An Electric Car: The Batteries

Safety First!

I designed the battery manager for the leading software supplier in the mobile phone business. The most important message I got from all that time was that batteries are dangerous! The example here - a mobile phone battery - will have less than a thousanth of the energy of an automotive traction battery. The comparison is with petrol tanks: the story is about equivalent to someone who had an accident with lighter fuel.

There is no way to say this enough: automotive traction batteries contain the same energy as the gas tank of a conventional car, and poor design or misuse will result in that energy being released in bad ways. That energy is generally stored in the form of corrosive acids and alkalis, poisonous metals, and other reagents many of which are highly inflammable. These batteries will spill if they are turned over, and the acid will do something to the bodywork of the car or the passengers rather like the film Alien.

I am not going to take responsibility here. You must do that yourself. If you don't, you may kill or maim yourself, your passengers, and a lot of innocent people.

Maybe you think you can find some junkyard dog lawyer who will push you into court in your wheelchair and explain that you killed a busload of people because of something you downloaded off the Internet. Maybe you're right. But most likely you'll be laughed out of court. The responsibility lies only with you.

Battery Theory

Battery Units

Most batteries have their capacity measured in units of Amp-hours, or Ah. The definition of an amp-hour is the discharge capacity times the time - normally over ten hours, but sometimes over three hours. So if a battery delivers 5.5A for 10 hours, its capacity is 55Ah at the ten hour rate; if another battery delivers 50A for 3 hours, it's capacity is 150Ah at the three hour rate.

When dealing with batteries, the manufacturers often talk about currents as a fraction (or multiple) of some constant value 'C'. C is simply the current in amps that equals the capacity of the battery in Ah. So a battery discharged at the 10-hour rate is measured at a current of 0.1C, and a battery discharged at the 3-hour rate is discharged at a current of C/3.

In our designs we are interested in the energy stored in a battery. We normally use kilowatt-hours, or kWh. The naive way to estimate this is to multiply the Ah figure by the nominal battery capacity in kV: so a 55Ah battery at a nominal 12v stores 0.66kWh; a 150Ah battery at a nominal 3.6V stores 0.54kWh. This is only an approximation, of course - to get an accurate figure the current must be integrated over the discharge voltage of the cell.

We use kWh because they are the units that are provided by electricity suppliers; and because a kWh is a sensible unit for the amount of stored energy used by a car - similar in energy terms to about 2/3 a litre (1/7 of an Imperial gallon, or a bit more than a pint) of petrol.

Peukert's Number

Discharge capacities are generally quoted for a 20-hour discharge, and discharging in one hour often results in 40% of the battery capacity being lost. This is a function of Peukert's Number. Here is a manufacturer's graph, for a lead acid leisure battery:-

Elecsol battery characteristics

Battery discharge currents and lifetimes can be modelled using something called Peukert's Equation. That looks like this:-

C = InT

where
C = amount of capacity removed
I = discharge current
n = Peukert's Number - a constant for the battery
T = discharge time

If Peukert's Equation is used for two discharges, the two answers can be plugged into this equation to give a value for Peukert's Number. Rearranging the above equation for two discharges gives:-

 (log(T2) - log(T1))  =n
 (log(I1) - log(I2))

Taking two points on the above graph, the 5A/20C point is 5A for 20 hours; and the 100A/20C point is 100A for about 40 minutes. Plugging T2=40mins, T1=60x20mins, I1=5A and I2=100A into the above equation gives a value of 1.135 for Peukert's Number at 20C.

It can also be seen that Peukert's Number is affected by temperature: it is also affected by battery wear.

To calculate the efficiency of a battery using Peukert's Number and the current used:-

E=I1-n

This calculation can be applied to both charging and discharging currents.

Here is a table of Peukert's Number against battery efficiencies:-

Peukert's Number Efficiency at 25A Efficiency at 45A Efficiency at 85A
1.5 20% 15% 11%
1.25 45% 38% 33%
1.2 53% 48% 41%
1.15 62% 57% 51%
1.1 72% 68% 64%
1.05 85% 83% 80%
1.02 94% 92% 91%
1 100% 100% 100%

Fuel metering

The perfect fuel meter for an electric car would read the amount of available charge in the battery measured in kWh. Since this is a unit of energy, what pushes the car down the road, this figure may be used to predict range available for a journey, in much the same way as for a petrol car. This is especially important for electric cars, as generally only one refuelling point is available.

