Multi-objective charging scheduling for electric vehicles at charging stations with renewable energy generation,

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Mul i-objec i e cha ging scheduling o elec ic ehicles a cha ging s a ions
wi h enewable ene gy gene a ion
A icleinG een Ene gy and In elligen T anspo a ion · Ma ch 2025
DOI: 10.1016/j.gei s.2025.100283
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Full leng h a icle
Mul i-objec i e cha ging scheduling o elec ic ehicles a cha ging s a ions
wi h enewable ene gy gene a ion
Lei Zhang
a
,
b
,
*
, Yingjun Ji
a
,
b
, Xiaohui Li
a
,
b
, Zhijia Huang
a
,
b
, Dingsong Cui
c
, Haibo Chen
c
,
Jingyu Gong
d
, Fabian B ee
d
, Ma k Junke
d
, Di k Uwe Saue
d
a
Collabo a i e Inno a ion Cen e o Elec ic Vehicles in Beijing, Beijing Ins i u e o Technology, Beijing 100081, China
b
Na ional Enginee ing Resea ch Cen e o Elec ic Vehicles, Beijing Ins i u e o Technology, Beijing 100081, China
c
Ins i u e o T anspo S udies, Uni e si y o Leeds, 34-40 Uni e si y Road, Leeds LS2 9JT, UK
d
Ins i u e o Powe Elec onics and Elec ical D i es, RWTH Aachen Uni e si y, 52056 Aachen, Ge many
HIGHLIGHTS GRAPHICAL ABSTRACT
A cha ging beha iou da abase is buil
using massi e EV ope a ing da a.
A cha ging scheduling scheme is p o-
posed o a public cha ging s a ion.
A cha ging pile alloca ion me hod is
p esen ed o cha ging powe con ol.
A mic o-g id sys em model is de eloped
o enewable ene gy in eg a ion.
Simula ion s udies e i y he e ec i e-
ness o he p oposed scheme.
ARTICLE INFO
Keywo ds:
Elec ic ehicles
Cha ging s a ions
Mic o-g id
V2G
Cha ging scheduling
ABSTRACT
The apid adop ion o elec ic ehicles (EVs) in ecen yea s has posed significan challenges o he sa e ope a ion
o local g ids, pa icula ly due o massi e cha ging ope a ions a public cha ging s a ions. This pape p oposes a
eal- ime cha ging scheduling scheme o enable e ficien Vehicle- o-G id (V2G) in e ac ions and acili a e
enewable ene gy in eg a ion a public cha ging s a ions while accoun ing o eal-wo ld EV cha ging beha io s.
Fi s , an EV cha ging/discha ging beha io da abase is de eloped o cap u e he empo al unce ain y and
cha ging cha ac e is ics o bo h as - and slow-cha ging ope a ions on weekdays and weekends. Then a cha ging
pile alloca ion mechanism is in oduced o op imize he cha ging powe dis ibu ion o each EV o maximize he
ope a ional e ficiency o he s udied cha ging s a ion. A mic o-g id sys em model is de eloped by inco po a ing
e ficien V2G in e ac ions and enewable ene gy in eg a ion. Finally, a comp ehensi e cha ging scheduling
scheme is p oposed o achie e a balanced op imiza ion o mul iple objec i es. Ex ensi e simula ion s udies a e
* Co esponding au ho . Collabo a i e Inno a ion Cen e o Elec ic Vehicles in Beijing, Beijing Ins i u e o Technology, Beijing 100081, China.
E-mail add ess: lei_zhang@bi .edu.cn (L. Zhang).
Con en s lis s a ailable a ScienceDi ec
G een Ene gy and In elligen T anspo a ion
jou nal homepage: www.jou nals.else ie .com/g een-ene gy-and-in elligen - anspo a ion
h ps://doi.o g/10.1016/j.gei s.2025.100283
Recei ed 19 Decembe 2024; Accep ed 19 Feb ua y 2025
A ailable online 1 Ma ch 2025
2773-1537/©2025 The Au ho (s). Published by Else ie L d on behal o Beijing Ins i u e o Technology P ess Co., L d. This is an open access a icle unde he CC BY
license (h p://c ea i ecommons.o g/licenses/by/4.0/).
G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
conduc ed o e alua e he pe o mance o he p oposed scheduling me hod. The esul s demons a e ha he
p oposed scheme achie es s ong pe o mance ac oss all h ee selec ed indica o s.
1. In oduc ion
1.1. Backg ound
Elec ic ehicles (EVs) ha e been widely ecognized as a iable so-
lu ion o add ess he challenges o global wa ming and ossil uel
deple ion [1–3]. Thei syne gis ic de elopmen wi h enewable ene gy
gene a ion is expec ed o accele a e he achie emen o ca bon neu ali y
[4,5]. In ecen yea s, wi h con inuous echnological ad ancemen s and
suppo i e go e nmen policies, he adop ion o EVs has been accele -
a ing apidly wo ldwide [6]. To mee he g owing cha ging demands,
cha ging in as uc u e, especially public cha ging s a ions, is being
ex ensi ely deployed [7]. Howe e , uncon olled la ge-scale cha ging
ope a ions pose significan challenges o he sa e ope a ion o he elec-
ici y g id [8]. Al hough g id ein o cemen s could be a solu ion, hei
easibili y is cons ained by exo bi an cos s [9]. On he o he hand, he
connec ion ime a a cha ging s a ion significan ly exceeds he ime
equi ed o mee he cha ging demand o mos EV cha ging sessions
[10]. This p o ides g ea oppo uni ies o implemen ing e ficien
cha ging scheduling s a egies. By easonably a anging he cha ging
ime, i is possible o educe he isk o g id o e load, lowe he cha ging
cos s o use s, and p omo e he in eg a ion o enewable ene gy gene -
a ion [11].
