Research Article Coordinated Control of PV Generation and EVs...

Research ArticleCoordinated Control of PV Generation and EVs ChargingBased on Improved DECell Algorithm

Guo Zhao12 Xueliang Huang12 and Hao Qiang13

1School of Electrical Engineering Southeast University Nanjing 210096 China2Jiangsu Key Lab of Smart Grid Technology and Equipment Zhenjiang 212009 China3School of Urban Rail Transit Changzhou University Changzhou 213164 China

Correspondence should be addressed to Guo Zhao zhaoguoabc126com

Received 25 September 2014 Revised 30 December 2014 Accepted 30 December 2014

Academic Editor Zhixiong Guo

Copyright copy 2015 Guo Zhao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Recently the coordination of EVsrsquo charging and renewable energy has become a hot research all around the globe Consideringthe requirements of EV owner and the influence of the PV output fluctuation on the power grid a three-objective optimizationmodel was established by controlling the EVs charging power during charging process By integrating the meshing method intodifferential evolution cellular (DECell) genetic algorithm an improved differential evolution cellular (IDECell) genetic algorithmwas presented to solve the multiobjective optimization model Compared to the NSGA-II and DECell the IDECell algorithmshowed better performance in the convergence and uniform distribution Furthermore the IDECell algorithm was applied toobtain the Pareto front of nondominated solutions Followed by the normalized sorting of the nondominated solutions the optimalsolutionwas chosen to arrive at the optimized coordinated control strategy of PV generation and EVs charging Compared to typicalcharging pattern the optimized charging pattern could reduce the fluctuations of PV generation output power satisfy the demandof EVs charging quantity and save the total charging cost

1 Introduction

With the increasing pressures of energy shortage environ-mental pollution and global warming the developments ofrenewable energies such as wind power and photovoltaic(PV) generation [1 2] have been paid more and more atten-tion In addition for the purposes of low-carbon emissionsand reducing environmental pollution the electric vehicle(EV) technology also obtained fast development and nowhas become a focus of national governments automakersand energy companies [3ndash6] However research shows thatEVsrsquo advantage of low emissions is more significant onlyin predominant low-carbon electricity area while it is notobvious in the region based on coal-fired power generationThis means that only as much as possible wind power PVpower and other renewable energies are adopted to chargethe EVs can EVsrsquo emission reduction benefits be full playTherefore the coordination and complementation of EVsrsquocharging and wind power or PV power have become a hotresearch all around the globe [7ndash12]

Recently most research has focused on the coordinationof EVs and renewable energy based on the coordinationscheduling and EVs charging stationrsquos capacity allocationPaper [13] derived the mathematical expectation analyticalexpressions of wind turbines outputs and EVs in the state ofthe V2G based on this a power system stochastic economicdispatch model was developed for the target of minimizationof total generation cost Paper [14] did research on outputprobability distribution of V2G wind power and PV gen-eration system set up a stochastic optimization schedulingmodel to stabilize the fluctuations of renewable energyoutputs and solved themodel by the cross entropy algorithmPaper [15] established a multiobjective optimization modelfor EV charging to decrease the equivalent load peak val-ley difference and regional grid electricity purchasing costthen transformed multiobjective optimization model into asingle objective optimization problem by fuzzy set theoryand adopted an improved particle swarm algorithm to solvethe model Paper [16] established a capacity optimizationmodel of the PV charging station to minimize the system

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2015 Article ID 497697 13 pageshttpdxdoiorg1011552015497697

2 International Journal of Photoenergy

comprehensive cost and maximize the utilization of renew-able energyWhile the cost of EVs charging and the influenceson the power grid are rarely simultaneously considered thisissue is practically valuable to EVs development

Considering the requirements of EV owner and the influ-ence of the PV output fluctuation on the power grid the issueof coordination of EVs and renewable energywould become amultiobjective optimization problem A three-objective opti-mization model of PV generation and EV charging systemincluding minimum cost full state of charge and minimalfluctuation of PV output power has been proposed

In order to solve the established three-objective optimiza-tion model an effective multiobjective optimization algo-rithm is needed In recent yearsmany classicalmultiobjectiveevolutionary algorithms had emerged such as NSGA-II [17]and Strength Pareto Evolutionary Algorithm II (SPEA2) [18]In 2007 Enrique Alba developed a novel multiobjective cellu-lar genetic algorithm (cMOGA) Later Nebro et al improvedthe cMOGA by introducing a feedback mechanism thusforming an improved cMOGA that is MOCell [19] Paretosolution obtained by MOCell has outstanding uniformitywhen solving the double target problem while it is disap-pointing in the three target problems In order to improve theperformance of MOCell Durillo et al combined differentialevolution (DE) algorithm with the MOCell and proposeda hybrid metaheuristic algorithm DECell [20] At presentthe DECell algorithm has been applied in the practicalengineering problems and achieved good effects [21]

For further improvement of DECell algorithmrsquos per-formance in solving multiobjective optimization problemmeshingmethod [22] is integrated into the basicDECell algo-rithm and acquired an improved DECell (IDECell) algo-rithm Through solving the multiobjective benchmark func-tions it is verified that IDECell algorithm is effective and fea-sible which can obtain more uniform distribution of Paretofront compared to NSGA-II and basic DECell algorithmFinally an optimized control strategy for coordinated controlof PV generation and EVs charging could be chosen bynormalized sorting of the nondominated solutions Com-pared to typical charging pattern the optimized chargingpattern could reduce the fluctuations of PV generation outputpower meet the demand of EVsrsquo charging and save the totalcharging cost

2 The Coordination Optimization Model ofPV Generation and EVs Charging

The main types of EVs are bus taxi and private car and soforthTheir charging patterns are divided into slow chargingconventional charging and fast charging Among them pri-vate cars aremainly used forwork leisure and entertainmentthe corresponding charging locations include office parkinglot residential parking lot and supermarket shopping centerparking lot Therefore the charging patterns could be chosenas slow charging or conventional charging when parkingin the office and residential parking lots In this paper theprivate cars charging in the office parking lot condition istaken as an example to study the coordinated optimizationcontrol strategy of PV generation and EVs charging and

DC AC DC AC

PV arrays

Local load

PV charging station

AC busPCC Grid

Intelligentcharging pile

Central control unit


380 V10 kV

middot middot middot




Figure 1 Structure of the PV charging station system

the charging time is from when they arrive at work locationsto when they leave

21 Power Balance Model of PV Charging Station System ThePV charging station researched in this paper is comprised ofPV arrays DCAC modules intelligent charging piles localload AC power source and central control unit the systemstructure is as shown in Figure 1

Under stable operation condition of the PV chargingstation system the tie line power is considered to be gridconnected power which can be calculated by the following

119875gs = 119875PV minus 119875EV minus 119875loss (1)

where 119875gs is the power transmitted to the grid 119875PV is theoutput power of PV generation system 119875EV is the totalconsumed power of EVs charging and 119875loss is the losspower of lines Besides all values of the variables above areinstantaneous values

22 Objective Functions

(1) Fluctuations of the Power Transmitted to the Grid In orderto investigate the optimal control strategy for coordinatedcharging the whole optimization period 119879 is divided equallyinto 119873 sections and the duration 119879

119873of each section can be

derived as 119879119873To reduce the influence of grid connected PV generation

on the power grid side it is needed to minimize the fluctua-tions of the power transmitted to the grid through the optimalcontrol of EVsrsquo charging power of each section in the chargingprocess Use standard deviation to estimate the fluctuationcharacteristic of the power transmitted to the grid Then thecorresponding objective function can be expressed as

min1198651= minradic

sum119873

119899=1|119875gs (119899) minus 119875gs|

2

119873

(2)

International Journal of Photoenergy 3

where 119875gs(119899) = 119875PV(119899)minussumnum EV119894

119875EV(119899 119894) is the average valueof power transmitted to the grid during the 119899th section 119875gs =

sum119873

119899=1[119875PV(119899) minus sum

num EV119894

119875EV(119899 119894)]119873 is the average value ofpower transmitted to the grid during the whole optimizationperiod 119875PV(119899) is the average value of PV generation outputpower during the 119899th section 119875EV(119899 119894) represents the averagecharging power of 119894th EV during 119899th section num EV is thetotal number of EV battery chargers

