Research ArticleEnergy Flow Chart-Based Energy Efficiency Analysis ofa Range-Extended Electric Bus

Xiaogang Wu Chen Hu and Jingfu Chen

College of Electrical and Electronic Engineering Harbin University of Science and Technology Xue Fu Road 52Harbin 150080 China

Correspondence should be addressed to Xiaogang Wu xgwuhrbusteducn

Received 13 December 2013 Accepted 29 January 2014 Published 9 March 2014

Academic Editor Hamid R Karimi

Copyright copy 2014 Xiaogang Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper puts forward an energy flow chart analysis method for a range-extended electric bus This method uses dissipationand cycle energy recycle efficiency and fuel-traction efficiency as evaluation indexes In powertrain energy efficiency analysis therange-extended electric bus is developed by Tsinghua University the driving cycle based on that of Harbin a northern ChinesecityThe CD-CS and blended methods are applied in energy management strategies Analysis results show with average daily rangeof 200 km auxiliary power of 10 kW CD-CS strategy recycle ability and fuel-traction efficiency are higher The input-recycledefficiency using the blended strategy is 2473 higher than CD-CS strategy while the output-recycled efficiency when using theblended strategy is 783 lower than CD-CS strategy

1 Introduction

Compared with conventional fuel vehicles application ofelectric vehicle decreases the dependency on petroleumand has the advantages of high energy efficiency and lowenvironmental impact [1ndash3] For a pure electric bus the costof a battery pack that can meet the driving range is too highmeanwhile vehicle weight is too large for adding a largebattery pack A range-extended electric vehicle is regarded asone of the most suitable solutions for powertrain schemesbecause of the maximum utility of the electric drive and theminimum capacity requirement of battery packs

The main powertrain configurations of range-extendedelectric vehicles are series plug-in hybrid electric vehicles[4] and the Chevrolet Volt produced by General MotorsCorporation (GM) [5] This paper will analyze a series plug-in hybrid electric bus

In the studies of energy efficiency and fuel economyof range-extended electric vehicles vehicle performance isanalyzed on the basis of energy consumption and greenhousegas emissions on the well-to-wheel and tank-to-wheel paths[6 7] Well-to-wheel fuel economy and greenhouse gas emis-sions data were obtained using the greenhouse gases regu-lated emissions and energy use in transportation (GREET)

software model The tank-to-wheel process is characterizedby the recuperation and fuel-traction efficiencies which arequantified and compared for two optimization-based energymanagement strategies

The improvement of fuel economy for a range-extendedelectric vehicle can be realized by matching powertrain partsand a model selection method [8ndash12] An optimal gen-setoperating line method can minimize fuel consumption at aset level of electric output power Series hybrid vehicles withdirect injected stratified charge (DISC) rotary engines areproven to be more efficient in pure electric mode in terms ofenergy consumption and greenhouse gases (GHG) emissionsthan in vehicles with reciprocating engines

Energy efficiency and fuel economy of range-extendelectric vehicles can be improved by studying energy man-agement strategy [13ndash16] Researchers use dynamic program-ming strategies and equivalent consumption minimizationstrategies as well as Pontryaginrsquos minimum principle strategyto analyze energy efficiency and fuel economy of range-extended electric vehicles and results show that optimizedenergy management strategy can improve energy efficiencyand fuel economy to a certain extent

In conclusion current studies on configuration analysisand energy management strategy on range-extended electric

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 972139 12 pageshttpdxdoiorg1011552014972139

2 Mathematical Problems in Engineering

Engine Generator Converter

Mechanical joint

Power battery

Traction motor controller

Traction motor

Mechanical joint

Transmission and main reducer

Electrical joint

Electrical joint

Electrical joint

Range-extender

Figure 1 Powertrain configuration of the range-extended electric bus

vehiclesmainly focus on passenger vehicles but work is rarelyconducted into range-extended electric buses Reference [17]asserts that a driving cycle significantly influences the energyefficiency and fuel economy of the vehicle It proposesthat construction and optimization of energy managementstrategy should consider different driving cycles A system ofenergy efficiency analysis based on a certain driving cycle isthe foundation of an optimal control strategy

This paper focuses on the application requirements of therange-extended electric bus developed by Tsinghua Univer-sity in Harbin and establishes the powertrain model of thebus based on the construction of the Harbin driving cycle Itexamines the energy efficiency of the range-extended electricbus with two different energymanagement strategies (CD-CSand blended) and proposes improvementmethods for energyefficiency

2 Configuration and Principle of theRange-Extended Electric Bus

The range-extended electric vehicle lies between the plug-in hybrid electric vehicle and pure electric vehicle Com-pared with a pure electric vehicle a range-extended electricvehicle is supplemented with an onboard power generationsystem (range-extender) [18 19]The range-extender consistsof engine generator and rectifier The engine continuallycharges the power battery so the driving range can be greatlyincreased to the level of a conventional internal combustionengine vehicle The engine and power battery of a range-extended electric bus can be optimized at the same time Theworking area of the engine can be optimized according to thedriving cycle and the engine efficiency can be improved Theengine can operate with low pollution and fuel consumptionAs for the battery working condition of the power battery canalso be optimized If the power battery can continually workin good condition without overcharging or overdischargingbattery life can be extended Braking energy can be recycledand energy consumption is decreased The range-extender

solves the problems of the energy consumption of air-conditioning lighting heating and other electric auxiliariesmaking the range-extended electric bus the most suitablesolution for city buses

A typical range-extended electric powertrain is shownin Figure 1 In a range-extended electric vehicle wheels aredriven directly by an electric motor The motor draws energyfrom a battery pack and drives in pure electric mode whenbattery energy is available Once the battery has been mostlydepleted the motor draws power from the range-extendercomposed of an internal combustion engine and generator inconjunction with a battery Range-extended electric vehiclesare designed with a predetermined all-electric range (AER)The AER represents the distance that the vehicle can travelusing the energy stored in its battery only without the engineand generator Vehicles with a higher AER must have largerheavier and more expensive battery systems The range-extended electric powertrain configuration is one of the mostattractive applications for the diesel engine

We can see the powertrain configuration of the range-extended electric bus discussed in this paper the energyflow conditions of different driving modes are analyzed asis shown in Figure 2 There are three driving modes pureelectric drive mode range-extended mode and regenerativebrake mode

Pure electric drivemode is shown in Figure 2(a) If SOC ishigh the powertrain begins pure electric mode whereby theengine stops and the motor will be driven by a power batteryCheaper electric energy from the power grid is fully utilizedFuel consumption and pollution are reduced in this mode IfSOC decreases to the set starting value the range-extenderbegins and the powertrain works in range-extended mode

Powertrain working in range-extended is shown inFigure 2(b) To increase driving range if SOCdecreases to theset starting value the range-extender starts to generate powerreducing the rate of electricity loss and ensuring the motorcan work to drive the busThis mode can be divided into twokinds One if the output power of range-extender is lowerthan the motor required power the lacking electric energy isprovided by battery the battery discharges Two if the output

Mathematical Problems in Engineering 3

Engine

Power battery

Inverter Traction motor

Mechanical joint

Electrical joint Electrical

jointMechanical

joint

Wheel

Wheel

Discharging

Driving

Main reducerRectifierGenerator

Range-extender

(a) Pure electric drive mode

Engine Inverter Tractionmotor

Mechanical joint

Electrical joint

Wheel

Wheel

Discharging

DrivingGenerating

Engine Inverter Traction Motor

Mechanical joint

Mechanical joint

Electrical joint

Electrical joint Electrical

jointMechanical

jointCharging

Wheel

Wheel

Generating Driving

Generator

RectifierGenerator

Rectifier

Main reducer

Main reducer

Power battery

Power battery

Range-extender

Range-extender

(b) Range-extended mode

Engine Inverter Traction motor

Mechanical joint

Electrical joint Electrical

jointMechanical

joint

Wheel

Wheel

Charging

Braking

Main reducerRectifierGenerator

Power battery

Range-extender

(c) Regenerative brake mode

Figure 2 Driving modes of the range-extended electric bus

4 Mathematical Problems in Engineering

Figure 3 The range-extended electric bus developed by TsinghuaUniversity

power of the range-extender is higher than the requiredmotor power the redundant electric energy is reserved inbattery charging the battery The output power of the range-extender is not directly influenced by the driving conditionsand can be optimized in the high efficiency working areas ofthe engine and motor

If the bus is braking the motor can work in regenerativebrake mode as is shown in Figure 2(c) The motor providesbraking torque for the vehicle wheels and braking energyis transferred into electric energy reserved in the batteryBraking energy is not transferred into heat and lost it isrecycled

For an individual axle drive bus only wheels driven by themotor can recycle braking energy Other wheels are stoppedby mechanical braking Braking energy is partly recycled andmechanical braking is also used on driven wheels for safety

The range-extended electric bus analyzed in this paperis developed by Tsinghua University shown in Figure 3The powertrain is designed based on matching powertrainparts and model selection found in [20] The generator is apermanent magnet generator and the traction motor is anasynchronous motor Key parameters of the powertrain arelisted in Table 1

3 System Modeling of the Range-ExtendedElectric Bus

To analyze energy efficiency and fuel economy of the range-extended electric bus system models based on benchmarksand modeling lines of [21ndash24] are built The basic model ofthe range-extended electric system can be divided into fourmodules range-extender module traction motor modulepower battery module and the vehicle longitudinal dynam-ics module Considering the high complexity of a dieselengine permanent magnet synchronous generator and therectifier and driving motor relevant components are testedby benchmarks and the characteristics MAP are determinedaccording to the test results Then the simulation modelsare built based on the MAP which replaces the complexmathematical description reduces modeling complexity andtherefore improves model credibility

Table 1 Powertrain parameters of range-extended electric bus

Vehicle

Size (length times width times

height)mm 11980 times 2550 times 3200

Vehicle masskg 13000Rated passengers 78Windward aream2 75

Air resistance coefficient119862119863

075

Rolling resistancecoefficient 119891 00076 + 000056119906

119886

Rolling radius 119903m 0512Speed ratio of main reducer

1198940

62

Speed ratio of transmission119894119892

234

Motor

Continuous powerkW 100Peak powerkW 180

Maximum torqueNsdotm 860Maximum speedrmin 4500Operating voltageV 300sim450

Engine DisplacementL 19PowerkW 824000 rmin

Generator Rated powerkW 50Rated torqueNsdotm 220

Power Battery Capacity 180AhOperating voltageV 350sim460

31 Range-Extender The range-extender includes a dieselengine a permanent magnet synchronous generator andrectifier System features can be described by the followingequations

119899eng = 119899119903

1

120591119890119904 + 1

119879eng = 1198911(120572 119899eng)

119862eng = 1198912(119899eng 119879eng)

120578gr = 1198913(119899eng 120582) sdot 120578119903

(1)

where 1198911is the accelerator characteristic MAP of the engine

1198912is fuel consumption characteristic MAP of the engine

1198913is the generator efficiency MAP 119899

119903is the enginersquos target

speed 120577119890is a time constant 120572 is the accelerator signal 119899eng is

the enginersquos actual speed 119879eng is the engine torque 120582 is thegenerator loading rate 120578

119903is the rectifier efficiency 119862eng is the

enginersquos instantaneous fuel consumption and 120578gr is the totalrate of the generator and rectifier

32 Traction Motor The traction motor module includes themotor and motor controllerThemotor model consists of the

Mathematical Problems in Engineering 5

Wheel Final drive Motor Converter

Battery

Wheel Final drive Motor Converter

Input way

Output way

Figure 4 Schema of recycle energy flow

steady state efficiency characteristic MAP and a first-orderprocess

120578119898= 1198911198981

(119899119898 119879119898)

119879119898= min (119879

119903 119879max) sdot

1

120591119898119904 + 1

119879max = 1198911198982

(119899119898)

(2)

where 120578119898is the motorrsquos electric efficiency 119899

119898is the motorrsquos

rotational speed 120577119898

is a time constant and 119879119898 119879119903 and

119879max are the motorrsquos actual torque target torque and torquecapacity respectively The function 119891

1198981denotes the motorrsquos

efficiency MAP and 1198911198982

denotes the motorrsquos maximumoutput torque characteristic MAP

33 Power Battery Thepower batterymodel is built based onthe119877intmodel which is equivalent to a variable voltage sourceand a variable resistance in series According to the batteryinternal resistance equivalent circuit the following equationcan be established

119880oc = 119864 (SOC 119879) minus 119868 sdot 119877 (SOC 119879) (3)

where SOC is the state of charge of the battery 119879 is thetemperature and 119868 is the battery current 119864 stands for theopen circuit voltage of the battery which is a function of SOC119879 is determined by the test and 119877 is the internal resistance ofthe battery

In this model the batteryrsquos SOC state uses ampere-hourintegral method to estimate [25] That is when the vehicle is

in operation it will use SOC as SOCint and at 119905moment it willuse SOC formula (4) to decide the following

SOC = SOCint minus1

119876119887

int

119905

1199050

120578bat119868bat119889119905 (4)

where 119876119887is rated capacity 120578bat is the batteryrsquos columbic

capacity and 119868bat is its charging and discharging current

34 Vehicle Longitudinal Dynamics The road load character-istic is assumed to be ideal in simulation that is zero air speedand good adhesion As the vehicle is traveling on the roadtraction motor needs to overcome driving resistance (119865