1.2. Li e a u e e iew
Al hough uncoo dina ed cha ging o EVs may ha e de imen al e -
ec s on he elec ici y g id [12,13], EVs can also unc ion as flexible
ene gy s o age de ices o suppo g id ope a ion h ough Vehicle- o-G id
(V2G) in e ac ions [14]. Especially in mic o-g id sys ems, EVs can be
in eg a ed as dis ibu ed ene gy esou ces, which is conduci e o be e
adap ing o he in e mi en cha ac e is ics o enewable ene gy gene -
a ion [15,16]. E ficien cha ging scheduling holds he key o ealizing
hese po en ials.
Analyzing EV cha ging beha io s is o g ea significance o o mu-
la ing e ec i e cha ging scheduling schemes [17,18]. In exis ing
esea ch, ime [19], spa ial [20], o ene gy models [21] a e o en used o
cha ac e ize he cha ging beha io s o EVs. When modeling he cha ging
beha io s o EVs a public cha ging s a ions, s a is ical fi ing is a
commonly used me hod [22]. Gene ally, i in ol es cons uc ing ime
and ene gy models based on comp ehensi e cha ging beha io da a [23].
Howe e , his app oach has limi a ions in cap u ing EV cha ging be-
ha io s in specific scena ios and ails o ully eflec he inhe en he -
e ogenei y o EV cha ging pa e ns.
Subs an ial e o s ha e also been made o de elop e ficien cha ging
scheduling schemes [24,25]. F om he pe spec i e o con ol a chi ec-
u e, exis ing me hods can be ca ego ized in o cen alized con ol [26],
dis ibu ed con ol [27] and hie a chical con ol [28]. The cen alized
con ol me hod di ec ly egula es EV cha ging ope a ions a he in ol ed
cha ging s a ions. Al hough i is s aigh o wa d o implemen , i equi es
a high con ol equency. The dis ibu ed con ol me hod ypically uses
Time-o -Use (TOU) p icing o encou age EVs o pa icipa e in sma
cha ging schemes, bu i s e ec i eness highly depends on he espon-
si eness o EV use s. The hie a chical con ol me hod combines he
cha ac e is ics o cen alized and dis ibu ed con ol app oaches. I o -
mula es mul iple op imiza ion objec i es om he pe spec i es o
di e en s akeholde s [29], such as g id ope a ion, financial benefi s, and
en i onmen al conside a ions. Fo g id ope a ion, he op imiza ion ob-
jec i es may include p e en ing g id o e load, minimizing peak-load
di e ences, educing dis ibu ion losses, and acili a ing equency
egula ion [30,31]. Financial benefi s usually ocus on he in e es s o he
powe g id, cha ging s a ions, and EV use s. En i onmen al conside -
a ions may in ol e ca bon emissions educ ion and enewable ene gy
in eg a ion [32]. Weigh ing he mul i-objec i e unc ion is a common
op imiza ion me hod o sol ing such p oblems [33]. Key con ol a i-
ables include cha ging ime [34], cha ging/discha ging a i s [35], and
cha ging/discha ging powe [36,37].
A public cha ging s a ions, a mic o-g id is o en implemen ed o
be e accommoda e enewable ene gy gene a ion. Many s udies ha e
been conduc ed on his opic as shown in Table 1. Some key conside -
a ions include EV model di e si y, unce ain y in enewable ene gy
gene a ion, impac o TOU p icing, and eal- ime scheduling (RTS).
Howe e , exis ing s udies usually add ess only one o se e al o hese
aspec s, and he e is a lack o esea ch ha simul aneously conside s all
o hem. Meanwhile, when o mula ing specific cha ging schedules, i is
o en assumed ha su ficien cha ging piles a e a ailable. Ne e heless,
his assump ion may no con o m o he ac ual si ua ion. Especially
du ing peak cha ging pe iods, public cha ging s a ions a e o en ully
occupied by EVs, and newly a i ing ehicles may ha e o wai o lea e
wi hou ulfilling hei cha ging needs a a pa icula cha ging s a ion
[38,39]. In addi ion, p e ious esea ch on EV cha ging scheduling mainly
ocuses on single-objec i e op imiza ion o ans o ms mul iple objec-
i es in o a single objec i e h ough weigh ed o mula ions [40]. These
me hods ely on s a ic scheduling schemes, which lack flexibili y and
adap abili y o dynamic changes in he ac ual cha ging p ocess, such as
fluc ua ions in enewable ene gy gene a ion, changes in EV a i al imes,
and a ia ions in g id condi ions. Mo eo e , mos o he exis ing s udies
assume idealized EV cha ging demands and beha io s, lacking suppo
Table 1
Compa ison wi h simila wo ks published in ecen yea s. (MO: Mul i-Objec i e, MS: Mul i-Scena io, MM: Mul i-cha ging Modes, MP: Mul i-powe Pile, DV: Decision
Va iable, PV: Pho o ol aic, WT: Wind Tu bine, DN: Dis ibu ion Ne wo k, G2V: G id- o-Vehicle.)
Re s. MO MS MM MP DV EV PV WT Load DN G2V V2G TOU RTS
[20]✓✓P ice ✓✓✓ ✓ ✓ ✓ ✓ ✓ ✓
[34]✓✓✓ Time ✓   ✓
[35]✓✓P ice ✓✓✓✓✓✓✓✓
[36]✓Powe ✓✓✓✓✓
[37]✓Powe ✓✓✓✓✓
[41]✓✓Powe ✓✓✓ ✓✓✓ ✓
[42]✓✓P ice ✓✓✓ ✓ ✓ ✓ ✓ ✓ ✓
[43]✓✓Time ✓   ✓✓
[44]✓✓P ice ✓   ✓✓✓ ✓
[45]✓✓P ice ✓✓✓ ✓✓ ✓ ✓ ✓
[46]✓✓P ice ✓✓✓✓✓✓✓✓
[47]✓✓P ice ✓✓✓ ✓✓ ✓ ✓ ✓
This wo k ✓✓✓ ✓Powe ✓✓✓ ✓ ✓ ✓ ✓ ✓ ✓
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
2
om eal-wo ld da a, which may lead o de ia ions be ween he p o-
posed scheduling s a egies and ac ual ope a ion scena ios.