(2) EVs Charging Cost According to TOU price of industrialelectricity in China the cost of EV charging can be calculatedby the following

cost = int

1199050+119879

1199050

119872(119905) 119875 (119905) 119889119905 (3)

where 1199050is the starting time of charging 119879 is duration of

charging and 1199050+119879 is the ending time of charging119872(119905) and

119875(119905) represent the unit price and charging power in time 119905respectively Take the total cost that all EVs need to pay tocharge as objection function

min1198652= min

119873

sum

119899=1

119872(119899)

num EVsum

119894

119875EV (119899 119894) 119879119873 (4)

(3) SOC of EV Battery The SOC of EV battery can be statedas

SOC (119905) = SOC0+

int1199050+119879

1199050

119875 (119905) 119889119905

119876

(5)

where SOC0represents the initial SOC of EV battery and 119876

is the rated capacity of EV battery After being discretized (5)can be rewritten as

SOC (119899) = SOC0+

sum119899

119895=1119875 (119895) 119879

119873

119876 (6)

In order to satisfy the userrsquos charging requirements theEV battery should be fully charged at the end of the optimiza-tion The discretized optimized model can be expressed as

min1198653= min

num EVsum

119894

|SOC (119873 119894) minus 1|2 (7)

23 Constraints

(1) Restriction of the Power Transmitted to the Grid Consider

119875gsmin le 119875gs (119899) le 119875gsmax (8)

where 119875gsmin and 119875gsmax represent the minimum value andmaximum value of grid connected power respectively whichcan be confirmed according to the agreement between PVcharging station system and power grid

(2) Restriction of Charging Power In order to reduce the lifeloss of EV battery the charging power of EV battery should

0

10

20 40 60 80 100

20

30

40

50

60

SOC ()

Pch

arge

max

(kW

)

Figure 2 The SOC curve

not exceed a certain limited value The charging power isconstrained by the following

0 lt 119875 (119905) le 119875chargemax (119905) (9)

where 119875chargemax(119905) represents the maximum acceptablecharging power of EV battery in time 119905 which is the functionof SOC and temperature of battery Temperature effect on119875charge max(119905) can be ignoredwhen somemeasures are taken tokeep the temperature of battery constantThen themaximumacceptable charging power can be expressed as follows

119875chargemax (119905) = 119891 (SOC) (10)

The quantitative relationship between 119875chargemax(119905) andSOC can be described by SOC curve which is shown inFigure 2

Except for the restriction 119875chargemax(119905) which is the max-imum acceptable charging power of EV battery the totalcharging power of all EVs in each section of the chargingperiod is also restricted by the following

num EVsum

119894

119875EV (119899 119894) le 119875PV (119899) (11)

(3) Restriction of EV Batteryrsquos SOC The SOC of EV batteryin each section of the charging period should be restricted bythe following

SOC (119899 + 1) = SOC (119899) +119875 (119899) 119879119873

119876

SOC0le SOC (119899) le 1 119899 = 1 2 119873

(12)

24Three-Objective OptimizationModel Based on the aboveformulas the global optimization of the coordinated control


of PV generation and EVs charging can be expressed as athree-objective optimization problem with constraints


sum119873

119899=1|119875gs (119899) minus 119875gs|

2

119873

min1198652= min

119873

sum

119899=1

119872(119899)

num EVsum

119894

119875EV (119899 119894) 119879119873

min1198653= min

num EVsum

119894

|SOC (119873 119894) minus 1|2

(13)

ST 119875gs min le 119875gs (119899) le 119875gs max

0 lt 119875 (119905) le 119875charge max (119905)

num EVsum

119894

119875EV (119899 119894) le 119875PV (119899)

SOC (119899 + 1) = SOC (119899) +119875 (119899) 119879119873

Q

SOC0le SOC (119899) le 1 119899 = 1 2 119873

(14)

3 IDECell Algorithm

31 Basic DECell Algorithm DECell is an improved multiob-jective optimization algorithm based on MOCell algorithmthe basic idea is to use MOCell as a search engine and thenuse the propagationmechanismof differential evolution (DE)instead of the crossover operating and mutation operatingof traditional genetic algorithm to generate new individualsso that the Pareto front of solution set can be obtained inmaintaining good uniformity and distribution breadth whilemoving closer and closer to the optimal front

(1) Basic Principle of DECell Algorithm The basic principlechart of DECell algorithm is as shown in Figure 3 Firstlyan initial population is generated randomly and an externalempty document for Pareto solution set is also generated andthen individuals of the initial population will be placed ina two-dimensional ring network and the neighbor structuretype could be defined too Secondly two different individualswill be selected from the neighbors of each current individualrandomly to constitute the three male parent individualsthen crossover operating and mutation operating of the DEstrategywill be carried out to produce an offspring individualIf the offspring individual dominates the current parentindividual or the offspring individual has greater crowdingdistance while both of them are nondominated replace thecurrent parent individual with the offspring individual andstore it to the external document Calculate the crowdingdistance of each nondominated individual in the externaldocument and delete the individual which has the mini-mum crowding distance when the quantity of the externaldocument exceeds its specified capacity Finally after thecompletion of each iteration select a number of individuals

Feedback

External document

Selecting

DE operation

If the offspringindividual is better than that current

then replace it

If it is adominant

then add it to the document

individual

Figure 3 Basic principle chart of DECell algorithm

1

0

2

3

45

6

f2

f1

Figure 4 Crowding distances of individual 3 and individual 4

from the external document to replace the same numberof individuals randomly selected from current populationso that the population could be updated constantly by thisfeedbackmechanism As a result the Pareto front of obtainedsolution set can keep the diversity while moving closer andcloser to the optimal front

(2) The Deficiency of Crowding Distance Strategy in DECellAlgorithm In DECell algorithm the crowding distance strat-egy is used to keep the solution setrsquos diversity the crowdingdistance of each individual of each evolution population iscalculated and the individual with great crowding distancevalue has the priority to be selected into the next generationpopulation However the limitation of this strategy is thatsome individuals with good distribution may be eliminatedwhile those with bad distribution may be reserved

As shown in Figure 4 individual 3 and individual 4are adjacent and both of them are relatively far from otherindividuals in this case their crowding distance valuesare relatively great and similar Therefore individual 3 and


f1

f2

ub2

ub1

lb1

lb2

Lower boundary point of area A

Upper boundary point of area A

A

B

C

Figure 5 Mesh and its boundaries

individual 4 will be eliminated or reserved simultaneouslyHowever in order to make the solution population maintaingood uniformity and distribution it is better to reserve oneand eliminate the other from individual 3 and 4 In view ofthis problem meshingmethod will be introduced to improvethe performance of DECell algorithm instead of the crowdingdistance strategy

32 Meshing Method For a 119903-objective optimization prob-lem set a grid with 2119903 boundaries 119897119887

119896and 119906119887

119896are the

according lower and upper boundary respectively where 119896 =1 2 119903 That shown in Figure 5 is a 2-objective grid with 4boundaries in total

A grid can be segmented into several small areas calledhypercube (HC) the amount of segmentation depends onthe size of evolution population and the objective number ofthe optimization problem Each HC could be expressed as 119903119894where 119894 = (119894

1 1198942 119894

119903) besides 119894

119896isin 1 sdot sdot sdot 119889 where 119889 is a

natural constant generally greater than 2which represents theamount of segmentation in each dimension In Figure 5 119889 isset as 6 therefore boundaries of each 119903119894 can be expressed as

forall119896 isin 1 sdot sdot sdot 119903

119903119906119887119896119894= [119897119887119896+ (

119894119896

119889) (119906119887119896minus 119897119887119896)] sdot 120596119896

119903119897119887119896119894= [119897119887119896+ (

(119894119896minus 1)

