energy optimal control strategy of phev based on pmp …

Research ArticleEnergy Optimal Control Strategy of PHEVBased on PMP Algorithm

Tiezhou Wu Yi Ding and Yushan Xu

Hubei Collaborative Innovation Center for High-Efficiency Utilization of Solar Energy Hubei University of TechnologyWuhan 430068 China

Correspondence should be addressed to Yi Ding 191593927qqcom

Received 7 September 2016 Revised 2 January 2017 Accepted 15 January 2017 Published 28 February 2017

Academic Editor Yongji Wang

Copyright copy 2017 Tiezhou 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

Under the global voice of ldquoenergy savingrdquo and the current boom in the development of energy storage technology at home andabroad energy optimal control of the whole hybrid electric vehicle power system as one of the core technologies of electricvehicles is bound to become a hot target of ldquoclean energyrdquo vehicle development and research This paper considers the constraintsto the performance of energy storage system in Parallel Hybrid Electric Vehicle (PHEV) fromwhich lithium-ion battery frequentlychargesdischarges PHEV largely consumes energy of fuel and their are difficulty in energy recovery and other issues in a singlecycle the research uses lithium-ion battery combined with super-capacitor (SC) which is hybrid energy storage system (Li-SCHESS) working together with internal combustion engine (ICE) to drive PHEV Combined with PSO-PI controller and Li-SCHESS internal power limited management approach the research proposes the PHEV energy optimal control strategy It is basedon revised Pontryaginrsquos minimum principle (PMP) algorithm which establishes the PHEV vehicle simulation model throughADVISOR software and verifies the effectiveness and feasibility Finally the results show that the energy optimization controlstrategy can improve the instantaneity of tracking PHEVminimum fuel consumption track implement energy saving and prolongthe life of lithium-ion batteries and thereby can improve hybrid energy storage system performance

1 Introduction

In 2015 the incident that the illegal use of emissions controlsoftware of Volkswagen further triggers a strong concernon cars ldquoenergy savingrdquo problem So it is essential to useenergy storage technologies to alleviate energy waste Con-sidering the key factor that restricts battery performanceand service life in lithium-ion battery this paper appliesLi-SC HESS to PHEV However how to coordinate eachof storage units chargingdischarging and optimize energymanagement of vehicle power system in real time is thekey to implement the performance optimization of Li-SCHESS and minimize fuel consumption in PHEV Santucciet al [1] proposes a new dynamic optimization method bycombining model predictive control with DP algorithm andconsidering the state of charge (SOC) each of SC and lithium-ion battery together with simplified battery aging modelsand others Masih-Tehrani et al [2] considers factors likefuel consumption periodic battery replacement and othersand proposes a DP algorithm based on PHEV management

costs which considerably improves energy economy ButDP algorithm has a larger calculation and is more time-consuming so it is difficult for practical application while theenergy optimal control strategy based on PMP algorithm isbecoming research focus in recent years with the advantagesof its fast speed and the smaller amount of calculation thanDP algorithm

In this paper PMP global optimization control algorithmhas been adopted which combines with Li-SC HESS internalpower limited management strategy thus taking an energyoptimal control to PHEV having an optimal managementof lithium-ion battery chargingdischarging states improvingthe Li-SC HESS performance and meanwhile ensuring thatthe vehicle fuel consumption during running can track thefuel consumption minimum trajectory in real time

2 PHEV Driven Model

21 Vehicle Structure of PHEV According to vehicle power-train structure HEV can be divided into SHEV PHEV and

HindawiJournal of Control Science and EngineeringVolume 2017 Article ID 6183729 11 pageshttpsdoiorg10115520176183729

2 Journal of Control Science and Engineering

Gearbox

Fuel tankInternal combustionengine

Hybrid energystorage system

Redu

cer

Mec

hani

cal c

oupl

er

Clutch

Motor

Tw 120596w

R(k)

120588 Talt 120596alt

Tice 120596ice

Figure 1 Vehicle Structure of PHEV

ICE DMT system

Alt

Battery

Onboardauxiliaries

DCDC SC

Electric supercharger

Mechanical power flow nodes

Electric power flow nodesDMT dynamic mechanical transmission

Pfuel Pice Pdr

Paltm Palte

Pbat

Paux

PDCi PDCo

PeSC

Figure 2 Power flow schematic of PHEV power system

S-PHEV wherein the SHEV control system is not consideredbecause of its relatively simple control and its large energyconversion which easily poses a threat to lithium-ion bat-teries life PHEV can make energy more efficient and fueleconomy relatively higher so in order to reduce fuel con-sumption asmuch as possible this paper selects PHEVpower-train structure with its power-type composition architecturebeing shown in Figure 1 and the corresponding power flowsof PHEV power system are shown in Figure 2 Its maincomponents include gearbox clutch mechanical couplingreducer alternator ICE fuel tank hybrid energy storagesystem and other modules The vehicle is equipped with a5-speed manual gearbox the AC alternator is connected toICE which owns a fixed speed ratio to reduce the weightand volume of mechanical transmission and simplify thestructure

From Figure 1 119879119908 119879ice and 119879alt are respectively thewheels ICE and alternator torque Nm 120596119908 120596ice and 120596alt arethe wheels ICE and alternator speed rpm 120578gb is the gearboxefficiency 119896 is the number of gearboxrsquos gears that correspondsto its gear ratio 119877(119896) 119876119897ℎV is fuel energy density kJkg

The vehicle power flow of PHEV power system is shownin Figure 2 the bidirection arrow indicates energy flowbeing bidirectional Under the power-train operating modein PHEV drive cycle one part of power comes from energy

conversion of ICE the other part is derived from Li-SCHESS power driving Considering the constraints of traf-fic environment and road situation the electric vehiclesare often in the state of standstill started acceleration orsmooth driving and deceleration If lithium-ion batteriesand SC output power can be allocated reasonably Li-SCHESS can effectively reduce fuel consumption and improvePHEV economic performance When vehicle starts in orderto reduce energy consumption of ICE SC provides highinstantaneous electric power by electric supercharging devicefirstly reducing lithium-ion lifetime impact because of itshigh current discharging When PHEV drives in steadylithium-ion batteries as the main power of Li-SC HESSsupply the portion of the power to alternator When thevehicle accelerates or drives uphill in order to meet thedemand of high power portion flat lithium-ion batterychargingdischarging process SC fills up the vacancy ofalternator power gaps peak change preferentially Whenthe vehicle brakes or drives downhill SC and lithium-ionbatteries recycle braking energy at the same time and SCtakes priority to recycle the energy of high current power atthe beginning

