Research ArticleOn the Optimization Strategy of EV Charging Station Localizationand Charging Piles Density

Wenzao Li,1,2 Lingling Yang ,1 Zhan Wen,1 Jiali Chen,1 and Xi Wu3

1College of Communication Engineering, Chengdu University of Information Technology, 610225, China2Network and Data Security Key Laboratory of Sichuan Province, University of Electronic Science and Technology of China,610054, China3School of Computer Science, Chengdu University of Information Technology, 610225, China

Correspondence should be addressed to Lingling Yang; yanglledu@sina.com

Received 18 December 2020; Revised 24 January 2021; Accepted 2 February 2021; Published 23 February 2021

Academic Editor: Zhili Zhou

Copyright © 2021 Wenzao Li et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The penetration rate of electronic vehicles (EVs) has been increasing rapidly in recent years, and the deployment of EVinfrastructure has become an increasingly important topic in some solutions of the Internet of Things (IoT). A reasonablebalance needs to be struck between the user experience and the deployment cost of charging stations and the number ofcharging piles. The deployment of EV’s charging station is a challenging problem due to the uneven distribution and mobility ofEV. Fortunately, EVs move with a certain regularity in the urban environment. It makes the deployment strategy design of EVcharging stations feasible. Therefore, we proposed a deployment strategy of EV charging station based on particle swarmoptimization algorithm to determine the charging station localization and number of charging piles. This strategy is designedbased on the nonuniform distribution of EV in a city scene map, at the same time, the distribution of EV at different times,which makes the strategy more reasonable. Extensive simulation results further demonstrated that the proposed strategy cansignificantly outperform the K-means algorithm in the urban environment.

1. Introduction

1.1. Background and Motivation. Electric vehicle (EV) hasgradually played a pivotal role in the people’s life due to therapid development of EV and the Internet of Things (IoT)technology. The first half of 2020 was attacked by theCOVID-19 virus, causing unprecedented deciles for vehiclesales. We can find that the number of global EV reachedmore than two hundred million in 2019, which is 9% higherthan for 2018 [1]. Therefore, the construction of EV infra-structure has a crucial impact on the experience of EV con-sumers. The distributed charging station localization andcharging pile density are two important issues in the funda-mental infrastructure construction [2, 3]. Obviously, it affectsthe construction cost and user service quality. Most of thestate-of-art estimation location approach for EV chargingstations depends on the distribution of vehicles [4]. Unfortu-nately, area EV density is changing at any time due to themovement of EV. Therefore, the static EVs’ distribution can-

not effectively reflect the effect of the charging station locali-zation strategy. Deploying many charging stations canimprove the user experience to some extent, but it will leadto increased construction costs. Conversely, it will increasethe charging queue time of users. Thus, the traditional sys-tematic approach usually discusses the solution to balancethe requirements between the customers’ experience andeconomic efficiency [5]. As the IoT technology evolves, rea-sonable charging pile layout will greatly benefit the develop-ment of intelligent transportation [6]. For such reason, wepropose the development strategy of charging stations underthe change of EV density in urban areas. Besides, we give acalculation approach of the number of charging piles for eachcharging station.

1.2. Limitations of Prior Work. There were various locationsestimating approaches, which were based on the range ofEV and traffic density in cities. Catalbas et al. proposed theestimation method. Besides, they have modeled it as a basic

HindawiWireless Communications and Mobile ComputingVolume 2021, Article ID 6675841, 13 pageshttps://doi.org/10.1155/2021/6675841

optimization problem [7]. It adopts the average number ofEVs and average driving distance as the important param-eters in the approach. But this method does not considerthe vehicle density changes. Schmidt and Eisel considerthe user charging habits, and these historical data can esti-mate the localization of charging stations [8]. Yan et al.also adopt the particle swarm optimization algorithm tosolve the localization problem of charging stations. It notonly considered the planning of charging station locationbut also include the capacity of charging stations [9]. Inthe above researches, some of them did not consider thedensity changes, and some researchers did not adopt morerealistic vehicle distribution data. Besides, the cost ofcharging stations and EV queuing time should be impor-tant factors in proposed algorithms.

