Research ArticleLithium-Ion Battery Cell-Balancing Algorithm for BatteryManagement System Based on Real-Time Outlier Detection

Changhao Piao12 Zhaoguang Wang1 Ju Cao1 Wei Zhang2 and Sheng Lu1

1 Institute of Pattern Recognition andApplications ChongQingUniversity of Posts andTelecommunications Chongqing 400065 China2Mechanical Engineering INHA University Incheon 400072 Republic of Korea

Correspondence should be addressed to Sheng Lu lushengcqupteducn

Received 16 March 2015 Revised 15 April 2015 Accepted 15 April 2015

Academic Editor Xiaosong Hu

Copyright copy 2015 Changhao Piao et alThis 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

A novel cell-balancing algorithm which was used for cell balancing of battery management system (BMS) was proposed in thispaper Cell balancing algorithm is a key technology for lithium-ion battery pack in the electric vehicle field The distance-basedoutlier detection algorithm adopted two characteristic parameters (voltage and state of charge) to calculate each cellrsquos abnormalvalue and then identified the unbalanced cells The abnormal and normal type of battery cells were acquired by online clusteringstrategy and bleeding circuits (R = 33 ohm) were used to balance the abnormal cells The simulation results showed that withthe proposed balancing algorithm the usable capacity of the battery pack increased by 0614Ah (95) compared to that withoutbalancing

1 Introduction

Electric vehicles (EV) arewidely viewed as an important tran-sitional technology for energy-saving and environmentallysustainable transportation [1] As the new traction batterypacks critical energy sources of EV lithium-ion (Li-ion)battery pack is drawing a vast amount of attention for itsexcellent advantages such as compact volume large capacitylower weight and higher safety [2ndash4] Single battery cellsare serially connected to a battery stack to achieve highercapacity and voltage However the charging process has tostop as soon as one cell is completely charged and the dis-charging process has to stop as soon as one cell is completelydischarged [5] The capacity of the whole battery pack isthus limited by the unbalanced cells required to be balanced(also called abnormal cells in this paper) in the pack whichcan reduce the usable capacity of the battery pack decreasethe energy usage efficiencies and shorten the lifetime ofbattery packTherefore battery cell balancing that is one basicfunction of BMS is necessary for battery pack in EV [6ndash9]

Two algorithms are commonly used for cell balancingvoltage-based balancing algorithm and state of charge-based

balancing algorithm The voltage-based balancing is thatwhen the difference between one cell voltage and the meanvalue of cell voltages is larger than the threshold 119881th thecell is probably considered to be an abnormal cell [10ndash12] This method is simple and easy operating while theexternal voltage of the cell is affected by its internal stateand environment On the other hand some researcherspointed that state of charge (SOC) can reflect the capacityof the battery pack in essence and proposed the SOC-basedbalancing algorithm which controls the range of the SOCsmaller than the threshold SOCth [13 14] However SOC thatis affected by battery model self-discharge temperature andother factors can only be calculated by voltage or currentindirectly and it is still difficult to get the accurate SOCof eachcell Unfortunately there are still no observations at presentabout applying outlier detection algorithm to cell balancing

Outlier detection algorithmwhich is an important branchof data mining is applied in many different domains [15ndash17] This paper innovatively proposed to use the algorithmto identify the abnormal cells The algorithm chooses char-acteristic parameters of battery cells and develops a flexibledistance function to get outliers (viz the unbalanced cells)

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 168529 12 pageshttpdxdoiorg1011552015168529

2 Mathematical Problems in Engineering

effectively [18 19] After getting the accurate category ofnormal and abnormal cells through clustering method theabnormal cells are balanced by passive balancing circuit Out-lier detection algorithm can recognize the abnormal batterycell accurately and improve the performance of battery packsuch as increasing the usable energy and extending lifetime

The research work is organized as follows Section 2describes the detailed processes of the proposed balancingalgorithmThe simulationmodels and test cycle are describedin Section 3 In the final section conclusions and finalremarks are given

2 Balancing Algorithm Based onOutlier Detection

21 Outlier Detection Algorithm As shown in Figure 1 theoutlier detection balancing algorithm includes two modulesthe unbalanced cells recognition module and the balanc-ing control module The former module gets normal andabnormal cells by outlier detection algorithm while the latterbalances the abnormal cells and gives feedback to the formerThere are 119873 battery cells in the power battery pack Andthe characteristic parameters of the cells are provided to theunbalanced cell recognition module [20]

The Li-ion batteryrsquos input-current 119868 and output-SOCcurrent 119868 and terminal voltage 119880 are shown in Figure 2 [21]The characteristic parameters of voltage and SOC are used tocalculate each cellrsquos outlier value

22 Unbalanced Cell Recognition Abnormal cells are pickedup as outlier point by the outlier detection method inunbalanced cells recognitionmodule First 119911-score standard-ized method is used to preprocess the attribute of batterySecond the outlier detectionmethod based on the distance ofmultidimensional attribute is adopted to calculate each cellrsquosoutlier value which is the summation of distances from onecell to the others Third the battery pack will be balanced ifthe abnormality range is not less than the threshold signedas VOA1 otherwise the unbalanced cells will be obtainedby the dynamic cluster method Finally passive equalizationis applied to the abnormal battery cells Figure 3 shows theprogress of recognizing abnormal cells

InputThe number of battery cells119873 and the initial thresholdof abnormality range VOA1 are input

Step 1 If the attribute values of the battery cells are equal theprocess ends and the pack is considered balanced otherwiseit goes to Step 2

Step 2 119885-score standardized method is adopted to pre-process the characteristic parameters for eliminating theinfluence of units Namely use the formula (1) to preprocessthe Voltage 119880 and the SOC as follows

119885119894119895=

Cell119894119895minus Cell

119895

120575119895

Power battery system

Balancing control

Imbalancedcells recognition

Figure 1 The design of the outlier detection balancing algorithm

Lithium-ion battery

State of charge SOC

Current I Current I

Voltage U

Figure 2 Input and output parameters of lithium-ion batterymodel

Cell119895=

sum119899

119894=1Cell119894119895

119899

120575119895=radicsum119899

119894=1(Cell119894119895minus Cell

119895)

119899 minus 1

(1)

where 119885119894119895(119894 = 1 40 and 119895 = 1 2) is the standardization

form of 119895th characteristic parameter of the 119894th cell (ie 11988512

denotes the standard SOC of the first cell) Cell119894119895represents

the original value of 119895th characteristic parameter of the 119894thcell (ie Cell

21denotes the original voltage of the second cell)

Cell119895describes the mean of 119895th parameters 120575

119895denotes the

standard deviation of the voltage or SOC when 119895 equals to 1or 2 respectively 119899 is the number of cells

Then Euclid-distance is used to calculate the abnormalvalue of each cell in the pack The calculation formula [22] isdefined as follows

1198632(119885119898 119885119899) = radic

10038161003816100381610038161198851198981 minus 11988511989911003816100381610038161003816

2+10038161003816100381610038161198851198982 minus 1198851198992

1003816100381610038161003816

2

119882 (119885119898) =

119899

sum

119898=1

2

sum

119895=1

1198632(119885119898 119885119899)

(2)

Mathematical Problems in Engineering 3

The range of outlier

The total number of

Standard process the selectedparameters and calculate

abnormal value of each cell

Select normal andabnormal initial cluster

center respectively

and cluster the cells dynamically

Yes

Step 1

Step 2

Step 3

Step 4

Step 5

The attribute valuesof cells are equal

Yes

Getting theabnormal cells

Balancedbattery pack

No

No

the battery cells N

Obtain the sums of squared error Je

until Je reaches the minimum

values gt VOA1

Figure 3 The process of acquiring abnormal battery cells

where 1198632(119885119898 119885119899) (119898 = 1 40 119899 = 1 40 119898 = 119899)

represents the Euclid-distance between the 119898th cell and the119899th cell 119885

119898represents the 119898th cell which has two attributes

(ie 119885119898

= (1198851198981 1198851198982)) 119882(119885

119898) denotes the summation

of Euclid-distance betweenthe 119898th cell and the others Thesmaller the 119882(119885

119898) is the more normal the 119898th cell is On

the contrary the119898th battery is probably abnormal

Step 3 If the range of outlier values (the difference outliervalue between cell with the lowest and that with the highestoutlier value) of the cells is smaller than the thresholdVOA1 the process ends and the pack is considered balancedotherwise it goes to Step 4 VOA1 is defined and updated bythe formulation as follows

VOA1 =sum119899

119898=1119882(119885119898)

119899 (3)

Step 4 Set the cell with the lowest and that with the highestoutlier value as initial clustering centroids

Step 5 The other cells are assigned to their nearest clustercentroid all at once followed by recalculation of clustercentroid Then the other cells are individually reassignedif doing so will reduce the sums of squared error andcluster centroids are recomputed after each reassignment

[23]The process of obtaining the minimum sums of squarederror 119869

119890is formulated as follows

119869119898=

119873119898

sum

119898=1

10038171003817100381710038171003817119885119898minus 119862119895

10038171003817100381710038171003817

2

119885119898isin 119878119895

119869119890=

119896

sum

119895=1

119869119898=

119896

sum

119895=1

119873119898

sum

119898=1

10038171003817100381710038171003817119885119898minus 119862119895

10038171003817100381710038171003817

2

119885119898isin 119878119895

(4)

where 119869119898denotes the squared error of119898th cell 119869

119890is the sums

of all the squared errors119862119895is initial cluster centroid 119878

119895is the

normal category or the abnormal categoryWhen 119869

119890converges to a global minimum the process

jumps to the next step

Output The battery pack is balanced or unbalanced

By this time the unbalanced cells are recognized by theoutlier detection algorithm and can be balanced with thepassive balancing circuit that will be described in detail innext section

23 Balancing Control At present the balancing circuit canbe divided into two main groups [24] passive balancingcircuit and active cell balancing circuit Typical passive cellbalancing circuit also named shunt method uses switchesto control balancing Specifically shunt method is designedto use a resistor to discharge the unbalanced cell detectedby outlier detection algorithm With active cell balancingcircuit charge can be transferred between the cells in batterypack by a capacitor or an inductor Very little energy wouldbe wasted in this case compared to the passive balancingmethod However more switches and associated componentsare needed in the active balancing circuit And these addi-tional components may lead to higher cost and unreliabilityPassive balancing circuit has already been used in manyapplications for its simple structure and reliability Hencepassive cell balancing circuit is applied in this paper Asshown in Figure 4 every battery has a balancing circuit whichcomprises a resistor and a switch in series

3 Simulation Experiments

In order to compare the efficiency of the outlier detectionbalancing algorithm with the traditional balancing algo-rithms in detail the constant-current charging-discharging(CCCD)model and the software-in-the-loop platform (SILP)model for the BMS were established in Sections 31 and 32respectively The simulations were conducted on an Intel23 GHz Windows platform with 4GB RAM and imple-mented in MatlabSimulink The battery pack is modeled inSimulink using the electric drives library As can be seenin Figure 5(a) the battery pack model consists of five Li-ionbatteries connected in series and each battery is made up ofeight cellswhich are also connected in series (see Figure 5(b))The rated capacity and nominal voltage of cell are 65 Ahand 36V respectively and the values of other parameters areshown in Table 1

4 Mathematical Problems in Engineering

Table 1 The parameters of battery cell

Parameters Value UnitNominal voltage 36 VRated capacity 65 AhMaximum capacity 65 AhFully charged voltage 42 VNominal discharge current 282 AInternal resistance 0005 OhmCapacity at nominal voltage 587 Ah

The switch control signal

S1 S2 SnR1 R2 Rn

minus + minus + minus +

Cell1 Cell2 Celln

middot middot middot

middot middot middot

Figure 4 Passive cell balancing circuit

And the SOC for a fully charged cell model is 100 andfor an empty cell model is 0 The SOC is calculated basedon Coulomb-counting as

SOC = 100 (1 minus 1

119876int

119905

0

119894 (119905) 119889119905) (5)

where119876 is the rated capacity 119905 is the charging or dischargingtime 119894(119905) is the charging or discharging current

