OVEMBER 2021-无代写
时间:2023-05-03
4752 IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 6, NOVEMBER 2021
Hierarchical Voltage Control Strategy in
Distribution Networks Considering Customized
Charging Navigation of Electric Vehicles
Xianzhuo Sun and Jing Qiu , Member, IEEE
Abstract—This paper proposes a three-layer hierarchical volt-
age control strategy for distribution networks considering the
customized charging navigation of electric vehicles (EVs). In the
first layer, optimal power flow (OPF) is performed to deter-
mine the day-ahead dispatch of on-load tap changer (OLTC) and
capacitor banks (CBs). The optimization problem is formulated
as a mixed-integer second-order cone programming (MISOCP)
which can be effectively solved. In the second layer, a cus-
tomized charging navigation strategy is proposed to conduct the
charging behaviors of EVs based on their own preferences. The
novel preference modes are designed for different types of EV
users to include not only the charge and time cost, but also the
willingness to participate in voltage regulation service (VRS).
The navigation problem is formulated as a mixed-integer linear
programming (MILP), which is then solved by CPLEX solvers
embedded with Dijkstra algorithm. In the third layer, charging
stations measure local voltage and regulate the charging power
of EVs to mitigate voltage violation. The charging selection and
power allocation process are performed dynamically consider-
ing the mutual effect between the second and third layers. The
economic compensation mechanism is also designed for both EV
users and charging stations. The proposed approach is tested on
the IEEE 33-bus distribution system coupled with a 24-bus trans-
portation system, and simulation results verify the effectiveness
both in charging navigation and mitigating voltage violation.
Index Terms—Hierarchical voltage control, customized charg-
ing navigation, preference modes, electric vehicles, Dijkstra
algorithm.
NOMENCLATURE
N, i Set/Index of nodes in network
E, ij Set/Index of the network branches
T, t Set/Index of time periods
1, 2, 3, 4 Set of EVs in fast charging, slow charg-
ing, battery swap charging and VRS
Tdi,j, Twi,j, Tci,j Travel, waiting and charging time of EV
i to CS j
Manuscript received October 27, 2020; revised March 2, 2021, May 4, 2021
and June 21, 2021; accepted July 1, 2021. Date of publication July 6, 2021;
date of current version October 21, 2021. This work was supported in part by
the ARC Research Hub under Grant IH180100020; in part by ARC Training
Centre under Grant IC200100023; and in part by ARC linkage Project under
Grant LP200100056. Paper no. TSG-01606-2020. (Corresponding author:
Jing Qiu.)
The authors are with the School of Electrical and Information
Engineering, The University of Sydney, Sydney, NSW 2006, Australia (e-mail:
xianzhuo.sun@sydney.edu.au; qiujing0322@gmail.com).
Color versions of one or more figures in this article are available at
https://doi.org/10.1109/TSG.2021.3094891.
Digital Object Identifier 10.1109/TSG.2021.3094891
Ci,j, Di,j Charge cost/travel distance of EV i to
CS j
ωij Binary indicator of charging selection of
EVs (1-EV i selects CS j, 0-otherwise)
rij, xij Resistance/reactance of branch ij
P(·)i,t Active power of PV, charging station/load
Q(·)i,t Reactive power of load/CBs
Pij,t, Qij,t Branch active/reactive power from i to j
νi,t, lij,t Square of voltage magnitude and current
Vmax, Vmin Maximum and minimum voltage value
tapt, cik,t Status of OLTC and kth capacitor at
bus i
NC Total number of charging stations.
I. INTRODUCTION
OVER the past few years, electric vehicles (EVs) havebeen booming due to their characteristics of emission
reduction and energy saving compared with conventional fuel-
based automobiles [1]. The International Energy Agency (IEA)
has reported that 13% of the global car fleet will be electric by
2030 with an annual average growth of 36% per year between
2019 and 2030 [2]. Moreover, distributed generations (DGs)
like photovoltaics (PVs) have also been increasing signifi-
cantly in active distribution networks (ADN) [3]. However,
the fluctuation of PVs and unpredictable charging loads of
EVs will impose great challenges on the safe operation of
power systems, especially for the voltage violation problems
in ADN [4].
The conventional voltage control is commonly performed
in a centralized manner to determine the day-ahead dispatch
of on-load tap changer (OLTC) and capacitor banks (CBs).
