Real-Time Implementation of Optimal Energy Management in ...

Zachary D. AsherMechanical and Aerospace Engineering,

Western Michigan University,

Kalamazoo, MI 49001

David A. TrinkoMechanical Engineering,

Colorado State University,

Fort Collins, CO 80524

Joshua D. PayneHybrids Research Group,

Toyota Motor Engineering and

Manufacturing NA, Inc.,

Ann Arbor, MI 48105

Benjamin M. GellerHybrids Research Group,

Toyota Motor Engineering and

Manufacturing NA, Inc.,

Ann Arbor, MI 48105

Thomas H. BradleyMechanical Engineering,

Colorado State University,

Fort Collins, CO 80524

Real-Time Implementationof Optimal Energy Managementin Hybrid Electric Vehicles:Globally Optimal Controlof Acceleration EventsWidely published research shows that significant fuel economy improvements throughoptimal control of a vehicle powertrain are possible if the future vehicle velocity is knownand real-time optimization calculations can be performed. In this research, however, weseek to advance the field of optimal powertrain control by limiting future vehicle opera-tion knowledge and using no real-time optimization calculations. We have realized opti-mal control of acceleration events (AEs) in real-time by studying optimal control trendsacross 384 real world drive cycles and deriving an optimal control strategy for specificacceleration event categories using dynamic programming (DP). This optimal controlstrategy is then applied to all other acceleration events in its category, as well as sepa-rate standard and custom drive cycles using a look-up table. Fuel economy improvementsof 2% average for acceleration events and 3.9% for an independent drive cycle wereobserved when compared to our rigorously validated 2010 Toyota Prius model. Our con-clusion is that optimal control can be implemented in real-time using standard vehiclecontrollers assuming extremely limited information about future vehicle operation isknown such as an approximate starting and ending velocity for an acceleration event.[DOI: 10.1115/1.4046477]

1 Introduction

Transportation provides significant economic benefits but isresponsible for approximately one third of the total global energyconsumption [1]. When this energy is generated from petroleumcombustion engines, petroleum trade is required [2], air pollutionthat is harmful to human health is released [3,4], and globalwarming is exacerbated through greenhouse gas emissions [5–7].To combat these issues, countries from all over the world haveimplemented fuel economy (FE) regulations [8–10] with manycountries taking the initiative to ban gasoline and diesel poweredvehicles outright between the years 2025–2040 [11–15]. The ParisClimate Agreement, which has been signed by every country inthe world [16,17], also limits greenhouse gas emissions, petro-leum importation, and air pollution (by extension) [18]. Improvingvehicle FE is a major initiative for meeting the Paris ClimateAgreement goals and many countries have adopted milestonessuch as the 50% fuel economy improvement worldwide by 2050challenges (50 by 50) [9,19–22].

Technologies used to increase FE include engine sizing,advanced engine control, friction/mass/drag reduction, and power-train electrification [23]. But, there are numerous technologiesthat are not currently being utilized for FE improvements such asimplementation of an optimal energy management strategy (opti-mal EMS), which has demonstrated FE improvements of up to30% for hybrid vehicles [24]. An optimal EMS is the applicationof optimal control to vehicle powertrain operation with theobjective of minimizing fuel consumption (maximizing FE). Thistechnique was first published in 2001 by Lin et al., who derived

the globally optimal control using dynamic programming (DP) fora hybrid electric truck [25]. Since then, researchers have investi-gated stochastically robust strategies [26–31] as well as fast com-putation strategies [32–36] with the goal of progressing thistechnology toward commercial implementation. To this day, thetechnology has still not been realized commercially due to thecomputational cost in processing sensor data (this data is requiredto make predictions, which are then used to derive the optimalEMS) and due to a research gap exploring the effect ofmisprediction [37].

A promising solution to realize optimal EMS implementation isto use a precomputed globally optimal EMS derived using DPrather than a real-time computed nonglobally optimal EMS suchas stochastic dynamic programming, equivalent consumptionminimization strategy (ECMS), or a heuristic method. ThisDP-computed look-up table implementation option did not seemfeasible until recent research established that FE improvementsare still achieved when a globally optimal EMS is subjected tomispredictions [38–40], which was further demonstrated as acomplete system by incorporating a perception model [41–44].These initial research findings demonstrate that this techniquecould be commercially implementable in the near term, but a rig-orous analysis for real-world driving using a specific implementa-tion scheme must first be conducted. This research fills thisdemonstrated need by choosing acceleration event (AE) imple-mentation studied using 384 real-world drive cycles. Justificationof AE implementation is presented in Sec. 2.4.

The research summarized this paper is still on-going and hasbeen in development since 2015. This paper presents the simula-tion findings, which are currently being used to develop a physicalvehicle demonstration. This paper builds from a previous novelresearch finding that discrete DP is surprisingly robust to velocityprediction error [40]; thus, there are numerous new and significant

Contributed by the Dynamic Systems Division of ASME for publication in theJOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript receivedAugust 27, 2019; final manuscript received January 29, 2020; published onlineMarch 18, 2020. Assoc. Editor: Scott Moura.

Journal of Dynamic Systems, Measurement, and Control AUGUST 2020, Vol. 142 / 081002-1Copyright VC 2020 by ASME

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contributions that this paper makes to the field of optimal EMS.These include:

(1) Rigorous analysis of optimal EMS implementation and theeffect of prediction error using 384 real-world drive cycles.

(2) Quantification of prediction accuracy required for optimalEMS using a rigorous study of driving segment categorization.

(3) Direct implementation of discrete dynamic programmingusing a precomputed look-up table.

(4) Implementation of optimal EMS in discrete accelerationevents.

(5) Use of optimal control matrix solutions that are a function ofvelocity, which only works for monotonic drive segments.

The control strategy described in this paper is not suboptimal orheuristic; instead, it is the globally optimal control solutionapplied in a way that takes advantage of its natural robustness(again this is a surprising conclusion from a previous study [40]).If the actual driving segment is different than what was predicted,the result will be suboptimal; otherwise, the result will be globallyoptimal. This is a new technique that other researchers missed intheir rush to investigate stochastic and fast-computation optimalEMS that followed the original discrete DP results from 2001.This paper continues to demonstrate that there is indeed a naturalrobustness of discrete DP for the hybrid electric vehicle (HEV)optimal EMS problem, which may be the key to commercialrealization.

2 Methods

To understand the FE improvement potential of AE optimalcontrol, first a large database of real world AEs is extracted fromreal-world drive cycles. These AEs are then organized intovarious categorization schemes. Next, two control methods aredeveloped using a validated 2010 Toyota Prius model: a baselineenergy management strategy (baseline EMS) and a globally opti-mal EMS. A custom battery state-of-charge (SOC) adjusted FEcalculation technique is developed for AEs to ensure unbiased FEcomparison.

Then, to determine the impact of AE category prediction indrive cycles, several steps are required. The first is to develop aset of drive cycles representing various styles of driving. Next,four control strategies are compared: (1) a baseline energy man-agement strategy (baseline EMS), (2) a full drive cycle predictionoptimal EMS, (3) an exact AE prediction optimal EMS, and (4) acategory AE prediction optimal EMS. By comparing the AE cate-gory prediction (which is real-time implementable and uses verylimited future information) with the baseline EMS as well as per-fect prediction optimal EMS, we will have determined the FEimprovement for modern vehicles and we will have determinedhow much of the maximum possible FE improvement is achieved.

2.1 Acceleration Event Dataset Development. Initialresearch on AEs suggests that velocity and fuel consumption canbe accurately modeled with sinusoidal and polynomial modelsthat satisfy a zero jerk condition consistent with real-world driving[45] but it is difficult to capture an inclusive set of AEs due to thevariability introduced by obstacles such as roundabouts, intersec-tions, and crossings for different vehicles’ traffic conditions androad types [46,47]. Additionally, substantial variations in driverbehavior in regard to AEs results in significantly different fuelconsumption rates [48] and many studies of AEs have becomeexperimental and data-driven [49].

In this research, data were recorded from several 2010 ToyotaPrius drivers in the California area. The data are composed of 384drive cycles measured at 10 Hz (0.1 s time-steps) with an averagetime length of 1086 s and an average velocity of 28.05 mph. Anexample drive cycle from the dataset is shown in Fig. 1. AEs canbe extracted from these drive cycles by identifying sections ofspeed data where the velocity increases in the next time-step, i.e.,vkþ1 � vk > 0 where k is a discrete time-step. But, for real-world

accelerations, there are short moments of steady or even decreas-ing speed within an AE and a two time-step evaluation will yielderroneous results. Additionally, the real-world drive data have ahigh resolution and a strict equality evaluation for steady sections(i.e., vk � vk�1 ¼ 0) is insufficient. To address these issues, AEswere extracted by searching for sections satisfying the followinglogic statement where � represents logical conjunction (i.e., an“and” statement)”

ðvkþ1 � vkÞ � 0:05 mph

�ðvkþ2 � vkþ1Þ � 0:05 mph



(1)

If Eq. (1) is true, then this section of the drive cycle is labeled asan AE. From these extracted AEs, if they either start from a nega-tive speed, last for one second or less, or only increase speed by5 mph or less then they are filtered out. A conceptual plot of theidentification of AEs in an example drive cycle is shown in Fig. 2.

Using this process, 7708 AEs are extracted from the 384 drivecycles for analysis. Since these AEs will be used to compare abaseline EMS and optimal EMS, we must ensure that the vehicleis at steady-state before and after each AE. To accomplish this,each of these AEs is prepended with 8 s of the initial velocity toensure the vehicle is at steady-state at the beginning of each AEand appended with 12 s of the final velocity to ensure the vehicleis at steady-state at the end of each AE. An example of the result-ing AE cycle is shown in Fig. 3. The 7708 AEs with the pre-pended and appended velocity states range from 22 s long to 76 slong and include speeds from 0 mph to 50 mph. To derive general-ized improved control strategies, this dataset of AEs must now becategorized.