119905)

rolling resistance (119865119891) air resistance (119865

119908) slope resistance

(119865119894) and acceleration resistance (119865

119895) Consider

119865119905= 119865119891+ 119865119908+ 119865119894+ 119865119895

119865119891= 119891119898119892 cos (119886 tan 119894)

119865119908=

1

2

1198621198891198601205881199062

119886

119865119894= 119898119892 sin (119886 tan 119894)

119865119895= 028120575119898

119889119906119886

119889119905

119865119905=

36120578119879119875motor119906119886

(5)

where 119891 is the rolling resistance coefficient 119898 is the vehiclemass 119892 is the acceleration of gravity 119894 is the road slope 119862

119889is

the coefficient of air resistance 119860 is the windward area 120588is the air density 119906

119886is the motor speed 120575 is the correction

coefficient of rotatingmass 120578119879is the overall efficiency of drive

system and 119875motor is the output power of the traction motor

6 Mathematical Problems in Engineering

Engine

Generator andrectifier

Battery

Traction motor

Auxiliary

Axle

Recuperation efficiencyFuel-to-traction efficiency

Efuel

120578eng

Eeng Eloss eng

120578gen120578bout

Egrid

EblossErec

EbrecEb

120578bin

inin

Emcloss Emin

Ebg

Eb

120578cir wEwin

Ecir

Eg

Eae + Erol + EcirErec

Eloss gen

120578mmiddotout120578

mmiddotin

Eloss m

Eau

Figure 5 Energy flow chart in energy efficiency analysis

4 Energy Efficiency Analysis Using EnergyFlow Chart

According to the energy efficiency analysis method of plug-in hybrid electric powertrain in [7] energy efficiency analysiscan be divided into the following three parts

41 Dissipation and Cycle Energy Traction power is usedto drive the wheels and vehicle auxiliaries the calculationequation is as follows

119875 (119905) = 119875ae (119905) + 119875rol (119905) + 119875au (119905) + 119875ac (119905) + 119875gr (119905) (6)

where 119875ae(119905) = 120588air119860119891119888119889V3(119905)2 is the power to overcome

air resistance 120588air is the air density 119860119891is the frontal area

119888119889is the air resistance coefficient V is the vehicle speed

119875rol(119905) = (119898V +119898119901)119892119888119903 cos(120572(119905))V(119905) is the power to overcomerolling resistance 119875ac(119905) = (119898V + 119898

119901)V(119905)V(119905)(119889V(119905)119889119905)

is the accelerationdeceleration power 119875gr(119905) = (119898V +

119898119901)119892 sin(120572(119905))V(119905) is the updown hill power V is the vehicle

speed 120572 is the road gradient 119898119901

is the battery massand 119875au(119905) is the auxiliaries power including air conditionbattery heat management system heating (seat heating andwindshield heating) lighting control system and brakingsteer consumption The average power of the auxiliaries is10 kW [26] assuming air-conditioning is working

Mathematical Problems in Engineering 7

Original data

N series data

segments

PretreatmentCharacteristic

values matrix

Calculating characteristic

valuesComponent

score coefficient

matrix

Principal component

analysis

Clustering analysis

Clustering analysis results

First kind

Second kind

Third kind

Extracting representative driving cycle of every kind

Harbin city

driving cycle

Constructing driving cycle

Figure 6 Construction process of Harbin city driving cycle

0 200 400 600 800 1000 1200 140005

101520253035404550

(k

mh

)

t (s)

Figure 7 Harbin city driving cycle

119875(119905) can be divided into two parts one is the dissipatedpower 119875dis(119905) = 119875ae(119905) + 119875rol(119905) + 119875au(119905) and the other isconserved power 119875cons(119905) = 119875ac(119905) + 119875gr(119905) As the initial andfinal altitude and speed are the same in a whole driving cyclethe reserved power is zero If braking energy can be fullyrecycled required traction energy 119864trac should be the sameas the dissipated energy 119864dis

119864trac = int

119905119891

1199050

119875 (119905) 119889119905 = int

119905119891

1199050

119875dis (119905) 119889119905 = 119864dis (7)

where 1199050and 119905119891are initial and final time If there is no barking

energy recycled

119864trac = int

119875(119905)gt0

119875 (119905) 119889119905

= int

119905119891

1199050

119875dis (119905) 119889119905 + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

= 119864dis + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

(8)

where int119875(119905)lt0

(minus119875(119905))119889119905 represents the cycle energy 119864cir whichis the temporal vehicle cycle energy in the form of kineticor potential energy and ultimately dissipated during friction

brakingTherefore (8) for vehicle without energy recycle canbe calculated as

119864trac = 119864dis + 119864cir (9)

In actual driving energy balance equation can be calcu-lated as

119864trac = 119864dis + 119864cir minus 119864rec (10)

where119864rec is the recycled net energy that is usable for tractionAccording to (7) and (10) it can be found that 119864rec = 119864cir

42 Recycle Efficiency of Barking Energy Recycle efficiency isdefined as

120578rec =119864rec119864cir

(11)

As 119864cir can be easily obtained in driving cycle the keymission is to calculate 119864rec Recycle energy consists of twoflow methods input and output As is shown in Figure 4recycle ability is determined by energy dissipation motortorque current of power battery and threshold charge value

Time set 119878 is defined as

119878 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) lt 0 119875

119887 (119905) lt 0 (12)

where 119875au is physical load in converter 119864119908 in is absolute inputenergy during 119878 and is calculated by

119864119908in = int

119878

1003816100381610038161003816119875 (119905) minus 119875au (119905)

1003816100381610038161003816119889119905 (13)

The energy reserved in battery is

119864119887 in = int

119878

10038161003816100381610038161003816119875119887 (119905) + 119868(119905)

2119877119899119888

10038161003816100381610038161003816119889119905 (14)

The energy loss is

119864loss in = 119864119908 in minus 119864

119887 in minus int

119878

119875au (119905) 119889119905 (15)

8 Mathematical Problems in Engineering

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

70

80

90

100SO

C (

)

s (km)

(a) CD-CS strategy

0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

SOC

()

s (km)

(b) Blended strategy

Figure 8 The SOC curve with the two different energy management strategies

The cycle-average wheel to battery energy efficiency is

120578wb in = 1 minus

119864loss in

119864119908 in

(16)

The recycle energy reserved in battery is

119864rec in = 119864cir120578wb in120578cir 119908 (17)

where 120578cir 119908 is the ratio between 119864119908and 119864cir

Time set119863 is defined as

119863 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) ge 0 119875

119887 (119905) ge 0 (18)

The associated motor energy loss in propelling is

119864loss 119898 = int

119863

119875loss 119898 (119905) 119889119905 (19)

The average motor efficiency is

120578119898 out = 1 minus

119864loss 119898119889

int119863119875119887 (119905) 120578con + 119875apu (119905) 120578con minus 119875au (119905) 119889119905

(20)

The battery energy loss during time119863 is

119864loss 119887 = int

119863

119868(119905)2119877119899119888119889119905 (21)

The battery efficiency in output way is

120578119887out = 1 minus

119864loss 119887119889

int119863119875119887 (119905) + 119868(119905)

2119877119899119887119889119905

(22)

The cycle-average battery to wheel energy efficiency is

120578bw out = 120578119887 out120578con120578119898 out120578119891119889120578119887119898 (23)

where 120578119887119898

is the ratio between the power that batteryprovides to the motor and the power emitted by batteryAccording to (16) and (23) the recycle energy for traction is

119864rec = 119864rec in120578bw out (24)

The cycle-average recycle efficiency is

120578rec =119864rec119864cir

= 120578cir119908120578wb in120578bw out (25)

43 Fuel-Traction Efficiency Fuel-traction efficiency is def-ined as

120578ft =

119864trac119864ef

=

119864dis + (1 minus 120578rec) 119864cir

119864ef (26)

where119864ef is the equal fuel energy the average consumption ofthe sum of diesel and electric energy 120578ft is the cycle-averageconversion efficiency from the total consumed energy to themechanical energy at the wheels and the electrical energy forthe auxiliaries Based on the initial and final SOC 119864ef can bedivided into diesel energy and electric energy

An energy flow chart can clearly show the direction ofenergy flow showing the sizes of losses from each individualpart It is one of the most effective methods for analyzingflow in the context of system performance Referring to theanalysis method in [27] this paper puts forward a powertrainenergy analysis method with energy flow chart for range-extended electric bus The powertrain energy flow chart isshown in Figure 5

5 Analysis Example with the DrivingCycle of Harbin City

To provide a credible reference for the match and controlof the range-extended electric bus energy efficiency analysis

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

Engine Generator Converter

Mechanical joint

Power battery

Traction motor controller

Traction motor

Mechanical joint

Transmission and main reducer

Electrical joint

Electrical joint

Electrical joint

Range-extender

Figure 1 Powertrain configuration of the range-extended electric bus

vehiclesmainly focus on passenger vehicles but work is rarelyconducted into range-extended electric buses Reference [17]asserts that a driving cycle significantly influences the energyefficiency and fuel economy of the vehicle It proposesthat construction and optimization of energy managementstrategy should consider different driving cycles A system ofenergy efficiency analysis based on a certain driving cycle isthe foundation of an optimal control strategy

This paper focuses on the application requirements of therange-extended electric bus developed by Tsinghua Univer-sity in Harbin and establishes the powertrain model of thebus based on the construction of the Harbin driving cycle Itexamines the energy efficiency of the range-extended electricbus with two different energymanagement strategies (CD-CSand blended) and proposes improvementmethods for energyefficiency

2 Configuration and Principle of theRange-Extended Electric Bus

The range-extended electric vehicle lies between the plug-in hybrid electric vehicle and pure electric vehicle Com-pared with a pure electric vehicle a range-extended electricvehicle is supplemented with an onboard power generationsystem (range-extender) [18 19]The range-extender consistsof engine generator and rectifier The engine continuallycharges the power battery so the driving range can be greatlyincreased to the level of a conventional internal combustionengine vehicle The engine and power battery of a range-extended electric bus can be optimized at the same time Theworking area of the engine can be optimized according to thedriving cycle and the engine efficiency can be improved Theengine can operate with low pollution and fuel consumptionAs for the battery working condition of the power battery canalso be optimized If the power battery can continually workin good condition without overcharging or overdischargingbattery life can be extended Braking energy can be recycledand energy consumption is decreased The range-extender

solves the problems of the energy consumption of air-conditioning lighting heating and other electric auxiliariesmaking the range-extended electric bus the most suitablesolution for city buses

A typical range-extended electric powertrain is shownin Figure 1 In a range-extended electric vehicle wheels aredriven directly by an electric motor The motor draws energyfrom a battery pack and drives in pure electric mode whenbattery energy is available Once the battery has been mostlydepleted the motor draws power from the range-extendercomposed of an internal combustion engine and generator inconjunction with a battery Range-extended electric vehiclesare designed with a predetermined all-electric range (AER)The AER represents the distance that the vehicle can travelusing the energy stored in its battery only without the engineand generator Vehicles with a higher AER must have largerheavier and more expensive battery systems The range-extended electric powertrain configuration is one of the mostattractive applications for the diesel engine

We can see the powertrain configuration of the range-extended electric bus discussed in this paper the energyflow conditions of different driving modes are analyzed asis shown in Figure 2 There are three driving modes pureelectric drive mode range-extended mode and regenerativebrake mode

Pure electric drivemode is shown in Figure 2(a) If SOC ishigh the powertrain begins pure electric mode whereby theengine stops and the motor will be driven by a power batteryCheaper electric energy from the power grid is fully utilizedFuel consumption and pollution are reduced in this mode IfSOC decreases to the set starting value the range-extenderbegins and the powertrain works in range-extended mode

Powertrain working in range-extended is shown inFigure 2(b) To increase driving range if SOCdecreases to theset starting value the range-extender starts to generate powerreducing the rate of electricity loss and ensuring the motorcan work to drive the busThis mode can be divided into twokinds One if the output power of range-extender is lowerthan the motor required power the lacking electric energy isprovided by battery the battery discharges Two if the output

Mathematical Problems in Engineering 3

Engine

Power battery

Inverter Traction motor

Mechanical joint

Electrical joint Electrical

jointMechanical

joint

Wheel

Wheel

Discharging

Driving

Main reducerRectifierGenerator

Range-extender

(a) Pure electric drive mode

Engine Inverter Tractionmotor

Mechanical joint

Electrical joint

Wheel

Wheel

Discharging

DrivingGenerating

Engine Inverter Traction Motor

Mechanical joint

Mechanical joint

Electrical joint

Electrical joint Electrical

jointMechanical

jointCharging

Wheel

Wheel

Generating Driving

Generator

RectifierGenerator

Rectifier

Main reducer

Main reducer

Power battery

Power battery

Range-extender

Range-extender

(b) Range-extended mode

Engine Inverter Traction motor

Mechanical joint

Electrical joint Electrical

jointMechanical

joint

Wheel

Wheel

Charging

Braking

Main reducerRectifierGenerator

Power battery

Range-extender

(c) Regenerative brake mode

Figure 2 Driving modes of the range-extended electric bus

4 Mathematical Problems in Engineering

Figure 3 The range-extended electric bus developed by TsinghuaUniversity

power of the range-extender is higher than the requiredmotor power the redundant electric energy is reserved inbattery charging the battery The output power of the range-extender is not directly influenced by the driving conditionsand can be optimized in the high efficiency working areas ofthe engine and motor