Here are several assumptions of the battery cell model inSimulink [21]

(a) The parameters of the model are deduced fromdischarging characteristics and assumed to be thesame for charging

(b) The internal resistance is supposed to be constantduring the charging and the discharging cycles anddoes not vary with the different amplitude of thecurrent

(c) The self-discharge of the battery is not representedand the battery has no memory effect

(d) The model does not take the temperature intoaccount

31 Constant Current Charging-DischargingModel and Simulation

311 CCCDModel and Test Condition As shown in Figure 6the CCCD model provides a 65-A (1C) constant chargingand discharge current for the battery pack In a seriallyconnected battery pack discharging or charging progress hasto be stopped immediately as soon as one of the terminalcell voltages falls below discharging voltage limit (DVL) orexceeds charging voltage limit (CVL) [2] The values of DVL

and CVL of the cell modeled in this paper are 3749V and42V and the SOC correspondingly reaches 30 and almost100

Figure 7 shows the simulated SOC current and voltageof 10th cell during one CCCD cycle The cell is charged bya 65-A constant current until voltage reaches CVL (42 V)and the corresponding SOC is almost 100 It is dischargedby the same current until voltage reaches DVL (3749V) andthe corresponding SOC is 30 The initial SOC and voltagesof the cells in the battery pack is that one cellrsquos SOC andvoltage are 4506 and 3794V while other cells are 3506and 3769V respectively The initial value of threshold VOA1of the proposed method is 1233

312 Simulation Results and Analysis The simulation resultsduring whole CCCD test cycle are shown in Table 2 for differ-ent balancing scenarios (no balancing voltage-based balanc-ing SOC-based balancing and outlier detection balancing)That the usable capacity calculated over balancing processof abnormal cell decreased by 0584Ah is the preconditionfor comparing the simulation results for different balancingscenarios

With no balancing the unbalanced cell (10th cell) inthe battery pack cannot be completely discharged beforecharging and the normal cells cannot be completely chargedbefore discharging during the whole test cycle as detailedin Figure 8 Hence the amount of usable energy of thepack decreased at the end of the charging process Withvoltage-based balancing the total voltage (charging cut-off)increased to 163017V and the SOC range of cells decreasedto 1030 but the frequency of balancing switch onoffreaches as high as 352 With outlier detection balancing thefrequency of the switching onoff was significantly reducedfrom 352 to 2 And the voltage variance (charging cut-off)and the SOC variance were reduced to 0008 and 0158respectively when compared with voltage-based and SOC-based balancing algorithm Additionally the charging time(after CCCD testing balancing algorithm off) of unbalancedbattery pack is 2091 s and the charging capacity is 3775Ahwhile balanced battery pack (same condition with unbal-anced pack testing) is 2413 s and 4389Ah respectively

The definitions of several evaluation standards in Table 2are as follows

Testing Time Time of the whole simulation process

Balancing Time Sum of the balancing time

Frequency of Switch on and off Sum of the balancing circuitswitch onoff times

Usable Capacity Decrease This can be calculated by theformula (6)

119862119894= int

119905

0

119894equ (119905) 119889119905

119894equ (119905) =119881119894 (119905)

119877

(6)

Mathematical Problems in Engineering 5

All parameters2

Parameters1

Battery5 ldquominusrdquo14

Battery1 ldquo+rdquo13

Battery1 ldquominusrdquo2

Battery1 ldquo+rdquo1

Vectorconcatenate1

Vectorconcatenate

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Cell 8

+

_

Cell 7

+

_

Cell 6

+

_

Cell 5

+

_

Cell 4

+

_

Cell 3

+

_

Cell 2

+

_

Cell 1

+_

Battery5

In1

In2Out1

Conn1

Conn2

Battery4

In1

In2Out1

Conn1

Conn2

Battery3

In1

In2Out1

Conn1

Conn2

Battery2

In1

In2Out1

Conn1

Conn2

Battery1

In1

In2Out1

Conn1

Conn2

Signals14

Input13

Signals2

Input1

(a) (b)

R

R

RR

RR

RR

RR

RR

RR

R1

R2

R3

R4

R5

R6

R7

R8

Figure 5 The schematic diagram of simulation model of pack (a) and battery (b)

where 119862119894is the decreased usable capacity of 119894th cell during

balancing process 119905 represents the balancing time 119894equ(119905) isthe balancing current 119881

119894(119905) denotes the voltage of battery at

119905 time 119877 (33 ohm) represents the resistance in cell balancingcircuit

As illustrated by Figure 9 when the voltage-based bal-ancing algorithm determined on and off the 10th cell asabnormal cell (upper plot) the outlier detection algorithmconstantly and accurately did that (lower plot) Meanwhilethe testing time of the simulation decreased to 23037 s whenimplemented outlier detection equalization algorithm onCCCD model The control signal ldquo1rdquo represents opening thebalancing circuit and ldquo0rdquo means shutting it down

The process that the battery pack transferred fromunbalanced state to balanced state using different balancing

algorithms under CCCD cycle is shown as Figure 10 AndFigure 11 shows the position variation of the abnormal cell(10th) detected by the proposed algorithm after balancedTheabnormal cell was closer to the other cells after it was balancedby outlier detection balancing algorithm

32 Software-in-the-Loop Platform Model ofBMS and Simulation

321 SILP Model of BMS and ECE + EUDC Test ConditionThe software-in-the-loop platform (SILP) model of BMS forelectric vehicles gives a new idea to test the validity andreliability for BMS and power battery in different properties[20 25] Generally speaking the model can also be used totest the feasibility and effectiveness of balance algorithms in

6 Mathematical Problems in Engineering

Powergui

DiscreteSwitch

Relay

Min

min

Max

max

Battery pack

Contr sigVoltage

SOC

Current

Conn1

Conn2

Balancingalgorithm

Voltage

SOCContr sig

1C

65

ge

++

minusminuss s

Ts = 01 s

Figure 6 The constant current charge-discharge model

Table 2 Performance comparisons of 3 algorithms under CCCD condition

Evaluation standard Balancing algorithmNo balancing Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 37171 29048 23037Balancing time (S) mdash 17681 17783 17775Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 352 2 2Charging cut-off

Total voltage (V) 161214 163017 162939 165738Voltage range (V) 0160 0058 0059 0055Voltage variance 0025 0009 0009 0008

Discharging cut-offTotal voltage (V) 149994 149965 154481 149965Voltage range (V) 0034 0005 0005 0001Voltage variance 0005 0001 0001 0

Charging time (S) 2091 2413 2413 2413SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0158

the early stage of design greatly improving the reliability ofthe algorithms In addition the SILP model can simulatemore different working conditions and the simulation resultshavemore significance in actual engineering when comparedwith the CCCD model The SILP model for BMS mainlyincludes driving cycle model driver model vehicle controlunit model battery management system software model

battery model power system model and wheel model Thewhole virtual environment model is shown in Figure 12

The ECE + EUDC test cycle is used for EU type approvaltesting of emissions and fuel consumption from light dutyvehicles As Figure 13 shows ECE + EUDC (bottom chart)cycle includes four ECE (upper left chart) segments repeatedwithout interruption followed by one EUDC (upper right

Mathematical Problems in Engineering 7

0 500 1000 1500 2000 2500 3000 350020406080

100

Time (s)

SOC

()

0 500 1000 1500 2000 2500 3000 3500

05

10

Time (s)Cu

rren

t (A

)

0 500 1000 1500 2000 2500 3000 35003638

44244

Time (s)

Volta

ge (V

)

minus5

minus10

Figure 7 The SOC current and voltage of 10th cell during one 1C CCCD test cycle

0 05 1 15 2 25 3 35 4 45 520

40

60

80

100

Time (s)

SOC

()

Abnormal cellNormal cells

times104

(a)

Abnormal cellNormal cells

0 05 1 15 2 25 3 35 4 45 536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 8 SOC (a) and voltage (b) of the unbalanced pack

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(a)

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(b)

Figure 9 Balancing control signal of voltage-based (a) and outlier detection (b) balancing

chart) segment According to Figure 14 the battery pack isdischarged with two ECE + EUDC cycle until 2400 s andcharged by the generator in the next 822 s since the SOCof thepack reduced to 30 Simulation test starts in the situationthat there is one cellrsquos SOC and voltage value are 6483 and4140V and the others are 5483 and 4063V respectively

322 Simulation Result and Analysis The simulation resultsduring thewhole ECE+EUDC test cycle are shown inTable 3for different balancing scenarios (no balancing voltage-based balancing SOC-based balancing and outlier detection

balancing algorithm)That the usable capacity calculated overbalancing process of abnormal cell decreased by 0584Ah isthe precondition for comparing the simulation results fordifferent balancing scenarios

With no balancing the unbalanced cell in the batterypack could not be completely discharged before charging andthe normal cells could not be completely charged before dis-charging during the whole test cycle as detailed in Figure 15Hence the amount of usable energy of the pack decreased atthe end of the charging process With voltage-based balanc-ing the total voltage (charging cut-off) increased to 164738V

8 Mathematical Problems in Engineering

0 05 1 15 2 25 3 35 4 45 5 5520406080

100

Time (s)

SOC

()

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

times104

(a)

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

0 05 1 15 2 25 3 35 4 45 5 5536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 10 SOC (a) and voltage (b) of pack with balancing algorithms during CCCD cycle

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(a)

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(b)

Figure 11 The position of the abnormal cell before it was balanced (a) and after it was balanced (b)

and the voltage variance (discharging cut-off) decreased to0003 but the frequency of balancing switch onoff reaches ashigh as 1150 With outlier detection balancing the frequencyof the switching onoff was significantly reduced from 1150to 2 and reduced the voltage variance (charging cut-off) andthe SOC variance to 0 and 0157 respectively when comparedwith voltage-based and SOC-based balancing algorithmFurthermore the proposed balancing algorithm increasedthe total charging cut-off voltage from 161214V to 165738Vwhen compared with the pack without balancing And it alsoreduced the discharging cut-off voltage variance and the SOCvariance to 0 and 0157 respectively

The process in which the battery pack transferred fromunbalanced state to balanced state with different balancingalgorithms under ECE + EUDC test cycle is shown as

Figure 16 With outlier detection balancing algorithm thecells in the battery pack can be completely chargeddischargeat the same time and thus increase the available energy storedin the pack

4 Conclusions

Aiming at the problem that present cell-balancing algorithmscannot identify the unbalanced cells in lithium-ion batterypack accurately in real-time an algorithm based on outlierdetection was proposed in this paper The unbalanced cellswere identified by the proposed balancing algorithms andbalanced by shunt method using switches After validatingthe efficiency of the balancing algorithms on two simulationmodels the advantages of the proposed algorithm have been

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical Problems in Engineering

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Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

effectively [18 19] After getting the accurate category ofnormal and abnormal cells through clustering method theabnormal cells are balanced by passive balancing circuit Out-lier detection algorithm can recognize the abnormal batterycell accurately and improve the performance of battery packsuch as increasing the usable energy and extending lifetime

The research work is organized as follows Section 2describes the detailed processes of the proposed balancingalgorithmThe simulationmodels and test cycle are describedin Section 3 In the final section conclusions and finalremarks are given

2 Balancing Algorithm Based onOutlier Detection

21 Outlier Detection Algorithm As shown in Figure 1 theoutlier detection balancing algorithm includes two modulesthe unbalanced cells recognition module and the balanc-ing control module The former module gets normal andabnormal cells by outlier detection algorithm while the latterbalances the abnormal cells and gives feedback to the formerThere are 119873 battery cells in the power battery pack Andthe characteristic parameters of the cells are provided to theunbalanced cell recognition module [20]

The Li-ion batteryrsquos input-current 119868 and output-SOCcurrent 119868 and terminal voltage 119880 are shown in Figure 2 [21]The characteristic parameters of voltage and SOC are used tocalculate each cellrsquos outlier value