2.2 Acceleration Event Categorization. Three different AEcategorization schemes were chosen for this dataset based on prin-ciple component analysis:

(1) Starting velocity and ending velocity categorization

vi; vf

Fig. 1 One of the drive cycles in the real-world drive cycledataset

Fig. 2 Example of the results from the AE extraction algorithm.Note that one AE is filtered out for having a velocity increaseless than 5 mph.

081002-2 / Vol. 142, AUGUST 2020 Transactions of the ASME

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(2) Time duration and ending velocity

t; vf

(3) Average acceleration and ending velocity

vf � vi

t; vf

where the variables vi, vf, and t are shown in Fig. 3.An example of the first categorization scheme, starting velocity

and ending velocity, that uses a new category every 3 mph isshown in Fig. 4. The x-axis shows the assigned AE category num-ber, e.g., category 1, 2, 3, etc. The left y-axis shows the velocityrange. For example category 1 captures all AEs that start at 0 mphand end at 7.8 6 1.5 mph. The right y-axis shows the number ofAEs in the AE category, for example, there are about 321 AEs incategory 1 (starting around 0 mph and end around 7.8 6 1.5 mph).Overall, Fig. 4 shows there are a high number of low velocity AEsand a small number of high velocity AEs in the dataset.

An example of the second categorization scheme, time dura-tion, and ending velocity, which uses a new category every 2.8 sand 4.4 mph, is shown in Fig. 5. The x-axis and right y-axis areconsistent with first categorization scheme plot, Fig. 4. But nowthe left y-axis shows the ending velocity (as red Xs) and the totaltime duration (as blue dots) of each category. For example,category 1 has a total time duration of 6.2 6 1.4 s and an endingvelocity of 12.2 6 2.2 mph for which there are 274 AEs. Note thatthe total time duration is shown without prepended and appendedvelocity (Fig. 3), which is used to ensure steady-state. Overall,Fig. 5 shows that, in general, there is a high number of short-duration AEs and a low number of long-duration AEs in thisdataset.

An example of the third categorization scheme, average accel-eration, and ending velocity, which uses a new category every0.02 g’s and 4.4 mph, is shown in Fig. 6. The x-axis and righty-axis are consistent with the other two categorization schemeplots, Figs. 4 and 5. The left y-axis shows the ending velocity (asred Xs) and the average acceleration (as blue dots) of each AE cat-egory. For example, AE category 1 has an average acceleration ofabout 0.11 6 0.01 g’s (g-force) and an ending velocity of approxi-mately 34.2 6 2.2 mph. Overall, Fig. 6 shows that the majority ofAEs in this dataset do not go above 1.13 g’s.

Note that there were very few AEs, which had an ending veloc-ity above 50 mph in this dataset. AEs that ended at a high velocitywere lumped into AEs with an ending velocity around 50 mph.

2.3 Baseline Energy Management Strategy Development.The vehicle model chosen for analysis is a 2010 Toyota Priusbecause it is a popular and well documented vehicle. It also hasthe highest FE of any vehicle in its class (excluding electricvehicles) [50], implying that FE improvements would be

Fig. 3 Example of prepending and appending constant veloc-ity of each AE to ensure steady-state

Fig. 4 Plot showing the velocity range and the number of AEs in each category for the starting velocity and ending velocitycategorization scheme

Fig. 5 Plot showing total duration, end velocity, and the number of AEs in each category for the time duration and endingvelocity categorization scheme

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challenging to demonstrate. Additionally, there is physicallymeasured validation data publicly available for this vehicle.

The baseline EMS must be a validated and high accuracy simu-lation of current real-world vehicle FE performance. Additionally,to compare alternate control strategies over thousands of shortsegments of driving, such as AEs, the vehicle model must havehigh enough fidelity to model FE changes from different controlswhile also having a relatively low computational cost. This typeof model is commonly known as a controls-oriented model sinceit must sacrifice some fidelity in order to lower computational costfor controls development.

To satisfy these requirements, a combination of a high fidelityvehicle model developed in the AUTONOMIE modeling software iscombined with an equation-based power-split vehicle model.The AUTONOMIE modeling software has shown strong correlationwith the current 2010 Toyota Prius physical vehicle operation[51] so it was used to derive the engine torque, engine speed,and engine power, which was then implemented in the equation-based power-split model. FE and SOC with respect to time arethen recorded.

To ensure that this model does not sacrifice FE predictionaccuracy, a thorough model validation study was conducted.The simulated FE from this model is validated against 2010Toyota Prius FE data physically measured by Argonne NationalLaboratory using all available drive cycles [52]. The publiclyavailable data are measured for the three standard U.S. Environ-mental Protection Agency (EPA) drive cycles: the city drivingfocused urban dynamometer drive schedule (UDDS), the high-way driving focused Highway Fuel Economy Test (HWFET),and the aggressive driving focused US06 cycle. All simulatedFE was within 1.5% of the physically measured data as shownin Table 1. A controls-oriented model is needed for this researchand the focus is not on model development; therefore, this issufficient validation for controls development. The equation-based power-split model was developed according to the litera-ture [53–56]. Each of the 7708 AEs is input into the 2010Toyota Prius Autonomie model and the engine torque, speed,and power output is recorded. For a given engine power, therequired electric power can be determined by subtracting thetotal propulsive power requirement as

Pelec ¼ Fpropv� PICE (2)

where Fprop is determined from a force balance on the vehicle as

Fprop ¼ m _v þ Crrmgþ 1

2Cdqairv

2Afront (3)

and Crr is the coefficient of rolling resistance, m is the mass of thevehicle, g is the acceleration due to gravity, Cd is the coefficientof drag, qair is the density of air, v is the vehicle velocity, Afront isthe frontal area, and _v is the vehicle acceleration (calculated usinga numerical derivative). Note that the additional force componentdue to an elevation angle is not a part of this study.

The resulting battery SOC at the next time-step is then calcu-lated via a difference quotient as

SOC k þ 1ð Þ ¼ SOC kð Þ � Voc �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2

oc � 4PbattRint

p2RintQbatt;o

Dt (4)

where Voc is the open-circuit voltage of 201.6 V, Rint is the batteryinternal resistance of 0.373 X, and Qbatt;o is the battery capacity of6.5 A�h.

The overall efficiency of the electrical components can then becaptured using response surface fits [57] of data available in theliterature [56]. Using the speed and torque, the electrical systemefficiency is determined and applied as

Pbatt ¼1

gelec

Pelec (5)

where gelec is a function of electric motor speed xEM, electricmotor torque TEM, generator speed xgen, and generator torqueTgen. The electric motor and generator efficiency maps areextracted from the AUTONOMIE modeling software, which are usedto compute gelec as a function of the torques and speeds of theelectric components.

The fuel consumption is then obtained using a brake-specificfuel consumption (BSFC) map. This map has to be derived sinceonly its general structure is available in the public domain [55].For the case of a 2010 Toyota Prius, a quadratic response surfacedoes not adequately match the BSFC structure; therefore, a cubicresponse surface is used, which shows strong correlation [55].This equation is defined in response surface literature [57] as

Fig. 6 Plot showing average acceleration, end velocity, and the number of AEs in each category for the average accelera-tion and ending velocity categorization scheme

Table 1 A comparison of simulated and measured fuel economy for standard EPA drive cycles

EPA drive cycle Simulated fuel economy Measured fuel economy [52] Percent difference

UDDS 76.6 mpg 75.6 mpg 1.3%HWFET 69.0 mpg 69.9 mpg –1.4%US06 44.9 mpg 45.3 mpg –1.0%


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BSFC ¼ A1 þ A2xICE þ A3TICE

þA4xICETICE þ A5x2ICE þ A6T2

ICE

þA7xICET2ICE þ A8x

2ICETICE þ A9T3

ICE (6)

where all A values are fitted constants, xICE is the engine speed,and TICE is the engine torque. The surface developed is shown inFig. 7. Once the BSFC response surface is developed, the idealoperating line [58] can be computed, which shows the minimumfuel consumption for any desired power (also shown in Fig. 7).

Finally, the engine, generator, and wheel speed are constrainedaccording to the planetary gear set equation from the literature[53]

xICE ¼ xgen

q1þ q

þ xring

1

1þ q(7)

where q¼ðNteeth;sun=Nteeth;ringÞ;Nteeth;generator¼30, and Nteeth;ring¼78 and is subject to operational speed limits of 13,500rpm for theelectric motor and 10,000rpm for the generator. The ring gearspeed is based on the vehicle speed as

xring ¼rfinal drivev

Rwheel

(8)

where rfinal drive is the final drive ratio of 3.267 and Rwheel is thewheel radius of 0.317 m.

2.4 Optimal Energy Management Strategy Development.An optimal EMS is developed, which derives the globally optimalcontrol of acceleration events.

2.4.1 Acceleration Event Justification. Acceleration portionsof driving require the most propulsive power and consume themost fuel relative to distance [48]; thus, they may represent theideal place to achieve a large portion of the maximum possible FEgains from optimal EMS. By applying optimal control only to spe-cific segments of a drive cycle, the globally optimal FE may notbe realized but it will provide a significant FE improvement com-pared to current technology and it helps progress optimal EMStoward commercial realization. A robust globally optimal FEimprovement for all dive cycles is a very large and complicatedproblem; therefore, it should be broken down into a subset of the

full problem, which then informs and provokes future solutions.This research investigates a subset of this general optimal EMSproblem through a comprehensive analysis of potential FEimprovements from a DP-derived optimal EMS applied to accel-eration events (AE) only.

