CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 10, NO. 6, NOVEMBER 2024 2457
Robust Expansion Planning of Electric Vehicle
Charging System and Distribution Networks
Yue Xiang, Senior Member, IEEE, Ping Xue, Yanliang Wang, Lixiong Xu, Wang Ma, Miadreza Shafie-khah,
Senior Member, IEEE, Junlong Li, and Junyong Liu, Member, IEEE
Abstract—Large integration of electric vehicles (EVs) brings
uncertainties and challenges for distribution networks. Reliability
and allocation of charging systems (charging stations and piles)
need strong support from the distribution network, whose expan-
sion planning would be also greatly impacted by the incremental
load from the charging system. To address this issue, a collabora-
tive planning scheme of the EV charging system and distribution
networks that combines economic and reliability benefits is
proposed, which is formulated as a two-stage distributionally
robust optimization model considering source-load uncertainties.
First, a candidate EVCS planning scheme is obtained using
queuing theory. Then, system reliability is quantified by adopting
the average energy not supplied index and correlated integrated
into the two-stage mixed-integer linear programming model.
Finally, it is solved to perform distributionally robust expansion
planning by the column and constraint generation algorithm.
Effectiveness and scalability of the proposed planning method
are illustrated by numerical case studies. Results indicate the
planning scheme that considers economic and reliability benefit
can perform better than traditional optimization methods.
Index Terms—Distribution network planning, distributionally
robust optimization, electric vehicle, reliability benefit.
I. INTRODUCTION
THE high demand for energy conservation and pollutionreduction must be satisfied under pressure of the envi-
ronmental and energy crisis. According to statistics, carbon
emissions in transportation account for approximately 30% of
the total economic and social carbon emissions, and 75% of
greenhouse gases and more than 90% of air pollutants are from
activities in cities. Thus, energy saving and emission reduction
in transportation are important to achieve the goal of “carbon
Manuscript received November 15, 2021; revised December 26, 2021,
accepted March 1, 2022. Date of online publication December 30, 2022; date
of current version March 27, 2023. This work was supported by the National
Natural Science Foundation of China (52111530067), and the Academy of
Finland project “Robust Distribution Network Planning to Facilitate Electric
Vehicle Integration” (341473).
Y. Xiang, Y. L. Wang, L. X. Xu, W. Ma, J. Y. Liu are with College of
Electrical Engineering, Sichuan University, Chengdu 610065, China.
P. Xue (corresponding author, email: xpsherry@foxmail.com) is with State
Grid Sichuan Technical Training Center, Sichuan Electric Vocational and
Technical College, and also the College of Electrical Engineering, Sichuan
University, Chengdu 610065, China.
M. Shafie-khah is with the School of Technology and Innovations, Univer-
sity of Vaasa, Vaasa 8130, Finland.
J. L. Li is with the Department of Electronic and Electrical Engineering,
University of Bath, Bath BA2 7AY, UK.
DOI: 10.17775/CSEEJPES.2021.08540
peak and carbon neutrality”. As clean and effective city
transport means electric vehicles (EVs) are being vigorously
developed. How to perform the planning of the EV charging
system reasonably has become an important topic in satisfying
growing charging demand. However, planning of the EV
charging system and the planning of the distribution network
interact with each other. Determination of the location and size
of the EV charging station needs to consider grid’s capacity
while meeting transportation constraints. Meanwhile, the grid
planning scheme also influences economy and reliability of
the EV charging system. Hence, performing collaborative
planning for the EV charging system and distribution network
can meet charging and power load demand while optimizing
coupled system operation. However, travel behavior of EV
users entails subjectivity and randomness and is constrained
by the operation of transportation and distribution networks.
Large-scale integration of EVs into distribution networks
brings operation risks and security challenges, particularly
when high penetration of distributed generation (DG) exists
in the grid. Therefore, we need to focus not only on the
economic benefit when performing EV charging system and
grid planning, but also on the reliability benefit of the planning
scheme. A new type of power system is urgently constructed to
perform adaptive planning for transportation and distribution
networks in consideration of economic and reliability benefits.
EV charging behavior involves transportation and distri-
bution networks. Thus, it is constrained by power flow and
traffic flow. Multiple factors, such as charging demand satis-
faction and grid adoption capacity, should be considered in
the planning of the EV charging station (EVCS). In [1], a
novel multiple-criteria decision-making method was proposed
to determine an optimal EVCS site. In [2], allocation of
administrative and residential EVCS was discussed based on
a smart charging/discharging schedule to determine optimal
capacity and location. Given characteristics of different types
of private cars, an optimal EVCS planning scheme was
proposed in [3] with minimum social cost of the overall
EV charging system. However, these studies did not consider
transportation constraints and ignored impacts of transporta-
tion network topology and traffic flow on EVCS planning.
Dynamic interactions between evolution coherence of charging
loads and traffic flows were captured in [4]. Reference [5]
considered elastic traffic flow requirements, such as charging
driving distance. However, the dynamic queuing process of
EV users in the station was not considered.
In existing studies on the collaborative planning of EVCS
2096-0042 © 2021 CSEE. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
2458 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 10, NO. 6, NOVEMBER 2024
and distribution networks, the objective function usually in-
volved maximizing economic benefit. However, they did not
discuss whether the planning scheme could meet system
operation requirements, particularly when multiple uncertain
factors exist in the system. In [6], expansion planning of
distribution network topology and EVCS was performed by
minimizing investment and operation costs. A bi-level optimal
allocation model for fast charging stations was proposed in [7].
The model coordinates investor benefit and user satisfaction
degree. In consideration of the uncertainty of different types
of charging load, a collaborative planning method for EVCS
and distribution network was proposed in [8] to minimize
investment and operation costs while maximizing captured
traffic flow. However, the reliability benefit of the planning
scheme was not considered in these studies. Reference [9] in-
troduced a comprehensive evaluation index system to quantify
the reliability level of distribution and transportation networks
but did not present the planning scheme. In [10], reliability-
correlated optimal planning of the distribution network and DG
was proposed, but EV integration into the distribution network
was ignored. In [11], a multi-objective optimal planning model
was proposed. This model is oriented to collaborative im-
provement of distribution network operation reliability and EV
travel reliability. Although reliability of the planning scheme
was examined in [11], load curtailment was calculated based
on system operation status, and failure rate was not considered.
This scenario does not apply to actual operation and planning
of the grid.
The main methods that describe uncertainty are stochastic
optimization (SO) and robust optimization (RO) [12], [13]. In
SO, characteristics of uncertain variables, such as wind power
supply, are described using probability distribution, which
has been applied early to power system planning [14], [15].
Reference [16] proposed a stochastic adaptive RO approach
for generation and transmission expansion planning problems
under a central planner perspective. Robust expansion planning
of an electrical distribution system and EVCS was performed
in [17]. Although SO and RO have already produced good
results, SO requires support of a large number of scenarios,
resulting in long calculation time, and RO needs to be utilized
in the worst scenario, possibly leading to a conservative
conclusion.
Given its good economic performance and conservative-
ness, distributionally robust optimization (DRO) has received
much attention in the field of unit commitment and optimal
scheduling. To address the uncertainty of DG power supply,
a novel DRO approach was proposed in [18] to operate an
energy hub system with an energy storage system. In [19],
a distributionally robust chance-constrained generation expan-
sion planning method was introduced considering long- and
short-term uncertainties. This situation shows a few studies
still utilize the DRO approach for collaborative planning of
the EV charging system and distribution networks.