22 Unbalanced Cell Recognition Abnormal cells are pickedup as outlier point by the outlier detection method inunbalanced cells recognitionmodule First 119911-score standard-ized method is used to preprocess the attribute of batterySecond the outlier detectionmethod based on the distance ofmultidimensional attribute is adopted to calculate each cellrsquosoutlier value which is the summation of distances from onecell to the others Third the battery pack will be balanced ifthe abnormality range is not less than the threshold signedas VOA1 otherwise the unbalanced cells will be obtainedby the dynamic cluster method Finally passive equalizationis applied to the abnormal battery cells Figure 3 shows theprogress of recognizing abnormal cells

InputThe number of battery cells119873 and the initial thresholdof abnormality range VOA1 are input

Step 1 If the attribute values of the battery cells are equal theprocess ends and the pack is considered balanced otherwiseit goes to Step 2

Step 2 119885-score standardized method is adopted to pre-process the characteristic parameters for eliminating theinfluence of units Namely use the formula (1) to preprocessthe Voltage 119880 and the SOC as follows

119885119894119895=

Cell119894119895minus Cell

119895

120575119895

Power battery system

Balancing control

Imbalancedcells recognition

Figure 1 The design of the outlier detection balancing algorithm

Lithium-ion battery

State of charge SOC

Current I Current I

Voltage U

Figure 2 Input and output parameters of lithium-ion batterymodel

Cell119895=

sum119899

119894=1Cell119894119895

119899

120575119895=radicsum119899

119894=1(Cell119894119895minus Cell

119895)

119899 minus 1

(1)

where 119885119894119895(119894 = 1 40 and 119895 = 1 2) is the standardization

form of 119895th characteristic parameter of the 119894th cell (ie 11988512

denotes the standard SOC of the first cell) Cell119894119895represents

the original value of 119895th characteristic parameter of the 119894thcell (ie Cell

21denotes the original voltage of the second cell)

Cell119895describes the mean of 119895th parameters 120575

119895denotes the

standard deviation of the voltage or SOC when 119895 equals to 1or 2 respectively 119899 is the number of cells

Then Euclid-distance is used to calculate the abnormalvalue of each cell in the pack The calculation formula [22] isdefined as follows

1198632(119885119898 119885119899) = radic

10038161003816100381610038161198851198981 minus 11988511989911003816100381610038161003816

2+10038161003816100381610038161198851198982 minus 1198851198992

1003816100381610038161003816

2

119882 (119885119898) =

119899

sum

119898=1

2

sum

119895=1

1198632(119885119898 119885119899)

(2)

Mathematical Problems in Engineering 3

The range of outlier

The total number of

Standard process the selectedparameters and calculate

abnormal value of each cell

Select normal andabnormal initial cluster

center respectively

and cluster the cells dynamically

Yes

Step 1

Step 2

Step 3

Step 4

Step 5

The attribute valuesof cells are equal

Yes

Getting theabnormal cells

Balancedbattery pack

No

No

the battery cells N

Obtain the sums of squared error Je

until Je reaches the minimum

values gt VOA1

Figure 3 The process of acquiring abnormal battery cells

where 1198632(119885119898 119885119899) (119898 = 1 40 119899 = 1 40 119898 = 119899)

represents the Euclid-distance between the 119898th cell and the119899th cell 119885

119898represents the 119898th cell which has two attributes

(ie 119885119898

= (1198851198981 1198851198982)) 119882(119885

119898) denotes the summation

of Euclid-distance betweenthe 119898th cell and the others Thesmaller the 119882(119885

119898) is the more normal the 119898th cell is On

the contrary the119898th battery is probably abnormal

Step 3 If the range of outlier values (the difference outliervalue between cell with the lowest and that with the highestoutlier value) of the cells is smaller than the thresholdVOA1 the process ends and the pack is considered balancedotherwise it goes to Step 4 VOA1 is defined and updated bythe formulation as follows

VOA1 =sum119899

119898=1119882(119885119898)

119899 (3)

Step 4 Set the cell with the lowest and that with the highestoutlier value as initial clustering centroids

Step 5 The other cells are assigned to their nearest clustercentroid all at once followed by recalculation of clustercentroid Then the other cells are individually reassignedif doing so will reduce the sums of squared error andcluster centroids are recomputed after each reassignment

[23]The process of obtaining the minimum sums of squarederror 119869

119890is formulated as follows

119869119898=

119873119898

sum

119898=1

10038171003817100381710038171003817119885119898minus 119862119895

10038171003817100381710038171003817

2

119885119898isin 119878119895

119869119890=

119896

sum

119895=1

119869119898=

119896

sum

119895=1

119873119898

sum

119898=1

10038171003817100381710038171003817119885119898minus 119862119895

10038171003817100381710038171003817

2

119885119898isin 119878119895

(4)

where 119869119898denotes the squared error of119898th cell 119869

119890is the sums

of all the squared errors119862119895is initial cluster centroid 119878

119895is the

normal category or the abnormal categoryWhen 119869

119890converges to a global minimum the process

jumps to the next step

Output The battery pack is balanced or unbalanced

By this time the unbalanced cells are recognized by theoutlier detection algorithm and can be balanced with thepassive balancing circuit that will be described in detail innext section

23 Balancing Control At present the balancing circuit canbe divided into two main groups [24] passive balancingcircuit and active cell balancing circuit Typical passive cellbalancing circuit also named shunt method uses switchesto control balancing Specifically shunt method is designedto use a resistor to discharge the unbalanced cell detectedby outlier detection algorithm With active cell balancingcircuit charge can be transferred between the cells in batterypack by a capacitor or an inductor Very little energy wouldbe wasted in this case compared to the passive balancingmethod However more switches and associated componentsare needed in the active balancing circuit And these addi-tional components may lead to higher cost and unreliabilityPassive balancing circuit has already been used in manyapplications for its simple structure and reliability Hencepassive cell balancing circuit is applied in this paper Asshown in Figure 4 every battery has a balancing circuit whichcomprises a resistor and a switch in series

3 Simulation Experiments

In order to compare the efficiency of the outlier detectionbalancing algorithm with the traditional balancing algo-rithms in detail the constant-current charging-discharging(CCCD)model and the software-in-the-loop platform (SILP)model for the BMS were established in Sections 31 and 32respectively The simulations were conducted on an Intel23 GHz Windows platform with 4GB RAM and imple-mented in MatlabSimulink The battery pack is modeled inSimulink using the electric drives library As can be seenin Figure 5(a) the battery pack model consists of five Li-ionbatteries connected in series and each battery is made up ofeight cellswhich are also connected in series (see Figure 5(b))The rated capacity and nominal voltage of cell are 65 Ahand 36V respectively and the values of other parameters areshown in Table 1

4 Mathematical Problems in Engineering

Table 1 The parameters of battery cell

Parameters Value UnitNominal voltage 36 VRated capacity 65 AhMaximum capacity 65 AhFully charged voltage 42 VNominal discharge current 282 AInternal resistance 0005 OhmCapacity at nominal voltage 587 Ah

The switch control signal

S1 S2 SnR1 R2 Rn

minus + minus + minus +

Cell1 Cell2 Celln

middot middot middot

middot middot middot

Figure 4 Passive cell balancing circuit

And the SOC for a fully charged cell model is 100 andfor an empty cell model is 0 The SOC is calculated basedon Coulomb-counting as

SOC = 100 (1 minus 1

119876int

119905

0

119894 (119905) 119889119905) (5)

where119876 is the rated capacity 119905 is the charging or dischargingtime 119894(119905) is the charging or discharging current

Here are several assumptions of the battery cell model inSimulink [21]

(a) The parameters of the model are deduced fromdischarging characteristics and assumed to be thesame for charging

(b) The internal resistance is supposed to be constantduring the charging and the discharging cycles anddoes not vary with the different amplitude of thecurrent

(c) The self-discharge of the battery is not representedand the battery has no memory effect

(d) The model does not take the temperature intoaccount

31 Constant Current Charging-DischargingModel and Simulation

311 CCCDModel and Test Condition As shown in Figure 6the CCCD model provides a 65-A (1C) constant chargingand discharge current for the battery pack In a seriallyconnected battery pack discharging or charging progress hasto be stopped immediately as soon as one of the terminalcell voltages falls below discharging voltage limit (DVL) orexceeds charging voltage limit (CVL) [2] The values of DVL

and CVL of the cell modeled in this paper are 3749V and42V and the SOC correspondingly reaches 30 and almost100

Figure 7 shows the simulated SOC current and voltageof 10th cell during one CCCD cycle The cell is charged bya 65-A constant current until voltage reaches CVL (42 V)and the corresponding SOC is almost 100 It is dischargedby the same current until voltage reaches DVL (3749V) andthe corresponding SOC is 30 The initial SOC and voltagesof the cells in the battery pack is that one cellrsquos SOC andvoltage are 4506 and 3794V while other cells are 3506and 3769V respectively The initial value of threshold VOA1of the proposed method is 1233

312 Simulation Results and Analysis The simulation resultsduring whole CCCD test cycle are shown in Table 2 for differ-ent balancing scenarios (no balancing voltage-based balanc-ing SOC-based balancing and outlier detection balancing)That the usable capacity calculated over balancing processof abnormal cell decreased by 0584Ah is the preconditionfor comparing the simulation results for different balancingscenarios

With no balancing the unbalanced cell (10th cell) inthe battery pack cannot be completely discharged beforecharging and the normal cells cannot be completely chargedbefore discharging during the whole test cycle as detailedin Figure 8 Hence the amount of usable energy of thepack decreased at the end of the charging process Withvoltage-based balancing the total voltage (charging cut-off)increased to 163017V and the SOC range of cells decreasedto 1030 but the frequency of balancing switch onoffreaches as high as 352 With outlier detection balancing thefrequency of the switching onoff was significantly reducedfrom 352 to 2 And the voltage variance (charging cut-off)and the SOC variance were reduced to 0008 and 0158respectively when compared with voltage-based and SOC-based balancing algorithm Additionally the charging time(after CCCD testing balancing algorithm off) of unbalancedbattery pack is 2091 s and the charging capacity is 3775Ahwhile balanced battery pack (same condition with unbal-anced pack testing) is 2413 s and 4389Ah respectively

The definitions of several evaluation standards in Table 2are as follows

Testing Time Time of the whole simulation process

Balancing Time Sum of the balancing time

Frequency of Switch on and off Sum of the balancing circuitswitch onoff times

Usable Capacity Decrease This can be calculated by theformula (6)

119862119894= int

119905

0

119894equ (119905) 119889119905

119894equ (119905) =119881119894 (119905)

119877

(6)

Mathematical Problems in Engineering 5

All parameters2

Parameters1

Battery5 ldquominusrdquo14

Battery1 ldquo+rdquo13

Battery1 ldquominusrdquo2

Battery1 ldquo+rdquo1

Vectorconcatenate1

Vectorconcatenate

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Cell 8

+

_

Cell 7

+

_

Cell 6

+

_

Cell 5

+

_

Cell 4

+

_

Cell 3

+

_

Cell 2

+

_

Cell 1

+_

Battery5

In1

In2Out1

Conn1

Conn2

Battery4

In1

In2Out1

Conn1

Conn2

Battery3

In1

In2Out1

Conn1

Conn2

Battery2

In1

In2Out1

Conn1

Conn2

Battery1

In1

In2Out1

Conn1

Conn2

Signals14

Input13

Signals2

Input1

(a) (b)

R

R

RR

RR

RR

RR

RR

RR

R1

R2

R3

R4

R5

R6

R7

R8

Figure 5 The schematic diagram of simulation model of pack (a) and battery (b)

where 119862119894is the decreased usable capacity of 119894th cell during

balancing process 119905 represents the balancing time 119894equ(119905) isthe balancing current 119881

119894(119905) denotes the voltage of battery at

119905 time 119877 (33 ohm) represents the resistance in cell balancingcircuit

As illustrated by Figure 9 when the voltage-based bal-ancing algorithm determined on and off the 10th cell asabnormal cell (upper plot) the outlier detection algorithmconstantly and accurately did that (lower plot) Meanwhilethe testing time of the simulation decreased to 23037 s whenimplemented outlier detection equalization algorithm onCCCD model The control signal ldquo1rdquo represents opening thebalancing circuit and ldquo0rdquo means shutting it down