Accurate prediction of future vehicle velocity information is amajor hurdle for optimal EMS realization, but the mispredictionresilience of DP can be harnessed to eliminate the second-by-second prediction requirement. This research seeks to accomplishthis goal by eschewing full second-by-second velocity predictionsin favor of only two approximate predictions such as approximateAE starting velocity, ending velocity, duration, or average accelera-tion. In this sense, the prediction requirement is largely reduced inthat the only prediction required is an approximate starting and end-ing velocity; thus, prediction of traffic conditions (as an example) isnot needed. Two approximate predictions, e.g., starting and endingvelocity, are feasible using global positioning system location andspeed limit information. In areas or times of high traffic, endingspeed can be readily predicted from travel time data instead [41].

Determination of which two predictions and how wide of anapproximation is required is the focus of this research paper. Pre-diction modeling is not within the scope of this research. Instead,only a prediction of the AE category (AE approximation) isassumed. First, we seek to understand how to characterize an AEcategorization scheme that results in significant and robust FEimprovements; then we seek to understand the total FE improve-ment and battery SOC impacts of this AE category precomputedoptimal EMS over a variety of drive cycles.

The goal of this study is to derive an optimal EMS for general,real-world, AEs but then apply the optimal EMS to many similarAEs, thus eliminating the need for real-time calculations. Thisstudy includes a rigorous investigation of an optimal EMS appliedto AEs as well as an implementation in several full drive cycles.

2.4.2 Optimal Energy Management Strategy Derivation. Notethat other researchers have proposed deriving the globally optimalEMS through Pontryagin’s minimization principle (PMP) andimplementing the solution in real-time using ECMS, but this solu-tion realizes the same control regardless of actual driving condi-tions. In response to this, researchers have proposed an “on-the-fly” correction to ECMS called adaptive ECMS (a-ECMS) but itis heavily dependent on velocity predictions; there are real-timecomputational concerns and many more misprediction scenariosthat still need to be evaluated [59]. Alternatively, DP provides anoptimal control solution matrix where optimal control is derivedfor every feasible input and SOC value, thus providing resiliencethat is not present in the PMP and ECMS technique.

Deterministic DP is used to derive the optimal EMS because itguarantees the globally optimal solution (subject to the discretiza-tion scheme); it is straightforward to implement for nonlinear dis-crete systems, and because it is consistent with previous research,which has shown that despite prediction errors, the DP-derivedcontrol matrix results in maintained FE improvements [40]. Thehigh computational cost of DP is bypassed in this researchbecause the end goal is to develop and save a DP derived globallyoptimal control as a look-up table, thus eliminating any need forreal-time calculation. This research investigates deriving an opti-mal EMS using DP for a single AE in a category and applying thecontrol matrix results to every other AE in the category.

The AE for which the optimal EMS is derived is referred toas the expected AE and is an estimate of the most commonAE within the category. As an example, category 1 in Fig. 4 hasa starting velocity of 0 mph and an ending velocity of7.8 6 1.5 mph. All of the AEs within category 1 are plotted inFig. 8(a). If the total duration of each of the AEs in category 1 isrecorded, shown in Fig. 8(b), it can be seen that a durationbetween 4.5 and 5 s is most common (this duration spans 40occurrences). This implies that for category 1, a total duration of4.5–5 s is an expected AE and all other durations are associatedwith mispredictions. Note that only one AE is used to derive the

Fig. 7 The approximated BSFC map response surface created


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optimal EMS in the 4.5–5 s duration, which is chosen at random.This ensures that only one optimal EMS is used for everycategory.

This is an important point and the foundation for this researchpaper: the optimal control is derived for only one AE in theexpected set and is applied to every other AE in the entire cate-gory. For the AE category shown in Fig. 8(a), the globally optimalcontrol is derived for one AE and this optimal control is applied toall other 300þ AEs, even AEs that take four times as long. Weseek to find the AE categorization scheme that maintains FEimprovements across the entire AE category.

After the expected AE is determined for each category in eachAE categorization scheme, the optimal EMS can be derived usingDP. DP finds the optimal solution using backward recursion,which eliminates solutions that are not optimal as defined by theBellman principle of optimality [60,61]. For every feasible statevariable value, the optimal solution is stored. An appropriate DPscheme consists of a dynamic equation shown in Eq. (9), a costfunction shown in Eq. (10), and state and control variable feasibil-ity constraints shown in Eqs. (12) and (13)

Sðk þ 1Þ ¼ SðkÞ þ f ðS; u;w; kÞDt (9)

J ¼XN�1

k¼0

f ðS; u;w;DtÞ (10)

SminðkÞ � SðkÞ � SmaxðkÞ ðk ¼ 0;…NÞ (11)

uminðkÞ � uðkÞ � umaxðkÞ ðk ¼ 0;…N � 1Þ (12)

where S is the state, u is the control, w is the exogenous fixedinput, k is the time-step number, Dt is the time-step value, J is thecost, and N is the final time-step number.

For an HEV optimal EMS derivation, the state is the batteryðSOCÞ, the control is the engine power ðPICEÞ, the exogenous

fixed input is the vehicle velocity (v), and the cost is the fuel massconsumed ðmfuelÞ with a penalty to enforce the same SOC finalvalue as the baseline EMS ðSOCf Þ. This formulation with theadded feasibility constraints of engine operation and battery SOCyields the following modified equations:

SOCðk þ 1Þ ¼ SOCðkÞ þ f ðSOC;PICE; v; kÞDt (13)

Cost ¼XN�1

k¼0

mfuelðPICE;DtÞ þWðSOCf � SOCðNÞÞ2 (14)

SOCmin � SOCðkÞ � SOCmax ðk ¼ 0;…NÞ (15)

PICE;min � PICEðkÞ � PICE;max ðk ¼ 0;…N � 1Þ (16)

where W is defined as a penalty weight, which forces charge sus-taining behavior.

This HEV optimal EMS derivation can then be tailored to rep-resent a 2010 Toyota Prius using the equation-based power-splitmodel described in Eq. (4) and Sec. 2.3. The resulting DP formu-lation for a 2010 Toyota Prius is

SOCðk þ 1Þ¼ SOCðkÞ � C1

þC2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiC3 � C4vðkÞ þ C5vðkÞ3 þ C6 _vðkÞvðkÞ � C7PICE

q(17)

Cost ¼XN�1

k¼0

f ðPICEÞ þWðSOCf � SOCðNÞÞ2 (18)

40% � SOCðkÞ � 80% ðk ¼ 0;…NÞ (19)

0 kW � PICEðkÞ � 73 kW ðk ¼ 0;…N � 1Þ (20)

Fig. 8 A visual representation of the characteristic AE selection process. The AEs with the most common totalduration are labeled in black while all other AEs are shown in brown.


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C8½f ðPICEÞ� þ C9vðkÞ � C10 (21)

where C1 through C10 are constants and W achieves the desiredeffect when it is set to 10,000. These equation derivations aredescribed in more detail in a previous publication [40]. Note thatthere are numerous control variable choices and other researchershave used engine speed, engine torque, run/stop/idle model, orcombinations of these. Control of just engine power was chosen toensure reduced computation time.

The following time-step, state, and engine power discretizationvalues are used, which were determined from a convergence test:

Dt ¼ 0:4 sec (22)

DSOC ¼ 0:001% (23)

DPICE ¼ 0:1 kW (24)

The solution to this problem is an optimal control matrix, whichprovides the minimum fuel consumption engine power for anyfeasible time and battery SOC during the AE. The optimal controlmatrix for a low velocity AE is shown in Fig. 9 and the optimalcontrol matrix for a high velocity AE is shown in Fig. 10. Forexample, if the battery SOC is 40% and the time since beginningthe AE is 3 s, Fig. 9 shows that approximately 20 kW of enginepower will provide the minimum fuel consumption solution (for alow velocity AE) while Fig. 10 shows that approximately 30 kWof engine power will provide the minimum fuel consumption solu-tion (for a high velocity AE).

A new and important finding from this research was discoveredwhen these optimal control matrices were applied to an AE forwhich it was not derived, i.e., the optimal EMS for an expectedAE is applied to a mispredicted AE. It was determined that if thetime input variable is converted to a velocity input variable, sig-nificantly more robust results were demonstrated. In other words,if the optimal EMS for an expected AE is applied to a mispre-dicted AE, it is better to determine the optimal control accordingto current velocity rather than current time. Note that this conver-sion is only possible because AEs are monotonic with respect tovelocity; otherwise, there would be multiple control actions forone velocity input.

Using a velocity input variable reduces large power fluctuationssince it provides an aspect of self-correction. For example, if theprediction is a large acceleration but the actual AE initiallyincreases velocity very slowly, high engine power will not beused as the time index increases. Looking at Fig. 10, this meansthat the yellow/white region of high power will not be used untilthe velocity increases significantly, which is not the case whenusing a time index.

2.5 Battery State of Charge Correction. When evaluatingalternate control strategies, it is likely that ending battery SOCðSOCf Þ for each strategy will be different. For full drive cycles,the Society of Automotive Engineers (SAE) J1711 standarddescribes how to determine a corrected FE [62]. Unfortunately,this technique gives erroneous results when applied short sectionsof driving such as AEs. SAE J1711 assumes a constant engineefficiency of 25%, which is not appropriate for a large dataset ofdiverse AEs since engine efficiency can be significantly differentfor different AEs. Additionally, the FE results for AEs are verysensitive to the FE correction technique since the fuel consump-tion relative to full drive cycles is low.