In summary, despite existing studies on collaborative plan-
ning of EVCS and distribution networks, the following limita-
tions remain. (1) The reliability benefit, which is calculated
based on failure rate information, has not been considered
in planning research. (2) A few studies utilized the DRO
approach for collaborative planning of EVCS and distribution
networks, and did not evaluate impacts of uncertain factors on
such planning.
To deal with these concerns, a two-stage distributionally
robust collaborative planning model of the EV charging sys-
tem and distribution network is proposed in consideration of
economic and reliability benefits. The main contributions of
this work are as follows:
• An optimal comprehensive target with balanced eco-
nomic and reliability benefit is achieved for collabora-
tive planning of EV charging system and distribution
network. Compared with traditional method, the opti-
mization model, which considers reliability benefit, can
cope with uncertainties better while maintaining good
operation benefit.
• A reliability benefit based on failure rate information
is considered during the planning process. Thus, the
obtained planning scheme is applicable to actual power
grid operation.
• A DRO approach is utilized to deal with uncertainties
of EV charging demand and DG output. Impact of
uncertainties on collaborative planning of the distribution
network and EV charging system is evaluated, and the
corresponding optimal integrated penetration is provided.
The remainder of this paper is organized as follows: The
framework of the study is introduced in Section II. Section III
presents optimization of the EVCS planning scheme based on
traffic flow. In Section IV, a proposed collaborative planning
model of the distribution network and EV charging system is
introduced together with a description of reliability benefit-
based correlation analysis. The solving algorithm of the two-
stage DRO model is presented in Section V. Effectiveness
and scalability of the proposed planning method are tested
in Section VI. Section VII concludes this work.
II. RESEARCH FRAMEWORK
Given the uncertainties of charging load and wind output, a
two-stage distributionally robust collaborative planning model
of EVCS and a distribution network that considers the relia-
bility benefit is proposed. The research framework is shown
in Fig. 1.
As shown in Fig. 1, work in this paper is divided into
three parts. For EVCS planning, it is optimized considering
traffic flow based on queuing theory, which is planned from
the perspective of people’s behavior and psychological needs
at the transportation network level. In this way, EVCS planning
is decoupled with distribution network planning. Neverthe-
less, the obtained EVCS planning scheme is not the optimal
solution since it still requires constraints from the distribu-
tion network. Hence, from this part, the candidate EVCS
planning scheme is determined and is to be embedded into
the collaborative planning model for optimal EVCS planning.
For reliability benefit quantification part, the reliability benefit
cannot be calculated directly with the expansion mixed-integer
linear programming (MILP) planning model for its nonlinear
characteristic. Thus, a correlation analysis method is used to
quantify the reliability benefit. When the correlation rule has
XIANG et al.: ROBUST EXPANSION PLANNING OF ELECTRIC VEHICLE CHARGING SYSTEM AND DISTRIBUTION NETWORKS 2459
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o
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 b
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 tran
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 an
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istrib
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n
 n
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 o
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 reliab
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NonlinearityNonlinearity
System optimization
assignment model
Historical data
generation
Considering
transportation
constraints, parking
demand, and grid's
adoption capacity
Reliability index
AENS calculation
considering failure
rate based historical
data
Equilibrium
traffic flow
Correlation rule
training 
 theoryQueuing analysisCorrelation
Candidate EVCS
planning scheme
Reliability benefit
quantification
minmum
investment,
operation, and
reliability costs
Optimization of
the two-stage
DRO planning
model
The mixed-
integer linear
programming
(MILP) model
Identification and
feasibility detection of
uncertain parameters
The second stageThe first stage
Optimize the
planning scheme by
cost minimization Iteration
CCG
The optimal collaborative planning scheme
Fig. 1. Research framework.
been trained, it can be embedded into the MILP model, thereby
improving calculation efficiency while ensuring its accuracy.
With the obtained candidate EVCS planning scheme and the
trained reliability correlation rule, a distributionally robust
planning model can be simulated to determine the optimal col-
laborative planning scheme of EVCS and distribution network
with a balanced economic and reliability benefit.
First, a candidate EVCS planning scheme is generated. A
system optimization assignment (SOA) model, which focuses
on EV users’ charging behavior, is introduced to obtain
equilibrium traffic flow in consideration of transportation
constraints, parking demand, and grid’s adoption capacity.
Then, queuing theory is utilized to obtain a candidate EVCS
configuration scheme. Second, the reliability calculation is
linearized so it can be embedded into the mixed-integer linear
programming (MILP) planning model. On this basis, the
reliability index of average energy not supplied (AENS) is
utilized to quantify system reliability. Third, reliability benefit
calculation is embedded into the MILP model based on data
obtained with the objective of achieving minimum investment
and operation costs. Last, the collaborative planning scheme of
the EV charging system and distribution network is optimized.
An optimal collaborative planning scheme is obtained at the
first stage with the objective of achieving minimum invest-
ment, operation, and reliability costs. An operational layer,
which is used for identification and feasibility detection of
uncertain parameters in the worst scenario, is considered at the
second stage. A column and constraint generation algorithm
is adopted to solve the MILP problem, which is linearized by
big-M and second-order cone relaxation.
III. EVCS OPTIMIZATION BASED ON TRAFFIC FLOW
A. Traffic Flow Assignment Model
Mobile EV charging demands at a specific traffic network
node can be moderately reflected by traffic flow distribution.
However, traffic flow and power flow data are generally dy-
namic and cannot be used directly during planning. Therefore,
a typical operation scenario is considered in planning. Typical
origin–destination (OD) data, which can be obtained from
transportation departments or research results, characterize
traffic flow distribution. On this basis, lowest travel cost
is considered the objective function, and a SOA model is
introduced to generate static traffic flow, which is expressed as:
min
∑
a∈NT
frata(fra) (1)
s.t.
∑
k
fpruk = qru fp
ru
k ≥ 0 (2)
fra =
∑
r
∑
u
∑
k
fpruk δ
ru
a,k (3)
ta(fra) = t
0
a
[
1 + b
(
fra
ca
)v]
(4)
where fra represents traffic flow on road a. fpruk is traffic
flow of the OD matrix with regard to ru in path k. qru is
total traffic flow with regard to ru. δrua,k is a 0–1 variable to
indicate whether ru is included in path k or not. ta represents
the function of the Bureau of Public Roads. t0a is travel time
on road a. ca is traffic capacity of road a, and b and v are
retardation coefficients. Traffic flow based on the SOA model
is defined as the “equilibrium traffic flow”.
B. Candidate Number of EVCS Charger Determination and
Charging Load Estimation
Charging demand is uncertain because of the randomness
of EV users’ charging behavior. The number of EVs arriving
at the charging station can be obtained based on spatiotem-
poral traffic flow data. Given the transfer and aggregation
characteristics of EVs, queuing theory is utilized to analyze
EV charging behavior and determine the optimal configuration
scheme of EVCS.
Users’ charging behavior in the charging station can be
characterized as a queuing system, where the EVCS charger
provides charging service and EVs are customers. Assume
the process of EVs arriving at the charging station obeys the
Poisson distribution. In this case, when all EVCS chargers
are in use, the first-come-first-served rule is followed. Others
wait until an EVCS charger becomes available. Otherwise,
users may choose to drive away if the waiting time exceeds
their tolerance level. Charging service time obeys negative
exponential distribution.
