Electrical Power
The flow of electricity can be thought of as similar to the flow
of liquid in a hose, where voltage is the amount of pressure and
current is the rate of flow. Bigger hoses have less resistance,
so more liquid will flow for a given pressure. Similarly in electronics,
lower resistances result in higher current flow at a given voltage.
The relationship between voltage, current and resistance is known
as Ohm's law, as follows:
Voltage = Current x Resistance
or V =
IR |
The amount of electrical power flowing through a circuit is simply
the product of the voltage times the current:
Power = Voltage x Current
or P = VI |
Substituting in ohm's law into the second equation, we can see
that the power lost by a circuit is equal to its resistance times
the square of the current:
This is important because in the case of a motor, doubling voltage
results in twice the current flow, so power is increased by a
factor of 4. But power loss (usually in the form of heat) also
increases by a factor of 4 as well.
Energy Storage
Batteries typically express their capacity in Amp-Hours (Ah). For
example, if a battery is rated to 100Ah, it means you can draw
100 amps from it for 1 hour before it goes flat. Double the current,
and it will take half as long to go flat, etc.
Sometimes you will come across C ratings for batteries, particularly
referring to discharge rates. C simply represents the capacity
of the battery in Ah, so if a 100Ah battery is rated to 5C, it
means you can draw a maximum of 500 amps from it.
Sometimes it is more useful to consider a battery's capacity in
watt-hours, since it is more representative of the actual stored
energy. To calculate this, simply multiply the amp-hour rating
by its nominal voltage. To convert watt hours to joules, multiply
by 3600 (the number of seconds in an hour, since 1 watt = 1 joule
per second).
Aerodynamic Drag and Rolling Resistance
The amount of power a vehicle needs in order to travel at a given
speed can be approximately calculated by adding the aerodynamic
drag and rolling resistance. Aerodynamic drag may be calculated
using the following formula:
Pdrag
= 0.5 ρ Cd A V³ |
|
Pdrag = aerodynamic drag
ρ = density of air, 1.2 kg/m³
Cd = coefficient of drag
A = frontal area of vehicle, in m²
V = velocity of vehicle, in m/s |
And rolling resistance may be calculated as follows:
Prr
= V Crr g m |
|
Prr = rolling resistance
V = velocity, in m/s
Crr = coefficient of rolling resistance
g = gravitational constant, 9.81 m/s⊃
m = mass of vehicle, in kg |
For example, at 60km/h (16.7m/s) a compact 1000kg vehicle with
good tires will have
- Aerodynamic drag of 0.5 x 1.2 x 0.3 x 2 x 16.7³ = 1676W.
- Rolling resistance of 16.7 x 0.01 x 9.81 x 1000 = 1638W
So, total power required to maintain the vehicle's speed at 60
km/h is about 3.3kW, or 4.4 hp. The other factor to consider is
transmission losses, which is typically between 10% (direct drive
setups) to 30% (such as all wheel drive vehicles).
Vehicle Efficiency
The efficiency of an electric vehicle is usually measured in watt-hours
per km (or mile), i.e the average amount of energy required to
drive the car a given distance.
A typical EV might have a 15kWh pack (1C rating), and have a 100
km range. Therefore it has an efficiency of 15000/100 or 150wh/km.
Highly efficient vehicles may go as low as 100wh/km. Larger vehicles
such as SUVs may be as high as 400wh/km. Aerodynamic drag and
rolling resistance (see above) are the primary factors influencing
this.
Wire Gauge Information
Most electrical wire/cable used for the power lines in EVs is rated
by the American Wire Gauge, or AWG. The most common size used
is 2/0 from battery to speed controller and 4/0 from speed controller
to motor, though of course requirements will vary depending on
the system's specifications. The table below outlines the specifications
of the larger cable gauges. Note that current ratings are continuous,
cables can usually withstand much higher currents for short periods.
| AWG |
Diameter
(mm) |
Turns of wire
per cm |
Area
(mm²) |
Copper Resistance
(ohms per km) |
Copper wire
current rating
with 60 ƒC insulation |
| 000000(6/0) |
14.73 |
0.68 |
170 |
0.10 |
400A |
| 00000(5/0) |
13.12 |
0.76 |
135 |
0.13 |
300A |
| 0000(4/0) |
11.68 |
0.85 |
107 |
0.16 |
250A |
| 000(3/0) |
10.4 |
0.96 |
85 |
0.2 |
200A |
| 00(2/0) |
9.266 |
1.08 |
67.4 |
0.25 |
160A |
| 0(1/0) |
8.251 |
1.21 |
53.5 |
0.33 |
130A |
| 1 |
7.348 |
1.36 |
42.4 |
0.4 |
110A |
| 2 |
6.544 |
1.53 |
33.6 |
0.5 |
95A |
| 3 |
5.827 |
1.72 |
26.7 |
0.65 |
85A |
| 4 |
5.189 |
1.93 |
21.2 |
0.8 |
70A |
|
 |
Sections
Units
| Metric |
Symbol |
Unit |
| Voltage |
V |
Volts, V |
| Current |
I |
Amperes, A |
| Resistance |
R |
Ohms, Ω |
| Power |
P |
Watts, W |
| Energy |
E |
Joules, J |
| Capacitance |
C |
Farads, F |
| Inductance |
L |
Henry, H |
Unit Converter
|