Since OLTC and CBs are manipulated in a relatively longer
timescale with discrete action domain, they lack fast-response
capability and may become ineffective to mitigate fast volt-
age violation in real-time [5]. In the meanwhile, EVs can be
dispatched and directly controlled to improve voltage quality
and profile, which may become one of the promising voltage
control resources in future distribution networks [6]–[7]. On
the one hand, EV charging behaviors can be guided by price
incentive mechanisms to some extent. On the other hand, EVs
can regulate the charging power or even discharge at charging
stations (CS) with the vehicle to grid (V2G) technology.
Considering the traffic information and charging pricing
mechanism, EVs can be dispatched to improve voltage profile
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in ADN with optimal charging navigation. References [8]–[9]
indicate that the time-of-use (TOU) rates can effectively incent
off-peak charging of EVs. In [10], a charging pricing strat-
egy for fast charging stations is developed to determine the
price scheme for voltage control. In [11], a double-layer smart
charging strategy is proposed for EVs in the working place to
satisfy both power grid and driver’s needs. To optimize the
route planning of EVs, [12] formulates EV route optimization
models to minimize the charging cost, while [13] studies
decentralized policies to minimize the queuing time of EVs.
In [14], a bi-level optimization model is proposed to coordinate
ADN and transportation network (TN) by adjusting the charg-
ing service fee at CS. A deep reinforcement learning-based
method is also proposed to solve the bi-level model with uncer-
tainties. The authors in [15] propose a distributed multi-agent
optimal energy scheduling and trading strategy for multi-
microgrids integrated with transportation networks. In [16],
a fast-charging navigation strategy is proposed based on the
mutual effect of dynamic queuing with multiple charging
objectives. In [17], a route selection and charging navigation
strategy is proposed to reduce travel cost with crowd sensing
technology. However, the above literatures seldom consider
the user’s preference in the dispatch process, more specifi-
cally, their willingness in voltage regulation service (VRS)
and the influence on charging navigation and voltage control
effect.
Moreover, direct charging/discharging control of EVs can
also be implemented to address voltage issues in distribution
networks [18]–[24]. In [18], an online optimal charging strat-
egy is proposed based on model predictive control (MPC)
and fuzzy rules. In [19], a novel control topology for bi-
directional DC fast charging is proposed to solve voltage
drop problems. References [20] and [21] propose voltage con-
trol strategies to coordinate OLTC, CBs and EVs to mitigate
voltage fluctuations caused by generation variations in renew-
able energy resources. Reference [22] proposes a voltage-
positioning optimization method to maximize both voltage
and fast-response reactive power margins with a convex inner
approximation of optimal power flow (OPF). In [23], a two-
stage Volt/Var control framework is proposed to minimize the
total regulation cost of OLTC and PVs with a fast online
distributed algorithm. In [24], a two-level coordinated volt-
age control scheme is proposed for EV chargers, and power
allocation among EVs is performed with rule-based meth-
ods. It is acknowledged that the real-time control of EVs
is usually performed separately from the dispatch process.
However, the dispatch results will influence the amount of
controllable resources available at CS, and neglecting their
mutual effect may lead to less effective in voltage con-
trol. For example, the CS is assumed to set lower charg-
ing prices to attract more charging EVs to reduce higher
voltage levels. Some EVs may be motivated by the lower
travel time cost and select another CS, while others fail
to arrive on time considering different route planning and
traffic conditions. Therefore, the charging demand will devi-
ate from the prediction, and voltage profiles cannot meet
the requirements only with the real-time power regulation
of EVs.
In practice, the uncoordinated dispatch and control of EVs
contribute to a large amount of active load at CS. The increas-
ing charging load and unexpected PV fluctuation will then
cause severe voltage violations. In this case, the charging
EVs have flexible active power control capability and can be
applied to voltage support. Compared with other existing reac-
tive power control devices, the active power control of EVs is
also more effective in distribution networks with higher R/X
ratios. To fill the existing research gaps mentioned above, this
paper proposes a three-layer hierarchical voltage control strat-
egy with customized charging navigation of EVs to mitigate
voltage violation problems in distribution networks. The major
contributions can be summarized as follows:
1) We propose a three-layer hierarchical voltage control
framework to mitigate fast voltage violation problems
with the dispatch and control of EVs. A rule-based
charging pricing method is proposed to reduce poten-
tial voltage violation risk in layer 1. The combined EV
dispatch and charging regulation process in layer 2 and
layer 3 also further improve the voltage control effect.