2460 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 10, NO. 6, NOVEMBER 2024
Parameter λ is the EV average arrival rate, i.e., the number
of EVs reaching the charging station per unit time. It can be
expressed as:
λj,t =
Hωεtfnj,t
∆t
∑
j∈ΩT fnj,t
(5)
where H is the total EV charging frequency on a typical day. w
is the approximate ratio of charging frequency in the charging
station to the total charging frequency. εt is the charging rate.
fnj,t is traffic flow in the charging station located in bus j
at time t, which can be accumulated by fra with the same
injecting direction. ∆t is the time step, and ΩT represents the
candidate set of charging station locations.
Indexes quantifying the station’s charging service can be
obtained as follows:
ρ =
λ
µ
(6)
β =
λ
sµ
(7)
ρ0 =
1∑s−1
n=0
ρn
n! +
ρs
s!(1−β)
(8)
Wq =
sρs+1ρ0
λs!(s− ρ)2 (9)
where µ is the EVCS chargers’ service efficiency. ρ is average
service rate of the charging system. β represents EVCS
chargers’ service rate. s is the number of chargers in the
station. ρ0 represents vacancy rate of the charging system,
and Wq is average waiting time.
The number of chargers in an EVCS should be reduced as
much as possible while still meeting users’ charging demand
to maximize return on investment. The minimum number
of EVCS chargers can be calculated by considering users’
average tolerance level of queuing time. The specific process
is shown in Fig. 2.
In addition, distance between two charging stations should
meet the geographical distance constraint.
dm−n ≥ dmin (10)
Generate equillibrium trafic flow based on (1)–(4)
Calculate average arriving number of EV based on (5)
Calculate the number of charger based on (6)–(8)
Calculate the average queuing timeWq based on (9)
Wq ≤Wmaxq
The candidate plan of tummber of chargers in each EVCS
s = s+ 1
Yes
No
Fig. 2. Determination of the candidate charger number in each EVCS.
where dm−n represents distance between bus m and n and
dmin is the allowed shortest distance between charging sta-
tions.
Fast- and low-charging loads can be estimated after the
candidate charging station configuration scheme is determined.
Fast-charging load at time t can be estimated by combining
EVCS charger’s configuration results as follows:
βCsj,t = βj,tsjPCD$, (11)
where PCD is power of the charger and $ is charging
efficiency of the charger.
Meanwhile, slow-charging load is aggregated to the corre-
sponding bus in the distribution network when a user charges
an EV through a charging pile in a residential or commercial
area. The number of charging piles in the node can be
estimated with (12). On this basis, low-charging load can be
calculated with (13).
NCPi =
H × (1− ω)×∑Tt=1 PLi,t
κ× (1− γ)×∑NDi=1∑Tt=1 PLi,t (12)
PCPi,t = PCPxi,tN
CP
i (13)
where κ represents charging capacity of the charging pile.
PLi,t indicates active load in bus i at time t. γ is vacancy
rate whose value is between 0 and 1. xi,t is charging demand
coefficient, which can be represented by parking demand in a
certain area, and PCP is charging power of the charging pile.
IV. COLLABORATIVE PLANNING MODEL OF THE
DISTRIBUTION NETWORK AND EV CHARGING SYSTEM
A. Objective Function
This study considers multi-objective planning with the high-
est economic and reliability benefits. Economic costs involve
investment cost F inv, operation cost F ope, and reliability cost
F rel. Formulations are as follows:
min F inv + F ope + F rel (14)
F inv = C invsub + C
inv
line + C
inv
EVCS + C
inv
WTG + C
inv
chargingpile
(15)
F ope =
Ns∑
s=1
ps (C
ope
sub + C
ope
WTGcur + C
ope
EVloadcur + C
ope
loss)
+ Copeline (16)
C invsub =
r0(1 + r0)
msub
r0(1 + r0)msub − 1
( ∑
i∈Ψsubnewe
Csub newxsub newi
+
∑
i∈Ψsubeex
Csub extxsub exti
)
(17)
C invchargingpile =
r0(1 + r0)
mpile
r0(1 + r0)mpile − 1
∑
i∈Ψpile
Cpilexpilei (18)
C invline =
r0(1 + r0)
mL
r0(1 + r0)mL − 1
∑
ij∈ΨL
CLLenijx
L
ij (19)
C invEVCS =
r0(1 + r0)
mCS
r0(1 + r0)mCS − 1∑
i∈ΨCS
xCSi (C
CS fix
i + siC
CS var
i ) (20)
XIANG et al.: ROBUST EXPANSION PLANNING OF ELECTRIC VEHICLE CHARGING SYSTEM AND DISTRIBUTION NETWORKS 2461
C invWTG =
r0(1 + r0)
mWTG
r0(1 + r0)mWTG − 1
∑
i∈ΨWTG
CWTGxWTGi (21)
Copesub = Dδ
sub
∑
t∈T
∑
i∈Ψsub
P subs,i,tx
sub
i (22)
Copeline = δ
L
∑
ij∈ΨL N
Lenij L
L N
ij (23)
CopeWTGcur = Dδ
WTGcur
∑
t∈T
∑
i∈ΨWTG
(PWTG,Pres,i,t − PWTGs,i,t )
(24)
CopeEVloadcur = Dδ
EVIoadcur
∑
t∈T
∑
i∈Ψpile
(PEVload, Pres,i,t − PEVIoads,i,t )
(25)
Copeloss = Dδ
loss
∑
t∈T
∑
ij∈ΨL N
(Is,ij,t)
2rij (26)
where i indicates a bus in the distribution network. t repre-
sents time. s represents scenario. Ns is number of scenarios.
ps represents probability of scenario occurrence. C invsub, C
inv
line,
C invEVCS, C
inv
WTG, and C
inv
chargingpile are investment costs of the
substation, line, EVCS, WTG, and charging pile, respectively.
Copesub and C
ope
line are operation cost of the substation and
line. CopeWTGcur is wind curtailment cost. C
ope
EVloadcur is EV
charging load shedding cost. Cmecops is cost of network loss.
msub,mpile,mL, mCS, and mWTG represent life cycle of the
corresponding device. Csub new and Csub ext are new con-
struction and expansion costs of the substation, respectively.
Cpile is unit investment price of the charging pile. CL is invest-
ment cost per unit length of the line. CWTG is investment price
for a single WTG. xsubi , x
sub new
i , x
sub ext
i , x
pile
i , x
L
ij , x
CS
i , and
xWTGi are corresponding decision variables. Lenij represents
length of the line. si is charger number in the station. D
is number of days in a year. δsub and δL are maintenance
price. δWTGcur and δEVloadcur are curtailment price of wind
and charging load. δloss is network loss price. P subs,i,t is output
power of the substation. PWTG,Pres,i,t , P
WTG
s,i,t , P
EVload,Pre
s,i,t , and
PEVloads,i,t are WTG forecasted output, WTG actual output,
forecasted charging load, and actual charging load, respec-
tively, and Ψsub,Ψsub new,Ψsub ext,Ψpile,ΨL,ΨCS,ΨwTG,
and ΨL N represent the set of corresponding devices’ locating
buses.
