research article energy management strategy implementation

Research ArticleEnergy Management Strategy Implementation for HybridElectric Vehicles Using Genetic Algorithm Tuned PontryaginrsquosMinimum Principle Controller

Aishwarya Panday and Hari Om Bansal

Department of Electrical and Electronics Engineering Birla Institute of Technology and Science Pilani Jhunjhunu 333031 India

Correspondence should be addressed to Aishwarya Panday aishwaryapandaypilanibits-pilaniacin

Received 31 October 2015 Accepted 11 January 2016

Academic Editor Aboelmagd Noureldin

Copyright copy 2016 A Panday and H O Bansal This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

To reduce apace extraction of natural resources to plummet the toxic emissions and to increase the fuel economy for roadtransportation hybrid vehicles are found to be promising Hybrid vehicles use batteries and engine to propel the vehicle whichminimizes dependence on liquid fuels Battery is an important component of hybrid vehicles and is mainly characterized by itsstate of charge level Here a modified state of charge estimation algorithm is applied which includes not only coulomb counting butalso open circuit voltage weighting factor and correction factor to track the run time state of charge efficiently Further presenceof battery and engine together needs a prevailing power split scheme for their efficient utilization In this paper a fuel efficientenergy management strategy for power-split hybrid electric vehicle using modified state of charge estimation method is developedHere the optimal values of various governing parameters are firstly computed with genetic algorithm and then fed to Pontryaginrsquosminimum principle to decide the threshold power at which engine is turned on This process makes the proposed method robustand provides better chance to improve the fuel efficiency Engine efficient operating region is identified to operate vehicle in efficientregions and reduce fuel consumption

1 Introduction

The invention of the automobile is one of the most ground-breaking advancements in technology Today it is impossibleto imagine the world without it anymore The automobileindustry contributes significantly to the growth of the worldrsquoseconomy and affects each level of population The presenttransportation structure heavily relies on internal combus-tion engine (ICE) based transportation which uses fossilfuels as a source of energy But due to toxic emissions of car-bon dioxide (CO

2) carbon monoxide (CO) nitrogen oxides

(NO119909) and unburned hydrocarbons (HCs) in large amount

they have caused environmental pollution and global warm-ing as well Exponential rise in population and personaltransportation resulted in multifold increase in automobilesaround the globe It has been causing severe environmentalproblems and a threat to human life Air pollution is a majorenvironmental jeopardy to health due to emissions ofCO

2[1]

23 percent of total CO2emissions in the world are caused

by the transport sector [2] of which roughly 73 percent wasgenerated by road transport [3] In future oil production willfall but its consumption will continue to rise so transportsector should eradicate dependence on oil by adapting thenew transportation mediums like electric or hybrid vehicleswhich are green and sustainable Hybrid vehicles are cleanefficient and environment friendly transportation meansHybrid electric vehicles (HEVs) use battery to store theelectrical energy for propelling the vehicle with good fueleconomy and less toxic emissions [4]

The presence of two power sources focuses on the needof designing an energy management strategy to split powerbetween them to minimize the fuel consumption and max-imize the power utilization Complex structure of HEVsmakes it challenging to design the control strategiesThe pre-liminary objective of the control strategy is to satisfy thedriverrsquos power demand with minimum fuel consumption

Hindawi Publishing CorporationInternational Journal of Vehicular TechnologyVolume 2016 Article ID 4234261 13 pageshttpdxdoiorg10115520164234261

2 International Journal of Vehicular Technology

Table 1 Comparison chart for real time optimization algorithms

Methods Structural complexity Computation time Type of solution Requirement of a priori knowledgeParticle swarm optimization No More Global NoEnergy consumption minimization strategy Yes Small Local NoPontryaginrsquos minimum principle No Small Local YesModel predictive No Small Global NoNeural network Yes Small Global Yes

Moreover fuel economy and emissions minimization areconflicting objectives a smart control strategy should satisfya trade-off between them

In optimization based control strategies the goal of acontroller is to minimize the cost functionThe cost functionfor an HEV may include the emission fuel consumptionand torque depending on the application Global optimumsolutions can be obtained by performing optimization over afixed driving cycle Due to causal nature of global optimiza-tion techniques they are not suitable for real-time analysisTherefore global criterion is reduced to an instantaneousoptimization by introducing a cost function that dependsonly on the present state of the system parameters Globaloptimization techniques do not consider variations of batterystate of charge (SOC) Hence a real-time optimization isperformed for power split while maintaining the batterychargeThe concept of real-time control strategy for efficiencyand emission optimization of a parallel HEV is proposed in[5] It considers all engine-motor torque pairs which forecastthe energy consumption and emissions for every given pointAn instantaneous fuel efficiency optimization strategy wasdeveloped for parallel hybrid vehicle with the charge sustain-ing mode in [6] Also to implement the global constraintthe authors developed a nonlinear penalty function in termsof battery SOC deviation from its desired value Literaturespeaks that real-time optimization techniques like ECMS [67] model predictive control (MPC) [8ndash10] Neural Network(NN) [11 12] particle swarm optimization (PSO) [13ndash15]and Pontryaginrsquos minimum principle (PMP) [16 17] are usedextensively Table 1 compares different real-time strategieswith its pros and cons In the presence of a priori knowledgePMPwith structural simplicity and limited computation timegives local solution to the optimization problemwhich in caseof particular assumption can provide the global optima [17]

Stockar et al used PMP to build an optimal supervisorycontroller by reducing a global optimization problem intolocal It reduces computational requirement and gives thefreedom to solve the problem in the continuous time domain[18] Stockar et al proposed amodel based control strategy tominimize the CO

2emission A supervisory energy manage-

ment strategy is implemented as a global optimization prob-lem and then converted into local and using PMP optimalenergy utilization for PHEVs is obtained A real-time optimalcontrol can be obtained using PMP as it uses instantaneousminimization of the Hamiltonian function [19] Kim et alstate that solution based on PMP can be global optimal undersome certain assumptions [20] Kim et al applied PMP based

control strategies to the PHEVs and found that it gives anumber of alternative solutions [21] PMP provides a near-optimal solution for optimal power management of HEVs iffuture driving conditions are known It is suggested to find theproper costate to keep SOC at a desired and predefined level

In this paper PMP is applied to solve the performanceindex of theHEV in terms of fuel consumptionThe requestedpower threshold is analyzed using PMP above which engineshould be on towork in its optimal efficient range and gener-ator can run to charge the battery tomaintain the appropriateSOC level in the battery

InHEVs speed and power required by vehicle SOC leveland engine off time play an important role to design energymanagement controller PMP computes threshold powerlevel but initially designer needs to define the other param-eters like optimal speed and torque ranges of engine motorand generator highest and lowest level of SOC target SOCspeed threshold and engine off threshold to minimize thefuel consumption using vehicle controller Optimal speed andtorque ranges of engine motor and generator are defined byexperiments done by the National Renewable Energy Lab-oratory (NREL) and provided in the package of AdvancedVehicle Simulator (ADVISOR) [22] But speed thresholdengine off time threshold and engine on SOC level aredetermined here using genetic algorithm (GA)which in turnalong with power threshold decides engine on threshold

GA is a heuristic search algorithm to solve optimizationand search problemsThis is a branch of artificial intelligenceinspired by Darwinrsquos theory of evolution GA is a robustand feasible approach with a wide range of search space andrapidly optimizes the parameters using simple operationsThey are proven to be effective to solve complex engineeringoptimization problems characterized by nonlinear multi-modal nonconvex objective functions GA is efficient atsearching the global optima without getting stuck in localoptima Unlike the conventional gradient based methodGA does not require any strong assumption or additionalinformation about objective parameters GA can also explorethe solution space very efficiently Piccolo et al utilize GA forenergy management of an on road vehicle and minimize thecost function containing fuel consumption and emission [23]Wang and Yang implemented a robust easy and real-timeimplementable FL based energy management strategy andused GA to tune and optimize the same [24] To optimize thefuel consumption and emissions in a series HEV GA basedcontrol strategy has been used by [25] It is a flexible andglobal optimal multiobjective control strategy which is found

International Journal of Vehicular Technology 3

to be better than thermostatic and divide rectangle (DIRECT)algorithm Wimalendra et al applied GA in parallel HEVto find the optimal power split for improved vehicle perfor-mance and also promises to give maximum fuel economy forknown driving cycle for a parallel HEV using GA [26]

This paper aims to develop an optimal controller based onPMP and GA to get the optimal power split between engineand battery to fulfill the driverrsquos speed and torque demandwhile compelling the engine to work in its efficient regionPMP is a powerful tool in optimal control theory which pro-vides the set of necessary conditions to get the global solutionof a constrained control problem

The paper is divided into different sections Section 2explains the vehicle dynamics with vehicle model and plane-tary gear set operation Section 3 explains power train controlmethodology involving engine speed control and tractiontorque control schemes Section 4 elaborates problem state-ment engine operating range description and proposed con-trol strategy Section 5 discusses simulation and result discus-sion and Section 6 concludes the paper