1.3. Challenges and Solutions. There are several challengesfor the localization of charging stations and charging piledensity determination. First, the density change of EV isnot only related to time, but also related to map informa-tion in urban environments. Therefore, to design the opti-mization algorithm, such as the heuristic method, shouldconsider dynamic changes of EV. Second, the distributeddata of EV needs to be closed to the actual situation whichis based on the map information. Besides, the EV shouldconform to the movement model of EV. And such manyEV distribution data collection is quite difficult. Third, asthe number of EVs increases, the number of charging sta-tions and charging piles should be flexible in the calcula-tion strategy. Under a certain number of EVinfrastructure scenario, user experiment is difficult toquantify. Based on the above challenges, we set up Work-ing Day Movement (WDM) models to obtain EVs’ posi-tion at different moments. Then, Improved ParticleSwarm Optimization (IPSO) algorithm and K-meansapproach solve the optimization problems after buildingan economic cost and user experience model.

1.4. Contributions and Organization. The contributions ofthis paper are summarized as follows. This paper modelsthe charging station localization and charging pile densitybased onmore reasonable data sets. Then, the proposed IPSOalgorithm, which outperforms the K-means approach, isused to determine the location of charging stations. Besides,a strategy is proposed to calculate the number of chargingpiles based on user queue time. It is a flexible method to cal-culate the number of charging piles based on the constraint ofuser queuing time. Finally, we compare and verify the pro-posed method based on the distribution of EVs at differenttime points. This verification approach is more persuasivein such scenarios.

The rest of this paper is organized as follows. In Section2.1, we introduce the scenario and system model. In Section2.2, we give the details of the proposed algorithm based onthe above scenario and the determination method of charg-ing piles. The simulation scenario and results are presentedin Section 3. Section 4 discusses related works, and finally,conclusion is in Section 5.

2. The Charging Station Deploying Scenario andSystem Model

In Urban areas, EVs are unevenly distributed in locationswhere roads are available. Besides, in the deployment ofcharging stations, the station service capacity of each charg-ing station needs to be considered. EV with reasonable radiuscoverage has multiple station choices, but different choiceswill lead to different charging costs. In this paper, we referto reference [10] to plan the charging station deploying sce-nario and system model. Therefore, the cost in this papermainly includes EV’s driving cost and charging station’s con-struction cost. From the perspective of user cost, we formu-lated this driving cost as the driving time cost between EVand charge station, energy consumption cost for the chargingroad, and queuing time or line time cost. The constructioncost is mainly reflected in the number of charging stationsand charging piles. Achieve the minimum amount in termsof satisfying the charging requirements for EVs. The cover-age of EVs with EV charging stations is the key point ofcharging station deployment. The driving cost φi

ζ is betweenthe current position of EV i and the charging station ζ, whichcan be represented as equation (1).

φiζ =Vi

TC vi, diζ� �

+ViTE vi, diζ� �

+ CiSL Nζ

� �, ð1Þ

where the ViTCðvi, diζÞ represents the travel time cost of

the EV i to the charging station ζ, ViTEðvi, diζÞ represents

the energy consumption cost of the EV i to the charging sta-tion ζ, and Ci

SLðNCSÞ represents the queue time cost of the EVi at the charging station ζ.

We also define the driving distance to the charging sta-tion. In the complex urban traffic situation, the constantspeed model is not conductive to the reality of the scenario.In order to simulate the driving situation of road more real-istically, we consider the nonlinear coefficient and back coef-ficient of road in the distance factor. The same in this paper,we consider the nonlinear coefficient of urban roads to calcu-late the distance traveled by EV, which can be given as equa-tion (2).

Diζ = λiζ ∗ γiζ ∗ diζ, ð2Þ

where the γiζ is the reentry coefficient of the EV journey

from the EV i to the charging station ζ, diζ represents the lin-

ear distance from the EV i to the charging station ζ, and λiζdenotes the nonlinear coefficient of the urban road fromthe EV i to the charging station ζ, which can be representedas the equation (3).

λiζ =dit_ζdiζ

: ð3Þ

The minimum value of λiζ is 1, and the smaller the λiζ , themore convenient the trip between the two points.

2 Wireless Communications and Mobile Computing

The time-consuming cost of EVs on road can be calcu-lated as equation (4).

ViTC vi, diζ� �

=TβtimeNc ∑ζ∈CS∑i∈CDD

iζ

� �vi

, ð4Þ

where the βtime represents the time cost of EVs, vi is theaverage driving speed of EVs, and T is the time period. Thecost of charging period for an EV is considered a relativelylong cycles to estimate for more realistic. At the same time,a year was chosen because it would cost the same as thecharging station cost. Nc is the number of daily charging ofEVs.

Nc =E1km ∗ k

B, ð5Þ

where the E1km represents the energy consumption ofEVs, k represents the daily mileage of EVs, and B representsthe battery capacity of EVs.

