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An energy reallocation model for estimation of equivalent greenhouse gas emissions of various charging behaviors of plugin hybrid electric vehicles.


This work presents a modeling approach for estimation of the equivalent greenhouse gas (GHG) emissions of plugin hybrid electric vehicles (PHEVs) for real driving patterns and charging behaviors. In general, modeling of the equivalent GHG for a trip made by a PHEV not only depends on the trip trace in question, but also on the electric range of the vehicle and energy consumption in previous trips since the last charging event. This can significantly increase the necessary computational burden of estimating the GHG emissions using numerical simulation tools, which are already computationally-expensive. The proposed approach allows a trip numerical simulation starting with a fully charged battery to be re-used for GHG estimation of a trip that starts with any initial state of charge by re-allocating the appropriate amount electric energy to an equivalent gas consumption. Thus, the proposed approach allows modeling of many charging behaviors with minimal additional computational effort beyond one numerical simulation for each drive trace. Validation of the proposed approach is established through comparative simulations using 1012 trip traces, where the error in estimated fuel consumption was less than 3% in most simulations. The full set of trip traces in California Household Travel Survey (CHTS) were then analyzed for the two PHEV models (with short and long electric range), for different charging behaviors and grid conditions.

CITATION: Hamza, K. and Laberteaux, K., "An Energy Reallocation Model for Estimation of Equivalent Greenhouse Gas Emissions of Various Charging Behaviors of Plugin Hybrid Electric Vehicles," SAE Int. J. Alt. Power. 5(1):2016.


Electrified powertrain vehicles have a key role to play in the reduction of global greenhouse gas (GHG) emissions according to several studies that follow and their market predict penetration [1,2,1]. These powertrains include plugin hybrid vehicles (PHEVs) which have an internal combustion engine (ICE), a battery and an electric drive, as well as battery-electric vehicles (BEVs), which have no ICE. A distinction is made between regular hybrids (HEVs) which have a relatively small battery and no electrical charging outlet, and plugin hybrids (PHEVs) have a charging outlet and a larger battery that can be electrically charged to propel the vehicle for a certain range with no/minimal reliance on the ICE. Electrified powertrains have two main advantages that allow for reduction of GHG emissions compared to conventional vehicles (CVs) that only have an ICE: i) energy consumption in the electric drive being fairly resilient to stop-and-go driving, and ii) consumption of electric energy that comes from the grid (PHEVs and BEVs), which can have cleaner sources than gasoline as the electric grid gets greener. With the initial cost of PHEVs being higher than CVs and HEVs and their lifecycle returns in terms of fuel savings somewhat uncertain to owners, economic incentives [4,5,6,7] have been in place to encourage their adoption. However, analysis of the societal benefits of PHEV incentives in terms of reducing GHG emissions (measured in kilograms of C02-equivalent) can be a complex task.

A number of numerical simulation tools (both proprietary and public-domain) are available, which have the capability to provide reasonable estimates of the energy consumption of various vehicle models for arbitrary speed traces, e.g. obtained from onboard devices in real vehicles monitored during travel surveys. However, such simulations are often computationally expensive. In order to gain insight to the GHG reduction benefit from HEVs, PHEVs, and BEVs as compared to a CV, it is possible to run the numerical simulation models for a sufficiently large/representative sample of trip speed traces collected in travel surveys, but such a simulation task requires large-scale computational capability, even for "single-mode" powertrains (CVs, HEVs and BEVs), which utilize a single "fueling" system (gas or electricity). Modeling of the equivalent GHG for PHEVs is even more challenging because of the "dual-mode" of operation depending on the initial state of charge (SoC) of the vehicle battery. In charge-depletion mode, the PHEV relies primarily on battery-stored electric energy (which came from the grid). On the other hand, in charge-sustaining mode, the vehicle relies on gasoline (or any other fossil fuel). Thus, in order to properly simulate the equivalent GHG of a trip made by a PHEV, one must also keep track of energy consumption by the vehicle in previous trips since the last charging event [8]. Complicating the simulation of PHEVs further is the fact that different charging behavior (e.g. overnight only, before every trip, etc.) also impacts the balance of charge-depletion and charge-sustaining modes, a topic this paper directly addresses. Moreover, as the grid gets greener (less equivalent CO2 per kWh), the electric GHG emissions of the PHEV are reduced, but its gas emissions remain largely unchanged. Thus, the grid effect not only shifts the average GHG per mile change, but also morphs the overall vehicle profile of the GHG emissions.

