Research Article Comprehensive Pricing Scheme of the EV ...

Research ArticleComprehensive Pricing Scheme of the EV ChargingStation considering Consumer Differences Based on IntegratedAHPDEA Methodology

Xingquan Ji1 ZiyangYin1 YuminZhang 1 XuanZhang1 HaishuGao1 andXinyi Zhang2

1College of Electrical Engineering and Automation Shandong University of Science and Technology Qingdao 266590 China2Qingdao Electric Power Supply Company of State Grid Shandong Electric Power Company Qingdao China

Correspondence should be addressed to Yumin Zhang ymzhang2019sdusteducn

Received 18 August 2020 Revised 25 September 2020 Accepted 27 September 2020 Published 10 October 2020

Academic Editor Ruben Specogna

Copyright copy 2020 Xingquan Ji et al +is 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

Scientific pricing of the electric vehicle charging station is closely related to consumer behavior inevitably Existing studies havenot considered the impacts of consumer differences on the charging price which will fail to meet the interests of various types ofconsumers +is paper proposes a novel pricing method based on consumer classification and comprehensive evaluationstrategies First the basis for consumer classification is established according to a single factor sensitivity analysis of the consumerbenefit model then the nonlinear expression of the basis is piecewise linearized Additionally with the principle of least fittingerror to determine consumersrsquo classification the initial charging price schemes for various types of consumers are formulatedSecond this paper defines evaluation indices and establishes the hierarchy model for comprehensive evaluation schemes Finallythe integrated analytic hierarchy process and data envelopment analysis are adopted for comprehensive evaluation of schemesSimulations results illustrate that the proposed method can formulate the comprehensive optimal charging price consideringconsumer differences and the method can reflect the impacts of both subjective and objective factors conveniently and accurately

1 Introduction

Electric vehicles (EVs) can reduce greenhouse gas emissionsand alleviate vehicle excessive dependence on petroleumresources [1] Research efforts are focusing on energy se-curity and low-carbon economy and under this situationEVs have become one of the primary choice alternatives forconventional fuel cars [2] With a series of governmentpublic policies support Shandong province will build350000 charging posts in five years [3] Tianjin has built 143chargingswitching stations which has realized a completecoverage of whole city [4] All these mean that the con-sumers using EVs are increasing rapidly EVs are becoming alarge-scale development trend as consumers seek ways toreduce emissions to protect the environment [5ndash7]

+ere are several factors influencing consumer prefer-ences and several studies have been conducted to under-stand how public policy affects consumer choices

manufacturer decisions and EV market growth [2] thatestablishes the market model of Chinese EVs consideringeight attributes In [8] the authors analyze the consumersrsquoattitude and demand for the EVs and indicates that thepurchase price and usage cost are the most important factorsfor purchase preferences of consumers In [9] the authorsaddress that consumer preferences are affected by rela-tionships between the product and service price of EV In[10] the authors compare and calculate total lifecycle costs(TLCC) of EVs with TLCC of the gasoline vehicle based onthe various driving range and the gasoline price and theresults indicate that TLCC of EV is more than TLCC ofgasoline vehicles In [11] the authors address the operationcost of the EV charging infrastructure and the simulationresults show that it is difficult for the EV charging infra-structure to gain profits In [12] the authors give a pricingrange of the EV charging station which can not only ensurethe profit of station operators but also improve the profit of

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 8657258 11 pageshttpsdoiorg10115520208657258

consumers compared to using the internal-combustion-engine vehicle In [13] the authors present a methodology toassess the coat-benefit and develop the service pricingstrategy of electric taxies in Shanghai China +erefore theservice pricing of charging is the crucial problem to en-courage consumer to using EVs +e charging station is oneof the indispensable components in the operation of the EVindustry [14] +e charging prices of the charging station arethe fees how much the consumers should pay the chargingstation operators for a certain amount of charging electricity(the sum of electricity and charging service charges) It is notonly the important reference factor for vehicle buyers tochoose EVs rather than ICV but also the main way foroperators to recover the cost of investment in charginginfrastructure and even is the principal means for powercompanies to motivate EVs consumers to change theircharging behaviors to optimize the distribution of the powerload [15] +erefore the reasonable pricing of EVs is the keyproblem to promote the development of the EV industry

In order to establish a reasonable charging servicingprice various forms of charging price strategies are for-mulated and implemented overseas and in China [16ndash19]On the cost of self-charging at home the standard electricitytariffs of EVs charging prescribed by the United StatesCalifornia Pacific Gas and Electric Company (PGEC) arebased on the residential pricing and the time-of-use (TOU)price is set from 5 centskWh to 28 centskWh [20 21]Japan implements the preferential policies for free chargingin the stage of demonstration Some cities in China such asHangzhou have also launched their own local policies andthe pricing of EV charging is based on the method of cost-benefit income However this pricing has prompted EVs tooperate too costly which is not conducive to the promotionof the EVs industry [22] +e National Development andReform Commission of China (NDRC) issues that Chinaimplements the supportive policy on the price of EVcharging and the service fees of electric vehicle chargingstations are performed by the local according to the principleof ldquopreferential and discountrdquo with the government guidancepricing management Meanwhile the NDRC gives a pref-erential price to the centralized charging stations for thepurpose of business and implements large industrial elec-tricity prices +e charging service fees are gradually formedthrough market competition with the development ofmarket [23] Since June 2015 Beijing has charged the servicefees according to the capacity of charge up for battery +eupper limit standard of the charge per kilowatt-hour is equalto 15 of the highest retail price of No 92 gasoline per literon the same day of the city In addition until January 2020the electric vehicle charging service fees will perform theprice of market regulation in accordance with the provisionsof the state [24] Xinjiang has outlined a standard EVscharging service fee the upper limit of tentative price of theelectric vehicle charging fee is 12 RMB yuankWh and theupper limit of the electric bus charging fee is temporarily set1 RMB yuankWh [25]

+e market mechanism can promote the development ofthe EVs industry +e positive influence of the commercialTOU price on the operation benefit of EVs charging is

discussed in [26] San Diego Gas and Electric Companyestablishes an analysis model considering the impacts ofTOU price on the charging behaviors +e model assessesthe relationship between the position of charging infra-structure (residential and nonresidential areas) and chargingprice and determines three kinds of charging price schemeswhich the private EV consumers can choose [27] With therapid growth of charging stations for EVs EVs chargingswitching business modes become more important How-ever from the views of both EVs operators and consumers amore reasonable charging price considering various types ofconsumers has not been established

In the initial development of EVs the price of EVcharging does not have the conditions to determine the pricebased on market competition +e comprehensive costpricing which can balance the interests of all parties andensure the operating income is more advantageous topromote the development of EVs [22] In principle thepricing of the EVs charging station should consider thetripartite interests of the government operators and con-sumers [28] In [12] based on the Game theory the authorsconstruct the benefit models of EV operators and consumersin terms of the standard charging stations and the standardEV +ey also calculate a reasonable pricing range forcharging In [29] the authors further consider the influenceof the time value of money in project TOU and the level ofgovernment subsidies

Visibly for formulation of charging price it is vital tofully consider the influence of various factors and improvethe comprehensive cost pricing model [30] However incurrent studies the EV consumers are often considered asonly one type (standard or typical) which is not consistentwith the fact that consumers have very visible individualdifference and thus the pricing of EV charging will notachieve the expected effect

Accordingly the individual difference of consumersshould be taken into consideration in the pricing of EVcharging and the comprehensive evaluation of EV chargingprice should be solved effectively +e Analytic HierarchyProcess (AHP) [31] and Data Envelopment Analysis (DEA)[32] are the common comprehensive evaluation methodswhich are widely used in all kinds of decision-makingproblems In [33 34] the authors explore the use of hier-archical structure for classifying evaluation indices andemploy the integrated AHPDEA method in the differentstages of evaluation which verifies the more practicality andeffectiveness in dealing with complex problems