B. Constraints
1) Investment Constraint
0 ≤
∑
y∈Γsub
xsubi,y ≤ 1 (27)∑
y∈ΓCS
xCSi,y = 1 (28)
0 ≤ xpilei ≤ N
pile
i (29)
0 ≤ xWTGi ≤ N
WTG
i (30)
0 ≤ CapWTG
∑
i∈ΨWTG
xWTGi ≤ LWTG
∑
i∈ΨBΩ
Loadi (31)
where Γsub indicates whether substation is newly constructed
or expanded. ΓCS represents candidates of EVCS. ΨB N
represents set of buses in the distribution network. N
pile
i and
N
WTG
i represent maximum number of installed charging piles
and WTGs. CapWTG is capacity of a single WTG. LWTG is
penetration limit of WTG in the grid, and Loadi is load in
bus i.
2) Branch Power Flow Constraint
Given the square of bus voltage and branch current is
required in power flow equations, which are nonlinear, branch
voltage and current should be transformed equivalently to
linearize the planning model. U∗s,i,t and I
∗
s,ij,t are used to
replace the square of the voltage and current as follows:
U∗s,i,t = (Us,i,t)
2, (32)
I∗s,ij,t = (Is,ij,t)
2 (33)
where U∗s,i,t and I
∗
s,ij,t are corresponding substitution vari-
ables.
With the big-M method [20], power flow equations can be
expressed as:∑
k∈pi(i)
(Ps,ki,t−rkiI∗s,ki,t)−
∑
j∈ς(i)
Ps,ki,t + P
sub
s,i,t + P
WTG
s,i,t
= PLoadi,t + P
EVCS
i,t + P
EVload
s,i,t (34)∑
k∈pi(i)
(Qs,ki,t−xkiI∗s,ki,t)−
∑
j∈ς(i)
Ps,ki,t +Q
sub
s,i,t +Q
WTG
s,i,t
= QLoadi,t (35)
U∗s,j,t ≤ U∗s,i,t − 2(rijPs,ij,t + xijQs,ij,t)
+ I∗s,ij,t[(rij)
2 + (xij)
2] +M(1− xLij) (36)
U∗s,j,t ≥ U∗s,i,t − 2(rijPs,ij,t + xijQs,ij,t)
+ I∗s,ij,t[(rij)
2 + (xij)
2]−M(1− xLij) (37)
I∗s,ij,tU
∗
s,i,t = (Ps,ij,t)
2 + (Qs,ij,t)
2 (38)
Equation (38) can be transformed further as follows:∥∥∥∥∥∥
2Ps,ij,t
2Qs,ij,t
I∗s,ij,t − U∗s,i,t
∥∥∥∥∥∥
2
≤ I∗s,ij,t + U∗s,i,t (39)
where pi(i) and ς(i) are set of buses whose parent/child is
bus i. r and x represent resistance and reactance, respectively,
and P and Q represent active power and reactive power,
respectively.
3) Security Constraint
(U)2 ≤ U∗s,i,t ≤ (U)2 (40)
0 ≤ I∗s,i,t ≤ (Iij)2 (41)
where U and U are the lower and upper limits of bus voltage,
respectively, and Iij is the upper limit of branch current.
4) Substation Injection Constraint
P subi ≤ P subs,i,t ≤ P
sub
i (42)
Qsub
i
≤ Qsubs,i,t ≤ Q
sub
i (43)
where P subi and P
sub
i are the lower and upper limits of
substation injection power, respectively, the same applies to
Q
sub
i and Q
sub
i
.
2462 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 10, NO. 6, NOVEMBER 2024
5) Branch Transmission Constraint
|Ps,ij,t| ≤ Pmaxij (44)
|Qs,ij,t| ≤ Qmaxij (45)
where Pmaxij and Q
max
ij are allowed maximum transmission
power, respectively.
6) WTG Injection Constraint
0 ≤ PWTGs,i,t ≤ PWTG,Pres,i,t (46)
QWTGs,i,t = tan[cos
−1(ρWTG)]PWTGs,i,t (47)
where ρWTG is the power factor of WTG.
7) Uncertain Low-Charging Power Constraint
0 ≤ PEVloads,i,t ≤ PEVload,Pres,i,t (48)
8) Radial Operation Constraint
NL N = NB N −Nsub(xsubi ) (49)
where NL N, NB N, and Nsub are the number of lines, buses,
and substations, respectively.
In addition, variable ε representing a small load is intro-
duced to ensure the network’s connection as follows:∑
j∈ζ(i)
P ′s,ki,t −
∑
k∈pi(i)
(P ′s,ki,t − rkiI∗∗s,ki,t) = ε (50)∑
j∈ζ(i)
Q′s,ki,t −
∑
k∈pi(i)
(Q′s,ki,t − xkiI∗′s,ki,t) = ε (51)
U∗′s,j,t ≤ U∗s,i,t − 2(rijP ′s,j,t + xijQ′s,j,s,)
+ I∗s,ij,t[(rij)
2 + (xij)
2] +M(1− xLij) (52)
U∗′s,j,t ≥ U∗′s,i,t − 2(rijP ′s,j,t + xijQ′s,j,j)
+ I∗′s,j,t[(rij)
2 + (xij)
2]−M(1− xLij) (53)∥∥∥∥∥∥
2P ′s,ij,t
2Qss,ij,t
I∗s,i,j,t − U∗∗s,j,t
∥∥∥∥∥∥
2
≤ I∗·s,j,t + U∗′s,j,t. (54)
C. Correlation-based Reliability Benefit Calculation
Economic and reliability costs are considered when optimal
investment planning is determined to ensure the planning
scheme can maintain good effects. Reliability cost is calculated
by considering load curtailment as follows:
F rel = σ
∑
i∈ΨS N
AENSi (55)
where σ is a penalty factor, ΨS N represents the network set,
and AENSi is the reliability index of AENS. Notably, (55)
cannot be solved directly in a linear programming algorithm.
Thus, a correlation analysis method is used to solve the multi-
objective optimization problem, thereby improving calculation
efficiency while ensuring calculation accuracy. Correlation
analysis based on multiple linear regression can be expressed
as follows:
Φi(X,Y ) = 0, X ∈ R(xsubi ,xLij ,x
pile
i ,x
CSs
i ,x
WTG
i ) (56)
where Φi indicates correlation analysis function, X is input
data, including network topology and load, and Y is output
data, namely, reliability index.
On the basis of data obtained, the correlation analysis is
embedded into the linear programming model to improve
calculation efficiency and accuracy. When historical data are
trained, input is the uncertain variable set, namely, R in
(56), and output is the reliability index. Numerous iteration
calculations are needed during data training process. However,
the optimization process in the linear programming calculation
with the trained correlation rule is direct and efficient with no
iteration. Then, the optimal planning scheme can be obtained.
V. TWO-STAGE DRO MODEL AND SOLVING ALGORITHM
A. DRO Model
Given the uncertainty of wind power and charging load, a
two-stage collaborative planning model of the distribution net-
work and EVCS is proposed. The first stage is the investment
stage, which determines the investment plan of the substation,
feeder, charging station, charging pile, and WTG. The second
stage is for obtaining the worst scenario probability distribu-
tion with the objective of achieving minimum operation cost.