Notable work in the literature on the modeling of electrified powertrain vehicles include the work of Lee et al. [9] which focused on modeling of the electrified power train. Later studies in [10,11,12] introduced simplified models for prediction of lifecycle cost and environmental impact. Optimization of usage, charging patterns and infrastructure layout were examined in [13,14,15,16,17]. Because the driving conditions can have significant effect on lifecycle economics and GHG emissions, detailed models of GHG performance were considered for different standard drive cycles [18,19,20]. Previous work by the authors [21] included large-scale simulations to estimate the energy consumption for various single-energy-input vehicle models (i.e CVs, HEVs, and BEVs) for real driving patterns encompassing all the speed traces of recorded vehicle trips in the California Household Travel Survey (CHTS) data set [22]. However, the simulations for PHEV models were not included, since examining the equivalent GHG for different charging patterns and grid greenness would require multiple repetitions of the large-scale simulations, which the authors deemed prohibitively expensive from a computational resources standpoint. The later sections of this paper propose and validate an "Energy reallocation model", which provides a much-reduced computational cost in simulating PHEVs under various charging behaviors. Specifically our proposed method requires only a single GHG simulation for any given PHEV model and speed trace, using a fully charged battery at the beginning of each trip. Then, if a different charging behavior needs to be modeled, our method calculates an equivalent amount of gas consumption based on the history of previous trips since the last charging event. This in turn allows for the goal of the work to be realized; simulation of multiple charging behaviors and levels of grid greenness, for different PHEV models.

This paper started with a motivation and brief review of relevant work in the literature. The rest of the manuscript is organized as follows: Next section presents an overview of the proposed energy reallocation model for estimation of equivalent GHG of PHEVs. Models for commonly-expected charging behaviors are presented next, which is followed by a verification study of the proposed model. Lastly, the GHG footprint of different range PHEVs for different charging behaviors and levels of grid greenness is briefly examined.


Large-scale simulations of 18 different vehicle models were conducted by the authors in previous work [21] using the publicly available software: Future Automotive Systems Technology Simulator (FASTSim), which is developed and maintained by NREL [23]. The simulations included all of the available vehicle trip traces in CHTS data set (65,652 trips by 2910 vehicles), and were conducted on a Windows Azure Platform [24]. Computational resources utilized were approx. 5400 CPU-hours (fifteen parallel processes running for approx. two weeks). Additional models are now considered for PHEVs (as pre-modeled in FASTSim) with nominal all-electric range of 10 and 40 miles, which will be termed PHEV10 and PHEV40 respectively.

Our simulations show that--at levels of GHG-equivalent per kWh corresponding to US national grid average or lower--a PHEV that starts each trip with a fully-charged battery obtains its lower bound for the minimum attainable GHG for that trip. However, experience and intuition suggest that a full charge before every trip is not typical for many PHEV drivers. Without our proposed energy reallocation model, in order to obtain more realistic estimates of the GHG emissions, FASTSim simulations would need to be repeated at different states of the battery at the beginning of each trip depending on the battery state in the previous trip, and whether or not the vehicle performed any charging in between the trips. Computational resources required to examine multiple driving and charging patterns using such an approach can be very large. Instead, a simplified model is proposed by the authors. This model, which is validated in a later section of the paper, leverages the fact that, whether delivered by an electric or gas powertrain, the energy delivered to the wheels of the vehicle for a specific portion of a trip is nearly the same. As such, we present a vehicle-specific process whereby the electric energy consumed for a given portion of a trip is converted into consumed gasoline. The amount converted depends on the amount of starting battery state-of-charge, based on a considered charging pattern and the preceding trips.