Because the private EV is becoming increasingly prev-alent as a means of transportation accounting for 85 of thecivilian cars [35] Considering that the individual consumeris more sensitive to the price of EV charging this paper takesthe private EV as an analysis object and proposes a novelpricing method of EV charging considering the consumerdifferences First set up the pricing method considering theinterests both of EV charging stationsrsquo operators and con-sumers comprehensively +en based on the analysis of thefactors affecting consumer interest changes this paperadopts the single factor sensitivity analysis to determine theprinciple of consumer classification and puts forward the

2 Mathematical Problems in Engineering

method of consumer classification Finally this paper es-tablishes the hierarchy model of evaluation defines theevaluation index and gives the calculation method of index+e optimal price for all types of consumers can be obtainedthrough the comprehensive decision-making of the initialcharging prices schemes based on the AHPDEA method+e effectiveness of the proposed method can be illustratedusing an actual EV charging station Simulation results verifythat the optimal charging prices applying to different typesof consumers can be determined and it can convenientlyreflect the demand response to price changes thus theexpected demand can be obtained by adjusting the price

2 The Methods on the Pricing of EV Charging

21 AWin-Win Pricing Strategy for Operator and ConsumerIf the pricing of EVs charging is conducive to the EVs in-dustry promotion it should follow the principle that boththe consumersrsquo comparative benefit (the use cost of EVs lessthan the use cost of the traditional internal-combustion-engine vehicle (ICV)) and the operatorsrsquo benefit (operatorcan profit) are positive So the reasonable pricing of EVcharging should balance the interests of both consumers andoperators

Yi(t) CIi minus COi ge 0 i 1 2 (1)

where Y1 is the benefit function of EVs operators Y2 is thecomparative benefit of consumers CI and CO are respec-tively the amounts of cash inflows and cash outflowsFigure 1 illustrates the structure chart of cash inflows andcash outflows based on the EVs charging mode

+e benefit model reflecting the interests of operatorsand consumers can be constructed by analyzing the mainfactors influencing the cost-benefit of operators and con-sumers Assume that the EV battery life is 8 years and theproject cycle is 16 years then the benefit function of op-erators and the comparative benefit function of consumersare shown in (2) and (3) respectively [26]

Y1(t)

Qc middot πc minusQc middot πp

η+ Sb + Sr1113888 1113889 t 0


η+ Sr1113888 1113889 tge 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

where Qc is the annual charging capacity of the chargingstations πc and πp are the charging prices and the feed-intariffs (FITs) respectively η is the loss of EV charging Sb andSr are respectively the station construction cost and theoperating cost Table 1 illustrates the parameters settingsvalue on the benefit function of EVs operators

Y2(t)

ΔCv + Dmil middot Fpm middot πf1113872 1113873 minus Bpe middot Eav + Dmil middot Epm middot πc + Dmil middot Epm middot Bpm1113872 1113873 t 0

Dmil middot Fpm middot πf1113872 1113873 minus Dmil middot Epm middot πc + Dmil middot Epm middot Bpm1113872 1113873 tge 1 an d tne 8 tne 16

Dmil middot Fpm middot πf + Bpr middot Eav1113872 1113873 minus Dmil middot Epm middot πc + Dmil middot Epm middot Bpm1113872 1113873 t 8 or t 16

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(3)

whereΔCv Cicv minus (Cev minus CIg) is the difference between thepurchase cost of the internal-combustion-engine vehicle andthe nude EV after subsidy Dmil and t are the annual distancedriven of EV and the service time respectively πf and Fpmare the fuel price and the fuel consumption per kilometerrespectively Eav is the average electricity capacity of thebattery Epm is the electricity consumption per kilometerBpe Bpr and Bpm are respectively the purchase cost per unitenergy of the battery recycling price andmaintenance costsVisibly the main factors influencing operators and con-sumers are the service charges converted by the charging

electricity tariffs siting costs and operating costs Table 2illustrates the parameters settings value on the comparativebenefit function of the consumer

According to the cost-benefit principle the economicindicators of profitability with the net present value (NPV)as the inspection cycle [26] the minimum profitablecharging price for EVs operators is

πc1 NPV1 1113944T

t0Y1(t) 1 + i0( 1113857

minus tπcπc1| ge 0

111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (4)

EVs consumers

Governmentsubsidies

Recycling costof the battery

Charging cost

Operators of the EVscharging station

Maintenancecosts of the battery

Operating cost

Electricitypurchase cost

Constructioncosts

Purchase cost ofEVs

Figure 1 Structure chart of cash inflows and cash outflows basedon the EVs charging mode

Mathematical Problems in Engineering 3

+emaximum acceptable charging price for consumers is

πc2 NPV2 1113944T

t0Y2(t) 1 + i0( 1113857


111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (5)

where T is the benchmark payback period of investment andT16 i0 is the benchmark yield and this paper takes 5 πc1and πc2 are the acceptable reasonable charging prices foroperators and consumers respectively +en the acceptablereasonable charging price range for both operators andconsumers is

πc πc1 le πc le πc211138681113868111386811138681113966 1113967 (6)

22 Construction Cost of EVs Charging Stations An EVscharging station generally contains the building partcharging part distribution monitoring communication andsecurity fire control part and other costs +e constructioncosts associated with providing charging infrastructure ofEVs charging stations are shown in Table 3

+e annual operation costs of an EVs charging stationgenerally contains labor costs utility bills communicationfees upkeep cost of battery and minimum attractive rate ofreturn +e operating costs of EVs charging stations areshown in Table 4

3 Consumer Classification

31 1e Basis of Consumer Classification As shown in (2) apart of the factors affecting consumersrsquo comparative benefitshas obvious individual differences and the determined price

using the single parameter to represent all consumers willfail to the accuracy +erefore if the consumer differencesare considered in formulation of the charging prices themodel corresponding to consumer classification will beestablished and it can take the interests of different types ofconsumers into account

+e differences of the purchase cost of the EV affect thecharging prices however it is not relevant to the behavior ofthe individual consumer using the EV+erefore this articledoes not consider the cost differences In (2) with the in-depth study of the parameters such as the fuel tax of the ICVthe prices of EV charging and maintenance costs of thebattery it can be found that they are all associated with theannual distance driven In order to further clarify the keyfactors influencing the comparative benefit of consumers itis necessary to perform the single-parameter sensitivityanalysis for the comparative benefit of consumers [36]

+e sensitivity of evaluation index to the influence factorcan be expressed with sensitivity coefficient

SAF ΔAAΔFF

(7)

where SAF is the sensitivity coefficient ΔAA is the changerate of evaluation index ΔFF is the change rate of theinfluence factor |SAF| is bigger namely the sensitivity co-efficient is high and it illustrates that the role of influencefactors cannot be ignored

Based on the comparative benefit model of consumers[26] this paper takes the NPV of consumers in a certainperiod as the evaluation index and takes the standard typesof consumers and the parameters of the EV charging stationas the base value Assume that the change range of each

Table 1 Parameters settings on the benefit function of EVs operators

Parameters Title Value UnitQc Annual charging capacity of charging stations 200 104 kWhπc Charging prices 178 RBM yuankWhπp Price of buying electricity from grid feed-in tariffs (FITs) 074 RBM yuankWhη Loss of EVs charging 092 Sb Cost associated with providing charging infrastructure of EVs charging stations 2415 RBM 104 yuanSr Operating costs 718 RBM 104 yuan