If the bus is braking the motor can work in regenerativebrake mode as is shown in Figure 2(c) The motor providesbraking torque for the vehicle wheels and braking energyis transferred into electric energy reserved in the batteryBraking energy is not transferred into heat and lost it isrecycled

For an individual axle drive bus only wheels driven by themotor can recycle braking energy Other wheels are stoppedby mechanical braking Braking energy is partly recycled andmechanical braking is also used on driven wheels for safety

The range-extended electric bus analyzed in this paperis developed by Tsinghua University shown in Figure 3The powertrain is designed based on matching powertrainparts and model selection found in [20] The generator is apermanent magnet generator and the traction motor is anasynchronous motor Key parameters of the powertrain arelisted in Table 1

3 System Modeling of the Range-ExtendedElectric Bus

To analyze energy efficiency and fuel economy of the range-extended electric bus system models based on benchmarksand modeling lines of [21ndash24] are built The basic model ofthe range-extended electric system can be divided into fourmodules range-extender module traction motor modulepower battery module and the vehicle longitudinal dynam-ics module Considering the high complexity of a dieselengine permanent magnet synchronous generator and therectifier and driving motor relevant components are testedby benchmarks and the characteristics MAP are determinedaccording to the test results Then the simulation modelsare built based on the MAP which replaces the complexmathematical description reduces modeling complexity andtherefore improves model credibility

Table 1 Powertrain parameters of range-extended electric bus

Vehicle

Size (length times width times

height)mm 11980 times 2550 times 3200

Vehicle masskg 13000Rated passengers 78Windward aream2 75

Air resistance coefficient119862119863

075

Rolling resistancecoefficient 119891 00076 + 000056119906

119886

Rolling radius 119903m 0512Speed ratio of main reducer

1198940

62

Speed ratio of transmission119894119892

234

Motor

Continuous powerkW 100Peak powerkW 180

Maximum torqueNsdotm 860Maximum speedrmin 4500Operating voltageV 300sim450

Engine DisplacementL 19PowerkW 824000 rmin

Generator Rated powerkW 50Rated torqueNsdotm 220

Power Battery Capacity 180AhOperating voltageV 350sim460

31 Range-Extender The range-extender includes a dieselengine a permanent magnet synchronous generator andrectifier System features can be described by the followingequations

119899eng = 119899119903

1

120591119890119904 + 1

119879eng = 1198911(120572 119899eng)

119862eng = 1198912(119899eng 119879eng)

120578gr = 1198913(119899eng 120582) sdot 120578119903

(1)

where 1198911is the accelerator characteristic MAP of the engine

1198912is fuel consumption characteristic MAP of the engine

1198913is the generator efficiency MAP 119899

119903is the enginersquos target

speed 120577119890is a time constant 120572 is the accelerator signal 119899eng is

the enginersquos actual speed 119879eng is the engine torque 120582 is thegenerator loading rate 120578

119903is the rectifier efficiency 119862eng is the

enginersquos instantaneous fuel consumption and 120578gr is the totalrate of the generator and rectifier

32 Traction Motor The traction motor module includes themotor and motor controllerThemotor model consists of the

Mathematical Problems in Engineering 5

Wheel Final drive Motor Converter

Battery

Wheel Final drive Motor Converter

Input way

Output way

Figure 4 Schema of recycle energy flow

steady state efficiency characteristic MAP and a first-orderprocess

120578119898= 1198911198981

(119899119898 119879119898)

119879119898= min (119879

119903 119879max) sdot

1

120591119898119904 + 1

119879max = 1198911198982

(119899119898)

(2)

where 120578119898is the motorrsquos electric efficiency 119899

119898is the motorrsquos

rotational speed 120577119898

is a time constant and 119879119898 119879119903 and

119879max are the motorrsquos actual torque target torque and torquecapacity respectively The function 119891

1198981denotes the motorrsquos

efficiency MAP and 1198911198982

denotes the motorrsquos maximumoutput torque characteristic MAP

33 Power Battery Thepower batterymodel is built based onthe119877intmodel which is equivalent to a variable voltage sourceand a variable resistance in series According to the batteryinternal resistance equivalent circuit the following equationcan be established

119880oc = 119864 (SOC 119879) minus 119868 sdot 119877 (SOC 119879) (3)

where SOC is the state of charge of the battery 119879 is thetemperature and 119868 is the battery current 119864 stands for theopen circuit voltage of the battery which is a function of SOC119879 is determined by the test and 119877 is the internal resistance ofthe battery

In this model the batteryrsquos SOC state uses ampere-hourintegral method to estimate [25] That is when the vehicle is

in operation it will use SOC as SOCint and at 119905moment it willuse SOC formula (4) to decide the following

SOC = SOCint minus1

119876119887

int

119905

1199050

120578bat119868bat119889119905 (4)

where 119876119887is rated capacity 120578bat is the batteryrsquos columbic

capacity and 119868bat is its charging and discharging current

34 Vehicle Longitudinal Dynamics The road load character-istic is assumed to be ideal in simulation that is zero air speedand good adhesion As the vehicle is traveling on the roadtraction motor needs to overcome driving resistance (119865

119905)

rolling resistance (119865119891) air resistance (119865

119908) slope resistance

(119865119894) and acceleration resistance (119865

119895) Consider

119865119905= 119865119891+ 119865119908+ 119865119894+ 119865119895

119865119891= 119891119898119892 cos (119886 tan 119894)

119865119908=

1

2

1198621198891198601205881199062

119886

119865119894= 119898119892 sin (119886 tan 119894)

119865119895= 028120575119898

119889119906119886

119889119905

119865119905=

36120578119879119875motor119906119886

(5)

where 119891 is the rolling resistance coefficient 119898 is the vehiclemass 119892 is the acceleration of gravity 119894 is the road slope 119862

119889is

the coefficient of air resistance 119860 is the windward area 120588is the air density 119906

119886is the motor speed 120575 is the correction

coefficient of rotatingmass 120578119879is the overall efficiency of drive

system and 119875motor is the output power of the traction motor

6 Mathematical Problems in Engineering

Engine

Generator andrectifier

Battery

Traction motor

Auxiliary

Axle

Recuperation efficiencyFuel-to-traction efficiency

Efuel

120578eng

Eeng Eloss eng

120578gen120578bout

Egrid

EblossErec

EbrecEb

120578bin

inin

Emcloss Emin

Ebg

Eb

120578cir wEwin

Ecir

Eg

Eae + Erol + EcirErec

Eloss gen

120578mmiddotout120578

mmiddotin

Eloss m

Eau

Figure 5 Energy flow chart in energy efficiency analysis

4 Energy Efficiency Analysis Using EnergyFlow Chart

According to the energy efficiency analysis method of plug-in hybrid electric powertrain in [7] energy efficiency analysiscan be divided into the following three parts

41 Dissipation and Cycle Energy Traction power is usedto drive the wheels and vehicle auxiliaries the calculationequation is as follows

119875 (119905) = 119875ae (119905) + 119875rol (119905) + 119875au (119905) + 119875ac (119905) + 119875gr (119905) (6)

where 119875ae(119905) = 120588air119860119891119888119889V3(119905)2 is the power to overcome

air resistance 120588air is the air density 119860119891is the frontal area

119888119889is the air resistance coefficient V is the vehicle speed

119875rol(119905) = (119898V +119898119901)119892119888119903 cos(120572(119905))V(119905) is the power to overcomerolling resistance 119875ac(119905) = (119898V + 119898

119901)V(119905)V(119905)(119889V(119905)119889119905)

is the accelerationdeceleration power 119875gr(119905) = (119898V +

119898119901)119892 sin(120572(119905))V(119905) is the updown hill power V is the vehicle

speed 120572 is the road gradient 119898119901

is the battery massand 119875au(119905) is the auxiliaries power including air conditionbattery heat management system heating (seat heating andwindshield heating) lighting control system and brakingsteer consumption The average power of the auxiliaries is10 kW [26] assuming air-conditioning is working

Mathematical Problems in Engineering 7

Original data

N series data

segments

PretreatmentCharacteristic

values matrix

Calculating characteristic

valuesComponent

score coefficient

matrix

Principal component

analysis

Clustering analysis

Clustering analysis results

First kind

Second kind

Third kind

Extracting representative driving cycle of every kind

Harbin city

driving cycle

Constructing driving cycle

Figure 6 Construction process of Harbin city driving cycle

0 200 400 600 800 1000 1200 140005

101520253035404550

(k

mh

)

t (s)

Figure 7 Harbin city driving cycle

119875(119905) can be divided into two parts one is the dissipatedpower 119875dis(119905) = 119875ae(119905) + 119875rol(119905) + 119875au(119905) and the other isconserved power 119875cons(119905) = 119875ac(119905) + 119875gr(119905) As the initial andfinal altitude and speed are the same in a whole driving cyclethe reserved power is zero If braking energy can be fullyrecycled required traction energy 119864trac should be the sameas the dissipated energy 119864dis

119864trac = int

119905119891

1199050

119875 (119905) 119889119905 = int

119905119891

1199050

119875dis (119905) 119889119905 = 119864dis (7)

where 1199050and 119905119891are initial and final time If there is no barking

energy recycled

119864trac = int

119875(119905)gt0

119875 (119905) 119889119905

= int

119905119891

1199050

119875dis (119905) 119889119905 + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

= 119864dis + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

(8)

where int119875(119905)lt0

(minus119875(119905))119889119905 represents the cycle energy 119864cir whichis the temporal vehicle cycle energy in the form of kineticor potential energy and ultimately dissipated during friction

brakingTherefore (8) for vehicle without energy recycle canbe calculated as

119864trac = 119864dis + 119864cir (9)

In actual driving energy balance equation can be calcu-lated as

119864trac = 119864dis + 119864cir minus 119864rec (10)

where119864rec is the recycled net energy that is usable for tractionAccording to (7) and (10) it can be found that 119864rec = 119864cir

42 Recycle Efficiency of Barking Energy Recycle efficiency isdefined as

120578rec =119864rec119864cir

(11)

As 119864cir can be easily obtained in driving cycle the keymission is to calculate 119864rec Recycle energy consists of twoflow methods input and output As is shown in Figure 4recycle ability is determined by energy dissipation motortorque current of power battery and threshold charge value

Time set 119878 is defined as

119878 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) lt 0 119875

119887 (119905) lt 0 (12)

where 119875au is physical load in converter 119864119908 in is absolute inputenergy during 119878 and is calculated by

119864119908in = int

119878

1003816100381610038161003816119875 (119905) minus 119875au (119905)

1003816100381610038161003816119889119905 (13)

The energy reserved in battery is

119864119887 in = int

119878

10038161003816100381610038161003816119875119887 (119905) + 119868(119905)

2119877119899119888

10038161003816100381610038161003816119889119905 (14)

The energy loss is

119864loss in = 119864119908 in minus 119864

119887 in minus int

119878

119875au (119905) 119889119905 (15)

8 Mathematical Problems in Engineering

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

70

80

90

100SO

C (

)

s (km)

(a) CD-CS strategy

0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

SOC

()

s (km)

(b) Blended strategy

Figure 8 The SOC curve with the two different energy management strategies

The cycle-average wheel to battery energy efficiency is

120578wb in = 1 minus

119864loss in

119864119908 in

(16)

The recycle energy reserved in battery is

119864rec in = 119864cir120578wb in120578cir 119908 (17)

where 120578cir 119908 is the ratio between 119864119908and 119864cir

Time set119863 is defined as

119863 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) ge 0 119875

119887 (119905) ge 0 (18)

The associated motor energy loss in propelling is

119864loss 119898 = int

119863

119875loss 119898 (119905) 119889119905 (19)

The average motor efficiency is

120578119898 out = 1 minus

119864loss 119898119889

int119863119875119887 (119905) 120578con + 119875apu (119905) 120578con minus 119875au (119905) 119889119905

(20)

The battery energy loss during time119863 is

119864loss 119887 = int

119863

119868(119905)2119877119899119888119889119905 (21)

The battery efficiency in output way is

120578119887out = 1 minus

119864loss 119887119889

int119863119875119887 (119905) + 119868(119905)

2119877119899119887119889119905

(22)

The cycle-average battery to wheel energy efficiency is

120578bw out = 120578119887 out120578con120578119898 out120578119891119889120578119887119898 (23)

where 120578119887119898

is the ratio between the power that batteryprovides to the motor and the power emitted by batteryAccording to (16) and (23) the recycle energy for traction is

119864rec = 119864rec in120578bw out (24)

The cycle-average recycle efficiency is

120578rec =119864rec119864cir

= 120578cir119908120578wb in120578bw out (25)

43 Fuel-Traction Efficiency Fuel-traction efficiency is def-ined as

120578ft =

119864trac119864ef

=

119864dis + (1 minus 120578rec) 119864cir

119864ef (26)

where119864ef is the equal fuel energy the average consumption ofthe sum of diesel and electric energy 120578ft is the cycle-averageconversion efficiency from the total consumed energy to themechanical energy at the wheels and the electrical energy forthe auxiliaries Based on the initial and final SOC 119864ef can bedivided into diesel energy and electric energy

An energy flow chart can clearly show the direction ofenergy flow showing the sizes of losses from each individualpart It is one of the most effective methods for analyzingflow in the context of system performance Referring to theanalysis method in [27] this paper puts forward a powertrainenergy analysis method with energy flow chart for range-extended electric bus The powertrain energy flow chart isshown in Figure 5