Our energy reallocation model is now explained in detail. For any given vehicle i and trip/, FASTSim calculates and outputs estimates of the amounts of gas ([G.sub.ij], gal) and electric energy ([E.sub.ij], kWh) that were consumed during the trip. Thus, the equivalent GHG emissions (measured in kg-CO2 equivalent) for the trip ([[GAMMA].sub.ij]) is calculated as:

[[GAMMA].sub.ij] =[[alpha].sub.G][G.sub.ij]+[[alpha].sub.E][E.sub.ij] (1)

And equivalent GHG per mile ([y.sub.ij]) is then calculated by dividing by the trip length:



[[alpha].sub.G] is the well-to-tank equivalent GHG for extraction, refinement and delivery, plus the GHG released during combustion per gallon of gas

[[alpha].sub.E ] is the equivalent GHG per kWh of electric energy (including battery charging efficiency)

[d.sub.j] is the trip length

It should be noted that the GHG equivalent per gallon of gas generally doesn't change much; for the US a value [[alpha].sub.G] of 11.893 kg-C02/gal is used, which corresponds to the sum of US-average well to tank [25], plus carbon content of typical gasoline (8.89 kg-C02/gal), as per [26]. On the other hand, equivalent GHG emissions created to produce a kWh of electric energy can vary quite a bit depending on location and time of the day.

With subscript i (representing a given vehicle) not shown in order to reduce clutter, the calculation is performed as:








[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are respectively the battery state of charge at the end of the previous trip (j-1), beginning of current trip (j), and end of the current trip. The state of charge can take any value between 0 and 1, with 1 implying that the battery is charged to its maximum charging limit, and 0 implies that the battery is at the charge sustain level

[f.sub.c] is a functional representation of the charging model.

[] [T.sub.[alpha]j], are the date/time at the end of the previous trip and beginning of current trip, respectively

[C.sub.max] is the battery charging capacity between maximum charging limit and charge sustaining level

[E.sub.cj] is the amount of electric energy (kWh) that would be re-allocated to an equivalent amount of gas

[E.sub.j], [G.sub.j] are respectively the amounts of electric energy (kWh) and gas (gal) used in the trip if it had been started with the battery at maximum state of charge

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are respectively the corrected amounts of electric energy (kWh) and gas (gal) used in the trip

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the corrected estimate of GHG (kg-C02) for the trip [beta] is the conversion constant from electrical energy that would have been used by the vehicle (if its trip had started with battery at maximum state of charge) to equivalent gas

Equation 3 determines the initial state of charge of the battery at the beginning of the trip/, which is a function of the charging behavior, and will be discussed in more detail in the next section. Eqn. 4 then checks if the amount of electric energy consumed in the trip (simulated starting at maximum charge) exceeds the amount available (considering the correct state of charge at the beginning of the trip), then determines (if any) the amount that should be re-allocated to an equivalent amount of gas. Eqns. 5, 6, 7 then respectively calculate the corrected amounts of electric energy, gas and GHG emissions. Lastly, Eqn. 8 calculates the battery state of charge at the end of the trip (so it can be used in estimating the starting state of charge for next trip).

It should be noted that primary assumptions to enable the calculation of equivalent amount of gas via the simple formula in Eqn. 6 are: i) The power management of the PHEV attempts to keep both the internal combustion engine and/or electric motor running at as close as possible to their maximum efficiency operational point (torque and rotational speed), and ii) efficiency of the electric motor does not change much over a relatively broad range of operation. If the assumptions hold true then electrical energy can be converted to equivalent gas consumption (or vice versa) with reasonable approximation accuracy, irrespective of the speed profile of the vehicle trip. Validity of these assumptions will be examined for the considered PHEV10 and PHEV40 models, after the next section introduces some charging behavior models.