2 Vehicle Dynamics

The vehicle movement behavior depends upon differentforces (aerodynamic drag rolling resistance and gradingresistance) along its moving direction Aerodynamic dragforce is encountered by air in the direction of vehicle move-ment at a particular speed Rolling resistance is a horizontalforce which acts on the wheel center in the opposite move-ment direction of the wheel Grade force acts on the vehicleeither in opposite or in the same directionwhen a vehicle goesup or down over a slope

119865119903=1

2120588119860119891119862119863(119881 minus 119881

119882)2

+ 119875119891119903+119872119892 sin120572 (1)

where119860119891is vehicle frontal area119862

119863is aerodynamic drag that

characterizes the shape of the vehicle body 120588 is air density119881 is vehicle speed and 119881

119882is component of wind speed with

vehicle moving direction 119875 is force acting on the center of astandstill tire 119891

119903is rolling resistance and 120572 is road angle

Figure 1 shows the main components of the HEVs thatis motor generator battery and engine [4] Presence of theengine and battery together in vehicle demands for coupler toadd their speeds In Toyota hybrid system (THS) planetarygear system (PGS) is used as a speed coupler PGS containscarrier sun ring gear and several pinion gears as shown inFigure 2 The ring gear is attached to the motor and finaldrive engine to the carrier and generator to the sun Gov-erning equations between different gear speeds and radii aregiven as follows

120596119903lowast 119903119903= minus120596119904lowast 119903119904+ 120596119888(119903119904+ 119903119903) (2)

where120596119903120596119904 and120596

119888are ring sun and carrier angular speeds

respectively and 119903119903 119903119904are ring and sun radii respectively

Neglecting energy losses in steady state operation and torques

Hybrid electric vehicle

Engine

Battery pack

Invertermg1

mg2

PGS

Power flow along series pathsPower flow along parallel paths

Figure 1 Power split hybrid architecture

Pinion

Sun

Carrier

Ring

120596r120596p

120596s

Figure 2 Operation of a planetary gear

acting on sun ring and carrier have the relationship as fol-lows

119879119888= minus119896119910119904119879119904= minus119896119910119903119879119903 (3)

119879119888 119879119904 and 119879

119903are the torques acting on carrier sun and ring

gear 119896119910119903

= (1 + 119894119892)119894119892and 119896

119910119904= (1 + 119894

119892) and 119894

119892is gear

ratio While moving engine speed 120596119890 motor speed 120596

119898 and

generator speed 120596119892are related as follows

119873119903

119873119904+ 119873119903

lowast 120596119898+

119873119904

119873119904+ 119873119903

lowast 120596119892= 120596119890 (4)

where 119873119903and 119873

119904are tooth number in ring and sun gear

respectively in Toyota Prius As 119873119903= 78 and 119873

119904= 30 (2)

becomes

72222 lowast 120596119898+ 02778 lowast 120596

119892= 120596119890 (5)

This equation describes that120596119898is directly proportional to the

linear speed of the vehicle with a quantitative change due totire radius and final drive ratio

21 Battery Modeling and SOC Estimation In general classi-cal SOC estimation is performed using ampere hour count-ing method (in ADVISOR also) but open circuit voltage


High vehicle speed regionconstant engine speed and

negative mg speed

Medium vehicle speed regionwith zero mg speed and

engine speed proportional tovehicle speed

RPM

Vehicle speed

Low vehicle speed regionconstant engine speed and

positive mg speed

VHVL

Figure 3 Various vehicle speed ranges

(OCV) also plays an important role in determining the SOCTang et al [27] and Verbrugge and Tate [28] identified thecontribution of both coulomb counting method (SOC

119894) and

open circuit voltage method (SOC119881) together to estimate the

accurate SOC References [29ndash31] have also identified theimportance of SOC

119881and SOC

119894in calculating the run-time

SOC The SOC estimation formula proposed by the authorsis given as follows

SOC = 119908SOC119881+ (1 minus 119908) (SOC

119894minus 120578) (6)

where 120578 is correction factor (CF) CF varies with the changingSOC load 119871 and temperature 119879 (ie CF = 119891(SOC

0 119871 119879))

and can be formulated as in (7)

120578298

= (1 minusSOC0

100) 119871 = 0 at 119879 = 298K

120578new(SOC119879) = 120578298 +(SOC1000)119879 minus 298

plusmn 120576

119871 gt 0 at any 119879

(7)

Estimating SOC by (7) and (8) will promise a better fuelefficiency ofHEV as accuracy of SOC estimation is improved

Battery plays a vital role inHEVs Inmost of the literatureenergymanagement techniques for HEVs have used batterieswith a single 119877int component which consists of ohmic andpolarization resistances But due to double-layer formationat the electrodesolution interface capacitive effects arise[32]This capacitance consists of purely electrical polarizationcapacitance and diffusion capacitance [33] The transientresponse of the battery is highly influenced by double-layeranddiffusion capacitancewhen the rates of reactions are highThis effect can be modeled using lumped capacitances inparallel with the resistances [34] Inclusion of diffusion anddouble-layer resistances and capacitances (119877 and 119862 compo-nents) will lead to the accurate SOC estimation In this paperto predict the run-time behavior of the battery 1 RC and 2 RCmodels along with modified SOC estimation techniques areused to analyze the effect on fuel efficiency

Rate of change of SOC depends on 119875 bat open circuitvoltage (OCV) and resistance 119877 offered by the battery cellsand capacity 119876

119901shown in

SOC =OCV minus radicOCV2 minus 4 lowast 119877 lowast 119875 bat

2 lowast 119877 lowast 119876119901

(8)

Required power of 119875 bat can be calculated as follows

119875bat = 120578119896

11988811198791198981198921

1205961198981198921

+ 120578119896

11988821198791198981198922

1205961198981198922

(9)

where 120578119896

1198881and 120578

119896

1198882are the efficiencies of 1198981198921 and 1198981198922

respectively and are obtained from the efficiency map of119898119892s Positive 119896 represents motoring operation and negative 119896represents generating operations Equations (6) (8) and (9)are applicable for different battery models proposed in theliterature

3 Powertrain Control Methodology

Power split HEVs have the potential to improve in fuel effi-ciency compared to series or parallel hybrids because enginespeed and torque can be decoupled completely or partiallyfrom the driven wheels through speed and torque couplingBy applying suitable control strategies fuel efficiency can beimproved provided it follows the control objectives like (1)driver torque and speed demand are fulfilled (2) engineoperates in its best efficiency region (3) target SOC levelmeets at the end of the trip and (4)maximumbraking energyis recuperated while braking or decelerating While makingthe control strategies different approaches can be followed aselaborated below

31 Engine Speed Control Strategy Vehicle speed ranges aredivided into three regions namely (1) low (2) medium and(3) high vehicle speed as shown in Figure 3 In low speed reg-ion motor fulfills the driver power demand and hence engineusage can be avoided which is inefficient also Low vehiclespeed 119881

119871 threshold can be decided by the lowest engine

speed allowed with zero motorgenerator speed as follows

119881119871=

120587119896119910119903119899119890 min119903119908

30119894119903119908

(ms) (10)


where 119899119890 min is the minimum engine speed allowed 119903

119908is the

wheel radius 119896119910119903= (1 + 119894

119892)119894119892 where 119894

119892is the gear ratio and

is defined as 119903119903119903119904and 119894119903119908

is the gear ratio of the ring gear todrive train wheels In this region motorgenerator operateswith a positive speed 119899

119898119892as follows

119899119898119892

= 119896119910119904(119899119890 min minus

30119894119903119908119881

120587119896119910119903119903119908

) (11)

119881 is the vehicle speed in ms (119881 le 119881119871) From (3) torque pro-

duced by motorgenerator applied to the sun gear has direc-tion opposite to its speedThereforemotorgenerator absorbspart of the engine power to charge the battery Power on themotorgenerator shaft 119875

119898119892can be expressed as (12) 119879

119898119892is

torque produced by motorgenerator

119875119898119892

=2120587

60119879119898119892

119899119898119892

=2120587

60119879119890119899119890 min minus

119894119903119908

119896119910119903119903119908

119879119890119881 (12)

When the vehicle speed is higher than 119881119871but lower than 119881

119867

given by (13) motorgenerator is deenergized and sun gear islocked to the stationary frame of the vehicle Drive train oper-ates in torque couplingmode Engine speed is proportional tothe vehicle speed Consider

119881119867=

120587119896119910119903119899119890 max119903119908

30119894119903119908

(ms) (13)

where 119899119890 max is the maximum engine RPM allowed In this

medium speed region all the engine power is delivered to thewheels

When the vehicle speed is higher than the 119881119867 for lim-

iting the engine speed below the maximum engine allowedspeed 119899

119890 max motorgenerator has to operate in the directionopposite to the engine speed It can be expressed as follows

