amount of energy going into the test-tube to produce the hydrogen (if that's what is fueling the fire). It is likely that his radio frequency machine is using much more power spliting the hydrogen-oxygen bonds in the salt water... if that's what's happening - than the amount of energy stored in the hydrogen gas.

Also, hydrogen burns in the presence of oxygen as an almost invisible flame (see: http://www.sti.nasa.gov/tto/spinoff1999/er5.htm). The video clearly shows an orange flame - again interesting. Sodium burns orange, so I wonder if the fuel is something in combination with the sodium... still very interesting.

[Darian L. Smith]

Have you thought about a combination of a scuderi engine and the saltwater fuel of John Kanzius? Another fossil free combination with alot of horsepower.

See Scuderi engine website, and John Kanzius on youtube.

Darian.

[John]

There's an open source study I'm doing relating to home power and local energy storage:

http://www.solarnetwork.net/

which might be another application of such ultracapacitors, if and when they every come out.

[Chuck]

Since you added in the replacement cost of the electric cars battery it would only be fair to add in some of the gas cars extra costs, and some alternatives for the electric costs.

1) Electric Car. You showed $0.15KWhr for the cost of electricity, which is my on peak max rate, how about charging during off peak hours, about $0.05/KWhr
2) Gas Car. 3 oil changes per year, $100 total
3) Gas Car. How about 1 brake job per 30000 miles, say $200/year. Electric just don't seem to use there pads much.
4) Gase car. Raditor flush 30000 miles, say $40 per year

It only make things worse for the gas car.

[Jesus]

Hey Rich ! its great to hear from you and read about all these interesting matters. About this last case I wonder if you have handy the same analysis for hybrid cars?
Thanks !!