To address these issues, a FE correction technique was imple-mented, which is a slight modification to the SAE standard. Eachrelative FE and SOC result for every AE within a category is plot-ted in Fig. 11. Relative increases are defined as

DFE ¼ FEOptimal EMS � FEBaseline EMS (25)

DSOC ¼ SOCf ;optimal EMS � SOCf ;baseline EMS (26)

Figure 11 shows a linear fit of all of the AE results (shown as adark line). The point where this blue line crosses the y-axis is the

Fig. 9 The optimal control matrix derived using dynamic pro-gramming for a low velocity acceleration event

Fig. 11 Illustration of SOC correction method

Fig. 10 The optimal control matrix derived using dynamic pro-gramming for a high velocity acceleration event


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average FE improvement for all AEs in this category. IndividualAE results for this category are determined by tracing a point towhere it crosses zero on the y-axis using the slope of the fit line.For example, the blue circle represents an AE with a SOC differ-ence of 0.7% and a FE difference of �6 mpg. The resulting SOCadjusted FE improvement for this AE result is then calculated tobe 3%, which can be seen by following the blue arrow to the blue“X.”

This example where an unadjusted FE value of �6 mpg isadjusted to þ3 mpg seems dramatic based on a þ0.7% SOC dif-ference but it makes sense in the context of AEs, which aretypically very short. For an individual AE, a large SOC differencetranslates to a large FE adjustment. In general, the linear fitdepends on the size of the vehicle engine and battery and is differ-ent for all vehicles. This technique is the same overall process asthe existing SAE J1711 standard and while charge adjusted FE

calculations may not be perfect, this is the best answer theresearch community currently has and it is standard practice.

2.6 Drive Cycle Development. Drive cycles are a series ofdata points representing vehicle velocity versus time or distance.Standardized drive cycles have been developed that representvarious types of driving, which includes city driving, highwaydriving, and aggressive driving for small vehicles [63], heavyduty vehicles [64], and buses [65]. Current U.S. policy is to use asmall number of city, highway, and aggressive drive cycles to rep-resent the concept of operation [66] so vehicle performance canbe evaluated [67]. Most researchers typically limit their conceptof operations to one or two drive cycles [63,65,68–72] but newresearch has shown that to ensure robust operation over a varietyof driving conditions, as many drive cycles as are available shouldbe included in the study [73].

To rigorously investigate the FE costs and benefits of AE pre-diction, numerous drive cycles are investigated. The drive cyclesinclude standard EPA drive cycles as well as developed real-world drive cycles. All real-world drive cycles were recordedfrom the controller area network bus of an instrumented vehicleusing the CANOE software. The drive cycles can be divided intothree categories: (1) city drive cycles, (2) highway drive cycles,and (3) aggressive drive cycles.

Four city drive cycles are analyzed. These include one citydrive cycle recorded in Denver, CO, which drives directly throughdowntown with moderate traffic levels and one city drive cyclerecorded in Fort Collins, CO, in low traffic conditions. Two EPAcity drive cycles were also selected which include the UDDS andthe New York City Cycle (NYCC). These four city cycles aresummarized in Table 2 and the velocity traces are shown inFig. 12.

Fig. 13 All of the highway and aggressive drive cycles ana-lyzed: Denver Highway Cycle (Denver, CO) (a), Fort CollinsHighway Cycle (Fort Collins, CO) (b), HWFET (c), and US06 (d)

Table 2 All drive cycles analyzed

Drive cycle Drive cycle SourceName Type

Denver city City Real WorldNYCC City U.S. EPAUDDS City U.S. EPAFort Collins city City Real WorldDenver highway Highway Real WorldFort Collins highway Highway Real WorldHWFET Highway U.S. EPAUS06 Aggressive U.S. EPA

Fig. 12 All of the city drive cycles analyzed: Denver City Cycle(Denver, CO) (a), NYCC (b), UDDS (c), and Fort Collins CityCycle (Fort Collins, CO) (d)


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Three highway drive cycles and one aggressive drive cycle arealso analyzed. The highway drive cycles include one drive cyclerecorded in Denver, CO, that transitions across two majorhighways and one drive cycle recorded on and around I-25 in FortCollins, CO. The last highway drive cycle used is the EPA’s high-way fuel economy test (HWFET). The aggressive drive cycleused is the EPA’s US06 cycle. These four drive cycles are shownin Table 2 and the velocity traces are shown in Fig. 13.

2.7 Control Strategy Implementation. There are four con-trol strategy implementations used, which are required to under-stand the FE improvements possible from modern vehicles as wellas to determine the maximum possible fuel economy improve-ment. The four control strategies are: (1) baseline EMS, (2) opti-mal EMS with full drive cycle perfect prediction, (3) optimalEMS with perfect AE prediction, and (4) optimal EMS with onlyAE category prediction. Each of these control strategies is shownin Figs. 14–17.

The baseline EMS models the current real world control ofmodern hybrid vehicles and was developed according to the meth-ods described in Sec. 2.3. The baseline EMS controls the vehicleaccording to a set of rules and because of this, a baseline EMS issometimes referred to as a “rules-based control strategy.” Thecontrol conceptual diagram for the baseline EMS is shown inFig. 14.

The optimal EMS for perfect full drive cycle prediction wasderived according to the methods described in Sec. 2.4. This is animportant and relevant data point to put FE improvement results

in perspective by identifying the maximum possible FE improve-ment. The control conceptual diagram for this globally optimalEMS is shown in Fig. 15.

The optimal EMS for perfect AE prediction was also derivedaccording to the methods described in Sec. 2.4. This is also animportant and relevant data point to put FE improvement resultsin perspective. Although it is not expected that AE prediction willprovide nearly the same result as full drive cycle prediction, itwill be beneficial to understand the portion of the FE improve-ment that can be gained from AE prediction. Additionally, it willalso be beneficial to understand the portion of possible FEimprovement from AE prediction that was achieved by our cate-gorization scheme. The goal of designing alternate AE controlstrategies is to show that the new control strategy achieves nearlythe same result as perfect prediction of the actual AE in the drivecycle. The control conceptual diagram for this optimal EMS isshown in Fig. 16. During portions of driving that are not AEs, thebaseline EMS is employed (rules-based control). As an example,if a drive cycle consists of an AE followed by steady-state fol-lowed by an AE, then the control strategy is an optimal EMS forthe first AE, the control strategy then reverts to the baseline EMSfor the steady-state portion, and then switches to an optimal EMSfor the second AE. This was realized in simulation only by firstrunning the vehicle model with the baseline EMS, removing por-tions of control that take place during an AE, and implementingthe optimal EMS for each AE that seeks a final SOC value, SOCf,that is coincident with the SOCf from the baseline EMS. In real-world operations, there would be a handoff between baseline

Fig. 14 A conceptual diagram of how vehicle powertrain control is currently implemented, the baseline EMS

Fig. 15 A conceptual diagram of how globally optimal vehicle powertrain control is implemented, the globally opti-mal EMS

Fig. 16 A conceptual diagram of how optimal vehicle powertrain control is implemented in acceleration eventsonly

Fig. 17 A conceptual diagram of how the proposed acceleration event optimal vehicle powertrain control isimplemented


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EMS and AE look-up table control, which we are replicating insimulation.

The optimal EMS for AE category prediction was also derivedaccording to the methods described in Sec. 2.4, except only oneoptimal EMS solution is computed for each AE category as shownin Fig. 8 (AE categories are discussed in Sec. 2.2). Note that thisAE category dataset does not include any of the drive cycles ana-lyzed for this study. Figure 17 shows how AE prediction categori-zation is implemented for each drive cycle. During portions ofdriving that are not AEs, the baseline EMS is employed (rules-based control). Implementing this control strategy in each drivecycle, results in sections of applying a precomputed optimal EMSand sections of applying the baseline EMS. For example, if a drivecycle starts with an AE, the optimal EMS for its associated AEcategory is implemented. Once the AE ends, the baseline EMS isimplemented. Then, if a second AE is identified, the optimal EMSfor its associated AE category can be applied once this second AEstarts. After the second AE, the baseline EMS is implementedagain. This process continues for the duration of the drive cycle.Because the optimal solution is defined for all feasible states ofthe vehicle, solutions for different values of battery SOC are avail-able. Battery SOC for this control strategy could vary significantlyfrom the baseline EMS as the drive cycle progresses but due tothe charge sustaining constraint in the optimal EMS formulation,charge sustaining operation is maintained. The major advantageof this control strategy is that optimal EMS calculations are notcomputed in real-time. The optimal EMS is essentially imple-mented as a look-up table, thus making it compatible with the cur-rent abilities of vehicle powertrain controllers.

3 Results

The results include an investigation of the FE improvementmechanism, an FE improvement calculation for every AE in everyAE category for each categorization scheme, the impact of feweror more AE categories on the overall FE improvement, and acomparison of all four control strategies for a representative caseof city driving, highway driving, and for the aggressive drivecycle.

3.1 Fuel Economy Improvement Mechanism. Applying theDP-derived optimal EMS to AEs results in a significant FEimprovement. It was observed that this FE improvement isachieved through two different engine control strategies.