1.3. Con ibu ions
In summa y, exis ing s udies ha e ce ain limi a ions in e ms o da a
suppo , objec i e conside a ion, and scheduling flexibili y. To add ess
hese issues, his s udy p oposes a eal- ime cha ging scheduling scheme
o acili a e e ficien enewable ene gy in eg a ion and V2G in e ac ions
a a public cha ging s a ion wi h a mic o-g id sys em. Fi s , an EV
cha ging beha io model based on eal-wo ld cha ging da a is de eloped.
The da ase consis s o 329,632 cha ging samples collec ed om 1268
cha ging s a ions in Beijing, co e ing he pe iod om Janua y 1, 2023, o
Feb ua y 19, 2023. Then a mul i-objec i e cha ging scheduling model is
o mula ed wi h enewable ene gy in eg a ion, along wi h a cha ging
pile alloca ion mechanism and an op imiza ion scheduling me hod. The
Pa e o on solu ion se is de i ed using he Non-domina ed So ing
Gene ic Algo i hm II (NSGA-II) [48], and he op imal solu ion is de e -
mined using he En opy and Technique o O de P e e ence by Simi-
la i y o an Ideal Solu ion (En opy-TOPSIS) [49]. The main
con ibu ions o his s udy a e summa ized as ollows:
1. A cha ging scheduling model based on eal-wo ld da a and a mul i-
objec i e op imiza ion amewo k is adop ed. I can p o ide
cha ging scheduling s a egies o di e en scena ios.
2. A cha ging pile alloca ion mechanism is designed o add ess he
limi ed a ailabili y o cha ging piles. I aims o maximize cha ging
pile u iliza ion while minimizing wai ing imes and cha ging aban-
donmen a e.
3. An e ficien cha ging scheduling model is p oposed, aking in o ac-
coun g id ope a ion, financial benefi s, and enewable ene gy in e-
g a ion. I can e ec i ely balance he conflic ing objec i es among
di e en s akeholde s.
4. A sliding window mechanism is de eloped o connec he mic oscopic
EV cha ging beha io s wi h he mac oscopic ope a ional objec i es o
he cha ging s a ion. I enables eal- ime adjus men o cha ging
schedules acco ding o he ac ual si ua ion, he eby imp o ing he
adap abili y o he scheduling scheme.
The emainde o he pape is o ganized as ollows. Sec ion 2in-
oduces he cons uc ed EV cha ging beha io da ase and de ails he
ex ac ion o EV cha ging beha io cha ac e is ics. Sec ion 3p esen s he
mul i-objec i e op imiza ion model o a cha ging s a ion wi h enew-
able ene gy in eg a ion. Sec ion 4elabo a es on he cha ging pile allo-
ca ion mechanism and he cha ging scheduling model o mula ion.
Sec ion 5p o ides case s udies unde ypical ope a ing condi ions, wi h
Fig. 1. Schema ic o he p oposed cha ging scheduling scheme o elec ic ehicles a public cha ging s a ions.
Table 2
Nomencla u e.
P ice
cha
/(CNY⋅kWh
-1
) Cha ging elec ici y p ice
P ice
dis
/(CNY⋅kWh
-1
) Discha ging elec ici y p ice
F–C Fas cha ging
S–C Slow cha ging
BL Base load
OTL To al load o o de ly cha ging
DTL To al load o diso de ly cha ging
D-C Diso de ly cha ging
O–C O de ly cha ging
SE SOC
e o
DL Diso de ly cha ging EV load
OL O de ly cha ging EV load
EVN To al numbe o EVs
POCN Numbe o EVs pa icipa ing in o de ly cha ging
ACN Numbe o EVs abandoned o cha ging
WCN Numbe o EVs wai ing o be cha ged
FSN Numbe o ailed solu ions
AST/s A e age sol ing ime
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
3
key conclusions summa ized in Sec ion 6. The schema ic o he p oposed
cha ging scheduling scheme is illus a ed in Fig. 1.
2. Analysis o EV cha ging beha io s
In his sec ion, an EV cha ging beha io da abase is de eloped using
eal-wo ld cha ging da a collec ed om 46 cha ging s a ions in Beijing.
The aw da a con ains some anomalies, edundancies, and missing
alues. A e da a p ocessing, ele an in o ma ion om some en ies in
he da abase is lis ed in Appendix Table A-2. Each da a sample includes
ba e y capaci y, s a ing SOC, ending SOC, and s a and end cha ging
imes. Based on weekdays and holidays, as well as as and slow cha ging,
he cha ging beha io s o di e en EVs we e ca ego ized in o ou sub-
da abases, om which cha ging beha io cha ac e is ics a e ex ac ed.
2.1. Ba e y capaci y and SOC dis ibu ion
The ba e y capaci ies o EVs a e dis ibu ed mainly be ween 45 kWh
and 62 kWh, as depic ed in Fig. 2(a). Fig. 2(b) and (c) illus a e he
s a ing SOC, ending SOC, and SOC a ia ion. I can be obse ed ha EVs
end o echa ge e en when hei emaining SOCs a e ela i ely high, and
he as majo i y o hem ha e an ending SOC o 100%. The SOC a i-
a ion du ing a single cha ging session p edominan ly alls wi hin he
ange o 20%–60%.
2.2. A i al ime
In his s udy, 4:00 am is designa ed as he s a o a day wi h he
lowes p obabili y o EV a i al, and he day ends a 4:00 am he nex
day. The day is di ided in o 96 ime in e als, each wi h a du a ion o 15
mins. When cha ging piles a e a ailable, he a i al ime a he cha ging
s a ion is conside ed as he s a cha ging ime. The dis ibu ion o EV
a i al imes is shown in Fig. 3.
As can be seen om Fig. 3, he e is no significan peak in he a i al
ime o as -cha ging EVs. On weekdays, he a i al ime o slow-cha ging
EVs exhibi s wo peaks, one in he mo ning and he o he in he e ening;
on weekends, he e is only one peak in he e ening. The s a is ical esul s
e eal he andomness o EV a i al imes a he cha ging s a ion and he
di e ences in EV cha ging beha io s be ween weekdays and weekends.