5 Analysis Example with the DrivingCycle of Harbin City

To provide a credible reference for the match and controlof the range-extended electric bus energy efficiency analysis

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Engine

Power battery

Inverter Traction motor

Mechanical joint

Electrical joint Electrical

jointMechanical

joint

Wheel

Wheel

Discharging

Driving

Main reducerRectifierGenerator

Range-extender

(a) Pure electric drive mode

Engine Inverter Tractionmotor

Mechanical joint

Electrical joint

Wheel

Wheel

Discharging

DrivingGenerating

Engine Inverter Traction Motor

Mechanical joint

Mechanical joint

Electrical joint

Electrical joint Electrical

jointMechanical

jointCharging

Wheel

Wheel

Generating Driving

Generator

RectifierGenerator

Rectifier

Main reducer

Main reducer

Power battery

Power battery

Range-extender

Range-extender

(b) Range-extended mode

Engine Inverter Traction motor

Mechanical joint

Electrical joint Electrical

jointMechanical

joint

Wheel

Wheel

Charging

Braking

Main reducerRectifierGenerator

Power battery

Range-extender

(c) Regenerative brake mode

Figure 2 Driving modes of the range-extended electric bus

4 Mathematical Problems in Engineering

Figure 3 The range-extended electric bus developed by TsinghuaUniversity

power of the range-extender is higher than the requiredmotor power the redundant electric energy is reserved inbattery charging the battery The output power of the range-extender is not directly influenced by the driving conditionsand can be optimized in the high efficiency working areas ofthe engine and motor

If the bus is braking the motor can work in regenerativebrake mode as is shown in Figure 2(c) The motor providesbraking torque for the vehicle wheels and braking energyis transferred into electric energy reserved in the batteryBraking energy is not transferred into heat and lost it isrecycled

For an individual axle drive bus only wheels driven by themotor can recycle braking energy Other wheels are stoppedby mechanical braking Braking energy is partly recycled andmechanical braking is also used on driven wheels for safety

The range-extended electric bus analyzed in this paperis developed by Tsinghua University shown in Figure 3The powertrain is designed based on matching powertrainparts and model selection found in [20] The generator is apermanent magnet generator and the traction motor is anasynchronous motor Key parameters of the powertrain arelisted in Table 1

3 System Modeling of the Range-ExtendedElectric Bus

To analyze energy efficiency and fuel economy of the range-extended electric bus system models based on benchmarksand modeling lines of [21ndash24] are built The basic model ofthe range-extended electric system can be divided into fourmodules range-extender module traction motor modulepower battery module and the vehicle longitudinal dynam-ics module Considering the high complexity of a dieselengine permanent magnet synchronous generator and therectifier and driving motor relevant components are testedby benchmarks and the characteristics MAP are determinedaccording to the test results Then the simulation modelsare built based on the MAP which replaces the complexmathematical description reduces modeling complexity andtherefore improves model credibility

Table 1 Powertrain parameters of range-extended electric bus

Vehicle

Size (length times width times

height)mm 11980 times 2550 times 3200

Vehicle masskg 13000Rated passengers 78Windward aream2 75

Air resistance coefficient119862119863

075

Rolling resistancecoefficient 119891 00076 + 000056119906

119886

Rolling radius 119903m 0512Speed ratio of main reducer

1198940

62

Speed ratio of transmission119894119892

234

Motor

Continuous powerkW 100Peak powerkW 180

Maximum torqueNsdotm 860Maximum speedrmin 4500Operating voltageV 300sim450

Engine DisplacementL 19PowerkW 824000 rmin

Generator Rated powerkW 50Rated torqueNsdotm 220

Power Battery Capacity 180AhOperating voltageV 350sim460

31 Range-Extender The range-extender includes a dieselengine a permanent magnet synchronous generator andrectifier System features can be described by the followingequations

119899eng = 119899119903

1

120591119890119904 + 1

119879eng = 1198911(120572 119899eng)

119862eng = 1198912(119899eng 119879eng)

120578gr = 1198913(119899eng 120582) sdot 120578119903

(1)

where 1198911is the accelerator characteristic MAP of the engine

1198912is fuel consumption characteristic MAP of the engine

1198913is the generator efficiency MAP 119899

119903is the enginersquos target

speed 120577119890is a time constant 120572 is the accelerator signal 119899eng is

the enginersquos actual speed 119879eng is the engine torque 120582 is thegenerator loading rate 120578

119903is the rectifier efficiency 119862eng is the

enginersquos instantaneous fuel consumption and 120578gr is the totalrate of the generator and rectifier

32 Traction Motor The traction motor module includes themotor and motor controllerThemotor model consists of the

Mathematical Problems in Engineering 5

Wheel Final drive Motor Converter

Battery

Wheel Final drive Motor Converter

Input way

Output way

Figure 4 Schema of recycle energy flow

steady state efficiency characteristic MAP and a first-orderprocess

120578119898= 1198911198981

(119899119898 119879119898)

119879119898= min (119879

119903 119879max) sdot

1

120591119898119904 + 1

119879max = 1198911198982

(119899119898)

(2)

where 120578119898is the motorrsquos electric efficiency 119899

119898is the motorrsquos

rotational speed 120577119898

is a time constant and 119879119898 119879119903 and

119879max are the motorrsquos actual torque target torque and torquecapacity respectively The function 119891

1198981denotes the motorrsquos

efficiency MAP and 1198911198982

denotes the motorrsquos maximumoutput torque characteristic MAP

33 Power Battery Thepower batterymodel is built based onthe119877intmodel which is equivalent to a variable voltage sourceand a variable resistance in series According to the batteryinternal resistance equivalent circuit the following equationcan be established

119880oc = 119864 (SOC 119879) minus 119868 sdot 119877 (SOC 119879) (3)

where SOC is the state of charge of the battery 119879 is thetemperature and 119868 is the battery current 119864 stands for theopen circuit voltage of the battery which is a function of SOC119879 is determined by the test and 119877 is the internal resistance ofthe battery

In this model the batteryrsquos SOC state uses ampere-hourintegral method to estimate [25] That is when the vehicle is

in operation it will use SOC as SOCint and at 119905moment it willuse SOC formula (4) to decide the following

SOC = SOCint minus1

119876119887

int

119905

1199050

120578bat119868bat119889119905 (4)

where 119876119887is rated capacity 120578bat is the batteryrsquos columbic

capacity and 119868bat is its charging and discharging current

34 Vehicle Longitudinal Dynamics The road load character-istic is assumed to be ideal in simulation that is zero air speedand good adhesion As the vehicle is traveling on the roadtraction motor needs to overcome driving resistance (119865

119905)

rolling resistance (119865119891) air resistance (119865

119908) slope resistance

(119865119894) and acceleration resistance (119865

119895) Consider

119865119905= 119865119891+ 119865119908+ 119865119894+ 119865119895

119865119891= 119891119898119892 cos (119886 tan 119894)

119865119908=

1

2

1198621198891198601205881199062

119886

119865119894= 119898119892 sin (119886 tan 119894)

119865119895= 028120575119898

119889119906119886

119889119905

119865119905=

36120578119879119875motor119906119886

(5)

where 119891 is the rolling resistance coefficient 119898 is the vehiclemass 119892 is the acceleration of gravity 119894 is the road slope 119862

119889is

the coefficient of air resistance 119860 is the windward area 120588is the air density 119906

119886is the motor speed 120575 is the correction

coefficient of rotatingmass 120578119879is the overall efficiency of drive

system and 119875motor is the output power of the traction motor

6 Mathematical Problems in Engineering

Engine

Generator andrectifier

Battery

Traction motor

Auxiliary

Axle

Recuperation efficiencyFuel-to-traction efficiency

Efuel

120578eng

Eeng Eloss eng

120578gen120578bout

Egrid

EblossErec

EbrecEb

120578bin

inin

Emcloss Emin

Ebg

Eb

120578cir wEwin

Ecir

Eg

Eae + Erol + EcirErec

Eloss gen

120578mmiddotout120578

mmiddotin

Eloss m

Eau

Figure 5 Energy flow chart in energy efficiency analysis

4 Energy Efficiency Analysis Using EnergyFlow Chart

According to the energy efficiency analysis method of plug-in hybrid electric powertrain in [7] energy efficiency analysiscan be divided into the following three parts

41 Dissipation and Cycle Energy Traction power is usedto drive the wheels and vehicle auxiliaries the calculationequation is as follows

119875 (119905) = 119875ae (119905) + 119875rol (119905) + 119875au (119905) + 119875ac (119905) + 119875gr (119905) (6)

where 119875ae(119905) = 120588air119860119891119888119889V3(119905)2 is the power to overcome

air resistance 120588air is the air density 119860119891is the frontal area

119888119889is the air resistance coefficient V is the vehicle speed

119875rol(119905) = (119898V +119898119901)119892119888119903 cos(120572(119905))V(119905) is the power to overcomerolling resistance 119875ac(119905) = (119898V + 119898

119901)V(119905)V(119905)(119889V(119905)119889119905)

is the accelerationdeceleration power 119875gr(119905) = (119898V +

119898119901)119892 sin(120572(119905))V(119905) is the updown hill power V is the vehicle

speed 120572 is the road gradient 119898119901

is the battery massand 119875au(119905) is the auxiliaries power including air conditionbattery heat management system heating (seat heating andwindshield heating) lighting control system and brakingsteer consumption The average power of the auxiliaries is10 kW [26] assuming air-conditioning is working

Mathematical Problems in Engineering 7

Original data

N series data

segments

PretreatmentCharacteristic

values matrix

Calculating characteristic

valuesComponent

score coefficient

matrix

Principal component

analysis

Clustering analysis

Clustering analysis results

First kind

Second kind

Third kind

Extracting representative driving cycle of every kind

Harbin city

driving cycle

Constructing driving cycle

Figure 6 Construction process of Harbin city driving cycle

0 200 400 600 800 1000 1200 140005

101520253035404550

(k

mh

)

t (s)

Figure 7 Harbin city driving cycle

119875(119905) can be divided into two parts one is the dissipatedpower 119875dis(119905) = 119875ae(119905) + 119875rol(119905) + 119875au(119905) and the other isconserved power 119875cons(119905) = 119875ac(119905) + 119875gr(119905) As the initial andfinal altitude and speed are the same in a whole driving cyclethe reserved power is zero If braking energy can be fullyrecycled required traction energy 119864trac should be the sameas the dissipated energy 119864dis

119864trac = int

119905119891

1199050

119875 (119905) 119889119905 = int

119905119891

1199050

119875dis (119905) 119889119905 = 119864dis (7)

where 1199050and 119905119891are initial and final time If there is no barking

energy recycled

119864trac = int

119875(119905)gt0

119875 (119905) 119889119905

= int

119905119891

1199050

119875dis (119905) 119889119905 + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

= 119864dis + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

(8)

where int119875(119905)lt0

(minus119875(119905))119889119905 represents the cycle energy 119864cir whichis the temporal vehicle cycle energy in the form of kineticor potential energy and ultimately dissipated during friction

brakingTherefore (8) for vehicle without energy recycle canbe calculated as

119864trac = 119864dis + 119864cir (9)

In actual driving energy balance equation can be calcu-lated as

119864trac = 119864dis + 119864cir minus 119864rec (10)

where119864rec is the recycled net energy that is usable for tractionAccording to (7) and (10) it can be found that 119864rec = 119864cir

42 Recycle Efficiency of Barking Energy Recycle efficiency isdefined as

120578rec =119864rec119864cir

(11)

As 119864cir can be easily obtained in driving cycle the keymission is to calculate 119864rec Recycle energy consists of twoflow methods input and output As is shown in Figure 4recycle ability is determined by energy dissipation motortorque current of power battery and threshold charge value

Time set 119878 is defined as

119878 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) lt 0 119875

119887 (119905) lt 0 (12)

where 119875au is physical load in converter 119864119908 in is absolute inputenergy during 119878 and is calculated by

119864119908in = int

119878

1003816100381610038161003816119875 (119905) minus 119875au (119905)

1003816100381610038161003816119889119905 (13)

The energy reserved in battery is

119864119887 in = int

119878

10038161003816100381610038161003816119875119887 (119905) + 119868(119905)

2119877119899119888

10038161003816100381610038161003816119889119905 (14)

The energy loss is

119864loss in = 119864119908 in minus 119864

119887 in minus int

119878

119875au (119905) 119889119905 (15)

8 Mathematical Problems in Engineering

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

70

80

90

100SO

C (

)

s (km)

(a) CD-CS strategy

0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

SOC

()

s (km)

(b) Blended strategy

Figure 8 The SOC curve with the two different energy management strategies

The cycle-average wheel to battery energy efficiency is

120578wb in = 1 minus

119864loss in

119864119908 in

(16)

The recycle energy reserved in battery is

119864rec in = 119864cir120578wb in120578cir 119908 (17)

where 120578cir 119908 is the ratio between 119864119908and 119864cir

Time set119863 is defined as

119863 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) ge 0 119875

119887 (119905) ge 0 (18)

The associated motor energy loss in propelling is

119864loss 119898 = int

119863

119875loss 119898 (119905) 119889119905 (19)

The average motor efficiency is

120578119898 out = 1 minus

119864loss 119898119889

int119863119875119887 (119905) 120578con + 119875apu (119905) 120578con minus 119875au (119905) 119889119905

(20)

The battery energy loss during time119863 is

119864loss 119887 = int

119863

119868(119905)2119877119899119888119889119905 (21)

