The most recent generation of EVs have opted for ac motors due to superior performance. In such a vehicle, the drivetrain consists of a battery bank, a power controller that converts electrical energy from dc to ac, a motor, and a transmission to the driven wheels, as shown in Fig. 13-4. Control over the vehicle is transmitted from the accelerator pedal electronically to the power converter, which then controls the rate of energy flow to the motor. Note that, although not shown in the figure, the EV drivetrain may also incorporate regenerative braking. Instead of dissipating kinetic energy as heat in the brake pads, as occurs in an ICEV, the EV can run the transmission in reverse, using the electric motor as a generator that creates drag on the wheels to slow the vehicle, while at the same time recharging the batteries.
The charge density of the battery technology has a strong influence on the overall range of the vehicle. Charge density can be measured either in terms of energy per unit of weight or per unit of volume. Suppose we take a simplified model of an EV in which charge availability is constant at all states of charge of the battery (i. e., whether full, half-full, and the like) and that the vehicle has constant average energy intensity in terms of the energy required per unit of mass of vehicle moved 1 km. The range R, in km, can be estimated as a function of battery weight as follows:
CD • Wbattoy
M(Wvehicle + ^battery)
where CD is the charge per mass of battery in watthours/kg (or Wh/kg), Wbatter is the mass of batteries in kg, Wvehicle is the mass of remainder of the vehicle in kg, not including the batteries, and m is the energy intensity of the vehicle, in Wh/kg-km (i. e., average watthours of battery capacity required to move 1 kg of the vehicle for 1 km). This equation can be rewritten to solve for Wbattery as a function of range R:
W _ R ‘ M • Wvehicle
‘ W battery (CD – R ‘M)
If we take the fixed cost of the vehicle to be Cflxed before adding the cost of the batteries, the total cost of the vehicle TC can be written as a function of range as shown:
TC _ C + W C
fixed battery battery
R • m • W (13-7)
_ C і r1 f’vehicle C
Cfxed (CD – R • m) Cbattery
from driver (accelerator)
where Cbattery is the unit cost of the batteries in $/kg. The use of these equations to estimate battery requirements and total cost as a function of range is illustrated in Example 13-3.
Example 13-3 A representative EV can be built with either lead-acid (Pb) or nickel-metal-hydride (NiMH) batteries. Regardless of battery type, the vehicle has the following values: W = 920 kg, m = 0.128 Wh/kg-km, and Cfixed = $14,000. Lead acid batteries have values of CD = 55 Wh/kg and Cbattery = $125/kWh. NiMH batteries have values of CD = 80 Wh/kg and Cbattery = $300/kWh. What mass of batteries is required, and what is the total cost, of a vehicle that has a range of (a) 200 km and (b) 300 km?
Solution For case (a), EV with 200 km range, from Eq. (13-6b) the weight requirement is
For Pb: Wbatfeiy = [200 x 0.128 x 920] / [55 – 200 x 0.128] = 801 kg
For NiMH: Wbatteiy = [200 x 0.128 x 920] / [80 – 200 x 0.128] = 434 kg
We can solve for the total cost of the vehicle using Eq. (13-7), or by converting cost per Wh to cost per kg. In the case of lead-acid, the value is (55 Wh/kg)($125/kWh)/(1000 Wh/kWh) = $6.88/kg. Similarly, for NiMH, the value is (80 Wh/kg)($300/kWh)/(1000 Wh/kWh) = $24.00/kg. The total cost of the vehicle is then
For Pb: TC = $14,000 + 801 kg ■ $6.88 / kg = $19,511 For NiMH: TC = $14,000 + 434 kg ■ $24.00 / kg = $24,424
For case (b), repeating the above calculations gives 2128 kg and $28,642 for the EV with lead-acid batteries, and 852 kg and $34,448 for the EV with NiMH batteries.
Discussion The NiMH battery has a large advantage in terms of saving weight, especially at the higher range of 300 km. With the cost figures given, this weight saving does not translate into a cost saving since the NiMH battery cost is also significantly higher at either 200 or 300 km range. However, this cost barrier is not insurmountable: the NiMH technology show promise of dropping in cost with further development, unlike the lead-acid, which is thought to have reached a cost plateau. Thus the results of this example point to emerging battery technologies such as NiMH as a means of developing a more cost-effective high-range EV in the future.
Figure 13-5 shows vehicle range per full charge as a function of battery weight for the vehicle in Example 13-3. At a range of 300 km, the batteries comprise more than 2/3 of the total mass of the vehicle in the case of lead-acid. Note also that this estimate is an optimistic simplification, since increasing vehicle weight by such a large amount will have a multiplier effect in terms of requiring additional strengthening of the vehicle body, a stronger electric motor, heavier brakes, and so on, to be able to support the extra batteries, further increasing weight. For NiMH, the total vehicle weight at a range of 300 km is 1775 kg, versus 3051 kg for the lead-acid.
As discussed in Example 13-3, if the cost of the alternative battery technology per kg is high, its use will reduce vehicle weight but not cost. As shown in Fig. 13-6, the greater charge density does not “break even” in terms of reducing overall vehicle cost until the range of the vehicle reaches approximately 350 km and the cost reaches $43,000. Above this range value, the cost for lead-acid increases rapidly, and the cost curve approaches a vertical asymptote around 430 km range, so that the vehicle cannot achieve this range for any cost.
Figure 13-5 Maximum range for a representative lead-acid battery EV in km on a single charge, as a function of mass of batteries installed.
If EVs capable of intercity travel are to gain a measurable share of the passenger vehicle market in the future, raising charge density and lowering cost per unit of energy storage in batteries, especially by shifting away from lead-acid battery technology to various emerging alternatives, will likely play an important role. Nickel-metal hydride batteries are already in use as secondary battery storage in hybrid vehicles, and some prototype EVs have used lithium-ion batteries with promising results. Costs for both types of batteries are declining, with values as low as $200/kWh reported. Repeating the analysis in Example 13-3 with either NiMH or lithium ion at this cost per kWh gives total cost values of $20,950 and $27,632, respectively, a much improved cost figure for
200 О О 1“
Growth in U. S. annual hybrid vehicle sales, 1999 to 2006.
the vehicle. Note that these figures should be interpreted carefully, since they do not take into account the full detail of how vehicle design affects overall cost.
Increasing production and economies of scale may help the new battery technologies as well. The Tesla roadster is projected to have a range of 320 km (200 mi) per charge, using lithium-ion batteries. Although this vehicle is aimed at the upper end of the car market due to its $100,000 price tag, the combination of R&D experience and economies of scale if demand rises may lead to cheaper lithium-ion-based EVs in the future.