119889) (119906119887119896minus 119897119887119896)] sdot 120596

119896

(15)

where 120596119896represents the width of each HC in 119896th dimension

120596119896

= range119896119889 and range

119896is the domain width in 119896th

dimension

On the basis of the above with the grid and the identi-fication for each HC it can be judged whether an individualfalls in a certain area Take individual 119911 = (119911

1 1199112 119911

119903) for

instance it can be confirmed that individual 119911 is located inarea 119903119894 when 119911

119896ge 119903119897119887119896119894and 119911119896lt 119903119906119887119896119894 forall119896 isin 1 sdot sdot sdot 119903

In Figure 5 there are three individuals located in area 119860one individual located in area 119861 and two individuals locatedin area119862 Tomaintain the evolution populationrsquos distributionit is needed to select the individuals with great gatheringdensity in the grid to deleteTherefore one or two individualsin the area 119860 should be deleted

33 Improvement of DECell Algorithm In order to improvethe performance of DECell algorithm solving the three-objective optimization problem meshing method is inte-grated into the basic DECell algorithm instead of the crowd-ing distance strategyAs a result an improveddifferential evo-lution cellular (IDECell) genetic algorithm was developedThe flowchart of IDECell algorithm is as shown in Figure 6

34 Verification of IDECell Algorithm In order to verify thefeasibility of IDECell algorithm apply IDECell algorithm tosolve two three-objective benchmark test functions DTLZ1and DTLZ2 What is more NSGA-II algorithm and basicDECell algorithm are also conducted for comparison DTLZ1and DTLZ2 are described as (16) and (17) respectively

DTLZ1

min1198911 (119909) = 05119909

11199092(1 + 119892 (119909))

min1198912 (119909) = 05119909

1(1 minus 119909

2) (1 + 119892 (119909))

min1198913 (119909) = 05 (1 minus 119909

1) (1 + 119892 (119909))

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2minus cos (20120587 (119909

119894minus 05))

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(16)

DTLZ2

min1198911 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) cos(119909

2

120587

2)

min1198912 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) sin(119909

2

120587

2)

min1198913 (119909) = (1 + 119892 (119909)) sin(1199091

120587

2)

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(17)

341 Performance Measures Unlike in single objective opti-mization there are two goals in a multiobjective optimiza-tion (1) convergence to the Pareto-optimal set and (2)

maintenance of diversity in solutions of the Pareto-optimal


Start

Initialization generate initial population randomly

and an external empty document

Define neighbor structure typeselect the current individual

and its two neighbors

Generate offspring individual by DE

Evaluate the fitness of the offspring individual

Replace current individual and send it to external document

Save current individual

Feedback select someindividuals in external document

to replace those of the same number in current population

End

Yes

No

No

Yes

Delete surplus individuals by meshing method

Yes

No

Output the nondominated solutions

Dominate current individual

The Number of individuals in

external document

exceeds the capacity

Meet the convergence

condition

G = G + 1

Figure 6 The flowchart of IDECell algorithm


set [23] These two tasks cannot be measured adequatelywith one performance metric Many performance metricshave been suggested [17 24 25] Here we use three practicalperformance metrics to evaluate the above two goals ina solution set obtained by a multiobjective optimizationalgorithm

(1) Generational DistanceThis metric is a value representingthe distance between the obtained Pareto front and theoptimal Pareto front and is defined as [24]

GD =(sum119899

119894=1119889119901

119894)1119901

119899 (18)

where 119899 is the number of solutions in the obtained Paretofront 119901 is the dimension of objective space and 119889

119894is the

Euclidean distance between each solution and the nearestmember of the optimal Pareto front A result of 0 indicatesthat the obtained Pareto front is optimal Pareto front Themetric GD takes a smaller value with better performance inconvergence

(2) Spread ΔThemetric Δ suggested by Deb et al measuresthe extent of spread achieved among the obtained solutions[17] We use this metric to calculate the nonuniformity in thedistribution

Δ =

119889119891+ 119889119897+ sum119899

119894=1

10038161003816100381610038161003816119889119894minus 119889

10038161003816100381610038161003816

119889119891+ 119889119897+ (119899 minus 1) times 119889

(19)

Here 119889119894is Euclidean distance between consecutive solutions

in the obtained nondominated set of solutions The param-eters 119889

119891and 119889

119897are the Euclidean distances between the

extreme solutions and the boundary solutions of the obtainednondominated set The parameter 119889 is the average of alldistances 119889

119894 assuming that there are 119899 solutions on the best

nondominated front The metric Δ takes a higher value withworse distributions of solutions within the extreme solutions

(3) Hypervolume Hypervolume (HV) metric [25] is used torepresent the volume of the objective space dominated by anapproximation Pareto set It is a comprehensive evaluationindicator of convergence and diversity and is defined as

HV = volume(|119876|

⋃

119894=1

V119894) (20)

where 119876 is the number of solutions in the obtained Paretofront For each individual 119881

119894represents the volume dom-

inated by the 119894th individual and the reference point 119908 =

(0 0)The greater value of theHV shows that the obtainedPareto front has wider coverage in the optimal Pareto front

342 Analysis of the Results Set the parameters of threealgorithms as follows adopt real number system for encodingand polynomial for mutation NSGA-II adopts simulationbinary crossover (SBX) operator DECell and IDECell adoptDE operator Population size is set as 200 the maximum

000

01

02

02 02

03

04

04 04

05

06

06 06

DTLZ1 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using DECell

f3(x

)

f2 (x) f 1

(x)

(b) DECell

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell

Figure 7 Pareto front of DTLZ1 gained by 3 multiobjective opti-mization algorithms

number of iterations is set as 1000 crossover probabilityis set as 09 mutation probability is 1len len is variabledimension the size of external document is set as 100 andthe number of feedback individuals is set to be 20 Altogether30 independent runs were performed per algorithm andtest problem in order to restrict the influence of randomeffects The simulation results gained by three optimizationalgorithms are shown as Figures 7 and 8

Obviously it can be seen from Figures 7 and 8 all threealgorithms can seek out a group of nondominated solutionsfor DTLZ1 and DTLZ2 Compared to other two optimizationalgorithms the Pareto front gained by IDECell algorithm has


Table 1 Comparison of performance metrics

Algorithm (problem) GD Δ HVMean Variance Mean Variance Mean Variance

NSGA-II (DTLZ1) 02036 01601 08651 00262 07221 00471DECell (DTLZ1) 00424 00427 06978 00145 07862 00524IDECell (DTLZ1) 00233 00607 05034 00092 08025 00413NSGA-II (DTLZ2) 02263 04644 09552 01227 06343 00793DECell (DTLZ2) 00196 00241 08987 02475 07064 00617IDECell (DTLZ2) 00177 00221 04954 00178 07285 00814

0 005 05

1 115 15

0

02

04

06

08

1

12

DTLZ2 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using DECell

f3(x

)

f2 (x)

f1(x

)

(b) DECell

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell


more uniform distribution The case that multiple optimalsolutions converge in a small area does not exist avoidingthe premature and local convergence during the processof genetic operation Furthermore quality measures havebeen introduced to compare the outcomes of multiobjectiveoptimization algorithms in a quantitative manner Table 1presents three algorithms performance as regards genera-tional distance spread and hypervolume over DTLZ1 andDTLZ2 When considering generational distance and hyper-volume the DECell algorithm and IDECell algorithm givebetter results than the NSGA-II algorithm because they com-bine the advantages of MOCell algorithm and DE algorithmBesides due to the introduction of the meshing method theIDECell algorithm shows better performance in the uniformdistribution than the other two algorithms over the testproblems As such it is verified that the IDECell algorithmis more suitable and reliable to solve the three-objectiveoptimization problem and is advantageous for policy makersto accurately make the best choice

4 Application of IDECell Algorithm inthe Coordinated Control of PV Generationand EVs Charging

Apply the IDECell algorithm to solve the established opti-mizationmodel for the coordinated control of PV generationand EVs charging the overall process can be described in thefollowing main steps