Table 2 Parameters settings on the comparative benefit function of consumers

Parameters Items Value UnitsΔCv Cicv minus (Cev minus CIg) +e difference between the purchase cost of the ICV and the nude EV after subsidy minus 3 RMB104 yuanCicv Purchase cost of the ICV 10 RMB104 yuanCev Purchase cost of the nude EVs 15 RMB104yuanCIg Government subsidies 2 RMB104 yuanDmil Annual distance driven of the EV 25000 kmyearT Annual service time of EVs hπf Fuel price 745 RMB yuanLFpm Fuel consumption per kilometer 0069 LkmEav Average electricity capacity of the battery 16 kWhEpm Electricity consumption per kilometer 014 kWhkmBpe Purchase cost per unit energy of the battery 3000 RMB yuankWhBpr Recycling price per unit energy of the battery 900 RMB yuankWhBpm Maintenance costs per unit energy of the battery 05 RMB yuankWh


factor is plusmn10 then the single-parameter sensitivity analysisfor the comparative benefit of consumers is shown inTable 5

As shown in Table 1 the fuel consumption per kilometerand oil price have the highest sensitivity among all pa-rameters both of them are the parameters related to thetraditional ICV and they are not relevant to consumerbehavior +e second is the annual distance driven and it isthe primary factor associated with consumer behaviorHowever all the other factors having higher sensitivity arenot relevant to the consumer behavior+erefore the annualdistance driven can be regarded as the main basis of con-sumer classification

321eMethod of Consumer Classification Assume that thetravel behavior of the private EV is consistent with the rulesof the traditional fuel vehicle [37] according to the findingsof the US Department of Transportation about the NationalHousehold Travel Survey (NHTS) [38] the distributionfunction curve of the proportion of consumers and the dailydistance driven are shown in Figure 2

Based on above analysis the method of classifyingconsumers according to the annual distance driven can beestablished as follows

(1) Select the appropriate samples that is the maximumdistance and the minimum distance should beeliminated+e daily distance driven of consumers is

less than 10 km the distance is very short and theimpact of charging prices on it is very small+erefore this part of consumers can be ignored Aswell as the part of consumers whose daily distancedriven is more than 120 km So this paper choosesthe consumers whose daily distance driven range is10 kmndash120 km (accounting for 73 of the totalsamples) as the sample to study

(2) +e piecewise linearization of the curve and thesegment results can be determined based on mini-mum fitting error Each piecewise corresponds to atype of consumers and the fitting error e can beexpressed using the average value of the standarddeviation

e 1N

1113944

N

i1

1n minus 1

1113944

n

j1

xi minus 1113954x

xi

1113888 1113889

211139741113972

(8)

where N is the number of segments of the piecewiselinearized curve xi is the true value of curve 1113954x is thelinear approximation value of xi n is the number offitting pointsTable 6 illustrates the segment results on the distancedriven range of consumers the distribution curve ofthe proportion of consumers and the correspondingfitting error +e best is that consumers are dividedinto four types Meanwhile the fitting error of

Table 3 Construction cost associated with providing charging infrastructure of EVs charging stations

Zone Items Number Cost (RBM 104 yuan) Cost (RBM 104 yuan)

Building part

Civil part 1 set 35053

46767HVAC part 1 set 3736Water supply and drainage part 1 set 4282

Civil electrical part 1 set 3696

Charging partOff-board charger for EVs 19 sets 42011

110261AC charging posts 30 2175DC charging posts 30 465

Distribution monitoringcommunication and securityand fire control

800 kVA dry-type transformers 2 26244

40897Supervision infrastructure 1 7308Communication infrastructure 1 3588

Security and fireproofing 1 3757

Other costCompile annually spreads 1 1306

43575Fixed other fee 1 36605Loan interest in the construction period 1 5664

Total cost 2415

Table 4 Operating costs of the EVs charging station

Items Cost (RMB 104 yuan) Calculation basis and remarksAnnual labor costs 468 Annual labor cost 13(persons) times 3000yuanmonth times 12monthAnnual utility bills 5 Experience valueAnnual communication fees 10 Experience valueAnnual upkeep cost of battery 10 Experience value

Minimum attractive rate of return 5 Calculate according to the slightly higher than thethree-year certificate of the deposit rate

Total 718


piecewise linearization cure is the minimum and thesegment results are shown in Figure 2

(3) Determine the typical values of consumers Becausethe daily distance driven of each consumer and thecorresponding distribution curve of the proportionof consumers are approximate linear relationship+erefore the average value of the daily distancedriven of each consumer can be regarded as thetypical values of distance driven of this consumerBased on the typical values of consumers the ac-ceptable charging price of this type of consumer canbe determined to form the initial charging pricescheme

4 Comprehensive Decision-Making ofCharging Prices

41 1e General Principle of Charging Price Evaluation+e comprehensive evaluation of the EV charging pricescheme and the decision-making goal are to select a com-prehensive optimal electricity price scheme which shouldconsider the economic interests of both the operators andconsumers and have good applicability and relatively higherlevel of satisfaction For this purpose this paper defines theevaluation criteria such as the economy applicability sat-isfaction and the specific indices which can be expressed asfollows

(1) Economy (P1) it illustrates whether the evaluationscheme is conducive to the economic index of theparticipantsSpecific indices taking the internal rate of return (I1)and dynamic payback period (I2) of consumers asindices to describe the economy of consumers thehigher I1 the smaller I2 and it illustrates that the betterthe economy of consumers to use the EV Taking theNPV (I3) and the dynamic payback period (I4) of theoperators as indices to describe their economy thehigher I3 the smaller I4 and it illustrates that the betterthe profitability of the EV charging station

(2) Applicability (P2) the index of the evaluationscheme considering the function of each type ofconsumerSpecific indices the proportion of consumer cor-responding to charging price (I5) and the standarddeviation of relative error of piecewise linearizeddistance driven of consumers (I6) express the ap-plication the higher I5 the smaller I6 and it illus-trates that the wider the applicable range of thecharging prices the better the applicable ability

(3) Satisfaction (P3) the index of acceptable degree ofparticipants to evaluation schemeSpecific indices the spread between charging pricesand expected price of operators (I7) and the spreadbetween determined charging price and strikecharging price (I8) express the satisfaction of par-ticipants +e smaller I7 the higher I8 and it meanshigher participants satisfaction Meanwhile thehigher the consumersrsquo acceptable price the moreconsumersrsquo surplus the easier consumer satisfactionwith the charging prices and the more beneficial tothe promotion of the EV industry

42 EstablishEvaluationCriteria andDetermine theWeight ofall Indexes Using AHP As analyzed in Section 41 thecomprehensive evaluation of charging price is a decision-making problem with multilevel and multifactor and thehierarchical structure of the model is shown in Figure 3

When using AHP to evaluate the charging price if youwant to rank all the schemes in order first you shoulddetermine the relative importance among all factors ofcriteria hierarchy that is weight +e method to determinethe weight of criteria hierarchy is as follows

Table 5 +e single-parameter sensitivity analysis for the com-parative benefit of consumers

Parameter +10 0 minus 10 SAF Sensitivity rankΔCv 174 144 114 208 8Dmil 262 144 061 819 3Fpm 310 144 minus 010 1153 1πf 298 144 minus 010 1069 2Bpe 063 144 224 563 6Eav 079 144 208 451 7Epm 037 144 262 743 4πc 061 144 239 576 5Bpm 120 144 168 167 9

0 50 100 150 200 250 300 350 400 450 5000

102030405060708090

100

(120 88)(90 80)

(60 67)

(30 40)

Prop

ortio

n of

cons

umer

s (

)

Daily distance driven (km)

(10 15)

Figure 2 +e daily distance driven of consumers and the corre-sponding proportion

Table 6 +e segment results of consumers and the correspondingfitting error

Piecewise block (km)Number of segments

3 4 5Shorter (10ndash32)Shorter (10ndash40) (10ndash30) (32ndash54)Middle (40ndash80) (30ndash60) (54ndash76)Long (80ndash120) (60ndash90) (76ndash98)Longer (90ndash120) (98ndash120)e 0033 0006 0008