For a low velocity AE, Fig. 18(a) compares the baseline EMSand optimal EMS engine power and 18(b) compares the baseline

EMS and optimal EMS engine operation points. Comparing thetwo control strategies in Fig. 18(a) reveals that the FE improve-ment is achieved using zero engine power for the first half of theAE and higher engine power than the baseline EMS for the secondhalf of the AE. The baseline EMS uses low consistent enginepower. Both the baseline EMS and the optimal EMS end at thesame SOC. Comparing the two control strategies in Fig. 18(b)shows that this change in engine power results in more efficientengine operation since the operation points are closer to the regionof highest efficiency. In other words, there is a delay in enginepower, and this control strategy can be thought of as delayedengine power control. Average delayed control results in a FEimprovement of approximately 5%.1

For a high velocity AE, Fig. 19(a) compares the baseline EMSand optimal EMS engine power and 19(b) compares the baselineEMS and optimal EMS engine operation points. Comparing thetwo control strategies in Fig. 19(a) reveals that the FE improve-ment is achieved using nearly constant engine power during theAE. Both the baseline EMS and the optimal EMS end at the sameSOC. Comparing the two control strategies in Fig. 19(b) showsthat this change in engine power results in more efficient engineoperation since the engine operation points are closer to theengine operating region of highest efficiency. In other words, theengine power increase is advanced in time and this control strat-egy can be thought of as advanced engine power control. Averageadvanced control results in a FE improvement of approximately2%.

3.2 Acceleration Event Categorization Scheme. Investiga-tion of the overall FE improvement from each of the AE categori-zation schemes can now be investigated. The FE improvementwas determined using Eq. (27) but the optimal EMS was onlyderived for one AE (the expected AE) in each category but wasapplied to every AE in the category (mispredicted AE).

In Fig. 20(a), results for categories defined by starting and end-ing velocity are shown, sorted according to FE improvement.Fig. 20(b) shows that the highest FE improvement is achieved forlow velocity accelerations, of which there are many instances inthe driving dataset. This figure also shows a FE loss for highvelocity accelerations, of which there are few instances in thedriving dataset.

Fig. 18 A comparison of baseline control and optimal control results for engine power (a) andengine operation (b). The engine control strategy is delayed.

1The FE improvement is calculated as

FE Improvement ¼ FEOptimal EMS � FEBaseline EMS

FEBaseline EMS

� 100% (27)


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In Fig. 21(a), results for categories defined by time durationand end velocity are shown, sorted according to FE improvement.When correlating the results with the FE improvement shown inFig. 21(b), it can be seen that the largest FE improvements are forlow velocity AEs that have a relatively long duration. Addition-ally, AEs with the longest duration tend to result in a general FEimprovement. High velocity, short-duration AEs give the lowestFE improvement.

In Fig. 22(a), results for categories defined by average accelera-tion and end velocity are shown, sorted according to FE improve-ment. When correlating the results with the FE improvementshown in Fig. 21(b), it can be seen that low-magnitude low-velocity AEs achieve the highest FE improvement. Additionally,high-magnitude, high-velocity AEs give the worst FE results.

Upon initial inspection, it is confusing that certain AE catego-ries in Figs. 21 and 22 have a FE improvement of over 10%,much higher than the categories in Fig. 20. This is because catego-rizing by duration and velocity magnitude filters out extremely

long and slow AEs, which have the largest FE improvements fromoptimal EMS. Categorizing by starting and ending velocity doesnot filter out these large FE improvement cases. This might seemto indicate that the AE categories in Figs. 21 and 22 are superiorbut the weighted total FE improvement analysis tells a differentstory.

In general, each of the categorization schemes has a similarweighted total FE improvement (shown in the inset table inFigs. 20(b), 21(b), and 22(b)) with the duration and average accel-eration categorization schemes have a higher overall variancethan the starting velocity categorization scheme. It was also foundthat greater FE improvements are achieved when the actual AEduration is equal to or longer than the expected AE duration. Thisphenomenon may warrant investigation in future work.

3.3 Number of Acceleration Event Categories. Next, weinvestigate the tradeoff between FE improvement and the number

Fig. 20 Plot comparing characteristic velocities to FE performance for each starting and ending velocity category, sorted bydecreasing mean FE improvement

Fig. 19 A comparison of baseline control and optimal control results for engine power (a) andengine operation (b). The engine control strategy is advanced.


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of categories. With too few categories, the drive cycle data willhave a large FE improvement variance and with too many catego-ries, the data are overfit and lack generalization. Note that thisalso gives insight into the effect of category misprediction, whichis essentially the case of too few categories.

FE results for various numbers of starting velocity and endingvelocity categories can be seen in Fig. 23. This figure showsthat when few starting and ending speed categories are used,there is a large FE variance. This figure also shows that when100 s of starting and ending velocity categories are used, the FEimprovement is slightly higher, but we are approaching the point

of an optimal EMS derived for every single AE, which resultsin an overfitting of data and a lack of generalization. For around15 starting and ending categories, there is a significant androbust FE improvement. This figure also shows that constrainingthe end velocity is more important than constraining the startingvelocity. High numbers of end velocity categories (and thereforestronger constraints on end velocity error) result in robust FEimprovements, with little regard to the number of start velocitycategories; conversely, if there are few end velocity categories,no number of start velocity categories can produce reliable FEbenefits.

Fig. 21 Plot comparing characteristic velocities to FE performance for each ending velocity and duration category, sorted bydecreasing mean FE improvement

Fig. 22 Plot comparing characteristic velocities to FE performance for each ending velocity and acceleration magnitude cate-gory, sorted by decreasing mean FE improvement


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FE results for various numbers of time duration and endingvelocity categories can be seen in Fig. 24. For few numbers of cat-egories (e.g., AE categorization scheme number> 120), the var-iance in FE improvement is very large, but when 100 s ofcategories are used, the FE results are actually worse. Significantand robust FE improvement is achieved with approximately tentime duration and end velocity categories. Figure 24 also showsthat the end velocity error is more important to constrain thanduration error.

FE results for various numbers of time duration and endingvelocity categories can be seen in Fig. 25. For few numbers of cat-egories, the variance in FE improvement is large, but with 100 sof categories, the FE results are actually worse. Figure 25 alsoshows that end velocity error is more important to constrain thanaverage acceleration error based on the similar relationship to thetime duration categorization case.

Overall AE misprediction is most prone to end velocity error,reasonably prone to duration and acceleration error, and least

Fig. 23 Plot comparing the number of starting and ending velocity categories to FE performance, sorted by decreasing meanFE improvement

Fig. 24 Plot comparing the number of duration and ending velocity categories to FE performance, sorted by decreasingmean FE improvement


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prone to start velocity error. A categorization of AEs according tostarting and ending velocity yields the largest FE improvements.This informs real-world implementation of this technique.

Note that the investigation of the number of AE categoriesindirectly provides information about what happens when the AEcategory itself is mispredicted. A specific AE categorizationscheme can be further justified by directly testing the effect of AEcategory misprediction. It is anticipated that this analysis will beincluded in future work.

3.4 Overall Drive Cycle Results. Four control strategies arerequired to properly analyze the results of the proposed AE cate-gorization control strategy: (1) the baseline EMS, (2) the globallyoptimal EMS from perfect full drive cycle prediction, (3) the opti-mal EMS from perfect AE prediction, and (4) the proposed AEcategorization prediction. Note that second control strategy, theglobally optimal EMS from perfect full drive cycle prediction, isthe maximum possible FE that can be achieved from an optimalEMS. The third control strategy, the optimal EMS from perfectAE prediction, is the maximum possible FE that can be achievedfrom only AE prediction with an optimal EMS. These four controlstrategies are then reduced to three FE results by calculating theFE improvement over the baseline EMS according to Eq. (27).

Figure 26 shows the FE results for all control strategies for alldrive cycles. As expected, perfect full drive cycle predictionresults in a significant FE improvement ranging from 3.9% for theUS06 cycle up to 15.1% for the Denver city cycle. Perfectly pre-dicting every AE in each drive cycle results in a sizable FEimprovement ranging from 0.5% for the US06 drive cycle up to5.1% for the NYCC drive cycle. Predicting only the AE categoryand applying a precomputed optimal EMS can result in significantFE improvements but the results span a 1.2% FE loss for theUS06 drive cycle up to a 3.9% FE improvement for the NYCCdrive cycle.

Table 3 compares some characteristics of each drive cycle. TheFort Collins highway cycle and the HWFET cycle have the fewestAEs and thus AEs only compose 13% and 10% of the drive cycle,respectively. The Denver City Cycle, the NYCC drive cycle, andthe UDDS drive cycle have the smallest AE average velocity. The

US06 drive cycle has a small number of AEs and the highest AEaverage velocity.

By comparing Fig. 26 and Table 3, trends can be discoveredregarding large FE improvement cases. Figure 26 shows that theDenver City Cycle, the NYCC, the UDDS, the Fort Collins CityCycle, and the Denver Highway Cycle all have a large FEimprovement from AE category prediction with a precomputedoptimal EMS. And Table 3 shows that these drive cycles have alarge number of AEs and the AE average velocity is low. There-fore, for drive cycles with lots of low velocity AEs, category pre-diction with a precomputed optimal EMS provides a significantFE improvement.

Other trends can also be discovered by comparing Fig. 26 andTable 3 relating to small FE improvement cases. Figure 26 showsthat the Fort Collins Highway and the HWFET drive cycles resultin the lowest FE improvement for AE category prediction with aprecomputed optimal EMS. Table 3 shows that these drive cyclesdo not have many AEs and the HWFET has high velocity AEs.Therefore, using an AE category prediction with a precomputedoptimal EMS does not provide a significant FE improvement fordrive cycles without many AEs.

Lastly, the FE loss scenario can be understood by comparingFig. 26 and Table 3. Figure 26 shows a 1.2% FE loss for theUS06 drive cycle when AE category prediction with a precom-puted optimal EMS is used. Table 3 shows that this drive cyclehas a significant amount of AEs, but the AEs are at a signifi-cantly higher velocity. This is important because high velocityAEs typically result in a FE loss due to the original dataset usedto precompute the optimal EMS not including many high-velocity AEs.