The battery efficiency in output way is

120578119887out = 1 minus

119864loss 119887119889

int119863119875119887 (119905) + 119868(119905)

2119877119899119887119889119905

(22)

The cycle-average battery to wheel energy efficiency is

120578bw out = 120578119887 out120578con120578119898 out120578119891119889120578119887119898 (23)

where 120578119887119898

is the ratio between the power that batteryprovides to the motor and the power emitted by batteryAccording to (16) and (23) the recycle energy for traction is

119864rec = 119864rec in120578bw out (24)

The cycle-average recycle efficiency is

120578rec =119864rec119864cir

= 120578cir119908120578wb in120578bw out (25)

43 Fuel-Traction Efficiency Fuel-traction efficiency is def-ined as

120578ft =

119864trac119864ef

=

119864dis + (1 minus 120578rec) 119864cir

119864ef (26)

where119864ef is the equal fuel energy the average consumption ofthe sum of diesel and electric energy 120578ft is the cycle-averageconversion efficiency from the total consumed energy to themechanical energy at the wheels and the electrical energy forthe auxiliaries Based on the initial and final SOC 119864ef can bedivided into diesel energy and electric energy

An energy flow chart can clearly show the direction ofenergy flow showing the sizes of losses from each individualpart It is one of the most effective methods for analyzingflow in the context of system performance Referring to theanalysis method in [27] this paper puts forward a powertrainenergy analysis method with energy flow chart for range-extended electric bus The powertrain energy flow chart isshown in Figure 5

5 Analysis Example with the DrivingCycle of Harbin City

To provide a credible reference for the match and controlof the range-extended electric bus energy efficiency analysis

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Figure 3 The range-extended electric bus developed by TsinghuaUniversity

power of the range-extender is higher than the requiredmotor power the redundant electric energy is reserved inbattery charging the battery The output power of the range-extender is not directly influenced by the driving conditionsand can be optimized in the high efficiency working areas ofthe engine and motor

If the bus is braking the motor can work in regenerativebrake mode as is shown in Figure 2(c) The motor providesbraking torque for the vehicle wheels and braking energyis transferred into electric energy reserved in the batteryBraking energy is not transferred into heat and lost it isrecycled

For an individual axle drive bus only wheels driven by themotor can recycle braking energy Other wheels are stoppedby mechanical braking Braking energy is partly recycled andmechanical braking is also used on driven wheels for safety

The range-extended electric bus analyzed in this paperis developed by Tsinghua University shown in Figure 3The powertrain is designed based on matching powertrainparts and model selection found in [20] The generator is apermanent magnet generator and the traction motor is anasynchronous motor Key parameters of the powertrain arelisted in Table 1

3 System Modeling of the Range-ExtendedElectric Bus

To analyze energy efficiency and fuel economy of the range-extended electric bus system models based on benchmarksand modeling lines of [21ndash24] are built The basic model ofthe range-extended electric system can be divided into fourmodules range-extender module traction motor modulepower battery module and the vehicle longitudinal dynam-ics module Considering the high complexity of a dieselengine permanent magnet synchronous generator and therectifier and driving motor relevant components are testedby benchmarks and the characteristics MAP are determinedaccording to the test results Then the simulation modelsare built based on the MAP which replaces the complexmathematical description reduces modeling complexity andtherefore improves model credibility

Table 1 Powertrain parameters of range-extended electric bus

Vehicle

Size (length times width times

height)mm 11980 times 2550 times 3200

Vehicle masskg 13000Rated passengers 78Windward aream2 75

Air resistance coefficient119862119863

075

Rolling resistancecoefficient 119891 00076 + 000056119906

119886

Rolling radius 119903m 0512Speed ratio of main reducer

1198940

62

Speed ratio of transmission119894119892

234

Motor

Continuous powerkW 100Peak powerkW 180

Maximum torqueNsdotm 860Maximum speedrmin 4500Operating voltageV 300sim450

Engine DisplacementL 19PowerkW 824000 rmin

Generator Rated powerkW 50Rated torqueNsdotm 220

Power Battery Capacity 180AhOperating voltageV 350sim460

31 Range-Extender The range-extender includes a dieselengine a permanent magnet synchronous generator andrectifier System features can be described by the followingequations

119899eng = 119899119903

1

120591119890119904 + 1

119879eng = 1198911(120572 119899eng)

119862eng = 1198912(119899eng 119879eng)

120578gr = 1198913(119899eng 120582) sdot 120578119903

(1)

where 1198911is the accelerator characteristic MAP of the engine

1198912is fuel consumption characteristic MAP of the engine

1198913is the generator efficiency MAP 119899

119903is the enginersquos target

speed 120577119890is a time constant 120572 is the accelerator signal 119899eng is

the enginersquos actual speed 119879eng is the engine torque 120582 is thegenerator loading rate 120578

119903is the rectifier efficiency 119862eng is the

enginersquos instantaneous fuel consumption and 120578gr is the totalrate of the generator and rectifier

32 Traction Motor The traction motor module includes themotor and motor controllerThemotor model consists of the

Mathematical Problems in Engineering 5

Wheel Final drive Motor Converter

Battery

Wheel Final drive Motor Converter

Input way

Output way

Figure 4 Schema of recycle energy flow

steady state efficiency characteristic MAP and a first-orderprocess

120578119898= 1198911198981

(119899119898 119879119898)

119879119898= min (119879

119903 119879max) sdot

1

120591119898119904 + 1

119879max = 1198911198982

(119899119898)

(2)

where 120578119898is the motorrsquos electric efficiency 119899

119898is the motorrsquos

rotational speed 120577119898

is a time constant and 119879119898 119879119903 and

119879max are the motorrsquos actual torque target torque and torquecapacity respectively The function 119891

1198981denotes the motorrsquos

efficiency MAP and 1198911198982

denotes the motorrsquos maximumoutput torque characteristic MAP

33 Power Battery Thepower batterymodel is built based onthe119877intmodel which is equivalent to a variable voltage sourceand a variable resistance in series According to the batteryinternal resistance equivalent circuit the following equationcan be established

119880oc = 119864 (SOC 119879) minus 119868 sdot 119877 (SOC 119879) (3)

where SOC is the state of charge of the battery 119879 is thetemperature and 119868 is the battery current 119864 stands for theopen circuit voltage of the battery which is a function of SOC119879 is determined by the test and 119877 is the internal resistance ofthe battery

In this model the batteryrsquos SOC state uses ampere-hourintegral method to estimate [25] That is when the vehicle is

in operation it will use SOC as SOCint and at 119905moment it willuse SOC formula (4) to decide the following

SOC = SOCint minus1

119876119887

int

119905

1199050

120578bat119868bat119889119905 (4)

where 119876119887is rated capacity 120578bat is the batteryrsquos columbic

capacity and 119868bat is its charging and discharging current

34 Vehicle Longitudinal Dynamics The road load character-istic is assumed to be ideal in simulation that is zero air speedand good adhesion As the vehicle is traveling on the roadtraction motor needs to overcome driving resistance (119865

119905)

rolling resistance (119865119891) air resistance (119865

119908) slope resistance

(119865119894) and acceleration resistance (119865

119895) Consider

119865119905= 119865119891+ 119865119908+ 119865119894+ 119865119895

119865119891= 119891119898119892 cos (119886 tan 119894)

119865119908=

1

2

1198621198891198601205881199062

119886

119865119894= 119898119892 sin (119886 tan 119894)

119865119895= 028120575119898

119889119906119886

119889119905

119865119905=

36120578119879119875motor119906119886

(5)

where 119891 is the rolling resistance coefficient 119898 is the vehiclemass 119892 is the acceleration of gravity 119894 is the road slope 119862

119889is

the coefficient of air resistance 119860 is the windward area 120588is the air density 119906

119886is the motor speed 120575 is the correction

coefficient of rotatingmass 120578119879is the overall efficiency of drive

system and 119875motor is the output power of the traction motor

6 Mathematical Problems in Engineering

Engine

Generator andrectifier

Battery

Traction motor

Auxiliary

Axle

Recuperation efficiencyFuel-to-traction efficiency

Efuel

120578eng

Eeng Eloss eng

120578gen120578bout

Egrid

EblossErec

EbrecEb

120578bin

inin

Emcloss Emin

Ebg

Eb

120578cir wEwin

Ecir

Eg

Eae + Erol + EcirErec

Eloss gen

120578mmiddotout120578

mmiddotin

Eloss m

Eau

Figure 5 Energy flow chart in energy efficiency analysis

4 Energy Efficiency Analysis Using EnergyFlow Chart

According to the energy efficiency analysis method of plug-in hybrid electric powertrain in [7] energy efficiency analysiscan be divided into the following three parts

41 Dissipation and Cycle Energy Traction power is usedto drive the wheels and vehicle auxiliaries the calculationequation is as follows

119875 (119905) = 119875ae (119905) + 119875rol (119905) + 119875au (119905) + 119875ac (119905) + 119875gr (119905) (6)

where 119875ae(119905) = 120588air119860119891119888119889V3(119905)2 is the power to overcome

air resistance 120588air is the air density 119860119891is the frontal area

119888119889is the air resistance coefficient V is the vehicle speed

119875rol(119905) = (119898V +119898119901)119892119888119903 cos(120572(119905))V(119905) is the power to overcomerolling resistance 119875ac(119905) = (119898V + 119898

119901)V(119905)V(119905)(119889V(119905)119889119905)

is the accelerationdeceleration power 119875gr(119905) = (119898V +

119898119901)119892 sin(120572(119905))V(119905) is the updown hill power V is the vehicle

speed 120572 is the road gradient 119898119901

is the battery massand 119875au(119905) is the auxiliaries power including air conditionbattery heat management system heating (seat heating andwindshield heating) lighting control system and brakingsteer consumption The average power of the auxiliaries is10 kW [26] assuming air-conditioning is working

Mathematical Problems in Engineering 7

Original data

N series data

segments

PretreatmentCharacteristic

values matrix

Calculating characteristic

valuesComponent

score coefficient

matrix

Principal component

analysis

Clustering analysis

Clustering analysis results

First kind

Second kind

Third kind

Extracting representative driving cycle of every kind

Harbin city

driving cycle

Constructing driving cycle

Figure 6 Construction process of Harbin city driving cycle

0 200 400 600 800 1000 1200 140005

101520253035404550

(k

mh

)

t (s)

Figure 7 Harbin city driving cycle

119875(119905) can be divided into two parts one is the dissipatedpower 119875dis(119905) = 119875ae(119905) + 119875rol(119905) + 119875au(119905) and the other isconserved power 119875cons(119905) = 119875ac(119905) + 119875gr(119905) As the initial andfinal altitude and speed are the same in a whole driving cyclethe reserved power is zero If braking energy can be fullyrecycled required traction energy 119864trac should be the sameas the dissipated energy 119864dis

119864trac = int

119905119891

1199050

119875 (119905) 119889119905 = int

119905119891

1199050

119875dis (119905) 119889119905 = 119864dis (7)

where 1199050and 119905119891are initial and final time If there is no barking

energy recycled

119864trac = int

119875(119905)gt0

119875 (119905) 119889119905

= int

119905119891

1199050

119875dis (119905) 119889119905 + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

= 119864dis + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

(8)

where int119875(119905)lt0

(minus119875(119905))119889119905 represents the cycle energy 119864cir whichis the temporal vehicle cycle energy in the form of kineticor potential energy and ultimately dissipated during friction

brakingTherefore (8) for vehicle without energy recycle canbe calculated as

119864trac = 119864dis + 119864cir (9)

In actual driving energy balance equation can be calcu-lated as

119864trac = 119864dis + 119864cir minus 119864rec (10)

where119864rec is the recycled net energy that is usable for tractionAccording to (7) and (10) it can be found that 119864rec = 119864cir

42 Recycle Efficiency of Barking Energy Recycle efficiency isdefined as

120578rec =119864rec119864cir

(11)

As 119864cir can be easily obtained in driving cycle the keymission is to calculate 119864rec Recycle energy consists of twoflow methods input and output As is shown in Figure 4recycle ability is determined by energy dissipation motortorque current of power battery and threshold charge value

Time set 119878 is defined as

119878 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) lt 0 119875

119887 (119905) lt 0 (12)

where 119875au is physical load in converter 119864119908 in is absolute inputenergy during 119878 and is calculated by

119864119908in = int

119878

1003816100381610038161003816119875 (119905) minus 119875au (119905)

1003816100381610038161003816119889119905 (13)

The energy reserved in battery is

119864119887 in = int

119878

10038161003816100381610038161003816119875119887 (119905) + 119868(119905)

2119877119899119888

10038161003816100381610038161003816119889119905 (14)

The energy loss is

119864loss in = 119864119908 in minus 119864

119887 in minus int

119878

119875au (119905) 119889119905 (15)

8 Mathematical Problems in Engineering

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

70

80

90

100SO

C (

)

s (km)

(a) CD-CS strategy

0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

SOC

()

s (km)

(b) Blended strategy

Figure 8 The SOC curve with the two different energy management strategies

The cycle-average wheel to battery energy efficiency is

120578wb in = 1 minus

119864loss in

119864119908 in

(16)

The recycle energy reserved in battery is

119864rec in = 119864cir120578wb in120578cir 119908 (17)

where 120578cir 119908 is the ratio between 119864119908and 119864cir

Time set119863 is defined as

119863 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) ge 0 119875

119887 (119905) ge 0 (18)