119899119898119892

= 119896119910119904(119899119890 max minus

30119896119910119904119894119903119908119881

120587119896119910119903119903119908

) (14)

where 119881 ge 119881119867 The motor generator is in motoring mode

and motoring power can be expressed as follows

119875119898119892

=2120587

60119879119898119892

119899119898119892

=119894119903119908

119896119910119903119903119908

119879119890119881 minus

2120587

60

119894119903119908

119896119910119903119903119908

119879119890119899119890 max

(15)

32 Traction Torque Control Strategy In low vehicle speedregion when sufficient SOC is available tractionmotor torque119879119898119905

can be given as follows

119879119898119905=60

2120587

119875119898119892

119899119905119898

= (119899119890 min119899119905119898

minus119894119903119908

119896119910119903119894119898119908

)119879119890

= minus(2120587119903119908

60119894119898119908

119899119890 min119881

minus119894119903119908

119896119910119903119894119898119908

)119879119890

(16)

where 119894119898119908

is gear ratio from the traction motor to the drivenwheels and 119899

119905119898is traction motor speed PGS 119898119892 and trac-

tion motor together function as an EVT because no energygoes into or out of the battery

In case of medium vehicle speed range only the torquecoupling mode is employed that is sun gear is locked to thevehicle stationary frame and engine speed is proportional tothe vehicle speed In high speed region engine speed is con-trolled by the enginemax speed 119899

119890 max and themotorgenera-tor works in motoring mode If the commanded tractiontorque is higher than the torque that the engine can producewith its optimal throttle at the speed of 119899

119890 max and SOC ofthe battery is lower than SOCmin and the battery cannot bedischarged any more to support motoring mode the enginewill be forced to operate at the higher speed (beyond theoptimal range) to fulfill the driver power demand In thiscase engine alone mode can be used with torque couplingor engine can run at somewhat higher speed so that a motorgenerator can work in generating mode to feed the tractionmotor to support engine by providing additional torque Forthe latter case 119899

119890can be calculated as in (17)

119899119890gt30119894119903119908119881

120587119896119910119903119903119908

(17)

If SOC is higher than the SOCmin then the engine shouldbe controlled at its 119899

119890 max with optimal throttle and tractionmotor provides additional torque to engine to support thedriver torque demand

If the commanded traction torque is smaller than theengine torque and SOC is lower than SOCmin engine is oper-ated according to (13) and tractionmotor works in generatingmode If SOC is in between range of SOCmin and SOCmaxtraction motor may be de-energized and engine alone modecan be projected If SOC is greater than the SOCmax enginebetter shuts down and traction motor alone can propel thevehicle

4 Proposed Energy Management Approach

In HEVs presence of both motor and engine together makesit inevitable to decide enginemotor onoff condition to min-imize the fuel consumption To split the power optimally bet-ween two power sources a cost function is derived The costfunction depends on various parameters like speed powerSOC and engine onoff time The various steps involved indeveloping the strategy are given below

41 Problem Statement The proposed cost function involvesrate of fuel consumption that is 119869 =

119891119905 where

119891119905is total

fuel consumption in a driving cycle 119891is the time rate of fuel

consumption and is given by 119891= ((119875119890lowast119892119890)(1000lowast120574

119891))(119897ℎ)

where119875119890is engine power 119892

119890is specific fuel consumption and

120574119891is mass density of fuel kgL So total fuel consumption in a

driving cycle is 119891119905= sum(119875

1198901198921198901000120574

119891)lowastΔ119905119894The cost function


Table 2 Vehicle components and drive cycle specifications

Vehicle component specification(Toyota Prius) Drive cycle specification (ECE EUDC)

Components Values Entities ValuesMotor 31 kW Maximum speed 7456mphEngine 43 kW Average speed 1995mphHeating value of gasoline119876HV

42600 Jg Maximum acceleration 346 fts2

Generator 15 kW Maximum deceleration minus456 fts2

Drag coefficient 03 No of stops 13Battery 40 kW Distance 679 milesFinal drive ratio 393 Time 1225 sFrontal area 1746m2

Wheel radius 0287mVehicle glider mass 918 kg

is minimized over ECE EUDC driving cycle subject to thefollowing constraints

120596119890min le 120596119890 le 120596119890max

1205961198981198921min le 1205961198981198921 le 1205961198981198921max

1205961198981198922min le 1205961198981198922 le 1205961198981198922max

119879119890min le 119879119890 le 119879119890max

1198791198981198921min le 1198791198981198921 le 1198791198981198921max

1198791198981198922min le 1198791198981198922 le 1198791198981198922max

SOCmin le SOC le SOCmax

(18)

where 120596119890min 120596119890max 1205961198981198921min 1205961198981198921max 1205961198981198922min 1205961198981198922max

119879119890min 119879119890max 1198791198981198921max 1198791198981198921min 1198791198981198922min 1198791198981198922max SOCmin

and SOCmax are theminimum andmaximum values of speedand torque considered as constraints range of engine 11989811989211198981198922 and SOC respectively

Torques and speeds of 1198981198921 and 1198981198922 are functions ofengine torque and speed requested driving speed and torqueand gear ratios of the vehicle as follows

1198791198981198921

= minus1

1 + 119877[119879119890]

1205961198981198921

= minus119877120577120596req + (1 + 119877) 120596119890

1198791198981198922

= minus1

(1 + 119877)[minus

(1 + 119877) 119879req

120577+ 119877119879119890]

1205961198981198922

= 120577120596req

(19)

where 1205961198981198921

1198791198981198921

1205961198981198922

1198791198981198922

120596119890 and 119879

119890are speeds and

torques11989811989211198981198922 engine respectively and 120596req and 119879req arethe requested speed and torque 119877 and 120577 are the gear ratioof PGS and the final drive ratio [35 36] As efficiency of anengine is a function of engine speed 120596

119890and torque 119879

119890 fuel

consumption will be 119891= 119891(120596

119890 119879119890)

Power requested should always be delivered by eithermotor engine or generator that is for the successful tripcompletion 119875requested = 119875delivered = 119875engine + 119875motor + 119875generator

Speed force and torque requested by ECE EUDC shownin Figure 4 are used to calculate power required at the wheelPositive forcetorque value shows that power is required topropel the vehicle and negative forcetorque specifies thatthe energy will be released and regenerative braking willbe applied to recuperate the released energy in the batteryVehicle componentrsquos and drive cycle specification are givenin Table 2

42 Determination of Efficient Operating Region of EngineIt is mandatory to identify enginersquos fuel efficient regionsbefore finding the optimal solution of the cost function Theenergy management controller should keep the engine in itsefficient region tominimize the liquid fuel consumption Fuelconsumption is ameasure of themass flow per unit time Fuelflow rate per useful power output is an important parameterto determine the efficiency of the engine and is called specificfuel consumption (SFC) that is 119904119891119888 =

119891119875 When the

engine power is measured as the net power from the crank-shaft SFC is called brake specific fuel consumption (BSFC)Low values of SFC or BSFC are always desirable The ratioof work produced to the amount of fuel energy suppliedper cycle is measure of engine efficiency (fuel conversionefficiency) 120578

119891= 119882119888119898119891119876HV = 119875

119891119876HV where 119882119888 is

work done in one cycle119898119891is fuel mass consumed per cycle

and 119876HV is the heating value of the fuel The efficiency canbe expressed as 120578

119891= 1(119904119891119888 lowast 119876HV) Engine characteristics

are decided by parameters like power torque mean effectivepressure SFC indicated brake power and torque and fuelconsumption characteristics

Fuel efficient region of the engine is mainly governed byrequesting power at the ring gear of PSG and maximum andminimum speeds of generator and vehicle idle speed Basedon power demand optimal120596lowast

119890and119879lowast119890points are determined

120596119890is controlled with generator torque that is generator

torque is so adjusted that engine runs at desired speed Engine


0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

Time (s)

Spee

d (m

ph)

(a)

0 200 400 600 800 1000 1200minus6000minus4000minus2000

020004000

Forc

e (N

)


0500

1000

Time (s)

Time (s)

Torq

ue (N

m)

(b)

Figure 4 ECE EUDC driving cycle (a) speed required (b) forceand torque required

maximum (120596119890 max) and minimum (120596

119890 min) speed are rangedusing the following equation

119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903

lowast 120596119892max

= 120596119890 max

119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903

lowast 120596119892min

= 120596119890 min

(20)

where120596ring is the speed requested at ring gearThe engine fuelefficiency map is shown in Figure 5 which infers that below acertain speed torque produced by the engine is less hence notefficient ICE is rated at a specific RPM level for maximumtorque and maximum power ICE cannot produce effectivetorque below ldquosomerdquo certain speed Maximum torque isachieved for a narrow range of speeds beyond which effi-ciency decreases The characteristic of the engine is shown inFigure 6This characteristic shows that enginersquos actual horse-power is lower than the ideal lab conditions further below

Speed (rads)30 60 90 120 150 180 210 240 270 300 330 360

102030405060708090

100110120

015

02

025

03

035

04

045

Torq

ue (N

m)

