comprehensive design methodology of input- and output-split...

2912 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 21, NO. 6, DECEMBER 2016

Comprehensive Design Methodology of Input-and Output-Split Hybrid Electric Vehicles: In

Search of Optimal ConfigurationHyunjun Kim and Dongsuk Kum, Member, IEEE

Abstract—Despite high potentials of power-split hybridelectric vehicles (PS-HEV), their design and control prob-lems are nontrivial. For instance, there exist 24 ways ofconnecting four components (two electric machines, anengine, and a vehicle wheel) with a planetary gear (PG),and more than thousand ways with two PGs. Furthermore,when PG and final drive ratios are considered design vari-ables, finding an optimal design that fulfills both high fueleconomy and short acceleration time is a challenge. In thispaper, a systematic configuration searching methodologyis proposed to find an optimal single PG PS-HEV config-uration for both performance metrics. First, by identifyingall the possible single PG configurations and reorganizingthem into a compound lever design space, the performancemetrics are explored in the continuous design space.Then, the designs are mapped onto the “fuel economy—acceleration performance” plane to solve the multiobjectiveconfiguration selection problem. Thus, a highly promisingconfiguration (“o6”), which outperforms Prius design inthe acceleration performance, is selected among ParetoFrontier. A case study has been conducted on a sport utilityvehicle specification. The study illustrates that the perfor-mance metrics of candidate configurations change signifi-cantly, and thus, selecting a proper configuration is crucialto evoke full potential of the given powertrain components.

Index Terms—Compound lever, lever analogy, multiob-jective configuration selection, power-split hybrid electricvehicle (PS-HEV), single planetary gear (PG).

NOMENCALTURE

Variable DefinitionR Number of ring gear teethS Number of sun gear teethPGratio PG ratio (=R/S)SRratio PG lever design variable (=S/R)

Manuscript received August 31, 2015; revised January 18, 2016 andApril 25, 2016; accepted May 18, 2016. Date of publication June 10,2016; date of current version December 13, 2016. Recommendedby Technical Editor C. Manzie. This work was supported in part bythe Basic Science Research Program through the National ResearchFoundation of Korea (NRF) by the Ministry of Science, Information andCommunications Technologies (ICT), and Future Planning under Grant2013R1A1A1060397, and in part by the Technology Innovation Program(10051876) funded by the Ministry of Trade, Industry, and Energy (MI,Korea).

The authors are with the Cho Chun Shik Graduate School of GreenTransportation, Korea Advanced Institute of Science and Technology,Daejeon 34141, Korea (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2016.2579646

FDratio (K) Final drive ratiod1 , d2 , d3 Connections between PG shafts and componentsα, β Compound lever design variableω Angular speed (rad/s)ω̇ Angular acceleration (rad/s)2

T Torque (N·m)I Rotational inertia (kg·m2)F Internal force of planetary gear (N)r Tire effective rolling radius (m)m Vehicle mass (kg)f0 , f1 , f2 Coast-down coefficients (N, N·(s/m), N·(s/m)2)FE Fuel economy (km/L)AT Acceleration time (s)p, q Weighting factor for FE and AT

I. INTRODUCTION

R ECENT energy and environmental concerns around theglobe motivated many countries such as E.U., Japan, and

U.S. to legislate fuel economy (FE) and emission regulations forground vehicles. As a result of these efforts coupled with tech-nological developments, hybrid electric vehicle (HEV) markethas been rapidly growing [1], and the world HEV market iscurrently dominated by power-split HEV mainly due to its highperformance [2].

Toyota Prius and Chevy Volt are the two most widely knownpower-split HEVs. Though they equip single planetary gear(PG), their component arrangements are different. Prius adoptsan input-split configuration, while a vehicle wheel and an elec-tric machine (EM) are connected to the same PG shaft, on theother hand, one of the Volt’s four operating modes is an output-split configuration with an engine and an EM sharing the samePG shaft [3]. Likewise, there are various ways of connectingfour components (an engine, a vehicle wheel, and two EMs)with three PG shafts such as a sun, a carrier, and a ring [4],[5]. For example, there are 24 configurations for single PG andmore than thousand configurations for double PGs. For thiscase, it would be an extremely time-consuming procedure oreven impossible to manually find an optimal configuration byevaluating performance of each configuration with design vari-ables such as planetary gear ratio (SRratio) and final drive ratios(FDratio). Moreover, the performance metrics vary significantlyas the design variables change even if the configuration is keptsame, and a certain combination of SRratio and FDratio evenmakes a configuration infeasible. Therefore, an entire designspace formed by the configurations and their design variables

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KIM AND KUM: COMPREHENSIVE DESIGN METHODOLOGY OF INPUT- AND OUTPUT-SPLIT HEV: IN SEARCH OF OPTIMAL CONfiGURATION 2913

TABLE IPS-HEV DESIGN STUDY LITERATURE

Configur- Design variables Performances

No. Author Year ation PGr a t io FDr a t io FE AP

[3] Zhang et al. 2012 � X X O X[6] Boehme et al. 2013 � X X � X[7] Bayrak et al. 2013 � X X O X[8] Zaremba et al. 2012 � � X � X[5] Liu et al. 2012 � O X O X[9] Li et al. 2010 � O X O X[10] Bayrak et al. 2014 � X O O X[11] Zhang et al. 2013 � O O O X[12] Cheong et al. 2011 � O O O X[13] Cheong et al. 2011 � O O O X[14] Yang et al. 2007 � � X � O[15] Yang et al. 2009 � � X � O

Proposed Methodology O O O O O

* O: fully covered, �: partially covered, X: not covered.

should be systematically analyzed and evaluated. In order to findan optimal power split (PS)-HEV configurations, recent studieshave proposed various design methodologies and explored thelarge design space considering at least one factor listed as fol-lows. (Literature on the PS-HEV design studies are summarizedin Table I.)