Step 1 (initialize the parameters) Set the parameters of119875119873119863

119865 CR 119889 119862 and 119866 119875 is the population size 119873119863represents

the size of external document 119865 is the zoom factor CR isthe crossover factor 119889 is the amount of segmentation 119862 isthe number of feedback individuals and 119866 is the maximumnumber of iterations for whole population

Step 2 (initialize the population randomly) Generate the ini-tial population randomly meeting the constraints describedin (14) 119883

11198832 119883

119875119883119894= (119875EV(1 119894) 119875EV(2 119894) 119875EV(119873 119894))

and generate an empty external document as wellThen placethe individuals of the initial population in a two-dimensionalring network and its neighbor structure type could be definedas Moore Compute the fitness value [119865

1(119883119894) 1198652(119883119894) 1198653(119883119894)]

according to (13) for each individual119883119894

Step 3 (generate the offspring individuals by DE) For eachindividual of current population select two individuals119883

1199032119866


and 1198831199033119866

from all neighbors of the current individual 1198831199031119866

1199031 1199032 and 1199033 are their index position respectively A newindividual can be obtained by crossover operation accordingto (21) 119881

119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866

) then to itspaternal individual 119883

119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866

)carry out the mutation operation according to (22) to getthe new offspring individual 119880

119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)

where119870 is a integer and 0 ⩽ 119870 ⩽ 119873 minus 1

Step 4 (evaluate the offspring individuals) Compute the fit-ness value [119865

1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1

)] according to (13)for offspring individual119880

119894119866+1 If119880119894119866+1

dominates its paternalindividual119883

119894119866 then replace the paternal individual and send

119880119894119866+1

to the external document

Step 5 (feedback) Sort the nondominated individuals storedin the external document using meshing method and deletethe redundant individuals when the quantity of the documentexceeds its specified capacity Select a number of individualsfrom the external document to replace the same number ofindividuals randomly selected from current population

Step 6 (check convergence) If the convergence criteria aremet stop and output the nondominant solutions Otherwisereturn to Step 3 In this IDECell the convergence criteriaare defined as the maximum number of iterations for wholepopulation (119866)

5 Numerical Simulation

In this study the whole optimization period 119879 is set to 800ndash1900 and divided into 12 sections with the duration119879

119873of one

hour Besides it is assumed that there are 100 EVs needed tobe charged in the office parking lot

51 Settings of Simulation

(1) Rated Capacity of EV Battery In the EV market there aredifferent battery types such as NiMH Lead Acid and Li-IonAccording to the Li-Ion battery equipped in ldquoE6 pioneerrdquoEV developed by BYD Co Ltd in completely dischargingsituations the demand for energy is 60 kWsdoth

(2) The Initial SOC of EV Battery Using probability distribu-tion model to describe the initial SOC of EV battery

119891 (SOC0 120583 120590) =

1

radic21205871205902119890minus(SOC0minus120583)

2(21205902) (23)

where SOC0represents the initial SOC of EV battery and it is

commonly between 005 and 05 It takes 120583 for 025 and takes120590 for 01 and 120583 is the average value of SOC and 120590 is standarddeviation

0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)

Valley pricePeak price

Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price

(3) TOU Price According to actual TOU price implementedin Jiangsu province in China the period of valley load isdefined as 000ndash0800 totally 8 h the period of peak loadis defined as 0900ndash1200 and 1800ndash2100 totally 8 h Theremaining time is the period of flat load Adopting the actualprice of electricity in the province the prices of peak flat andvalley load period are 0869 YuankWsdoth 0687 YuankWsdothand 0365 YuankWsdoth The histogram of TOU price is shownin Figure 9

(4) The Daily Output Power of PV Generation The dailyoutput power of PV generation before regulation can bepredicted and the average value per hour of output power isshown in Table 2

(5) Parameters of IDECell Algorithm The parameters ofIDECell algorithm are set as shown in Table 3

(6) Typical Charging Pattern of EV Battery In order to verifythe effectiveness of optimized charging strategy which can beobtained by optimization algorithm adopt a typical chargingpattern for comparison the charging profile of which isconsistent with the charging characteristics of battery Atpresent the typical strategy for EV battery charging is a two-stage method The first stage is constant-current chargingprocess which has a constant current and limited voltage andthe second stage is constant-voltage charging process whichhas a constant voltage and limited current During the wholecharging process most of the charging time would be thefirst stage in which the charging power has little change Asa result EV battery could be considered as a constant powerload so that the constant-voltage charging process could be


0200

400600

020

4060

80100

0500

100015002000250030003500400045005000

Pareto front using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)

Pareto front using DECell

(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000

Pareto front using IDECell

f3(x

)

f2 (x) f 1

(x)

(c) IDECell

Figure 10 Pareto front gained by 3 multiobjective optimization algorithms

Table 2 Average value per hour of output power of PV generation

Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0

Table 3 Parameters of IDECell algorithm

Parameter F CR d P G 119873119863

CValue 08 02 10 200 1000 100 20

ignored In this study we employ constant power chargingway for typical charging pattern

52 The Results and Analysis of Simulation

(1) Performance Comparison of Three Algorithms Solve thethree-objective optimization model established previouslyusing NSGA-II algorithm DECell algorithm and IDECellalgorithm respectively and nondominated solutions couldbe obtained The corresponding Pareto fronts are as shownin Figure 10

It can be seen from Figure 10 NSGA-II algorithm is notapplicable to be used to solve the presented three-objectiveoptimization problem in this paper due to its worst conver-gence and distributivity of three algorithms Nevertheless theoptimization results gained by DECell algorithm and IDEalgorithm are more ideal relatively Furthermore comparedto the basic DECell algorithm distribution of the Pareto frontgained by the IDECell algorithm has a significant improve-ment to be more uniform As a consequence it is verifiedthat IDECell algorithm is feasible and effective for solvingthe three-objective optimization model of the coordinatedcontrol of PV generation and EVs charging

(2) Selection of the Optimal Solution So as to get the bestcoordinated control strategy of PV generation and EVscharging it is required to select an optimal solution from thenondominated solution set by a certain method Thus calcu-late the normalized value for each nondominated solution ofthe Pareto solution set according to (24) and then sort them

119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)

where 119891119894represents the normalized value of the 119894th solution

119891119894(119899) is the fitness value for 119899th optimization objective


Table 4 Standard deviation under different charging patterns

Condition Without EVs Typical charging pattern Optimized charging patternStandard deviation (kW) 46214 37929 27714Reduction mdash 1791 4002

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)

Figure 11 EV charging power for each period

of 119894th solution 119891min(119899) is the minimum fitness value for119899th optimization objective of all solutions 119891max(119899) is themaximum fitness value for 119899th optimization objective of allsolutions

On this basis the solution which has the minimumnormalized value can be selected as the optimal solution

(3) Comparison between the Optimal Charging Pattern andTypical Charging Pattern As the optimal solution is selectedand its corresponding control strategy is considered to be theoptimal charging pattern for EVs the charging power curveof EV battery is as shown in Figure 11 Different from thetypical charging pattern the charging power of the optimalcharging pattern changes each period

According to (6) the SOC of the EV battery can becomputed and its changing curve is shown in Figure 12 FromFigure 12 the SOC of EV battery is closed to be 100 at theend of the whole optimization period charged by the optimalcharging pattern It is confirmed that the optimal pattern canmeet the need of EV charging commendably

Figure 13 shows the fluctuation curves of the powertransmitted to the grid under different conditions the spe-cific standard deviation values are calculated and shown inTable 4 Both Figure 13 and Table 3 clearly indicate thatthe optimal charging pattern for EV battery can obviouslyreduce the fluctuations of the power transmitted to the gridcompared to the typical charging pattern

Figure 14 shows the energy demand of different chargingpatterns as it can be seen the optimized charging pattern canshift amass of peak load to valley load and flat load which canreduce the charging costs directly

In addition Table 5 lists the charging cost of differentcharging patterns It is clearly seen that the optimized

0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)