(1) Determine the weight of criteria hierarchy Becausethe number of the criteria hierarchy is less thedifference among the criteria is very visible +ispaper adopts the 1sim9 scale method to construct thejudgment matrix P which realizes the quantitativecomparison of each element on the same hierarchyIf there are m criteria related to the overall goal thejudgment matrix is

P

P11 P12 middot middot middot P1j middot middot middot P1m


⋮ ⋮ ⋮ ⋮

Pi1 Pi2 middot middot middot Pij middot middot middot Pim

⋮ ⋮ ⋮ ⋮

Pm1 Pm2 middot middot middot Pmj middot middot middot Pmm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)

where the values of Pij(i j 1 2 n) are 1 3 5 7and 9+ey respectively denote the different degreesfrom the equal importance to extreme importancecomparing criterion iwith criterion j When we needto refine the value of importance Pij can also be 2 46 and 8

(2) Determine the weight between criteria hierarchy andthe target hierarchy +e square root method [19] isusually adopted to determine the weight value

First calculate the product Mi of all elements in everyrow of the judgment matrix P

Mi 1113945n

j1Pij i 1 2 m (10)

+en calculate the mth root of Mi

wi Mi

m1113968

i 1 2 m (11)

Finally Wi [w1 w2 wm]T is normalized

wi wi

1113936mj1 wj

i 1 2 m (12)

+en the coefficient vector constituted (of) byw (wP1 wP2 wPm ) is the relative weight of each cri-terion Similarly the weight of the index hierarchy relative toa certain criterion can be obtained

+e basis constructing the judgment matrix is qualitativesubjective judgment of the decision-makers however thenumber of indices in index hierarchy is more and the

importance of each index is difficult to distinguish subjec-tively Meanwhile each index exists a correlation withmultiple criteria at the same time Adopting the judgmentmatrix will affect the objectivity of the final result +ereforethis article only adopts the DEA model which has betterobjectivity to analyze the index hierarchy

43 1e Charging Prices Schemes are Ranked under the SingleCriterion Using DEA According to the foregoing discus-sion the input and output index sets of the economy ap-plicability and satisfaction of evaluation schemes are shownin Table 7 +e calculation method of each economic indexcan be seen in [26] and the other indices can be obtained bydefinition

+e DEA method regards the need decision-makingscheme as the decision-making unit (DMU) Assume thatthere are n DMU each DMU has m input x and s output ythey are respectively the consume cost of resource causedby the DMU and the benefit produced by DMU +en theefficiency evaluation of a certain evaluation criterion for thek(1le kle n) DMU is performed and the optimizationproblem on the variables with the input weight coefficient ofv (v1 v2 vm) and the output weight coefficient u

(u1 u2 um) can be formed as shown in the followingequationfd12

maxu

Tyk

vT

xk

VPk

stu

Tyj

vTxj

le 1

j 1 2 n vge 0 uge 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)

where xj (x1j x2j xmj)T and yj (y1j y2j ysj)

T

j 1 2 n VPk is the optimal efficiency index for the kth

DMU under the evaluation criteria+erefore the evaluation is transferred into ranking for

relative effectiveness of multiple DMU which enhances theobjectivity of the evaluation decision-making +e optimalefficiency indices V

P1k V

P2k and V

P3k can be obtained by

calculating the input index and the output index in Table 7

44 Comprehensive Evaluation of Initial Charging PriceScheme When the weights of evaluation criteria and theranks of the schemes under the single evaluation criterionare determined the comprehensive ranking of each DMU

Total target G

Criteria 1 (P1) Criteria 2 (P2) Criteria m (Pm)

Index 1 (I1) Index n (In)Index 2 (I2)

Targethierarchy

Criteria hierarchy

Index hierarchy

Figure 3 Hierarchy model for comprehensive evaluation


for the total target of evaluating can be normalized and theweighted sum can be got according to (13) +en thecomprehensive evaluation of initial scheme can be carriedout according to the size of the comprehensive sequencingweight Qi the greater the Qi the better the correspondingscheme

Qi wP1

VP1i

11139364i1 V

P1i

+ wP2

VP2i

11139364i1 V

P2i

+ wP3

VP3i

11139364i1 V

P3i

(14)

It should be pointed out that the input indices andoutput indices must be positive due to the limitations of thetraditional DEA model +e evaluation index of the NPVand the internal rate of return may be negative in thecharging price decision-making +erefore it is necessary todivide the input indices and output indices into groups andto process multiindex comprehensively before evaluationusing DEA [39]

5 Simulation Result and Discussion

In this section the simulation results and the performance ofthe proposed evaluation method can be solved using theMATLAB software In order to test the effectiveness of theproposed method this paper selects a charging station ofShandong province China [40] and the strike price of thecharging station is 082 yuankWh

+ree kinds of scenarios for pricing of EV chargingstations are analyzed as follows

Scenario 1 base scenario without considering theconsumer classificationScenario 2 considering the consumer classificationScenario 3 considering the changes of subjectiveweight on criteria

+e 500 kV power transmission system is constructed inPSCADEMTDC as shown in Figure 3 +e system includesthree transmission lines whose lengths are 100 km 200 kmand 100 km respectively R1 and R2 are the two relays on themiddle line Now the new traveling wave polarity com-parison protection can be studied by different fault locationsand different fault types

51 Scenario 1 1e Pricing of EV Charging Stations withoutconsidering the Consumer Classification Under the scenariowithout considering the consumer differences this paperselects the typical consumers as an example and the dailydistance driven range of typical consumers is 75 km [24]+eprofitable charging price for the operators can be got with

the basic method on charging pricing which is presented inSection 2

+e profitable charging price for operators is

πc11113868111386811138681113868 πc1 ge 228 yuankWh1113966 1113967 (15)

+e acceptable charging price for consumers is

πc21113868111386811138681113868 πc2 le 272 yuankWh1113966 1113967 (16)

+en the acceptable reasonable charging price range πc

for both operators and consumers is

πc 228 yuankWhle πc le 272 yuankWh11138681113868111386811138681113966 1113967 (17)

52 Scenario 2 1e Pricing of EV Charging Stations consid-ering the Consumer Classification According to the abovefour types of consumer classification four types of initialcharging price schemes can be determined with the men-tioned method and the results are shown in Table 8 +ecalculated values of the corresponding evaluationindicesI1simI7 are shown in Table 9 In order to ensure thecomparability of the indices the parameters of consumersare the unified value in the calculation of index I1 and indexI2 which corresponding to the daily distance driven is75 km

In general first the most important for comprehensiveoptimal decision-making of charging pricing is to ensure theeconomy of both operators and consumers Second if theapplicability is slightly more important through comparingapplicability with satisfaction then the judgment matrix ofevaluation criteria can be constructed with AHP and it is asfollows

P =

1

Economy Applicability Satisfaction

12

13

1

12

13

1

12

13

Economy

Applicability

Satisfaction

(18)

+e weight vector of the three criteria can be obtainedwith the square root method

w wP1 w

P2 wP31113872 1113873 (05396 02970 01634) (19)

+e optimal efficiency indices VP1 VP2 and VP3 can becalculated with DEA and the results are shown in Table 10

For the above four schemes the comprehensive rankingfor the weights of evaluation schemes can be calculatedaccording to (13) and is shown in Table 11

As shown in Table 11 the comprehensive ranking ofeach scheme are as follows 2 4 3 and 1 It means thatscheme 2 is the comprehensive optimal scheme meanwhilethe acceptable reasonable charging price rangeπc for bothoperators and consumers is


Further analysis shows that the efficiency indices VP3 ofscheme 2 is 1 and VP1 and VP2 are respectively 07053 and05533 So the applicability of the reasonable charging price

Table 7 +e index sets of the economy applicability and satis-faction of evaluation scheme