1) Configurations—components arrangement with a PG.2) Design variables—PGratio , FDratio .3) Performance metrics—FE, acceleration perfor-

mance (AP).Zhang et al., Boehme et al., and Bayrak et al. compared the

FE or the transmission efficiency of the PS-HEV configurationsand found better configurations. Zhang et al. evaluated the FE ofPrius and Volt configurations with various number of clutches[3]. Boehme et al. compared three configurations: input split,compound split, and two mode power split [6]. While they con-sidered a few configurations, Bayrk et al. tried to search the bestconfiguration among relatively large design space by automati-cally generating single PG and double PG configurations [7].

Although aforementioned studies found alternative configu-ration, there still remain a possibility to find better configurationsif PGratio and FDratio are set as the design variables. Zarembaet al., Liu et al., and Li et al. adopted PGratio as a design vari-able. Zaremba et al. pointed out PGratio could affect operatingpoints of EM within a selected configuration [8]. In [5] and [9],Liu et al. evaluated the fuel economy of double PG PS-HEVconfigurations along with the various PGratio and Li et al. alsofound an optimal configuration and PGratio of hydraulic hybridvehicle (HHV). In contrast, Bayrak et al. adopted FDratio (2–6)as a design variable to find a good PS-HEV design [10].

Both SRratio and FDratio were adopted as the designvariables in following studies. Zhang et al. searched anoptimal configuration among six input-split configurationswith corresponding SRratio and FDratio [11]. Although bothdesign variables are used, the acceleration performance orthe feasibility was not assessed. On the other hand, Cheonget al. checked the drivability of the input-, output- andcompound-coupled HHV configurations, and then, the FE of

feasible designs are assessed to find an optimal design and anoptimal pump size [12], [13]. Despite the assessment of thedrivability as well as the FE, the drivability is given by a cityand a highway driving cycle, thus their methodology could notguarantee the high speed drivability and a full-load accelerationperformance. Yang et al. also evaluated both the fuel economyand the acceleration performance to find an optimal SRratio ofsix input-split and six output-split configurations, however, theyselected an optimal configuration by solving a single-objectiveoptimization problem of each performance metric instead ofconsidering two performance metrics together [14], [15].

Therefore, in order to find an optimal single PG split HEVpowertrain configuration, a systematic design methodology,which evaluates performance over the entire design space andsolves a multiobjective (FE and AP) configuration selectionproblem, is required.

The remainder of this paper is organized as follows: InSection II, PS-HEV design methodology is newly proposed,which consists of two main parts. Note that this paper focuseson the optimal configuration selection part. In Section III, adesign space conversion map between the PG and compoundlever design spaces is derived to systematically analyze the sin-gle PG split HEV designs and to visualize the performancemetrics in a continuous design space. In Section IV, dynamicprogramming (DP) is employed to evaluate the FE and the ac-celeration performance of all possible designs and a multiob-jective configuration selection problem is solved. Section Vdepicts the performance variation of the single PG configura-tions by applying the proposed design methodology to sportutility vehicle (SUV). Finally, Section VI provides concludingremarks.

II. OVERVIEW OF DESIGN METHODOLOGY

This section provides an overview of the entire designmethodology of input- and output-split hybrid electric vehicle.The focus of this paper is to find an optimal configuration for agiven set of vehicle parameters, and the design method for find-ing good kinematic diagrams (schematic designs) will be intro-duced in the future work. In the following sections, both optimalconfiguration search and kinematic diagram search methods aresummarized in order to give readers the big picture of the entireprocedure.

A. Optimal Configuration Selection

In Section III, both the strengths and the weakness of thePG design space and the compound lever design space aresummarized and PS-HEV modeling equations are derived foreach design space. In summary, all of the single PG PS-HEVdesigns can be analyzed by one generic equation in the com-pound lever space, whereas individual model must be derivedfor each of 24 configuration when modeled in the PG designspace. Therefore, the compound lever design space is adoptedso that every possible PS-HEV designs can be described bysimply varying two lever parameters. Furthermore, when thePS-HEV designs are represented with the compound lever, de-sign spaces of 24 single PG configurations can be sequentially


located on the continuous design space. In Section IV, the fueleconomy and the acceleration performance of the all singlePG designs are evaluated using DP across the compound leverdesign space. All of the results are plotted on the “SRratio −FDratio” plane to illustrate the influence of two design variableson the performance metrics. Results are also plotted on the “fueleconomy—acceleration performance” plane and clustered intothe 24 configurations using the conversion map, which is de-rived in Section III. Accordingly, the optimal configuration andthe corresponding design variables can be immediately selectedfrom the performance map. As a result of applying the afore-mentioned design methodology, a novel configuration is foundhighly promising; much faster acceleration performance thanthat of Prius. (6.25 s faster in 0–160 km/h time.)

B. Kinematic Diagram Generation

During the design of a novel hybrid electric vehicle, draw-ing a kinematic diagram is an essential step because such dia-grams can provide critical information about interconnectionsbetween PG shafts and locations of the components in thenew powertrain. Therefore, the next step toward the manu-facturing of the optimal configuration is to develop an auto-mated feasible kinematic diagram search algorithm that sys-tematically generates good kinematic diagrams for any givenconfiguration.