The associated motor energy loss in propelling is

119864loss 119898 = int

119863

119875loss 119898 (119905) 119889119905 (19)

The average motor efficiency is

120578119898 out = 1 minus

119864loss 119898119889

int119863119875119887 (119905) 120578con + 119875apu (119905) 120578con minus 119875au (119905) 119889119905

(20)

The battery energy loss during time119863 is

119864loss 119887 = int

119863

119868(119905)2119877119899119888119889119905 (21)

The battery efficiency in output way is

120578119887out = 1 minus

119864loss 119887119889

int119863119875119887 (119905) + 119868(119905)

2119877119899119887119889119905

(22)

The cycle-average battery to wheel energy efficiency is

120578bw out = 120578119887 out120578con120578119898 out120578119891119889120578119887119898 (23)

where 120578119887119898

is the ratio between the power that batteryprovides to the motor and the power emitted by batteryAccording to (16) and (23) the recycle energy for traction is

119864rec = 119864rec in120578bw out (24)

The cycle-average recycle efficiency is

120578rec =119864rec119864cir

= 120578cir119908120578wb in120578bw out (25)

43 Fuel-Traction Efficiency Fuel-traction efficiency is def-ined as

120578ft =

119864trac119864ef

=

119864dis + (1 minus 120578rec) 119864cir

119864ef (26)

where119864ef is the equal fuel energy the average consumption ofthe sum of diesel and electric energy 120578ft is the cycle-averageconversion efficiency from the total consumed energy to themechanical energy at the wheels and the electrical energy forthe auxiliaries Based on the initial and final SOC 119864ef can bedivided into diesel energy and electric energy

An energy flow chart can clearly show the direction ofenergy flow showing the sizes of losses from each individualpart It is one of the most effective methods for analyzingflow in the context of system performance Referring to theanalysis method in [27] this paper puts forward a powertrainenergy analysis method with energy flow chart for range-extended electric bus The powertrain energy flow chart isshown in Figure 5

5 Analysis Example with the DrivingCycle of Harbin City

To provide a credible reference for the match and controlof the range-extended electric bus energy efficiency analysis

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

Wheel Final drive Motor Converter

Battery

Wheel Final drive Motor Converter

Input way

Output way

Figure 4 Schema of recycle energy flow

steady state efficiency characteristic MAP and a first-orderprocess

120578119898= 1198911198981

(119899119898 119879119898)

119879119898= min (119879

119903 119879max) sdot

1

120591119898119904 + 1

119879max = 1198911198982

(119899119898)

(2)

where 120578119898is the motorrsquos electric efficiency 119899

119898is the motorrsquos

rotational speed 120577119898

is a time constant and 119879119898 119879119903 and

119879max are the motorrsquos actual torque target torque and torquecapacity respectively The function 119891

1198981denotes the motorrsquos

efficiency MAP and 1198911198982

denotes the motorrsquos maximumoutput torque characteristic MAP

33 Power Battery Thepower batterymodel is built based onthe119877intmodel which is equivalent to a variable voltage sourceand a variable resistance in series According to the batteryinternal resistance equivalent circuit the following equationcan be established

119880oc = 119864 (SOC 119879) minus 119868 sdot 119877 (SOC 119879) (3)

where SOC is the state of charge of the battery 119879 is thetemperature and 119868 is the battery current 119864 stands for theopen circuit voltage of the battery which is a function of SOC119879 is determined by the test and 119877 is the internal resistance ofthe battery

In this model the batteryrsquos SOC state uses ampere-hourintegral method to estimate [25] That is when the vehicle is

in operation it will use SOC as SOCint and at 119905moment it willuse SOC formula (4) to decide the following

SOC = SOCint minus1

119876119887

int

119905

1199050

120578bat119868bat119889119905 (4)

where 119876119887is rated capacity 120578bat is the batteryrsquos columbic

capacity and 119868bat is its charging and discharging current

34 Vehicle Longitudinal Dynamics The road load character-istic is assumed to be ideal in simulation that is zero air speedand good adhesion As the vehicle is traveling on the roadtraction motor needs to overcome driving resistance (119865

119905)

rolling resistance (119865119891) air resistance (119865

119908) slope resistance

(119865119894) and acceleration resistance (119865

119895) Consider

119865119905= 119865119891+ 119865119908+ 119865119894+ 119865119895

119865119891= 119891119898119892 cos (119886 tan 119894)

119865119908=

1

2

1198621198891198601205881199062

119886

119865119894= 119898119892 sin (119886 tan 119894)

119865119895= 028120575119898

119889119906119886

119889119905

119865119905=

36120578119879119875motor119906119886

(5)

where 119891 is the rolling resistance coefficient 119898 is the vehiclemass 119892 is the acceleration of gravity 119894 is the road slope 119862

119889is

the coefficient of air resistance 119860 is the windward area 120588is the air density 119906

119886is the motor speed 120575 is the correction

coefficient of rotatingmass 120578119879is the overall efficiency of drive

system and 119875motor is the output power of the traction motor

6 Mathematical Problems in Engineering

Engine

Generator andrectifier

Battery

Traction motor

Auxiliary

Axle

Recuperation efficiencyFuel-to-traction efficiency

Efuel

120578eng

Eeng Eloss eng

120578gen120578bout

Egrid

EblossErec

EbrecEb

120578bin

inin

Emcloss Emin

Ebg

Eb

120578cir wEwin

Ecir

Eg

Eae + Erol + EcirErec

Eloss gen

120578mmiddotout120578

mmiddotin

Eloss m

Eau

Figure 5 Energy flow chart in energy efficiency analysis

4 Energy Efficiency Analysis Using EnergyFlow Chart

According to the energy efficiency analysis method of plug-in hybrid electric powertrain in [7] energy efficiency analysiscan be divided into the following three parts

41 Dissipation and Cycle Energy Traction power is usedto drive the wheels and vehicle auxiliaries the calculationequation is as follows

119875 (119905) = 119875ae (119905) + 119875rol (119905) + 119875au (119905) + 119875ac (119905) + 119875gr (119905) (6)

where 119875ae(119905) = 120588air119860119891119888119889V3(119905)2 is the power to overcome

air resistance 120588air is the air density 119860119891is the frontal area

119888119889is the air resistance coefficient V is the vehicle speed

119875rol(119905) = (119898V +119898119901)119892119888119903 cos(120572(119905))V(119905) is the power to overcomerolling resistance 119875ac(119905) = (119898V + 119898

119901)V(119905)V(119905)(119889V(119905)119889119905)

is the accelerationdeceleration power 119875gr(119905) = (119898V +

119898119901)119892 sin(120572(119905))V(119905) is the updown hill power V is the vehicle

speed 120572 is the road gradient 119898119901

is the battery massand 119875au(119905) is the auxiliaries power including air conditionbattery heat management system heating (seat heating andwindshield heating) lighting control system and brakingsteer consumption The average power of the auxiliaries is10 kW [26] assuming air-conditioning is working

Mathematical Problems in Engineering 7

Original data

N series data

segments

PretreatmentCharacteristic

values matrix

Calculating characteristic

valuesComponent

score coefficient

matrix

Principal component

analysis

Clustering analysis

Clustering analysis results

First kind

Second kind

Third kind

Extracting representative driving cycle of every kind

Harbin city

driving cycle

Constructing driving cycle

Figure 6 Construction process of Harbin city driving cycle

0 200 400 600 800 1000 1200 140005

101520253035404550

(k

mh

)

t (s)

Figure 7 Harbin city driving cycle

119875(119905) can be divided into two parts one is the dissipatedpower 119875dis(119905) = 119875ae(119905) + 119875rol(119905) + 119875au(119905) and the other isconserved power 119875cons(119905) = 119875ac(119905) + 119875gr(119905) As the initial andfinal altitude and speed are the same in a whole driving cyclethe reserved power is zero If braking energy can be fullyrecycled required traction energy 119864trac should be the sameas the dissipated energy 119864dis

119864trac = int

119905119891

1199050

119875 (119905) 119889119905 = int

119905119891

1199050

119875dis (119905) 119889119905 = 119864dis (7)

where 1199050and 119905119891are initial and final time If there is no barking

energy recycled

119864trac = int

119875(119905)gt0

119875 (119905) 119889119905

= int

119905119891

1199050

119875dis (119905) 119889119905 + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

= 119864dis + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

(8)

where int119875(119905)lt0

(minus119875(119905))119889119905 represents the cycle energy 119864cir whichis the temporal vehicle cycle energy in the form of kineticor potential energy and ultimately dissipated during friction

brakingTherefore (8) for vehicle without energy recycle canbe calculated as

119864trac = 119864dis + 119864cir (9)

In actual driving energy balance equation can be calcu-lated as

119864trac = 119864dis + 119864cir minus 119864rec (10)

where119864rec is the recycled net energy that is usable for tractionAccording to (7) and (10) it can be found that 119864rec = 119864cir

42 Recycle Efficiency of Barking Energy Recycle efficiency isdefined as

120578rec =119864rec119864cir

(11)

As 119864cir can be easily obtained in driving cycle the keymission is to calculate 119864rec Recycle energy consists of twoflow methods input and output As is shown in Figure 4recycle ability is determined by energy dissipation motortorque current of power battery and threshold charge value

Time set 119878 is defined as

119878 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) lt 0 119875

119887 (119905) lt 0 (12)

where 119875au is physical load in converter 119864119908 in is absolute inputenergy during 119878 and is calculated by

119864119908in = int

119878

1003816100381610038161003816119875 (119905) minus 119875au (119905)

1003816100381610038161003816119889119905 (13)

The energy reserved in battery is

119864119887 in = int

119878

10038161003816100381610038161003816119875119887 (119905) + 119868(119905)

2119877119899119888

10038161003816100381610038161003816119889119905 (14)

The energy loss is

119864loss in = 119864119908 in minus 119864

119887 in minus int

119878

119875au (119905) 119889119905 (15)

8 Mathematical Problems in Engineering

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

70

80

90

100SO

C (

)

s (km)

(a) CD-CS strategy

0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

SOC

()

s (km)

(b) Blended strategy

Figure 8 The SOC curve with the two different energy management strategies

The cycle-average wheel to battery energy efficiency is

120578wb in = 1 minus

119864loss in

119864119908 in

(16)

The recycle energy reserved in battery is

119864rec in = 119864cir120578wb in120578cir 119908 (17)

where 120578cir 119908 is the ratio between 119864119908and 119864cir

Time set119863 is defined as

119863 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) ge 0 119875

119887 (119905) ge 0 (18)

The associated motor energy loss in propelling is

119864loss 119898 = int

119863

119875loss 119898 (119905) 119889119905 (19)

The average motor efficiency is

120578119898 out = 1 minus

119864loss 119898119889

int119863119875119887 (119905) 120578con + 119875apu (119905) 120578con minus 119875au (119905) 119889119905

(20)

The battery energy loss during time119863 is

119864loss 119887 = int

119863

119868(119905)2119877119899119888119889119905 (21)

The battery efficiency in output way is

120578119887out = 1 minus

119864loss 119887119889

int119863119875119887 (119905) + 119868(119905)

2119877119899119887119889119905

(22)

The cycle-average battery to wheel energy efficiency is

120578bw out = 120578119887 out120578con120578119898 out120578119891119889120578119887119898 (23)

where 120578119887119898

is the ratio between the power that batteryprovides to the motor and the power emitted by batteryAccording to (16) and (23) the recycle energy for traction is

119864rec = 119864rec in120578bw out (24)

The cycle-average recycle efficiency is

120578rec =119864rec119864cir

= 120578cir119908120578wb in120578bw out (25)

43 Fuel-Traction Efficiency Fuel-traction efficiency is def-ined as

120578ft =

119864trac119864ef

=

119864dis + (1 minus 120578rec) 119864cir

119864ef (26)

where119864ef is the equal fuel energy the average consumption ofthe sum of diesel and electric energy 120578ft is the cycle-averageconversion efficiency from the total consumed energy to themechanical energy at the wheels and the electrical energy forthe auxiliaries Based on the initial and final SOC 119864ef can bedivided into diesel energy and electric energy

An energy flow chart can clearly show the direction ofenergy flow showing the sizes of losses from each individualpart It is one of the most effective methods for analyzingflow in the context of system performance Referring to theanalysis method in [27] this paper puts forward a powertrainenergy analysis method with energy flow chart for range-extended electric bus The powertrain energy flow chart isshown in Figure 5

5 Analysis Example with the DrivingCycle of Harbin City

To provide a credible reference for the match and controlof the range-extended electric bus energy efficiency analysis

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

Engine

Generator andrectifier

Battery

Traction motor

Auxiliary

Axle

Recuperation efficiencyFuel-to-traction efficiency

Efuel

120578eng

Eeng Eloss eng

120578gen120578bout

Egrid

EblossErec

EbrecEb

120578bin

inin

Emcloss Emin

Ebg

Eb

120578cir wEwin

Ecir

Eg

Eae + Erol + EcirErec

Eloss gen

120578mmiddotout120578

mmiddotin

Eloss m

Eau

Figure 5 Energy flow chart in energy efficiency analysis

4 Energy Efficiency Analysis Using EnergyFlow Chart

According to the energy efficiency analysis method of plug-in hybrid electric powertrain in [7] energy efficiency analysiscan be divided into the following three parts

41 Dissipation and Cycle Energy Traction power is usedto drive the wheels and vehicle auxiliaries the calculationequation is as follows