Evaluation criteria Input index Output indexEconomy P1 I2 I4 I1 I3Applicability P2 I6 I5Satisfaction P3 I7 I8


of the second type of consumers is not good However underthe premise of ensuring the interests of both the consumersand operators the overall satisfaction is very high +ereforethe comprehensive ranking for the weights of evaluationscheme is the maximum +e VP2 of scheme 4 is 1 but thecharging price at this period is high for most consumerswhich will seriously affect its overall economy and satisfactionand reduce its comprehensive ranking for weights +eeconomy of scheme 3 is optimal but its applicability andsatisfaction is low and due to the importance of the twocriteria that cannot be ignored the comprehensive rankingfor weight is relatively low+e charging price of scheme 1 foroperators is too low which will seriously influence itseconomy and satisfaction and the applicability is also poorerso the comprehensive ranking for weight is the minimum

Comparing the above two scenarios it can be found thatthere exists feasible price range in both cases however theformer price range upper limit is higher than the latter one+e latter considers different influences of charging priceson the benefits of all types of consumers and on the basis ofreasonable classification the charging price determinedusing the AHPDEA method can take the interests of mostconsumers into account therefore it is more reasonable

53 Scenario 3 1e Impact of Criteria Weight Changes on thePricing of EV Charging Stations In the comprehensive de-cision-making of charging price the different importance

degrees among criteria reflect the tendency and actual de-mand of decision makers and show the weights of criteriawith AHP At different stages of EV development the role ofcharging price is different and lays particular emphasis onthe formulation of price So the evaluation criteria weightswith AHP will change accordingly In this paper the weightsunder three extreme situations are discussed and the resultsare shown in Table 12 +e judgment matrix correspondingto situation 1 is

P =

1

Satisfaction Applicability Economy

19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)

+e same method may be easily adapted to obtainjudgment matrix under other situations

As shown in Table 12 when the criteria weights areassigned different values subjectively the evaluation resultswill be different+us different settings of evaluation criteriaweights using AHP can realize the formulation of chargingprices in terms of different requirements On the other handalthough scheme 3 specially emphasizes on the applicabilitywhich will enable scheme 4 to become the comprehensiveoptimal scheme the results of optimal and worst schemesare the same in other test cases +erefore it verifies that theproposed method for pricing of the EV charging station has

Table 8 Consumer classification and the initial charging price schemes

Schemes Classification (daily distancedriven)

Daily distance driven ofconsumers (km)

Proportion ofconsumers ()

Average daily distancedriven (km)

πc2 (yuankWh)

1 Short 10ndash30 25 20 0992 Middle 30ndash60 27 45 2323 Long 60ndash90 13 75 2774 Longer 90ndash120 8 105 296

Table 9 Index values of each initial charging price schemes

Schemes I1 () I2 (year) I3 (million yuan) I4 (year) I5 () I6 I7 (yuankWh) I8 (yuankWh)1 92 2 minus 30412 106 25 00082 129 0172 19 12 1076 15 27 00122 004 1503 5 16 1173 9 13 00042 049 1954 1 21 16229 8 8 00020 068 214

Table 10 +e optimal efficiency indices of each scheme

Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839

Table 11 Comprehensive ranking for the weights of evaluation scheme

Schemes 1 2 3 4Qi 02155 03401 02457 02527


better practicability+eDEAmethod can guarantee the roleof objective factors in evaluation schemes thus even if theweights of criteria hierarchy have changed the scientific andreasonable results most beneficial to majority consumers(scheme 2 has the highest proportion of consumers) can alsobe concluded

6 Conclusion

+e impacts of consumer differences on the formulation ofcharging prices cannot be ignored therefore this paperproposes a method on pricing of the EV charging stationwhich can take the interests of different consumers intoaccount +is method realizes effective classification ofconsumers with the private EV by sensitivity analysis andpiecewise linearization Based on the formation of the initialpricing schemes for various types of consumers the expertexperience and the relative efficiency indices of each schemecan respectively deal with by using AHP and DEAmethodsproperly +is method not only ensures the organic com-bination of subjective and objective factors in the schemeevaluation but also can reflect the emphasis of the evaluationscheme +erefore the comprehensive optimal chargingprice considering the economic interests of various types ofconsumers can be obtained

Simulation results demonstrate that the formulation ofcharging price using the proposed method is more rea-sonable when considering the fact that there exist differ-ences among the EV consumers Meanwhile when thepricing requirements change the proposed method can alsobe easily expressed by changing the relative weight of eachcriterion

Data Availability

+e data used to support this study are collected from theNational Power Grid Corp and China Electric Power Press+ey are available in the public domain so the authors haveno restriction on that

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National ScienceFoundation of China (Nos 51477091 and 51407106) and inpart by Youth Natural Science Foundation of China (No

61803233) and the Fundamental Research Funds of Shan-dong University (2015WLJH43)

References

[1] Y Zhang P You and L Cai ldquoOptimal charging scheduling bypricing for EV charging station with dual charging modesrdquoIEEE Transactions on Intelligent Transportation Systemsvol 20 no 9 pp 3386ndash3396 2019

[2] N Kang Y Ren F M Feinberg and P Y PapalambrosldquoPublic investment and electric vehicle design a model-basedmarket analysis framework with application to a USAndashChinacomparison studyrdquo Design Ence vol 2 2016

[3] China National Government Shandong Promote the Devel-opment of the Electric Vehicle Industry China NationalGovernment Jinan China 2016

[4] China National Government Tianjin Has Built 143 SeatChargingSwitching Stations Which Has Realized a CompleteCoverage of Whole City China National Government TianjinChina 2016

[5] G Zarazua de Rubens L Noel J Kester and B K Sovacoolldquo+e market case for electric mobility investigating electricvehicle business models for mass adoptionrdquo Energy vol 194Article ID 116841 2020

[6] +e National Development and Reform Commission(NDRC) Notice on Electricity Price Policy Issues ConcerningElectric Vehicle +e National Development and ReformCommission (NDRC) Beijing China 2015

[7] Shandong Province Government Order ImplementationOpinions on Speeding up the Installation of Fast ShandongProvince Charging Infrastructure Shandong Province Gov-ernment Order Jinan China 2016

[8] J-C Tu and C Yang ldquoKey factors influencing consumersrsquopurchase of electric vehiclesrdquo Sustainability vol 11 no 14p 3863 2019

[9] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[10] L Zhang and Y Liu ldquoAnalysis of new energy vehicles industrypolicy in Chinarsquos cities from the perspective of policy in-strumentsrdquo Energy Procedia vol 104 2016

[11] L G Gonzalez E Siavichay and J L Espinoza ldquoImpact of EVfast charging stations on the power distribution network of aLatin American intermediate cityrdquo Renewable and Sustain-able Energy Reviews vol 107 2019

[12] Q Zhang Y Hu W Tan C Li and Z Ding ldquoDynamic time-of-use pricing strategy for electric vehicle charging consid-ering user satisfaction degreerdquo Applied Sciences vol 10 no 9p 3247 2020

[13] N Wang Y Liu G Fu and Y Li ldquoCost-benefit assessmentand implications for service pricing of electric taxies in

Table 12 Analysis of subjective weights under three extreme situations

Situations Characteristics w (wp1 wp2 wp3 ) Q (Q1 Q2 Q3 Q4) Ranking schemes

1 Satisfaction is the most importantignore applicability and economy (00909 00909 08182) (00465 07248 01195 01092) 2 3 4 1

2 Economy is the most importantignore applicability and satisfaction (08182 00909 00909) (02181 02992 02470 02358) 2 3 4 1

3 Applicability is the most importantignore economy and satisfaction (00909 08182 00909) (02238 02457 02370 02935) 4 2 3 1