III. DESIGN SPACE OF INPUT- AND OUTPUT-SPLIT HEV

First, the 24 single PG design spaces and the PG de-sign variables, such as SRratio and FDratio , are introduced inSection III-A. Second, the compound lever design spacesand their design variables, α, β, and FDratio , are defined inSection III-B. It should be noted that α and β indicate the relativelocations of the EMs on the compound lever. In Section III-C,the relationship between the two design spaces is examined andthe design space conversion map is constructed. As a result, anoptimal PS-HEV design can be found in the compound leverdesign space, and then, the optimal design variables (e.g., α, β,and FDratio) can be converted into configuration and PG designvariables (e.g., SRratio and FDratio).

A. Single Planetary Gear Design Space

1) Planetary Gear Set and its Lever Analogy: A PGplays a key role in the PS-HEV because it allows an engineor output power to split into two flow paths, mechanical andelectrical. Since a PG consists of sun, planets, and ring gears,in which the carrier holds the planet gears, three drive shaftscome out of the PG as illustrated in Fig. 1. During transients,the dynamics of the PG is quite difficult to understand, and thus,a PG lever (elementary lever) is often employed to visualize itsdynamic behavior. In the lever diagram, three nodes representthe ring, carrier, and sun gears. The x directional locations ofthe three nodes represent the rotational speeds, which satisfy thefollowing kinematic constraint at all times.

ωsS + ωrR = ωc(S + R) (1)

Fig. 1. Planetary gear set and its lever representation.

Fig. 2. Twenty-four single PG configurations: the suffix “-s” stands forthe configurations that have a switched arrangement between the twoEMs. Note that “i1” is Prius configuration and “o6s” is Volt configuration.

where S and R are the radii (or number of teeth) of the sun gearand ring gear, respectively. ωs , ωr , and ωc are the rotationalspeed of the sun, carrier, and ring gear, respectively. In the leverdiagram, the position of each node on the x-axis represents therotational speed. Note that acceleration relationships can alsobe derived by differentiating (1) [16].

2) Twenty-Four Single PG Configurations: Twenty-foursingle PG configurations, which are listed in Fig. 2, can be gen-erated from the four powertrain components (engine, vehiclewheel, and two EMs) and the single PG. Configurations, “i1–i6” and “i1s–i6s,” are the input-split configurations that have ashared connection between electric machine (EM) and vehiclewheel. “o1–o6” and “o1s–o6s” are the output-split configura-tions with a shared connection between EM and engine. In pre-vious studies, only 12 configurations (“i1–i6” and “o1s–o6s”) of24 configurations were taken into account because researchersbelieved that the large electric machine (EM A) should be cou-pled with the vehicle for the input-split configurations and thesmall EM (EM B) should be coupled with the engine for output-split configurations [4], [14], [15]. This assumption, however,is made based on engineering intuition and eliminated theother 12 configurations that are potentially good. Therefore, 24


TABLE IITWENTY-FOUR EQUATIONS OF INPUT- AND OUTPUT-SPLIT HEV

configurations are considered configuration candidates in thisstudy. In fact, later in this paper, one of these 12 new configura-tions is revealed to be very promising.

3) Modeling of PS-HEV Powertrain With a single PG:The dynamic modeling equations of the 24 configurations arederived, and that of “Prius (i1)” configuration is listed in equa-tion (2) as an example. [17]. In this model, the inertias of thering, carrier, and sun gears are assumed to be lumped with thoseof the powertrain components [16]. Then, the dynamic equationsof the input-split configuration is derived as follows:

⎡⎢⎢⎢⎢⎢⎣

Ii 0 0 d1

0 mr 2

K 2 + IA 0 d2

0 0 IB d3

d1 d2 d3 0

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎣

ω̇i

ω̇o

ω̇B

F

⎤⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎣

Ti

TA − Tload

TB

0

⎤⎥⎥⎥⎥⎦

(2)

where d1 = 1+SRratio , d2 = –1, and d3 = –SRratio

Tload =r

K(f0 + f1v + f2v

2) (3)

where Ii , IA , and IB and Ti , TA , and TB are the inertias andthe torques of engine, EM A, and EM B, respectively. Tload isthe torque load defined as (4), which includes coast-down co-efficients, f0 , f1 , and f2 . In (2)–(3), SRratio is calculated fromthe relationship between the radii (or number of teeth) of sunand ring gear, K refers FDratio . dn (n = 1, 2, and 3) reflects theconnection between the components and the PG shafts, whichvaries with the configurations as shown in Table II. Since eachconfiguration has a different set of dn values, a correspond-ing dynamic equation must be used to assess the performancemetrics of the 24 single PG configurations. Moreover, discon-tinuity in the PG design space, which arises from the differentdynamic equations, hinders engineers finding larger trends infuel economy and acceleration performance with respect to theentire single PG design space. Therefore, the compound lever,which incorporates the 24 PG design spaces in a single space,

Fig. 3. Compound lever with the four powertrain components.

is adopted, and thus, the performance metrics can be assessedin the continuous design space.