The cost of energy consumption for EVs to reach thecharging station can be calculated as equation (6).

ViTE vi, diζ� �

= TmNc 〠ζ∈CS

〠i∈CD

DiζE1km

!, ð6Þ

where the m denotes the electricity price in the plannedarea.

The construction cost of the charging station is com-posed of the fixed construction cost and the annual operatingcost of the charging station, which can be calculated by equa-tion (7).

CζSC Nζ

� �= 〠

ζ∈CSf ζ Nζ

� �RZ + uζ Nζ

� �, ð7Þ

where the CζSCðNζÞ implies the construction cost of the

charging station.The fixed construction cost f ζðNζÞ of the charging sta-

tion ζ can be denoted as function (8).

f ζ Nζ

� �=Wζ + qζNζ +mζ, ð8Þ

where the Wζ is the fixed investment cost of each charg-ing station, qζ is the construction investment cost related tothe charger in the charging station, mζ is the investment costrelated to the transformer in the charging station, and Nζ isthe number of charging piles in charging station ζ.

By reading a large number of references and combin-ing the simulation environment of this paper, the annualoperating cost of the charging station ζ can be representedas function (9). The coefficient of f ζ was adopted by thereference [10].

uζ Nζ

� �= 0:1f ζ Nζ

� �: ð9Þ

RZ is the discount factor of the charging station whichcan be represented as function (10).

RZ =rr 1 + rrð Þmsð Þ1 + rrð Þms−1 , ð10Þ

where the rr is the discount rate and ms is the depre-ciation period of the charging station.

The construction of the charging station not only needsto consider the construction cost of the charging station, butalso needs to consider the driving cost of EVs. This paperfocuses the total cost of charging stations and EVs. Itincludes the charging stations’ construction cost and EV’sdriving cost. We establish a mathematical model for thelocation of EV charging stations, which can be describedas equation (11).

Costtotal = CζSC Nζ

� �+ φi

ζ, ð11Þ

where the Costtotal is the total cost, CζSCðNζÞ is the construc-

tion cost of the charging station, and φiζ is the EV’s driving

cost.

2.1. The Determination Method on the Deployment Numberof Charging Pile in Charging Station. The EV needs to waitin line for idle charging pile for energy supplement. Inorder to reduce the waiting time and increase the userexperience, queuing theory is a more effective solution.Queuing theory is through statistical research on thearrival and service time of service objects, to obtain statis-tical laws of quantitative indicators such as waiting time,queue length, and length of a busy period. It can improvethe structure of the service system or reorganize the ser-vice objects according to above laws. So that the servicesystem not only meets or closes to the requirements ofthe service’s target, but also can make the organization’sexpenses the most economical or some indicators are opti-mal. The planning of the number of charging piles foreach EV charging station is to meet the needs of EVsand to optimize the economics of the charging station.Therefore, this strategy adopted queuing theory multiser-vice desk model (M/M/S) to establish charging stations’capacity allocation model. In the queuing system of thecharging station, the arrival time of EV obeys the Poissondistribution with the parameter λ, and the service time ofeach service desk is independent of each other and obeysthe negative exponential distribution with the parameterμ. The average queue length Ls of the EV at the chargingstation can be denoted as function (12).

Ls =P0ρ

NζρNζ

Nζ! 1 − ρNζ

� �2 + ρ, ð12Þ

3Wireless Communications and Mobile Computing

where the P0 is the probability that all charging pilesin the charging station are idle, which can be representedas function (13).

P0 = 〠Nζ−1

n=0

ρn

n!+

ρNζ

Nζ! 1 − ρNζ

� �24

35−1

, ð13Þ

where the n is the number of EVs.

ρNζ=

ρ

Nζ

=λ

Nζμ: ð14Þ

The residence time of the EV at the charging stationcan be represented as function (15).

Ws =Lsλ: ð15Þ

The cost of the waiting time of an EV at a chargingstation can be represented as function (16).

CiSL Nζ

� �= TβtimeNc 〠

ζ∈CS〠i∈CD

Ws −1μ

� � !: ð16Þ

The objective function of this paper can be representedas function (17).

Cost = min Costtotalð Þ, ð17Þ

where the cost is the lowest cost considering the costof the charging station (construction cost and annualoperating cost) and the cost of the EV (road travel timecost, energy consumption cost, and waiting time cost atcharging station).