Chinardquo Energy for Sustainable Development vol 27pp 137ndash146 2015

[14] C D Korkas S Baldi P Michailidis andE B Kosmatopoulos ldquoA cognitive stochastic approximationapproach to optimal charging schedule in electric vehiclestationsrdquo in Proceedings of the 2017 25th MediterraneanConference on Control and Automation (MED) pp 484ndash489Valletta Malta July 2017

[15] C D Korkas S Baldi S Yuan and E B Kosmatopoulos ldquoAnadaptive learning-based approach for nearly optimal dynamiccharging of electric vehicle fleetsrdquo IEEE Transactions on In-telligent Transportation Systems vol 19 no 7 pp 2066ndash20752018

[16] T P Lyon M Michelin A Jongejan and T Leahy ldquoIs ldquosmartchargingrdquo policy for electric vehicles worthwhilerdquo EnergyPolicy vol 41 pp 259ndash268 2012

[17] K Yuan Y Song Y Shao C Sun and Z Wu ldquoA chargingstrategy with the price stimulus considering the queue ofcharging station and EV fast charging demandrdquo EnergyProcedia vol 145 pp 400ndash405 2018

[18] M Pourabdollah B Egardt N Murgovski and A GrauersldquoEffect of driving charging and pricing scenarios on optimalcomponent sizing of a PHEVrdquo Control Engineering Practicevol 61 pp 217ndash228 2017

[19] T Rui C Hu G Li J Tao and W Shen ldquoA distributedcharging strategy based on day ahead price model for PV-powered electric vehicle charging stationrdquo Applied SoftComputing vol 76 pp 638ndash648 2019

[20] E Howland ldquoCalifornia PUC approves SDGampE TOU pilotrdquoPlatts Megawatt Daily p 4ndash5 2017

[21] J L Paul ldquoMarkets for power in the United States an interimassessmentrdquo Energy Journal vol 1ndash36 2006

[22] C Madina I Zamora and E Zabala ldquoMethodology forassessing electric vehicle charging infrastructure businessmodelsrdquo Energy Policy vol 89 pp 284ndash293 2016

[23] +e National Development and Reform Commission 1eNotice on Electricity Price Policy Issues Concerning the ElectricVehicle +e National Development and Reform CommissionBeijing China 2014

[24] Beijing Development and Reform Committee 1e Notice onElectric Vehicle Charging Fees Issues Concerning the BeijingCity Beijing Development and Reform Committee BeijingChina 2015

[25] Xinjiang Province Government Order Standard the EVsCharging Service Fee Xinjiang Province Government OrderUrumqi China 2016

[26] B C Farhar D Maksimovic W A Tomac and T C CoburnldquoA field study of human factors and vehicle performanceassociated with PHEV adaptationrdquo Energy Policy vol 93pp 265ndash277 2016

[27] L Noel G Zarazua de Rubens J Kester and B K SovacoolldquoUnderstanding the socio-technical nexus of Nordic electricvehicle (EV) barriers a qualitative discussion of range pricecharging and knowledgerdquo Energy Policy vol 138 Article ID111292 2020

[28] L Wang Z L Fu W Guo R Liang and H Y Shao ldquoWhatinfluences sales market of new energy vehicles in ChinaEmpirical study based on survey of consumersrsquo purchasereasonsrdquo Energy Policy vol 142 2020

[29] K Lu S Liu X S Niu W L Xue Y Zhu and Z J ZhuldquoPricing method of electric vehicle charging by using cost-benefit analysisrdquo Journal of Power System and Automationvol 26 no 3 pp 76ndash80 2014

[30] Z Wei Y Li Y Zhang and L Cai ldquoIntelligent parking garageEV charging scheduling considering battery charging char-acteristicrdquo IEEE Transactions on Industrial Electronics vol 65no 3 pp 2806ndash2816 2018

[31] X Han Z Wei Z Hong and S Zhao ldquoOrdered chargecontrol considering the uncertainty of charging load ofelectric vehicles based on Markov chainrdquo Renewable Energyvol 161 pp 419ndash434 2020

[32] K Huang Y Wu C Wang Y Xie and W Gui ldquoA projectiveand discriminative dictionary learning for high-dimensionalprocess monitoring with industrial applicationsrdquo IEEETransactions on Industrial Informatics vol 99 2020

[33] F Sitorus J J Cilliers and P R Brito-Parada ldquoAn integratedconstrained fuzzy stochastic analytic hierarchy processmethod with application to the choice problemrdquo ExpertSystems with Applications vol 138 Article ID 112822 2019

[34] Y Yu X Han M Yang and J Yang ldquoProbabilistic predictionof regional wind power based on spatiotemporal quantileregressionrdquo in Proceedings of the 2019 IEEE Industry Appli-cations Society Annual Meeting Baltimore MD USA Sep-tember 2019

[35] Z Ding Y Lu K Lai M Yang and W J Lee ldquoOptimalcoordinated operation scheduling for electric vehicle aggre-gator and charging stations in an integrated electricity-transportation systemrdquo International Journal of ElectricalPower amp Energy Systems vol 121 Article ID 106040 2020

[36] L Sun J Qiu X Han X Yin and Z Dong ldquoPer-use-sharerental strategy of distributed BESS in joint energy and fre-quency control ancillary services marketsrdquo Applied Energyvol 277 Article ID 115589 2020

[37] S Hardman A Jenn G Tal et al ldquoA review of consumerpreferences of and interactions with electric vehicle charginginfrastructurerdquo Transportation Research Part D Transportand Environment vol 62 pp 508ndash523 2018

[38] X Li C Liu and J Jia ldquoOwnership and usage analysis ofalternative fuel vehicles in the United States with the 2017national Household travel survey datardquo Sustainability vol 11no 8 p 2262 2019

[39] C Guo Z Peng and J Ding ldquoDEA index construction forcomprehensive evaluation of sustainable developmentrdquoChinarsquos Population Resources and Environment vol 26 no 3pp 9ndash17 2016

[40] J Yang H Chen M Duan and S Qi ldquoResearch on multi-stage planning of electric vehicle charging stationrdquo ShandongElectric Power Technology vol 42 no 8 pp 18ndash22 2015


consumers compared to using the internal-combustion-engine vehicle In [13] the authors present a methodology toassess the coat-benefit and develop the service pricingstrategy of electric taxies in Shanghai China +erefore theservice pricing of charging is the crucial problem to en-courage consumer to using EVs +e charging station is oneof the indispensable components in the operation of the EVindustry [14] +e charging prices of the charging station arethe fees how much the consumers should pay the chargingstation operators for a certain amount of charging electricity(the sum of electricity and charging service charges) It is notonly the important reference factor for vehicle buyers tochoose EVs rather than ICV but also the main way foroperators to recover the cost of investment in charginginfrastructure and even is the principal means for powercompanies to motivate EVs consumers to change theircharging behaviors to optimize the distribution of the powerload [15] +erefore the reasonable pricing of EVs is the keyproblem to promote the development of the EV industry

In order to establish a reasonable charging servicingprice various forms of charging price strategies are for-mulated and implemented overseas and in China [16ndash19]On the cost of self-charging at home the standard electricitytariffs of EVs charging prescribed by the United StatesCalifornia Pacific Gas and Electric Company (PGEC) arebased on the residential pricing and the time-of-use (TOU)price is set from 5 centskWh to 28 centskWh [20 21]Japan implements the preferential policies for free chargingin the stage of demonstration Some cities in China such asHangzhou have also launched their own local policies andthe pricing of EV charging is based on the method of cost-benefit income However this pricing has prompted EVs tooperate too costly which is not conducive to the promotionof the EVs industry [22] +e National Development andReform Commission of China (NDRC) issues that Chinaimplements the supportive policy on the price of EVcharging and the service fees of electric vehicle chargingstations are performed by the local according to the principleof ldquopreferential and discountrdquo with the government guidancepricing management Meanwhile the NDRC gives a pref-erential price to the centralized charging stations for thepurpose of business and implements large industrial elec-tricity prices +e charging service fees are gradually formedthrough market competition with the development ofmarket [23] Since June 2015 Beijing has charged the servicefees according to the capacity of charge up for battery +eupper limit standard of the charge per kilowatt-hour is equalto 15 of the highest retail price of No 92 gasoline per literon the same day of the city In addition until January 2020the electric vehicle charging service fees will perform theprice of market regulation in accordance with the provisionsof the state [24] Xinjiang has outlined a standard EVscharging service fee the upper limit of tentative price of theelectric vehicle charging fee is 12 RMB yuankWh and theupper limit of the electric bus charging fee is temporarily set1 RMB yuankWh [25]