22 Li-SC HESS Model As PHEV energy storage deviceLi-SC HESS owns its control module which is also one

Journal of Control Science and Engineering 3

BatteryPower

inverter M

SC DCDC

ibat

ubat

isciL

Lusc uconv

Figure 3 The topology of Li-SC HESS

part of the whole vehicle control Selecting Li-SC HESSappropriate equivalent circuit model which includes itstopology the equivalent circuit model of each storage ele-ment and control variables is the precondition for thestudy on PHEV power system energy optimization controlstrategyWhen the vehicle is in state of accelerating ormovinguphill this structure can quickly respond to the demandof alternatorrsquos high instantaneous power and it can alsorecover energy when the vehicle is in state of deceleratingand braking Besides with respect to the topology structurebetween lithium-ion batteries and SC each Li-SC HESStopology will make a difference in its component partsdifferent practical applications and different connectionslike the 4 kinds as follows SC and lithium batteries paralleldirectly SC and lithium-ion batteries parallel through eachindependent DCDC converter lithium-ion batteries (SC)connects to DCDC and then parallel with SC (lithium-ionbatteries) Considering the advantages of HESS combinationtype energy conversion efficiency the complexity of systemstructure and others SC connects to DCDC converter andthen parallels with lithium-ion batteries (Figure 3) whichis more suitable for the requirements of current dynamicsand the low cost of PHEV Compared with the independentlyconfigured DCDC converters in parallel its control methodis relatively simpler and the efficiency is relatively higherwhich can better meet the needs of reducing vehicle fuelconsumption in this paper

221 Lithium-Ion Battery Equivalent Model This paperselects first-order RC parallel circuit as lithium-ion batteryequivalent model (Figure 4) due to its low cost and lesscalculation now the model has been accepted by somelithium-ion battery businesses such as Sony and Panasonic

Under different road conditions the current will changedramatically with different power demands of the alternatorenvironmental factors such as battery temperaturewill also beaffected thus forming a threat to the lithium-ion battery lifeand safety From Figure 4 lithium-ion battery state of chargeSOCbat(119905) is represented as follows

SOCbat (119905)= 1119876bat0

int1198790120572 (119868bat (119905)) 120573 (119879bat (119905)) 119868bat (119905) 119889119905

+ SOCbat0

Vbat Cbat

Ebat

R1_bat

R2_bat

Figure 4 Lithium-ion battery equivalentmodel based onfirst-orderRC parallel circuit

119898 sdot 119888119901 sdot 119889119879bat (119905)119889119905= 119868bat (119905)2 sdot 1198772 bat+ 11198771 bat [119881bat (119905) minus 119864bat (119905) minus 1198772 bat119868bat (119905)]2

minus ℎ119888119860 [119879bat (119905) minus 119879119886] (1)

From (1) 119876bat0 is battery capacity 120572(119868bat(119905)) and120573(119879bat(119905)) are battery impact factor of chargingdischargingrate and thermal effect which respectively represent thebattery current 119868bat(119905) and temperature 119879bat(119905) SOCbat0 is theinitial value of battery state of charge (SOC)119898 stands for thebattery quality 119888119901 represents batteryrsquos specific heat capacity119881bat is the terminal voltage of batteriesrsquo equivalent modelℎ119888 means the convective heat transfer coefficient 119860 is theequivalent surface area 119879119886 is batteryrsquos ambient temperature

From (1) SOCbat(119905) is related to 119879bat(119905) and 119868bat(119905) in thecurrent time as 119879bat(119905) is a function of 119868bat(119905) So SOCbat(119905)can be eventually represented by 119868bat(119905) as with formula (2)as follows

SOCbat (119905) = 1119876bat0

int119905sim0

120590 (119868bat (119905)) 119868bat (119905) 119889119905+ SOCbat0 997904rArr

SOCbat (119905) = minus119868bat (SOCbat (119905))119876bat0

SOCbat (0) = SOCbat0

(2)

Similarly the instantaneous power 119875bat(119905) and the corre-sponding current 119868bat(SOCbat(119905)) are shown in formula (3)wherein 119877bat is the battery equivalent resistance

119875bat (119905) = 119877bat1198682bat (119905) + 119864bat119868bat (119905)

119868bat (119905) = 119864bat minus radic1198642bat minus 4119877bat119875bat (119905)2119877bat

119877bat = 1198771 bat 119862bat + 1198772 bat(3)


Res_sc

Vsc

CscRepsc

Figure 5 SC equivalent model based on first-order RC parallelcircuit

222 SC Equivalent Model Similarly considering the struc-tural flexibility and lower computing costs choosing theequivalent first-order RC parallel circuit structure as SCequivalent model like Figure 5 the physical significance ofeach parameter is clear enough Under the PHEV powersystems complex conditions this model can well describelarge current and voltage fluctuations which also has arelatively high degree of practical engineering

From Figure 5 the voltage119881sc(119905) of119862sc is similar to119881bat(119905)above the expression SOCsc(119905) of SC instantaneous power119875sc(119905) and the current 119868sc(SOCsc(119905)) are shown in formula (4)as follows

SOCsc (119905) = 119889SOCsc (119905)119889119905 = 119889 (119881sc (119905) 119862sc119881scmax119862sc)119889119905= SOCsc (119905) 119881scmax minus radic(SOCsc (119905) 119881scmax)2 minus 4119877sc119875sc (119905)

2119877sc119881scmax119862sc

SOCsc (0) = SOCsc0

119875sc (119905) = 119877sc1198682sc (SOCsc (119905)) + 119881sc119868sc (SOCsc (119905))119868sc (SOCsc (119905))

= SOCsc (119905) 119881scmax minus radic(SOCsc (119905) 119881scmax)2 minus 4119877sc119875sc (119905)2119877sc

(4)

Where 119877sc is SC equivalent resistance which is composed ofthe equivalent circuit of 119877ep sc paralleling with 119862sc and thenconnecting with 119877es sc119881scmax is the maximum voltage of119881sc119875sc(119905) is the instantaneous power of SC SOCsc0 is the initialvalue of SOC

3 Problem Description of PHEVEnergy Management Optimization

31 Selection of Control Objective Function In response tothe development goals of green energy economy it shouldmake better performance of Li-SC HESS minimizing ICEenergy consumption reducing economic costs and reducingenvironmental pollution This paper makes ICE minimum

energy consumption as a control target variable Throughoutthe drive cycle [0 119879] of PHEV power systems it assumesthat ICE energy consumption function 119876119888 is