Accurate fuel metering in practical batteries has a major problem: it can only be done under very specific conditions. For most battery chemistries (the obvious exception is nickel-cadmium and similar cells) the battery fuel level as a percentage may be accurately determined by measuring the off-load voltage, after the cells have had a while to rest and depolarise. Unfortunately, this means that this reading cannot be obtained unless you stop and park for an hour or so.

The other method of fuel metering is current integration. If the current is integrated over time (adjusted using Peukert's Number) then the total amount of charge (in Ah) can be calculated. If the battery's capacity and initial condition are both known, then by calculating the amount of current that has been removed, (and, if partially charged, how much has been added) we can calculate how much remains. Unfortunately to do this we also need to know the usable capacity - something that tends to drop over the life of the battery.

The most practical arrangement is to use off-load voltage to calculate the percentage available in the battery when the vehicle has been parked for a while, and to use current integration from fully charged to give the amount available in Ah, and so in kWh. From comparing these two the total capacity of the battery may be calculated.

So if, for example, a car with a fully charged but rather worn 24kWh battery is driven 30 miles, consuming 6kWh, and parked for an hour. The battery voltage is measured after the hour, and discovered to represent a 33% discharge. So at this point 6kWh = 33%, the total capacity of the battery is 18kWh, and 12kWh remains. If the fuel gauge is supposed to read "full" at 24kWh, the needle should point at the 1/2 position on the gauge. If the car is driven for another 9kWh, during this journey the fuel gauge should drop from 1/2 to 1/8. If the vehicle is now charged again, even when the battery is fully charged its fuel gauge should not read more than 3/4, since the battery capacity is really only 18kWh. This trend of the fuel gauge getting lower and lower on full charge is a sign of battery wear and should indicate eventally that the battery needs replacing.

This fuel gauging method has the advantage that the driver is unlikely to get nasty surprises, but it does require that information about the battery's history is kept in non volatile storage - and that the battery meter system wakes up every few minutes to measure the off-load voltage of the battery.

Charging

Generally batteries are charged in two stages: first there is a bulk charge which is as rapid as possible consistent with the battery limits and the available power; then there is a finishing charge stage, which depends a lot on the battery technology. For some cells and some conditions (particularly extremes of temperature or very deep discharge) an initial charge regime may be required.

The initial charge is normally a low constant current, to give the battery a chance to recover from abuse, or more normally to allow the temperature to return to the limits for bulk charging. On cold days the current will warm the cells, but if the battery is very hot it will allow some heat to be lost. Until the conditions for bulk charge (or finishing charge) are attained, this charging will be continued.

The bulk charge is normally done if the battery is less than 80% charged (although levels vary, so consult the specs). There is normally a limit for bulk charging in terms of temperature - the temperature must fall within certain limits. The bulk charging limits are what are used for regenerative braking, so if the battery contition is not suitable for bulk charge, regenerative braking must use a protective shunt resistor to absorb the current. The maximum level of regenerative braking must be set to the maximum bulk charging rate - typically from 0.3C for lithium batteries to 1.0C for lead acid.

The finishing charge is generally very specific to the battery technology and critical for obtaining good cycle life. It should be re-designed for each battery type: variations include constant current, constant voltage or pulsed current. The decision of when to terminate finishing charge is also important: variations include zero delta voltage, zero current at constant voltage, or simply a current-time-product. These must be designed with the data for your chosen cells.

Operation limits

The batteries under consideration have several limits which define their use in an electric vehicle. These limits are: weight; voltage; peak power; continuous power; and capacity.

Weight and capacity are the obvious ones to consider. Unless the battery is capable of delivering the power without overloading the vehicle, range will be low. Even if the vehicle is not actually overloaded by the batteries, if it is close to the limits then performance will suffer. Obviously capacity and weight interrelate - add more of one and you get more of the other.

Voltage is needed because most motors relate speed to voltage. If the voltage delivered by the batteries is less than the motors expect, then the motors will not rotate as fast as they should, and the vehicle will be slow. If the batteries deliver just enough voltage for the top speed when fully charged, then as they discharge the top speed will drop.

