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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 $0.69 kg-CO2-eq/kW h$ 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.

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