119876119888 = int119879

0119875fuel (119879ice (119905) 120596ice (119905)) 119889119905 (5)

where 119879 is the end time in calculation 119875fuel(119879ice(119905) 120596ice(119905)) isthe instantaneous fuel power at time 119905 and the correspondingspeed and torque of ICE are 120596ice(119905) and 119879ice(119905)32 Objective Function Control Variable Constraints PHEVenergy optimalmanagement requires considering the restric-tions of the objective function from a global point of viewmainly from vehicle structure constraints both physicalmodel constraints of ICE and alternator and Li-SCHESS stateconstraints

321 Vehicle Structural Constraints Designing the rationalenergy optimal control strategy usually regards the vehicledriving force and vehicle speed as the given system statusconditions which are denoted as 119865V(119905)N and V(kmh)and also are converted into wheel torque 119879119908(119905) and wheelspeed 120596119908(119905) of backward system in driving period for theconvenience of description That means being respectivelyconverted into the superposition of 119879ice(119905) and 119879alt(119905) and120596ice(119905) and 120596alt(119905) (the torque and speed of alternator outputare 119879alt(119905) and 120596alt(119905)) The specific relationship description isshown in formula (6)

119879119908 (119905) = 119877 (119896 (119905)) 120578gb (119879ice (119905) + 120588119879alt (119905))= 119877 (119896 (119905)) 120578gb119879ps (119905)

120596119908 (119905) = 120596ice (119905)119877 (119896 (119905)) =120596alt (119905)120588119877 (119896 (119905))

(6)

From (6) 119896(119905) is the number of vehicle gear the drivingcycle is usually defined by 120596119908(119905) and 119896(119905) When 120596119908(119905) and119896(119905) are already known it is pretty easy to deduce the kineticsequation (5) of ICE fuel consumption function at the desiredwheel torque 119879119908(119905)322 ICE and Alternator Physical Model Control ConstraintsICE is a complex system many of its physical phenomenaare not easy to be modeled like the burning process In thiscase the research ignores the temperature dependence of ICEand its dynamic characteristics and then get the distributiongraph of instantaneous fuel consumption function under theaction of119879ice(119905) and120596ice(119905)with the static look-up table (LUT)showing as Figure 6 Similarly as given119879alt and120596alt combinedwith the relevant alternator LUT method efficiency functionof electric motor and the corresponding maximum currentgraph can be derived from Figures 7 and 8

As it can be seen from Figures 6ndash8 when ICE andalternator speed are given the corresponding torques are


8

4

0Fuel

cons

umpt

ion

(gs

)

150

75

0

ICE torque (Nm)1000

3000

5000

ICE speed (rps)

Figure 6 Distribution graph of instantaneous fuel consumptionfunction under the action of 119879ice(119905) 120596ice(119905)

1

06

02

Alt

effici

ency

200

100

0

Alt current (A) 0

7500

15000

Alt speed (rps)

Figure 7 Graph of Alt efficiency function curve under the actionof 119868alt 120596alt

constrained by their maximum available torque So formula(7) is defined as follows

120596icemin le 120596ice (119905) le 120596icemax119879icemin (120596ice (119905)) le 119879ice (119905) le 119879icemax (120596ice (119905))

120596altmin le 120596alt (119905) le 120596altmax119879altmin (120596alt (119905)) le 119879alt (119905) le 119879altmax (120596alt (119905))

(7)

Formula (6) shows that the spindle torque 119879ps(119905) =119879ice(119905)+120588119879alt(119905) considering the alternator torque constraintsat any time 119905 both of the ICE minimum 119879icemin(120596ice(119905)) andmaximum 119879icemax(120596ice(119905)) satisfies formula (8)

119879icemin (120596ice (119905)) = max 119879icemin (120596ice (119905)) 119879ps (119905)minus 120588119879altmax (120596alt (119905))

119879icemax (120596ice (119905)) = min 119879icemax (120596ice (119905)) 119879ps (119905)minus 120588119879altmin (120596alt (119905))

(8)

200

100

0

Alt

curr

ent_

max

(A)

100

60

20

Alt current (A) 0

5000

10000

Alt speed (rps)

Figure 8 Graph of Alt maximum current curve under the actionof 119868alt 120596alt

323 Li-SC HESS Control Constraints Among energy stor-age element SOC is an important parameter of over-chargingoverdischarging and cycle-life of storage elementsAccording to Li-SC HESS equivalent mathematical modelin order to minimize the chargingdischarging times inthe certain drive cycle SOCbat(119905) should be limited andso it is the same with battery current 119868bat(119905) during thechargingdischarging process and SOCsc(119905) 119868sc(119905) is shownin equation (9)

SOCbatmin le SOCbat (119905) le SOCbatmax119868batmin le 119868bat (119905) le 119868batmax

SOCscmin le SOCsc (119905) le SOCscmax119868scmin le 119868sc (119905) le 119868scmax

(9)

Since lithium-ion battery and SC are all energy bufferdevices in the continued charging state assessing fuel econ-omy of the energy optimization control PMP algorithmshould meet the need of the end constraints conditions ofΔSOCbat asymp 0 and ΔSOCsc asymp 0 that is formula (10)

ΔSOCbat ≜ SOCbat (119879) minus SOCbat (0) ΔSOCsc ≜ SOCsc (119879) minus SOCsc (0) (10)

4 Energy Optimal Management StrategyBased on PMP Algorithm

41 Construction of Hamiltonian Function With the con-sumption function 119876119888 in formula (5) when the final timeis given energy consumption can be converted into aLagrange problem with constrained terminal state whichcorresponded to Hamilton function as formula (11)

119867119886 (SOCbat SOCsc 119879ice 119868DC119900 1205821 1205822)= 119875fuel (119879ice 120596ice) minus 1205821 119868bat (SOCbat)119876bat0

sdot sdot sdot

minus 1205822 119868sc (SOCsc 119868DC119900)119876bat0+ 120582119889Φ(SOCsc)

(11)


From (11) In order to connect the dynamic characteristicsof both lithium-ion battery and SC this research considersSC characteristics that it has the priority to respond largecurrent changes quickly and its protection to overchargeand overdischarge and then it brings in a dynamic buffervariable Φ(SOCsc) as a penalty function to restrain Li-SCHESS dynamic processes which are described in the formula(12)

119889 ≜ Φ (SOCsc)= [SOCsc minus SOCscmin]2 sg (SOCscmin minus SOCsc)+ [SOCscmax minus SOCsc]2 sg (SOCsc minus SOCscmax)

(12)