119875 (119905) = 119875ae (119905) + 119875rol (119905) + 119875au (119905) + 119875ac (119905) + 119875gr (119905) (6)

where 119875ae(119905) = 120588air119860119891119888119889V3(119905)2 is the power to overcome

air resistance 120588air is the air density 119860119891is the frontal area

119888119889is the air resistance coefficient V is the vehicle speed

119875rol(119905) = (119898V +119898119901)119892119888119903 cos(120572(119905))V(119905) is the power to overcomerolling resistance 119875ac(119905) = (119898V + 119898

119901)V(119905)V(119905)(119889V(119905)119889119905)

is the accelerationdeceleration power 119875gr(119905) = (119898V +

119898119901)119892 sin(120572(119905))V(119905) is the updown hill power V is the vehicle

speed 120572 is the road gradient 119898119901

is the battery massand 119875au(119905) is the auxiliaries power including air conditionbattery heat management system heating (seat heating andwindshield heating) lighting control system and brakingsteer consumption The average power of the auxiliaries is10 kW [26] assuming air-conditioning is working

Mathematical Problems in Engineering 7

Original data

N series data

segments

PretreatmentCharacteristic

values matrix

Calculating characteristic

valuesComponent

score coefficient

matrix

Principal component

analysis

Clustering analysis

Clustering analysis results

First kind

Second kind

Third kind

Extracting representative driving cycle of every kind

Harbin city

driving cycle

Constructing driving cycle

Figure 6 Construction process of Harbin city driving cycle

0 200 400 600 800 1000 1200 140005

101520253035404550

(k

mh

)

t (s)

Figure 7 Harbin city driving cycle

119875(119905) can be divided into two parts one is the dissipatedpower 119875dis(119905) = 119875ae(119905) + 119875rol(119905) + 119875au(119905) and the other isconserved power 119875cons(119905) = 119875ac(119905) + 119875gr(119905) As the initial andfinal altitude and speed are the same in a whole driving cyclethe reserved power is zero If braking energy can be fullyrecycled required traction energy 119864trac should be the sameas the dissipated energy 119864dis

119864trac = int

119905119891

1199050

119875 (119905) 119889119905 = int

119905119891

1199050

119875dis (119905) 119889119905 = 119864dis (7)

where 1199050and 119905119891are initial and final time If there is no barking

energy recycled

119864trac = int

119875(119905)gt0

119875 (119905) 119889119905

= int

119905119891

1199050

119875dis (119905) 119889119905 + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

= 119864dis + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

(8)

where int119875(119905)lt0

(minus119875(119905))119889119905 represents the cycle energy 119864cir whichis the temporal vehicle cycle energy in the form of kineticor potential energy and ultimately dissipated during friction

brakingTherefore (8) for vehicle without energy recycle canbe calculated as

119864trac = 119864dis + 119864cir (9)

In actual driving energy balance equation can be calcu-lated as

119864trac = 119864dis + 119864cir minus 119864rec (10)

where119864rec is the recycled net energy that is usable for tractionAccording to (7) and (10) it can be found that 119864rec = 119864cir

42 Recycle Efficiency of Barking Energy Recycle efficiency isdefined as

120578rec =119864rec119864cir

(11)

As 119864cir can be easily obtained in driving cycle the keymission is to calculate 119864rec Recycle energy consists of twoflow methods input and output As is shown in Figure 4recycle ability is determined by energy dissipation motortorque current of power battery and threshold charge value

Time set 119878 is defined as

119878 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) lt 0 119875

119887 (119905) lt 0 (12)

where 119875au is physical load in converter 119864119908 in is absolute inputenergy during 119878 and is calculated by

119864119908in = int

119878

1003816100381610038161003816119875 (119905) minus 119875au (119905)

1003816100381610038161003816119889119905 (13)

The energy reserved in battery is

119864119887 in = int

119878

10038161003816100381610038161003816119875119887 (119905) + 119868(119905)

2119877119899119888

10038161003816100381610038161003816119889119905 (14)

The energy loss is

119864loss in = 119864119908 in minus 119864

119887 in minus int

119878

119875au (119905) 119889119905 (15)

8 Mathematical Problems in Engineering

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

70

80

90

100SO

C (

)

s (km)

(a) CD-CS strategy

0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

SOC

()

s (km)

(b) Blended strategy

Figure 8 The SOC curve with the two different energy management strategies

The cycle-average wheel to battery energy efficiency is

120578wb in = 1 minus

119864loss in

119864119908 in

(16)

The recycle energy reserved in battery is

119864rec in = 119864cir120578wb in120578cir 119908 (17)

where 120578cir 119908 is the ratio between 119864119908and 119864cir

Time set119863 is defined as

119863 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) ge 0 119875

119887 (119905) ge 0 (18)

The associated motor energy loss in propelling is

119864loss 119898 = int

119863

119875loss 119898 (119905) 119889119905 (19)

The average motor efficiency is

120578119898 out = 1 minus

119864loss 119898119889

int119863119875119887 (119905) 120578con + 119875apu (119905) 120578con minus 119875au (119905) 119889119905

(20)

The battery energy loss during time119863 is

119864loss 119887 = int

119863

119868(119905)2119877119899119888119889119905 (21)

The battery efficiency in output way is

120578119887out = 1 minus

119864loss 119887119889

int119863119875119887 (119905) + 119868(119905)

2119877119899119887119889119905

(22)

The cycle-average battery to wheel energy efficiency is

120578bw out = 120578119887 out120578con120578119898 out120578119891119889120578119887119898 (23)

where 120578119887119898

is the ratio between the power that batteryprovides to the motor and the power emitted by batteryAccording to (16) and (23) the recycle energy for traction is

119864rec = 119864rec in120578bw out (24)

The cycle-average recycle efficiency is

120578rec =119864rec119864cir

= 120578cir119908120578wb in120578bw out (25)

43 Fuel-Traction Efficiency Fuel-traction efficiency is def-ined as

120578ft =

119864trac119864ef

=

119864dis + (1 minus 120578rec) 119864cir

119864ef (26)

where119864ef is the equal fuel energy the average consumption ofthe sum of diesel and electric energy 120578ft is the cycle-averageconversion efficiency from the total consumed energy to themechanical energy at the wheels and the electrical energy forthe auxiliaries Based on the initial and final SOC 119864ef can bedivided into diesel energy and electric energy

An energy flow chart can clearly show the direction ofenergy flow showing the sizes of losses from each individualpart It is one of the most effective methods for analyzingflow in the context of system performance Referring to theanalysis method in [27] this paper puts forward a powertrainenergy analysis method with energy flow chart for range-extended electric bus The powertrain energy flow chart isshown in Figure 5

5 Analysis Example with the DrivingCycle of Harbin City

To provide a credible reference for the match and controlof the range-extended electric bus energy efficiency analysis

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Original data

N series data

segments

PretreatmentCharacteristic

values matrix

Calculating characteristic

valuesComponent

score coefficient

matrix

Principal component

analysis

Clustering analysis

Clustering analysis results

First kind

Second kind

Third kind

Extracting representative driving cycle of every kind

Harbin city

driving cycle

Constructing driving cycle

Figure 6 Construction process of Harbin city driving cycle

0 200 400 600 800 1000 1200 140005

101520253035404550

(k

mh

)

t (s)

Figure 7 Harbin city driving cycle

119875(119905) can be divided into two parts one is the dissipatedpower 119875dis(119905) = 119875ae(119905) + 119875rol(119905) + 119875au(119905) and the other isconserved power 119875cons(119905) = 119875ac(119905) + 119875gr(119905) As the initial andfinal altitude and speed are the same in a whole driving cyclethe reserved power is zero If braking energy can be fullyrecycled required traction energy 119864trac should be the sameas the dissipated energy 119864dis

119864trac = int

119905119891

1199050

119875 (119905) 119889119905 = int

119905119891

1199050

119875dis (119905) 119889119905 = 119864dis (7)

where 1199050and 119905119891are initial and final time If there is no barking

energy recycled

119864trac = int

119875(119905)gt0

119875 (119905) 119889119905

= int

119905119891

1199050

119875dis (119905) 119889119905 + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

= 119864dis + int

119875(119905)lt0

(minus119875 (119905)) 119889119905

(8)

where int119875(119905)lt0

(minus119875(119905))119889119905 represents the cycle energy 119864cir whichis the temporal vehicle cycle energy in the form of kineticor potential energy and ultimately dissipated during friction

brakingTherefore (8) for vehicle without energy recycle canbe calculated as

119864trac = 119864dis + 119864cir (9)

In actual driving energy balance equation can be calcu-lated as

119864trac = 119864dis + 119864cir minus 119864rec (10)

where119864rec is the recycled net energy that is usable for tractionAccording to (7) and (10) it can be found that 119864rec = 119864cir

42 Recycle Efficiency of Barking Energy Recycle efficiency isdefined as

120578rec =119864rec119864cir

(11)

As 119864cir can be easily obtained in driving cycle the keymission is to calculate 119864rec Recycle energy consists of twoflow methods input and output As is shown in Figure 4recycle ability is determined by energy dissipation motortorque current of power battery and threshold charge value

Time set 119878 is defined as

119878 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) lt 0 119875

119887 (119905) lt 0 (12)

where 119875au is physical load in converter 119864119908 in is absolute inputenergy during 119878 and is calculated by

119864119908in = int

119878

1003816100381610038161003816119875 (119905) minus 119875au (119905)

1003816100381610038161003816119889119905 (13)

The energy reserved in battery is

119864119887 in = int

119878

10038161003816100381610038161003816119875119887 (119905) + 119868(119905)

2119877119899119888

10038161003816100381610038161003816119889119905 (14)

The energy loss is

119864loss in = 119864119908 in minus 119864

119887 in minus int

119878

119875au (119905) 119889119905 (15)

8 Mathematical Problems in Engineering

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

70

80

90

100SO

C (

)

s (km)

(a) CD-CS strategy

0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

SOC

()

s (km)

(b) Blended strategy

Figure 8 The SOC curve with the two different energy management strategies

The cycle-average wheel to battery energy efficiency is

120578wb in = 1 minus

119864loss in

119864119908 in

(16)

The recycle energy reserved in battery is

119864rec in = 119864cir120578wb in120578cir 119908 (17)

where 120578cir 119908 is the ratio between 119864119908and 119864cir

Time set119863 is defined as

119863 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) ge 0 119875

119887 (119905) ge 0 (18)

The associated motor energy loss in propelling is

119864loss 119898 = int

119863

119875loss 119898 (119905) 119889119905 (19)

The average motor efficiency is

120578119898 out = 1 minus

119864loss 119898119889

int119863119875119887 (119905) 120578con + 119875apu (119905) 120578con minus 119875au (119905) 119889119905

(20)

The battery energy loss during time119863 is

119864loss 119887 = int

119863

119868(119905)2119877119899119888119889119905 (21)

The battery efficiency in output way is

120578119887out = 1 minus

119864loss 119887119889

int119863119875119887 (119905) + 119868(119905)

2119877119899119887119889119905

(22)

The cycle-average battery to wheel energy efficiency is

120578bw out = 120578119887 out120578con120578119898 out120578119891119889120578119887119898 (23)

where 120578119887119898

is the ratio between the power that batteryprovides to the motor and the power emitted by batteryAccording to (16) and (23) the recycle energy for traction is

119864rec = 119864rec in120578bw out (24)

The cycle-average recycle efficiency is

120578rec =119864rec119864cir

= 120578cir119908120578wb in120578bw out (25)

43 Fuel-Traction Efficiency Fuel-traction efficiency is def-ined as

120578ft =

119864trac119864ef

=

119864dis + (1 minus 120578rec) 119864cir

119864ef (26)

where119864ef is the equal fuel energy the average consumption ofthe sum of diesel and electric energy 120578ft is the cycle-averageconversion efficiency from the total consumed energy to themechanical energy at the wheels and the electrical energy forthe auxiliaries Based on the initial and final SOC 119864ef can bedivided into diesel energy and electric energy

An energy flow chart can clearly show the direction ofenergy flow showing the sizes of losses from each individualpart It is one of the most effective methods for analyzingflow in the context of system performance Referring to theanalysis method in [27] this paper puts forward a powertrainenergy analysis method with energy flow chart for range-extended electric bus The powertrain energy flow chart isshown in Figure 5

5 Analysis Example with the DrivingCycle of Harbin City

To provide a credible reference for the match and controlof the range-extended electric bus energy efficiency analysis

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

70

80

90

100SO

C (

)

s (km)

(a) CD-CS strategy

0 20 40 60 80 100 120 140 160 18020

30

40

50

60

70

80

90

100

SOC

()

s (km)

(b) Blended strategy

Figure 8 The SOC curve with the two different energy management strategies

The cycle-average wheel to battery energy efficiency is

120578wb in = 1 minus

119864loss in

119864119908 in

(16)

The recycle energy reserved in battery is

119864rec in = 119864cir120578wb in120578cir 119908 (17)

where 120578cir 119908 is the ratio between 119864119908and 119864cir

Time set119863 is defined as

119863 = 119905 | 119905 isin [1199050 119905119891] 119875 (119905) minus 119875au (119905) ge 0 119875

119887 (119905) ge 0 (18)

The associated motor energy loss in propelling is

119864loss 119898 = int

119863

119875loss 119898 (119905) 119889119905 (19)