Charging behaviors can vary significantly between different owners of vehicles. Unfortunately, to the best of the authors' knowledge, neither CHTS nor any other publicly-available data set has detailed information of charging events by PHEVs. Thus it is important to consider multiple charging scenario models. This section presents models for calculating [S.sub.oj] in Eqn. 3 for extreme max/min scenarios, as well as some intermediate ones.

Fully Charged before Every Trip

In this scenario, it is assumed that the PHEV battery is always charged to its maximum charge limit before every trip. Though this scenario is largely unrealistic, it represents a lower bound (when the grid is sufficiently green) for minimum attainable GHG footprint of the vehicle. For this scenario, Eqn. 3 becomes:

[S.sub.o,j] = 1 (9)

Never Charge

In this scenario, as the name implies, the PHEV is being used as if it was a regular gas hybrid. Though the scenario also appears unrealistic for most owners who likely paid more to purchase the vehicle (compared to a regular hybrid) then not use its plugin capability, some reports [27] indicate that few owners choose to do so.

Furthermore, this scenario represents an upper bound (when the grid is sufficiently green) on the worst possible GHG footprint of the vehicle. For this scenario, Eqn. 3 becomes:

[S.sub.o,j] = 0 (10)

Overnight Charging

This scenario is often used as a baseline in PHEV studies (18-20), and it represents what is expected from a large fraction of vehicle owners, who would plug their vehicles to charge overnight. For this scenario, Eqn. 3 becomes:


Opportune Charging

This scenario extends overnight charging and attempts to take advantage of charging opportunities in between trips. The scenario can be formulated as a probabilistic model that be tuned in Monte-Carlo simulations to calibrate aggregate behaviors to match real-life observations, such as for example: report by Idaho National Lab finds "PHEV owners charge 1.4 times per day on average" [28], For the probabilistic model, Eqn. 3 becomes:



[T.sub.c] is a threshold for minimum required time between trips to allow for full charging

[P.sub.c] is the probability (tunable parameter) for a charging event to happen when the time between trips exceeds a threshold

rand () is a function to generate pseudo-random numbers uniformly distributed between 0 and 1

A limiting case of this scenario is when vehicle always charge to full when given enough opportunity time between two trips. Assuming [T.sub.c] is smaller than the overnight time in which the vehicle is not in use, Eqn. 12 reduces into:



An examination is conducted for the accuracy in estimation of gas consumption by a PHEV via the energy re-allocation model in Eqns. 5, 6, 7. To generate reference data to compare against, trip traces of whole days of driving in the CHTS data set were concatenated into a long trip trace and simulated via FASTSim. The result of simulation for the concatenated trip would then be a reference for gas and electric power consumption for the overnight charging behavior. Limiting the analysis to concatenated trips longer than 80 miles (so that a PHEV40 would have a reasonable number of miles in charge sustaining mode), and excluding traces longer than 7 hours (due to capability limitations of FASTSim), a total of 962 concatenated traces were generated from the possible 6602 days of vehicle trip traces. Thus, the generated reference samples include approximately 10% of the total number of trips in the CHTS data set. Additional test samples were also examined for the never-charge behavior (by manipulating the battery state of charge in FASTSim to start at charge sustaining level) for the top 50 highest amount of energy converted among the 962 samples for both the PHEVs thereby examining larger amounts of reallocated energy.

Electric Energy to Equivalent Gas Simulations

To identify the vehicle-specific parameters ([C.sub.max], [beta]), both PHEV10 and PHEV40 models were simulated via FASTSim for the standard drive cycles UDDS (EPA standard for city driving) [29] and HWFET (EPA standard for highway driving) [29], FASTSim conducts the simulations for each driving cycle, once in charge depletion mode only (i.e. starting with a fully charged battery, both the PHEV10 and PHEV40 will complete either test cycle without entering charge sustaining mode), and another time in charge sustaining mode only (running the test cycle where the battery is empty at the start of the cycle). The constant ([beta]) is then calculated as ratio between electrical energy used to complete the charge-depletion only run and the equivalent gas consumption used in charge-sustaining only run. The identified values for the vehicle constants are listed in Table 1. It is be noted that the constant ([C.sub.max]) is the difference between the maximum charging limit and charge sustaining level, which is typically less than the nominal battery capacity. This is because for optimum battery life, the charge controller avoids reaching the both states of a completely charged or a completely depleted battery. As anticipated, the value of the constant ([beta]) does not differ much when calculated from different drive cycles, and the adopted value for remainder of this paper was averaged between the UDDS and HWFET values.