From (12) sg(119909) ≜ 0 119909 lt 0 1 119909 ge 0 119889(119905) ge 0forall119905 isin [0 119879] only if SOCsc satisfies formula (12) it should be119889(119905) = 0There119883119889(119905) = int1199050 119889(119905)119889119905+119883119889(0) and its terminalconstraint condition is119883119889(119879) = 119883119889(0) = 042 Solution of Extreme Value of Li-SC HESS Output Coeffi-cient According to Hamiltonian function equation (11) thisresearch seeks these necessary conditions for the minimumvalue of 119876119888 that is a set of costate equations (formula (13))for the sake of solving the initial value of these costatevariables

SOClowastbat = 120597119867120572 (sdot)1205971205821 = minus119868bat (SOClowastbat)119876bat0

lowast1 = minus 120597119867120572 (sdot)120597SOCbat= 120582lowast1119876bat0

120597119868bat (SOClowastbat)120597SOCbat

SOClowastsc = 120597119867120572 (sdot)1205971205822 = minus119868sc (SOClowastsc 119868lowastDC0)119862sc

lowast2 = minus 120597119867120572 (sdot)120597SOCsc= 120582lowast1119876bat0

120597119868bat (SOClowastbat)120597SOCsc+ 120582lowast2119862sc

sdot 120597119868sc (SOClowastsc 119868lowastDC119900)120597SOCsc

sdot sdot sdotminus 2120582lowast119889 [SOClowastsc minus SOCscmin]sdot sg (SOCscmin minus SOClowastsc) sdot sdot sdotminus 2120582lowast119889 [SOCscmax minus SOClowastsc]sdot sg (SOClowastsc minus SOCscmax)

lowast119889 = minus120597119867120572 (sdot)120597120582119889 = [SOClowastsc minus SOCscmin]2

sdot sg (SOCscmin minus SOClowastsc) + [SOCscmax minus SOClowastsc]2sdot sg (SOClowastsc minus SOCscmax)

(13)

SOClowastbat (119879) asymp SOClowastbat (0) = SOCbat0SOClowastbat isin [SOCbatmin SOCbatmax]

SOClowastsc (T) asymp SOClowastsc (0) = SOCsc0SOClowastsc isin [SOCscmin SOCscmax]

119883lowast119889 (0) = 0120597119868sc (SOCsc)120597SOCsc

= minus 119881scmax119868sc (SOCsc)radic(SOCsc119881scmax)2 minus 4119877sc119875sc

lowast1 = 0lowast2 = 0lowast119889 = 0

(14)

120582lowast1 = 12058210120582lowast2 = 12058220120582lowast119889 = 1205821198890119867119886 (SOClowastbat SOClowastsc 119879lowastice 119868lowastDC119900 120582lowast1 120582lowast2 120582lowast119889)

le 119867119886 (SOClowastbat SOClowastsc 119879ice 119868DCo 120582lowast1 120582lowast2 120582lowast119889) forall119905 isin [0 119879] forall (119879ice 119868DC119900) isin Ω

(15)

where Ω = 119879ice isin (119879icemin(120596ice(119905) 119879icemax(120596ice(119905)))) 119868DC119900 isin(119868DC119900 119868DC119900) is the capacities of control variable 119879ice and119868DC119900

From (13)ndash(15) it shows that solving the optimal controlproblem is transformed into solving the initial conditionsSOCbat0 and SOCsc0 of Li-SC HESS state of charge andcostate variable initial value 1205820 = (12058210 12058220 1205821198890) As SOCbat0SOCsc0 can be given directly then it is further simplifiedinto solving the initial output coefficients 12058210 and 12058220 ofeach energy storage element and the penalty intensity factor1205821198890 under the constraints of the boundary condition in thevehicle driving cycle Besides the initial value of the costate1205820 requires the minimum value of the control variables 119879iceand 119868DC119900 within the allowable range Ω So define 1199041 ≜minus1205821119864bat(SOCbat)119876bat0 1199042 ≜ minus1205822SOCsc119862sc the Hamilto-nian mathematical model of the system can be expressed asformula (16)

119867119886 (SOCbat SOCsc 119879ice 119868DC119900 1199041 1199042)= 119875fuel (119879ice 120596ice) + 1199041119875bat119894 (SOCbat) sdot sdot sdot+ 1199042119875sc119894 (SOCsc 119868DC119900) + 120582119889Φ(SOCsc)

(16)

From (16) 119875fuel(119879ice 120596ice) 119875bat119894(SOCbat) and 119875sc119894(SOCsc119868DC119900) respectively correspond to ICE fuel consumptionpower internal lithium-ion battery power and SC powerat current time so it is the same with 1199041 1199042 and 120582119889 asthe weighting factor of Li-SC HESS It is apparent that thepractical significance of Hamiltonian function is described as


the equivalent fuel power function it is also to be the sum ofPHEV weighted power within a certain drive period whichis consistent with the law of conservation of energy So itverifies the feasibility of PMP algorithm in the application ofthe actual object So PMP algorithm can be transformed intoan online ldquo120582-controlrdquo method under the optimal solution ofminimum fuel consumption

43 ldquo120582-Controlrdquo Based PSO-PI Real-Time OptimizationAlthough the costate variable initial value 1205820 is a constantin off-line HESS output power differs from different cycledriving conditions in drive cycle So using the PMP algo-rithm is difficult to ensure the real-time characteristic ofldquo120582-controlrdquo In order to respond to the online noncausaloptimal control strategy this research uses PSO (ParticleSwarm Optimization) algorithm to optimize the parametersof PI closed-loop controller (PSO-PI controller) which isto improve the characteristics of flexibility and adaptabilityof feedback closed-loop controller besides its robustnessand fast convergence speed easily implementing and highcomputational efficiency

Considering SOC(119905) of each energy storage unit of Li-SC HESS the research assumes that the reference value ofLi-SC HESS SOC(119905) is SOCref under the computer controlsystem environment set the sampling period 119879 and 119905 =119896119879 and introduce the PI feedback closed-loop equation(17) corresponding to the PSO-PI control block diagram(Figure 9)

(119905) = 1205820 + 119896119901 (SOCref minus SOC (119905))+ 119896119894119896sum119894=1

(SOCref minus SOC (119894)) (17)

