Research Papers

Optimal Plug-In Hybrid Electric Vehicle Design and Allocation for Minimum Life Cycle Cost, Petroleum Consumption, and Greenhouse Gas Emissions

[+] Author and Article Information
Ching-Shin Norman Shiau

Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213cshiau@alumni.cmu.edu

Nikhil Kaushal

Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213nkaushal@alumni.cmu.edu

Chris T. Hendrickson

Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213cth@cmu.edu

Scott B. Peterson

Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213speterson@cmu.edu

Jay F. Whitacre

Engineering and Public Policy, and Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213whitacre@andrew.cmu.edu

Jeremy J. Michalek1

Mechanical Engineering, and Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213jmichalek@cmu.edu

A blended-strategy PHEV uses a mix of the electric motor and gasoline engine to power the vehicle in CD mode. We confine our scope to the all-electric strategy for simplicity since blended-strategy operation characteristics are sensitive to control parameters.

AER is defined as energy-equivalent electric propulsion distance for blended-mode PHEVs, but we consider only all-electric PHEVs in this study (8).

This pattern was also observed experimentally by (16).

We model allocation of vehicles to drivers as a dictated assignment based on driver daily travel distance and do not model market mechanisms or consumer choice (17-18). As such, we find the best possible outcome for reducing petroleum consumption, life cycle cost, or GHG emissions, which is a lower bound for market-based outcomes.

We exclude public transportation data and vehicles that traveled zero or more than 200 miles. We fit the distribution to the weighted data of total distance traveled on the survey day.

The deviation between data and the exponential fit in the 0–4 mile region has little effect on base case results because 0–4 mile trips contribute little to the social objectives in this study (the curves in Figs.  555).

Examination of alternative driving cycles and the correlation between driving cycle and driving distance is left for future work.

Simulation results are generally optimistic for all vehicles in that they do not account for factors such as vehicle wear, improper maintenance and tire pressure, aggressive driving cycles, extreme accessory loadings, or terrain and weather variation.

An alternative approach for design optimization with metamodel is the Kriging method (23-24), which is not in the scope of this study.

We truncated acceleration data points greater than 13.0 s to improve the metamodel fit and fit μCD, μCS, and uCS using quadratic terms to avoid overfitting.

Deep discharging cycles may cause power fade in Li-ion battery cell (16), which we ignore in this study.

The regression in Ref. 15 focused on finding the degradation from energy arbitrage, but in this paper the regression variables were chosen to enable predictions about degradation due to driving and recharging. The degradation model is optimistic in that it does not account for temperature and time-based degradation; however, future battery designs will likely have improved degradation characteristics.

The industry standard of defining battery EOL as 80% of initial capacity has less optimistic cost implications for PHEVs. We examine this in sensitivity analysis. See also Ref. 25.

Petroleum makes up less than 1.6% of the U.S. electricity grid mix (27), and we ignore it here.

The life cycle GHG emissions of electricity is estimated based on the average emissions 0.69kg-CO2-eq/kWh of the U.S. grid mixture (29) with 9% transmission loss (30). We examine alternative grid source scenarios in sensitivity analysis for bounding. For a more detailed dynamic forecast of expected future marginal grid mix associated with PHEV charging, see Ref. 28.

We assume that all vehicles must be replaced every 150,000 miles, the U.S. average vehicle life (32). This assumption may be unrealistic for vehicles driven very short or very long daily distances because other time-based factors also play a role in vehicle deterioration. We examine implications in sensitivity analysis.

To obtain a comparable vehicle base cost cBASE for PHEV, HEV, and CV, we use the 2008 Prius manufacturer suggested retail price (MSRP) $21,600 and subtract 20% dealer mark-up (35), $3250 NiMH battery pack (36), $1556 base engine cost, and $1902 base motor cost, in 2008 dollars (14,37), ignoring salvage value (future discounting can make battery salvage value insignificant). The resulting vehicle base cost is cBASE=$11,183. We examine alternative cost models in sensitivity analysis.

Future battery costs are uncertain. The Li-ion battery cost of $400/kW h (38), and the NiMH battery cost of $600/kW h (39) are chosen to represent an optimistic but realistic estimate of near-term battery costs in mass production, and we examine a range of costs in our sensitivity analysis.

