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Lithium-ion batteries

A great many things hinge on the properties of lithium-ion batteries, such as:

Among the types of rechargeable batteries, lithium-ion batteries have the largest energy per mass (.8 MJoules/kg) and they dominate the market for phones, laptops, drones, and electric vehicles. Article.

Lithium-ion batteries cost $100 per MegaJoule and the cost is decreasing rapidly. A small electric car battery (50 MJoules) costs $5000.

All lithium-ion batteries contain lithium and world lithium reserves are large enough to supply the world with electric cars. 70% of lithium-ion batteries contain cobalt. Cobalt reserves are in short supply but battery types not containing cobalt exist. Article.

Electric vehicles outperform gasoline vehicles in all ways except range, and if you splurge on the battery you can have the range (plus ludicrous power). Electric vehicles are simpler, cheaper, quieter, and more reliable than gasoline vehicles. Electric motors can be put on anything, such as bikes, kick scooters, and skates. A flying car powered by lithium-ion batteries can fly for 45 minutes and cover 100 km.

Lithium sulfur batteries are a future technology that has a larger energy per mass than existing lithium-ion battery types, and they don't contain cobalt.

For off-grid homes, batteries are ideal for energy storage. Article.

The Tesla Corporation Gigafactory produces 200 TerraJoules of lithium-ion batteries per year, enough to supply 4 million electric cars (each with a 50 MJoule battery).


Lithium-ion batteries

All lithium-ion batteries contain lithium and they can also contain cobalt, manganese, nickel, and aluminum. The battery types are:

Battery   Energy/Mass  Market  Commercialized
 type      MJoule/kg    frac

LiS         1.44       0        Future
LiCoO2       .95       .29      1991
LiNiCoAlO2   .79       .10      1999
LiNiCoMnO2   .74       .29      2008
LiMn2O4      .54       .10      1999
LiFePO4      .47       .22      1996

Lithium-ion battery metal content

1 MJoule battery, lithium content = .023 kg
1 MJoule battery, cost            =  100 $
Typical ecar battery energy       =  100 MJoule
Battery energy/mass               =   .8 MJoule/kg
Battery power/mass                = 1200 Watt/kg
If a battery contains metals in addition to lithium then we calculate the cost of each metal in the table below. We also include the copper conductors. Cobalt reserves are in short supply and the other metals are in abundant supply.
Mass:  Mass of the element in a 1 MJoule battery
Cost:  Price of the element in a 1 MJoule battery
Cars:  # of cars that can be made with the world's reserves

Metal   Mining  Reserves  Cost/kg  Mass  Price    Cars
        Bkg/yr    Bkg      $/kg     kg     $    billions

Cobalt       .12     7     30      .195   5.86      .36
Lithium      .6     30     20      .023    .46    13
Nickel      2.2     78     15      .195   2.92     4
Manganese  18.5    690      2.3    .182    .42    38
Aluminum   58     7000      1.7    .089    .15   278
Copper     18      700      6.2    .12     .74    58

Battery types
              Energy/Mass  Power/Mass  Recharge  Year  Anode  Cathode   Market fraction of
               MJoule/kg    Watt/kg                                     Lithium-ion batteries

Lithium air          6.12               No     Future  Li    O2
Aluminum air         4.68     200       No     1970    Al    O2
Lithium thionyl      2.00     700       No     1973    Li    SOCl2
Zinc air             1.59               No     1932    Zn    O2
Lithium-ion sulfur   1.44     670       Yes    Future  Li    S               0
Lithium metal        1.01     400       No     1976    Li    MnO2
Lithium-ion CoNiAlO2  .79               Yes    1999    Li    CoNiAlO2         .10
Lithium-ion CoNiMnO2  .74    1200       Yes    2008    Li    CoNiMnO2         .29
Lithium-ion CoO2      .70     200       Yes    1991    Li    CoO2             .29
Lithium-ion Mn2O4     .54    1200       Yes    1999    Li    Mn2O4            .10
Lithium-ion FePO4     .47    1200       Yes    1996    Li    FePO4            .22
Alkaline              .40               Yes    1992    Zn    MnO2
NiMH                  .34    1000       Yes    1990    MH    NiO(OH)
Lead acid             .15     180       Yes    1881    Pb    PbO2
NiCd                  .14     200       Yes    1960    Cd    NiO(OH)

Energy storage

Pumped hydro reservoir

The largest energy storage stations are "pumped hydro" stations, where water is pumped to an elevated reservoir when energy is available and returned to the lower reservoir when energy is needed. The cheapest system types are pumped hydro and underground compressed air. For small-scale energy storage such as homes, batteries are the cheapest option. The types of energy storage are:

                   Cost    Cost   Efficiency  Cycles
                   kJ/$   Watt/$

Pumped hydro         26       .7      .8       Infinite    Pump water to an elevated reservoir
Air, underground     60      1.0      .7       Infinite    Compress air
Air, above ground     9       .5      .7       Infinite    Compress air
Battery, Li-ion      10     10        .9       1000
Battery, Lead acid   10     10        .9       1000
Flywheel               .45    .5      .85      Infinite
Gasoline          30000      2.0      .35      -           Using a generator with 2 Watts/$
Solar cell            -       .5      -        -
Wind turbine          -       .25     -        -           Blade diameter = 2.5 meters

The largest energy storage systems for each type of storage are:

                                         GWatt hours

California, San Luis        Pumped hydro    126
Tennessee, Raccoon Mtn.     Pumped hydro     36
Virginia, Bath County       Pumped hydro     31
California, Kern County     Compressed air    3
Alabama, McIntosh CAES      Compressed iar    2.9
Arizona, Solana             Thermal salt      1.7
Spain, Andasol              Thermal salt      1.03
Australia, Hornsdale        Battery, Li-ion    .129
California, Primus Power    Battery, ZnCl      .075
Japan, Hokkaido Project     Battery, Li-ion    .060
China, National Wind        Battery, Li-ion    .036
New York, Beacon            Flywheel           .005

The average American home uses 1400 Watts of electricity. 1 GWatt hour is enough to power 30000 homes for 1 day.