From (17) there are two parameters 119896119901 and 119896119894 of PIcontroller to be optimized According to the ITAE (integralof time multiplied by the absolute value of error) indicatorsconsidering the steady-state error the performance of settlingtime small overshoot and oversmooth it uses criterion ITAEof PSO algorithm to calculate the objective function Inaddition every potential optimal solution of optimizationproblems to be optimized in PSO algorithm represents aparticle in one of the solvable space such as particle 119894 whichcorresponds to the fitness value of 119894-particle fitness func-tion This research introduces the particle current position119909119894 = (1199091198941 1199091198942 119909119894119889) 119894 = 1 2 119899 current speed ]119894 =(]1198941 ]1198942 ]119894119889) all particlesrsquo best flying position trajectory119875119894 = (1199011198941 1199011198942 119901119894119889) monomer extreme value 119901best119894 =(119901best1198941 119901best1198942 119901best119894119889) group extreme value 119901gbest119894 =(119901gbest1198941 119901gbest1198942 119901gbest119894119889) and inertia weight ℎ and thenupdates and iterates the particle according to formula (18)

119869 = int+infin0

119905 |119890 (119905)| 119889119905]119894119889119896+1 = ℎ]119894119889119896 + 11988811199031 times (119901best119894119889119896 minus 119909119894119889119896) + 11988821199032

times (119901gbest119894119889119896 minus 119909119894119889119896)

119909119894119889119896+1 = 119909119894119889119896 + ]119894119889119896+1ℎ = ℎinitial minus [(ℎinitial minus ℎend)] lowast 119896119896max

(18)

From (18) 119889 = 1 2 119863 ℎ is the inertia weight 1199031and 1199032 are the random numbers between (0 1) 1198881 and 1198882are the nonnegative constant evolution factor 119909119894119889119896 and ]119894119889119896are the updated position and speed of particle 119894 at the 119896thiteration among 119863-dimensional space ℎinitial is the initialinertia weight 119896max is the maximum number of iterationsℎend is the inertia weight when 119896max Taking ℎinitial = 09 andℎend = 04 to ensure a strong initial global search capabilitythe latter part of the algorithm facilitates local search

Themain steps of PSO-PI controller parameter optimiza-tion are as follows

(1) Assuming that the particle 119894 has parameters 119896119901 119896119894group scale current iteration number 119896 and the itera-tion maximum number 119896max inertia weight learningfactor monomer extreme value 119901best119894 and groupextreme value 119901gbest119894 and so on then initialize 119909119894 and]119894 of particle 119894 randomly

(2) Update the 119909119894119889119896 and ]119894119889119896 of particle 119894 according toformula (18) and then calculate its fitness value 119869119894

(3) Compare 119869119894 with the corresponding 119901best119894 if 119869119894 gt119901best119894 update the position of 119901best119894 instead of thecurrent position of 119875119894

(4) Similarly compare 119869119894 with the corresponding 119901gbest119894if 119869119894 gt 119901gbest119894 update the position of 119901gbest119894 instead ofthe current position of 119875119894

(5) Judge the termination constraints of PSO algorithmif it is terminated go directly to step (6) otherwiserepeat steps (2)ndash(4)

(6) Output the optimized parameter values 119896119901 and 119896119894Since PI controller is not adaptive itself add PSO algo-

rithm to adjust the parameters of the controller the self-adaptability is improved to achieve the purpose of fasttracking and controlling the covariable in PMP algorithmWhen group scale is set to 30 the maximum calculationperiod to is set to 100 and both 1198881 and 1198882 are set to 150425the convergence curve of the best individual fitness functionis shown in Figure 10

44 Management of Li-SC HESS Limited Power Above theresearch takes the vehicle dynamic character and minimalfuel consumption as the main analysis object and initiallyestablishes energy optimization management method ofPHEV power system Although the allocated processingfactors can ensure the coordinated allocation of powerbetween lithium-ion battery and SC SOC constraints duringcontrolling just to prevent Li-SC HESS overcharge andoverdischarge which are the basic conditions In order tofurther improve Li-SC HESS performance it needs to makea real-time management of the power of Li-SC HESS eachenergy storage unit during the chargingdischarging state


PSO-PIcontrol

Energy optimalmanagement ofPMP algorithm

HEV

Vechicle signals

SOCref +

minus

e(t)

1205820

120582(t) SOC (t)

Figure 9 PSO-PI real-time optimization ldquo120582-controlrdquo block diagram

01

0605

0405

0205

0005

0805

20 40 60 80 100Number of iterations

GA-PIPSO-PI

J

Figure 10 The convergence curve of the best individual fitnessfunction

The vehicle energy optimization control flow chart is shownin Figure 11

According to the lithium-ion batteryrsquos characteristicsof low power density strong energy density and lim-ited life the research adopts the preresponse principle ofSC when the demanded power of the alternator changesand dictates that when SOCsc of SC reaches the limitingvalue of serious chargeovercharge Li-SC HESS prohibitsits chargedischarge When SOCsc has not reached seriouscritical limits it will be divided into the normal workingsection (SOClow SOChigh) and power limitationmanagementsection (SOChigh SOCmax) cup (SOCmin SOClow) That is asfollowsΔ119875bat and Δ119875sc are the amended power of lithium-ionbattery and SC respectively and there is Δ119875bat = minusΔ119875scDuring the normal operation SOCsc isin (SOClow SOChigh)Δ119875sc = 0 and the power of each storage device does notchange When the discharging power exceeds the limit therule of power correction is shown in formula (19) Similarlythere is formula (20) when the charging power exceeds thelimitΔ119875sc = 0 SOCsc gt SOCsc maxΔ119875sc = 119875sc ref ( SOCsc minus SOCsc high

SOCsc max minus SOCsc high) = 119860

SOCsc isin (SOCsc high SOCsc max) Δ119875sc = minus119875sc ref ( SOCsc low minus SOCsc

SOCsc low minus SOCsc min) = 119861

SOCsc isin (SOCsc min SOCsc low) Δ119875sc = minus119875sc ref SOCsc lt SOCsc low

(19)

Δ119875sc = minus119875sc ref SOCsc gt SOCsc maxΔ119875sc = minus119860 SOCsc isin (SOCsc high SOCsc max) Δ119875sc = minus119861 SOCsc isin (SOCsc min SOCsc low) Δ119875sc = 0 SOCsc lt SOCsc low

(20)

5 Results and Analysis

PHEV with Li-SC HESS in this paper is obtained by thesecondary development of PHEVmodel based on ADVISORsoftware (Figure 12)

Taking into account of the majority of domestic small carusers daily and mainly using in the city the research adoptsthe urban road cycling conditions (CYC-UDDS) The real-time curve of driving cycle speed is shown in Figure 13(a)The gear position curve of the driving cycle is shown inFigure 13(b) Integrating Figures 13(a) and 13(b) it can beseen that the vehicle speed of the driving cycle is well-tracked with gear position changes which basically meets theevaluation requirements of vehicles driving cycle actually Italso verifies the feasibility of energy-optimized controllingelectric vehicles by PMP algorithm