To mi iga e he influence o ou lie s, he Gaussian Mix u e Model (GMM)
is employed o cu e fi ing, and a esidual analysis is also conduc ed
[50,51]. I can be seen ha he esidual be ween he fi ed cu e and he
o iginal da a fluc ua es a ound 0, indica ing ha he fi ed cu e p o ides
a good app oxima ion. No malizing he alues ob ained om he GMM
fi ing yields he p obabili y dis ibu ion o EV a i als wi hin one day. In
he simula ion, EV in o ma ion is ex ac ed om he cons uc ed EV
beha io da abase.
2.3. EV cha ging and pa king du a ions
EVs usually s a cha ging immedia ely upon a i al a he cha ging
s a ion and con inue o pa k o some ime a e cha ging comple ion.
The du a ion o pa king a e cha ging ope a ion is defined as he idle
ime. The dis ibu ions o EV cha ging and pa king du a ions a e p e-
sen ed in Fig. 4.
I can be no ed ha mos as -cha ging EVs can each hei a ge
SOCs wi hin 3 h and s ay o o e 1 h a e cha ging comple ion. Mos
slow-cha ging EVs can each hei a ge SOCs wi hin 8 h and s ay o
o e 10 h a e cha ging comple ion. The idle ime a e EV cha ging
comple ion p o ides an oppo uni y o cha ging scheduling. By making
use o his idle ime, he o e all EV cha ging load can o some ex en be
shi ed, he eby educing he impac o EV cha ging on he g id.
3. Op imiza ion model
The s udied cha ging s a ion is in eg a ed in o a mic o-g id wi h
enewable ene gy gene a ion, as shown in Fig. 5. An Ene gy In o ma ion
Dispa ch Cen e (EIDC) is esponsible o egula ing he powe flows
among di e en uni s, and he dis ibu ion ne wo k se es as an auxilia y
powe sou ce. When he powe supply exceeds he powe demand, he
excess ene gy is ei he consumed by he basic powe usage o he
cha ging s a ion o ans e ed o o he nodes in he dis ibu ion ne wo k.
As depic ed in Fig. 6, he EV cha ging/discha ging p ocess is di ided in o
T ime slo s, each wi h an in e al o Δ . The powe balance equa ion is
gi en by
PDN þPWT þPPV ¼Pload þP*
cha Pdis (1)
whe e P
DN
is he o e all powe gene a ion; P
WT
is he ac ual WT powe
gene a ion; P
PV
is he ac ual PV powe gene a ion; P
load
is he base loads
wi hin he same dis ibu ion ne wo k; P*
cha is he o al load o EV
cha ging; P
dis
is he o al load o EV discha ging.
Du ing he cha ging p ocess, he ac ual cha ging powe om he
supply side is he a ed powe P*
cha; du ing he discha ging p ocess, he
ac ual discha ging powe P
dis
is a iable.
3.1. WT and PV powe gene a ion
In his pa , he WT and PV powe o ecas ing models a e de eloped
o p edic enewable powe gene a ion in eal- ime.
Fig. 2. EV cha ging cha ac e is ics dis ibu ions: (a) Ba e y capaci y. (b) S a ing and ending SOC. (c) SOC a ia ion.
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
4

(1) The WT powe o ecas ing model is gi en by Re . [20]
Pp edic ed
WT ¼8
>
>
>
<
>
>
>
:
0; < in; > ou
P*
WT
 in
* in
; in   *
P*
WT; *  ou
(2)
whe e Pp edic ed
WT is he es ima ed WT ou pu powe ;
in
,
ou
and * a e he
cu -in wind speed, cu -ou wind speed, and a ed wind speed; P*
WT is he
a ed WT powe .
(2) The PV powe o ecas ing model is gi en by Re . [35]
Pp edic ed
PV ¼
η
PVGA (3)
whe e Pp edic ed
PV is he es ima ed PV ou pu powe ;
η
PV
is he PV con e -
sion e ficiency; Gis he sola adia ion in ensi y; Ais he exposu e a ea.
3.2. The load o EV cha ging and discha ging
P
EV
is used o ep esen he o al load o EV cha ging and discha ging
du ing ime pe iod , which is gi en by
PEV ¼P*
cha Pdis (4)
The ela ionship be ween he ac ual and he a ed o al powe o EV
cha ging and discha ging du ing ime pe iod can be gi en by
Pcha ¼
η
chaP*
cha (5)
Pdis ¼
η
disP*
dis (6)
whe e
η
cha
and
η
dis
a e he cha ging and discha ging e ficiencies.
The o e all cha ging and discha ging powe s can be ob ained by
Pcha ¼X
n¼N
n¼1
Pe ;chaðnÞ(7)
Pdis ¼X
n¼N
n¼1
Pe ;disðnÞ(8)
whe e P
e ,cha
and P
e ,dis
a e he ac ual cha ging and discha ging powe s
o he n- h EV. Simila ly, each EV sa isfies
Pe ;cha ¼
η
chaP*
e ;cha (9)
Pe ;dis ¼
η
disP*
e ;dis (10)
whe e P*
e ;cha and P*
e ;dis a e he a ed cha ging and discha ging powe s o
a single EV.
3.3. Op imiza ion objec i es
The p ima y con ol objec i es a e o mi iga e he powe fluc ua ions
in he dis ibu ion ne wo k, educe cha ging cos s o EV use s, and
accommoda e mo e enewable ene gy gene a ion.
(1) Load fluc ua ion in he dis ibu ion ne wo k
The o al load o he dis ibu ion ne wo k du ing he ime pe iod is
gi en by
PLoad ¼Pload þPEV (11)
The Dis ibu ion Ne wo k Load Fluc ua ion (DNLF) du ing he
scheduling pe iod can be desc ibed as
Fig. 3. The dis ibu ion o he a i al ime o EVs: (a) Fas -cha ging on weekdays. (b) Slow-cha ging on weekdays. (c) Fas -cha ging on weekends. (d) Slow-cha ging on weekends.