Peak power is needed to accelerate and to climb hills. Generally peak power limits arise out of the effect of high current flows on internal components of the battery: there may be unexpected chemical effects, or even mechanical degradation of the electrodes by high current effects. Exceeding the peak power of a cell is likely to shorten its life.

Some cells will deliver peak power and no more. If they have a high internal resistance, drawing more current simply results in less voltage. In a car implemented with cells of this type, a heavy right foot might not damage the cells, but might not deliver much acceleration either.

Continuous power matters for motorway driving. Power is mainly related to air resistance, and air resistance goes up as the square of speed. A battery with good peak power delivery but poor continuous power delivery may allow the car to reach 100mph, but for any reasonable distance only 60mph might be used. Typical effects of exceeding continuous power limits will be overheating of the cells. For this reason, a temperature gauge in the battery packs is vital.

Battery Technologies

Battery technologies are discussed on individual pages, but here is a table with a summary:-

Chemistry Wh/Kg
theoretical
Wh/Kg
practical
Efficiency price Cycles Lifetime
(years)
Hazardous? Poisonous? Environmental
Lead Acid 128.8 63.2 49% competitive
very cheap surplus
300-500 10-15 corrosive:sulphuric acid sulphuric acid, lead salts lead
Nickel Cadmium 194.0 38.7 20% high 800-1000 20-50 corrosive: potassium hydroxide cadmium cadmium
Nickel Iron 233.3 52 22% ??? >2000 >80 corrosive: potassium hydroxide - -
Nickel Zinc 318.6 51 16% high 500 10 corrosive: potassium hydroxide zinc zinc
Lithium ion ??? 130.9 ??? high 500 5 flammable:lithium lithium lithium

The theoretical figures are for a cell consisting of nothing but active materials. Small differences between theoretical and practical figures imply that future technology will not improve so much.

Hazards that are underlined are particularly severe.

Quick Battery Design

Practical Batteries

Manufacturer Part Chemistry Voltage Capacity Weight(kg) Dimensions(mm) Peak Power Continuous Power Cost Cycles Peukert Number Energy Weight
Wh/kg
Wear Cost
(per kWh per cycle)
Notes
Theoretical Reagents Only Nickel Zinc 1.7 26.8Ah
45.6Wh
0.143kg - 161W 32W - 800-1000 - 318.6 - 1 mole of electrons
Theoretical Reagents Only Nickel Iron 1.2 26.8Ah
32.2Wh
0.138kg - 161W 32W - 2000 - 233.3 - 1 mole of electrons
Theoretical Reagents Only Nickel Cadmium 1.2 26.8Ah
32.2Wh
0.166kg - 161W 32W - 800-1000 - 194.0 - 1 mole of electrons
Thunder Sky LP9393A Lithium Ion 2.6-4.3 (nom. 3.6) 160Ah @ 3.6v
576Wh
5.5kg 145x62x230 720W (900W) 120W $250.00 500@80%
1500@50%
1.016 130.9 $0.87
$0.46
Experimental
Theoretical Reagents Only Lead Acid 2.0 26.8Ah
53.6Wh
0.416kg - 670W 26.8W - 500 - 128.8 - 1 mole of electrons
SAFT VL_2P3S Li-ion 10.8 84Ah@3hr
907.2Wh
8kg ?x?x? ??? ??? ~€2200 1500 ??? 113.4 ~€1.62 about 30p a mile!
Valence Technology Saphion U-Charge Lithium Ion 12v nom. 45Ah @ 12v
461Wh
7kg 197x132x186(U1) 1200W 1200W ??? 2000@80%
1.036 66 ??? Lead Acid Replacement
Elecsol 80/100 Lead-acid
carbon fibre
12 100Ah
1.2kWh
19kg 277x175x190 ??? ??? £84.00 500 1.15 63.2 £0.14 May suffer on >50% discharge
Flooded
Trojan 27TMH Lead-acid 12 115Ah
1.38kWh
26.4kg 324x171x248 ??? ??? £105.00 500 1.22 52.3 £0.15 flooded
Eagle-Picher ??? NiFe 6.25 200Ah
1.25kWh
24.1kg 261x181x249 6.3kW? 1300W(1h rate) $284 >2000 1 52 <$0.11 Reconditioned
Evercel MB-100 Nickel-Zinc 13.2 85Ah
1.122kWh
22kg 298x171x225 6.6kW 3.3kW $350 300
2000@40%
1.04 51 $1.04
$0.39
Capacity at 3C rate
Low toxicity
may be discontinued
Optima D34 Lead-acid AGM 12 55Ah
0.492kWh
19.5kg 254x173x199 8.7kW
870A@10v
8.7kW
870A@10v
$143.00 350
700
3400@30%
1.04 33.8 $0.48
$0.24
$0.16
See advanced charging
Optima 31 Lead-acid AGM 12 70Ah
0.84kWh
27.2kg 326x165x242 10.125kW
1125A@9v
10.125kW
1125A@9v
?? 350
700
3400@30%
1.04 33.8 $0.48
$0.24
$0.16
See advanced charging
Hawker SBS SBS-60 Lead-acid AGM 12 51Ah
0.612kWh
18.5kg 220x121x260 4.5kW@10v 441W(1h rate) £43.95 400? 1.18 33.1 £0.18 Bargain basement battery
Exide Marathon T12V100 Lead-acid AGM 12 100Ah
0.612kWh
37.5kg 548x115x230 10.8kW@6v 840W(1h rate) £12.00 (eBay) 400? 1.20 32 £0.025? Surplus stock
Hawker Odyssey PC1700 Lead-acid AGM 12 70Ah
0.84kWh
27.2kg ?x?x? ??? ??? $200 400 1.06 30.9 $0.60 Good Peukert - lots of lead!
Suntopway TN60 NiFe Pocket Plate 1.25 60Ah
0.075kWh
3.1kg dry 134x70x280 375W? 75W(1h rate) ??? >2000 1 24 (dry) ???  

