A plug-in hybrid has a fuel economy of 20 km/L (47.3 mpg) when running on gasoline, and is able to travel 8 km (5 mi) on 1 kWh of charge. Its range on a full charge is 80 km (50 mi), before it begins to use the ICE. Gasoline costs $0.79/L ($3.00/gal) and electricity costs $0.12/kWh. Over a

Question

A plug-in hybrid has a fuel economy of 20 km/L (47.3 mpg) when running on gasoline, and is able to travel 8 km (5 mi) on 1 kWh of charge. Its range on a full charge is 80 km (50 mi), before it begins to use the ICE. Gasoline costs $0.79/L ($3.00/gal) and electricity costs $0.12/kWh.

Over a two-week period, the vehicle accrues the following distance of travel each day:

Day	km	Day	km
1	60.8	8	182.4
2	27.2	9	144
3	105.6	10	33.6
4	22.4	11	38.4
5	62.4	12	70.4
6	72	13	25.6
7	427.2	14	52.8

Thus days 7 to 9 involve an extended intercity trip, and the other days involve driving in and around the vehicle’s home base. Assuming that the vehicle has access to recharging each night, and that it only recharges the amount necessary to offset the kilometers traveled that day, calculate (a) the effective fuel economy, (b) the energy cost per km (for combined electricity and gas), and (c) the energy cost per km if it were only a hybrid with no plug-in capability.

Accepted Answer

For each day, we subtract off 80 km of driving, and if there is a positive amount remaining, assign it to ICE propulsion. Thus on day 1, there is 0 km ICE use, and the vehicle uses (60.8)/ (8 km/kWh ) = 7.6 kWh of electricity that must be recharged the following night; on day 3, 25.6 km
are powered with the ICE, consuming 1.3 L, and so on.

(a) On the basis of this type of daily calculation, in total 1325 km (828 mi) are driven in two weeks, of which 539 km (337 mi) require the use of the ICE. At the given fuel economy of 20 km/L, the fuel consumed is 27 L. Thus the (effective) fuel economy is (1325 km)/ (27 L) = 49.1 km/L (116 mpg).

(b) At the given cost, 27 L of fuel cost $21.37. The remaining 786 km (491 mi) are driven using electric power, requiring 98.2 kWh of electricity, which costs $11.78. Thus dividing the total $33.15 of energy cost among the total distance driven gives $0.025/km ($0.04/mi).

(c) Assuming that the gasoline-only HEV achieves the same 20 km/L fuel economy over the entire distance traveled as does the PHEV when driving on gas, the fuel consumption is 66.2 L (17.5 gal), which costs $52.50. Dividing energy cost by distance driven gives ($52.50)/ (1325 km) = $0.04/km ($0.063/mi).

Discussion The treatment of fuel economy in this example is simplistic, because, depending on the design of the specific PHEV drivetrain, the drive controller might occasionally activate the ICE while there is still charge in the secondary battery, in order to deliver sufficient total power for hard acceleration or climbing a grade. However, inclusion of this level of detail would likely not lead to a dramatic change in the results, so that the overall fuel economy would still exceed 42 km/L (100 mpg).

The focus on gasoline consumption as the figure of merit in this example stems from the concern about volatility of gas prices at the pump, and about energy security in countries such as the United

States that depend heavily on imports. A more complete comparison of the HEV versus PHEV would take into account the total energy consumption for both gasoline and electricity, and the total CO[latex]_2[/latex] emissions. In some circumstances, a PHEV might save gasoline but increase energy and CO[latex]_2[/latex]. The comparison in this case is left as an exercise at the end of the chapter.

Question 13.4: A plug-in hybrid has a fuel economy of 20 km/L (47.3 mpg) wh...

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