The two-stage distributionally robust planning model can be
expressed in the form of a matrix as follows:
min
x
Ax+ max
ps∈ΩP
Ns∑
s=1
ps min
ys∈Y (x,ξs)
(Bys +Kξs) (57)
Cx ≤ c (58)
Dx = d (59)
Ex+ Fys = e (60)
Gys ≤ g (61)
‖Hys‖2 ≤ hTys (62)
Iys ≤ ξs (63)
where x represents a discrete investment variable at the first
stage, y indicates a continuous operation variable at the second
stage, ξ represents forecasted wind power and charging load,
and ΩP is the set of scenarios. Eqs. (58) and (59) represent
inequality and equation constraints at the first stage. Eq. (60)
represents coupling of variables, such as power flow constraint,
at the first and second stages. Eq. (61) represents the inequality
constraint at the second stage, (62) represents the second-order
cone constraints, and (63) represents the inequality constraints
for uncertain variables and their forecasting value.
On the basis of the initial probability distribution of the typ-
ical scenario, norm-1 and nor-inf co-constraints are utilized to
limit probability distribution fluctuation range. The confidence
set can be expressed as follows:
ΩP =
{ps}

ps ≥ 0, s = 1, · · · , Ns∑Ns
s=1 ps = 1∑Ns
s=1 |ps − p0s| ≤ θ1
max1≤s≤Ns |ps − p0s| ≤ θ∞
 (64)
where θ1 and θ∞ indicate the tolerance value of the norm-1
and norm-inf constraint. ps satisfies the confidence level as
follows:
Pr
{
Ns∑
s
∣∣ps − p0s∣∣ ≤ θ1
}
≥ 1− 2Nse−2Mθ1/Ns (65)
XIANG et al.: ROBUST EXPANSION PLANNING OF ELECTRIC VEHICLE CHARGING SYSTEM AND DISTRIBUTION NETWORKS 2463
Pr
{
max
1≤s≤Ns
∣∣ps − p0s∣∣ ≤ θ∞} ≥ 1− 2Nse−2Mθ∞ (66)
The right-hand sides of (65) and (66) are set as α1 and α∞.
Then, θ1 and θ∞ are obtained as follows:
θ1 =
Ns
2L
ln
2Ns
1− α1 (67)
θ∞ =
1
2Ns
ln
2Ns
1− α∞ (68)
where L is the amount of historical data.
B. Solving Algorithm
The two-stage distributionally robust model, shown in (57),
can be divided into a master problem (MP) and a subproblem
(SP), which can be solved based on a CCG algorithm. The
model of MP is expressed as
MP: min
x,yms ∈Y (x,ξs),W
Ax+W (69)
max
ps∈ΩP
Ns∑
s=1
pms min
yms ∈Y (x,ξs)
(Byms +Kξs) ,
∀m = 1, 2, · · · ,M (70)
s.t. Cx ≤ c (71)
Dx = d (72)
Ex+ Fyms = e, ∀m = 1, 2, · · · ,M (73)
Gyms ≤ g, ∀m = 1, 2, · · · ,M (74)
‖Hyms ‖2 ≤ hTyms , ∀m = 1, 2, · · · ,M (75)
Iyms ≤ ξs, ∀m = 1, 2, · · · ,M, (76)
where M is the number of iterations.
SP is optimized under the known investment plan. That is,
after investment variables at the first stage are given, SP can
be solved as follows:
SP: fSP (x∗) = max
ps∈ΩP
Ns∑
s=1
pms min
yms ∈Y (x,ξs)
(Byms ,Kξs)
∀m = 1, 2, · · · ,M (77)
The above-mentioned model can be solved by dividing it
into two layers. Confidence set ΩP is not associated with con-
straints of the variable at the second stage. Consequently, the
minimum problem in the inner layer is solved first. Then, the
maximum problem to obtain the worst probability distribution
is optimized. The solving process has been presented by [21].
VI. CASE STUDIES
A. Input Data
A modified 54-node distribution network and the Sioux–
Falls transportation network are used in this study as the test
system. Four substations with three existing substations are
considered. Substations 51, 52, and 53 have initial capacities
of 5, 10, and 2 MW, respectively; among them, substations
52 and 53 consider expanding. One candidate substation
(substation 54) to be constructed is also considered. Moreover,
five charging stations in 11 candidate locations, 17 candidate
feeders, and 15 candidate WTG locations are considered. The
unit installation capacity and maximum installation number of
WTG are 0.25 MW and 40, respectively. Prices of network
loss, power generation, and wind curtailment are set with
reference to [21] and [22]. Value of the penalty factor σ is set
to 250 to comprehensively consider economic and reliability
benefits of the planning scheme. When σ is set to 250, the
benefits of economy and reliability can be well balanced,
reflecting characteristics of the planning scheme that considers
reliability while maintaining its economy. Low- and fast-
charging powers are 10 and 60 kW, respectively. The OD
matrix on a typical day can be seen in [23]. Forecasting
scenario of low-charging load and WTG output are shown in
Figs. 3 and 4. Other parameters, including topology of trans-
portation and distribution network and corresponding coupling
information, candidate substation planning schemes, some
basic investment and operation parameters, and traffic data, are
given in https://docs.qq.com/pdf/DR2ZUZUFTZkNBWm9B.
B. Analysis of The EVCS Planning Scheme
According to the traffic flow assignment model proposed
in this study, 19 possible EVCS configuration schemes are
obtained, including EVCS planning location and number of
chargers in the station.
L
o
w
-c
h
ar
g
in
g
 l
o
ad
 (
k
W
)
900
400
300
200
100
0
0 20 30 40 5010
Bus No. in distribution network
Fig. 3. Low-charging load forecast.
W
T
G
 o
u
tp
u
t 
co
ef
fi
ci
en
t
0.6
0.5
0.4
Time (h)
5 10 15 20
P
ar
k
in
g
 d
em
an
d
 c
o
ef
fi
ci
en
t
1.0
0.8
0.6
0.4
0.2
Commercial area
Residential area
WTG
Fig. 4. WTG output forecast.
2464 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 10, NO. 6, NOVEMBER 2024
TABLE I
CANDIDATE PLANNING SCHEMES OF EVCS
Schemes Bus in the Distribution Network6 26 33 31 30 13 15 27 28 47 14
1 7 10 0 9 0 7 0 0 0 8 0
2 7 9 0 9 0 7 0 0 0 0 9
3 7 9 0 9 0 0 0 0 0 8 9
4 7 10 0 0 9 7 0 0 0 8 0
5 7 10 0 0 9 7 0 0 0 0 9
6 7 9 0 0 9 0 0 0 0 8 9
7 7 10 0 0 0 7 0 0 0 8 9
8 7 0 0 9 0 6 0 10 0 0 9
9 7 0 0 9 0 7 0 0 0 8 10
10 7 0 0 9 0 0 0 10 0 8 9
11 7 0 0 0 9 6 0 10 0 0 9
12 7 0 0 0 9 7 0 0 0 8 10
13 7 0 0 0 8 0 0 10 0 8 9
14 0 9 0 9 0 6 0 0 0 8 9
15 0 9 0 0 9 6 0 0 0 8 9
16 0 0 0 9 0 6 0 10 0 8 9
17 0 0 0 8 0 0 0 9 10 7 8
18 0 0 0 0 8 6 0 10 0 8 9
19 0 0 0 0 7 0 0 9 10 7 8
Nineteen EVCS-optimized schemes meet charging demand
based on traffic flow. Corresponding fast-charging load can
be estimated according to the planning scheme. For example,
for Schemes 1 and 19, estimated fast-charging load is shown
in Fig. 5. Fast-charging load within 1 day basically shows
a normal distribution because the EVCSs are all located in a
business district where the charging peak is concentrated from
12:00 to 15:00. EVCS candidates are applied to the distribution
network optimization problem, and the planning results are
shown in the next part.