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
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Fig. 4. The dis ibu ion o cha ging and pa king ime o EVs: (a) Fas cha ging. (b) Slow-cha ging. Cumula i e p obabili y dis ibu ion and idle ime dis ibu ion o
cha ging and pa king ime o EVs: (c) Fas -cha ging. (d) Slow-cha ging.
Fig. 5. Illus a ion o a ypical mic o-g id wi h EV cha ging and enewable ene gy gene a ion.
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
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DNLF ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
TX
¼T
¼1
ðPLoadð ÞPLoadÞ2
u
u
(12)
whe e PLoad is he a e age load o he dis ibu ion ne wo k du ing he EV
cha ging and discha ging p ocesses.
(2) Cha ging cos s o EVs
The cha ging cos o a single EV du ing he ime pe iod can be gi en
by
C¼γchaP*
e ;chaΔ γdisPe ;disΔ (13)
whe e γ
cha
and γ
dis
a e he eal- ime cha ging and discha ging p ices.
Since an EV is ei he in he cha ging o discha ging mode a a specific
ime, i mus sa is y
P*
e ;cha ⋅Pe ;dis ¼0(14)
Then he Elec ic Vehicle Cha ging Cos (EVCC) o e Tscheduling
pe iods can be desc ibed as
EVCC ¼X
¼T
¼1
Cð Þ(15)
(3) Real- ime ene gy consump ion di e ence
The powe s gene a ed by he WT and PV sys ems canno be accu a ely
p edic ed. P
di
is defined as he di e ence be ween he o ecas enew-
able ene gy gene a ion and he EV cha ging and discha ging powe
du ing ime pe iod , which is gi en by
Pdi ¼PEV ðPp edic ed
PV þPp edic ed
WT Þ(16)
To maximize he u iliza ion o enewable ene gy gene a ion, he EV
cha ging and discha ging load cu e should closely ma ch he p edic ed
enewable powe gene a ion. This can be achie ed by minimizing he
Real- ime Ene gy Consump ion Di e ence (RECD), which is gi en by
RECD ¼1
TX
¼T
¼1
Pdi ð Þ(17)
3.4. Cons ain s
(1) The capaci y o he dis ibu ion equipmen
In ime pe iod , he o al load o he dis ibu ion ne wo k should be
wi hin he capaci y ange o he dis ibu ion equipmen , which can be
exp essed as
P
MTF PDN Pþ
MTF (18)
whe e Pþ
MTF and P
MTF a e he maximum cha ging and discha ging powe s
ha he dis ibu ion equipmen can wi hs and.
(2) The ou pu powe o MG
The WT and PV ou pu powe limi s a e desc ibed as
0Pp edic ed
WT P*
WT (19)
0Pp edic ed
PV P*
PV (20)
The ela ionship be ween he cha ging and discha ging powe s o EVs
and he cha ging and discha ging powe s o cha ging piles is gi en by
Pe ;cha ¼
η
chaPpile;cha (21)
Pe ;dis ¼1
η
dis
Ppile;dis (22)
The mul i-s age cons an cu en cha ging me hod is o en employed
o as cha ging con ol [52], as shown in Fig. 7. The powe bounda ies
o as cha ging du ing ime pe iod can be gi en by
η
chaPmin
pile;cha Pe ;cha minð
η
chaPmax
pile;cha;Pcc
cha Þ(23)
1
η
dis
Pmin
pile;dis Pe ;dis min1
η
dis
Pmax
pile;dis;Pcc
dis (24)
Fo slow-cha ging, he Al e na ing Cu en cha ging a e is gene ally
less han 0.2 C, which can be gi en by
η
chaPmin
pile;cha Pe ;cha 
η
chaPmax
pile;cha (25)
1
η
dis
Pmin
pile;dis Pe ;dis 1
η
dis
Pmax
pile;dis (26)
whe e Pmin
pile;cha and Pmin
pile;dis a e he minimum cha ging and discha ging
powe s o sus ain cha ging/discha ging sessions, and 0.2 kW is adop ed
in his s udy; Pmax
pile;cha and Pmax
pile;dis a e he maximum cha ging and dis-
cha ging powe s o he cha ging piles, and i is assumed ha
Pmax
pile;cha ¼Pmax
pile;dis (27)
whe e Pcc
cha and Pcc
dis a e he uppe bounds o he cha ging and dis-
cha ging powe in he mul i-s age cons an -cu en cha ging ope a ion.
(3) SOC
Fig. 6. Compa ison be ween o de ly cha ging and diso de ly
cha ging p ocesses.
Fig. 7. Illus a ion o he mul i-s age cons an -cu en cha ging p ocess.
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
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Th oughou he en i e p ocess o EV cha ging and discha ging ope -
a ions, i should mee
0SOCe 100% (28)
The a ia ion o SOC o a single EV be ween adjacen ime pe iods
can be desc ibed as
SOCð Þ¼SOCð 1ÞþPe ;chaΔ
Ee

P*
e ;disΔ
Ee
(29)
whe e E
e
is he ba e y capaci y.
The o e all SOC a ia ion can be gi en by
SOCe ;end ¼SOCe ;s a þΔ
Ee X
¼ end
¼ s a Pe ;chað ÞP*
e ;disð Þ(30)
whe e SOC
e , s a
and SOC
e ,end
a e he s a and end SOCs;
s a
and
end
a e he s a and end ime. I is e iden ha he powe du ing he s a and
end pe iods sa isfies
P eal
e ;s a s a ¼Pe ;s a Δ (31)
P eal
e ;end end ¼Pe ;endΔ (32)
0< s a ; end Δ (33)
whe e P eal
e ;s a and P eal
e ;end a e he ac ual powe s a he s a and end pe-
iods; P
e ,s a
and P
e ,end
a e he a e age powe s a he s a and end
pe iods.
SOCe ;accep ed ¼SOCe ;s a þ0:8SOCe ;expec ed SOCe ;s a (34)
whe e SOC
e , expec ed
is he expec ed end SOC a e cha ging comple ion.