In general, AE category prediction with a precomputed optimalEMS results in half to 90% of the FE improvement from perfectAE prediction. This strategy does not require real-time computa-tions and requires very limited predictions. The FE improvementresults from perfect AE prediction compared to full drive cycleprediction are dependent on how many AEs are in the drive cycle.But, for drive cycles with a large number of AEs, the FE improve-ment can be significant for a relatively low prediction require-ment. For example, 18% of the NYCC drive cycle is composed ofAEs, but half of the maximum FE improvement can be realized

Fig. 25 Plot comparing the number of average acceleration and ending velocity categories to FE performance, sorted bydecreasing mean FE improvement


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by only predicting AEs; so by predicting aspects of 18% of thisdrive cycle, 50% of the maximum FE can be achieved.

3.5 Individual Drive Cycle Results. The FE results shown inFig. 26 can be further explored by investigating the second-by-second engine operation and battery SOC for each AE in eachdrive cycle. There are three unique FE results: (1) nearly the sameFE improvement from AE category prediction and perfect AE pre-diction, (2) an overall FE improvement but a reduction when com-pared to perfect AE prediction, and (3) a FE loss when comparedto the baseline EMS. A representative drive cycle from each of

these results will be presented and discussed. All additional drivecycles are shown.

The drive cycle that results in nearly the same FE improvementfrom AE category prediction and perfect AE prediction is theDenver Highway drive cycle. As shown in Fig. 26, perfect AEprediction results in a 2.4% FE improvement while AE categoryprediction results in a 2.0% FE improvement. The velocitytrace for this drive cycle with AEs identified is shown inFig. 27(a). Figures 27(b) and 27(c) show a second-by-second FEimprovement and battery SOC results along the drive cycle. Forfull drive cycle prediction, there is a significant SOC excursioncompared to the baseline EMS but also a significant FE improve-ment. Perfect AE prediction and AE category prediction providenearly the same overall FE improvement, but there are significantdifferences in individual AE operation. For example, the AE thatstarts at 847 s results in more fuel consumption for AE categoryprediction and a banking of battery SOC. These differences evenout over the drive cycle.

One drive cycle that results in an overall FE improvement but areduction when compared to perfect AE prediction is the NYCCdrive cycle. As shown in Fig. 26, perfect AE prediction results ina 5.1% FE improvement while AE category prediction results in a3.9% FE improvement. The velocity trace, AE identification,second-by-second FE results for each control strategy, and batterySOC are shown in Fig. 28. For each control strategy, there is a sig-nificant FE improvement with limited SOC excursion. Addition-ally, when comparing perfect AE prediction and AE categoryprediction, the overall FE improvements are similar but results foreach AE can vary. For example, the AE that starts at 145 s resultsin more fuel consumption but SOC banking, which is evened outonce the next AE starts,

The drive cycle that results in a FE loss when compared to thebaseline EMS is the US06 drive cycle. As shown in Fig. 26, per-fect AE prediction results in a 0.5% FE improvement while AEcategory prediction results in a 1.2% FE loss. The velocity trace,AE identification, second-by-second FE results for each controlstrategy, and battery SOC are shown in Fig. 29. Minimal FEimprovements are achieved for each perfectly predicted AE, butfor category AE prediction, FE losses are frequent. For example,AEs at 50 s, 90 s, 140 s, etc. Results in FE losses. This indicatesthat the optimal EMS derived for this category does notadequately capture aggressive driving. As discussed in Sec. 2.4,high-velocity accelerations were not frequent in this dataset andwhen this issue is compounded with highly aggressive AEs, whichare also not prevalent in the dataset, there is no optimal controlrepresentative of this driving to implement. In other words, theAE dataset used to derive the optimal EMS must be inclusive ofcurrent driving habits or FE losses are possible.

4 Conclusions

In this study, a dataset of 7708 AEs was extracted from 384real-world drive cycles. These AEs were organized according tomultiple categorization schemes: end velocity and (1) startingvelocity, (2) time duration, and (3) average acceleration. A base-line EMS for a 2010 Toyota Prius was derived using a combina-tion of the AUTONOMIE modeling software and an equation-based

Fig. 26 All FE results shown as a percentage improvementover the baseline EMS FE. Note that all optimal EMS are derivedusing DP.

Table 3 All drive cycles analyzed

Drive cycle Number of AEs AE portion of drive cycle Average v for AEs

Denver city 28 18% 15.3 m= secNYCC 13 18% 14.9 m= secUDDS 22 22% 17.4 m= secFort Collins city 19 23% 20.5 m= secDenver highway 18 20% 23.4 m= secFort Collins highway 11 13% 18.2 m= secHWFET 4 10% 23.4 m= secUS06 12 26% 25.7 m= sec


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Fig. 27 The Denver Highway Cycle, which shows a close correlation between AE category prediction and perfect AEprediction

Fig. 28 The NYCC drive cycle, which shows a similar correlation between AE category prediction and perfect AE prediction


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power-split model, which was rigorously validated against real-world performance. An optimal EMS was derived using DP forperfect full drive cycle prediction, perfect AE prediction, and foronly the most common AE in each category, which expands upona previous research finding that FE improvements are maintainedfor a DP-derived optimal EMS on a similar drive cycle [40]. Eachof these four control strategies was tested on four EPA drivecycles and four real-world drive cycles, which represent city driv-ing, highway driving, and aggressive driving. The results showthat FE improvements can be obtained using “delayed control” forlow-velocity AEs and by using “advanced control” for high veloc-ity AEs. The most significant and robust FE improvements can beobtained using starting velocity and ending velocity AE categori-zation with around 15 categories of each. A FE improvementbetween half to 90% of perfect AE prediction is possible which,in turn, represents one fourth to half of the FE improvementresults of full drive cycle prediction. But FE losses are possible ifthe AEs used to derive the optimal EMS are not representative ofcurrent driving habits.

There are several novel techniques and approaches developedin this work, which were discussed in previous sections, and thereare three overall significant findings: (1) with proper categoriza-tion, a DP-derived globally optimal EMS implemented in AEsdemonstrates a striking robustness to prediction error, (2) approxi-mate predictions of AEs, which typically compose only 20% of adrive cycle, could result in as much as 50% of the maximum pos-sible FE improvement, and (3) a DP-derived globally optimalEMS can be implemented in AEs as a look-up table with onlyknowledge of an approximate ending velocity of the AE. In otherwords, a DP-derived optimal EMS that controls AEs obtains sig-nificant FE improvements and can be implemented in vehiclestoday using the limited computational power of current vehiclecontrollers with no new hardware.

Acknowledgment

This research is the result of four years of collaborative effortbetween the Gasoline Hybrid Research Group at Toyota MotorEngineering & Manufacturing North America and Colorado StateUniversity. This would not have been possible without the supportand guidance from Heraldo Sefanon at Toyota and the contribu-tions of numerous students including David Baker, Thomas Cum-mings, and Abril Galang.

Funding Data

� Toyota (Funder ID: 10.13039/100009584).

References[1] International Energy Agency, 2017, “Key World Energy Statistics,” Interna-

tional Energy Agency, Vienna, Austria, Report.[2] van Moerkerk, M., and Crijns-Graus, W., 2016, “A Comparison of Oil Supply

Risks in EU, US, japan, china and India Under Different Climate Scenarios,”Energy Policy, 88, pp. 148–158.

[3] International Energy Agency, 2016, “World Energy Outlook Special Report:Energy and Air Pollution,” International Energy Agency, Vienna, Austria,Report.

[4] World Health Organization, 2016, “World Health Statistics 2016: MonitoringHealth for the Sustainable Development Goals (SDGs),” World Health Organi-zation, Geneva, Switzerland, Report.

[5] National Research Council, Division on Earth and Life Studies, Board onAtmospheric Sciences and Climate, and America’s Climate Choices: Panel onAdvancing the Science of Climate Change, 2011, Advancing the Science of Cli-mate Change, National Academies Press, Washington, DC.

[6] International Energy Agency, 2016, “CO2 Emissions from Fuel Combustion,”International Energy Agency, Vienna, Austria, Report.

[7] International Energy Agency, 2017, “CO2 Emissions from Fuel Combustion2017,” International Energy Agency, Vienna, Austria, Report.

[8] Atabani, A. E., Badruddin, I. A., Mekhilef, S., and Silitonga, A. S., 2011, “AReview on Global Fuel Economy Standards, Labels and Technologies in theTransportation Sector,” Renewable Sustainable Energy Rev., 15(9), pp.4586–4610.

Fig. 29 The US06 drive cycle, which shows worse results between AE category prediction and perfect AE prediction


Dow




estern Michigan U


http://dx.doi.org/10.1016/j.enpol.2015.10.015

http://dx.doi.org/10.1016/j.rser.2011.07.092

[9] Global Fuel Economy Initiative, 2009, “50 by 50 Global Fuel Economy Initia-tive,” Global Fuel Economy Initiative, London, Report.

[10] Global Fuel Economy Initiative, 2017, “Global Fuel Economy: An Update ForCOP22,” Global Fuel Economy Initiative, London, Report.

[11] Ewing, J., 2017, “France Plans to End Sales of Gas and Diesel Cars by 2040,”The New York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/07/06/business/energy-environment/france-cars-ban-gas-diesel.html

[12] Sengupta, S., 2017, “Both Climate Leader and Oil Giant? A Norwegian Para-dox,” The New York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/06/17/world/europe/norway-climate-oil.html

[13] Castle, S., 2017, “Britain to Ban New Diesel and Gas Cars by 2040,” The NewYork Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/07/26/world/europe/uk-diesel-petrol-emissions.html

[14] Bradsher, K., 2017, “China Hastens the World Toward an Electric-Car Future,”The New York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/10/09/business/china-hastens-the-world-toward-an-electric-car-future.html

[15] Anand, G., 2017, “India, Once a Coal Goliath, is Fast Turning Green,” TheNew York Times, New York, accessed Mar. 9, 2020, https://www.nytimes.com/2017/06/02/world/asia/india-coal-green-energy-climate.html

[16] Jacobs Juncture, M., 2016, “High Pressure for Low Emissions: How Civil SocietyCreated the Paris Climate Agreement,” Wiley Online Library, Hoboken, NJ.