Figure 12 The SOC changing curve of EV battery

0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12

Power without EVsPower with EVs

Power with EVs optimized

T (h)

Pow

er (1

000

kW)

Figure 13 The fluctuation curves of the power transmitted to thegrid

Table 5 Cost under different charging patterns

Condition Typical chargingpattern

Optimizedcharging pattern

Cost (Yuan) 44656 39773Reduction in cost mdash 101

charging pattern can bring an evident reduction in the costof EVs charging

6 Conclusions

The coordinated control of PV generation and EVs charginghas been studied In order to stabilize the fluctuation of


8

49 43

Typical charging pattern

Energy demand in valley timeEnergy demand in peak timeEnergy demand in flat time


915

76

Optimized charging pattern

Figure 14 Energy demand of different charging patterns

the PV generation output power and minimize the total costfor EVs charging while meeting the SOC requirement of EVbatteries a three-objective optimization model is establishedby controlling the EVs charging power during chargingprocess

To solve the proposed multiobjective optimization prob-lem effectively an IDECell algorithm is developed by inte-grating the meshing method into the DECell algorithmThe modified algorithm is initially successfully applied tosolve two benchmark test problems thus validating the newapproach Compared to NSGA-II and DECell algorithmIDECell has the best performance in the convergence anduniform distribution according to the simulation results

With the presented IDECell algorithm an optimizedstrategy for coordination control of PV generation and EVscharging has been achieved by a normalization processFinally the results of simulations show that the obtainedstrategy is effective and reliable Under this strategy the totalcost for EVs charging has been reduced by 101 and thestandard deviation of PV generation output also has beendecreased to 27714 kW from 37929 kW of typical chargingpattern

Conflict of Interests

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

Acknowledgments

This work is supported by the National High-Tech Researchamp Development Program of China (ldquo863rdquo Program) (Grantno 2012AA050210) Provincial Science and Technology Sup-porting Program (Grant no BE2011174) and CooperativeInnovation Fund of Industry Education and Academy ofJiangsu Province (Grant no BY2014037-29)

References

[1] L Xu X Ruan C Mao B Zhang and Y Luo ldquoAn improvedoptimal sizing method for wind-solar-battery hybrid powersystemrdquo IEEE Transactions on Sustainable Energy vol 4 no 3pp 774ndash785 2013

[2] R-H Liang and J-H Liao ldquoA fuzzy-optimization approach forgeneration scheduling with wind and solar energy systemsrdquoIEEE Transactions on Power Systems vol 22 no 4 pp 1665ndash1674 2007

[3] Z Hu Y Song Z Xu Z Luo K Zhan and L Jia ldquoImpacts andutilization of electric vehicles integration into power systemsrdquoProceedings of the Chinese Society of Electrical Engineering vol32 no 4 pp 1ndash10 2012 (Chinese)

[4] U C Chukwu and S M Mahajan ldquoV2G parking lot with pvrooftop for capacity enhancement of a distribution systemrdquoIEEE Transactions on Sustainable Energy vol 5 no 1 pp 119ndash127 2014

[5] S Zhang Z Hu Y Song H Liu and M Bazargan ldquoResearchon unit commitment considering interaction between batteryswapping station and power gridrdquo Proceedings of the ChineseSociety of Electrical Engineering vol 32 no 10 pp 49ndash55 2012(Chinese)

[6] N Rotering and M Ilic ldquoOptimal charge control of plug-inhybrid electric vehicles in deregulated electricitymarketsrdquo IEEETransactions on Power Systems vol 26 no 3 pp 1021ndash1029 2011

[7] J Ma and C N Nian ldquoA scheme for renewable grid for EV of2020 in Chongming islandrdquo Agricultural Equipment amp VehicleEngineering pp 1ndash7 2011 (Chinese)

[8] A Y Saber and G K Venayagamoorthy ldquoPlug-in vehicles andrenewable energy sources for cost and emission reductionsrdquoIEEE Transactions on Industrial Electronics vol 58 no 4 pp1229ndash1238 2011

[9] Z S Li H B Sun and Q L Guo ldquoStudy on wind-EV com-plementation on the transmission grid side considering carbonemissionrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 32 no 10 pp 41ndash48 2012 (Chinese)

[10] D Yu S Song B Zhang and X Han ldquoSynergistic dispatchof PEVs charging and wind power in Chinese regional powergridsrdquo Automation of Electric Power Systems vol 35 no 14 pp24ndash29 2011 (Chinese)

[11] A Y Saber and G K Venayagamoorthy ldquoResource schedulingunder uncertainty in a smart grid with renewables and plug-invehiclesrdquo IEEE Systems Journal vol 6 no 1 pp 103ndash109 2012

[12] D Y Yu H L Huang M Lei X Li B Zhang and X HanldquoCO2reduction benefit by coordinated dispatch of electric

vehicle charging and wind powerrdquoAutomation of Electric PowerSystems vol 36 no 10 pp 14ndash18 2012 (Chinese)


[13] J Zhao F Wen Y Xue Z Dong and J Xin ldquoPower systemstochastic economic dispatch considering uncertain outputsfromplug-in electric vehicles andwind generatorsrdquoAutomationof Electric Power Systems vol 34 no 20 pp 22ndash29 2010(Chinese)

[14] G B Wang J H Zhao and F QWen ldquoStochastic optimizationdispatching of plug-in hybrid electric vehicles in coordinationwith renewable generation in distribution systemsrdquoAutomationof Electric Power Systems vol 36 no 19 pp 22ndash29 2012(Chinese)

[15] X Q Zhang J Liang L Zhang D Yu X Han and F ZhangldquoApproach for plug-in electric vehicles charging schedulingconsidering wind and photovoltaic power in chinese regionalpower gridsrdquo Transactions of China Electrotechnical Society vol28 no 2 pp 28ndash35 2013 (Chinese)

[16] Z Chen X N Xiao and X Y Lu ldquoMulti-objective optimizationfor capacity configuration of PV-based electric vehicle chargingstationsrdquo Transactions of China Electrotechnical Society vol 28no 6 pp 238ndash248 2013 (Chinese)

[17] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002

[18] Z Wei Y x Feng J r Tan J Wu D Yang and J WangldquoResearch on quality performance conceptual design based onSPEA2rdquo Computers and Mathematics with Applications vol 57no 11-12 pp 1943ndash1948 2009

[19] A J Nebro J J Durillo F Luna B Dorronsoro and E AlbaldquoMOCell a cellular genetic algorithm for multiobjective opti-mizationrdquo International Journal of Intelligent Systems vol 24no 7 pp 726ndash746 2009

[20] J J Durillo A J Nebro F Luna and E Alba ldquoSolving three-objective optimization problems using a new hybrid cellulargenetic algorithmrdquo in Parallel Problem Solving from NaturemdashPPSN X 10th International Conference Dortmund GermanySeptember 13-17 2008 Proceedings vol 5199 of Lecture Notes inComputer Science pp 661ndash670 2008

[21] Y Zhang X D Zheng and X Y Wan ldquoOptimization designof hydrodynamic sliding bearing based on differential cellulargenetic algorithmrdquo Journal of Mechanical Transmission vol 38no 9 pp 64ndash68 2014 (Chinese)

[22] S L Ho Y P Zhao and W N Fu ldquoAn efficient parameterizedmesh method for large shape variation in optimal designs ofelectromagnetic devicesrdquo IEEE Transactions on Magnetics vol48 no 11 pp 4507ndash4510 2012

[23] J J Durillo Barrionuevo Metaheuristics for Multi-ObjectiveOptimization Design Analysis and Applications Universidadde Malaga 2011

[24] D A van Veldhuizen and G B Lamont ldquoOn measuring multi-objective evolutionary algorithm performancerdquo in Proceedingsof the Congress on Evolutionary Computation pp 204ndash211 July2000

[25] E Zitzler and L Thiele ldquoMultiobjective evolutionary algo-rithms a comparative case study and the strength Paretoapproachrdquo IEEETransactions onEvolutionaryComputation vol3 no 4 pp 257ndash271 1999