Practical Battery Packs

These are figures for battery packs aimed at about the 60v-75v mark, and incorporating around 200kg-250kg of batteries. Here are the cheapest; the best power; the best range; and the best for the environment.

There is also a Utopian battery, which might be a felt electrode nickel-iron unit.

Technology Manufacturer Part Quantity Nominal
Voltage
Discharged
Voltage
Charged
Voltage
Weight Peak Power Nominal Capacity 1h Energy 3h Energy Price Price/kWh cycle
at 1h rate
Notes
Nickel Iron Felt Electrode I wish Utopia Cell 60 75v 60v 99v 225kg 75kW 400Ah 30kWh 30kWh £1500 $0.025 Fantasy Battery
Theoretical Performance
Lithium Ion Thunder Sky LP9393A 40 (2x20) 72v 56v 86v 220kg 36kW 320Ah 23kWh 23kWh $10,000 $0.87 Best range
Nickel Iron Eagle-Picher ??? 10 63v 50v 83v 241kg 63kW? 200Ah 13kWh 13kWh $2840 <$0.11 Best Environment
Lead Acid AGM Optima D34 12 (2x6) 72v 57.6v 96v 234kg 104kW 110Ah 5.4kWh 6.9kWh $1,716 $0.45 Best power
Lead Acid AGM Exide T12V100 6 72v 57.6v 96v 225kg 65kW 104Ah 4.7kWh 6.0kWh £72 £0.02 Best Price

Conclusions

The best option is the Optimas - more or less what the whole EV community agrees on. If we could get the Thunder Sky lithiums for a better price, they'd be a winner. But the whole EV community is waiting for the price of lithium batteries to drop.

One thing that may be attractive about the Thunder Sky batteries is the relative weight. Less weight means more acceleration, and by giving up the prodigious range of the lithium batteries the motor and battery can end up weighing much less than the equivalent ICE powerplant. That means ground rockets...

What is clear is that range is going to be strongly influenced by driving style: between 65mph and 75mph there is a loss of 20%-30% of range caused by drag and by Peukert's Number.

What that also implies is that having a power meter is a really important part of good driving style: the rev counter really ought to be converted into a power meter, and efficiency (a function of power and of Peukert number) needs to be on the scale.


This page is part of an Open Source Electric Car Project, and is written and maintained by Simon. At this stage these pages are constantly under revision. Thoughts and comments are welcome.