2.2. The Constraints of Formulated Model. In determining thenumber of charging piles, the number of charging pilesshould be a reasonable value. Similarly, the constraints ofcharging stations and electric vehicles are reflected in thedistance traveled. The number of EV services is also fixedin the charging station. Therefore, we enumerate the relevantconstraints in the problem in this subsection.

The number of charging piles in each charging station ζcan be represented as function (18).

Nζ ∈ Nζ,min,Nζ,max�

, ð18Þ

where the Nζ,min is the minimum number of charging pilesincluded in the charging station ζ andNζ,max is the maximumnumber of charging piles included in the charging station ζ.

The distance constraint between charging stations can berepresented as function (19).

Dcs_ζ1,ζ2 ≥Dmin, ð19Þ

where the Dmin is the minimum distance between twocharging stations ζ1 and ζ2.

The distance constraint from the EV i to the chargingstation ζ can be represented as function (20).

Di_ζ ≤Dmax, ð20Þ

where the Dmax is the maximum distance to the chargingstation ζ when the EV i needs to be charged.

In order to avoid the long queue of EVs at the chargingstation and ensure the stability of the queuing system, thearrival rate of EVs should be less than the product of theservice rate of the charging station and the number of charg-ing piles, which can be represented as function (21).

λ ≤ μNζ: ð21Þ

Direction of time8thhour 16thhour 24thhour 40thhour 48thhour32ndhour

Sampling forcalculation

Sampling forcalculation

Sampling forcalculation

Sampling forcalculation

Sampling forcalculation

Sampling forcalculation

Figure 1: The strategy for location determination of charging stations.

8thhour

16thhour

24thhour

min(D1+D2+D3)

D1

D2

D3

Figure 2: Schematic diagram of the final location of the chargingstation.

4 Wireless Communications and Mobile Computing

The residence time limit of EV i at charging station ζ canbe represented as function (22).

Ws ≤Ws−max, ð22Þ

where theWs−max is the maximum residence time of the EV iat the charging station ζ (Ws−max = 40 minÞ.

3. The Details of Proposed Algorithm in theCharging Station Deployment Scenario

3.1. Location Data Acquisition under Dynamic Change ofEVs. As the density of EVs varies with the time in theurban areas, the change should be fully considered in thedeployment approach. In order to obtain the distributeddata of EVs that are closer to the real scene, the Opportu-nistic Network Environment (ONE) is adopted as the datagenerator [11]. Fortunately, the movement of EVs is regu-larly in urban areas. They move daily among offices,homes, and markets that result in the regularity of density

changes [12]. Therefore, we use the Working Day Move-ment (WDM) model to collect EV distribution data setat different times for the localization approach [13]. Obvi-ously, such a strategy can effectively avoid the process ofmeasuring dynamic changes with distributed data.

We comprehensively consider the location distributionof EVs at 8th hour, 16th hour, and 24th hour and formulatea strategy for the location and capacity of charging stations.Then, we use the position distribution of EVs at 32nd hour,40th hour, and 48th hour to verify whether the strategy is opti-mal, which can be represented as Figure 1:

3.2. The Final Location of the Charging Station. In this paper,the main purpose is to plan the deployment of charging sta-tions in the city. Therefore, according to the location distri-bution of EVs at different times, the optimal location ofcharging stations will vary to a certain extent. Therefore, wehave formulated a strategy for determining the location ofthe charging station, considering the deployment of thecharging station at 8th hour, 16th hour, and 24th hour, and

Input: EV location data set U ,U = fðx1, y1Þ, ðx2, y2Þ,⋯, ðxm, ymÞg.Output: the location and number of charging stations and the number of charging piles in the charging station under the optimal costmin ðCosttotalÞ.1: According to the location and quantity of EVs in the planned area, estimate the range of the number of charging stations in theplanned area ½Nmin,Nmax�2: Set the initial value of the number of charging stations NCS =Nmin3: while ðNmin ≤NCS ≤NmaxÞ4: Randomly select NCS group data from U as the initial position data set CS of the charging station, CS = fðX1, Y1Þ, ðX2, Y2Þ,⋯, ðXNCS

, YNCSÞg

5: repeat6: LetCζ =∅ð1 ≤ ζ ≤NCSÞ7: for i = 1, 2,⋯,m do8: Calculate the Euclidean distance diζ from EV i, ðxi, yiÞ to each charging station ζð1 ≤ ζ ≤NCSÞ,ðXζ, YζÞ9: According to the principle of closest distance, determine which charging station each EV belongs to: αi =arg minζ∈f1,2,⋯,NCSgd

iζ

10: Assign EVsðxi, yiÞ to the corresponding charging stations: Cαi= Cαi

∪ fðxi, yiÞg11: end for12: for ζ = 1, 2,⋯,NCS do13: Calculate the location of the new charging station: ðXζ, YζÞ′ = 1/∣Cζ ∣ ∑ðx,yÞ∈Cζ