+e market mechanism can promote the development ofthe EVs industry +e positive influence of the commercialTOU price on the operation benefit of EVs charging is

discussed in [26] San Diego Gas and Electric Companyestablishes an analysis model considering the impacts ofTOU price on the charging behaviors +e model assessesthe relationship between the position of charging infra-structure (residential and nonresidential areas) and chargingprice and determines three kinds of charging price schemeswhich the private EV consumers can choose [27] With therapid growth of charging stations for EVs EVs chargingswitching business modes become more important How-ever from the views of both EVs operators and consumers amore reasonable charging price considering various types ofconsumers has not been established

In the initial development of EVs the price of EVcharging does not have the conditions to determine the pricebased on market competition +e comprehensive costpricing which can balance the interests of all parties andensure the operating income is more advantageous topromote the development of EVs [22] In principle thepricing of the EVs charging station should consider thetripartite interests of the government operators and con-sumers [28] In [12] based on the Game theory the authorsconstruct the benefit models of EV operators and consumersin terms of the standard charging stations and the standardEV +ey also calculate a reasonable pricing range forcharging In [29] the authors further consider the influenceof the time value of money in project TOU and the level ofgovernment subsidies

Visibly for formulation of charging price it is vital tofully consider the influence of various factors and improvethe comprehensive cost pricing model [30] However incurrent studies the EV consumers are often considered asonly one type (standard or typical) which is not consistentwith the fact that consumers have very visible individualdifference and thus the pricing of EV charging will notachieve the expected effect

Accordingly the individual difference of consumersshould be taken into consideration in the pricing of EVcharging and the comprehensive evaluation of EV chargingprice should be solved effectively +e Analytic HierarchyProcess (AHP) [31] and Data Envelopment Analysis (DEA)[32] are the common comprehensive evaluation methodswhich are widely used in all kinds of decision-makingproblems In [33 34] the authors explore the use of hier-archical structure for classifying evaluation indices andemploy the integrated AHPDEA method in the differentstages of evaluation which verifies the more practicality andeffectiveness in dealing with complex problems

Because the private EV is becoming increasingly prev-alent as a means of transportation accounting for 85 of thecivilian cars [35] Considering that the individual consumeris more sensitive to the price of EV charging this paper takesthe private EV as an analysis object and proposes a novelpricing method of EV charging considering the consumerdifferences First set up the pricing method considering theinterests both of EV charging stationsrsquo operators and con-sumers comprehensively +en based on the analysis of thefactors affecting consumer interest changes this paperadopts the single factor sensitivity analysis to determine theprinciple of consumer classification and puts forward the








Y1(t)


η+ Sb + Sr1113888 1113889 t 0


η+ Sr1113888 1113889 tge 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)


Y2(t)




⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(3)




πc1 NPV1 1113944T

t0Y1(t) 1 + i0( 1113857


111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (4)

EVs consumers

Governmentsubsidies


Charging cost



Operating cost


Constructioncosts

Purchase cost ofEVs




πc2 NPV2 1113944T

t0Y2(t) 1 + i0( 1113857


111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (5)


πc πc1 le πc le πc211138681113868111386811138681113966 1113967 (6)








SAF ΔAAΔFF

(7)















e 1N

1113944

N

i1

1n minus 1

1113944

n

j1

xi minus 1113954x

xi

1113888 1113889

211139741113972

(8)




Building part












Total cost 2415




Total 718













0 50 100 150 200 250 300 350 400 450 5000

102030405060708090

100

(120 88)(90 80)

(60 67)

(30 40)

Prop

ortio

n of

cons

umer

s (

)


(10 15)







P



⋮ ⋮ ⋮ ⋮


⋮ ⋮ ⋮ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




Mi 1113945n

j1Pij i 1 2 m (10)


wi Mi

m1113968

i 1 2 m (11)


wi wi

1113936mj1 wj

i 1 2 m (12)







maxu

Tyk

vT

xk

VPk

stu

Tyj

vTxj

le 1

j 1 2 n vge 0 uge 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


T




P1k V

P2k and V




Total target G



Targethierarchy

Criteria hierarchy

Index hierarchy




Qi wP1

VP1i

11139364i1 V

P1i

+ wP2

VP2i

11139364i1 V

P2i

+ wP3

VP3i

11139364i1 V

P3i

(14)










πc11113868111386811138681113868 πc1 ge 228 yuankWh1113966 1113967 (15)


πc21113868111386811138681113868 πc2 le 272 yuankWh1113966 1113967 (16)






P =

1


12

13

1

12

13

1

12

13

Economy

Applicability

Satisfaction

(18)


w wP1 w

P2 wP31113872 1113873 (05396 02970 01634) (19)













P =

1


19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)








πc2 (yuankWh)





Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839


Schemes 1 2 3 4Qi 02155 03401 02457 02527



6 Conclusion



Data Availability




Acknowledgments



References























































Y1(t)


η+ Sb + Sr1113888 1113889 t 0


η+ Sr1113888 1113889 tge 1

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)


Y2(t)




⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(3)




πc1 NPV1 1113944T

t0Y1(t) 1 + i0( 1113857


111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (4)

EVs consumers

Governmentsubsidies


Charging cost



Operating cost


Constructioncosts

Purchase cost ofEVs




πc2 NPV2 1113944T

t0Y2(t) 1 + i0( 1113857


111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (5)


πc πc1 le πc le πc211138681113868111386811138681113966 1113967 (6)








SAF ΔAAΔFF

(7)















e 1N

1113944

N

i1

1n minus 1

1113944

n

j1

xi minus 1113954x

xi

1113888 1113889

211139741113972

(8)




Building part












Total cost 2415




Total 718













0 50 100 150 200 250 300 350 400 450 5000

102030405060708090

100

(120 88)(90 80)

(60 67)

(30 40)

Prop

ortio

n of

cons

umer

s (

)


(10 15)







P



⋮ ⋮ ⋮ ⋮


⋮ ⋮ ⋮ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




Mi 1113945n

j1Pij i 1 2 m (10)


wi Mi

m1113968

i 1 2 m (11)


wi wi

1113936mj1 wj

i 1 2 m (12)







maxu

Tyk

vT

xk

VPk

stu

Tyj

vTxj

le 1

j 1 2 n vge 0 uge 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


T




P1k V

P2k and V




Total target G



Targethierarchy

Criteria hierarchy

Index hierarchy




Qi wP1

VP1i

11139364i1 V

P1i

+ wP2

VP2i

11139364i1 V

P2i

+ wP3

VP3i

11139364i1 V

P3i

(14)










πc11113868111386811138681113868 πc1 ge 228 yuankWh1113966 1113967 (15)


πc21113868111386811138681113868 πc2 le 272 yuankWh1113966 1113967 (16)






P =

1


12

13

1

12

13

1

12

13

Economy

Applicability

Satisfaction

(18)


w wP1 w

P2 wP31113872 1113873 (05396 02970 01634) (19)













P =

1


19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)








πc2 (yuankWh)





Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839


Schemes 1 2 3 4Qi 02155 03401 02457 02527



6 Conclusion



Data Availability




Acknowledgments



References


















































πc2 NPV2 1113944T

t0Y2(t) 1 + i0( 1113857


111386811138681113868111386811138681113868111386811138681113868

⎧⎨

⎩

⎫⎬

⎭ (5)


πc πc1 le πc le πc211138681113868111386811138681113966 1113967 (6)








SAF ΔAAΔFF

(7)















e 1N

1113944

N

i1

1n minus 1

1113944

n

j1

xi minus 1113954x

xi

1113888 1113889

211139741113972

(8)




Building part












Total cost 2415




Total 718













0 50 100 150 200 250 300 350 400 450 5000

102030405060708090

100

(120 88)(90 80)

(60 67)

(30 40)

Prop

ortio

n of

cons

umer

s (

)


(10 15)







P



⋮ ⋮ ⋮ ⋮


⋮ ⋮ ⋮ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




Mi 1113945n

j1Pij i 1 2 m (10)


wi Mi

m1113968

i 1 2 m (11)


wi wi

1113936mj1 wj

i 1 2 m (12)







maxu

Tyk

vT

xk

VPk

stu

Tyj

vTxj

le 1

j 1 2 n vge 0 uge 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


T




P1k V

P2k and V




Total target G



Targethierarchy

Criteria hierarchy

Index hierarchy




Qi wP1

VP1i

11139364i1 V

P1i

+ wP2

VP2i

11139364i1 V

P2i

+ wP3

VP3i

11139364i1 V

P3i

(14)










πc11113868111386811138681113868 πc1 ge 228 yuankWh1113966 1113967 (15)


πc21113868111386811138681113868 πc2 le 272 yuankWh1113966 1113967 (16)






P =

1


12

13

1

12

13

1

12

13

Economy

Applicability

Satisfaction

(18)


w wP1 w

P2 wP31113872 1113873 (05396 02970 01634) (19)













P =

1


19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)








πc2 (yuankWh)





Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839


Schemes 1 2 3 4Qi 02155 03401 02457 02527



6 Conclusion



Data Availability




Acknowledgments



References
























































e 1N

1113944

N

i1

1n minus 1

1113944

n

j1

xi minus 1113954x

xi

1113888 1113889

211139741113972

(8)




Building part












Total cost 2415




Total 718













0 50 100 150 200 250 300 350 400 450 5000

102030405060708090

100

(120 88)(90 80)

(60 67)

(30 40)

Prop

ortio

n of

cons

umer

s (

)


(10 15)







P



⋮ ⋮ ⋮ ⋮


⋮ ⋮ ⋮ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




Mi 1113945n

j1Pij i 1 2 m (10)


wi Mi

m1113968

i 1 2 m (11)


wi wi

1113936mj1 wj

i 1 2 m (12)







maxu

Tyk

vT

xk

VPk

stu

Tyj

vTxj

le 1

j 1 2 n vge 0 uge 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


T




P1k V

P2k and V




Total target G



Targethierarchy

Criteria hierarchy

Index hierarchy




Qi wP1

VP1i

11139364i1 V

P1i

+ wP2

VP2i

11139364i1 V

P2i

+ wP3

VP3i

11139364i1 V

P3i

(14)










πc11113868111386811138681113868 πc1 ge 228 yuankWh1113966 1113967 (15)


πc21113868111386811138681113868 πc2 le 272 yuankWh1113966 1113967 (16)






P =

1


12

13

1

12

13

1

12

13

Economy

Applicability

Satisfaction

(18)


w wP1 w

P2 wP31113872 1113873 (05396 02970 01634) (19)













P =

1


19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)








πc2 (yuankWh)





Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839


Schemes 1 2 3 4Qi 02155 03401 02457 02527



6 Conclusion



Data Availability




Acknowledgments



References




























































0 50 100 150 200 250 300 350 400 450 5000

102030405060708090

100

(120 88)(90 80)

(60 67)

(30 40)

Prop

ortio

n of

cons

umer

s (

)


(10 15)







P



⋮ ⋮ ⋮ ⋮


⋮ ⋮ ⋮ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




Mi 1113945n

j1Pij i 1 2 m (10)


wi Mi

m1113968

i 1 2 m (11)


wi wi

1113936mj1 wj

i 1 2 m (12)







maxu

Tyk

vT

xk

VPk

stu

Tyj

vTxj

le 1

j 1 2 n vge 0 uge 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


T




P1k V

P2k and V




Total target G



Targethierarchy

Criteria hierarchy

Index hierarchy




Qi wP1

VP1i

11139364i1 V

P1i

+ wP2

VP2i

11139364i1 V

P2i

+ wP3

VP3i

11139364i1 V

P3i

(14)










πc11113868111386811138681113868 πc1 ge 228 yuankWh1113966 1113967 (15)


πc21113868111386811138681113868 πc2 le 272 yuankWh1113966 1113967 (16)






P =

1


12

13

1

12

13

1

12

13

Economy

Applicability

Satisfaction

(18)


w wP1 w

P2 wP31113872 1113873 (05396 02970 01634) (19)













P =

1


19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)








πc2 (yuankWh)





Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839


Schemes 1 2 3 4Qi 02155 03401 02457 02527



6 Conclusion



Data Availability




Acknowledgments



References


















































P



⋮ ⋮ ⋮ ⋮


⋮ ⋮ ⋮ ⋮


⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




Mi 1113945n

j1Pij i 1 2 m (10)


wi Mi

m1113968

i 1 2 m (11)


wi wi

1113936mj1 wj

i 1 2 m (12)







maxu

Tyk

vT

xk

VPk

stu

Tyj

vTxj

le 1

j 1 2 n vge 0 uge 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


T




P1k V

P2k and V




Total target G



Targethierarchy

Criteria hierarchy

Index hierarchy




Qi wP1

VP1i

11139364i1 V

P1i

+ wP2

VP2i

11139364i1 V

P2i

+ wP3

VP3i

11139364i1 V

P3i

(14)










πc11113868111386811138681113868 πc1 ge 228 yuankWh1113966 1113967 (15)


πc21113868111386811138681113868 πc2 le 272 yuankWh1113966 1113967 (16)






P =

1


12

13

1

12

13

1

12

13

Economy

Applicability

Satisfaction

(18)


w wP1 w

P2 wP31113872 1113873 (05396 02970 01634) (19)













P =

1


19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)








πc2 (yuankWh)





Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839


Schemes 1 2 3 4Qi 02155 03401 02457 02527



6 Conclusion



Data Availability




Acknowledgments



References


















































Qi wP1

VP1i

11139364i1 V

P1i

+ wP2

VP2i

11139364i1 V

P2i

+ wP3

VP3i

11139364i1 V

P3i

(14)










πc11113868111386811138681113868 πc1 ge 228 yuankWh1113966 1113967 (15)


πc21113868111386811138681113868 πc2 le 272 yuankWh1113966 1113967 (16)






P =

1


12

13

1

12

13

1

12

13

Economy

Applicability

Satisfaction

(18)


w wP1 w

P2 wP31113872 1113873 (05396 02970 01634) (19)













P =

1


19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)








πc2 (yuankWh)





Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839


Schemes 1 2 3 4Qi 02155 03401 02457 02527



6 Conclusion



Data Availability




Acknowledgments



References





















































P =

1


19

19

9

1

1

9

1

1

Satisfaction

Applicability

Economy

(21)








πc2 (yuankWh)





Schemes VP1 VP2 VP3

1 06667 07622 000352 07053 05533 13 07375 07738 010614 06822 1 00839


Schemes 1 2 3 4Qi 02155 03401 02457 02527



6 Conclusion



Data Availability




Acknowledgments



References


















































6 Conclusion



Data Availability




Acknowledgments



References

















































Research Article Comprehensive Pricing Scheme of the EV ...

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