C. Contrastive Analysis Based on Different Cases
According to Part B, 19 possible EVCS configuration
schemes are obtained and analyzed. On this basis, a total
of 10,000 scenarios are generated by stochastic simulation to
represent the uncertainty of the WTG output and EV charging
load. Then, the K-means clustering method is used to obtain
four typical scenarios. The following cases are defined to
verify effectiveness of the proposed planning method.
Case 1: Optimal planning based on the deterministic opti-
mization method ignoring reliability benefit.
Case 2: Optimal planning based on DRO method ignoring
reliability benefit.
Case 3: Optimal planning based on the deterministic opti-
mization method considering reliability benefit.
Case 4: Optimal planning based on DRO method consider-
ing reliability benefit.
As shown in Table II, a contrastive analysis based on Case
1 and Case 2 is performed, where the planning results differ
based on the two different optimization methods. Comparison
of Case 1 and Case 2 indicate the feeder changes from line
54–22 to line 22–23 by applying the DRO method. A probable
reason is the distance of line 54–22 is short, resulting in
low investment and maintenance costs; meanwhile, substation
51 has enough backup to undertake the load increase. The
uncertainty is considered using DRO. Thus, compared with the
traditional method, the DRO method exhibits a growth trend
in planning of WTG and charging piles. WTG locations with
increased investment installation, such as buses 25, 39, and 27,
are all distributed at the end of the transmission line. Thus,
compared with upgrading the substation, expanding the WTG
installation can increase efficiency if the load is increased at
the end of the line. In addition, Fig. 6 indicates the investments
on charging piles increase when the DRO method is utilized,
particularly for bus 41. The reason is that low-charging load
is estimated based on corresponding power load. The power
load is inherently large for bus 41. Therefore, charging piles
at bus 41 increase after considering the uncertainty.
Tables II and III show the charging load curtailment, genera-
tion, and total operation costs using the DRO method are lower
than those using traditional deterministic optimization method.
This finding indicates planning results based on DRO can
effectively ensure a reliable power supply and good economic
benefit while coping with uncertain scenarios.
F
as
t-
ch
ar
g
in
g
 l
o
ad
 (
k
W
)
250
200
150
100
50
300
0
6
33
30
15
28
14 0
(a)
24
4
8
12
16
20
Bus No.
Tim
e (
h)
47
26
31
13
27
F
as
t-
ch
ar
g
in
g
 l
o
ad
 (
k
W
)
250
200
150
100
50
300
0
0
24
4
8
12
16
20
Bus No. T
im
e (
h)
(b)
6
33
30
15
28
1447
26
31
13
27
Fig. 5. Fast-charging load estimation with certain EVCS schemes. (a) Scheme 1. (b) Scheme 19.
XIANG et al.: ROBUST EXPANSION PLANNING OF ELECTRIC VEHICLE CHARGING SYSTEM AND DISTRIBUTION NETWORKS 2465
C
h
ar
g
in
g
 p
il
e 
in
v
es
tm
en
t
100
80
60
40
20
0
5 10 15 20 25 35 40 45 5030
Bus
Case 1
Case 2
Fig. 6. Planning results of the charging pile based on deterministic optimi-
zation and DRO methods.
TABLE II
PLANNING RESULTS BASED ON DETERMINISTIC OPTIMIZATION AND
DRO METHODS IGNORING RELIABILITY BENEFIT
Investment Scheme Cost
(×108 yuan)Sub Line EVCS WTG
Case 1 52(0,0) 54–21 41–42 Scheme 4 20(12) 42(0) 2.0003
53(0,1) 54–22 42–48 25(4) 6(0)
54(0,1,0) 54–30 48–49 39(8) 26(6)
30–29 49–50 16(14) 31(13)
53–41 37–31 50(5) 30(6)
13(12) 27(4)
28(0) 47(4)
14(0)
Case 2 52(0,0) 22–23 41–42 Scheme 4 20(11) 42(0) 1.9714
53(0,1) 54–21 42–48 25(9) 6(0)
54(0,1,0) 54–30 48–49 39(9) 26(6)
30–29 49–50 16(14) 31(13)
53–41 37–31 50(5) 30(0)
13(12) 27(5)
28(0) 47(4)
14(0)
TABLE III
COSTS BASED ON DETERMINISTIC OPTIMIZATION AND DRO METHODS
IGNORING RELIABILITY BENEFIT
Costs/(×108 yuan)
Invest-
ment
Line
Operation
Genera-
tion
Network
Loss
Wind
Curtail-
ment
EV Charging
Load
Curtailment
Case 1 0.4401 0.0060 1.5209 0.0178 0 0.0155
Case 2 0.4393 0.0059 1.4996 0.0181 0 0.0085
Presence of the reliability benefit is considered when mak-
ing a decision, and comparative results are shown in Tables IV
and V. Planning results of the charging piles are similar to the
results above. Thus, these results are not listed here.
Table IV indicates that network topology changes from
line 41–42 to line 42–47 after considering the reliability
benefit. The reason is that line 42–47 has a section switch,
which can reduce response time and restore power supply
quickly when a shortage occurs. Moreover, the expanding
scheme for substation 53 changes from Scheme b to Scheme
a, because of its power supply pressure due to change of
network topology. Therefore, substation 52 must be upgraded
to ensure a reliable power supply for the new increase in load.
TABLE IV
PLANNING RESULTS BASED ON DETERMINISTIC OPTIMIZATION AND
DRO METHODS CONSIDERING THE RELIABILITY BENEFIT
Investment Scheme Cost
(×108 yuan)Sub Line EVCS WTG
Case 3 52(1,0) 54–21 42–47 Scheme 4 20(11) 42(6) 2.7389
53(1,0) 54–22 42–48 25(3) 6(0)
54(0,1,0) 54–30 48–49 39(30) 26(6)
30–29 49–50 16(5) 31(11)
53–41 37–31 50(6) 30(6)
13(0) 27(4)
28(0) 47(0)
14(0)
Case 4 52(1,0) 54–21 42–47 Scheme 4 20(11) 42(0) 2.7110
53(1,0) 54–22 42–48 25(9) 6(0)
54(0,1,0) 54–30 48–49 39(9) 26(6)
30–29 49–50 16(14) 31(13)
53–41 37–31 50(5) 30(0)
13(12) 27(5)
28(0) 47(4)
14(0)
In addition, the WTG investment planning results based on
deterministic optimization method have changed greatly after
reliability benefits are considered. The reason is that planning
schemes based on deterministic optimization method can only
respond to a specific scenario, and maintaining them to be
stable when the environment changes is difficult. By contrast,
investment planning based on DRO highly tends to withstand
fluctuation of the outside environment, thereby confirming
effectiveness of the proposed method.
Table V shows the operation benefit from deterministic
optimization and DRO methods after considering the relia-
bility benefit. System reliability is mainly related to network
topology. Thus, reliability costs in Table V are identical. When
the reliability benefit is considered, system operation cost, in-
cluding generation, network loss, charging load, and shedding
costs, decreases. In particular, the EV load curtailment cost
decreases by nearly 50%. This finding indicates the operation
benefit is improved after considering the reliability benefit.