(1)The comparison results of PHEV power system beforeand after when working normally in the vehicle drivingcycle Li-SC HESS can provide or absorb some of the energythrough alternator reducing fuel consumption ICE Figures14(a) and 14(b) respectively represent the alternator torquecurve of vehicle power system controlled by PMP energyoptimization algorithm

Comparing Figure 14(a) with Figure 14(b) it is easy toknow that after using PMP algorithm the alternator torquecurve fluctuation changes more dramatically than beforeand the alternator power requirements increase significantlyAccording to the conservation of energy it indicates thatthe part of ICE fuel consumption absorbed by alternatorincreases clearly

(2) The result of real-time optimization of output coef-ficients by PSO algorithm in order to demonstrate thecharacteristic of real-time tracking by PSO-PI controller theresearch obtains the output coefficient 120582(119905) curve (Figure 15)of Hamiltonian function under the action of single lithium-ion battery

FromFigure 15 this control strategy can also adjust ICE tomoving along its track of minimum fuel energy consumptionthrough the alternator real-timely and it also further vali-dates the rationality and feasibility of PMP algorithm


PHEV power system main module

Minimum energyconsumption function of ICE

Constraints aresatisfied

PMP algorithmoptimization

PSO-PI control inreal-time

End

No

Yes

Hybrid energy storagesystem module

SC PreconditioningPrinciple

Power limitationmanagement

Yes

No1205820

120582(t)

SOCSC isin [SOChigh SOCmax]cup [SOCmin SOClow ]

Figure 11 The overall flow chart of PHEV energy optimization control

wheel andaxle ⟨wh⟩

vehicle ⟨veh⟩

total fuel used (gal)gal

torquecoupler ⟨tc⟩ power

bus ⟨pb⟩

⟨vc⟩ par

electric assist control strategy ⟨cs⟩

motorcontroller ⟨mc⟩ par

mechanical accessoryloads ⟨acc⟩

gearbox ⟨gb⟩

fuelconverter⟨fc⟩

final drive ⟨fd⟩

exhaust sys⟨ex⟩

energystorage ⟨ess⟩electric acc

loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩

UltracapacitorSystem

PSO-PI Controller

Version ampCopyright

AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off

⟨sdo⟩ par⟨cs⟩

ex_cat_tmp

⟨cyc⟩

Figure 12 PHEV simulation model

Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)

Figure 13 (a) Under CYC-UDDS real-time curve of driving cycle speed (b) Under CYC-UDDS gear position curve of the driving cycle


0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)

Figure 14 (a) Before PMP energy optimization algorithm (b) After PMP energy optimization algorithm

1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)

PSO optimized real-time tracking 120582

120582(t)

Figure 15 Output coefficient curve of real-timely optimized Hamiltonian function by PSO-PI controller

73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)

Figure 16 (a) SOC curve of a single lithium-ion battery energy storage (b) SOC curve of Li-SC HESS

The simulation situation between the single lithium-ionbattery energy storage and Li-SC HESS It can be knownfrom Figures 16(a) and 16(b) that the state of charge oflithium battery or SC is consistent with the end constraintsof Pontryaginrsquos minimum principle Besides as is shown inFigures 17(a) and 17(b) together with Figure 16(b) since Li-SC HESS is embedded with SC in the vehicle driving cycleit can significantly reduce the output of lithium-ion batteryThe charge and discharge currents of lithium-ion battery areclearly smaller than the single lithium-ion batteries whichnot onlywell smooth the chargingdischarging process of bat-teries but also obviously reduce the corresponding lithium-ion batteriesrsquo chargingdischarging cycle times Finally itreflects the good coordinate ability between Li-SCHESS eachenergy storage element which can extend batteryrsquos life Andit also validates the validity and effectiveness of this energy-optimized control method for designed PHEV with Li-SCHESS

6 Summary

The research designs a kind of PHEV that introduces Li-SCHESS Compared with traditional vehicles This PHEV hasthe advantages of both ICE and Li-SCHESS For example the

internal ICE can use existing gas station resources and reducethe overall investment costs Meanwhile it can alleviate thedifficulty more effectively than pure electric vehicles whensolving the problems brought from defrosting air condition-ers and other pieces of large energy consumption equipmentLi-SC HESS can help extend battery life and extend thedriving ranges of cars In particular the embedment of SCmakes Li-SC HESS well suited to start the vehicle the speedchange and energy recovery during braking Mainly PHEVenergy optimization control strategy can effectively reducevehicle exhaust emissions benefit for the urban environmentwhich has a high research value

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The research group would like to thank the ldquoResearch onElectric Vehicle Li-ion battery and SCHybrid Energy StorageSystem Energy Management Strategyrdquo (Grant no 51677058)for funding this research


0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250

SC currentBattery current

Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)

Figure 17 (a) Current curve of a single lithium-ion battery energy storage (b) Current curve of Li-SC HESS

References

[1] A Santucci A Sorniotti andC Lekakou ldquoPower split strategiesfor hybrid energy storage systems for vehicular applicationsrdquoJournal of Power Sources vol 258 pp 395ndash407 2014

[2] M Masih-Tehrani M-R Harsquoiri-Yazdi V Esfahanian and ASafaei ldquoOptimum sizing and optimum energy managementof a hybrid energy storage system for lithium battery lifeimprovementrdquo Journal of Power Sources vol 244 pp 2ndash10 2013

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 athttpswwwhindawicom

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



Gearbox

Fuel tankInternal combustionengine

Hybrid energystorage system

Redu

cer

Mec

hani

cal c

oupl

er

Clutch

Motor

Tw 120596w

R(k)

120588 Talt 120596alt

Tice 120596ice

Figure 1 Vehicle Structure of PHEV

ICE DMT system

Alt

Battery

Onboardauxiliaries

DCDC SC

Electric supercharger

Mechanical power flow nodes

Electric power flow nodesDMT dynamic mechanical transmission

Pfuel Pice Pdr

Paltm Palte

Pbat

Paux

PDCi PDCo

PeSC

Figure 2 Power flow schematic of PHEV power system

S-PHEV wherein the SHEV control system is not consideredbecause of its relatively simple control and its large energyconversion which easily poses a threat to lithium-ion bat-teries life PHEV can make energy more efficient and fueleconomy relatively higher so in order to reduce fuel con-sumption asmuch as possible this paper selects PHEVpower-train structure with its power-type composition architecturebeing shown in Figure 1 and the corresponding power flowsof PHEV power system are shown in Figure 2 Its maincomponents include gearbox clutch mechanical couplingreducer alternator ICE fuel tank hybrid energy storagesystem and other modules The vehicle is equipped with a5-speed manual gearbox the AC alternator is connected toICE which owns a fixed speed ratio to reduce the weightand volume of mechanical transmission and simplify thestructure