Figure 5 Engine efficiency map of Toyota Prius

Speed (RPM)

Enginersquos maximum horsepowerunder ideal lab conditions

Enginersquos maximumhorsepower underactual conditions

Engine torque none belowa certain RPM

Hor

sepo

wer

Figure 6 Generalized engine speed-torque characteristics

a certain speed and no positive torque is achieved For theconsidered engine model maximum power of 43 kw andmaximum torque of 101N-m are provided by engine at 4000RPM So it is required to operate the engine in its mostefficient region for the better performance and lesser fuelconsumption

43 Optimization Strategies The proposed fuel efficiencyoptimization problem depends on various parameters of thevehicle These parameters may have cross effects also Theproposed method uses firstly GA to identify optimal valuesof various governing parameters and then these values are fit-ted into PMP to produce optimum fuel efficiency

431 Genetic Algorithm To optimize a nonlinear problemusing GA chosen parameters will not be treated as inde-pendent variables The combined effect of these parametersreflects on optimized output Genetic algorithm was devisedby John Holland in early 1970rsquos to imitate natural propertiesbased on natural evolution To obtain the solution of a prob-lem the algorithm is started with a set of solutions knownas population A new population is formed by choosing ran-dom solutions of one population and is assumed that new


Start

Step 2 initialization of populationSet of random solutions are initialized

in a predefined search space

Step 3 evaluation of a solutionEvery solution is evaluated and checked

for its feasibility and fitness values areassigned

(Decipher the solution vector)

Step 1 representation of solutionA solution vector x is initialized

Step 5 variation operators(a) Crossover two solutions are picked from the mating pool at random and

an information exchange is made between the solutions to create one or moreoffspring solutions

(b) Mutation perturbs a solution to its vicinity with a small mutation probabilityMutation uses a biased distribution to be able to move to a solution close to the

original solution

Onegeneration of

GA iscompleted

Step 4 reproduction operatorsSelects good strings in a population and

forms a mating pool

x(L)i le x le x(U)i

Figure 7 Genetic algorithm process flow

population is better than the old one This course is repeatedover numerous iterations or until some termination criteriais satisfied [37 38] The flow of the algorithm is shown inFigure 7

432 Pontryaginrsquos Minimum Principle PMP was proposedby Russian mathematician Lev Semenovich in 1956 It givesthe best possible control to take a dynamical system fromone state to another in the presence of constraints for somestate or input control PMP is a special case of Euler-Lagrangeequation of calculus of variations For an optimum solutionPMP provides only necessary conditions and the sufficientconditions are satisfied by Hamilton-Jacobi-Bellman equa-tion In PMP the number of nonlinear second-order differen-tial equations linearly increaseswith dimension so the controlbased on PMP takes less computational time for getting anoptimal trajectory but it could be a local optimal not a global

solution Trajectory obtained by PMP could be considered aglobal optimal trajectory under certain assumptions Theseare as follows (1) trajectory obtained from PMP is uniqueand satisfies the necessary and boundary conditions (2)some geometrical properties of the optimal field provide thepossibility of optimality clarification and (3) as a generalstatement of the second approach the absolute optimality ismathematically proven by clear proposition [17 39]

To optimize any problem using PMP the Hamiltonianis formed first and then minimized with respect to controlinput Then state and costate equations are obtained by fol-lowing the set procedureThe flowdiagram can be corrugatedas in Figure 8

For performancemeasure of the form 119869 = 119878(119909(119905) 119906(119905) 119905)+

int119905119891

1199050119881(119909(119905) 119906(119905) 119905) with the terminal cost 119878(119909(119905) 119906(119905) 119905)

instantaneous cost int1199051198911199050119881(119909(119905) 119906(119905) 119905) and the state equation


Start

Hamiltonian formation

Run the vehicle in ADVISOR to get thevehicle parameters to make state equation

Minimize H with respect to SOC

Solve the set of 2n state and costate equations with boundary conditions

State equation S OC and objectivefunction mf is formed

H(xlowast(t) P_batlowast(t) 120582lowast(t) t) le H(x(t) P_bat(t) 120582(t) t)

H = + 120582 lowast S OCmf

120597H120597P_bat = 0 obtain value of control input

S OC =120597H

120597120582 120582 = minus

120597H

120597SOC

Figure 8 PMP process flow

of the form 119909(119905) = 119891(119909(119905) 119906(119905) 119905) Hamiltonian constructionsinvolve instantaneous cost and state equation with a timevarying vector multiplier 120582 as follows

119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)

According to PMP optimal control trajectory 119906lowast(119905)

optimal state trajectory 119909lowast(119905) and corresponding optimal

costate trajectory 120582lowast(119905)minimize the Hamiltonian such that

119867(119909lowast(119905) 119906lowast(119905) 120582lowast(119905) 119905)

le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)

The following relations and constraints (23) must hold withthe above condition

lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)

Initial conditions 1199090and final condition [119867lowast + 120597119878120597119909]

119905119891120597119905119891+

[(120597119878120597119909)lowastminus 120582lowast(119905)]1015840

119905119891120575119909119891both are assumed to be zero

If PMP conditions are satisfied the solution will beextrenal and if a global solution exists it will be the globalsolution

5 Strategy Analysis Simulation andResult Discussion

The engine in its efficient operating range and motor withsufficient SOCwill lead to fuel efficient strategy Speed powerSOC and engine onoff time are the deciding factors andtheir threshold values must be determined to run an HEVwith maximum fuel efficiency

GA first finds optimal values of engine on SOC speedand engine off time (cs min off time cs eng on soc cs elec-tric launch spd and cs eng min spd) thresholds while ful-filling the driver demand that is requested trace (road map)shouldmeet at each instant of time over a road trip Impropervalues of these parameters will reduce the fuel efficiencyAfter selecting threshold values of vehicular parameters using


Table 3 Fuel economy comparison for different battery models

Battery model Fuel economy (mpgge) Trace analysisWith GA Without GA Percentage improvement

119877int conventional model 559208 449785 243278 With trace miss119877int modellowast 606184 510401 187662 No trace miss1 RC modellowast 606250 513732 1800 No trace miss2 RC modellowast 605423 511247 18428 No trace misslowastWith modified SOC estimation method

le cs_electric_launch_spd lt

le cs_min_off_time lt

le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge

le cs_eng_min_spd lt

Figure 9 Engine onoff decision

GA they are now fed to PMPwhich finally reckons thresholdpower to turn the engine on The effect of this hybrid controlstrategy is visible in terms of improved efficiency as shown inTable 3 Four different cases are analyzed here (1) 119877int batterymodel with conventional SOC estimation used in ADVISORand (2) 119877int (3) 1 RC and (4) 2 RC battery models withmodified SOC estimation method [29 31] A considerableimprovement is observed in fuel efficiency using modifiedSOC estimation method over conventional Models withmodified SOC estimation give 8-9 percent improvement overconventional methods Modified SOC estimation methodwith119877int 1 RC and 2RCmodels do notmakemuchdifferencein efficiencies as their OCVs resistances and capacityvariations are close to each other To take care of the actualbattery behavior one should consider 119877 and 119862 componentsinstead of 119877int only in HEV analysis One RC battery modelis used here further to avoid the complexity of 2 RC modelsFigure 9 provides required conditions to turn the engine onoff Here cs min pwr decides minimum power commandedof the engine below this engine should be principally shutoff cs electric launch spd is a vehicle speed threshold belowwhich engine will be off cs min off time is the shortestallowed duration of the engine off period after this time haspassed the engine may restart if high power is requestedBelow cs eng on soc value the engine must be on Belowcs eng min spd fuel can be cut that is engine does not usefuel

0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)

Requested speedAchieved speed

Figure 10 Vehicle requested and delivered speed comparison

0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current

Figure 11 Battery current over the trip

To verify the correctness of proposed strategy requestedspeed and delivered speed of the vehicle are comparedand shown in Figure 10 The figure infers that these twomatch perfectly and there is no trace miss Vehicle requestedpower is fulfilled by different components alone or togetherFigure 4(b) signifies the time instances of negative torquethat is kinetic energy (=12MV2) stored in vehicles trans-lating mass can be stored during these moments if thedeceleration rate is greater than 10 kmh The traction motoroperates as generator to recuperates the energy and chargesbattery as shown in Figure 11 Positive current flow delivers


0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off

SOC variationEngine off case (high)

(b)

Figure 12 SOC status (a) SOC variation over the trip and (b) SOCvariation with engine onoff condition

the current from the battery and negative current signifies thecondition of battery getting charged

Battery SOC variation over the trip and with engineonoff is shown in Figure 12 at 25∘Cwith initial SOC as 80 andtarget as 70 percent Figure 13 shows the motor and engineefficiency points and promise to work in most efficient rangepossible while acquiring the trace and maintaining SOC