B. Compound Lever Design Space

1) Lever Analogy for Analysis of PS-HEV: Originally,the compound lever was proposed to simplify the analysis andmodeling of an automatic transmission that equips multiple PGs.The compound lever is a four-node virtual lever and each nodecan be connected to one of four powertrain components as il-lustrated in Fig. 3. Generally, the vehicle wheel is located at theorigin, and the engine is placed above the wheel node at a dis-tance 1 from the origin. Then, the design variable, α, is definedby the distance from the vehicle node to the EM A node, and βis similarly defined by the distance to the EM B. Note that thex-directional distance of each node from the y-axis representsthe rotational speed of each component, same as the PG lever inFig. 1 [18], [19].

2) Single PG Designs in Compound Lever DesignSpace: The most powerful feature of the compound (four-node) lever is that this single model can describe input-,output-, and compound-split hybrid powertrain configurationsusing only three design variables, α, β, and K. For example,if α equals to 0 and β is larger than 1, the compound lever’sperformance is indentical to the performance of Prius secondgeneration’s configuration (i1). Similarly, performance of Volt


Fig. 4. Four special cases of compound lever (α or β is equal to 1 or 0).(a) Compound lever, α = 0. (b) Compound lever, β = 0. (c) Compoundlever, α = 1. (d) Compound lever, β = 1.

first generation’s split mode (o6s) can be analyzed using thecompound lever with β = 1 and α < 0. As an extension of theseexamples, Fig. 4 shows four special cases of the compound lever,which can depict all 24 single PG configurations. Since singlePG has only three shafts, one of two EMs must be colocatedwith either the engine or the vehicle wheel. That is, either α or βmust be equal to 0 or 1, and thus, four special cases of the com-pound lever correspond to the 12 input-split or 12 output-splitPS-HEV configurations. Fig. 4(a) and (b) represents the input-split configurations (e.g., one EM is colocated with the vehiclewheel). Fig. 4(c) and (d) represents the output-split HEVs (e.g.,one EM is colocated with the engine).

3) Modeling of PS-HEV Powertrain with CompoundLever: From acceleration constraints between compound levernodes, a lever dynamic equations is expressed as follows [20]:

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

Ii 0 0 0 α β

0 Im 0 0 1 − α 1 − β

0 0 IA 0 −1 0

0 0 0 IA 0 −1

α 1 − α −1 0 0 0

β 1 − β 0 −1 0 0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

ω̇i

ω̇o

ω̇A

ω̇B

F1

F2

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

Ti

−Tload

TA

TB

0

0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

. (4)

Since internal force terms, F1 and F2 , do not provide anysignificant meaning in the virtual lever, it can be eliminated fora simplified powertrain model. After eliminating them, the leverdynamic equation can finally be rewritten as follows:

⎡⎢⎢⎢⎢⎢⎣

ω̇i

ω̇o

ω̇A

ω̇B

⎤⎥⎥⎥⎥⎥⎦

= Iαβ−1

⎡⎢⎢⎢⎢⎢⎣

Ti + αTA + βTB

−Tload + (1 − α)TA + (1 − β)TB

0

0

⎤⎥⎥⎥⎥⎥⎦

(5)

Fig. 5. Relationship between the six input-split configurations andone of the four special lever. (a) Six input–split configurations (Line1).(b) Compound lever with various β.

Iαβ−1 =

⎡⎢⎢⎢⎢⎢⎣

Ti 0 αIA βIB

0 Im (1 − α)IA (1 − β)IB

−α (α − 1) 1 0

−β (β − 1) 0 1

⎤⎥⎥⎥⎥⎥⎦

.

C. Design Space Conversion Map Between CompoundLever and Single PG Configurations

Two different design spaces of the single PG PS-HEV areintroduced in the previous sections. One is the PG design spacewith SRratio and FDratio , and the other is the compound leverdesign space with α, β, and K. Due to the discrete nature of thePG design spaces, understanding a big picture of the entire singlePG design space is not trivial. On the other hand, continuousdesign space of the compound lever helps engineers to figure outhow the performance metrics change within the design space.Furthermore, the relationship between 24 configurations canalso be understood. Therefore, in this section, the conversionmap between the PG design space and the compound leverdesign space is constructed in order to go back and forth betweentwo design spaces.

1) Relationship between Compound and PG Levers:Since for the input- and output-split configurations, one of thecompound lever design variables (α or β) is fixed to 1 or 0, onecan find the relationships between the PG design variables andthe compound lever design variables by comparing the locationof either the EM A or EM B node. Six input-split configurationsin Fig. 5(a) (also the first row in Fig. 2) show that the locationof the EM B moves toward bottom from the top end of thesingle PG lever. These changes can also be reproduced by simplydecreasing the design variable β in the compound lever as shownin Fig. 5(b). If β is greater than 1, the compound lever representseither “i1” or “i2.” Similarly, the lever with β less than 1 andgreater than 0, corresponds to “i3” or “i4.” For negative β,the compound lever becomes “i5” or “i6.” Fig. 6 illustrates anexample of the comparison between two levers. Fig. 6(a) is PGlever representations of Prius second generation and (b) is thecompound lever representation of the same configuration. FromFig. 6(a) and (b), a proportional equation is derived as follows:

S : R = 1 : β − 1. (6)


Fig. 6. Two different representations for Prius configuration. (a) i1(Prius) - PG lever, (b) i1 (Prius) - Compound lever.