ðx, yÞ14: if ðXζ, YζÞ′ = ðXζ, YζÞ then15: Update the current charging station location ðXζ, YζÞ to ðXζ, YζÞ′16: else17: Keep the current mean vector unchanged18: end if19: end for20: until the current charging station location is no longer updated21: Current output: division of service scope of charging stationsC = C1, C2,⋯, CNCS

22: Use queuing theory [M/M/S] to calculate the number of charging piles in the charging stationNpiles = fNC1,NC2

,⋯,NCNCSg

23: Calculate the total cost of deploying NCS charging stations CostNCS, CostNCS

= CostCS_construction + CostCS_run +CostEV_road_time + CostEV_road_energy + CostEV_line_time。24 end while25: Calculate the total cost of deploying different numbers of charging stations and get the total cost data set Costtotal, Costtotal= fCostNmin

, CostNmin+1,⋯, CostNmaxg

Algorithm 1. K-means algorithm

5Wireless Communications and Mobile Computing

determining the final location deployment strategy for thecharging station, which can be described as Figure 2.

According to the location distribution of EVs, the opti-mal location of the charging station and the number ofcharging piles in the charging station are calculated when dif-ferent numbers of charging stations are deployed.

3.3. The Details of Proposed Localization Algorithm. K-meansalgorithm is a clustering algorithm based on distance. In theK-means algorithm, first, randomly select N points to formthe cluster center, and then, divide the data in the data setinto the clusters where the nearest cluster center is located,so the data set samples will be divided into several disjoint

Input: EV position data setU , U = fðx1, y1Þ, ðx2, y2Þ,⋯, ðxm, ymÞg.Output: the location and number of charging stations and the number of charging piles in the charging station under the optimal costmin ðCosttotalÞ.1: According to the location and quantity of EVs in the planned area, estimate the range of the number of charging stations in theplanned area ½Nmin,Nmax�2: Set the initial value of the number of charging stations NCS =Nmin3: while ðNmin ≤NCS ≤NmaxÞ4: Set the maximum number of iterations of the algorithmMaxIter, particle population size PopSize, random values r1, r2,learning factors c1, c2, inertia weight ω5: for i = 1, 2,⋯,PopSize do6: Randomly select NCS group data from U as the charging station initial position data set Xi, Xi =fðX1, Y1Þ, ðX2, Y2Þ,⋯, ðXNCS

, YNCSÞg

i. Initial particle velocity Vi, Vi = r and

7: Use the Voronoi diagram to divide the service scope of the charging station A, A = fA1, A2,⋯, ANCSg

8: Assign EVs ðxm, ymÞ to the nearest charging station ANCS, ANCS

= ANCS∪ fðxm, ymÞg

9: Use queuing theory [M/M/S] to calculate the number of charging piles in the charging station Npiles,Npiles = fNC1

,NC2,⋯,NCNCS

g10: Calculate the total cost when deploying NCS charging stations in combination with constraint conditionsCost1i11: The optimal statistical particle individual is Pbest_i, Pbest_i = fðX1, Y1Þ, ðX2, Y2Þ,⋯, ðXNCS

, YNCSÞg

i12: end for13: The particle population cost data set is Cost1, Cost1 = fCost11, Cost12,⋯, Cost1PopSizeg14: The optimal data set of individual particles is P1best, P1best = fPbest_1, Pbest_2,⋯, Pbest_PopSizeg15: Set the particle global optimal value Best1, Best1 = min ðCost1Þ, the corresponding particle is the global optimal particle gbest116: repeat17: for j = 1, 2,⋯, PopSize do18: Update particle velocity V j, V j = ω ∗V j + c1r1ðPbest_j − XjÞ + c2r2ðgbest1 − XjÞ19: Update particle position Xj, Xj = Xj +V j