The detailed MINLP reformulation is available in Ref. 26 or by contacting the authors. In the discounted cost cases, the integral in the objective function does not reduce to a closed form expression, so we use numerical integration with random multistart approach. Comparisons with known global solutions in Ref. 26 suggest high confidence of global optimality for the multistart solutions.

We use the notation PHEVx to denote a PHEV with an AER of x miles.

For a daily travel distance of 30 miles, about 85% of CV emissions and 75% of electrified vehicle emissions are associated with the use phase, while battery production emissions contribute less than 5% of life cycle GHGs for a PHEV40. These ratios are similar to the findings in Ref. 2.

When driven 30 miles/day, vehicle capital cost is about half of annualized cost of CV ownership, whereas it makes up 90% if driven only 1 mile/day. By comparison, at 30 miles/day vehicle capital cost is about 70% of annualized cost for HEVs and 80% of annualized cost for a PHEV20, with 10% of capital costs due to batteries.

The minimum cost in the three-vehicle case is 0.3% lower than the two-vehicle case, indicating that further vehicle segmentation refinement is of marginal value.

The National Research Council estimated environmental damage costs of carbon emissions as $10–100 per ton-CO2-eq, with a middle estimate of $30 (50), and the Department of Energy projects carbon allowance prices of $20–93/ton from the Waxman–Markey bill by 2020 (51).

The emission factors are at the power plant gate, and 9% transmission and distribution loss to outlet is applied in the PHEV GHG calculations (30).

For comparison, using the most optimistic 2050 emission scenarios in Ref. 28, NPV of CO2 cost savings for PHEVs over HEVs at $100/ton and 5% discounting are around $1100 or about 4.6% of HEV life cycle cost.

We do not account for social costs of petroleum consumption or criteria pollutants here.


Corresponding author.

J. Mech. Des 132(9), 091013 (Sep 20, 2010) (11 pages) doi:10.1115/1.4002194 History: Received December 20, 2009; Revised July 15, 2010; Published September 20, 2010; Online September 20, 2010

Plug-in hybrid electric vehicle (PHEV) technology has the potential to reduce operating cost, greenhouse gas (GHG) emissions, and petroleum consumption in the transportation sector. However, the net effects of PHEVs depend critically on vehicle design, battery technology, and charging frequency. To examine these implications, we develop an optimization model integrating vehicle physics simulation, battery degradation data, and U.S. driving data. The model identifies optimal vehicle designs and allocation of vehicles to drivers for minimum net life cycle cost, GHG emissions, and petroleum consumption under a range of scenarios. We compare conventional and hybrid electric vehicles (HEVs) to PHEVs with equivalent size and performance (similar to a Toyota Prius) under urban driving conditions. We find that while PHEVs with large battery packs minimize petroleum consumption, a mix of PHEVs with packs sized for 2550miles of electric travel under the average U.S. grid mix (or 3560miles under decarbonized grid scenarios) produces the greatest reduction in life cycle GHG emissions. Life cycle cost and GHG emissions are minimized using high battery swing and replacing batteries as needed, rather than designing underutilized capacity into the vehicle with corresponding production, weight, and cost implications. At 2008 average U.S. energy prices, Li-ion battery pack costs must fall below $590/kW h at a 5% discount rate or below $410/kW h at a 10% rate for PHEVs to be cost competitive with HEVs. Carbon allowance prices offer little leverage for improving cost competitiveness of PHEVs. PHEV life cycle costs must fall to within a few percent of HEVs in order to offer a cost-effective approach to GHG reduction.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Battery state of charge characteristics

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Figure 2

Framework of optimal PHEV design and allocation

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Figure 3

Probability density function for vehicle miles traveled per day

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Figure 4

(a) Peterson energy-based degradation model; (b) Rosenkranz DOD-based degradation model

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Figure 5

Optimal two-segment PHEV design and allocations for minimizing petroleum consumption, life cycle cost, and GHG emissions for the base case scenario

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Figure 6

Optimal three-segment vehicle design and allocation for various scenarios. The base case assumes the buy-lease battery scenario, Peterson battery degradation model, $400/kW h Li-ion cost, $600/kW h NiMH cost, $3.30/gal gasoline, $0.11/kW h electricity, average U.S. grid GHG emissions, $0/ton-CO2-eq allowance price, and 5% discount rate.



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