From Figure 1 119879119908 119879ice and 119879alt are respectively thewheels ICE and alternator torque Nm 120596119908 120596ice and 120596alt arethe wheels ICE and alternator speed rpm 120578gb is the gearboxefficiency 119896 is the number of gearboxrsquos gears that correspondsto its gear ratio 119877(119896) 119876119897ℎV is fuel energy density kJkg

The vehicle power flow of PHEV power system is shownin Figure 2 the bidirection arrow indicates energy flowbeing bidirectional Under the power-train operating modein PHEV drive cycle one part of power comes from energy

conversion of ICE the other part is derived from Li-SCHESS power driving Considering the constraints of traf-fic environment and road situation the electric vehiclesare often in the state of standstill started acceleration orsmooth driving and deceleration If lithium-ion batteriesand SC output power can be allocated reasonably Li-SCHESS can effectively reduce fuel consumption and improvePHEV economic performance When vehicle starts in orderto reduce energy consumption of ICE SC provides highinstantaneous electric power by electric supercharging devicefirstly reducing lithium-ion lifetime impact because of itshigh current discharging When PHEV drives in steadylithium-ion batteries as the main power of Li-SC HESSsupply the portion of the power to alternator When thevehicle accelerates or drives uphill in order to meet thedemand of high power portion flat lithium-ion batterychargingdischarging process SC fills up the vacancy ofalternator power gaps peak change preferentially Whenthe vehicle brakes or drives downhill SC and lithium-ionbatteries recycle braking energy at the same time and SCtakes priority to recycle the energy of high current power atthe beginning

22 Li-SC HESS Model As PHEV energy storage deviceLi-SC HESS owns its control module which is also one


BatteryPower

inverter M

SC DCDC

ibat

ubat

isciL

Lusc uconv





SOCbat (119905)= 1119876bat0

int1198790120572 (119868bat (119905)) 120573 (119879bat (119905)) 119868bat (119905) 119889119905

+ SOCbat0

Vbat Cbat

Ebat

R1_bat

R2_bat



minus ℎ119888119860 [119879bat (119905) minus 119879119886] (1)



SOCbat (119905) = 1119876bat0

int119905sim0




(2)




119877bat = 1198771 bat 119862bat + 1198772 bat(3)


Res_sc

Vsc

CscRepsc





2119877sc119881scmax119862sc

SOCsc (0) = SOCsc0



(4)





119876119888 = int119879

0119875fuel (119879ice (119905) 120596ice (119905)) 119889119905 (5)



119879119908 (119905) = 119877 (119896 (119905)) 120578gb (119879ice (119905) + 120588119879alt (119905))= 119877 (119896 (119905)) 120578gb119879ps (119905)

120596119908 (119905) = 120596ice (119905)119877 (119896 (119905)) =120596alt (119905)120588119877 (119896 (119905))

(6)




8

4

0Fuel

cons

umpt

ion

(gs

)

150

75

0

ICE torque (Nm)1000

3000

5000

ICE speed (rps)


1

06

02

Alt

effici

ency

200

100

0

Alt current (A) 0

7500

15000

Alt speed (rps)





(7)




(8)

200

100

0

Alt

curr

ent_

max

(A)

100

60

20

Alt current (A) 0

5000

10000

Alt speed (rps)





(9)






sdot sdot sdot


(11)




(12)












(13)






(14)



(15)




(16)









119869 = int+infin0




(18)












PSO-PIcontrol


HEV

Vechicle signals

SOCref +

minus

e(t)

1205820

120582(t) SOC (t)


01

0605

0405

0205

0005

0805


GA-PIPSO-PI

J








(19)


(20)














End

No

Yes




Yes

No1205820

120582(t)




vehicle ⟨veh⟩



bus ⟨pb⟩

⟨vc⟩ par




gearbox ⟨gb⟩



exhaust sys⟨ex⟩


loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩


PSO-PI Controller


AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off


ex_cat_tmp

⟨cyc⟩


Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)



0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










BatteryPower

inverter M

SC DCDC

ibat

ubat

isciL

Lusc uconv





SOCbat (119905)= 1119876bat0

int1198790120572 (119868bat (119905)) 120573 (119879bat (119905)) 119868bat (119905) 119889119905

+ SOCbat0

Vbat Cbat

Ebat

R1_bat

R2_bat



minus ℎ119888119860 [119879bat (119905) minus 119879119886] (1)



SOCbat (119905) = 1119876bat0

int119905sim0




(2)




119877bat = 1198771 bat 119862bat + 1198772 bat(3)


Res_sc

Vsc

CscRepsc





2119877sc119881scmax119862sc

SOCsc (0) = SOCsc0



(4)





119876119888 = int119879

0119875fuel (119879ice (119905) 120596ice (119905)) 119889119905 (5)



119879119908 (119905) = 119877 (119896 (119905)) 120578gb (119879ice (119905) + 120588119879alt (119905))= 119877 (119896 (119905)) 120578gb119879ps (119905)

120596119908 (119905) = 120596ice (119905)119877 (119896 (119905)) =120596alt (119905)120588119877 (119896 (119905))

(6)




8

4

0Fuel

cons

umpt

ion

(gs

)

150

75

0

ICE torque (Nm)1000

3000

5000

ICE speed (rps)


1

06

02

Alt

effici

ency

200

100

0

Alt current (A) 0

7500

15000

Alt speed (rps)





(7)




(8)

200

100

0

Alt

curr

ent_

max

(A)

100

60

20

Alt current (A) 0

5000

10000

Alt speed (rps)





(9)






sdot sdot sdot


(11)




(12)












(13)






(14)



(15)




(16)









119869 = int+infin0




(18)












PSO-PIcontrol


HEV

Vechicle signals

SOCref +

minus

e(t)

1205820

120582(t) SOC (t)


01

0605

0405

0205

0005

0805


GA-PIPSO-PI

J








(19)


(20)














End

No

Yes




Yes

No1205820

120582(t)




vehicle ⟨veh⟩



bus ⟨pb⟩

⟨vc⟩ par




gearbox ⟨gb⟩



exhaust sys⟨ex⟩


loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩


PSO-PI Controller


AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off


ex_cat_tmp

⟨cyc⟩


Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)