6 Conclusion

In this paper a modified SOC estimation method is usedto track the run-time SOC of the batteries and an optimalcontrol based EMS is developed and implemented to controlthe engine onoff status While implementing the strategy allthe important consideration like aerodynamic drag vehicleglider mass accessory loads prescribed SOC level condi-tions and so forth are given utmost attention PMP alongwith GA and with modified SOC estimation techniquespresents promising EMS Various governing parameters ofvehicle are firstly optimized using GA and then a power

0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)

0 50 100 150 200 250 300 350 400 450 500minus80minus60minus40minus20

020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)

Figure 13 Operating points (a) engine and (b) motor

threshold calculation is performed using PMP Calculation ofthresholds initially using GA gives better chance to improvethe fuel efficiency Here fuel efficiency is derived for differentbattery models incorporating modified and conventionalSOC estimation methods This proposed EMS yields betterefficiency as compared to the default strategy available

Conflict of Interests

The authors declare that they have no conflict of interests

References

[1] G J Jos G J-M Olivier and A H W Jeroen Trends in GlobalCO2Emissions PBL Netherlands Environmental Assessment

Agency 2012[2] L Schipper H Fabian and J Leather ldquoTransport and carbon

dioxide emissions forecasts options analysis and evaluationrdquoWorking Paper 9 Asian Development Bank 2009

[3] Japan Automobile Manufacturers Association Inc ReducingCO2Emissions in the Global Road Transport Sector Japan Auto-

mobile Manufacturers Association Inc 2008


[4] M Ehsani Y Gao and A EmadiModern Electric Hybrid Elec-tric and Fuel Cell Vehicles-Fundamentals Theory and Designchapter 2ndash9 CRC Press New York NY USA 2010

[5] V H Johnson K B Wipke and D J Rausen ldquoHEV controlstrategy for real-time optimization of fuel economy and emis-sionsrdquo Society Automotive Engineers vol 109 no 3 pp 1677ndash1690 2000

[6] G Paganelli G Ercole A Brahma Y Guezennec and G Riz-zoni ldquoGeneral supervisory control policy for the energy opti-mization of charge-sustaining hybrid electric vehiclesrdquo SocietyAutomotive Engineers Review vol 22 no 4 pp 511ndash518 2001

[7] G Paganelli M Tateno A Brahma G Rizzoni and YGuezennec ldquoControl development for a hybrid-electric sport-utility vehicle strategy implementation and test resultsrdquo inProceedings of the American Control Conference pp 5064ndash5069Arlington Va USA June 2001

[8] A Sciarretta M Back and L Guzzella ldquoOptimal control ofparallel hybrid electric vehiclesrdquo IEEE Transactions on ControlSystems Technology vol 12 no 3 pp 352ndash363 2004

[9] M Debert G Colin Y Chamaillard L Guzzella A Ketfi-Cherif and B Bellicaud ldquoPredictive energy management forhybrid electric vehiclesmdashprediction horizon and battery capac-ity sensitivityrdquo in Proceedings of the 6th IFAC SymposiumAdvances in Automotive Control (AAC rsquo10) pp 270ndash275 July2010

[10] R Beck F Richert A Bollig et al ldquoModel predictive control ofa parallel hybrid vehicle drivetrainrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 2670ndash2675 IEEEDecember 2005

[11] I Arsie M Graziosi C Pianese G Rizzo and M SorrentinoldquoOptimization of supervisory control strategy for parallelhybrid vehicle with provisional load estimaterdquo in Proceedings ofthe 7th International Symposium on Advanced Vehicle Control(AVEC rsquo04) pp 483ndash488 Arnhem The Netherlands August2004

[12] D Prokhorov ldquoToyota prius HEV neurocontrolrdquo in Proceedingsof the International Joint Conference onNeural Networks (IJCNNrsquo07) pp 2129ndash2134 IEEE Orlando Fla USA August 2007

[13] M Huang and H Yu ldquoOptimal multilevel hierarchical controlstrategy for parallel hybrid electric vehiclerdquo in Proceedings of theIEEE Conference Vehicle Power and Propulsion (VPPC rsquo06) pp1ndash4 Windsor UK September 2006

[14] M Huang and H Yu ldquoOptimal control strategy based on PSOfor powertrain of parallel hybrid electric vehiclerdquo in Proceedingsof the IEEE International Conference on Vehicular Electronicsand Safety (ICVES rsquo06) pp 352ndash355 IEEE Beijing ChinaDecember 2006

[15] ZWang B HuangW Li and Y Xu ldquoParticle swarm optimiza-tion for operational parameters of series hybrid electric vehiclerdquoin Proceedings of the IEEE International Conference Robotics andBiomimetics pp 682ndash688 Kunming China December 2006

[16] L Serrao and G Rizzoni ldquoOptimal control of power split for ahybrid electric refuse vehiclerdquo in Proceedings of the AmericanControl Conference (ACC rsquo08) pp 4498ndash4503 Seattle WashUSA June 2008

[17] N Kim D Lee W Cha S and H Peng ldquoOptimal controlof a plug-in hybrid electric vehicle (PHEV) based on drivingpatternsrdquo in Proceedings of the International Battery Hybrid andFuel Cell Electric Vehicle Symposium pp 1ndash9 Stavanger NorwayMay 2009

[18] S Stockar V Marano G Rizzoni and L Guzzella ldquoOptimalcontrol for plug-in hybrid electric vehicle applicationsrdquo inProceedings of the American Control Conference (ACC rsquo10) pp5024ndash5030 Baltimore Md USA July 2010

[19] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[20] N Kim A Rousseau and D Lee ldquoA jump condition of PMP-based control for PHEVsrdquo Journal of Power Sources vol 196 no23 pp 10380ndash10386 2011

[21] N Kim S W Cha and H Peng ldquoOptimal equivalent fuelconsumption for hybrid electric vehiclesrdquo IEEE Transactions onControl Systems Technology vol 20 no 3 pp 817ndash825 2012

[22] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[23] A Piccolo L Ippolito V Galdi and A Vaccaro ldquoOptimisationof energy flow management in hybrid electric vehicles viagenetic algorithmsrdquo in Proceedings of the IEEEASME Interna-tional Conference on Advanced Intelligent Mechatronics vol 1pp 434ndash439 Como Italy July 2001

[24] A Wang andW Yang ldquoDesign of energy management strategyin hybrid electric vehicles by evolutionary fuzzy system Part IItuning fuzzy controller by genetic algorithmsrdquo in Proceedings ofthe 6th World Congress on Intelligent Control and Automation(WCICA rsquo06) pp 8324ndash8328 Dalian China 2006

[25] B Huang X Shi and Y Xu ldquoParameter optimization of powercontrol strategy for series hybrid electric vehiclerdquo in Proceedingsof the IEEE Congress on Evolutionary Computation (CEC rsquo06)pp 1989ndash1994 Vancouver Canada July 2006

[26] R S Wimalendra L Udawatta E M C P Edirisinghe and SKarunarathna ldquoDetermination ofmaximumpossible fuel econ-omy of HEV for known drive cycle genetic algorithm basedapproachrdquo in Proceedings of the 4th International Conference onInformation and Automation for Sustainability (ICIAFS rsquo08) pp289ndash294 IEEE Colombo Sri Lanka December 2008

[27] X Tang X Mao J Lin and B Koch ldquoLi-ion battery parameterestimation for state of chargerdquo in Proceedings of the IEEEAmerican Control Conference (ACC rsquo11) pp 941ndash946 IEEE July2011

[28] M Verbrugge and E Tate ldquoAdaptive state of charge algorithmfor nickel metal hydride batteries including hysteresis phenom-enardquo Journal of Power Sources vol 126 no 1-2 pp 236ndash2492004

[29] A Panday and H O Bansal ldquoTemperature dependent circuit-based modeling of high power Li-ion battery for plug-inhybrid electrical vehiclesrdquo in Proceedings of the InternationalConference on Advances in Technology and Engineering (ICATErsquo13) pp 1ndash6 IEEE Mumbai India January 2013

[30] A Panday and H O Bansal ldquoHybrid electric vehicle perfor-mance analysis under various temperature conditionsrdquo EnergyProcedia vol 75 pp 1962ndash1967 2015

[31] A Panday H O Bansal and P Srinivasan ldquoThermoelectricmodeling and online SOC estimation of Li-ion battery forplug-in hybrid electric vehiclesrdquo Modelling and Simulation inEngineering vol 2016 Article ID 2353521 12 pages 2016

[32] E Cliffs Electrochemical Systems Prentice-Hall 2nd edition1991


[33] B E Conway ldquoTransition from lsquoSupercapacitorrsquo to lsquoBatteryrsquobehavior in electrochemical energy storagerdquo Journal of theElectrochemical Society vol 138 no 6 pp 1539ndash1548 1991

[34] M Chen and G A Rincon-Mora ldquoAccurate electrical batterymodel capable of predicting runtime and I-V performancerdquoIEEE Transactions on Energy Conversion vol 21 no 2 pp 504ndash511 2006