The used NSGA-II algo i hm ine i ably esul s in a di e ence be ween
SOC
e ,end
and SOC
e , expec ed
, which is gi en by
SOCe o ¼∣SOCe ;end SOCe ;expec ed ∣(35)
The e o should be main ained wi hin a ce ain ange, which is gi en
by
SOCe o 0:1% (36)
4. Con ol s a egy
To enhance he ope a ional e ficiency o he cha ging s a ion,
cha ging piles a e fi s alloca ed o he a i ing EVs, and hen cha ging
scheduling is implemen ed.
4.1. Cha ging pile alloca ion
Fas cha ging piles wi h di e en maximum powe s a e ins alled a
he cha ging s a ion, while all slow cha ging piles ha e he same
maximum powe . To e ficien ly alloca e cha ging piles o he a i ing
EVs, a Minimum Powe Alloca ion Me hod (F-MPAM) and a Random
Powe Alloca ion Me hod (F-RPAM) a e p oposed o as -cha ging
EVs, and he Random Powe Alloca ion Me hod (S-RPAM) is p e-
sen ed o slow-cha ging EVs. Se e al assump ions a e made o
simplifica ion:
Fig. 8. Flowcha o he p oposed EV as -cha ging pile alloca ion me hod.
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
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Fig. 15. Simula ion esul s o Tuesday: (a) Scena io 1; (b) Scena io 2; (c) Scena io 3; (d) Scena io 4; (e) Compa ison o dis ibu ion ne wo k load unde o de ly and
diso de ly cha ging; ( ) SOC e o .
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
15

NA me hod abandons cha ging wi hou wai ing o an idle pile, while F-
MPAM and F-RPAM educe he pile idle a e as EVs a e willing o wai .
Compa ed wi h F-RPAM, F-MPAM has a sligh ly lowe abandonmen a e
and a e age wai ing ime while main aining a simila pile idle a e. This
is because F-MPAM p e e s using slow-cha ging piles o some EVs,
lea ing mo e as -cha ging piles a ailable. The usage o as - cha ging
piles o as -cha ging EVs is depic ed in Fig. 12(c). F-RPAM shows a
mo e uni o m p e e ence o all he cha ging piles. F equen use o
cha ging piles can educe hei li espans [55]. In an o de ly cha ging
scena io, EVs a e expec ed o ha e su ficien idle ime o load shi ing.
F-MPAM makes some EVs o iginally op ing o high-powe cha ging
choose low-powe cha ging, educing hei idle ime and po en ially
limi ing hei pa icipa ion in cha ging scheduling. The e o e, om he
EV use 's pe spec i e, F-MPAM sligh ly educes he abandonmen a e
and a e age wai ing ime. F om he cha ging s a ion's pe spec i e,
F-MPAM may comp omise he po en ial o EVs o pa icipa e in cha ging
scheduling. Thus, he F-RPAM me hod is mo e sui able o he Lucheng
cha ging s a ion, while he F-MPAM me hod may ha e be e easibili y
when ehicle- o-pile a ios a e ela i ely high.
The abandonmen a e, wai ing a e, a e age wai ing ime, and pile
idle a e o slow-cha ging EVs a e shown in Fig. 12(d). Wi h he
inc easing ehicle- o-pile a io, hese me ics change in a simila pa e n
o as -cha ging EVs unde he S-RPAM me hod. When he ehicle - o-pile
a io is fixed, he abandonmen a e unde S-RPAM is significan ly lowe
han ha unde NA. When he a io exceeds 1.5, he fi s h ee me ics
s a o inc ease while he pile idle a e dec eases. The e o e, he S-RPAM
me hod can e ec i ely balance he ope a ing cos s o he cha ging s a ion
and he sa is ac ion o EV use s, and hus i is adop ed as he cha ging pile
alloca ion algo i hm o slow-cha ging EVs in subsequen simula ion
s udies. Fo he Lucheng cha ging s a ion, he ideal slow-cha ging
ehicle- o-pile a io is a ound 1.5, while i s ac ual a io is less han 0.5.
The cha ging pile alloca ion mechanism can significan ly imp o e he
ope a ional e ficiency o cha ging s a ions. The abandonmen a e,
cha ging wai ing a e, a e age cha ging wai ing ime, cha ging pile idle
a e, and cha ging pile usage can se e as e ficien indica o s o
comp ehensi ely e alua ing cha ging s a ion ope a ions [56]. Fo a
cha ging s a ion wi h limi ed cha ging capaci y, he cha ging pile allo-
ca ion mechanism is essen ial o unleashing he po en ial o cha ging
scheduling.
5.2.2. Cha ging scheduling esul s
(1) Scheduling esul s o one EV
Analyzing he scheduling esul s o a single EV p o ides aluable
insigh s in o he op imiza ion app oach. Conside an EV wi h he basic
in o ma ion p esen ed in Table 8, ope a ing wi hin a 10- ime-slo pe iod
wi h no o he EVs cha ging simul aneously. In eali y, he ac ual
cha ging/discha ging e ficiency o EVs can be influenced by ac o s such
as ba e y empe a u e [57]. Howe e , due o he lack o ele an da a,
fixed alues we e u ilized in he simula ion. The cha ging and dis-
cha ging p ices, base load, and o ecas enewable ene gy gene a ion a e
illus a ed in Fig. 13(a) and (b).
Upon ecei ing he EV's in o ma ion, EIDC employs he NSGA-II al-
go i hm o ob ain he Pa e o- on solu ion se . Then he En opy-TOPSIS
me hod is u ilized o de e mine he op imal cha ging schedule o he EV.
Fig. 13(c) depic s he Pa e o- on , and Fig. 13(d) shows he compa ison
be ween he op imal cha ging schedule and he diso de ly cha ging load.
The o al load compa ison is p esen ed in Fig. 13(b). The p ocess o
ob aining he EV in o ma ion and de i ing he op imal cha ging schedule
akes app oxima ely 2.01 s.