For small scale energy storage such as an off-grid home, a generator can help. They typically cost ½ $/Watt.

Data on cost of energy storage


Home energy system

A house can use either grid electricity, a gasoline generator, or a system of solar cells and batteries. Grid electricity is cheapest, gasoline is slightly more expensive, and solar cells and batteries are much more expensive.

House, electrical power         =  1000 Watts          Typical for a small house
Energy for one day              =    86 MJoules
Li-ion battery Energy/$         =   .01 MJoule/$
Generator efficiency            =    .3
Generator cost                  =     2 Watts/$
Solar cell cost                 =    .5 Watts/$
Solar cell average power        =    50 Watts/meter2
Cost of grid electricity        =    36 MJoules/$
Gasoline energy per mass        =    48 MJoules/kg
Gasoline cost per mass          =    .5 $/kg
Gasoline energy per dollar      =    96 MJoules/$
Cost, 1 year of grid electricity=   870 $
Cost, 1 year of gasoline        =  1090 $              1 year of gasoline to supply a 1 kWatt generator
Cost, 1000 Watt generator       =   500 $
Cost, 1000 Watt solar cell      =  2000 $
Cost, battery, 1 day of energy  =  8600 $              1 Day at 1 kWatt

Battery energy and power

Battery energy is often given in "Watt hours" or "Ampere hours".

Voltage          =  V         Volts
Charge           =  C         Coulombs    (1 Amphour = 3600 Coulombs)
Electric current =  I         Amperes
Electric power   =  P  =  VI  Watts
Time             =  T         seconds
Energy           =  E  =  PT  Joules
                       =  CV  Joules
1 Watt hour = 3600 Joules = 1 Watt * 3600 seconds

1 Amp hour = 3600 Coulombs = 1 Coulombs/second * 3600 seconds

A battery with a voltage of 3.7 Volts that delivers 1 Ampere for 1 hour has an energy of
Energy = 1 Ampere * 3.7 Volts * 3600 seconds = 13320 Joules


Electric vehicles


Battery packs

A single battery is a "cell" and a set of cells is a "pack". Packs are used to multiply the energy and power of cells.

Battery packs are notorous for catching fire, but cell technology has reached the point where it's now possible to make safe battery packs, and the design is simple enough so that anyone can construct their own packs.

Cells can be combined in series and/or parallel. Connecting in series multiples voltage, and voltage is helpful for achieving high power in a motor.

Connecting in series is easier than in parallel. If it's possible to achieve the required power without parallelization then one should do so, and this is usually possible with modern cells.

Series packs have the advantage that the cells can easily be extracted and charged individually, and cells can be interchanged between packs. One can also construct a set of series packs and swap them in like gun clips.

High power electric bikes use a voltage of 72 Volts. If we use one series array of C cells then a pack provides 4440 Watts and 1.2 MJoules. Any electric device requiring less than this much power can be powered by a series pack.

The properties of a modern high-power cell are:

Type         =  "C"
Voltage      =   3.7 Volts
Energy       =  60   kJoules
Power        = 155   Watts
Mass         =  92   grams
Energy/mass  = 650   kJoules/kg
Power/mass   =1680   Watts/kg
Current      =  42   Amperes
Manufacturer = "Basen"
When the cells are connected in series the values for voltage and power are:
Cells   Voltage    Power
         Volts     kWatts

   1      3.7        .15
   2      7.4        .30
   3     11          .45     Electric kick scooter
   4     15          .60
   6     24          .90     Electric bike
  10     36         1.5
  20     72         3.0      Compact electric car
  96    356        15.0      Large electric car

Battery pack strategy

Electric bike motors use either 36, 48, or 72 Volts. The following table shows how to build a battery pack for each motor power.

Power  Volts  Cells  Series  Parallel  Current   Cell      Cell    Cell  Cell  Cell
kWatt                                  Amperes  Amperes  Amphours   $    type  ID#

   .5   36     10
   .75  36     10      10       1         21      25       2.1      4     A    LG HD4
  1.5   48     13      13       1         31      30       2.0      4.5   A    Sony VTC4
  3     72     20      20       1         42      60       4.5      4.5   C    Basen
  6     72     40      20       2         83     120       4.5      4.5   C    Basen
 12     72     80      20       3        167     180       4.5      4.5   C    Basen

Cells     Total number of cells, equal to the number of cells connected in series
          times the number of cells connected in parallel.
Series    Number of cells connected in series. For example, 20 batteries
          with 3.6 volts each connected in series produces a voltage of 72 Volts.
Parallel  Number of cells connected in parallel.
Current   Current required to provide given power
Cell      Maximum current of a cell

History
                  MJoules/kg   Recharge

1932  Zinc air          1.59     N
1949  Alkaline           .59     N
1973  Lithium thionyl   1.8      N
1976  LiMnO2            1.01     N
1989  LiFeS2            1.07     N
1989  Aluminum air      4.68     N
Lab   Lithium air       6.1      N

1881  Lead acid          .14     Y
1901  NiFe               .09     Y
1960  NiCd               .14     Y
1975  NiH2               .23     Y
1991  Lithium-ion        .95     Y
1992  Rechargeable alk.  .4      Y
Lab   Lithium sulfur    1.44     Y

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