The process that the battery pack transferred fromunbalanced state to balanced state using different balancing

algorithms under CCCD cycle is shown as Figure 10 AndFigure 11 shows the position variation of the abnormal cell(10th) detected by the proposed algorithm after balancedTheabnormal cell was closer to the other cells after it was balancedby outlier detection balancing algorithm

32 Software-in-the-Loop Platform Model ofBMS and Simulation

321 SILP Model of BMS and ECE + EUDC Test ConditionThe software-in-the-loop platform (SILP) model of BMS forelectric vehicles gives a new idea to test the validity andreliability for BMS and power battery in different properties[20 25] Generally speaking the model can also be used totest the feasibility and effectiveness of balance algorithms in

6 Mathematical Problems in Engineering

Powergui

DiscreteSwitch

Relay

Min

min

Max

max

Battery pack

Contr sigVoltage

SOC

Current

Conn1

Conn2

Balancingalgorithm

Voltage

SOCContr sig

1C

65

ge

++

minusminuss s

Ts = 01 s

Figure 6 The constant current charge-discharge model

Table 2 Performance comparisons of 3 algorithms under CCCD condition

Evaluation standard Balancing algorithmNo balancing Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 37171 29048 23037Balancing time (S) mdash 17681 17783 17775Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 352 2 2Charging cut-off

Total voltage (V) 161214 163017 162939 165738Voltage range (V) 0160 0058 0059 0055Voltage variance 0025 0009 0009 0008

Discharging cut-offTotal voltage (V) 149994 149965 154481 149965Voltage range (V) 0034 0005 0005 0001Voltage variance 0005 0001 0001 0

Charging time (S) 2091 2413 2413 2413SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0158

the early stage of design greatly improving the reliability ofthe algorithms In addition the SILP model can simulatemore different working conditions and the simulation resultshavemore significance in actual engineering when comparedwith the CCCD model The SILP model for BMS mainlyincludes driving cycle model driver model vehicle controlunit model battery management system software model

battery model power system model and wheel model Thewhole virtual environment model is shown in Figure 12

The ECE + EUDC test cycle is used for EU type approvaltesting of emissions and fuel consumption from light dutyvehicles As Figure 13 shows ECE + EUDC (bottom chart)cycle includes four ECE (upper left chart) segments repeatedwithout interruption followed by one EUDC (upper right

Mathematical Problems in Engineering 7

0 500 1000 1500 2000 2500 3000 350020406080

100

Time (s)

SOC

()

0 500 1000 1500 2000 2500 3000 3500

05

10

Time (s)Cu

rren

t (A

)

0 500 1000 1500 2000 2500 3000 35003638

44244

Time (s)

Volta

ge (V

)

minus5

minus10

Figure 7 The SOC current and voltage of 10th cell during one 1C CCCD test cycle

0 05 1 15 2 25 3 35 4 45 520

40

60

80

100

Time (s)

SOC

()

Abnormal cellNormal cells

times104

(a)

Abnormal cellNormal cells

0 05 1 15 2 25 3 35 4 45 536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 8 SOC (a) and voltage (b) of the unbalanced pack

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(a)

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(b)

Figure 9 Balancing control signal of voltage-based (a) and outlier detection (b) balancing

chart) segment According to Figure 14 the battery pack isdischarged with two ECE + EUDC cycle until 2400 s andcharged by the generator in the next 822 s since the SOCof thepack reduced to 30 Simulation test starts in the situationthat there is one cellrsquos SOC and voltage value are 6483 and4140V and the others are 5483 and 4063V respectively

322 Simulation Result and Analysis The simulation resultsduring thewhole ECE+EUDC test cycle are shown inTable 3for different balancing scenarios (no balancing voltage-based balancing SOC-based balancing and outlier detection

balancing algorithm)That the usable capacity calculated overbalancing process of abnormal cell decreased by 0584Ah isthe precondition for comparing the simulation results fordifferent balancing scenarios

With no balancing the unbalanced cell in the batterypack could not be completely discharged before charging andthe normal cells could not be completely charged before dis-charging during the whole test cycle as detailed in Figure 15Hence the amount of usable energy of the pack decreased atthe end of the charging process With voltage-based balanc-ing the total voltage (charging cut-off) increased to 164738V

8 Mathematical Problems in Engineering

0 05 1 15 2 25 3 35 4 45 5 5520406080

100

Time (s)

SOC

()

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

times104

(a)

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

0 05 1 15 2 25 3 35 4 45 5 5536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 10 SOC (a) and voltage (b) of pack with balancing algorithms during CCCD cycle

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(a)

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(b)

Figure 11 The position of the abnormal cell before it was balanced (a) and after it was balanced (b)

and the voltage variance (discharging cut-off) decreased to0003 but the frequency of balancing switch onoff reaches ashigh as 1150 With outlier detection balancing the frequencyof the switching onoff was significantly reduced from 1150to 2 and reduced the voltage variance (charging cut-off) andthe SOC variance to 0 and 0157 respectively when comparedwith voltage-based and SOC-based balancing algorithmFurthermore the proposed balancing algorithm increasedthe total charging cut-off voltage from 161214V to 165738Vwhen compared with the pack without balancing And it alsoreduced the discharging cut-off voltage variance and the SOCvariance to 0 and 0157 respectively

The process in which the battery pack transferred fromunbalanced state to balanced state with different balancingalgorithms under ECE + EUDC test cycle is shown as

Figure 16 With outlier detection balancing algorithm thecells in the battery pack can be completely chargeddischargeat the same time and thus increase the available energy storedin the pack

4 Conclusions

Aiming at the problem that present cell-balancing algorithmscannot identify the unbalanced cells in lithium-ion batterypack accurately in real-time an algorithm based on outlierdetection was proposed in this paper The unbalanced cellswere identified by the proposed balancing algorithms andbalanced by shunt method using switches After validatingthe efficiency of the balancing algorithms on two simulationmodels the advantages of the proposed algorithm have been

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

The range of outlier

The total number of

Standard process the selectedparameters and calculate

abnormal value of each cell

Select normal andabnormal initial cluster

center respectively

and cluster the cells dynamically

Yes

Step 1

Step 2

Step 3

Step 4

Step 5

The attribute valuesof cells are equal

Yes

Getting theabnormal cells

Balancedbattery pack

No

No

the battery cells N

Obtain the sums of squared error Je

until Je reaches the minimum

values gt VOA1

Figure 3 The process of acquiring abnormal battery cells

where 1198632(119885119898 119885119899) (119898 = 1 40 119899 = 1 40 119898 = 119899)

represents the Euclid-distance between the 119898th cell and the119899th cell 119885

119898represents the 119898th cell which has two attributes

(ie 119885119898

= (1198851198981 1198851198982)) 119882(119885

119898) denotes the summation

of Euclid-distance betweenthe 119898th cell and the others Thesmaller the 119882(119885

119898) is the more normal the 119898th cell is On

the contrary the119898th battery is probably abnormal

Step 3 If the range of outlier values (the difference outliervalue between cell with the lowest and that with the highestoutlier value) of the cells is smaller than the thresholdVOA1 the process ends and the pack is considered balancedotherwise it goes to Step 4 VOA1 is defined and updated bythe formulation as follows

VOA1 =sum119899

119898=1119882(119885119898)

119899 (3)

Step 4 Set the cell with the lowest and that with the highestoutlier value as initial clustering centroids

Step 5 The other cells are assigned to their nearest clustercentroid all at once followed by recalculation of clustercentroid Then the other cells are individually reassignedif doing so will reduce the sums of squared error andcluster centroids are recomputed after each reassignment

[23]The process of obtaining the minimum sums of squarederror 119869

119890is formulated as follows

119869119898=

119873119898

sum

119898=1

10038171003817100381710038171003817119885119898minus 119862119895

10038171003817100381710038171003817

2

119885119898isin 119878119895

119869119890=

119896

sum

119895=1

119869119898=

119896

sum

119895=1

119873119898

sum

119898=1

10038171003817100381710038171003817119885119898minus 119862119895

10038171003817100381710038171003817

2

119885119898isin 119878119895

(4)

where 119869119898denotes the squared error of119898th cell 119869

119890is the sums

of all the squared errors119862119895is initial cluster centroid 119878

119895is the

normal category or the abnormal categoryWhen 119869

119890converges to a global minimum the process

jumps to the next step

Output The battery pack is balanced or unbalanced

By this time the unbalanced cells are recognized by theoutlier detection algorithm and can be balanced with thepassive balancing circuit that will be described in detail innext section

23 Balancing Control At present the balancing circuit canbe divided into two main groups [24] passive balancingcircuit and active cell balancing circuit Typical passive cellbalancing circuit also named shunt method uses switchesto control balancing Specifically shunt method is designedto use a resistor to discharge the unbalanced cell detectedby outlier detection algorithm With active cell balancingcircuit charge can be transferred between the cells in batterypack by a capacitor or an inductor Very little energy wouldbe wasted in this case compared to the passive balancingmethod However more switches and associated componentsare needed in the active balancing circuit And these addi-tional components may lead to higher cost and unreliabilityPassive balancing circuit has already been used in manyapplications for its simple structure and reliability Hencepassive cell balancing circuit is applied in this paper Asshown in Figure 4 every battery has a balancing circuit whichcomprises a resistor and a switch in series

3 Simulation Experiments

In order to compare the efficiency of the outlier detectionbalancing algorithm with the traditional balancing algo-rithms in detail the constant-current charging-discharging(CCCD)model and the software-in-the-loop platform (SILP)model for the BMS were established in Sections 31 and 32respectively The simulations were conducted on an Intel23 GHz Windows platform with 4GB RAM and imple-mented in MatlabSimulink The battery pack is modeled inSimulink using the electric drives library As can be seenin Figure 5(a) the battery pack model consists of five Li-ionbatteries connected in series and each battery is made up ofeight cellswhich are also connected in series (see Figure 5(b))The rated capacity and nominal voltage of cell are 65 Ahand 36V respectively and the values of other parameters areshown in Table 1

4 Mathematical Problems in Engineering

Table 1 The parameters of battery cell

Parameters Value UnitNominal voltage 36 VRated capacity 65 AhMaximum capacity 65 AhFully charged voltage 42 VNominal discharge current 282 AInternal resistance 0005 OhmCapacity at nominal voltage 587 Ah

The switch control signal

S1 S2 SnR1 R2 Rn

minus + minus + minus +

Cell1 Cell2 Celln

middot middot middot

middot middot middot

Figure 4 Passive cell balancing circuit

And the SOC for a fully charged cell model is 100 andfor an empty cell model is 0 The SOC is calculated basedon Coulomb-counting as

SOC = 100 (1 minus 1

119876int

119905

0

119894 (119905) 119889119905) (5)

where119876 is the rated capacity 119905 is the charging or dischargingtime 119894(119905) is the charging or discharging current

Here are several assumptions of the battery cell model inSimulink [21]

(a) The parameters of the model are deduced fromdischarging characteristics and assumed to be thesame for charging

(b) The internal resistance is supposed to be constantduring the charging and the discharging cycles anddoes not vary with the different amplitude of thecurrent

(c) The self-discharge of the battery is not representedand the battery has no memory effect

(d) The model does not take the temperature intoaccount

31 Constant Current Charging-DischargingModel and Simulation

311 CCCDModel and Test Condition As shown in Figure 6the CCCD model provides a 65-A (1C) constant chargingand discharge current for the battery pack In a seriallyconnected battery pack discharging or charging progress hasto be stopped immediately as soon as one of the terminalcell voltages falls below discharging voltage limit (DVL) orexceeds charging voltage limit (CVL) [2] The values of DVL

and CVL of the cell modeled in this paper are 3749V and42V and the SOC correspondingly reaches 30 and almost100

Figure 7 shows the simulated SOC current and voltageof 10th cell during one CCCD cycle The cell is charged bya 65-A constant current until voltage reaches CVL (42 V)and the corresponding SOC is almost 100 It is dischargedby the same current until voltage reaches DVL (3749V) andthe corresponding SOC is 30 The initial SOC and voltagesof the cells in the battery pack is that one cellrsquos SOC andvoltage are 4506 and 3794V while other cells are 3506and 3769V respectively The initial value of threshold VOA1of the proposed method is 1233