TABLE IIICONVERSION EQUATIONS BETWEEN α, β, AND SRratio

Configuration i1 i2 i3 i4 i5 i6

α 0 0 0 0 0 0β 1 + 1

x 1 + x 11 + x

x1 + x −x − 1

x

Configuration i1s i2s i3s i4s i5s i6s

α 1 + 1x 1 + x 1

1 + xx

1 + x −x − 1x

β 0 0 0 0 0 0

Configuration o1 o2 o3 o4 o5 o6

α 1 1 1 1 1 1β 1 + 1

x 1 + x 11 + x

x1 + x −x − 1

x

Configuration o1s o2s o3s o4s o5s o6s

α 1 + 1x 1 + x 1

1 + xx

1 + x −x − 1x

β 1 1 1 1 1 1

* x: sun/ring gear ratio (= SR r a t io ).

That is, the relationship between the PG lever variables (Sand R) and the compound lever variables (α and β) is rewrittenas: α = 0 and β = 1 + R/S = 1 + 1/SRratio . Likewise, theserelationships can also be applied to other configurations in Fig. 2,and the conversion map between the PG lever and the compoundlever is constructed in following section.

2) Conversion Map Between Two Design Spaces: Theconversion relationship between α, β, and SRratio are derivedand listed in Table III by applying above method to other con-figurations. The design space conversion map for the single PGPS-HEV is obtained with this table and the feasible SRratiorange is assumed to [0.2:0.7] as shown in Fig. 7. All the possi-ble single PG configurations are placed on four lines on “α − βplane,” and the other regions only can be filled with the multiplePG configurations. “i1–i6” and “i1s–i6s” put on β-axis (Line1)and α-axis (Line2), respectively, because those configurationsare realized from the compound lever with α = 0 and β = 0.Similarly, output-split configurations, “o1–o6” and “o1s–o6s”individually put on Line 3 and Line 4. Note that, the directionof each arrow corresponds the way SRratio increases.

For the sake of the conversion map, the performances of allthe single PG PS-HEV designs can be evaluated with usingonly one equation. Furthermore, the performance trends overthe design parameters can easily be observed by plotting theperformance on the continuous design plane. Finally, the infor-mation about the configuration and the PG design variables aredirectly converted from the lever design variables.

Fig. 7. Design space conversion map for input- and output-split HEV.

IV. PERFORMANCE ASSESSMENTS

In the literatures, the main focus of HEV design optimizationhas been their fuel economy, and the acceleration performancehas often been overlooked [3], [5]–[12]. However, design opti-mization for only fuel economy can be misleaded, because anoptimal design in the fuel economy sense may result in pooracceleration performance or even infeasible as a vehicular pow-ertrain. Thus, both the fuel economy and the acceleration perfor-mance must be considered together over the entire design space.In order to solve multiobjective configuration selection problemof single PG PS-HEV, two performance measures are evaluatedover the compound lever design space and plotted on the “fueleconomy—acceleration time” plane. These performance indi-cators (or designs) are grouped together by the configurationso that the performance of each configuration can be comparedwith each other. Moreover, one can select an optimal 1 PG de-sign among Pareto Frontier, and the lever design variables (α,β, and FDratio) of the selected design are converted into thePG design variables (SRratio and FDratio) using the conversionmap.

A. Vehicle and Component Specification

The vehicle and the component specifications are adoptedfrom Prius second generation. Prius second generation is a com-pact sedan equipped with 50-kW Atkinson cycle engine, 50-kWEM A, and 30-kW EM B. Vehicle and component parametersare summarized in Table IV.

B. Fuel Economy Assessment

1) Fuel Economy DP Formulation: Both horizon and in-stantaneous optimization methods, such as DP and equivalent


TABLE IVVEHICLE AND COMPONENT SPECIFICATIONS [21], [22]

Component Parameter Value

Vehicle Mass (m ) 1365 kgCoast-down f0 = 88.6, f1 = 0.14, f2 = 0.36coefficientsWheel radius (r ) 0.305 m

Engine Inertia (Ii ) 0.18 kg·m2

Speed (ωi , m a x ) 4500 r/minTorque (Ti , m a x ) 112 N·m at 4500 r/minPower (Pi , m a x ) 53 kW at 4500 r/min

EM A Inertia (IA ) 0.0226 kg·m2

Speed (ωA , m a x ) 6700 r/minTorque (TA , m a x ) 400 N·m at [0:1250] r/minPower (PA , m a x ) 50 kW at 1250 r/min

EM B Inertia (IB ) 0.0087 kg·m2

Speed (ωB , m a x ) 10000 r/minTorque (TB , m a x ) 154 N·m at [0:1865] r/minPower (PB , m a x ) 30 kW at 1865 r/min

TABLE VDP FORMULATION FOR THE FUEL ECONOMY ASSESSMENT

Design Space Four Lever Space (with α and β )F D r a t io : [2:0.5:5]

Cost Fuel consumption (gram)

Stage Time Driving cycle: UDDS, HWFET [28]

Control Ti [0 :T i , m a x

5 0 : Ti , m a x ]

ωi [ωi , m in :ω i , m a x −ω i , m in

5 0 : ωi , m a x ]

State SOC [0.4:0.001:0.8]

Subject to 0.4 ≤ SOC ≤ 0.8, SOCinitial = SOCfinal

ωi , m in ≤ ωi ≤ ωi , m a x

0 ≤ Ti ≤ Ti , m a x (ωi )ωA , m in ≤ ωA ≤ ωA , m a x

TA , m in (ωA ) ≤ TA ≤ TA , m a x (ωA )ωB , m in ≤ ωB ≤ ωB , m a x

TB , m in (ωB ) ≤ TB ≤ TB , m a x (ωB )

fuel consumption minimization strategy (ECMS) respectively,have often been adopted to evaluate the fuel economy poten-tial of HEVs [3], [5], [9], [11], [14], [15], [23]–[25]. AlthoughECMS is widely known for its suboptimal solutions and lowercomputational loads [26], cost function of ECMS should betuned for every different designs in order to guarantee the subop-timality across the entire compound lever design space. There-fore, in this study, DP is employed to ensure the global optimalityfor all designs [27].