[17] Christoff, P., 2016, “The Promissory Note: COP 21 and the Paris ClimateAgreement,” Environ. Polit., 25(5), pp. 765–787.

[18] International Energy Agency, 2015, “Energy and Climate Change—WorldEnergy Outlook Special Report,” International Energy Agency, Vienna, Aus-tria, Report.

[19] United Nations Framework Convention on Climate Change, 2015, “Paris Dec-laration on Electro-Mobility and Climate Change and Call to Action,” UnitedNations Framework Convention on Climate Change, Bonn, Germany, epub.

[20] Global Fuel Economy Initiative, 2016, “Global Fuel Economy: An Update forCOP22,” Global Fuel Economy Initiative, London, Report.

[21] Global Fuel Economy Initiative, 2017, “GFEI Action for More Fuel EfficientVehicles: COP23 Update (Global Fuel Economy—An Update For Cop23),”Global Fuel Economy Initiative, London, Report.

[22] Global Fuel Economy Initiative, 2011, “50 by 50 Prospects and Progress,”Global Fuel Economy Initiative, London, Report.

[23] Office of Transportation, Air Quality U.S. Environmental Protection AgencyNational Highway Traffic Safety Administration U.S. Department of Transpor-tation, and the California Air Resources Board, 2016, Draft Technical Assess-ment Report: Midterm Evaluation of Light-Duty Vehicle Greenhouse GasEmission Standards and Corporate Average Fuel Economy Standards for ModelYears 2022–2025,” Report No. EPA-420-D-16-900.

[24] Lin, C.-C., Peng, H., Grizzle, J. W., Liu, J., and Busdiecker, M., 2003, “ControlSystem Development for an Advanced-Technology Medium-Duty Hybrid Elec-tric Truck,” SAE Paper No. 2003-01-3369.

[25] Lin, C.-C., Kang, J.-M., Grizzle, J. W., and Peng, H., 2001, “EnergyManagement Strategy for a Parallel Hybrid Electric Truck,” Proceedings of theAmerican Control Conference (Cat. No.01CH37148), Vol. 4, Arlington, VA,June 25–27, pp. 2878–2883.

[26] Lin, C.-C., Kim, M.-J., Peng, H., and Grizzle, J. W., 2006, “System-LevelModel and Stochastic Optimal Control for a PEM Fuel Cell Hybrid Vehicle,”ASME J. Dyn. Syst. Meas. Control, 128(4), pp. 878–890.

[27] Kolmanovsky, I. V., Lezhnev, L., and Maizenberg, T. L., 2008, “Discrete-TimeDrift Counteraction Stochastic Optimal Control: Theory and Application-Motivated Examples,” Automatica., 44(1), pp. 177–184.

[28] Opila, D. F., Wang, X., McGee, R., and Grizzle, J. W., 2013, “Real-TimeImplementation and Hardware Testing of a Hybrid Vehicle Energy Manage-ment Controller Based on Stochastic Dynamic Programming,” ASME J. Dyn.Syst. Meas. Control, 135(2), p. 021002.

[29] Vagg, C., Akehurst, S., Brace, C. J., and Ash, L., 2016, “Stochastic DynamicProgramming in the Real-World Control of Hybrid Electric Vehicles,” IEEETrans. Control Syst. Technol., 24(3), pp. 853–866.

[30] Musardo, C., Rizzoni, G., Guezennec, Y., and Staccia, B., 2005, “A-ECMS: AnAdaptive Algorithm for Hybrid Electric Vehicle Energy Management,” Eur. J.Control, 11(4–5), pp. 509–524.

[31] Yang, C., Du, S., Li, L., You, S., Yang, Y., and Zhao, Y., 2017, “AdaptiveReal-Time Optimal Energy Management Strategy Based on Equivalent FactorsOptimization for Plug-in Hybrid Electric Vehicle,” Appl. Energy, 203(Suppl.C), pp. 883–896.

[32] Borhan, H., and Vahidi, A., 2012, “Model Predictive Control of a Hybrid Elec-tric Powertrain With Combined Battery and Ultracapacitor Energy Storage Sys-tem,” Int. J. Powertrains, 1(4), p. 351.

[33] HomChaudhuri, B., Vahidi, A., and Pisu, P., 2017, “Fast Model PredictiveControl-Based Fuel Efficient Control Strategy for a Group of ConnectedVehicles in Urban Road Conditions,” IEEE Trans. Control Syst. Technol.,25(2), pp. 760–767.

[34] Bianchi, D., Rolando, L., Serrao, L., Onori, S., Rizzoni, G., Al-Khayat, N.,Hsieh, T.-M., and Kang, P., 2010, “A Rule-Based Strategy for a Series/ParallelHybrid Electric Vehicle: An Approach Based on Dynamic Programming,”ASME Paper No. DSCC2010-4233.

[35] Onori, S., Serrao, L., and Rizzoni, G., 2016, “Equivalent Consumption Minimi-zation Strategy,” Hybrid Electric Vehicles (Springer Briefs in Electrical andComputer Engineering), Springer, London, pp. 65–77.

[36] Paganelli, G., Guezennec, Y., and Rizzoni, G., 2002, “Optimizing ControlStrategy for Hybrid Fuel Cell Vehicle,” SAE Paper No. 2002-01-0102.

[37] Asher, Z. D., Patil, A. A., Wifvat, V. T., Frank, A. A., Samuelsen, S., and Brad-ley, T. H., 2019, “Identification and Review of the Research Gaps Preventing a

Realization of Optimal Energy Management Strategies in Vehicles,” SAE Int.J. Alt. Power., 8(2), pp. 133–149.

[38] Asher, Z. D., Cummings, T., and Bradley, T. H., 2016, “The Effect of Hill Plan-ning and Route Type Identification Prediction Signal Quality on Hybrid VehicleFuel Economy,” SAE Paper No. 2016-01-1240.

[39] Cummings, T., Bradley, T. H., and Asher, Z. D., 2015, “The Effect of TripPreview Prediction Signal Quality on Hybrid Vehicle Fuel Economy,” IFAC-PapersOnLine, 48(15), pp. 271–276.

[40] Asher, Z. D., Baker, D. A., and Bradley, T. H., 2017, “Prediction Error Appliedto Hybrid Electric Vehicle Optimal Fuel Economy,” IEEE Trans. Control Syst.Technol., 26(6), pp. 2121–2134.

[41] Asher, Z. D., Tunnell, J. A., Baker, D. A., Fitzgerald, R. J., Banaei-Kashani, F.,Pasricha, S., and Bradley, T. H., 2018, “Enabling Prediction for Optimal FuelEconomy Vehicle Control,” SAE Paper No. 2018-01-1015.

[42] Baker, D., Asher, Z. D., and Bradley, T., 2018, “V2V Communication BasedReal-World Velocity Predictions for Improved HEV Fuel Economy,” SAEPaper No. 2018-01-1000.

[43] Gaikwad, T. D., Asher, Z. D., Liu, K., Huang, M., and Kolmanovsky, I., 2019,“Vehicle Velocity Prediction and Energy Management Strategy: Part 2—Integration of Machine Learning Vehicle Velocity Prediction With OptimalEnergy Management to Improve Fuel Economy,” SAE Paper No. 2019-01-1212.

[44] Asher, Z., Baker, D., and Bradley, T. H., 2019, “Systems and Methods for Pre-diction Windows for Optimal Powertrain Control,” U.S. Patent No. USPTO20190375421:A1.

[45] Akcelik, R., and Biggs, D. C., 1987, “Acceleration Profile Models for Vehiclesin Road Traffic,” Transp. Sci., 21(1), pp. 36–54.

[46] Akcelik, R., and Besley, M., 2001, “Acceleration and Deceleration Models,”23rd Conference of Australian Institutes of Transport Research (CAITR 2001),Monash University, Melbourne, Australia, Vol. 10, Dec. 10–12, p. 12.

[47] Wang, J., Dixon, K., Li, H., and Ogle, J., 2004, “Normal Acceleration Behaviorof Passenger Vehicles Starting From Rest at All-Way Stop-Controlled Inter-sections,” Transp. Res. Rec.: J. Transp. Res. Board, 1883(1), pp. 158–166.

[48] LeBlanc, D. J., Sivak, M., and Bogard, S., 2010, “Using Naturalistic DrivingData to Assess Variations in Fuel Efficiency Among Individual Drivers,”University of Michigan, Ann Arbor, MI.

[49] Long, G., 2000, “Acceleration Characteristics of Starting Vehicles,” Transp.Res. Rec.: J. Transp. Res. Board, 1737(1), pp. 58–70.

[50] The U.S. Department of Energy Office of Energy Efficiency and RenewableEnergy, 2018, “2018 Best and Worst Fuel Economy Vehicles,” The U.S. Depart-ment of Energy Office of Energy Efficiency and Renewable Energy, Washington,DC, accessed Mar. 5, 2020, https://www.fueleconomy.gov/feg/best-worst.shtml

[51] Kim, N., Rousseau, A., and Rask, E., 2012, “Autonomie Model ValidationWith Test Data for 2010 Toyota Prius,” SAE Paper No. 2012-01-1040.

[52] Argonne National Lab, 2015, “Downloadable Dynamometer Database, Apr.Title of the Publication Associated with this Dataset: Test Summary Sheet,”Argonne National Lab, Lemont, IL.