312 Simulation Results and Analysis The simulation resultsduring whole CCCD test cycle are shown in Table 2 for differ-ent balancing scenarios (no balancing voltage-based balanc-ing SOC-based balancing and outlier detection balancing)That the usable capacity calculated over balancing processof abnormal cell decreased by 0584Ah is the preconditionfor comparing the simulation results for different balancingscenarios

With no balancing the unbalanced cell (10th cell) inthe battery pack cannot be completely discharged beforecharging and the normal cells cannot be completely chargedbefore discharging during the whole test cycle as detailedin Figure 8 Hence the amount of usable energy of thepack decreased at the end of the charging process Withvoltage-based balancing the total voltage (charging cut-off)increased to 163017V and the SOC range of cells decreasedto 1030 but the frequency of balancing switch onoffreaches as high as 352 With outlier detection balancing thefrequency of the switching onoff was significantly reducedfrom 352 to 2 And the voltage variance (charging cut-off)and the SOC variance were reduced to 0008 and 0158respectively when compared with voltage-based and SOC-based balancing algorithm Additionally the charging time(after CCCD testing balancing algorithm off) of unbalancedbattery pack is 2091 s and the charging capacity is 3775Ahwhile balanced battery pack (same condition with unbal-anced pack testing) is 2413 s and 4389Ah respectively

The definitions of several evaluation standards in Table 2are as follows

Testing Time Time of the whole simulation process

Balancing Time Sum of the balancing time

Frequency of Switch on and off Sum of the balancing circuitswitch onoff times

Usable Capacity Decrease This can be calculated by theformula (6)

119862119894= int

119905

0

119894equ (119905) 119889119905

119894equ (119905) =119881119894 (119905)

119877

(6)

Mathematical Problems in Engineering 5

All parameters2

Parameters1

Battery5 ldquominusrdquo14

Battery1 ldquo+rdquo13

Battery1 ldquominusrdquo2

Battery1 ldquo+rdquo1

Vectorconcatenate1

Vectorconcatenate

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Cell 8

+

_

Cell 7

+

_

Cell 6

+

_

Cell 5

+

_

Cell 4

+

_

Cell 3

+

_

Cell 2

+

_

Cell 1

+_

Battery5

In1

In2Out1

Conn1

Conn2

Battery4

In1

In2Out1

Conn1

Conn2

Battery3

In1

In2Out1

Conn1

Conn2

Battery2

In1

In2Out1

Conn1

Conn2

Battery1

In1

In2Out1

Conn1

Conn2

Signals14

Input13

Signals2

Input1

(a) (b)

R

R

RR

RR

RR

RR

RR

RR

R1

R2

R3

R4

R5

R6

R7

R8

Figure 5 The schematic diagram of simulation model of pack (a) and battery (b)

where 119862119894is the decreased usable capacity of 119894th cell during

balancing process 119905 represents the balancing time 119894equ(119905) isthe balancing current 119881

119894(119905) denotes the voltage of battery at

119905 time 119877 (33 ohm) represents the resistance in cell balancingcircuit

As illustrated by Figure 9 when the voltage-based bal-ancing algorithm determined on and off the 10th cell asabnormal cell (upper plot) the outlier detection algorithmconstantly and accurately did that (lower plot) Meanwhilethe testing time of the simulation decreased to 23037 s whenimplemented outlier detection equalization algorithm onCCCD model The control signal ldquo1rdquo represents opening thebalancing circuit and ldquo0rdquo means shutting it down

The process that the battery pack transferred fromunbalanced state to balanced state using different balancing

algorithms under CCCD cycle is shown as Figure 10 AndFigure 11 shows the position variation of the abnormal cell(10th) detected by the proposed algorithm after balancedTheabnormal cell was closer to the other cells after it was balancedby outlier detection balancing algorithm

32 Software-in-the-Loop Platform Model ofBMS and Simulation

321 SILP Model of BMS and ECE + EUDC Test ConditionThe software-in-the-loop platform (SILP) model of BMS forelectric vehicles gives a new idea to test the validity andreliability for BMS and power battery in different properties[20 25] Generally speaking the model can also be used totest the feasibility and effectiveness of balance algorithms in

6 Mathematical Problems in Engineering

Powergui

DiscreteSwitch

Relay

Min

min

Max

max

Battery pack

Contr sigVoltage

SOC

Current

Conn1

Conn2

Balancingalgorithm

Voltage

SOCContr sig

1C

65

ge

++

minusminuss s

Ts = 01 s

Figure 6 The constant current charge-discharge model

Table 2 Performance comparisons of 3 algorithms under CCCD condition

Evaluation standard Balancing algorithmNo balancing Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 37171 29048 23037Balancing time (S) mdash 17681 17783 17775Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 352 2 2Charging cut-off

Total voltage (V) 161214 163017 162939 165738Voltage range (V) 0160 0058 0059 0055Voltage variance 0025 0009 0009 0008

Discharging cut-offTotal voltage (V) 149994 149965 154481 149965Voltage range (V) 0034 0005 0005 0001Voltage variance 0005 0001 0001 0

Charging time (S) 2091 2413 2413 2413SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0158

the early stage of design greatly improving the reliability ofthe algorithms In addition the SILP model can simulatemore different working conditions and the simulation resultshavemore significance in actual engineering when comparedwith the CCCD model The SILP model for BMS mainlyincludes driving cycle model driver model vehicle controlunit model battery management system software model

battery model power system model and wheel model Thewhole virtual environment model is shown in Figure 12

The ECE + EUDC test cycle is used for EU type approvaltesting of emissions and fuel consumption from light dutyvehicles As Figure 13 shows ECE + EUDC (bottom chart)cycle includes four ECE (upper left chart) segments repeatedwithout interruption followed by one EUDC (upper right

Mathematical Problems in Engineering 7

0 500 1000 1500 2000 2500 3000 350020406080

100

Time (s)

SOC

()

0 500 1000 1500 2000 2500 3000 3500

05

10

Time (s)Cu

rren

t (A

)

0 500 1000 1500 2000 2500 3000 35003638

44244

Time (s)

Volta

ge (V

)

minus5

minus10

Figure 7 The SOC current and voltage of 10th cell during one 1C CCCD test cycle

0 05 1 15 2 25 3 35 4 45 520

40

60

80

100

Time (s)

SOC

()

Abnormal cellNormal cells

times104

(a)

Abnormal cellNormal cells

0 05 1 15 2 25 3 35 4 45 536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 8 SOC (a) and voltage (b) of the unbalanced pack

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(a)

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(b)

Figure 9 Balancing control signal of voltage-based (a) and outlier detection (b) balancing

chart) segment According to Figure 14 the battery pack isdischarged with two ECE + EUDC cycle until 2400 s andcharged by the generator in the next 822 s since the SOCof thepack reduced to 30 Simulation test starts in the situationthat there is one cellrsquos SOC and voltage value are 6483 and4140V and the others are 5483 and 4063V respectively

322 Simulation Result and Analysis The simulation resultsduring thewhole ECE+EUDC test cycle are shown inTable 3for different balancing scenarios (no balancing voltage-based balancing SOC-based balancing and outlier detection

balancing algorithm)That the usable capacity calculated overbalancing process of abnormal cell decreased by 0584Ah isthe precondition for comparing the simulation results fordifferent balancing scenarios

With no balancing the unbalanced cell in the batterypack could not be completely discharged before charging andthe normal cells could not be completely charged before dis-charging during the whole test cycle as detailed in Figure 15Hence the amount of usable energy of the pack decreased atthe end of the charging process With voltage-based balanc-ing the total voltage (charging cut-off) increased to 164738V

8 Mathematical Problems in Engineering

0 05 1 15 2 25 3 35 4 45 5 5520406080

100

Time (s)

SOC

()

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

times104

(a)

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

0 05 1 15 2 25 3 35 4 45 5 5536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 10 SOC (a) and voltage (b) of pack with balancing algorithms during CCCD cycle

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(a)

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(b)

Figure 11 The position of the abnormal cell before it was balanced (a) and after it was balanced (b)

and the voltage variance (discharging cut-off) decreased to0003 but the frequency of balancing switch onoff reaches ashigh as 1150 With outlier detection balancing the frequencyof the switching onoff was significantly reduced from 1150to 2 and reduced the voltage variance (charging cut-off) andthe SOC variance to 0 and 0157 respectively when comparedwith voltage-based and SOC-based balancing algorithmFurthermore the proposed balancing algorithm increasedthe total charging cut-off voltage from 161214V to 165738Vwhen compared with the pack without balancing And it alsoreduced the discharging cut-off voltage variance and the SOCvariance to 0 and 0157 respectively

The process in which the battery pack transferred fromunbalanced state to balanced state with different balancingalgorithms under ECE + EUDC test cycle is shown as

Figure 16 With outlier detection balancing algorithm thecells in the battery pack can be completely chargeddischargeat the same time and thus increase the available energy storedin the pack

4 Conclusions

Aiming at the problem that present cell-balancing algorithmscannot identify the unbalanced cells in lithium-ion batterypack accurately in real-time an algorithm based on outlierdetection was proposed in this paper The unbalanced cellswere identified by the proposed balancing algorithms andbalanced by shunt method using switches After validatingthe efficiency of the balancing algorithms on two simulationmodels the advantages of the proposed algorithm have been

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Table 1 The parameters of battery cell

Parameters Value UnitNominal voltage 36 VRated capacity 65 AhMaximum capacity 65 AhFully charged voltage 42 VNominal discharge current 282 AInternal resistance 0005 OhmCapacity at nominal voltage 587 Ah

The switch control signal

S1 S2 SnR1 R2 Rn

minus + minus + minus +

Cell1 Cell2 Celln

middot middot middot

middot middot middot

Figure 4 Passive cell balancing circuit

And the SOC for a fully charged cell model is 100 andfor an empty cell model is 0 The SOC is calculated basedon Coulomb-counting as

SOC = 100 (1 minus 1

119876int

119905

0

119894 (119905) 119889119905) (5)

where119876 is the rated capacity 119905 is the charging or dischargingtime 119894(119905) is the charging or discharging current

Here are several assumptions of the battery cell model inSimulink [21]

(a) The parameters of the model are deduced fromdischarging characteristics and assumed to be thesame for charging

(b) The internal resistance is supposed to be constantduring the charging and the discharging cycles anddoes not vary with the different amplitude of thecurrent

(c) The self-discharge of the battery is not representedand the battery has no memory effect

(d) The model does not take the temperature intoaccount

31 Constant Current Charging-DischargingModel and Simulation

311 CCCDModel and Test Condition As shown in Figure 6the CCCD model provides a 65-A (1C) constant chargingand discharge current for the battery pack In a seriallyconnected battery pack discharging or charging progress hasto be stopped immediately as soon as one of the terminalcell voltages falls below discharging voltage limit (DVL) orexceeds charging voltage limit (CVL) [2] The values of DVL

and CVL of the cell modeled in this paper are 3749V and42V and the SOC correspondingly reaches 30 and almost100

Figure 7 shows the simulated SOC current and voltageof 10th cell during one CCCD cycle The cell is charged bya 65-A constant current until voltage reaches CVL (42 V)and the corresponding SOC is almost 100 It is dischargedby the same current until voltage reaches DVL (3749V) andthe corresponding SOC is 30 The initial SOC and voltagesof the cells in the battery pack is that one cellrsquos SOC andvoltage are 4506 and 3794V while other cells are 3506and 3769V respectively The initial value of threshold VOA1of the proposed method is 1233

312 Simulation Results and Analysis The simulation resultsduring whole CCCD test cycle are shown in Table 2 for differ-ent balancing scenarios (no balancing voltage-based balanc-ing SOC-based balancing and outlier detection balancing)That the usable capacity calculated over balancing processof abnormal cell decreased by 0584Ah is the preconditionfor comparing the simulation results for different balancingscenarios