The average motor efficiency is

120578119898 out = 1 minus

119864loss 119898119889

int119863119875119887 (119905) 120578con + 119875apu (119905) 120578con minus 119875au (119905) 119889119905

(20)

The battery energy loss during time119863 is

119864loss 119887 = int

119863

119868(119905)2119877119899119888119889119905 (21)

The battery efficiency in output way is

120578119887out = 1 minus

119864loss 119887119889

int119863119875119887 (119905) + 119868(119905)

2119877119899119887119889119905

(22)

The cycle-average battery to wheel energy efficiency is

120578bw out = 120578119887 out120578con120578119898 out120578119891119889120578119887119898 (23)

where 120578119887119898

is the ratio between the power that batteryprovides to the motor and the power emitted by batteryAccording to (16) and (23) the recycle energy for traction is

119864rec = 119864rec in120578bw out (24)

The cycle-average recycle efficiency is

120578rec =119864rec119864cir

= 120578cir119908120578wb in120578bw out (25)

43 Fuel-Traction Efficiency Fuel-traction efficiency is def-ined as

120578ft =

119864trac119864ef

=

119864dis + (1 minus 120578rec) 119864cir

119864ef (26)

where119864ef is the equal fuel energy the average consumption ofthe sum of diesel and electric energy 120578ft is the cycle-averageconversion efficiency from the total consumed energy to themechanical energy at the wheels and the electrical energy forthe auxiliaries Based on the initial and final SOC 119864ef can bedivided into diesel energy and electric energy

An energy flow chart can clearly show the direction ofenergy flow showing the sizes of losses from each individualpart It is one of the most effective methods for analyzingflow in the context of system performance Referring to theanalysis method in [27] this paper puts forward a powertrainenergy analysis method with energy flow chart for range-extended electric bus The powertrain energy flow chart isshown in Figure 5

5 Analysis Example with the DrivingCycle of Harbin City

To provide a credible reference for the match and controlof the range-extended electric bus energy efficiency analysis

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

Diesel engine

Generator and rectifier loss

Fuel energy28042

9283

Engine loss

Generator and

11875

18759

100 Motor and motor

Traction motor

controller loss

917

681

Generating loss

8421

2492

6595

Battery

5914

12849

1875

8515

68

897

767

385

Vehicle bridge

331

711Braking energy intheory

4316 Auxiliary

1598

Battery charge

(14817 kWh)

rectifier

Charge

loss

(6102 kWh)

(202 kWh) (4082 kWh)

(5423 kWh)

(8376kWh)

(148kWh)

(1435kWh)

(1547kWh)

(2176kWh)

(408 kWh)

(1853kWh)

1705(3713 kWh)

268(5833kWh)

(3477kWh)(2584 kWh)

(2796 kWh)

(1287 kWh)

(167kWh)

(9393kWh)

Egrid

Figure 9 Energy flow chart with CD-CS strategy

should be carried out within a driving cycle Based on theauthorsrsquo location the Harbin city driving cycle has beenchosen for this paper and the construction process is shownin Figure 6

The constructed Harbin city driving cycle is shown inFigure 7 acceleration and deceleration are frequent Themaximum acceleration is 194ms2 the idle proportion is223 themaximum speed is 50 kmh and the average speedis 145 kmh

The analysis processmainly compares theCD-CS strategywith the switching controlmethod on the range-extender andblended strategy with power following controlmethod on therange-extender According to the research the daily averagerange for Harbin city bus line 101 is 150ndash180 km the initialSOC is 100 and the auxiliariesrsquo power is 10 kW SOC curveswith the two different driving cycles are shown in Figure 8

Figure 9 shows the energy flow chart with CD-CS strat-egy and Figure 10 shows the energy flow chart with blendedstrategy

Based on Figure 5 the input and output recycle efficien-cies can be obtained as is shown in Figure 11 The input-recycled efficiency of the blended strategy is 2473 higherthan that of CD-CS strategy The output-recycled efficiencyof the blended strategy is 783 lower than that of the CD-CSstrategy

Figure 12 consists of recycle efficiency fuel-traction effi-ciency and energy consumptionwith the twodifferent energymanagement strategies As is shown in Figure 12(a) therecycle efficiency is 3680 with CD-CS strategy and 5132with blended strategyWith CD-CS strategy the fuel-tractionefficiency is 3891 but with blended strategy it is 3326The fuel-traction efficiency is limited by engine efficiency and

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

Diesel engine

Generator andrectifier

Traction motor

Fuel energy3028

9333

Engine loss

Generator and rectifier loss

11875

100 Motor and motorcontroller loss

88

1259

Generating loss

842

6595

Battery

5914

942

1875

8217

68

897

1116

20947

Vehicle bridge

3082

2454

711Braking energy intheory

5882 Auxiliary

032

4503

6958

Battery chargeloss202

(6589 kWh)

(2031kWh) (4558kWh)

(534 kWh)

(274 kWh) (1788 kWh)(243kWh)

(1514 kWh)(205 kWh)

(4406kWh) (128 kWh)

(98kWh)

(1287 kWh) (2584 kWh)(07 kWh)

(148kWh)

(1435kWh) (2176kWh)

(408 kWh)

(1547 kWh)

Charge

Egrid

Figure 10 Energy flow chart with blended strategy

65468920

0002000400060008000

10000

CD-CS Blended

Efficiency

()

(a) System input-recycled efficiency

6665

5882

54005600580060006200640066006800

CD-CS Blended

Efficiency

()

(b) System output-recycled efficiency

Figure 11 Comparison of powertrain input- and output-recycled efficiency with different energy management strategies

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

36805132

000100020003000400050006000

CD-CS Blended

Efficiency(

)

(a) The recycle efficiency in the two different strategies

3819

3326

3000310032003300340035003600370038003900

CD-CS Blended

Efficiency

()

(b) The fuel-traction efficiency in the two different strategies

640650660670680690700710720

CD-CS Blended

Energy (kWh)

66443

7123

(c) The energy consumption in two different strategies

Figure 12 Comparison of recycle efficiency fuel-traction efficiency and energy consumption with different energy management strategies

is also influenced by other electric and mechanical lossessuch as the battery power converter and motor and drivesystem Energy consumption is 66443 kWh with the CD-CS strategy and 4787 kWh lower than that with the blendedstrategy The CD-CS strategy has a better recycle ability andfuel-traction efficiency It is worth noting that the yearly rangeof one bus inHarbin is nearly 70000 km and the energy savedwith the CD-CS strategy would be considerable

6 Conclusions

For a range-extended electric bus developed by TsinghuaUniversity this paper analyzes the energy efficiency withtwo different energy management strategies (CD-CS andblended) using an energy flow chart method Harbin citydriving cycle is taken for analysis The recycle efficiency andfuel-traction efficiency are evaluation indexes

Analysis results from the energy flow chart show thatthe energy loss mainly occurs at the engine Engine energyloss reaches 18759 of the whole driving energy using theCD-CS strategy and 20947 with the blended strategy Asthe CD-CS strategy uses a thermostat control method itscharging loss is 385 of total driving energy while theblended strategy only has a 2 charging loss Of thesetwo energy management strategies the CD-CS strategy caneffectively reduce the engine loss but has a higher chargingloss compared with the blended strategy

Energy efficiency results show that over the Harbin citydriving cycle the input-recycled efficiency of the blendedstrategy is 2473 higher than that of the CD-CS strategyand that the output-recycled efficiency of the blended strategyis 783 lower than that of the CD-CS strategy With theCD-CS strategy the recycle efficiency is 3680 but withblended strategy it is 5132 Using the CD-CS strategy thefuel-traction efficiency is 3891 but with blended strategyit is 3326 In comparison of the two nonoptimized energymanagement strategies powertrain energy efficiency is better

with CD-CS than with blended strategy We suggest that aCD-CS energy management strategy is more appropriate forthe driving conditions on urban Harbin roads

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation (NNSF) of China (Grant no 51105220)

References

[1] G Wang ldquoAdvanced vehicles costs energy use and macroe-conomic impactsrdquo Journal of Power Sources vol 196 no 1 pp530ndash540 2011

[2] P Baptista M Tomas and C Silva ldquoPlug-in hybrid fuel cellvehicles market penetration scenariosrdquo International Journal ofHydrogen Energy vol 35 no 18 pp 10024ndash10030 2010

[3] H Li X Jing and H R Karimi ldquoOutput-feedback based 119867infin

control for active suspension systems with control delayrdquo IEEETransactions on Industrial Electronics vol 61 no 1 pp 436ndash4462014

[4] T-W Chun Q-V Tran H-H Lee H-G Kim and E-C NholdquoSimulator for monitoring the operations of range extenderelectric vehiclesrdquo Journal of Power Electronics vol 11 no 4 pp424ndash429 2011

[5] RMatthe L Turner andHMettlach ldquoVOLTECbattery systemfor electric vehicle with extended rangerdquo SAE InternationalJournal of Engines vol 4 no 1 pp 1944ndash1962 2011

[6] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using advanced vehicle simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Mathematical Problems in Engineering

[7] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[8] D H Lee N W Kim and J R Jeong ldquoComponent sizing andengine optimal operation line analysis for a plug-in hybrid elec-tric transit busrdquo International Journal of Automotive Technologyvol 14 no 3 pp 459ndash469 2013

[9] S Varnhagen A Same J Remillard and J W Park ldquoAnumerical investigation on the efficiency of range extendingsystems using Advanced Vehicle Simulatorrdquo Journal of PowerSources vol 196 no 6 pp 3360ndash3370 2011

[10] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and HSagha ldquoDevelopment of a hybrid energy storage sizing algo-rithm associated with the evaluation of power managementin different driving cyclesrdquo Journal of Mechanical Science andTechnology vol 26 no 12 pp 4149ndash4159 2012

[11] J Waldner J Wise C Crawford and Z Dong ldquoDevelopmentand testing of an advanced extended range electric vehiclerdquo SAE2011-01-0913 2011

[12] A M Joshi H Ezzat N Bucknor and M Verbrugge ldquoOpti-mizing battery sizing and vehicle lightweighting for an extendedrange electric vehiclerdquo SAE 2011-01-1078 2011

[13] M Cipek M Coric B Skugor J Kasac and J Deur ldquoDynamicprogramming-based optimization of control variables of anextended range electric vehiclerdquo SAE 2013-01-1481 2013

[14] B Skugor and J Deur ldquoInstantaneoun optimization-basedenergymanagement control strategy for extended range electricvehiclerdquo SAE 2013-01-1460 2013

[15] L Xu F Yang andM Hu ldquoComparison of energymanagementstrategies for a range extended electric city busrdquo Journal ofUniversity of Science and Technology of China vol 42 no 8 pp640ndash647 2012

[16] C Hou M Ouyang and L Xu ldquoApproximate Pontryaginrsquosminimum principle applied to the energy management of plug-in hybrid electric vehiclesrdquo Journal of Applied Energy vol 115pp 174ndash189 2014

[17] X Wu J Du and C Hu ldquoEnergy efficiency and fuel economyanalysis of a series hybrid electric bus in different Chinese citydriving cyclesrdquo International Journal of Smart Home vol 7 no5 pp 353ndash368 2013

[18] E D Tate O H Michael and J S Peter ldquoThe electrification ofthe automobile from conventional hybrid to plug-in hybridsto extended-range electric vehiclesrdquo SAE 2008-01-0458 2008

[19] K Dominik P Sylvain and K Jason ldquolsquoFairrsquo comparison ofpowertrain configurations for plug-in hybrid operation usingglobal optimizationrdquo SAE 2009-01-1334 2009

[20] X Wu and L Lu ldquoSystemmatching and simulation of a plug-inseries hybrid electric vehiclerdquo Automotive Engineering vol 35no 7 pp 573ndash582 2013

[21] H-S Xiong G-J Cao L-G Lu M-G Ouyang and J-Q LildquoSimulation system of series hybrid powertrain for city bus andits applicationsrdquo Journal of System Simulation vol 22 no 5 pp1134ndash1138 2010

[22] Q Yang J Huang G Wang and H Reza Karimi ldquoAn adaptivemetamodel-based optimization approach for vehicle suspen-sion system designrdquoMathematical Problems in Engineering vol2014 Article ID 965157 9 pages 2014

[23] J Rubio-Massegu F Palacios-Quinonero J M Rossell andH Reza Karimi ldquoStatic output-feedback control for vehiclesuspensions a single-step linear matrix inequality approachrdquo

Mathematical Problems in Engineering vol 2013 Article ID907056 12 pages 2013

[24] Q Lu H Reza Karimi and K Gunnar Robbersmyr ldquoA data-based approach for modeling and analysis of vehicle collisionby LPV-ARMAX modelsrdquo Journal of Applied Mathematics vol2013 Article ID 452391 9 pages 2013

[25] Z Li L Lu and M Ouyang ldquoComparison of methods forimproving SOC estimation accuracy through an ampere-hourintegeration approachrdquo Journal of Tsinghua University vol 50no 8 pp 1293ndash1301 2010

[26] J CampbellWWatts andDKittelson ldquoReduction of accessoryoverdrive and parasitic loading on a parallel electric hybrid citybusrdquo SAE 2012-01-1005 2012

[27] S Campanari G Manzolini and F Garcia de la IglesialdquoEnergy analysis of electric vehicles using batteries or fuel cellsthrough well-to-wheel driving cycle simulationsrdquo Journal ofPower Sources vol 186 no 2 pp 464ndash477 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of