Figure 1 shows plots for amount of re-allocated electric energy (kWh) and the amount of equivalent gas (gal) in the 1012 test samples. The solid line in Fig. La, Lb represents the proposed energy re-allocation model of Eqn. 6, with slope of the line being constant ([beta]). For reference, values for UDDS and HWFET charge depletion (kWh) and charge sustaining (gal-gas) are also displayed. The circles and diamonds represent the "correct" amount of reallocated energy, determined by running the concatenated day-long trace through FASTSim for the 962 overnight only charging (circles, starts the day with one full charge) and 50 never charge (diamonds, starts the day with a depleted battery). Their verticle distance from the line represent the error of our proposed energy reallocation model. While the model seems to provide good approximation at the observable scale of Fig. 1, an examination of the percentage error in estimation of gas consumption is presented next.

Errors in Estimated Gas Consumption

Percentage error in estimated gas consumption is calculated as:



[e.sub.k] is the percentage error for the test sample k

[[??].sub.j] is the estimated gas consumption using the model

[[??].sub.k] is the estimated gas consumption via FASTSim simulation of the whole test day (all trips concatenated into one speed trace, for given charging model)

Box plots for the absolute values of ([e.sub.k]) for all test samples are shown in Fig. 2. Box plots are a convenient way for displaying statistical distributions, where the lower, middle and top lines in the box represent the 25th quartile, median and 75th quartile respectively. The top and bottom tics represent the minimum and maximum non-outlier samples, while outlier samples (or furthest outlier) are marked with a '+' sign in the plot. Criteria for classifying a sample as an outlier may differ. The one adopted in this paper is when the sample is further off from its closest quartile by more than 1.5 times the difference between 75th and 25th quartiles (which corresponds to being outside 99.3% probability limits of an assumed Gaussian distribution). Observing Fig. 2, outlier samples had error up to approx. 7% and 4% in the PHEV40 and PHEV10 models respectively. However, for the vast majority of samples, the absolute value error remained below 2%. While per-day errors in estimated gas consumption via the energy re-allocation model (even in outlier test samples) are fairly small, since these per-day errors are likely both positive and negative, it is expected that using the model to estimate the GHG for several vehicles and trips (as in next section) would drive the errors even much lower, approaching the median values ([less than or equal to]1%) in Fig. 2.

Errors in Estimated GHG for Aggregated Trips

To test the hypothesis that error in estimation of GHG decreases when multiple vehicle trips are averaged, a Monte-Carlo simulation was conducted, details of which available from the authors upon request. Key findings in the Monte-Carlo simulation are summarized as:

* Three different "batch sizes" of the number of trip days over-which CO2-Eq. per mile is averaged (Table 2)

* Two different values for GHG equivalent per kWh of grid electrical power (Table 2)

* Box plots for error in averaged GHG per mile are shown in Fig. 3 for both PHEV models and all 3x2 combinations of vehicle trip-days and GHG per kWh. For example, the right-most box plots in Fig. 3.a implies that if one were to average the GHG-equivalent per mile (calculated via Eqns. 5, 6, 7, for [[alpha].sub.E] = 0.32) over 100 vehicle trip days, then the error in the GHG per mile estimate is highly likely to be between +0.12% and +0.59% (upper and lower tics of the box plot) for the PHEV40. And in worst cases (furthest outliers among 100,000 Monte-Carlo samples), the error would be between -0.12% and +0.73% for the PHEV40

The primary observation from Fig. 3 is that the larger the batch size (number of trip-days for averaging C02-Eq./mile), the less likely for the error in average GHG per mile to be off the median value of the error for the respective PHEV model. But even at a batch size as small as 25 vehicle trip-days (which one might encounter when attempting to study a fringe group of a sub-population of vehicles), the remains between 0.0% and +1.2% (overestimation) for the PHEV10, and between -0.6% (underestimation) and +1.2% (overestimation) for the PHEV40. These errors in estimation of GHG per mile are small enough. Thus it is deemed unnecessary to re-run the large-scale FASTSim simulations for different PHEV charging behaviors, and the energy reallocation model will instead be used in the next section.