A compa ison o a ious indica o s is p esen ed in Table 9.I is
e iden ha he p oposed scheduling me hod leads o ema kable e-
duc ions in o al load fluc ua ion, use cha ging cos , and enewable
ene gy cu ailmen .
(2) Scheduling esul s o e a week
This sec ion akes in o accoun he cha ging beha io s o bo h as -
and slow-cha ging EVs on weekends and weekdays. Using he ac ual
daily a i al numbe s o EVs shown in Table 5 and in eg a ing wi h he
enewable ene gy gene a ion o ecas model, a week-long simula ion was
conduc ed o he Lucheng cha ging s a ion. In he simula ion, each EV
was fi s assigned o a cha ging pile, and hen a cha ging schedule was
de eloped and implemen ed. Fou o de ly cha ging scheduling scena ios
we e conside ed:
Scena io 1: The op imiza ion objec i e solely ocuses on DNFL and
EVCC, neglec ing he cons ain s o enewable ene gy gene a ion and
V2G capabili y.
Scena io 2: All h ee objec i es a e conside ed, excep o he V2G
capabili y cons ain .
Scena io 3: The op imiza ion model only conside s DNFL and EVCC,
neglec ing he enewable ene gy gene a ion cons ain .
Scena io 4: The op imiza ion model akes in o accoun bo h he ob-
jec i es and cons ain s.
The basic load da a o a esiden ial communi y in Beijing we e used as
he p edic ed basic load o one week, as shown in Fig. 14(a). By inco -
po a ing eal- ime wind speed and ligh in ensi y da a om San F an-
cisco, he p edic ed powe cu es o wind u bines and pho o ol aic
powe gene a ion we e de i ed. The cha ging scheduling esul s o a
week a e p esen ed in Fig. 14. Fo cla i y, he esul s o Tuesday a e
sepa a ely illus a ed in Fig. 15, wi h di e en colo s ep esen ing TOU.
The changes in he o al load combining he base and EV loads a e
depic ed in Figs. 14(b) and Fig. 15(e). I can be obse ed ha , compa ed
o diso de ly cha ging, he o al load fluc ua ion is educed in all he ou
scena ios, wi h he load shi ing om he peak o he alley pe iod. This
load shi ing is beneficial o he g id as i helps balance he powe de-
mand o e ime. The cha ging scheduling esul s in Fig. 14(c)–( ) indi-
ca e ha he EV cha ging loads shi om he peak o he no mal pe iod
in all he ou scena ios. The o al V2G discha ging powe du ing he
alley pe iod is significan ly lowe han ha du ing he no mal and peak
pe iods. The RECD fluc ua es a ound 0, sugges ing ha enewable ene gy
is e ec i ely u ilized in eal- ime du ing he cha ging and discha ging
p ocesses. As shown in Fig. 15( ), he de ia ions be ween he expec ed
and ac ual end SOCs a e wi hin a easonable ange.
The cha ging scheduling esul s o he en i e week a e p esen ed in
Tables 10 and 11, wi h he daily simula ion esul s p o ided in Appendix
A-1. The abandonmen a e, wai ing ime, and cha ging scheduling
pa icipa ion a e a e 0.23%, 0%, and 97.70%, espec i ely, and he
success a e o sol ing he op imiza ion o mula ion is 100%. These
e i y he e ec i eness o he p oposed cha ging scheduling scheme and
i s abili y o mee eal- ime implemen a ion equi emen .
Table 10
The pa icipa ion a e o o de ly cha ging o he en i e week.
EVN POCN ACN WCN FSN
2,172 2,122 5 0 0
Table 11
The esul s o o de ly cha ging scheduling o he en i e week. DNLF ep esen s
he o al load fluc ua ion wi hin a week (T¼672), EVCC deno es he a e age
cha ging cos o all EVs, and RECD indica es he a e age enewable ene gy
consump ion defici pe ime slo .
Objec i e DNLF EVCC RECD SE AST
Scena io0 695.11 25.89 192.47 ––
Scena io1 664.67 24.98 –0.092,7% 2.00
Scena io2 672.16 25.28 188.88 0.092,7% 2.25
Scena io3 647.83 23.83 –0.088,3% 2.28
Scena io4 667.74 24.71 191.56 0.088,2% 2.37
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
16
Fu he mo e, fluc ua ions in cha ging demand and a ia ions in
enewable ene gy gene a ion eme ge as wo sensi i i y ac o s ha
significan ly influence he a ainmen o he s udy's objec i es. Con-
ce ning cha ging demand fluc ua ions, as i idly illus a ed in Figs. 3 and
15, he numbe o EVs a i ing a he cha ging s a ion a ies ac oss
di e en pe iods h oughou he day. Fewe EVs cha ge om
04:00–08:00 and 20:00–04:00, wi h lowe o e all load and educed
fluc ua ion a nigh compa ed o 08:00–20:00. Fig. 14 indica es ha
enewable ene gy gene a ion on Tuesday is much highe han on F iday,
wi h i s consump ion cu e fluc ua ing a ound ze o. This means EV
cha ging mainly employ enewable ene gy. Appendix 1 shows highe
enewable ene gy gene a ion educes he alues o he h ee p oposed
indica o s. I indica es ha he p oposed cha ging scheduling scheme can
e ec i ely balance he conflic ing objec i es. Mo eo e , i can e ficien ly
in eg a e d i ing beha io s in o he cha ging scheduling p ocess, while
also aking in o accoun he conce ns o g id ope a ion, cha ging cos s,
and enewable ene gy in eg a ion.
(3) Impac o ime s ep selec ion
The simula ion encompasses 503 EVs, among which he e a e 350
as -cha ging EVs and 153 slow-cha ging EVs. The ehicle- o-cha ging
pile a io is se o be he same as ha in Sec ion 5.2.1. The enewable
ene gy gene a ion and he basic load a e p esen ed in14(a), and i is
designa ed as Scena io 4.