[35] J Liu H Peng and Z Filipi ldquoModeling and analysis ofthe Toyota hybrid systemrdquo in Proceedings of the IEEEASMEInternational Conference on Advanced Intelligent Mechatronicspp 134ndash139 IEEE Monterey Calif USA July 2005

[36] C Mi M A Masrur and D W Gao Hybrid Electric VehiclesPrinciples and Applications with Practical Perspective JohnWiley amp Sons London UK 2011

[37] S Sumathi and P Surekha Computational Intelligence Para-digm Theory and Application Using MATLAB chapter 13 CRCPress New York NY USA 2010

[38] K Deb ldquoPractical optimization using evolutionary methodsrdquoKanGAL Report 2005008 2005

[39] V F Krotov Global Methods in Optimal Control Theory MarcelDekker New York NY USA 1996

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Table 1 Comparison chart for real time optimization algorithms

Methods Structural complexity Computation time Type of solution Requirement of a priori knowledgeParticle swarm optimization No More Global NoEnergy consumption minimization strategy Yes Small Local NoPontryaginrsquos minimum principle No Small Local YesModel predictive No Small Global NoNeural network Yes Small Global Yes

Moreover fuel economy and emissions minimization areconflicting objectives a smart control strategy should satisfya trade-off between them

In optimization based control strategies the goal of acontroller is to minimize the cost functionThe cost functionfor an HEV may include the emission fuel consumptionand torque depending on the application Global optimumsolutions can be obtained by performing optimization over afixed driving cycle Due to causal nature of global optimiza-tion techniques they are not suitable for real-time analysisTherefore global criterion is reduced to an instantaneousoptimization by introducing a cost function that dependsonly on the present state of the system parameters Globaloptimization techniques do not consider variations of batterystate of charge (SOC) Hence a real-time optimization isperformed for power split while maintaining the batterychargeThe concept of real-time control strategy for efficiencyand emission optimization of a parallel HEV is proposed in[5] It considers all engine-motor torque pairs which forecastthe energy consumption and emissions for every given pointAn instantaneous fuel efficiency optimization strategy wasdeveloped for parallel hybrid vehicle with the charge sustain-ing mode in [6] Also to implement the global constraintthe authors developed a nonlinear penalty function in termsof battery SOC deviation from its desired value Literaturespeaks that real-time optimization techniques like ECMS [67] model predictive control (MPC) [8ndash10] Neural Network(NN) [11 12] particle swarm optimization (PSO) [13ndash15]and Pontryaginrsquos minimum principle (PMP) [16 17] are usedextensively Table 1 compares different real-time strategieswith its pros and cons In the presence of a priori knowledgePMPwith structural simplicity and limited computation timegives local solution to the optimization problemwhich in caseof particular assumption can provide the global optima [17]

Stockar et al used PMP to build an optimal supervisorycontroller by reducing a global optimization problem intolocal It reduces computational requirement and gives thefreedom to solve the problem in the continuous time domain[18] Stockar et al proposed amodel based control strategy tominimize the CO

2emission A supervisory energy manage-

ment strategy is implemented as a global optimization prob-lem and then converted into local and using PMP optimalenergy utilization for PHEVs is obtained A real-time optimalcontrol can be obtained using PMP as it uses instantaneousminimization of the Hamiltonian function [19] Kim et alstate that solution based on PMP can be global optimal undersome certain assumptions [20] Kim et al applied PMP based

control strategies to the PHEVs and found that it gives anumber of alternative solutions [21] PMP provides a near-optimal solution for optimal power management of HEVs iffuture driving conditions are known It is suggested to find theproper costate to keep SOC at a desired and predefined level

In this paper PMP is applied to solve the performanceindex of theHEV in terms of fuel consumptionThe requestedpower threshold is analyzed using PMP above which engineshould be on towork in its optimal efficient range and gener-ator can run to charge the battery tomaintain the appropriateSOC level in the battery

InHEVs speed and power required by vehicle SOC leveland engine off time play an important role to design energymanagement controller PMP computes threshold powerlevel but initially designer needs to define the other param-eters like optimal speed and torque ranges of engine motorand generator highest and lowest level of SOC target SOCspeed threshold and engine off threshold to minimize thefuel consumption using vehicle controller Optimal speed andtorque ranges of engine motor and generator are defined byexperiments done by the National Renewable Energy Lab-oratory (NREL) and provided in the package of AdvancedVehicle Simulator (ADVISOR) [22] But speed thresholdengine off time threshold and engine on SOC level aredetermined here using genetic algorithm (GA)which in turnalong with power threshold decides engine on threshold

GA is a heuristic search algorithm to solve optimizationand search problemsThis is a branch of artificial intelligenceinspired by Darwinrsquos theory of evolution GA is a robustand feasible approach with a wide range of search space andrapidly optimizes the parameters using simple operationsThey are proven to be effective to solve complex engineeringoptimization problems characterized by nonlinear multi-modal nonconvex objective functions GA is efficient atsearching the global optima without getting stuck in localoptima Unlike the conventional gradient based methodGA does not require any strong assumption or additionalinformation about objective parameters GA can also explorethe solution space very efficiently Piccolo et al utilize GA forenergy management of an on road vehicle and minimize thecost function containing fuel consumption and emission [23]Wang and Yang implemented a robust easy and real-timeimplementable FL based energy management strategy andused GA to tune and optimize the same [24] To optimize thefuel consumption and emissions in a series HEV GA basedcontrol strategy has been used by [25] It is a flexible andglobal optimal multiobjective control strategy which is found





2 Vehicle Dynamics


119865119903=1

2120588119860119891119862119863(119881 minus 119881

119882)2

+ 119875119891119903+119872119892 sin120572 (1)









where120596119903120596119904 and120596





Engine

Battery pack

Invertermg1

mg2

PGS



Pinion

Sun

Carrier

Ring

120596r120596p

120596s



119879119888= minus119896119910119904119879119904= minus119896119910119903119879119903 (3)

119879119888 119879119904 and 119879


gear 119896119910119903

= (1 + 119894119892)119894119892and 119896

119910119904= (1 + 119894

119892) and 119894

119892is gear


119898 and


119873119903

119873119904+ 119873119903

lowast 120596119898+

119873119904

119873119904+ 119873119903

lowast 120596119892= 120596119890 (4)

where 119873119903and 119873



119904= 30 (2)

becomes

72222 lowast 120596119898+ 02778 lowast 120596

119892= 120596119890 (5)






negative mg speed



RPM

Vehicle speed


positive mg speed

VHVL



119894) and



119881and SOC



SOC = 119908SOC119881+ (1 minus 119908) (SOC

119894minus 120578) (6)


0 119871 119879))


120578298

= (1 minusSOC0

100) 119871 = 0 at 119879 = 298K

120578new(SOC119879) = 120578298 +(SOC1000)119879 minus 298

plusmn 120576

119871 gt 0 at any 119879

(7)




119901shown in


2 lowast 119877 lowast 119876119901

(8)


119875bat = 120578119896

11988811198791198981198921

1205961198981198921

+ 120578119896

11988821198791198981198922

1205961198981198922

(9)

where 120578119896

1198881and 120578

119896








119881119871=

120587119896119910119903119899119890 min119903119908

30119894119903119908

(ms) (10)



119908is the

wheel radius 119896119910119903= (1 + 119894

119892)119894119892 where 119894


is defined as 119903119903119903119904and 119894119903119908



119899119898119892

= 119896119910119904(119899119890 min minus

30119894119903119908119881

120587119896119910119903119903119908

) (11)




119898119892is


119875119898119892

=2120587

60119879119898119892

119899119898119892

=2120587

60119879119890119899119890 min minus

119894119903119908

119896119910119903119903119908

119879119890119881 (12)


119867


119881119867=

120587119896119910119903119899119890 max119903119908

30119894119903119908

(ms) (13)






119899119898119892

= 119896119910119904(119899119890 max minus

30119896119910119904119894119903119908119881

120587119896119910119903119903119908

) (14)



119875119898119892

=2120587

60119879119898119892

119899119898119892

=119894119903119908

119896119910119903119903119908

119879119890119881 minus

2120587

60

119894119903119908

119896119910119903119903119908

119879119890119899119890 max

(15)



119879119898119905=60

2120587

119875119898119892

119899119905119898

= (119899119890 min119899119905119898

minus119894119903119908

119896119910119903119894119898119908

)119879119890

= minus(2120587119903119908

60119894119898119908

119899119890 min119881

minus119894119903119908

119896119910119903119894119898119908

)119879119890

(16)

where 119894119898119908








119899119890gt30119894119903119908119881

120587119896119910119903119903119908

(17)







119891119905 where

119891119905is total



119891))(119897ℎ)





1198901198921198901000120574











120596119890min le 120596119890 le 120596119890max

1205961198981198921min le 1205961198981198921 le 1205961198981198921max

1205961198981198922min le 1205961198981198922 le 1205961198981198922max

119879119890min le 119879119890 le 119879119890max

1198791198981198921min le 1198791198981198921 le 1198791198981198921max

1198791198981198922min le 1198791198981198922 le 1198791198981198922max


(18)