With no balancing the unbalanced cell (10th cell) inthe battery pack cannot be completely discharged beforecharging and the normal cells cannot be completely chargedbefore discharging during the whole test cycle as detailedin Figure 8 Hence the amount of usable energy of thepack decreased at the end of the charging process Withvoltage-based balancing the total voltage (charging cut-off)increased to 163017V and the SOC range of cells decreasedto 1030 but the frequency of balancing switch onoffreaches as high as 352 With outlier detection balancing thefrequency of the switching onoff was significantly reducedfrom 352 to 2 And the voltage variance (charging cut-off)and the SOC variance were reduced to 0008 and 0158respectively when compared with voltage-based and SOC-based balancing algorithm Additionally the charging time(after CCCD testing balancing algorithm off) of unbalancedbattery pack is 2091 s and the charging capacity is 3775Ahwhile balanced battery pack (same condition with unbal-anced pack testing) is 2413 s and 4389Ah respectively

The definitions of several evaluation standards in Table 2are as follows

Testing Time Time of the whole simulation process

Balancing Time Sum of the balancing time

Frequency of Switch on and off Sum of the balancing circuitswitch onoff times

Usable Capacity Decrease This can be calculated by theformula (6)

119862119894= int

119905

0

119894equ (119905) 119889119905

119894equ (119905) =119881119894 (119905)

119877

(6)

Mathematical Problems in Engineering 5

All parameters2

Parameters1

Battery5 ldquominusrdquo14

Battery1 ldquo+rdquo13

Battery1 ldquominusrdquo2

Battery1 ldquo+rdquo1

Vectorconcatenate1

Vectorconcatenate

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Cell 8

+

_

Cell 7

+

_

Cell 6

+

_

Cell 5

+

_

Cell 4

+

_

Cell 3

+

_

Cell 2

+

_

Cell 1

+_

Battery5

In1

In2Out1

Conn1

Conn2

Battery4

In1

In2Out1

Conn1

Conn2

Battery3

In1

In2Out1

Conn1

Conn2

Battery2

In1

In2Out1

Conn1

Conn2

Battery1

In1

In2Out1

Conn1

Conn2

Signals14

Input13

Signals2

Input1

(a) (b)

R

R

RR

RR

RR

RR

RR

RR

R1

R2

R3

R4

R5

R6

R7

R8

Figure 5 The schematic diagram of simulation model of pack (a) and battery (b)

where 119862119894is the decreased usable capacity of 119894th cell during

balancing process 119905 represents the balancing time 119894equ(119905) isthe balancing current 119881

119894(119905) denotes the voltage of battery at

119905 time 119877 (33 ohm) represents the resistance in cell balancingcircuit

As illustrated by Figure 9 when the voltage-based bal-ancing algorithm determined on and off the 10th cell asabnormal cell (upper plot) the outlier detection algorithmconstantly and accurately did that (lower plot) Meanwhilethe testing time of the simulation decreased to 23037 s whenimplemented outlier detection equalization algorithm onCCCD model The control signal ldquo1rdquo represents opening thebalancing circuit and ldquo0rdquo means shutting it down

The process that the battery pack transferred fromunbalanced state to balanced state using different balancing

algorithms under CCCD cycle is shown as Figure 10 AndFigure 11 shows the position variation of the abnormal cell(10th) detected by the proposed algorithm after balancedTheabnormal cell was closer to the other cells after it was balancedby outlier detection balancing algorithm

32 Software-in-the-Loop Platform Model ofBMS and Simulation

321 SILP Model of BMS and ECE + EUDC Test ConditionThe software-in-the-loop platform (SILP) model of BMS forelectric vehicles gives a new idea to test the validity andreliability for BMS and power battery in different properties[20 25] Generally speaking the model can also be used totest the feasibility and effectiveness of balance algorithms in

6 Mathematical Problems in Engineering

Powergui

DiscreteSwitch

Relay

Min

min

Max

max

Battery pack

Contr sigVoltage

SOC

Current

Conn1

Conn2

Balancingalgorithm

Voltage

SOCContr sig

1C

65

ge

++

minusminuss s

Ts = 01 s

Figure 6 The constant current charge-discharge model

Table 2 Performance comparisons of 3 algorithms under CCCD condition

Evaluation standard Balancing algorithmNo balancing Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 37171 29048 23037Balancing time (S) mdash 17681 17783 17775Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 352 2 2Charging cut-off

Total voltage (V) 161214 163017 162939 165738Voltage range (V) 0160 0058 0059 0055Voltage variance 0025 0009 0009 0008

Discharging cut-offTotal voltage (V) 149994 149965 154481 149965Voltage range (V) 0034 0005 0005 0001Voltage variance 0005 0001 0001 0

Charging time (S) 2091 2413 2413 2413SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0158

the early stage of design greatly improving the reliability ofthe algorithms In addition the SILP model can simulatemore different working conditions and the simulation resultshavemore significance in actual engineering when comparedwith the CCCD model The SILP model for BMS mainlyincludes driving cycle model driver model vehicle controlunit model battery management system software model

battery model power system model and wheel model Thewhole virtual environment model is shown in Figure 12

The ECE + EUDC test cycle is used for EU type approvaltesting of emissions and fuel consumption from light dutyvehicles As Figure 13 shows ECE + EUDC (bottom chart)cycle includes four ECE (upper left chart) segments repeatedwithout interruption followed by one EUDC (upper right

Mathematical Problems in Engineering 7

0 500 1000 1500 2000 2500 3000 350020406080

100

Time (s)

SOC

()

0 500 1000 1500 2000 2500 3000 3500

05

10

Time (s)Cu

rren

t (A

)

0 500 1000 1500 2000 2500 3000 35003638

44244

Time (s)

Volta

ge (V

)

minus5

minus10

Figure 7 The SOC current and voltage of 10th cell during one 1C CCCD test cycle

0 05 1 15 2 25 3 35 4 45 520

40

60

80

100

Time (s)

SOC

()

Abnormal cellNormal cells

times104

(a)

Abnormal cellNormal cells

0 05 1 15 2 25 3 35 4 45 536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 8 SOC (a) and voltage (b) of the unbalanced pack

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(a)

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(b)

Figure 9 Balancing control signal of voltage-based (a) and outlier detection (b) balancing

chart) segment According to Figure 14 the battery pack isdischarged with two ECE + EUDC cycle until 2400 s andcharged by the generator in the next 822 s since the SOCof thepack reduced to 30 Simulation test starts in the situationthat there is one cellrsquos SOC and voltage value are 6483 and4140V and the others are 5483 and 4063V respectively

322 Simulation Result and Analysis The simulation resultsduring thewhole ECE+EUDC test cycle are shown inTable 3for different balancing scenarios (no balancing voltage-based balancing SOC-based balancing and outlier detection

balancing algorithm)That the usable capacity calculated overbalancing process of abnormal cell decreased by 0584Ah isthe precondition for comparing the simulation results fordifferent balancing scenarios

With no balancing the unbalanced cell in the batterypack could not be completely discharged before charging andthe normal cells could not be completely charged before dis-charging during the whole test cycle as detailed in Figure 15Hence the amount of usable energy of the pack decreased atthe end of the charging process With voltage-based balanc-ing the total voltage (charging cut-off) increased to 164738V

8 Mathematical Problems in Engineering

0 05 1 15 2 25 3 35 4 45 5 5520406080

100

Time (s)

SOC

()

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

times104

(a)

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

0 05 1 15 2 25 3 35 4 45 5 5536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 10 SOC (a) and voltage (b) of pack with balancing algorithms during CCCD cycle

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(a)

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(b)

Figure 11 The position of the abnormal cell before it was balanced (a) and after it was balanced (b)

and the voltage variance (discharging cut-off) decreased to0003 but the frequency of balancing switch onoff reaches ashigh as 1150 With outlier detection balancing the frequencyof the switching onoff was significantly reduced from 1150to 2 and reduced the voltage variance (charging cut-off) andthe SOC variance to 0 and 0157 respectively when comparedwith voltage-based and SOC-based balancing algorithmFurthermore the proposed balancing algorithm increasedthe total charging cut-off voltage from 161214V to 165738Vwhen compared with the pack without balancing And it alsoreduced the discharging cut-off voltage variance and the SOCvariance to 0 and 0157 respectively

The process in which the battery pack transferred fromunbalanced state to balanced state with different balancingalgorithms under ECE + EUDC test cycle is shown as

Figure 16 With outlier detection balancing algorithm thecells in the battery pack can be completely chargeddischargeat the same time and thus increase the available energy storedin the pack

4 Conclusions

Aiming at the problem that present cell-balancing algorithmscannot identify the unbalanced cells in lithium-ion batterypack accurately in real-time an algorithm based on outlierdetection was proposed in this paper The unbalanced cellswere identified by the proposed balancing algorithms andbalanced by shunt method using switches After validatingthe efficiency of the balancing algorithms on two simulationmodels the advantages of the proposed algorithm have been

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

All parameters2

Parameters1

Battery5 ldquominusrdquo14

Battery1 ldquo+rdquo13

Battery1 ldquominusrdquo2

Battery1 ldquo+rdquo1

Vectorconcatenate1

Vectorconcatenate

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Sig

Cell 8

+

_

Cell 7

+

_

Cell 6

+

_

Cell 5

+

_

Cell 4

+

_

Cell 3

+

_

Cell 2

+

_

Cell 1

+_

Battery5

In1

In2Out1

Conn1

Conn2

Battery4

In1

In2Out1

Conn1

Conn2

Battery3

In1

In2Out1

Conn1

Conn2

Battery2

In1

In2Out1

Conn1

Conn2

Battery1

In1

In2Out1

Conn1

Conn2

Signals14

Input13

Signals2

Input1

(a) (b)

R

R

RR

RR

RR

RR

RR

RR

R1

R2

R3

R4

R5

R6

R7

R8

Figure 5 The schematic diagram of simulation model of pack (a) and battery (b)

where 119862119894is the decreased usable capacity of 119894th cell during

balancing process 119905 represents the balancing time 119894equ(119905) isthe balancing current 119881

119894(119905) denotes the voltage of battery at

119905 time 119877 (33 ohm) represents the resistance in cell balancingcircuit

As illustrated by Figure 9 when the voltage-based bal-ancing algorithm determined on and off the 10th cell asabnormal cell (upper plot) the outlier detection algorithmconstantly and accurately did that (lower plot) Meanwhilethe testing time of the simulation decreased to 23037 s whenimplemented outlier detection equalization algorithm onCCCD model The control signal ldquo1rdquo represents opening thebalancing circuit and ldquo0rdquo means shutting it down

The process that the battery pack transferred fromunbalanced state to balanced state using different balancing

algorithms under CCCD cycle is shown as Figure 10 AndFigure 11 shows the position variation of the abnormal cell(10th) detected by the proposed algorithm after balancedTheabnormal cell was closer to the other cells after it was balancedby outlier detection balancing algorithm

32 Software-in-the-Loop Platform Model ofBMS and Simulation

321 SILP Model of BMS and ECE + EUDC Test ConditionThe software-in-the-loop platform (SILP) model of BMS forelectric vehicles gives a new idea to test the validity andreliability for BMS and power battery in different properties[20 25] Generally speaking the model can also be used totest the feasibility and effectiveness of balance algorithms in

6 Mathematical Problems in Engineering

Powergui

DiscreteSwitch

Relay

Min

min

Max

max

Battery pack

Contr sigVoltage

SOC

Current

Conn1

Conn2

Balancingalgorithm

Voltage

SOCContr sig

1C

65

ge

++

minusminuss s

Ts = 01 s

Figure 6 The constant current charge-discharge model

Table 2 Performance comparisons of 3 algorithms under CCCD condition

Evaluation standard Balancing algorithmNo balancing Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 37171 29048 23037Balancing time (S) mdash 17681 17783 17775Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 352 2 2Charging cut-off

Total voltage (V) 161214 163017 162939 165738Voltage range (V) 0160 0058 0059 0055Voltage variance 0025 0009 0009 0008

Discharging cut-offTotal voltage (V) 149994 149965 154481 149965Voltage range (V) 0034 0005 0005 0001Voltage variance 0005 0001 0001 0

Charging time (S) 2091 2413 2413 2413SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0158

the early stage of design greatly improving the reliability ofthe algorithms In addition the SILP model can simulatemore different working conditions and the simulation resultshavemore significance in actual engineering when comparedwith the CCCD model The SILP model for BMS mainlyincludes driving cycle model driver model vehicle controlunit model battery management system software model

battery model power system model and wheel model Thewhole virtual environment model is shown in Figure 12