The fuel economy DP problem is formulated as shown inTable V, and solved across the entire single PG design space(α = 0, β = 0, α = 1, or β = 1). In terms of FDratio , 2 and5 are used for lower and upper boundaries, which include notonly Prius (K = 4.11) but also Volt (K = 3.02) designs. Notethat, to reduce the computational load of FE assessments, ac-celerating efforts of engine and two EMs are assumed to benegligible.

2) Fuel Economy DP Result: Fig. 8 shows the completefuel economy map across the entire input- and output-split HEV

design space for the city and the highways driving cycle. Eachrow of the plot corresponds to each line in Fig. 7, where thedesign of Prius second generation can be found in (a) and (e),and the design of Volt 1st generation is located in (d) and (h).Five dark gray areas near α or β = −1, 0, 0.5, 1, and 2 representdesigns that cannot be realized by a single PG (e.g., outside of thefeasible SRratio range). The light gray region depicts infeasibledesigns that cannot meet power demands of the given drivingcycle, while the colored region with contour lines indicatesthe feasible designs. By evaluating the fuel economy of all thedesigns and drawing a fuel economy contour on “α−FDratio”or “β−FDratio” plane, the fuel economy trend of the single PGPS-HEV can be observed at a glance. In both the city and thehighway driving cycle, the fuel economies of Line 1 and Line3 tend to be higher than those of Line 2 and 4. This indicatesthat “Prius (i1)” employs a good input-split configuration fromthe fuel economy perspective, whereas the “Volt (o6s)” doesnot use a good output-split configuration for the given vehiclespecification.

C. Acceleration Performance Assessment

1) Acceleration Performance DP Formulation: For fastevaluations of 0–100 km/h and 100–160 km/h times, an in-stantaneous approach was considered. The optimality of thisapproach, however, was found inconsistent for some part ofthe design space because maximizing output torque for thecurrent time step sometimes results in poor output torque athigher vehicle speeds. Thus, in this study, DP is employed againto assess the acceleration performance as listed in Table VI. TheDP problem is formulated to find minimum 0–160 km/h timesacross the entire input- and output-split designs. Unlike the fueleconomy DP, vehicle velocity is selected as stage variable sothat the time spent to get to the next stage can be computedas a cost, and minimizing the summation of these costs resultsin the best 0–160 km/h times. Note that, the battery size is as-sumed to be large enough to provide power to the two electricmachines.

2) Acceleration Performance DP Results: In this sec-tion, the DP results, minimum 0–100 km/h and 100–160 km/htimes, are plotted over the same design space with FE DP re-sult. On the contrary to the FE contour plot, lower number(red color) indicates better acceleration performance since lower0–160 km/h time leads to better acceleration performance. Sim-ilar to the FE assessment, Lines 1 and 3 in Fig. 9 show bet-ter acceleration performance than those of the other two lines.However, the feasible regions of fuel economy and accelerationperformance results are far different. Although high FDratiotends to guarantee fast acceleration, if too high FDratio is se-lected, a vehicle may not be able to reach 160 km/h. If theacceleration performance had not been assessed, these infea-sible designs could have been considered good designs withhigh FE. Thus, both the fuel economy and the accelerationperformance must be taken into account together for selectingoptimal PS-HEV design. Finding an optimum design maximiz-ing both two performance metrics, however, is still not trivialbecause there are four different performance criteria; city fuel


Fig. 8. UDDS and HWFET fuel economy contour plots of the lever design spaces. Note that, since the vehicle and component specifications arePrius 2nd generation, the fuel economy of ‘Volt design (α = −2.24, β = 1, F Dratio = 3.02)’ might not be exactly same with Volt 1st generation’sone. (a) City Fuel Economy: Input–split, Line1(α = 0). (b) City Fuel Economy: Input–split, Line2(β = 0). (c) City Fuel Economy: Input–split, Line3(α= 1). (d) City Fuel Economy: Input–split, Line4(α = 1). (e) Highway Fuel Economy: Input–split, Line1(α = 0). (f) Highway Fuel Economy: Input–split,Line2(β = 0). (g) Highway Fuel Economy: Input–split, Line3(α = 1). (h) Highway Fuel Economy: Input–split, Line3(β = 1).

economy, highway fuel economy, 0–100 km/h time, and 100–160 km/h time. Therefore, a systematic design selection methodis necessary to find the optimal configuration and optimal designvariables.