1198791198981198921

= minus1

1 + 119877[119879119890]

1205961198981198921

= minus119877120577120596req + (1 + 119877) 120596119890

1198791198981198922

= minus1

(1 + 119877)[minus

(1 + 119877) 119879req

120577+ 119877119879119890]

1205961198981198922

= 120577120596req

(19)

where 1205961198981198921

1198791198981198921

1205961198981198922

1198791198981198922

120596119890 and 119879



119890and torque 119879

119890 fuel


119890 119879119890)




119891119875 When the


119891= 119882119888119898119891119876HV = 119875

119891119876HV where 119882119888 is










0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

Time (s)

Spee

d (m

ph)

(a)


020004000

Forc

e (N

)


0500

1000

Time (s)

Time (s)

Torq

ue (N

m)

(b)




119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 max

119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 min

(20)


Speed (rads)30 60 90 120 150 180 210 240 270 300 330 360

102030405060708090

100110120

015

02

025

03

035

04

045

Torq

ue (N

m)


Speed (RPM)




Hor

sepo

wer






Start










original solution

Onegeneration of

GA iscompleted


forms a mating pool

x(L)i le x le x(U)i







int119905119891




Start









S OC =120597H

120597120582 120582 = minus

120597H

120597SOC



119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)





le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)


lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)


119905119891120597119905119891+













le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













2 Vehicle Dynamics


119865119903=1

2120588119860119891119862119863(119881 minus 119881

119882)2

+ 119875119891119903+119872119892 sin120572 (1)









where120596119903120596119904 and120596





Engine

Battery pack

Invertermg1

mg2

PGS



Pinion

Sun

Carrier

Ring

120596r120596p

120596s



119879119888= minus119896119910119904119879119904= minus119896119910119903119879119903 (3)

119879119888 119879119904 and 119879


gear 119896119910119903

= (1 + 119894119892)119894119892and 119896

119910119904= (1 + 119894

119892) and 119894

119892is gear


119898 and


119873119903

119873119904+ 119873119903

lowast 120596119898+

119873119904

119873119904+ 119873119903

lowast 120596119892= 120596119890 (4)

where 119873119903and 119873



119904= 30 (2)

becomes

72222 lowast 120596119898+ 02778 lowast 120596

119892= 120596119890 (5)






negative mg speed



RPM

Vehicle speed


positive mg speed

VHVL



119894) and



119881and SOC



SOC = 119908SOC119881+ (1 minus 119908) (SOC

119894minus 120578) (6)


0 119871 119879))


120578298

= (1 minusSOC0

100) 119871 = 0 at 119879 = 298K

120578new(SOC119879) = 120578298 +(SOC1000)119879 minus 298

plusmn 120576

119871 gt 0 at any 119879

(7)




119901shown in


2 lowast 119877 lowast 119876119901

(8)


119875bat = 120578119896

11988811198791198981198921

1205961198981198921

+ 120578119896

11988821198791198981198922

1205961198981198922

(9)

where 120578119896

1198881and 120578

119896








119881119871=

120587119896119910119903119899119890 min119903119908

30119894119903119908

(ms) (10)



119908is the

wheel radius 119896119910119903= (1 + 119894

119892)119894119892 where 119894


is defined as 119903119903119903119904and 119894119903119908



119899119898119892

= 119896119910119904(119899119890 min minus

30119894119903119908119881

120587119896119910119903119903119908

) (11)




119898119892is


119875119898119892

=2120587

60119879119898119892

119899119898119892

=2120587

60119879119890119899119890 min minus

119894119903119908

119896119910119903119903119908

119879119890119881 (12)


119867


119881119867=

120587119896119910119903119899119890 max119903119908

30119894119903119908

(ms) (13)






119899119898119892

= 119896119910119904(119899119890 max minus

30119896119910119904119894119903119908119881

120587119896119910119903119903119908

) (14)



119875119898119892

=2120587

60119879119898119892

119899119898119892

=119894119903119908

119896119910119903119903119908

119879119890119881 minus

2120587

60

119894119903119908

119896119910119903119903119908

119879119890119899119890 max

(15)



119879119898119905=60

2120587

119875119898119892

119899119905119898

= (119899119890 min119899119905119898

minus119894119903119908

119896119910119903119894119898119908

)119879119890

= minus(2120587119903119908

60119894119898119908

119899119890 min119881

minus119894119903119908

119896119910119903119894119898119908

)119879119890

(16)

where 119894119898119908








119899119890gt30119894119903119908119881

120587119896119910119903119903119908

(17)







119891119905 where

119891119905is total



119891))(119897ℎ)





1198901198921198901000120574











120596119890min le 120596119890 le 120596119890max

1205961198981198921min le 1205961198981198921 le 1205961198981198921max

1205961198981198922min le 1205961198981198922 le 1205961198981198922max

119879119890min le 119879119890 le 119879119890max

1198791198981198921min le 1198791198981198921 le 1198791198981198921max

1198791198981198922min le 1198791198981198922 le 1198791198981198922max


(18)





1198791198981198921

= minus1

1 + 119877[119879119890]

1205961198981198921

= minus119877120577120596req + (1 + 119877) 120596119890

1198791198981198922

= minus1

(1 + 119877)[minus

(1 + 119877) 119879req

120577+ 119877119879119890]

1205961198981198922

= 120577120596req

(19)

where 1205961198981198921

1198791198981198921

1205961198981198922

1198791198981198922

120596119890 and 119879



119890and torque 119879

119890 fuel


119890 119879119890)




119891119875 When the


119891= 119882119888119898119891119876HV = 119875

119891119876HV where 119882119888 is










0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

Time (s)

Spee

d (m

ph)

(a)


020004000

Forc

e (N

)


0500

1000

Time (s)

Time (s)

Torq

ue (N

m)

(b)




119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 max

119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 min

(20)


Speed (rads)30 60 90 120 150 180 210 240 270 300 330 360

102030405060708090

100110120

015

02

025

03

035

04

045

Torq

ue (N

m)


Speed (RPM)




Hor

sepo

wer






Start










original solution

Onegeneration of

GA iscompleted


forms a mating pool

x(L)i le x le x(U)i







int119905119891




Start









S OC =120597H

120597120582 120582 = minus

120597H

120597SOC



119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)





le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)


lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)


119905119891120597119905119891+













le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











negative mg speed



RPM

Vehicle speed


positive mg speed

VHVL



119894) and



119881and SOC



SOC = 119908SOC119881+ (1 minus 119908) (SOC

119894minus 120578) (6)


0 119871 119879))


120578298

= (1 minusSOC0

100) 119871 = 0 at 119879 = 298K

120578new(SOC119879) = 120578298 +(SOC1000)119879 minus 298

plusmn 120576

119871 gt 0 at any 119879

(7)




119901shown in


2 lowast 119877 lowast 119876119901

(8)


119875bat = 120578119896

11988811198791198981198921

1205961198981198921

+ 120578119896

11988821198791198981198922

1205961198981198922

(9)

where 120578119896

1198881and 120578

119896








119881119871=

120587119896119910119903119899119890 min119903119908

30119894119903119908

(ms) (10)



119908is the

wheel radius 119896119910119903= (1 + 119894

119892)119894119892 where 119894


is defined as 119903119903119903119904and 119894119903119908



119899119898119892

= 119896119910119904(119899119890 min minus

30119894119903119908119881

120587119896119910119903119903119908

) (11)




119898119892is


119875119898119892

=2120587

60119879119898119892

119899119898119892

=2120587

60119879119890119899119890 min minus

119894119903119908

119896119910119903119903119908

119879119890119881 (12)


119867


119881119867=

120587119896119910119903119899119890 max119903119908

30119894119903119908

(ms) (13)






119899119898119892

= 119896119910119904(119899119890 max minus

30119896119910119904119894119903119908119881

120587119896119910119903119903119908

) (14)



119875119898119892

=2120587

60119879119898119892

119899119898119892

=119894119903119908

119896119910119903119903119908

119879119890119881 minus

2120587

60

119894119903119908

119896119910119903119903119908

119879119890119899119890 max

(15)



119879119898119905=60

2120587

119875119898119892

119899119905119898

= (119899119890 min119899119905119898

minus119894119903119908

119896119910119903119894119898119908

)119879119890

= minus(2120587119903119908

60119894119898119908

119899119890 min119881

minus119894119903119908

119896119910119903119894119898119908

)119879119890

(16)

where 119894119898119908








119899119890gt30119894119903119908119881

120587119896119910119903119903119908

(17)







119891119905 where

119891119905is total



119891))(119897ℎ)