Prior to conducting comparisons of charging behaviors, notable cases for grid electrical power GHG equivalent per kWh (well to battery) were calculated (Table 3). The calculations are based on GREET models [25] for electric generation by different fuel types, and with consideration of transmission and charging efficiency. The fuel mixes considered are i) US-2014 average mix [30], ii) California-2014 mix [31], and a future scenario that corresponds to California target of reaching 33% from renewables by 2025 (fuel mix for 2025 estimated by scaling down the non-renewables in CA-2014 without altering their relative fractions in the generation mix).

Using the values for the grid generation mix in Table 3, the energy reallocation model was run for all the recorded trips in the CHTS data set for both PHEV models for four different charging behaviors. The resulting histograms for GHG-equivalent per mile are shown in Fig. 4. The considered charging behaviors are: i) Fully charged before every trip, ii) Deterministic opportune charging (charging to full whenever there is a time window of four hours between trips), iii) Overnight charging, and iv) Never charge. Insights observable in Fig. 4 include:

* In the "Never charge" model, probability distributions for GHG per mile are largely unimodal for both PHEV models, and unaffected by level of greenness of the grid. This is no surprise since never charging means a vehicle will run in only one mode (charge-sustaining) and that mode only consumes gas (no electric energy from the grid).

* If it were possible to ensure the fully charged before every trip condition, then the PHEV40 has a long enough electric range to do the vast majority of trip miles in charge depletion mode (minimal/no use of gas). This is observable where the probability distribution of GHG per mile for the PHEV40 appears unimodal for the "Fully-charged every trip" condition

* On the other hand, the electric range of the PHEV10 is insufficient to conduct majority of the trips in charge depletion mode, and thus its GHG per mile probability distribution appears bimodal (except Never-charge), with one peak corresponding to miles driven in charge depletion mode, and another corresponding to charge sustaining mode (using gas)

* As charging behaviors result in longer trip chains (opportune and overnight charging) for the PHEV40, its probability distributions starts to become a bimodal as well.

* As the length of trip chains gets longer, the charge-depletion peak in the bimodal distribution becomes less significant, while the charge sustaining peak becomes more significant.

* As the grid get greener, the difference between the centroid of the charge-depletion and charge-sustaining peaks in the bimodal distribution becomes more significant

* The PHEV10 appears to be a more energy-efficient (less GHG per mile in charge sustaining mode, as observed in the never charge condition) than the PHEV40. This is also apparent in the low-GHG peak of the bimodal distributions. However, the PHEV40 often has a higher fraction of miles driven in the charge-depletion peak, which could make it have less of an overall average GHG per mile as the grid gets greener and charging opportunities during the day increase

* The bimodal distribution at the large population level poses interesting research questions that may be investigated in futre work: Does the majority of the population have near-evenly split fraction of miles between the different modes? Or, are there sub-populations of vehicle owners that can drive most of their trips in only one of the modes? And if true, what battery size is optimum for each sub-population?


This paper presented an approach for computationally efficient estimation of the equivalent GHG emissions of plugin hybrid electric vehicles for real driving patterns under different charging behavior and various levels of grid greenness. Validation of the GHG estimation model was conducted via 1012 day-long concatenated sample traces from California Household Travel Survey. Estimated error in fuel consumption was less than 3% for most considered cases, and approaches a median value less than 1% when multiple vehicle trip days are collectively considered. The model was then used to examine the GHG footprint in drive traces that correspond to all of California.