20: Calculate the total cost when deploying NCS charging stations in combination with constraint conditionsCost2 j21: Get the optimal position of each particle Pbest_2j22: ifCost2j ≤ Cost1j then23: Pbest_j = Pbest_2j24: else25: Keep the current particle position Pbest_j unchanged26: end if27: end for28: The particle population cost data set is Cost2, Cost2 = fCost21, Cost22,⋯, Cost2PopSizeg29: Set the global optimal value Best2, Best2 = min ðCost2Þ, determine the global optimal particle gbest230: ifBest2 ≤ Best1 then31: gbest1=gbest232: else33: Keep the current particle position gbest1 unchanged34: end if35: until the number of cycles reaches MaxIter36: end while37: Current output: output the optimal location for deploying NCS charging stations38: Use the optimal location to calculate the total cost of deployingNCS charging stationsCostNCS

and the number of charging piles inthe charging station.39: Calculate the total cost of deploying different numbers of charging stations and get the total cost data set Costtotal,Costtotal = fCostNmin

, CostNmin+1,⋯, CostNmaxg

Algorithm 2. Improved Particle Swarm Optimization (IPSO) algorithm

6 Wireless Communications and Mobile Computing

subsets. In each cluster, the distance from the objects in thesubset to the center of the subset is less than the distance tothe centers of other subsets. Finally, recalculate the new clus-ter center based on the new cluster. In the location of the

charging station, we assume that the EV is charged at thenearest charging station.

In the K-means algorithm, the center of each cluster is thelocation of the charging station, and the data set is the

Table 1: The key simulation parameters.

Parameter Value

Fixed investment (Wζ) 2 million

Investment related to the unit price of the charging piles in the charging station (q) 0.35 million

The investment cost related to the transformer in the charging station (eζ) 0.2 million

Discount rate (rr) 0.08

Charging station depreciation period (ms) 20 years

Average driving speed of EVs (v) 30 km/h

Time period (T) 365 days

Nonlinear coefficient of the urban road (λi ζ) 1.2

Minimum number of charging piles in the charging station (Nζ,min) 3

Maximum number of charging piles in the charging station (Nζ,max) 30

Minimum number of charging stations (Nmin) 3

Maximum number of charging stations (Nmax) 6

Minimum distance between two charging stations ζ1, ζ2(Dmin) 1.2 km

Maximum distance to the charging station ζ when the EV i needs to be charged 3 km

3

The number of charging stations

40%

60%

80%

100%

Perc

enta

ge

Value of 8th hour (K-means)Value of 8th hour (IPSO)

Value of 24th hour (K-means)Value of 24th hour (IPSO)

Average value (K-means)Average value (IPSO)

Value of 16th hour (K-means)Value of 16th hour (IPSO)

The number of charging stations

40%

60%

80%

100%Pe

rcen

tage

The number of charging stations

40%

60%

80%

100%

Perc

enta

ge

The number of charging stations

40%

60%

80%

100%

Perc

enta

ge

4 5 6 3 4 5 6

3 4 5 6 3 4 5 6

Figure 3: The ratio of actual total cost to estimated total cost.

7Wireless Communications and Mobile Computing

K-means

1

Charging station ID

0

5

10

15

20

25

Initi

al v

alue

of t

he n

umbe

r of c

harg

ing

pile

s

Initi

al v

alue

of t

he n

umbe

r of c

harg

ing

pile

s

IPSO

Charging station ID

0

5

10

15

20

25

8th hour16th hour24th hour

2 3 4 1 2 3 4

Figure 4: The initial number of charging piles in the charging station.

15 16 17 18 19 20 21 22

The number of charging piles

0102030405060708090

100

Ave

rage

que

ue ti

me

Charging station 1

15 16 17 18 19 20

The number of charging piles

0102030405060708090

100

Ave

rage

que

ue ti

me

Charging station 2

11 12 13 14 15

The number of charging piles

0102030405060708090

100

Ave

rage

que

ue ti

me

Charging station 3

7 10 11 12

The number of charging piles

0102030405060708090

100

Ave

rage

que

ue ti

me

Charging station 4

Wmax8th hour

16th hour24th hour

8 9

Figure 5: The relationship between the number of charging pile and the queue time of EVs (K-means algorithm).

8 Wireless Communications and Mobile Computing

location of the EV. We get N clusters, and the data set con-tained in each cluster is the location of the EV served bythe charging station. Therefore, we obtain the location distri-bution of the charging stations and the service range of thecharging station through the K-means algorithm. When theN charging stations are deployed, then we can obtain thenumber of charging piles in the charging station throughthe proposed method. The specific implementation of thealgorithm can be represented in Algorithm 1:

By Algorithm 1, we can obtain the locations of the charg-ing stations. Besides, the number of charging piles of a charg-ing station can be determined. When different numbers ofcharging stations are deployed at different times, then wecan obtain the final charging station location by the chargingstation location determination strategy. It also comprehen-sively considers the number of charging piles in the chargingstation at each time to determine the final number of charg-ing piles.