1198901198921198901000120574











120596119890min le 120596119890 le 120596119890max

1205961198981198921min le 1205961198981198921 le 1205961198981198921max

1205961198981198922min le 1205961198981198922 le 1205961198981198922max

119879119890min le 119879119890 le 119879119890max

1198791198981198921min le 1198791198981198921 le 1198791198981198921max

1198791198981198922min le 1198791198981198922 le 1198791198981198922max


(18)





1198791198981198921

= minus1

1 + 119877[119879119890]

1205961198981198921

= minus119877120577120596req + (1 + 119877) 120596119890

1198791198981198922

= minus1

(1 + 119877)[minus

(1 + 119877) 119879req

120577+ 119877119879119890]

1205961198981198922

= 120577120596req

(19)

where 1205961198981198921

1198791198981198921

1205961198981198922

1198791198981198922

120596119890 and 119879



119890and torque 119879

119890 fuel


119890 119879119890)




119891119875 When the


119891= 119882119888119898119891119876HV = 119875

119891119876HV where 119882119888 is










0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

Time (s)

Spee

d (m

ph)

(a)


020004000

Forc

e (N

)


0500

1000

Time (s)

Time (s)

Torq

ue (N

m)

(b)




119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 max

119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 min

(20)


Speed (rads)30 60 90 120 150 180 210 240 270 300 330 360

102030405060708090

100110120

015

02

025

03

035

04

045

Torq

ue (N

m)


Speed (RPM)




Hor

sepo

wer






Start










original solution

Onegeneration of

GA iscompleted


forms a mating pool

x(L)i le x le x(U)i







int119905119891




Start









S OC =120597H

120597120582 120582 = minus

120597H

120597SOC



119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)





le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)


lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)


119905119891120597119905119891+













le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119908is the

wheel radius 119896119910119903= (1 + 119894

119892)119894119892 where 119894


is defined as 119903119903119903119904and 119894119903119908



119899119898119892

= 119896119910119904(119899119890 min minus

30119894119903119908119881

120587119896119910119903119903119908

) (11)




119898119892is


119875119898119892

=2120587

60119879119898119892

119899119898119892

=2120587

60119879119890119899119890 min minus

119894119903119908

119896119910119903119903119908

119879119890119881 (12)


119867


119881119867=

120587119896119910119903119899119890 max119903119908

30119894119903119908

(ms) (13)






119899119898119892

= 119896119910119904(119899119890 max minus

30119896119910119904119894119903119908119881

120587119896119910119903119903119908

) (14)



119875119898119892

=2120587

60119879119898119892

119899119898119892

=119894119903119908

119896119910119903119903119908

119879119890119881 minus

2120587

60

119894119903119908

119896119910119903119903119908

119879119890119899119890 max

(15)



119879119898119905=60

2120587

119875119898119892

119899119905119898

= (119899119890 min119899119905119898

minus119894119903119908

119896119910119903119894119898119908

)119879119890

= minus(2120587119903119908

60119894119898119908

119899119890 min119881

minus119894119903119908

119896119910119903119894119898119908

)119879119890

(16)

where 119894119898119908








119899119890gt30119894119903119908119881

120587119896119910119903119903119908

(17)







119891119905 where

119891119905is total



119891))(119897ℎ)





1198901198921198901000120574











120596119890min le 120596119890 le 120596119890max

1205961198981198921min le 1205961198981198921 le 1205961198981198921max

1205961198981198922min le 1205961198981198922 le 1205961198981198922max

119879119890min le 119879119890 le 119879119890max

1198791198981198921min le 1198791198981198921 le 1198791198981198921max

1198791198981198922min le 1198791198981198922 le 1198791198981198922max


(18)





1198791198981198921

= minus1

1 + 119877[119879119890]

1205961198981198921

= minus119877120577120596req + (1 + 119877) 120596119890

1198791198981198922

= minus1

(1 + 119877)[minus

(1 + 119877) 119879req

120577+ 119877119879119890]

1205961198981198922

= 120577120596req

(19)

where 1205961198981198921

1198791198981198921

1205961198981198922

1198791198981198922

120596119890 and 119879



119890and torque 119879

119890 fuel


119890 119879119890)




119891119875 When the


119891= 119882119888119898119891119876HV = 119875

119891119876HV where 119882119888 is










0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

Time (s)

Spee

d (m

ph)

(a)


020004000

Forc

e (N

)


0500

1000

Time (s)

Time (s)

Torq

ue (N

m)

(b)




119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 max

119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 min

(20)


Speed (rads)30 60 90 120 150 180 210 240 270 300 330 360

102030405060708090

100110120

015

02

025

03

035

04

045

Torq

ue (N

m)


Speed (RPM)




Hor

sepo

wer






Start










original solution

Onegeneration of

GA iscompleted


forms a mating pool

x(L)i le x le x(U)i







int119905119891




Start









S OC =120597H

120597120582 120582 = minus

120597H

120597SOC



119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)





le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)


lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)


119905119891120597119905119891+













le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















120596119890min le 120596119890 le 120596119890max

1205961198981198921min le 1205961198981198921 le 1205961198981198921max

1205961198981198922min le 1205961198981198922 le 1205961198981198922max

119879119890min le 119879119890 le 119879119890max

1198791198981198921min le 1198791198981198921 le 1198791198981198921max

1198791198981198922min le 1198791198981198922 le 1198791198981198922max


(18)





1198791198981198921

= minus1

1 + 119877[119879119890]

1205961198981198921

= minus119877120577120596req + (1 + 119877) 120596119890

1198791198981198922

= minus1

(1 + 119877)[minus

(1 + 119877) 119879req

120577+ 119877119879119890]

1205961198981198922

= 120577120596req

(19)

where 1205961198981198921

1198791198981198921

1205961198981198922

1198791198981198922

120596119890 and 119879



119890and torque 119879

119890 fuel


119890 119879119890)




119891119875 When the


119891= 119882119888119898119891119876HV = 119875

119891119876HV where 119882119888 is










0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

Time (s)

Spee

d (m

ph)

(a)


020004000

Forc

e (N

)


0500

1000

Time (s)

Time (s)

Torq

ue (N

m)

(b)




119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 max

119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 min

(20)


Speed (rads)30 60 90 120 150 180 210 240 270 300 330 360

102030405060708090

100110120

015

02

025

03

035

04

045

Torq

ue (N

m)


Speed (RPM)




Hor

sepo

wer






Start










original solution

Onegeneration of

GA iscompleted


forms a mating pool

x(L)i le x le x(U)i







int119905119891




Start









S OC =120597H

120597120582 120582 = minus

120597H

120597SOC



119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)





le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)


lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)


119905119891120597119905119891+













le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

Time (s)

Spee

d (m

ph)

(a)


020004000

Forc

e (N

)


0500

1000

Time (s)

Time (s)

Torq

ue (N

m)

(b)




119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 max

119873119903

119873119904+ 119873119903

lowast 120596ring +119873119904

119873119904+ 119873119903


= 120596119890 min

(20)


Speed (rads)30 60 90 120 150 180 210 240 270 300 330 360

102030405060708090

100110120

015

02

025

03

035

04

045

Torq

ue (N

m)


Speed (RPM)




Hor

sepo

wer






Start










original solution

Onegeneration of

GA iscompleted


forms a mating pool

x(L)i le x le x(U)i







int119905119891




Start









S OC =120597H

120597120582 120582 = minus

120597H

120597SOC



119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)





le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)


lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)


119905119891120597119905119891+













le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start










original solution

Onegeneration of

GA iscompleted


forms a mating pool

x(L)i le x le x(U)i







int119905119891




Start









S OC =120597H

120597120582 120582 = minus

120597H

120597SOC



119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)





le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)


lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)


119905119891120597119905119891+













le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start









S OC =120597H

120597120582 120582 = minus

120597H

120597SOC



119867(119909 (119905) 119906 (119905) 120582 (119905) 119905)

= 119881 (119909 (119905) 119906 (119905) 119905) + 120582119879(119905) lowast (119905)

(21)





le 119867 (119909 (119905) 119906 (119905) 120582 (119905) 119905)

(22)


lowast(119905) =

120597119867


lowast

(119905) = minus120597119867


(23)


119905119891120597119905119891+













le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















le cs_min_pwr lt

Engi

ne o

ff

Engi

ne o

n

gt cs_eng_on_soc ge




0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

35

Time (s)

Spee

d (m

s)



0 200 400 600 800 1000 1200 1400minus60

minus40

minus20

0

20

40

60

Time (s)

Curr

ent (

A)

Battery current




0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 200 400 600 800 1000 1200 1400064

066

068

07

072

074

076

078

08

Time (s)

SOC

()

SOC variation(a)

0 200 400 600 800 1000 1200 14000

01

02

03

04

05

06

07

08

09

1

Time (s)

SOC

() a

nd en

gine

off


(b)




6 Conclusion


0 50 100 150 200 250 300 350 400 450minus40minus20

020406080

100120140160

Engine speed

Engi

ne to

rque

Efficiency points

(a)


020406080

100120

Motor speed

Mot

or to

rque

Efficiency points

(b)





References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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