[53] Rajamani, R., 2011, Vehicle Dynamics and Control, Springer Science & Busi-ness Media, Berlin.

[54] Arata, J. P., III, 2011, “Simulation and Control Strategy Development ofPower-Split Hybrid-Electric Vehicles,” Ph.D. thesis, Georgia Institute of Tech-nology, Atlanta, GA.

[55] Kawamoto, N., Naiki, K., Kawai, T., Shikida, T., and Tomatsuri, M., 2009,“Development of New 1.8-Liter Engine for Hybrid Vehicles,” SAE Paper No.2009-01-1061.

[56] Burress, T. A., Campbell, S. L., Coomer, C., Ayers, C. W., Wereszczak, A. A.,Cunningham, J. P., Marlino, L. D., Seiber, L. E., and Lin, H.-T., 2011,“Evaluation of the 2010 Toyota Prius Hybrid Synergy Drive System,” OakRidge National Lab, Oak Ridge, TN, Report.

[57] Gunst, R. F., 1996, “Response Surface Methodology: Process and ProductOptimization Using Designed Experiments,” Technometrics, 38(3), pp. 284–286.

[58] Frank, A. A., 2000, “Control Method and Apparatus for Internal CombustionEngine Electric Hybrid Vehicles,” U.S. Patent No. USPTO 6054844.

[59] Yang, S., Wang, W., Zhang, F., Hu, Y., and Xi, J., 2018, “Driving-Style-Ori-ented Adaptive Equivalent Consumption Minimization Strategies for HEVs,”IEEE Trans. Veh. Technol., 67(10), pp. 9249–9261.

[60] Bertsekas, D. P., Bertsekas, D. P., Bertsekas, D. P., and Bertsekas, D. P., 1995,Dynamic Programming and Optimal Control, Vol. 1, Athena Scientific, Belmont, MA.

[61] Bellman, R., 1956, “Dynamic Programming and Lagrange Multipliers,” Proc.Natl. Acad. Sci. U. S. A, 42(10), pp. 767–769.

[62] SAE International, 2002, “Recommended Practice for Measuring the ExhaustEmissions and Fuel Economy of Hybrid-Electric Vehicles,” SAE Paper No. J1711.

[63] Montazeri-Gh, M., and Naghizadeh, M., 2003, “Development of Car Drive Cyclefor Simulation of Emissions and Fuel Economy,” Proceedings of 15th EuropeanSimulation Symposium, Delft, The Netherlands, Oct. 26–29.

[64] Gautam, M., Clark, N., Riddle, W., Nine, R., and Wayne, W. S., and others,2002, “Development and Initial Use of a Heavy-Duty Diesel Truck Test Sched-ule for Emissions Characterization,”

[65] Sandoval Leon, J. A., 2011, “Study of Transit Bus Duty Cycle and Its Influenceon Fuel Economy and Emissions of Diesel-Electric Hybrids,” Ph.D. thesis,West Virginia University, Ann Arbor, United States.

[66] Fairley, R. E., and Thayer, R. H., 1997, “The Concept of Operations: TheBridge From Operational Requirements to Technical Specifications,” Ann.Software Eng., 3(1), pp. 417–432.

[67] U.S. Environmental Protection Agency, 2006, “Final Technical Support Docu-ment: Fuel Economy Labeling of Motor Vehicle Revisions to Improve Calcula-tion of Fuel Economy Estimates,” Office of Transportation and Air Quality,Report No. EPA420-R-06-017.


Dow




estern Michigan U


https://www.globalfueleconomy.org/data-and-research/publications/50by50-global-fuel-economy-initiative

https://www.globalfueleconomy.org/media/412594/gfei-cop22-update-lr-spreads.pdf

https://www.nytimes.com/2017/07/06/business/energy-environment/france-cars-ban-gas-diesel.html

https://www.nytimes.com/2017/07/06/business/energy-environment/france-cars-ban-gas-diesel.html

https://www.nytimes.com/2017/06/17/world/europe/norway-climate-oil.html

https://www.nytimes.com/2017/06/17/world/europe/norway-climate-oil.html

https://www.nytimes.com/2017/07/26/world/europe/uk-diesel-petrol-emissions.html

https://www.nytimes.com/2017/07/26/world/europe/uk-diesel-petrol-emissions.html

https://www.nytimes.com/2017/10/09/business/china-hastens-the-world-toward-an-electric-car-future.html

https://www.nytimes.com/2017/10/09/business/china-hastens-the-world-toward-an-electric-car-future.html

https://www.nytimes.com/2017/06/02/world/asia/india-coal-green-energy-climate.html

https://www.nytimes.com/2017/06/02/world/asia/india-coal-green-energy-climate.html

http://dx.doi.org/10.1080/09644016.2016.1191818

https://unfccc.int/news/the-paris-declaration-on-electro-mobility-and-climate-change-and-call-to-action

http://dx.doi.org/10.4271/2003-01-3369

http://dx.doi.org/10.1115/1.2362785

http://dx.doi.org/10.1016/j.automatica.2007.06.002

http://dx.doi.org/10.1115/1.4007238

http://dx.doi.org/10.1115/1.4007238

http://dx.doi.org/10.1109/TCST.2015.2498141


http://dx.doi.org/10.3166/ejc.11.509-524

http://dx.doi.org/10.3166/ejc.11.509-524

http://dx.doi.org/10.1016/j.apenergy.2017.06.106

http://dx.doi.org/10.1504/IJPT.2012.049645


http://dx.doi.org/10.1115/DSCC2010-4233

http://dx.doi.org/10.4271/2002-01-0102

http://dx.doi.org/10.4271/08-08-02-0009

http://dx.doi.org/10.4271/08-08-02-0009

http://dx.doi.org/10.4271/2016-01-1240

http://dx.doi.org/10.1016/j.ifacol.2015.10.039

http://dx.doi.org/10.1016/j.ifacol.2015.10.039



http://dx.doi.org/10.4271/2018-01-1015

http://dx.doi.org/10.4271/2018-01-1000

http://dx.doi.org/10.4271/2019-01-1212

https://patentimages.storage.googleapis.com/8d/dd/6a/054642b942ab70/US20190375421A1.pdf

https://patentimages.storage.googleapis.com/8d/dd/6a/054642b942ab70/US20190375421A1.pdf

http://dx.doi.org/10.1287/trsc.21.1.36

https://www.researchgate.net/publication/238778191_Acceleration_and_deceleration_models

http://dx.doi.org/10.3141/1883-18

https://deepblue.lib.umich.edu/handle/2027.42/78449

http://dx.doi.org/10.3141/1737-08

http://dx.doi.org/10.3141/1737-08

https://www.fueleconomy.gov/feg/best-worst.shtml

http://dx.doi.org/10.4271/2012-01-1040

https://smartech.gatech.edu/handle/1853/42790

http://dx.doi.org/10.4271/2009-01-1061

https://info.ornl.gov/sites/publications/files/Pub26762.pdf

http://dx.doi.org/10.1080/00401706.1996.10484509

https://patentimages.storage.googleapis.com/da/aa/bb/50e3f2baf53493/US6054844.pdf

http://dx.doi.org/10.1109/TVT.2018.2855146

http://dx.doi.org/10.1073/pnas.42.10.767

http://dx.doi.org/10.1073/pnas.42.10.767

http://dx.doi.org/10.4271/J1711

https://pdfs.semanticscholar.org/e712/344e6d28683bc24f90a5a7f87560a70252f5.pdf

https://pdfs.semanticscholar.org/e712/344e6d28683bc24f90a5a7f87560a70252f5.pdf

https://researchrepository.wvu.edu/cgi/viewcontent.cgi?article=4055&mp;context=etd

http://dx.doi.org/10.1023/A:1018985904689

http://dx.doi.org/10.1023/A:1018985904689

[68] Chen, L., Zhu, F., Zhang, M., Huo, Y., Yin, C., and Peng, H., 2011, “Design andAnalysis of an Electrical Variable Transmission for a Series–Parallel HybridElectric Vehicle,” IEEE Trans. Veh. Technol., 60(5), pp. 2354–2363.

[69] Ganji, B., Kouzani, A. Z., and Trinh, H. M., 2010, “Drive Cycle Analysis of thePerformance of Hybrid Electric Vehicles,” Life System Modeling and IntelligentComputing, Springer, Berlin, Heidelberg, pp. 434–444.

[70] Barnitt, R. A., Brooker, A. D., and Ramroth, L., 2010, “Model-Based Analysis ofElectric Drive Options for Medium-Duty Parcel Delivery Vehicles,” NationalRenewable Energy Lab (NREL), Golden, CO, Report No. NREL/CP-5400-49253.

[71] Amrhein, M., and Krein, P. T., 2005, “Dynamic Simulation for Analysis ofHybrid Electric Vehicle System and Subsystem Interactions, Including PowerElectronics,” IEEE Trans. Veh. Technol., 54(3), pp. 825–836.

[72] Aceves, S. M., and Smith, J. R., 1996, “Hybrid and Conventional HydrogenEngine Vehicles That Meet EZEV Emissions,” Lawrence Livermore NationalLab, Livermore, CA, Report No. UCRL-JC-125891, CONF-970210-6.

[73] Geller, B. M., and Bradley, T. H., 2015, “Analyzing Drive Cycles for HybridElectric Vehicle Simulation and Optimization,” ASME J. Mech. Des., 137(4),p. 041401.


Dow




estern Michigan U



https://www.nrel.gov/docs/fy11osti/49253.pdf


https://www.osti.gov/servlets/purl/496115

http://dx.doi.org/10.1115/1.4029583

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