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: Wvehicle = 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

Question

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 $_{vehicle}$ = 920 kg, m = 0.128 Wh/kg · km, and C $_{fixed}$ = $14,000. Lead acid batteries have values of CD = 55 Wh/kg and C $_{battery}$ = $125/kWh. NiMH batteries have values of CD = 80 Wh/kg and C $_{battery}$ = $300/kWh. Wha 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? $^5$

$^5$ Values of cost and charge density data for batteries are taken from Husain (2003).

Accepted Answer

For case (a), EV with 200 km range, from Eq. (13-6b) the weight requirement is

[latex]W_{ ext {battery }}=\frac{R \cdot \mu \cdot W_{ ext {vehicle }}}{(C D-R \cdot \mu)}[/latex] (13-6b)

For Pb: W[latex]_{battery}[/latex] = [200 × 0.128 × 920] / [55 – 200 × 0.128] = 801 kg

For NiMH: W[latex]_{battery}[/latex] = [200 × 0.128 × 920] / [80 – 200 × 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

[latex]T C=C_{ ext {fixed }}+W_{ ext {battery }} C_{ ext {battery }}[/latex]

[latex]=C_{ ext {fixed }}+\frac{R \cdot \mu \cdot W_{ ext {vehicle }}}{(C D-R \cdot \mu)} C_{ ext {battery }} [/latex] (13-7)

For Pb:TC =$14, 000 + 801 kg. $6.88/kg= $19, 511

For NiMH :TC = $14, 000 + 434 kg ⋅ $24.00/kg = $24, 424

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.

Question 13.3: A representative EV can be built with either lead-acid (Pb) ...

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