D. Selection of the Optimal Configuration

1) Fuel Economy Versus Acceleration Time: In orderto select an optimal design that balances fuel economy andacceleration performance, city and highway fuel economies,and 0–100 km/h and 100–160 km/h times are combined first.The combined fuel economy (km/L) and combined accelerationperformance (s) for all designs are computed as follows:

FEcombined =1

pF E U D D S

+ (1−p)F E H W F E T

(7)

ATcombined = qAT 0−100 + (2 − q)AT 100−160 (8)

where FEUDDS , FEHWFET , and FEcombined represent UDDScycle, HWFET cycle, and combined fuel economy, respectively.AT0−100 , AT100−160 , and ATcombined are 0–100 km/h, 100–160 km/h, and combined acceleration times, respectively. Notethat, for the combined fuel economy, (10) is adopted from U.S.federal FE test with p = 0.43 [29]. The combined accelerationtime (ATcombined ) is a weighted sum of 0–100 km/h and 100–160 km/h acceleration times. That is, when q = 1, the combined

TABLE VIDP FORMULATION FOR THE MINIMIZATION OF 0–160 KM/H TIME

Design Space Four Lever Space (with α and β )F D r a t io : [2:0.5:5]

Cost Time (s)

Stage Velocity [0:1:160] (km/h)

Control Ti [0 :T i , m a x

4 0 : Ti , m a x ]

TA [TA , m in :T A , m a x

2 0 : TA , m a x ]

TB [TB , m in :T B , m a x

2 0 : TB , m a x ]

State ωi [ωi , m in :ω i , m a x −ω i , m in

4 0 : ωi , m a x ]

Subject to ωi , m in ≤ ωi ≤ ωi , m a x

0 ≤ Ti ≤ Ti , m a x (ωi )ωA , m in ≤ ωA ≤ ωA , m a x

TA , m in (ωA ) ≤ TA ≤ TA , m a x (ωA )ωB , m in ≤ ωB ≤ ωB , m a x

TB , m in (ωB ) ≤ TB ≤ TB , m a x (ωB )

acceleration time is equal to 0–160 km/h time. In this study,q = 1.5 is selected to ensure sufficient weight is put on the0–100 km/h performance, because vehicle is more frequentlyoperated in low-speed range.

Fig. 10 illustrates the performance metrics of all designs plot-ted on the “fuel economy—acceleration performance” plane.It also shows a Pareto frontier, where designers can select an


Fig. 9. 0–100 km/h and 100–160 km/h contour plots of the lever design spaces. Note that, since the vehicle and component specifications are Priussecond generation, the acceleration time of “Volt design (α = −2.24, β = 1, FDratio = 3.02)” might not be exactly same with Volt first generation’sone.

Fig. 10. Performance map of the single PG PS-HEV design with Priusspecification: each marker represents single PG PS-HEV design. Possi-ble performance area with “Prius configuration (i1),” “new configuration(o6),” and “Volt configuration (o6s)” are colored with blue, red, and green.

optimal design based on a target vehicle performance. For in-stance, if absolutely maximum fuel economy is desired for thetarget vehicle, the designers should select “Prius configuration(i1).” On the other hand, if both the high fuel economy andshort acceleration time are desired, configuration “o6” wouldbe an optimal choice. In fact, Fig. 10 shows that the optimal

Fig. 11. Performance comparison between three designs: “Prius (i1),”‘optimal design (o6),” and ‘optimal design of Volt configuration (o6s).”

configuration (= new configuration), “o6,” offers much betteracceleration performance than ‘i1,” while offering a comparablefuel economy. By the virtue of a full design domain search and amultiobjective configuration selection, a counter intuitive resultis observed; the performances of “Volt configuration (o6s)” arefar behind compared to those of ‘new configuration (o6).” Thatis, connecting a large EM with an engine is much better foroutput-split HEV than connecting a small EM with an engine.Additionally, in Fig. 11, four normalized performance metricsare visualized in order to compare “Prius (i1),” “optimal designof Volt configuration (o6s),” and “Optimal configuration (o6).”Fuel economies and acceleration times are normalized by theirmaximum value and their minimum value, respectively. The nor-malized fuel economies are scaled to clearly visualize the differ-ence between designs. Definitions of normalized performance


Fig. 12. Accumulated fuel consumption of “new configuration (o6),”“Volt configuration (o6s),” and “Prius configuration (i1)” and their operat-ing points.

metrics are as follows:

FEcycle,norm =(

FEcycle,design

FEcycle,max

)3

(9)

ATvelocity ,norm =(

ATvelocity ,min

ATvelocity,design

)(10)

where “cycle” is “UDDS” or “HWFET” and “velocity” is “0–100” or “100–160.” In Appendix, the performance metrics ofselected configurations are listed in Table VII in Appendix.

2) Comparison of Three Selected Designs: Time Re-sponse and Operating Points: Fig. 12 illustrates accumu-lated fuel consumption over the UDDS cycle and optimal op-erating points of the engine and the two electric machines for“Prius configuration (i1),” “new configuration (o6),” and “Voltconfiguration (o6s)” during the fuel economy assessment. Al-though the accumulated fuel consumption trajectories of thosethree designs seem similar, the operation of each component issignificantly different. The most notable difference is the engineoperation of new configuration. The engine tends to operate itshigher torque regions while the operating points of Prius config-uration locate on lower torque region, which results in slightlybetter fuel economy during UDDS cycle. In terms of EM op-erations, more interesting differences are observed in the EMB map. The EM B of Prius configuration always operates asa generator in the fourth quadrant (negative torque at positive

Fig. 13. Tractive fore and velocity profile of “new configuration (o6),”“Volt configuration (o6s),” and “Prius configuration (i1)” and their operat-ing points.

Fig. 14. Performance map of the single PG PS-HEV design with SUVspecification. Possible performance area with i1, 1s, and o6 are coloredwith blue, pink, and red, respectively.


speed) of the efficiency map. The EM B of new configuration,however, operates in all quadrants except the third quadrant,which makes the EM operate as both motor and generator. In-stead, the EM A operation of “o6” is somewhat limited. ForVolt configuration, the operation of the engine is similar to thatof new configuration. On the other hand, the EM operations ofthose two configurations are quite different. In fact, the EM Aof “o6” operates similar to EM B of “o6s,” and the EM A ofo6 operates similar to EM B of “o6s.” Knowing that “o6s” issimply EM switched version of “o6” configuration, these resultsare quite intuitive.