The particle swarm algorithm adopts a group of initial-ized groups to search in parallel in the search space and real-izes the evolution of the population through the competitionand cooperation between individuals in the population. Inthe particle swarm algorithm, each particle represents apotential solution to the problem, and the fitness functionis used to judge the quality of the particle. The initial valueof the particle swarm is a group of random particles, search-ing for the optimal solution according to iterations. In eachiteration, the particles update their position and velocity

according to the individual optimal value and the global opti-mal value.

The IPSO algorithm adopts differential evolution algo-rithm to increase the activity of particles in the particleswarm. Therefore, the particles can jump out of the localoptimum to better global optimum.

In this algorithm, we use the site of the charging station asthe dimension of each particle. If N charging stations need tobe defined, the dimension of the particle is 2N . According tothe size of PopSize, each charging station randomly generatesPopSize site coordinates at the same time. Then, the servicerange of the charging station is divided according to the Vor-onoi diagram to obtain the number of charging piles. Then,we can calculate the fitness value of each particle and updatethe speed and position of the particle through the speed andposition update formula. Finally, find the optimal solutionthrough a number of iterations. Therefore, after calculatingby the IPSO algorithm, we obtain the location distributionstates and the service range of the charging station. We canalso obtain the number of charging piles through the methodof determining the number of charging piles when N charg-ing stations are deployed. The specific implementation of thealgorithm can be represented in Algorithm 2:

In Algorithm 2, we obtain the location of the chargingstation and the number of charging piles in the charging sta-tion when different numbers of charging stations aredeployed. Then, the charging station location determinationstrategy can be used to obtain the final charging station

11 12 13 14 15

The number of charging piles

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Figure 6: The relationship between the number of charging pile and the queue time of EVs (IPSO algorithm).

9Wireless Communications and Mobile Computing

location. And to determine the final number of charging pilesis feasible.

4. The Simulation Scenario and Results

Based on collecting several node distribution data of the Hel-sinki city map on ONE simulator, we carried out numericalexperiments. This paper sets the simulation parametersbased on the reference [14] simulation environment, whichcan be represented as Table 1.

In this paper, we estimate that the cost of the final locationand capacity solution is 1:5 ∗ 107. Due to the mobility of EVs,there are certain differences in the locations of EVs at differenttime periods. We considered the position distribution of EVsin the 8th hour, 16th hour, and 24th hour time points and cal-culated the actual total cost of deploying different numbersof charging stations in different time periods as a percentageof the estimated total cost. The result of the K-means algo-rithm and the IPSO algorithm can be represented as Figure 3.

From Figure 3, we can observe that both of two algo-rithms are optimal with 4 stations in the deployment area.

When planning the number of charging piles in a chargingstation, use queuing theory to calculate the number of charg-ing piles in each charging station. Because the queuing timeof EVs is considered in this paper, when there is no queuingtime limit, the number of charging piles in the charging stationis the initial value of the number of charging piles. When 4charging stations are deployed in different time periods, the

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Figure 8: Average queue time of EVs.

10 Wireless Communications and Mobile Computing

initial number of charging piles in each charging station isobtained. The calculation results under the K-means algo-rithm and the IPSO algorithm can be represented as Figure 4:

When there is a queuing time limit, the number of chargingpiles is increased on the basis of the initial value. Through calcu-lation, the relationship between the number of charging piles inthe charging station and the queuing time of EVs can beobtained. The calculation results under the K-means algorithmcan be represented as Figure 5, and the calculation results underthe IPSO algorithm can be represented as Figure 6:

As it is shown in Figures 5 and 6, the dotted line y = 10represents the maximum queuing time Wmax of EVs at thecharging station. By observing Figures 5 and 6, we can findthat as the number of charging piles in the charging stationincreases, the average queue time of EVs at the charging sta-

tion gradually decreases. The dotted ellipse indicates that nomatter what time period, when the number of charging pilesis deployed at the charging station ζ, the queue time of EVs atthe charging station ζ is within 10 minutes. Therefore, whenusing the K-means algorithm, we finally select the number ofcharging piles in the charging station to be [22; 20; 15; 12].When using the IPSO algorithm, we finally select the numberof charging piles in the charging station as [24; 15; 15; 13].

In order to verify the effectiveness, we chose multipletime points (32nd hour, 40th hour, and 48th hour) to calculatethe cost. The ratio of the total cost of each time to the esti-mated total cost can be represented as Figure 7.