The du a ion o he ime s ep o cha ging scheduling is adjus able. To
de e mine he op imal ime s ep, simula ions we e ca ied ou wi h he
du a ions o 3 min, 5 min, and 15 min. The esul s a e p esen ed in
Fig. 16(a) and Table 12. I is e iden ha inc easing he ime-s ep
du a ion has only li le influence on he pe o mance o he p oposed
scheme bu can ema kably educe he compu a ional in ensi y. In
p ac ical applica ions, when he idle ime o EVs is su ficien ly long, a
long ime-s ep du a ion is ecommended o sho en he op imiza ion-
sol ing ime; when he EV idle ime is es ic ed, a sho ime-s ep
du a ion is ad isable o be e accomoda e enewable ene gy gene a ion.
6. Conclusion
This pape p oposes a eal- ime cha ging scheduling scheme o enable
e ficien Vehicle- o-G id in e ac ions and acili a e enewable ene gy
in eg a ion a public cha ging s a ions. A cha ging pile alloca ion
mechanism is p oposed, which can inc ease he u iliza ion a e o
cha ging piles, educe EV wai ing ime, wai ing a e, and abandonmen
a e, and de e mine he op imal ehicle- o-cha ging pile a io. An o de ly
cha ging scheme based on a sliding window mechanism is also de el-
oped. Nume ical esul s show ha he p oposed scheme can educe he
dis ibu ion ne wo k load fluc ua ion, a e age cha ging cos , and eal-
ime ene gy consump ion di e ence. Fu u e esea ch will u he inco -
po a e he impac s o a ficflow and dis ibu ion capaci y limi a ions.
CRediT au ho ship con ibu ion s a emen
Lei Zhang: W i ing –o iginal d a , In es iga ion, Funding acquisi-
ion, Fo mal analysis. Yingjun Ji: W i ing –o iginal d a , In es iga ion,
Da a cu a ion. Xiaohui Li: Resou ces, Fo mal analysis. Zhijia Huang:
Da a cu a ion, Concep ualiza ion. Dingsong Cui: W i ing – e iew &
edi ing, Visualiza ion. Haibo Chen: Resou ces, P ojec adminis a ion.
Jingyu Gong: W i ing – e iew &edi ing, Resou ces. Fabian B ee :
Valida ion, Me hodology. Ma k Junke : Resou ces, P ojec adminis a-
ion. Di k Uwe Saue : Supe ision, Funding acquisi ion.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing financial
in e es s o pe sonal ela ionships ha could ha e appea ed o influence
he wo k epo ed in his pape .
Lei Zhang epo s financial suppo was p o ided by he Minis y o
Science and Technology o he People's Republic o China.
Fig. 16. Compa ison a di e en ime esolu ions: (a) O de ly cha ging load. (b) Solu ion de i a ion ime.
Table 12
Compa ison o di e en ime s eps. (DNLF ep esen s he o al load fluc ua ion
wi hin a day (T¼96), EVCC deno es he a e age cha ging cos o all EVs, and
RECD indica es he a e age enewable ene gy consump ion defici pe ime slo .)
Time s ep/min DNLF EVCC RECD AST FSN
3 694.56 11.77 377.01 6.84 6
5 686.06 11.81 374.08 5.09 0
15 676.73 11.53 370.87 2.96 0
L. Zhang e al. G een Ene gy and In elligen T anspo a ion 4 (2025) 100283
17
Acknowledgemen s
This wo k was suppo ed in pa by he Minis y o Science and Tech-
nology o he People's Republic o China [G an No. 2022YFE0103000].
This wo k was also join ly suppo ed by se e al in e na ional p ojec s,
namely EU- unded p ojec s ZEV - UP (No.101138721), ePowe Mo e
(No.101192753), and FlexFlee (No.03EMF0407) unded by he Ge man
Fede al Minis y o Digi al and T anspo and he EU.
A Appendix.
Table A-2
Pa ial en ies o he p ep ocessed elec ic ehicle cha ging beha io da abase.
S a ime End ime S a SOC/% End SOC/% Ba e y/kWh Fas /Slow cha ging Wo kday/Holiday
2021-01-09 21:09:56 2021-01-10 02:07:45 15 98 52 Fas cha ging Holiday
2021-01-10 02:07:46 2021-01-10 20:08:31 8 100 65 Slow cha ging Holiday
2021-01-20 08:04:31 2021-01-20 10:03:22 11 100 52 Fas cha ging Wo kday
2021-01-21 09:09:06 2021-01-21 21:46:21 5 98 48 Slow cha ging Wo kday
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Table A-1
Specific nume ical alues o a ious indica o s calcula ed o he en i e week. (DNLF ep esen s he o al load fluc ua ion wi hin a day (T¼96), EVCC deno es he
a e age cha ging cos o all EVs, and RECD indica es he a e age enewable ene gy consump ion defici pe ime slo .)
Pa Day Mon Tue Wed Thu F i Sa Sun
Indica o s EVN 288 320 321 316 281 336 310
POCN 277 310 313 310 278 331 303
ACN1111001
WCN0000000
Scena io0 DNLF 671.92 667.31 685.95 665.47 672.17 627.70 785.10
EVCC 26.12 25.62 25.32 25.39 26.79 26.33 25.73
RECD 182.89 103.55 188.80 165.49 224.10 199.95 176.43
Scena io1 DNLF 651.73 628.90 674.09 628.81 644.00 636.58 758.03
EVCC 25.07 24.95 24.26 24.68 25.82 25.14 25.04
Scena io2 DNLF 657.81 632.09 685.25 636.11 655.07 642.39 765.70
EVCC 25.33 25.06 24.58 24.94 26.37 25.50 25.30
RECD 168.12 117.52 212.64 165.27 229.82 240.47 188.30
Scena io3 DNLF 632.70 614.12 657.96 608.90 625.44 616.12 746.40
EVCC 23.74 23.97 23.18 23.45 24.40 24.08 24.04
Scena io4 DNLF 647.53 627.72 680.80 628.05 650.77 639.60 767.55
EVCC 24.59 24.32 24.03 24.48 25.69 24.99 24.96
RECD 170.44 120.16 216.46 176.13 230.20 240.29 187.26
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