TABLE V
COSTS BASED DETERMINISTIC OPTIMIZATION AND DRO METHOD
CONSIDERING THE RELIABILITY BENEFIT
Costs/(×108 yuan)
Relia-
bility
Invest-
ment
Line
Opera-
tion
Genera-
tion
Network
loss
Wind
Curtail-
ment
EV Charging
Load
Curtailment
Case 3 0.7283 0.4572 0.0059 1.5200 0.0162 0 0.0113
Case 4 0.7283 0.4582 0.0059 1.4980 0.0159 0 0.0047
D. Contrastive Analysis Based on Different EV Penetrations
Figure 7 shows planning results on different EV penetra-
tions. Extent of substation expansion increases as EV penetra-
tion increases from 0.1 to 0.3. For network topology, topology
based on a method that ignores the reliability benefit also
changes with increase in EV penetration; when the reliability
benefit is considered, the topology changes only after EV
penetration exceeds 20%. This scenario indicates the method
proposed in this study, i.e., the method that considers the
reliability benefit, can cope with load increments and ensure
the effectiveness of planning better than the traditional method
2466 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 10, NO. 6, NOVEMBER 2024
(a) (b)
(c) (d)
(e) (f)
Fig. 7. Planning results based on different EV penetrations. (a) 0.1 is set
as EV penetration ignoring reliability benefit. (b) 0.1 is set as EV penetration
considering reliability benefit. (c) 0.2 is set as EV penetration ignoring
reliability benefit. (d) 0.2 is set as EV penetration considering reliability
benefit. (e) 0.3 is set as EV penetration ignoring reliability benefit. (f) 0.3
is set as EV penetration considering reliability benefit.
can (i.e., the method without considering the reliability benefit
of the planning scheme). With the increase in EV penetration,
the EVCS planning scheme based on the traditional method
changes from Scheme 4 to Scheme 5 and finally to Scheme
2, thereby increasing cost. With a method that considers the
reliability benefit, the planning scheme of EVCS is maintained
at Scheme 15. This finding further proves that EVCS planning
based on the proposed method can accommodate charging
load increments while maintaining good economic benefit.
The total costs of WTG investment are identical because
the penetration limit of WTG is fixed. However, distribution
of WTG installation differs to adapt to change in network
topology and load increase. Investment on the charging pile
also increases correspondingly.
Figure 8 shows total planning cost change with increase
in EV penetration. Planning cost considering the reliability
benefit is higher than one based on the traditional method.
However, the growth rate of the cost based on the traditional
method is higher than one considering the reliability benefit.
Moreover, the relative increase rate of Cost A to Cost B
is downward. These findings further explain that investment
planning considering the reliability benefit is more suitable for
a power system with multi-energy integration and fast-growing
load than investment planning based on the traditional method.
C
o
st
 (
1
0
8
 y
u
an
)
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.0
0.5
0.0
0.1 0.2 0.3
0.12
0.16
0.20
0.24
0.28
0.32
1.5
8.0%
8.3%
10.4%
10.3%
R
el
at
iv
e 
co
st
 i
n
cr
ea
si
n
g
 r
at
e 
o
f 
C
o
st
 A
 t
o
 C
o
st
 B
EV penetration
Cost A: considering reliability benefit
Cost B: ignoring reliability benefit
Relative increasing rate
Fig. 8. Cost of planning schemes based on different EV penetrations.
E. Contrastive Analysis Based on Different DG Penetrations
Changes in network topology and WTG investment are
analyzed in this section by considering DG integration in
the grid. For a planning scheme that considers the reliability
benefit, network topology remains unchanged until WTG
penetration exceeds 50%. However, for a planning scheme
based on the traditional method, network topology changes
with the increase in WTG penetration, further verifying the
applicability and effectiveness of the method proposed in this
study. Fig. 9 presents changes in network topology under
different WTG penetrations. Fig. 10 shows a comparison of
WTG planning schemes based on different WTG penetrations.
Bus 31 and 33 are incorporated into substation 51 from other
power supply regions when DG penetration is increased from
0.5 to 0.6. Hence, WTG investment in this area is increased,
particularly for bus 25, which is located close to the new
load point. With the traditional method, only substations 51
and 52 remain when WTG penetration is 60%. Although the
substation investment is reduced, topology at this time cannot
resist environmental changes and cannot guarantee system
operation reliability, particularly when large-scale renewable
energy is integrated into the distribution network. Costs of
the planning schemes are shown in Table VI. Total cost
decreases as operation cost decreases. However, reliability
and investment costs start to increase when DG penetration
exceeds 50%. With reference to the previous analysis of
network topology, the optimal DG penetration is presumably
50% at the current load level.
F. Contrastive Analysis Based on DRO and RO Approach
To analysis performance of DRO approach used in this
paper, a robust optimization method is adopted to perform the
contrastive simulation. Range of uncertain variables in RO is
XIANG et al.: ROBUST EXPANSION PLANNING OF ELECTRIC VEHICLE CHARGING SYSTEM AND DISTRIBUTION NETWORKS 2467
DG
Penetration
Raliability
(a) (b) (c)
Fig. 9. Planning results of network topology based on different conditions. (a) WTG penetration = 0.5 considering the reliability benefit. (b) WTG penetration
= 0.6 considering the reliability benefit. (c) WTG penetration = 0.6 ignoring the reliability benefit.
In
st
al
l 
n
u
m
b
er
30
25
20
15
10
5
25
16
42
26
30
27
47 0.3
0.4
0.5
0.6
Candidate DG install bus
DG
 pe
net
rat
ion
20
14
28
13
31
6
50
39
Fig. 10. WTG planning results based on different WTG penetrations.
TABLE VI
COSTS OF PLANNING SCHEMES BASED ON DIFFERENT WTG
PENETRATIONS
WTG
Penetration
Objective Function (×108 yuan)
Reliability
Cost
Investment
Cost
Operation
Cost Total
0.3 0.7283 0.4642 1.6735 2.8677
0.4 0.7283 0.4577 1.5245 2.7122
0.5 0.7283 0.4362 1.426 2.5922
0.6 0.7508 0.4812 1.2452 2.4772
0.2 times the predicted value. The following cases are defined
to do performance analysis.
Case 5: Optimal planning based on RO approach ignoring
reliability benefit.
Case 6: Optimal planning based on RO approach consider-
ing reliability benefit.
Planning results based on Case 5 and Case 6 are shown
in Tables VII and VIII. Comparing Case 5 and Case 2,
which can be seen from Tables VII and II, it can be found
that network topology is changed. Applying the obtained
distribution planning result to perform simulation operation,
the result is given the reliability level of distribution network
based Case 5 is greater than Case 2 (F relCase 5 is 0.7559 and
F relCase 2 is 0.7691). However, investment and operation cost of
planning scheme based Case 5 is larger than Case 2, while the
reliability level of Case 2 is also within an acceptable range. It
shows compared to RO method, DRO method achieves good
balance in economy and conservativeness. For Case 6 and Case
4, which is shown in Table VIII, planning results have no sig-
nificant difference. This is because after considering reliability
benefit during planning process, the investment scheme can
cope with uncertainties better, which also verifies effectiveness
of the proposed method in this paper. Nonetheless, a cost
based RO approach is still larger than DRO method. This also
TABLE VII
PLANNING RESULTS BASED ON RO METHOD IGNORING
RELIABILITY BENEFIT
Investment Scheme Cost
(×108 yuan)Sub Line EVCS WTG
Case 5 52(0,0) 10–31 53–41 Scheme 4 20(6) 42(0) 2.0769
53(0,1) 54–21 41–42 25(1) 6(0)
54(0,1,0) 54–22 42–48 39(7) 26(8)
54–30 48–49 16(15) 31(6)
30–29 49–50 50(3) 30(5)
13(25) 27(3)
28(0) 47(8)
14(1)
TABLE VIII
PLANNING RESULTS BASED ON RO METHOD CONSIDERING
RELIABILITY BENEFIT
Investment Scheme Cost
(×108 yuan)Sub Line EVCS WTG
Case 6 52(1,0) 54–21 42–47 Scheme 4 20(9) 42(6) 2.8020
53(1,0) 54–22 42–48 25(3) 6(0)
54(0,1,0) 54–30 48–49 39(31) 26(8)
30–29 49–50 16(5) 31(10)
53–41 37–31 50(6) 30(5)
13(0) 27(5)
28(0) 47(0)
14(0)
2468 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 10, NO. 6, NOVEMBER 2024
confirms the good economy of DRO method.