The ECE + EUDC test cycle is used for EU type approvaltesting of emissions and fuel consumption from light dutyvehicles As Figure 13 shows ECE + EUDC (bottom chart)cycle includes four ECE (upper left chart) segments repeatedwithout interruption followed by one EUDC (upper right

Mathematical Problems in Engineering 7

0 500 1000 1500 2000 2500 3000 350020406080

100

Time (s)

SOC

()

0 500 1000 1500 2000 2500 3000 3500

05

10

Time (s)Cu

rren

t (A

)

0 500 1000 1500 2000 2500 3000 35003638

44244

Time (s)

Volta

ge (V

)

minus5

minus10

Figure 7 The SOC current and voltage of 10th cell during one 1C CCCD test cycle

0 05 1 15 2 25 3 35 4 45 520

40

60

80

100

Time (s)

SOC

()

Abnormal cellNormal cells

times104

(a)

Abnormal cellNormal cells

0 05 1 15 2 25 3 35 4 45 536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 8 SOC (a) and voltage (b) of the unbalanced pack

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(a)

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(b)

Figure 9 Balancing control signal of voltage-based (a) and outlier detection (b) balancing

chart) segment According to Figure 14 the battery pack isdischarged with two ECE + EUDC cycle until 2400 s andcharged by the generator in the next 822 s since the SOCof thepack reduced to 30 Simulation test starts in the situationthat there is one cellrsquos SOC and voltage value are 6483 and4140V and the others are 5483 and 4063V respectively

322 Simulation Result and Analysis The simulation resultsduring thewhole ECE+EUDC test cycle are shown inTable 3for different balancing scenarios (no balancing voltage-based balancing SOC-based balancing and outlier detection

balancing algorithm)That the usable capacity calculated overbalancing process of abnormal cell decreased by 0584Ah isthe precondition for comparing the simulation results fordifferent balancing scenarios

With no balancing the unbalanced cell in the batterypack could not be completely discharged before charging andthe normal cells could not be completely charged before dis-charging during the whole test cycle as detailed in Figure 15Hence the amount of usable energy of the pack decreased atthe end of the charging process With voltage-based balanc-ing the total voltage (charging cut-off) increased to 164738V

8 Mathematical Problems in Engineering

0 05 1 15 2 25 3 35 4 45 5 5520406080

100

Time (s)

SOC

()

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

times104

(a)

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

0 05 1 15 2 25 3 35 4 45 5 5536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 10 SOC (a) and voltage (b) of pack with balancing algorithms during CCCD cycle

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(a)

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(b)

Figure 11 The position of the abnormal cell before it was balanced (a) and after it was balanced (b)

and the voltage variance (discharging cut-off) decreased to0003 but the frequency of balancing switch onoff reaches ashigh as 1150 With outlier detection balancing the frequencyof the switching onoff was significantly reduced from 1150to 2 and reduced the voltage variance (charging cut-off) andthe SOC variance to 0 and 0157 respectively when comparedwith voltage-based and SOC-based balancing algorithmFurthermore the proposed balancing algorithm increasedthe total charging cut-off voltage from 161214V to 165738Vwhen compared with the pack without balancing And it alsoreduced the discharging cut-off voltage variance and the SOCvariance to 0 and 0157 respectively

The process in which the battery pack transferred fromunbalanced state to balanced state with different balancingalgorithms under ECE + EUDC test cycle is shown as

Figure 16 With outlier detection balancing algorithm thecells in the battery pack can be completely chargeddischargeat the same time and thus increase the available energy storedin the pack

4 Conclusions

Aiming at the problem that present cell-balancing algorithmscannot identify the unbalanced cells in lithium-ion batterypack accurately in real-time an algorithm based on outlierdetection was proposed in this paper The unbalanced cellswere identified by the proposed balancing algorithms andbalanced by shunt method using switches After validatingthe efficiency of the balancing algorithms on two simulationmodels the advantages of the proposed algorithm have been

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

Powergui

DiscreteSwitch

Relay

Min

min

Max

max

Battery pack

Contr sigVoltage

SOC

Current

Conn1

Conn2

Balancingalgorithm

Voltage

SOCContr sig

1C

65

ge

++

minusminuss s

Ts = 01 s

Figure 6 The constant current charge-discharge model

Table 2 Performance comparisons of 3 algorithms under CCCD condition

Evaluation standard Balancing algorithmNo balancing Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 37171 29048 23037Balancing time (S) mdash 17681 17783 17775Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 352 2 2Charging cut-off

Total voltage (V) 161214 163017 162939 165738Voltage range (V) 0160 0058 0059 0055Voltage variance 0025 0009 0009 0008

Discharging cut-offTotal voltage (V) 149994 149965 154481 149965Voltage range (V) 0034 0005 0005 0001Voltage variance 0005 0001 0001 0

Charging time (S) 2091 2413 2413 2413SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0158

the early stage of design greatly improving the reliability ofthe algorithms In addition the SILP model can simulatemore different working conditions and the simulation resultshavemore significance in actual engineering when comparedwith the CCCD model The SILP model for BMS mainlyincludes driving cycle model driver model vehicle controlunit model battery management system software model

battery model power system model and wheel model Thewhole virtual environment model is shown in Figure 12

The ECE + EUDC test cycle is used for EU type approvaltesting of emissions and fuel consumption from light dutyvehicles As Figure 13 shows ECE + EUDC (bottom chart)cycle includes four ECE (upper left chart) segments repeatedwithout interruption followed by one EUDC (upper right

Mathematical Problems in Engineering 7

0 500 1000 1500 2000 2500 3000 350020406080

100

Time (s)

SOC

()

0 500 1000 1500 2000 2500 3000 3500

05

10

Time (s)Cu

rren

t (A

)

0 500 1000 1500 2000 2500 3000 35003638

44244

Time (s)

Volta

ge (V

)

minus5

minus10

Figure 7 The SOC current and voltage of 10th cell during one 1C CCCD test cycle

0 05 1 15 2 25 3 35 4 45 520

40

60

80

100

Time (s)

SOC

()

Abnormal cellNormal cells

times104

(a)

Abnormal cellNormal cells

0 05 1 15 2 25 3 35 4 45 536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 8 SOC (a) and voltage (b) of the unbalanced pack

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(a)

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(b)

Figure 9 Balancing control signal of voltage-based (a) and outlier detection (b) balancing

chart) segment According to Figure 14 the battery pack isdischarged with two ECE + EUDC cycle until 2400 s andcharged by the generator in the next 822 s since the SOCof thepack reduced to 30 Simulation test starts in the situationthat there is one cellrsquos SOC and voltage value are 6483 and4140V and the others are 5483 and 4063V respectively

322 Simulation Result and Analysis The simulation resultsduring thewhole ECE+EUDC test cycle are shown inTable 3for different balancing scenarios (no balancing voltage-based balancing SOC-based balancing and outlier detection

balancing algorithm)That the usable capacity calculated overbalancing process of abnormal cell decreased by 0584Ah isthe precondition for comparing the simulation results fordifferent balancing scenarios

With no balancing the unbalanced cell in the batterypack could not be completely discharged before charging andthe normal cells could not be completely charged before dis-charging during the whole test cycle as detailed in Figure 15Hence the amount of usable energy of the pack decreased atthe end of the charging process With voltage-based balanc-ing the total voltage (charging cut-off) increased to 164738V

8 Mathematical Problems in Engineering

0 05 1 15 2 25 3 35 4 45 5 5520406080

100

Time (s)

SOC

()

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

times104

(a)

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

0 05 1 15 2 25 3 35 4 45 5 5536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 10 SOC (a) and voltage (b) of pack with balancing algorithms during CCCD cycle

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(a)

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(b)

Figure 11 The position of the abnormal cell before it was balanced (a) and after it was balanced (b)

and the voltage variance (discharging cut-off) decreased to0003 but the frequency of balancing switch onoff reaches ashigh as 1150 With outlier detection balancing the frequencyof the switching onoff was significantly reduced from 1150to 2 and reduced the voltage variance (charging cut-off) andthe SOC variance to 0 and 0157 respectively when comparedwith voltage-based and SOC-based balancing algorithmFurthermore the proposed balancing algorithm increasedthe total charging cut-off voltage from 161214V to 165738Vwhen compared with the pack without balancing And it alsoreduced the discharging cut-off voltage variance and the SOCvariance to 0 and 0157 respectively

The process in which the battery pack transferred fromunbalanced state to balanced state with different balancingalgorithms under ECE + EUDC test cycle is shown as

Figure 16 With outlier detection balancing algorithm thecells in the battery pack can be completely chargeddischargeat the same time and thus increase the available energy storedin the pack

4 Conclusions

Aiming at the problem that present cell-balancing algorithmscannot identify the unbalanced cells in lithium-ion batterypack accurately in real-time an algorithm based on outlierdetection was proposed in this paper The unbalanced cellswere identified by the proposed balancing algorithms andbalanced by shunt method using switches After validatingthe efficiency of the balancing algorithms on two simulationmodels the advantages of the proposed algorithm have been

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

0 500 1000 1500 2000 2500 3000 350020406080

100

Time (s)

SOC

()

0 500 1000 1500 2000 2500 3000 3500

05

10

Time (s)Cu

rren

t (A

)

0 500 1000 1500 2000 2500 3000 35003638

44244

Time (s)

Volta

ge (V

)

minus5

minus10

Figure 7 The SOC current and voltage of 10th cell during one 1C CCCD test cycle

0 05 1 15 2 25 3 35 4 45 520

40

60

80

100

Time (s)

SOC

()

Abnormal cellNormal cells

times104

(a)

Abnormal cellNormal cells

0 05 1 15 2 25 3 35 4 45 536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 8 SOC (a) and voltage (b) of the unbalanced pack

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(a)

0 05 1 15 2 25 3 35 40

02040608

1

Time (s)

Con

trol s

igna

l

times104

(b)

Figure 9 Balancing control signal of voltage-based (a) and outlier detection (b) balancing

chart) segment According to Figure 14 the battery pack isdischarged with two ECE + EUDC cycle until 2400 s andcharged by the generator in the next 822 s since the SOCof thepack reduced to 30 Simulation test starts in the situationthat there is one cellrsquos SOC and voltage value are 6483 and4140V and the others are 5483 and 4063V respectively

322 Simulation Result and Analysis The simulation resultsduring thewhole ECE+EUDC test cycle are shown inTable 3for different balancing scenarios (no balancing voltage-based balancing SOC-based balancing and outlier detection

balancing algorithm)That the usable capacity calculated overbalancing process of abnormal cell decreased by 0584Ah isthe precondition for comparing the simulation results fordifferent balancing scenarios

With no balancing the unbalanced cell in the batterypack could not be completely discharged before charging andthe normal cells could not be completely charged before dis-charging during the whole test cycle as detailed in Figure 15Hence the amount of usable energy of the pack decreased atthe end of the charging process With voltage-based balanc-ing the total voltage (charging cut-off) increased to 164738V

8 Mathematical Problems in Engineering

0 05 1 15 2 25 3 35 4 45 5 5520406080

100

Time (s)

SOC

()

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

times104

(a)

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

0 05 1 15 2 25 3 35 4 45 5 5536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 10 SOC (a) and voltage (b) of pack with balancing algorithms during CCCD cycle

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(a)

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(b)

Figure 11 The position of the abnormal cell before it was balanced (a) and after it was balanced (b)

and the voltage variance (discharging cut-off) decreased to0003 but the frequency of balancing switch onoff reaches ashigh as 1150 With outlier detection balancing the frequencyof the switching onoff was significantly reduced from 1150to 2 and reduced the voltage variance (charging cut-off) andthe SOC variance to 0 and 0157 respectively when comparedwith voltage-based and SOC-based balancing algorithmFurthermore the proposed balancing algorithm increasedthe total charging cut-off voltage from 161214V to 165738Vwhen compared with the pack without balancing And it alsoreduced the discharging cut-off voltage variance and the SOCvariance to 0 and 0157 respectively