2) A customized charging navigation strategy is proposed
for EV users based on their own preferences. The pref-
erence modes are designed for different types of EVs
with different charging requirements, which consider not
only the charge and time cost, but also the willingness
of customers to participate in VRS.
3) The dynamic interaction between EVs charging nav-
igation and real-time control process is modeled and
considered. The EV’s charging selection is influenced
by the present charging process at CS. Moreover, the
power allocation is conducted every minute to include
the varying arrival and departure times of EVs, while the
economic compensation mechanism is also designed for
both CS and EVs in VRS.
II. PROPOSED THREE-LAYER HIERARCHICAL VOLTAGE
CONTROL FRAMEWORK
A. Overview
This paper proposes a three-layer hierarchical voltage con-
trol framework to build a bridge between intra-day dispatch
and real-time charging/discharging control of EVs, which is
illustrated in Fig. 1. In layer 1, OPF is performed to obtain
the hourly dispatch results of OLTC and CBs based on fore-
casted PV, EV and load data. The hourly PV and load power
can be forecasted based on deep neural networks and extreme
learning machine [25]. The hourly EV charging demand at
CS is forecasted with the trip chain theory to consider the
spatial-temporal characteristics in daily driving activities [26].
Note that the dispatch results have already been determined
ahead of the day and will be updated every hour in the intra-
day control process. The modified TOU charging price is also
determined considering the voltage level at each CS. In layer 2,
an optimization model is formulated to dispatch EVs with
updated traffic and charging information. The model considers
user’s charging requirements and willingness of participating
in VRS, and designs an optimal charging route for each EV. In
layer 3, CS measures local voltage and regulates active power
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4754 IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 6, NOVEMBER 2021
Fig. 1. Proposed three-layer hierarchical voltage control framework.
output to mitigate voltage violation based on local P(V) curves.
Since the arrival time of EVs varies with different route selec-
tions and traffic conditions, the power allocation process is
dynamically changed.
The timescales and the related information exchange in
three layers are also well explained in Fig. 1. The centralized
optimization in layer 1 is performed once in the day-ahead
time schedule. The dispatch results of OLTC and CBs are
transferred to layer 3, while the modified charging prices are
broadcast to each EV in layer 2. Note that all the information
is updated every hour in the intra-day. The EV dispatch in
layer 2 is performed every 15 minutes and the charging selec-
tion will influence the charging demand in layer 3. Finally,
the real-time voltage control in layer 3 is conducted every
minute to mitigate fast voltage violations. Since the charging
information like waiting time and available fast chargers vary
with different time periods, the CS in layer 3 will also send
them to EVs in layer 2 every 15 minutes and in turn influence
their charging selections.
Moreover, the CS may operate independently of the grid in
commercial or non-commercial modes. To motivate the CS to
participate in voltage regulation, the distribution system opera-
tor can provide some economic incentives and compensations.
On the one hand, the distribution networks can benefit from
the optimal operation and improvement of voltage profiles. On
the other hand, the CS and EV users can also benefit from the
savings of economic cost.
B. Customized Charging Navigation
A number of factors, like state of charge (SOC), charging
price and travel distance, have an influence on the charging
selection of EVs. It is assumed that an EV user will go to CS
for charging if the remaining SOC is below a certain level.
The defined “Customized” here means EVs will make a route
selection and charging navigation based on their own prefer-
ences and requirements. In this study, we not only consider
the time and economic cost, but also the user’s willingness
to participate in VRS for different types of EVs. Therefore,
we propose to model the following six preference modes in
charging navigation.
1) Preference Mode 1: EV users assign higher priority
to time and would like to minimize total time cost, which
includes the cost of travel time, waiting time and charg-
ing time.
min
NC∑
j=1
(
Tdi,j + Twi,j + Tci,j
) · ωij ∀i ∈ 1. (1)
2) Preference Mode 2: EV users care more about travel time
than charging time and will select the path with the short-
est time. Since EVs have enough time once arriving at the
destination, they will select slow charging mode.
min
NC∑
j=1
Tdi,j · ωij ∀i ∈ 2. (2)
3) Preference Mode 3: EV users select the same route and
charging mode as Mode 2, but they are willing to participate
in VRS for more economic benefits.