Specific cost analysis is conducted in Tables IX and X. It
can be seen that network operation cost based on RO method is
larger than DRO method whether or not the reliability benefit
is considered. This is because for RO method, it is operated in
the worst scenario. For DRO approach, it can ensure a degree
of reliable grid operation while maintaining good economy.
In general, when performing the collaborative planning of
EVCS and distribution network, planning results based on
DRO approach can achieve good balance in economy and
conservativeness.
TABLE IX
COSTS BASED ON DRO AND RO METHOD IGNORING
RELIABILITY BENEFIT
Case Costs (×10
8 yuan)
Invest-
ment
Line
Opera-
tion
Genera-
tion
Network
Loss
Wind
Curtail-
ment
EV Charging
Load
Curtailment
2 0.4393 0.0059 1.4996 0.0181 0 0.0085
5 0.4413 0.0060 1.5896 0.0215 0 0.0185
TABLE X
COSTS BASED ON DRO AND RO METHOD CONSIDERING THE
RELIABILITY BENEFIT
Case Costs (×10
8 yuan)
Relia-
bility
Invest-
ment
Line
Opera-
tion
Genera-
tion
Network
loss
Wind
Curtail-
ment
EV Charging
Load
Curtailment
4 0.7283 0.4582 0.0059 1.4980 0.0159 0 0.0047
6 0.7283 0.4576 0.0059 1.5851 0.0169 0 0.0082
VII. CONCLUSION
Given the uncertainty of charging load and wind power out-
put, a two-stage distributionally robust collaborative planning
model of the EV charging system and distribution network,
which considers the reliability benefit, is proposed in this
study. The following conclusions are drawn from the case
studies.
1) Compared with a traditional method, an optimization
model that considers the reliability benefit can cope with
uncertainties better while maintaining good operation bene-
fit. Operation costs, such as network loss cost, decrease at
different levels, particularly EV load curtailment cost, which
decreases by nearly 50%.
2) Distribution network planning results in topology ob-
tained with the traditional method, which ignores the reliability
benefit, and change with increase in EV penetration. However,
with the proposed method that considers the reliability benefit,
the topology changes only after EV penetration exceeds 20%.
3) Optimal DG penetration is 50% when network topology
and investment and operation costs are considered comprehen-
sively. When DG penetration exceeds 50%, network topology
must be replanned, and reliability and investment costs in-
crease.
4) Compared with the deterministic optimization method,
the DRO method considers real-time uncertainty of renewable
energy and charging load, thereby simulating the distribution
network with multi-energy integration effectively. Planning
results based on DRO method can also achieve good balance
in economy and conservativeness, which helps power system
planners make a suitable grid expansion scheme.
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Yue Xiang received the B.S. and Ph.D. degrees from
Sichuan University, China, in 2010 and 2016, re-
spectively. From 2013 to 2014, he was a joint Ph.D.
student at the Department of Electrical Engineering
and Computer Science, University of Tennessee,
Knoxville, US and also a visiting scholar at the De-
partment of Electronic and Electrical Engineering,
University of Bath, UK in 2015. Currently, he is a
Professor at the College of Electrical Engineering,
Sichuan University, China. His main research inter-
ests are electric vehicles, power system planning and
optimal operations, renewable energy integration and smart grids.
Ping Xue received the B.S. and M.S. degrees from
Sichuan University, China, in 2019 and 2022, re-
spectively. Currently, she is working at State Grid
Sichuan Technical Training Center, and also the
Sichuan Electric Vocational and Technical College.
Her main research interests are electric vehicles, dis-
tribution network planning and optimal operations.
Yanliang Wang received the B.Eng. degree from
Chengdu University of Technology, China, in 2021.
He received the M.S. degree in Electrical Engineer-
ing, Sichuan University, China, in 2024. His research
focuses on electric vehicles.
Lixiong Xu received the B.S., M.S., and Ph.D. de-
grees from Sichuan University, Chengdu, China, in
2003, 2006, and 2014, respectively. He is currently
an Associate Professor in Power System with the
College of Electric Engineering, Sichuan University.
His research interests include AI in smart grids,
power system security and stability.
Wang Ma received the B.S. and M.S. degrees
in Electrical Engineering from Sichuan University,
Chengdu, China, in 2019 and 2022, respectively.
Her research interests include distribution network
operation and dynamic reconfiguration.
Miadreza Shafie-khah received his first Ph.D. in
Electrical Engineering from Tarbiat Modares Uni-
versity, Tehran, Iran. He received his second Ph.D.
in Electromechanical Engineering and first postdoc
from the University of Beira Interior (UBI), Covilha,
Portugal. He received his second postdoc from the
University of Salerno, Salerno, Italy. Currently, he
is a Professor at the University of Vaasa, Vaasa,
Finland. He is an Editor of the IEEE Transactions on
Sustainable Energy, an Associate Editor of the IEEE
Systems Journal, an Associate Editor of the IEEE
Access, an editor of the IEEE Open Access Journal of Power and Energy
(OAJPE), an Associate Editor for IET-RPG, the guest Editor-in-Chief of the
IEEE OAJPE, the guest editor of IEEE Transactions on Cloud Computing,
and the guest editor of more than 14 Special Issues. He was considered one of
the Outstanding Reviewers of the IEEE Transactions on Sustainable Energy,
in 2014 and 2017, one of the Best Reviewers of the IEEE Transactions on
Smart Grid, in 2016 and 2017, and one of the Outstanding Reviewers of
the IEEE Transactions on Power Systems, in 2017 and 2018, and one of the
Outstanding Reviewers of IEEE OAJPE, in 2020. He has co-authored more
than 420 papers that received more than 10000 citations with an h-index
equal to 55. He is also the volume editor of the book “Blockchain-based
Smart Grids”, Elsevier, 2020. He is a Top Scientist in the Guide2Research
Ranking in computer science and electronics, and he has won five Best Paper
Awards at IEEE Conferences. His research interests include power market
simulation, market power monitoring, power system optimization, demand
response, electric vehicles, price and renewable forecasting and smart grids.
Junlong Li received the B.Eng. degree in College
of Electrical Engineering from Sichuan University,
Chengdu, China, in 2015 and 2019. He received the
Ph.D. degree in Electronic and Electrical Engineer-
ing at the University of Bath, in 2023. His main
research interests include edge-cloud computing in
power systems and energy management system.
Junyong Liu received his Ph.D. degree from Brunel
University, UK, in 1998. He is a Professor in the
college of Electrical Engineering, Sichuan Univer-
sity, China. His main research interests are power
system planning, operation, stability and computer
applications.