By observing Figure 7, we can find that when 4 chargingstations are deployed in different time periods, the cost is thelowest. It shows that whether it is based on the K-means

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Figure 10: Location and service range of charging stations.

11Wireless Communications and Mobile Computing

algorithm or the IPSO algorithm, it is relatively better todeploy 4 charging stations when planning the charging sta-tion. At the same time, we can find that when 4 charging sta-tions are deployed, the total cost when using the IPSOalgorithm is better than the K-means algorithm.

In the 32nd hour, 40th hour, and 48th hour time points, theaverage queuing time of EVs is calculated by queuing theory.The average queue time of EVs can be shown in Figure 8:

From Figure 8, we apply the termination method to cal-culate the number of charging piles at the charging station.And the average queue time of EVs can be less than 10minutes, which meets the original design intention.

At different moments, based on the K-means algorithmand the IPSO algorithm, the charging station location and ser-vice range are described in Figure 9(K-means algorithm_8th

hour and K-means algorithm_16th hour), Figure 10(K-meansalgorithm_24th hour and IPSO algorithm_8th hour), andFigure 11(IPSO algorithm _16th hour and IPSO algorithm_24th hour). It can be seen from these figures that the resultsof the two algorithms are similar to those of the service areadivision. However, the cost of the calculation based on the ser-vice area still shows the pros and cons of the two solutions.

With the K-means algorithm, the actual total cost ofdeploying 4 charging stations is 50.70% of the estimated totalcost. With the particle swarm algorithm, the actual total costof deploying 4 charging stations is 46.45% of the estimatedtotal cost. With the IPSO algorithm, the actual total cost ofdeploying 4 charging stations is 46.04% of the estimated totalcost. The total cost of IPSO algorithm is 9.19% lower than theK-means algorithm in such scenario.

5. Related Works

The planning of EV charging stations and charging piles andsome short-range communication techniques are attractiveresearch fields for charging demand intelligence guidance[15–17]. At the same time, it is also an important issue in

Smart Cities (SC) [18]. The difficulties focus on charging sta-tion determination in charging planning. Eisel et al. formu-lated the charging problem based on user’s charging habitsand proposed a method for selecting the location of chargingstations [19]. Tang et al. proposed a weighted Voronoi dia-gram (VD) approach to determine the location of EV chargingstations [20]. Nahum and Hadas proposed a multiobjectiveoptimal allocation approach for bus charging planning [21].It can be found from these studies that EV charging problemis a typical resource allocation problem. Therefore, the heuris-tic algorithm and clusteringmethod can get better results. Par-ticle swarm optimization has advantages in this kind ofproblem [22, 23]. But there are some problems with the aboveresearch. First, the implementations of the proposed algo-rithms are based on different system models, which areincomplete for result analysis. Second, the simulated data setdoes not take into account the variation of EV density. Thevalidation of algorithm results is not sufficiently supported.Third, some researchers discussed the location of charging sta-tions, and some discussed the number of charging piles; thus,it lacked systematic and comprehensive analysis.

6. Conclusions

The charging station localization and charging pile determi-nation based on the distribution of EVs can effectivelydecrease the cost of users and urban construction. Thereare many detects in the direct addressing of the static EV’sdistribution data, because the distribution of EVs changeswith time and geographic area. Thus, this paper introducesa strategy with IPSO-based algorithm, which is used fordetermining the location of the charging station. Besides,we also provide an approach to determine the number ofcharging piles in a charging station according to userdemand. And based on this strategy, we proposed theaddressing method based on K-means algorithm. Thoughnumerical experiments are based on more realistic data set,

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Figure 11: Location and service range of charging stations.

12 Wireless Communications and Mobile Computing

we found that the algorithm based on IPSO outperforms theK-means. Moreover, we have fully discussed the results,which have great significance to the EV charging stationdeployment and user’s experiments.

Data Availability

The underlying data can be obtained by the correspondingauthor. Correspondence should be addressed to LinglingYang.

Conflicts of Interest

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

Acknowledgments

We thank all the reviewers and editors who have contributedto the quality of this paper. At the same time, we also appre-ciate the support by Sichuan Science and Technology Pro-gram (No. 2019ZDZX0005) and the fund from theNetwork and Data Security Key Laboratory of Sichuan Prov-ince, University of Electronic Science and Technology ofChina (UESTC) (No. NDS2021-7). Our preliminary workcan be seen in the literature [24].

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