Fig. 13 shows the tractive force and the corresponding vehiclevelocity profiles for the three designs (“i1,” “o6,” and “o6s”).Prius configuration offers the highest torque at low speed (below40 km/h), thus good launching performance, thanks to the hightorque EM A direct drive. However, the tractive force of newconfiguration becomes larger than that of Prius configurationat higher vehicle speed, which is why new configuration out-performs Prius configuration. Observing EM B operations inFig. 13, one can find that EM B of Prius configuration operatesas a generator even during full-load conditions, but the EM B ofnew configuration operates as a motor along its maximum torqueline. Such operation of o6 is reasonable because the vehicle isconnected to carrier, and thus three power sources (engine andtwo motors) can work together to propel the vehicle, thanks toits configuration. Prius configuration, however, has the vehicleconnected to the ring gear, and thus, EM B must produce re-action (negative) torque and operate as a generator at all times.The Volt configuration also provides this motoring capability,but it cannot utilize full potential of EM A up to 80 km/h.These results imply that selecting an optimal configuration isextremely important in order to fully utilize the potentials ofpowertrain components for both fuel economy and accelerationperformance.

V. CASE STUDY: SUVS

In this section, the proposed optimal configuration selectionmethodology is repeated with the SUV specification. From theresult of the case study, insight into the relationship between thespecification and the optimal configuration is provided.

A. Case Study: Reduced SUV Specification

The vehicle and component specifications of the SUV areadopted from Toyota Highlander’s engine, EM A, and EM B,and they are reduced by 17 %, 27 %, and 45 %, respectively. Asthe results, the max power of each component becomes 95, 90,and 60 kW [30]. With the SUV specification, the performancemap can be derived as shown in Fig. 14 where the different as-pect is observed comparing to previous performance map. Only“o6” is an outstanding configuration and other configurationsseem to become relatively poor than “o6.” This result impliesthat an optimal configuration and its design variables vary ac-cording to the vehicle and component specifications. Therefore,importance of selecting a proper configuration for given condi-tions is emphasized once again.

VI. CONCLUSION

In this paper, a new design methodology is proposed to findan optimal configuration for PS-HEV with a single PG. Theproposed methodology was applied to find the optimal singlePG PS-HEV configurations based on two performance metrics;the fuel economy and acceleration performance, where bothSRratio and FDratio are considered design variables. Throughthe analysis, configuration “o6” is newly revealed as good can-didate configurations among the 24 single PG configurations.The acceleration performance of optimal configuration (o6) withSRratio = 0.40, FDratio = 3.00 is dramatically improved withslight drop in fuel economy when the Prius specification is used.As observed in the operating points plot, the optimal configura-tion (o6) educes the maximum torques of two electric machines,whereas Prius configuration (i1) inevitably use one of the EM asa generator, and this is why the configuration “o6” outperformsin acceleration performance. By the virtue of the newly proposedmethodology, which adopts the full design domain search andthe multiobjective configuration selection of single PG PS-HEV,these findings are revealed and shed light on the importance ofsearching an optimal configuration and corresponding designvariables considering both the fuel economy and the accelera-tion performance. In addition, by repeating the proposed designmethodology with the different vehicle and components speci-fications, the importance of selecting a proper configuration forgiven specifications is again emphasized. However, one limita-tion is worth noting. Although the optimal configuration and thecorresponding design variables are selected, kinematic diagramshould be generated to fully develop a new power-split hybridelectric vehicle powertrain. Therefore, in order to systematicallygenerate all the feasible schematic designs for any given config-urations (e.g., configuration “o6”), the future work will includesystematical kinematic diagram generation.

APPENDIX

Here, design variables and performance metrics of selectedconfiguration for each specification are listed in Tables VIIand VIII.

TABLE VIIDESIGN VARIABLES AND PERFORMANCE METRICS OF SELECTED

CONFIGURATIONS: PRIUS SPECIFICATION


TABLE VIIIDESIGN VARIABLES AND PERFORMANCE METRICS OF SELECTEDCONFIGURATIONS: REDUCED-COMPONENT SUV SPECIFICATION

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Hyunjun Kim received the master’s degree fromthe Graduate School of Green Transportation,Korea Advanced Institute of Science and Tech-nology, Daejeon, Korea, in 2015, where he iscurrently working toward the Ph.D. degree.

His current research interests include de-sign optimization of the input-, output-, andcompound-split hybrid electric vehicles.

Dongsuk Kum (M’13) received the Ph.D. de-gree in mechanical engineering from the Univer-sity of Michigan, Ann Arbor, MI, USA, in 2010.

He is currently an Assistant Professor with theGraduate School of Green Transportation, KoreaAdvanced Institute of Science and Technology(KAIST), Daejeon, Korea, and is the Director ofthe Vehicle Dynamics and Controls Laboratory.His research interests include modeling, control,and design of advanced vehicular systems withparticular interests in hybrid electric vehicles and

autonomous vehicles. Prior to joining KAIST, he worked for the Gen-eral Motors Reserach and Development Propulsion Systems ResearchLaboratory, Warren, MI, as a Visiting Research Scientist. His works atGeneral Motors focused on advanced propulsion system technologies in-cluding hybrid electric vehicles, flywheel hybrid, and waste heat recoverysystems.

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