0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Res_sc

Vsc

CscRepsc





2119877sc119881scmax119862sc

SOCsc (0) = SOCsc0



(4)





119876119888 = int119879

0119875fuel (119879ice (119905) 120596ice (119905)) 119889119905 (5)



119879119908 (119905) = 119877 (119896 (119905)) 120578gb (119879ice (119905) + 120588119879alt (119905))= 119877 (119896 (119905)) 120578gb119879ps (119905)

120596119908 (119905) = 120596ice (119905)119877 (119896 (119905)) =120596alt (119905)120588119877 (119896 (119905))

(6)




8

4

0Fuel

cons

umpt

ion

(gs

)

150

75

0

ICE torque (Nm)1000

3000

5000

ICE speed (rps)


1

06

02

Alt

effici

ency

200

100

0

Alt current (A) 0

7500

15000

Alt speed (rps)





(7)




(8)

200

100

0

Alt

curr

ent_

max

(A)

100

60

20

Alt current (A) 0

5000

10000

Alt speed (rps)





(9)






sdot sdot sdot


(11)




(12)












(13)






(14)



(15)




(16)









119869 = int+infin0




(18)












PSO-PIcontrol


HEV

Vechicle signals

SOCref +

minus

e(t)

1205820

120582(t) SOC (t)


01

0605

0405

0205

0005

0805


GA-PIPSO-PI

J








(19)


(20)














End

No

Yes




Yes

No1205820

120582(t)




vehicle ⟨veh⟩



bus ⟨pb⟩

⟨vc⟩ par




gearbox ⟨gb⟩



exhaust sys⟨ex⟩


loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩


PSO-PI Controller


AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off


ex_cat_tmp

⟨cyc⟩


Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)



0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










8

4

0Fuel

cons

umpt

ion

(gs

)

150

75

0

ICE torque (Nm)1000

3000

5000

ICE speed (rps)


1

06

02

Alt

effici

ency

200

100

0

Alt current (A) 0

7500

15000

Alt speed (rps)





(7)




(8)

200

100

0

Alt

curr

ent_

max

(A)

100

60

20

Alt current (A) 0

5000

10000

Alt speed (rps)





(9)






sdot sdot sdot


(11)




(12)












(13)






(14)



(15)




(16)









119869 = int+infin0




(18)












PSO-PIcontrol


HEV

Vechicle signals

SOCref +

minus

e(t)

1205820

120582(t) SOC (t)


01

0605

0405

0205

0005

0805


GA-PIPSO-PI

J








(19)


(20)














End

No

Yes




Yes

No1205820

120582(t)




vehicle ⟨veh⟩



bus ⟨pb⟩

⟨vc⟩ par




gearbox ⟨gb⟩



exhaust sys⟨ex⟩


loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩


PSO-PI Controller


AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off


ex_cat_tmp

⟨cyc⟩


Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)



0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












(12)












(13)






(14)



(15)




(16)









119869 = int+infin0




(18)












PSO-PIcontrol


HEV

Vechicle signals

SOCref +

minus

e(t)

1205820

120582(t) SOC (t)


01

0605

0405

0205

0005

0805


GA-PIPSO-PI

J








(19)


(20)














End

No

Yes




Yes

No1205820

120582(t)




vehicle ⟨veh⟩



bus ⟨pb⟩

⟨vc⟩ par




gearbox ⟨gb⟩



exhaust sys⟨ex⟩


loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩


PSO-PI Controller


AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off


ex_cat_tmp

⟨cyc⟩


Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)



0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119869 = int+infin0




(18)












PSO-PIcontrol


HEV

Vechicle signals

SOCref +

minus

e(t)

1205820

120582(t) SOC (t)


01

0605

0405

0205

0005

0805


GA-PIPSO-PI

J








(19)


(20)














End

No

Yes




Yes

No1205820

120582(t)




vehicle ⟨veh⟩



bus ⟨pb⟩

⟨vc⟩ par




gearbox ⟨gb⟩



exhaust sys⟨ex⟩


loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩


PSO-PI Controller


AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off


ex_cat_tmp

⟨cyc⟩


Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)



0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PSO-PIcontrol


HEV

Vechicle signals

SOCref +

minus

e(t)

1205820

120582(t) SOC (t)


01

0605

0405

0205

0005

0805


GA-PIPSO-PI

J








(19)


(20)














End

No

Yes




Yes

No1205820

120582(t)




vehicle ⟨veh⟩



bus ⟨pb⟩

⟨vc⟩ par




gearbox ⟨gb⟩



exhaust sys⟨ex⟩


loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩


PSO-PI Controller


AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off


ex_cat_tmp

⟨cyc⟩


Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)



0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















End

No

Yes




Yes

No1205820

120582(t)




vehicle ⟨veh⟩



bus ⟨pb⟩

⟨vc⟩ par




gearbox ⟨gb⟩



exhaust sys⟨ex⟩


loads ⟨acc⟩

drive cycle

fc_emis

ex_calc

clutch ⟨cl⟩


PSO-PI Controller


AND

HC CONOx PM (gs)

emis

Goto ⟨sdo⟩time

DCDC

ClockAltia_off


ex_cat_tmp

⟨cyc⟩


Veh_spd_r

0 100 200 300 400 500 600 700 800 900 10000

20406080

100120

Veh_

spd_

r

(a)Gearbox ratio

0 100 200 300 400 500 600 700 800 900 1000

12345

0Gea

rbox

Rat

io

(b)



0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 100 200 300 400 500 600 700 800 900 10000

5

10

Alte

rnat

orto

rque

(Nm

)

Time (s)

(a)

05

1015

0 100 200 300 400 500 600 700 800 900 1000

Alte

rnat

orto

rque

(Nm

)

Time (s)

(b)


1614121008060402

0 100 200 300 400 500 600 700 800 900 1000Time (s)


120582(t)


73574

74575

75576

Time (s)0 100 200 300 400 500 600 700 800 900 1000

SOC b

at(

)

(a)

75

80

85

90

95SO

C (

) SCBattery

Time (s)0 100 200 300 400 500 600 700 800 900 1000

(b)



6 Summary



Competing Interests


Acknowledgments



0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(b)


References





RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 100 200 300 400 500 600 700 800 900 1000Time (s)

0

10

20

30

40

50

60

70Ba

ttery

curr

ent (

A)

Battery current

minus10

minus20

minus30

(a)

minus150

minus100

minus50

0

50

100

150

200

250


Curr

ent (

A)

0 100 200 300 400 500 600 700 800 900 1000Time (s)

(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









energy optimal control strategy of phev based on pmp …

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