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


comprehensive cost and maximize the utilization of renew-able energyWhile the cost of EVs charging and the influenceson the power grid are rarely simultaneously considered thisissue is practically valuable to EVs development

Considering the requirements of EV owner and the influ-ence of the PV output fluctuation on the power grid the issueof coordination of EVs and renewable energywould become amultiobjective optimization problem A three-objective opti-mization model of PV generation and EV charging systemincluding minimum cost full state of charge and minimalfluctuation of PV output power has been proposed

In order to solve the established three-objective optimiza-tion model an effective multiobjective optimization algo-rithm is needed In recent yearsmany classicalmultiobjectiveevolutionary algorithms had emerged such as NSGA-II [17]and Strength Pareto Evolutionary Algorithm II (SPEA2) [18]In 2007 Enrique Alba developed a novel multiobjective cellu-lar genetic algorithm (cMOGA) Later Nebro et al improvedthe cMOGA by introducing a feedback mechanism thusforming an improved cMOGA that is MOCell [19] Paretosolution obtained by MOCell has outstanding uniformitywhen solving the double target problem while it is disap-pointing in the three target problems In order to improve theperformance of MOCell Durillo et al combined differentialevolution (DE) algorithm with the MOCell and proposeda hybrid metaheuristic algorithm DECell [20] At presentthe DECell algorithm has been applied in the practicalengineering problems and achieved good effects [21]

For further improvement of DECell algorithmrsquos per-formance in solving multiobjective optimization problemmeshingmethod [22] is integrated into the basicDECell algo-rithm and acquired an improved DECell (IDECell) algo-rithm Through solving the multiobjective benchmark func-tions it is verified that IDECell algorithm is effective and fea-sible which can obtain more uniform distribution of Paretofront compared to NSGA-II and basic DECell algorithmFinally an optimized control strategy for coordinated controlof PV generation and EVs charging could be chosen bynormalized sorting of the nondominated solutions Com-pared to typical charging pattern the optimized chargingpattern could reduce the fluctuations of PV generation outputpower meet the demand of EVsrsquo charging and save the totalcharging cost

2 The Coordination Optimization Model ofPV Generation and EVs Charging

The main types of EVs are bus taxi and private car and soforthTheir charging patterns are divided into slow chargingconventional charging and fast charging Among them pri-vate cars aremainly used forwork leisure and entertainmentthe corresponding charging locations include office parkinglot residential parking lot and supermarket shopping centerparking lot Therefore the charging patterns could be chosenas slow charging or conventional charging when parkingin the office and residential parking lots In this paper theprivate cars charging in the office parking lot condition istaken as an example to study the coordinated optimizationcontrol strategy of PV generation and EVs charging and

DC AC DC AC

PV arrays

Local load

PV charging station

AC busPCC Grid


Central control unit


380 V10 kV





Figure 1 Structure of the PV charging station system

the charging time is from when they arrive at work locationsto when they leave

21 Power Balance Model of PV Charging Station System ThePV charging station researched in this paper is comprised ofPV arrays DCAC modules intelligent charging piles localload AC power source and central control unit the systemstructure is as shown in Figure 1

Under stable operation condition of the PV chargingstation system the tie line power is considered to be gridconnected power which can be calculated by the following

119875gs = 119875PV minus 119875EV minus 119875loss (1)

where 119875gs is the power transmitted to the grid 119875PV is theoutput power of PV generation system 119875EV is the totalconsumed power of EVs charging and 119875loss is the losspower of lines Besides all values of the variables above areinstantaneous values

22 Objective Functions

(1) Fluctuations of the Power Transmitted to the Grid In orderto investigate the optimal control strategy for coordinatedcharging the whole optimization period 119879 is divided equallyinto 119873 sections and the duration 119879

119873of each section can be

derived as 119879119873To reduce the influence of grid connected PV generation

on the power grid side it is needed to minimize the fluctua-tions of the power transmitted to the grid through the optimalcontrol of EVsrsquo charging power of each section in the chargingprocess Use standard deviation to estimate the fluctuationcharacteristic of the power transmitted to the grid Then thecorresponding objective function can be expressed as


sum119873

119899=1|119875gs (119899) minus 119875gs|

2

119873

(2)




sum119873

119899=1[119875PV(119899) minus sum

num EV119894



cost = int

1199050+119879

1199050

119872(119905) 119875 (119905) 119889119905 (3)




min1198652= min

119873

sum

119899=1

119872(119899)

num EVsum

119894

119875EV (119899 119894) 119879119873 (4)


SOC (119905) = SOC0+

int1199050+119879

1199050

119875 (119905) 119889119905

119876

(5)



SOC (119899) = SOC0+

sum119899

119895=1119875 (119895) 119879

119873

119876 (6)


min1198653= min

num EVsum

119894

|SOC (119873 119894) minus 1|2 (7)

23 Constraints





0

10

20 40 60 80 100

20

30

40

50

60

SOC ()

Pch

arge

max

(kW

)



0 lt 119875 (119905) le 119875chargemax (119905) (9)


119875chargemax (119905) = 119891 (SOC) (10)



num EVsum

119894

119875EV (119899 119894) le 119875PV (119899) (11)


SOC (119899 + 1) = SOC (119899) +119875 (119899) 119879119873

119876

SOC0le SOC (119899) le 1 119899 = 1 2 119873

(12)





sum119873

119899=1|119875gs (119899) minus 119875gs|

2

119873

min1198652= min

119873

sum

119899=1

119872(119899)

num EVsum

119894

119875EV (119899 119894) 119879119873

min1198653= min

num EVsum

119894

|SOC (119873 119894) minus 1|2

(13)


0 lt 119875 (119905) le 119875charge max (119905)

num EVsum

119894

119875EV (119899 119894) le 119875PV (119899)

SOC (119899 + 1) = SOC (119899) +119875 (119899) 119879119873

Q

SOC0le SOC (119899) le 1 119899 = 1 2 119873

(14)

3 IDECell Algorithm



Feedback

External document

Selecting

DE operation


then replace it

If it is adominant


individual


1

0

2

3

45

6

f2

f1






f1

f2

ub2

ub1

lb1

lb2



A

B

C




119896and 119906119887

119896are the



1 1198942 119894

119903) besides 119894




119903119906119887119896119894= [119897119887119896+ (

119894119896

119889) (119906119887119896minus 119897119887119896)] sdot 120596119896

119903119897119887119896119894= [119897119887119896+ (

(119894119896minus 1)

119889) (119906119887119896minus 119897119887119896)] sdot 120596

119896

(15)


120596119896



dimension


1 1199112 119911

119903) for






DTLZ1

min1198911 (119909) = 05119909

11199092(1 + 119892 (119909))

min1198912 (119909) = 05119909

1(1 minus 119909

2) (1 + 119892 (119909))

min1198913 (119909) = 05 (1 minus 119909

1) (1 + 119892 (119909))

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2minus cos (20120587 (119909

119894minus 05))

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(16)

DTLZ2

min1198911 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) cos(119909

2

120587

2)

min1198912 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) sin(119909

2

120587

2)

min1198913 (119909) = (1 + 119892 (119909)) sin(1199091

120587

2)

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(17)




Start











End

Yes

No

No

Yes


Yes

No




external document



condition

G = G + 1





GD =(sum119899

119894=1119889119901

119894)1119901

119899 (18)


119894is the



Δ =

119889119891+ 119889119897+ sum119899

119894=1

10038161003816100381610038161003816119889119894minus 119889

10038161003816100381610038161003816

119889119891+ 119889119897+ (119899 minus 1) times 119889

(19)



119891and 119889







⋃

119894=1

V119894) (20)






000

01

02

02 02

03

04

04 04

05

06

06 06

DTLZ1 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using DECell

f3(x

)

f2 (x) f 1

(x)

(b) DECell

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell








0 005 05

1 115 15

0

02

04

06

08

1

12

DTLZ2 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using DECell

f3(x

)

f2 (x)

f1(x

)