The process in which the battery pack transferred fromunbalanced state to balanced state with different balancingalgorithms under ECE + EUDC test cycle is shown as

Figure 16 With outlier detection balancing algorithm thecells in the battery pack can be completely chargeddischargeat the same time and thus increase the available energy storedin the pack

4 Conclusions

Aiming at the problem that present cell-balancing algorithmscannot identify the unbalanced cells in lithium-ion batterypack accurately in real-time an algorithm based on outlierdetection was proposed in this paper The unbalanced cellswere identified by the proposed balancing algorithms andbalanced by shunt method using switches After validatingthe efficiency of the balancing algorithms on two simulationmodels the advantages of the proposed algorithm have been

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

0 05 1 15 2 25 3 35 4 45 5 5520406080

100

Time (s)

SOC

()

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

times104

(a)

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

0 05 1 15 2 25 3 35 4 45 5 5536373839

4414243

Time (s)

Volta

ge (V

)

times104

(b)

Figure 10 SOC (a) and voltage (b) of pack with balancing algorithms during CCCD cycle

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(a)

34 36 38 40 42 44 46

377

3775

378

3785

379

3795

SOC ()

Volta

ge (V

)

Normal cellsOriginal abnormal cell

(b)

Figure 11 The position of the abnormal cell before it was balanced (a) and after it was balanced (b)

and the voltage variance (discharging cut-off) decreased to0003 but the frequency of balancing switch onoff reaches ashigh as 1150 With outlier detection balancing the frequencyof the switching onoff was significantly reduced from 1150to 2 and reduced the voltage variance (charging cut-off) andthe SOC variance to 0 and 0157 respectively when comparedwith voltage-based and SOC-based balancing algorithmFurthermore the proposed balancing algorithm increasedthe total charging cut-off voltage from 161214V to 165738Vwhen compared with the pack without balancing And it alsoreduced the discharging cut-off voltage variance and the SOCvariance to 0 and 0157 respectively

The process in which the battery pack transferred fromunbalanced state to balanced state with different balancingalgorithms under ECE + EUDC test cycle is shown as

Figure 16 With outlier detection balancing algorithm thecells in the battery pack can be completely chargeddischargeat the same time and thus increase the available energy storedin the pack

4 Conclusions

Aiming at the problem that present cell-balancing algorithmscannot identify the unbalanced cells in lithium-ion batterypack accurately in real-time an algorithm based on outlierdetection was proposed in this paper The unbalanced cellswere identified by the proposed balancing algorithms andbalanced by shunt method using switches After validatingthe efficiency of the balancing algorithms on two simulationmodels the advantages of the proposed algorithm have been

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

ICE

Vehicle dynamics

Car speed kmh Drive shaft

Carr

ier

Sun

Ring

Throttle Engine

ICE controller

En

NCtrl

HCU

SOC

P

Fault

Pedal

Motor speed

Gen speed

ICE speed

Car speed

Motor torque

Gen torque

Enable

ICE ref

Control com

[v]

[Bat]

[Wmot]

[Relay]

[Wmot]

[Wgen]

[Wgen]

[Wice]

BatMotor speedTorque ref1Torque ref2Generator speedConn1Conn2

Motor

Generator

Driver modle

V0

V

PedalCycle modle

Battery model

Control

Bat

Conn1

Conn2

BMS software model

Batt

Relay

Control

SOC

P

Fault

Pedal

[V]

[T]

Nlowast

ECE + EUDC

minusKminus

Torquelowast

Figure 12 Software-in-the-loop platform model for BMS

0 50 100 150 2000

10

20

30

40

50

Time (s)

Spee

d (k

mh

)

ECE cycle

(a)

0 100 200 300 4000

20

40

60

80

100

120

Time (s)

Spee

d (k

mh

)

EUDC cycle

(b)

0 200 400 600 800 1000 12000

20406080

100120

Time (s)

Spee

d (k

mh

)

4 lowast ECE + EUDC cycle

(c)

Figure 13 One ECE + EUDC cycle

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

Table 3 Performance comparisons of 3 algorithms under 4 lowast ECE + EUDC condition

Evaluation standard Balancing algorithmNo balance Voltage-based balancing SOC-based balancing Outlier detection balancing

Testing time (S) mdash 57264 39074 22052Balancing time (S) mdash 16666 15795 15752Usable capacity decrease (AH) mdash 0584 0584 0584Frequency of switch on and off mdash 1150 2 2Charging cut-off

Total voltage (V) 161214 164738 164963 165738Voltage range (V) 0174 0058 0003 0003Voltage variance 0028 0009 0004 0

Discharging cut-offTotal voltage (V) 149994 149965 150882 149965Voltage range (V) 0034 0005 0002 0002Voltage variance 0005 0003 0 0

SOC range of cells () 10 1030 1025 0999SOC variance of cells 1581 0162 0162 0157

0 500 1000 1500 2000 2500 3000345

Time (s)

Volta

ge (V

)

0 500 1000 1500 2000 2500 3000

050

Time (s)

Curr

ent (

A)

0 500 1000 1500 2000 2500 30000

50100

Time (s)

SOC

()

minus50

Figure 14 Voltage current and SOC of the pack during one ECE + EUDC diving cycle

0 05 1 15 2 25 3 35 4 45 5203040506070

Time (s)

SOC

()

times104

Abnormal cellNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5343638

442

Time (s)

Volta

ge (V

)

times104

Abnormal cellNormal cells

(b)

Figure 15 SOC (a) and voltage (b) of the unbalanced pack

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

0 05 1 15 2 25 3 35 4 45 5 55102030405060

Time (s)

SOC

()

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(a)

0 05 1 15 2 25 3 35 4 45 5 5532343638

442

Time (s)

Volta

ge (V

)

times104

Voltage-based balanceSOC-based balance

Outlier detection blanceNormal cells

(b)

Figure 16 SOC (a) and voltage (b) of pack with balancing algorithms during ECE + EUDC test cycle

pointed out in the context of simulation and analysis Theoutlier detection equalization algorithm is able to recognizethe abnormal battery cell accurately and to increase the usableenergy and extend the lifetime of battery pack which hasextensive application prospect and theory value

Further work will focus on taking the temperature of cellsinto account during whole charging and discharging process

Conflict of Interests

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

Acknowledgment

Thiswork is supported by CQCSTC (CSTC2013yykfC60005cstc2014jcyjA60004 and CSTC2013jcsf-jcssX0022)

References

[1] J B Zhang L G Lu and Z Li ldquoKey technologies and funda-mental academic issues for traction battery systemrdquo Journal ofAutomotive Safety and Energy vol 3 no 2 pp 87ndash104 2012

[2] M Einhorn W Roessler and J Fleig ldquoImproved performanceof serially connected Li-ion batteries with active cell balancingin electric vehiclesrdquo IEEE Transactions on Vehicular Technologyvol 60 no 6 pp 2448ndash2457 2011

[3] S G Xu Q S Zhong and R J Zhu ldquoResearch of equalizingcharge control strategy for power batteryrdquo ElectricMachines andControl vol 16 pp 62ndash65 2012

[4] A G Xu S J Xie and X B Liu ldquoDynamic voltage equalizationfor series-connected ultracapacitors in EVHEV applicationsrdquoIEEE Transactions Vehicular Technology vol 58 no 8 pp 3981ndash3987 2009

[5] L Maharjan S Inoue H Akagi and J Asakura ldquoState-of-charge (soc)-balancing control of a battery energy storagesystem based on a cascade PWM converterrdquo IEEE Transactionson Power Electronics vol 24 no 6 pp 1628ndash1636 2009

[6] T-H Kim N-J Park N R-Y Kim and D-S Hyun ldquoA highefficiency zero voltage-zero current transition converter forbattery cell equalizationrdquo inProceedings of the 27thAnnual IEEEApplied Power Electronics Conference andExposition (APEC rsquo12)pp 2590ndash2595 IEEE Orlando Fla USA February 2012

[7] J J Fu B J Qi and H J Wu ldquoDynamic bi-directionequalization system research for lithium-ion batteriesrdquo ChinaMeasurement Technology vol 31 pp 10ndash12 2005

[8] M Einhorn W Guertlschmid T Blochberger et al ldquoA currentequalization method for serially connected battery cells usinga single power converter for each cellrdquo IEEE Transactions onVehicular Technology vol 60 no 9 pp 4227ndash4237 2011

[9] Y M Ye K W E Cheng and Y P B Yeung ldquoZero-current switching switched-capacitor zero-voltage-gap auto-matic equalization system for series battery stringrdquo IEEE Trans-actions on Power Electronics vol 27 no 7 pp 3234ndash3242 2012

[10] J Xu S Q Li C Mi Z Chen and B Cao ldquoSOC based batterycell balancing with a novel topology and reduced componentcountrdquo Energies vol 6 no 6 pp 2726ndash2740 2013

[11] S Yarlagadda T T Hartley and I Husain ldquoA battery man-agement system using an active charge equalization techniquebased on aDCDC converter topologyrdquo in Proceedings of the 3rdAnnual IEEEEnergy ConversionCongress and Exposition (ECCErsquo11) pp 1188ndash1195 IEEE Phoenix Ariz USA September 2011

[12] Y Y Wu and H Liang ldquoA study on equalization charging forEV traction batteryrdquo Automotive Engineering no 16 pp 382ndash385 2004

[13] CH PiaoW L FuGH Lei andCDCho ldquoOnline parameterestimation of theNi-MHbatteries based on statisticalmethodsrdquoEnergies vol 3 no 2 pp 206ndash215 2010

[14] Z Y Huang and Y H Cao ldquoEstimation for SOC of LiFePO4Li-ion battery based on GA-RBF neural networkrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) vol 25 no 3 pp 412ndash417 2013

[15] C H Piao Z Huang L Su and S Lu ldquoResearch on outlierdetection algorithm for evaluation of battery system safetyrdquoAdvances in Mechanical Engineering vol 14 no 1 pp 65ndash702014

[16] K K Wang G X Gui W Ni and G L Gou ldquoFastoutlierdatamining algorithm based on cell in large datasetsrdquo Journal ofChongqing University of Posts and Telecommunications (NaturalScience Edition) no 5 pp 673ndash677 2010

[17] H D Wang Y H Tong S H Tan S E Tang and D Q YangldquoResearch progress on outlier miningrdquo CAAI Transactions onIntelligent Systems no 5 pp 67ndash74 2006

[18] VChandola A Banerjee andVKumar ldquoAnomaly detection fordiscrete sequences a surveyrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 5 pp 823ndash839 2012

[19] F Angiulli and C Pizzuti ldquoOutlier mining in large high-dimensional data setsrdquo IEEE Transactions on Knowledge andData Engineering vol 17 no 2 pp 203ndash215 2005

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Mathematical Problems in Engineering

[20] C H Piao Q F Yu C X Duan L Su and Y Zhang ldquoVirtualenvironment modeling for battery management systemrdquo Jour-nal of Electrical EngineeringampTechnology vol 9 no 5 pp 1729ndash1738 2014

[21] O Tremblay and L-A Dessaint ldquoExperimental validation ofa battery dynamic model for EV applicationsrdquo World ElectricVehicle Journal vol 2 pp 930ndash939 2009

[22] F Angiulli S Basta and C Pizzuti ldquoDistance-based detectionand prediction of outliersrdquo IEEETransactions onKnowledge andData Engineering vol 18 no 2 pp 145ndash160 2006

[23] H Spath and J Goldschmidt Cluster Dissection and AnalysisTheory FORTRAN Programs Examples Halsted Press NewYork NY USA 1985

[24] M Daowd N Omar P van den Bossche and J van MierloldquoPassive and active battery balancing comparison based onMATLAB simulationrdquo in Proceedings of the 7th IEEE VehiclePower and Propulsion Conference (VPPC rsquo11) pp 1ndash7 IEEEChicago Ill USA September 2011

[25] P Chen C H Piao C X Duan and S Lu ldquoModeling ofbattery management system software in virtual simulationenvironmentrdquo Automotive Safety and Energy vol 4 no 1 pp67ndash74 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of