Two PHEV models were examined, one with a shorter all-electric range but higher energy efficiency, and one with longer all-electric range, with the examination observing different charging behaviors and grid greenness. In many scenarios, distribution of the equivalent GHG per mile exhibited a bimodal probability distribution, which understandably corresponds to different modes of driving that relate to the primary energy source. It was also observed that the charging behavior, grid greenness and likely individual usage patterns all play roles in which vehicle has the minimum GHG footprint, with no clear winner for all conditions.

A primary-interest research activity that could be pursued in future work would be to further examine the bimodal distribution of equivalent GHG per mile for different sub-populations of vehicle owners. This may help answer the question of whether a certain battery size/electric range is universally best, or whether different owners are best served by differently designed vehicles.


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[C.sub.max] - Maximum charging capacity of battery

[E.sub.ij] - Electric energy (kWh) consumed in trip/ by vehicle i

[E.sub.cj] - Amount of electric energy that is re-allocated to an equivalent amount of gas for tripj'

[[??].sub.j] - Corrected amount of electric energy for trip j

[G.sub.ij] - Gas (gal) consumed in trip j by vehicle i

[[??].sub.j] - Corrected amount of gas for trip j

[S.sub.oj] - Initial SoC battery for trip j

[] - Final SoC battery for trip j

[T.sub.oj] - Date/Time at the start of trip j

[] - Date/Time at the end of trip j

[d.sub.j] - Distance travelled in trip j

[e.sub.k] - Percentage error in test sample k

[f.sub.c] - Functional representation of charging model

[[GAMMA].sub.ij] - GHG (kg C02-equivalent) produced in trip j by vehicle i

[[??].sub.ij] - Corrected amount of GHG produced in trip j by vehicle i

[[alpha].sub.E] - GHG equivalent (kg C02-equivalent/kWh) for electric energy

[[alpha].sub.G] - GHG equivalent (kg C02-equivalent/gal) for gas

[beta] - Conversion constant (gal-gas/kWh) for energy reallocation model

[y.sub.ij] - GHG (kg CO2-equivalent/mile) produced in trip j by vehicle i

BEV - Battery-Electric Vehicle

CHTS - California Household Travel Survey

CV - Conventional Vehicle

FASTSim - Future Automotive Systems Technology Simulator

GHG - Greenhouse Gas

GREET - Greenhouse gases, Regulated Emissions, and Energy use in Transportation model

HEV - Hybrid Electric Vehicle

ICE - Internal Combustion Engine

PHEV - Plugin Hybrid Electric Vehicle

PHEV10 - PHEV with nominal all-electric range of 10 miles

PHEV40 - PHEV with nominal all-electric range of 40 miles

SoC - State of Charge of vehicle battery

Karim Hamza and Ken Laberteaux

Toyota Research Institute-North America

Table 1. Identified constants for PHEV models.

                              PHEV10  PHEV40

[C.sub.max] (kWh)             1.75    10.39
[beta]-UDDS(gal-gas/kWh)      0.0799   0.0848
[beta]-HWFET (gal-gas/kWh)    0.0803   0.0814
[beta]-adopted (gal-gas/kWh)  0.0801   0.0832

Table 2. Monte-Carlo simulation parameters for estimation of error in
GHG per mile via energy reallocation models.

batchSize (number of trip-days for
averaging C02-Ea/mile)                   {25,50, 100}
[[alpha].sub.E] (kg C02-Eq./kWh)          {0.32, 0.62}
[[alpha].sub.G] (kg C02-Eq/gal-gas)       11.893
nMC (number of simulation runs)      100,000

Table 3. Equivalent GHG per unit electric power for considered grid

Grid Mix                                [[alpha].sub.E]

2014 US grid average (US-2014)               0.62
2014 California grid average (CA-2014)       0.42
Future California scenario (CA-2025)         0.32
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Author:Hamza, Karim; Laberteaux, Ken
Publication:SAE International Journal of Alternative Powertrains
Article Type:Report
Date:May 1, 2016
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