(b) DECell

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell









11198832 119883

119875119883119894= (119875EV(1 119894) 119875EV(2 119894) 119875EV(119873 119894))


1(119883119894) 1198652(119883119894) 1198653(119883119894)]



1199032119866


and 1198831199033119866



119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866


119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866


119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)



1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1


119894119866+1 If119880119894119866+1



119880119894119866+1






119873of one





119891 (SOC0 120583 120590) =

1


2(21205902) (23)



0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)


Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price






0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




sum119873

119899=1[119875PV(119899) minus sum

num EV119894



cost = int

1199050+119879

1199050

119872(119905) 119875 (119905) 119889119905 (3)




min1198652= min

119873

sum

119899=1

119872(119899)

num EVsum

119894

119875EV (119899 119894) 119879119873 (4)


SOC (119905) = SOC0+

int1199050+119879

1199050

119875 (119905) 119889119905

119876

(5)



SOC (119899) = SOC0+

sum119899

119895=1119875 (119895) 119879

119873

119876 (6)


min1198653= min

num EVsum

119894

|SOC (119873 119894) minus 1|2 (7)

23 Constraints





0

10

20 40 60 80 100

20

30

40

50

60

SOC ()

Pch

arge

max

(kW

)



0 lt 119875 (119905) le 119875chargemax (119905) (9)


119875chargemax (119905) = 119891 (SOC) (10)



num EVsum

119894

119875EV (119899 119894) le 119875PV (119899) (11)


SOC (119899 + 1) = SOC (119899) +119875 (119899) 119879119873

119876

SOC0le SOC (119899) le 1 119899 = 1 2 119873

(12)





sum119873

119899=1|119875gs (119899) minus 119875gs|

2

119873

min1198652= min

119873

sum

119899=1

119872(119899)

num EVsum

119894

119875EV (119899 119894) 119879119873

min1198653= min

num EVsum

119894

|SOC (119873 119894) minus 1|2

(13)


0 lt 119875 (119905) le 119875charge max (119905)

num EVsum

119894

119875EV (119899 119894) le 119875PV (119899)

SOC (119899 + 1) = SOC (119899) +119875 (119899) 119879119873

Q

SOC0le SOC (119899) le 1 119899 = 1 2 119873

(14)

3 IDECell Algorithm



Feedback

External document

Selecting

DE operation


then replace it

If it is adominant


individual


1

0

2

3

45

6

f2

f1






f1

f2

ub2

ub1

lb1

lb2



A

B

C




119896and 119906119887

119896are the



1 1198942 119894

119903) besides 119894




119903119906119887119896119894= [119897119887119896+ (

119894119896

119889) (119906119887119896minus 119897119887119896)] sdot 120596119896

119903119897119887119896119894= [119897119887119896+ (

(119894119896minus 1)

119889) (119906119887119896minus 119897119887119896)] sdot 120596

119896

(15)


120596119896



dimension


1 1199112 119911

119903) for






DTLZ1

min1198911 (119909) = 05119909

11199092(1 + 119892 (119909))

min1198912 (119909) = 05119909

1(1 minus 119909

2) (1 + 119892 (119909))

min1198913 (119909) = 05 (1 minus 119909

1) (1 + 119892 (119909))

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2minus cos (20120587 (119909

119894minus 05))

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(16)

DTLZ2

min1198911 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) cos(119909

2

120587

2)

min1198912 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) sin(119909

2

120587

2)

min1198913 (119909) = (1 + 119892 (119909)) sin(1199091

120587

2)

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(17)




Start











End

Yes

No

No

Yes


Yes

No




external document



condition

G = G + 1





GD =(sum119899

119894=1119889119901

119894)1119901

119899 (18)


119894is the



Δ =

119889119891+ 119889119897+ sum119899

119894=1

10038161003816100381610038161003816119889119894minus 119889

10038161003816100381610038161003816

119889119891+ 119889119897+ (119899 minus 1) times 119889

(19)



119891and 119889







⋃

119894=1

V119894) (20)






000

01

02

02 02

03

04

04 04

05

06

06 06

DTLZ1 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using DECell

f3(x

)

f2 (x) f 1

(x)

(b) DECell

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell








0 005 05

1 115 15

0

02

04

06

08

1

12

DTLZ2 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using DECell

f3(x

)

f2 (x)

f1(x

)

(b) DECell

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell









11198832 119883

119875119883119894= (119875EV(1 119894) 119875EV(2 119894) 119875EV(119873 119894))


1(119883119894) 1198652(119883119894) 1198653(119883119894)]



1199032119866


and 1198831199033119866



119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866


119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866


119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)



1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1


119894119866+1 If119880119894119866+1



119880119894119866+1






119873of one





119891 (SOC0 120583 120590) =

1


2(21205902) (23)



0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)


Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price






0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




sum119873

119899=1|119875gs (119899) minus 119875gs|

2

119873

min1198652= min

119873

sum

119899=1

119872(119899)

num EVsum

119894

119875EV (119899 119894) 119879119873

min1198653= min

num EVsum

119894

|SOC (119873 119894) minus 1|2

(13)


0 lt 119875 (119905) le 119875charge max (119905)

num EVsum

119894

119875EV (119899 119894) le 119875PV (119899)

SOC (119899 + 1) = SOC (119899) +119875 (119899) 119879119873

Q

SOC0le SOC (119899) le 1 119899 = 1 2 119873

(14)

3 IDECell Algorithm



Feedback

External document

Selecting

DE operation


then replace it

If it is adominant


individual


1

0

2

3

45

6

f2

f1






f1

f2

ub2

ub1

lb1

lb2



A

B

C




119896and 119906119887

119896are the



1 1198942 119894

119903) besides 119894




119903119906119887119896119894= [119897119887119896+ (

119894119896

119889) (119906119887119896minus 119897119887119896)] sdot 120596119896

119903119897119887119896119894= [119897119887119896+ (

(119894119896minus 1)

119889) (119906119887119896minus 119897119887119896)] sdot 120596

119896

(15)


120596119896



dimension


1 1199112 119911

119903) for






DTLZ1

min1198911 (119909) = 05119909

11199092(1 + 119892 (119909))

min1198912 (119909) = 05119909

1(1 minus 119909

2) (1 + 119892 (119909))

min1198913 (119909) = 05 (1 minus 119909

1) (1 + 119892 (119909))

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2minus cos (20120587 (119909

119894minus 05))

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(16)

DTLZ2

min1198911 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) cos(119909

2

120587

2)

min1198912 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) sin(119909

2

120587

2)

min1198913 (119909) = (1 + 119892 (119909)) sin(1199091

120587

2)

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(17)




Start











End

Yes

No

No

Yes


Yes

No




external document



condition

G = G + 1





GD =(sum119899

119894=1119889119901

119894)1119901

119899 (18)


119894is the



Δ =

119889119891+ 119889119897+ sum119899

119894=1

10038161003816100381610038161003816119889119894minus 119889

10038161003816100381610038161003816

119889119891+ 119889119897+ (119899 minus 1) times 119889

(19)



119891and 119889







⋃

119894=1

V119894) (20)






000

01

02

02 02

03

04

04 04

05

06

06 06

DTLZ1 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using DECell

f3(x

)

f2 (x) f 1

(x)

(b) DECell

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell








0 005 05

1 115 15

0

02

04

06

08

1

12

DTLZ2 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using DECell

f3(x

)

f2 (x)

f1(x

)

(b) DECell

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell









11198832 119883

119875119883119894= (119875EV(1 119894) 119875EV(2 119894) 119875EV(119873 119894))


1(119883119894) 1198652(119883119894) 1198653(119883119894)]



1199032119866


and 1198831199033119866



119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866


119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866


119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)



1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1


119894119866+1 If119880119894119866+1



119880119894119866+1






119873of one





119891 (SOC0 120583 120590) =

1


2(21205902) (23)



0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)


Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price






0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


f1

f2

ub2

ub1

lb1

lb2



A

B

C




119896and 119906119887

119896are the



1 1198942 119894

119903) besides 119894




119903119906119887119896119894= [119897119887119896+ (

119894119896

119889) (119906119887119896minus 119897119887119896)] sdot 120596119896

119903119897119887119896119894= [119897119887119896+ (

(119894119896minus 1)

119889) (119906119887119896minus 119897119887119896)] sdot 120596

119896

(15)


120596119896



dimension


1 1199112 119911

119903) for






DTLZ1

min1198911 (119909) = 05119909

11199092(1 + 119892 (119909))

min1198912 (119909) = 05119909

1(1 minus 119909

2) (1 + 119892 (119909))

min1198913 (119909) = 05 (1 minus 119909

1) (1 + 119892 (119909))

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2minus cos (20120587 (119909

119894minus 05))

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(16)

DTLZ2

min1198911 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) cos(119909

2

120587

2)

min1198912 (119909) = (1 + 119892 (119909)) cos(1199091

120587

2) sin(119909

2

120587

2)

min1198913 (119909) = (1 + 119892 (119909)) sin(1199091

120587

2)

119892 (119909) =

12

sum

119894=3

(119909119894minus 05)

2

ST 0 le 119909119894le 1 (119894 = 1 2 12)

(17)




Start











End

Yes

No

No

Yes


Yes

No




external document



condition

G = G + 1





GD =(sum119899

119894=1119889119901

119894)1119901

119899 (18)


119894is the



Δ =

119889119891+ 119889119897+ sum119899

119894=1

10038161003816100381610038161003816119889119894minus 119889

10038161003816100381610038161003816

119889119891+ 119889119897+ (119899 minus 1) times 119889

(19)



119891and 119889







⋃

119894=1

V119894) (20)






000

01

02

02 02

03

04

04 04

05

06

06 06

DTLZ1 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using DECell

f3(x

)

f2 (x) f 1

(x)

(b) DECell

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell








0 005 05

1 115 15

0

02

04

06

08

1

12

DTLZ2 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using DECell

f3(x

)

f2 (x)

f1(x

)

(b) DECell

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell









11198832 119883

119875119883119894= (119875EV(1 119894) 119875EV(2 119894) 119875EV(119873 119894))


1(119883119894) 1198652(119883119894) 1198653(119883119894)]



1199032119866


and 1198831199033119866



119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866


119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866


119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)



1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1


119894119866+1 If119880119894119866+1



119880119894119866+1






119873of one





119891 (SOC0 120583 120590) =

1


2(21205902) (23)



0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)


Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price






0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Start











End

Yes

No

No

Yes


Yes

No




external document



condition

G = G + 1





GD =(sum119899

119894=1119889119901

119894)1119901

119899 (18)


119894is the



Δ =

119889119891+ 119889119897+ sum119899

119894=1

10038161003816100381610038161003816119889119894minus 119889

10038161003816100381610038161003816

119889119891+ 119889119897+ (119899 minus 1) times 119889

(19)



119891and 119889







⋃

119894=1

V119894) (20)






000

01

02

02 02

03

04

04 04

05

06

06 06

DTLZ1 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using DECell

f3(x

)

f2 (x) f 1

(x)

(b) DECell

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell








0 005 05

1 115 15

0

02

04

06

08

1

12

DTLZ2 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using DECell

f3(x

)

f2 (x)

f1(x

)

(b) DECell

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell









11198832 119883

119875119883119894= (119875EV(1 119894) 119875EV(2 119894) 119875EV(119873 119894))


1(119883119894) 1198652(119883119894) 1198653(119883119894)]



1199032119866


and 1198831199033119866



119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866


119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866


119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)



1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1


119894119866+1 If119880119894119866+1



119880119894119866+1






119873of one





119891 (SOC0 120583 120590) =

1


2(21205902) (23)



0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)


Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price






0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




GD =(sum119899

119894=1119889119901

119894)1119901

119899 (18)


119894is the



Δ =

119889119891+ 119889119897+ sum119899

119894=1

10038161003816100381610038161003816119889119894minus 119889

10038161003816100381610038161003816

119889119891+ 119889119897+ (119899 minus 1) times 119889

(19)



119891and 119889







⋃

119894=1

V119894) (20)






000

01

02

02 02

03

04

04 04

05

06

06 06

DTLZ1 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using DECell

f3(x

)

f2 (x) f 1

(x)

(b) DECell

0

01

02

03

04

05

06

002

0406

002

0406

DTLZ1 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell








0 005 05

1 115 15

0

02

04

06

08

1

12

DTLZ2 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using DECell

f3(x

)

f2 (x)

f1(x

)

(b) DECell

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell









11198832 119883

119875119883119894= (119875EV(1 119894) 119875EV(2 119894) 119875EV(119873 119894))


1(119883119894) 1198652(119883119894) 1198653(119883119894)]



1199032119866


and 1198831199033119866



119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866


119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866


119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)



1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1


119894119866+1 If119880119894119866+1



119880119894119866+1






119873of one





119891 (SOC0 120583 120590) =

1


2(21205902) (23)



0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)


Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price






0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





0 005 05

1 115 15

0

02

04

06

08

1

12

DTLZ2 using NSGA-II

f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using DECell

f3(x

)

f2 (x)

f1(x

)

(b) DECell

005

115

005

115

0

02

04

06

08

1

12

DTLZ2 using IDECell

f3(x

)

f2 (x) f1

(x)

(c) IDECell









11198832 119883

119875119883119894= (119875EV(1 119894) 119875EV(2 119894) 119875EV(119873 119894))


1(119883119894) 1198652(119883119894) 1198653(119883119894)]



1199032119866


and 1198831199033119866



119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866


119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866


119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)



1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1


119894119866+1 If119880119894119866+1



119880119894119866+1






119873of one





119891 (SOC0 120583 120590) =

1


2(21205902) (23)



0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)


Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price






0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


and 1198831199033119866



119894119866= (V1198941119866

V1198942119866

V119894119895119866

V119894119873119866


119894119866= (1199091198941119866

1199091198942119866

119909119894119895119866

119909119894119873119866


119894119866+1= [1199061198941119866+1

1199061198942119866+1

119906119894119895119866+1

119906119894119873119866+1

]

119881119894119866

= 1198831199031119866

+ 119865 sdot (1198831199032119866

minus 1198831199033119866

) (21)

119906119894119895119866+1

= V119894119895119866

rand119895lt CR or 119895 = 119870

119909119894119895119866

others(22)



1(119880119894119866+1

) 1198652(119880119894119866+1

) 1198653(119880119894119866+1


119894119866+1 If119880119894119866+1



119880119894119866+1






119873of one





119891 (SOC0 120583 120590) =

1


2(21205902) (23)



0

01

02

03

04

05

06

07

08

09

1

1 3 5 7 9 11 13 15 17 19 21 23Time (h)


Flat price

Elec

tric

ity p

rice (

Yuan

kW

middoth)

Figure 9 TOU price






0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f1

(x)

(a) NSGA-II

0500

100015002000250030003500400045005000

f3(x

)

0200

400600

0

50

100

f2 (x)

f1(x

)


(b) DECell

0

200

400600

020

4060

80100

0500

100015002000250030003500400045005000


f3(x

)

f2 (x) f 1

(x)

(c) IDECell



Time (h) Power (kW)1 02 03 04 05 06 9327 82328 4799 7636810 6273211 8500412 9986813 15333214 14467215 10083216 145917 15303218 10406819 4564820 1396821 022 023 024 0



CValue 08 02 10 200 1000 100 20






119891119894=

3

sum

119899=1

(119891119894 (119899) minus 119891min (119899)

119891max (119899) minus 119891min (119899)) (24)






0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12

Char

ging

pow

er (k

W)

T (h)









0

02

04

06

08

1

12

1 2 3 4 5 6 7 8 9 10 11 12

SOC

(100

)

T (h)


0

02

04

06

08

1

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12



T (h)

Pow

er (1

000

kW)







6 Conclusions



8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


8

49 43




915

76








Acknowledgments


References





































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Research Article Coordinated Control of PV Generation and EVs...

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