min
NC∑
j=1
Tdi,j · ωij ∀i ∈ 2 ∩ 4. (3)
4) Preference Mode 4: EV users assign higher priority to
profit and would like to minimize total charge cost. They are
motivated by charging price in route planning, and can select
fast or slow charging service based on their own needs.
min
NC∑
j=1
Ci,j · ωij ∀i ∈ 1 ∪ 2. (4)
5) Preference Mode 5: EV users aim to minimize total
charge cost and are also willing to participate in VRS for
extra economic compensation. They will select slow charging
in this preference mode.
min
NC∑
j=1
Ci,j · ωij ∀i ∈ 2 ∩ 4. (5)
6) Preference Mode 6: EV users assign higher priority to
time and would like to minimize total time cost. Different from
Mode 1, they will select the path with the shortest time and
battery swap charging mode.
min
NC∑
j=1
Tdi,j · ωij ∀i ∈ 3 ∩ 4 (6)
These preference modes are designed for different types
of EVs considering actual user behaviors. For instance,
Preference Mode 1 is more common for EV taxis since they
need more working time to earn profits. Preference Mode 2-
5 are designed for private EVs, while Mode 6 with battery-
swapping is especially for EV buses. Preference Mode 2 cor-
responds to scenarios that EVs will go shopping or meal at
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SUN AND QIU: HIERARCHICAL VOLTAGE CONTROL STRATEGY IN DISTRIBUTION NETWORKS 4755
some places. Preference Mode 3 and 5 are for EVs participat-
ing in VRS. Note that VRS is only available for slow charging
service.
It is admitted that the proposed six preference modes cannot
include all the possibilities of EV user’s routing and charging
selections. They only include the most common cases and are
taken as typical examples in the test system. Note that the pref-
erence modes can also be expanded with more comprehensive
analysis and the accessibility of enough EV data. Moreover,
it is unnecessary for the system operator to accurately learn
the user’s preference in the proposed framework. The voltage
deviation caused by the uncertainty of EV forecast and prefer-
ence mode selections can be mitigated by the real-time voltage
control strategy in layer 3.
C. Layer 1: Centralized Optimization Formulation
The centralized optimization is performed in the first layer
to determine the dispatch results of OLTC and CBs at
one-hour snapshot. To minimize the total power loss in dis-
tribution networks, the optimization problem is formulated as
follows.
min
tapt,cik,t
∑
t∈T1
∑
ij∈E
lij,trij (7)
{
PPVj,t − PCSj,t − PLj,t = ∑jk∈E
(
Pjk,t + ljk,trjk
) − ∑ij∈E Pij,t
QCBj,t − QLj,t = ∑jk∈E
(Qjk,t + ljk,txjk
) − ∑ij∈E Qij,t
(8)
vi,t = vj,t + 2
(
Pij,trij + Qij,txij
) + lij,t
(
r2ij + x2ij
)
(9)
∥∥∥∥∥∥∥
2Pij,t
2Qij,t
lij,t − vj,t
∥∥∥∥∥∥∥
2
≤ lij,t + vj,t ∀ij ∈ E (10)
{
V2min ≤ vi,t ≤ V2max
v1,t =
(
Vs + tapt · VT
)2 (11)
T∑
t=1
∣∣tapt+1 − tapt
∣∣ ≤ tapmax (12)
{∑T
t=1
∣∣cik,t+1 − cik,t
∣∣ ≤ capik,max
QCBi,t = ∑k cik,tqik,t
(13)
where equation (7) is the objective function. To focus on volt-
age security issues and achieve a more unified voltage profile,
this paper adopts the objective of minimizing network power
loss in distribution networks. Note that other objectives like
maximizing the total profit can also be used. If the TOU
charging prices are optimized in advance and adopted with-
out modification, the minimization of network power loss is
equivalent to the maximization of the total profit of distribu-
tion networks [18]. Equations (8)-(9) indicate active, reactive
power flow and voltage relationships between two neighbor-
ing nodes. Note that we only adopt a constant power load
model in (8), but other load models like ZIP and exponential
loads can also be formulated with binomial approximation or
linear regression methods introduced in [27]. Equation (10) is
the convex relaxation of power flow equality constraints based
on second-order cone programming [28]. Equation (11) is the
upper and lower voltage constraints in square form. The pri-
mary voltage of the transformer at the slack bus Vs is assumed
to be 1.0 p.u., while VT=0.01 p.u. is the voltage regulation
for one tap step. In this paper, we only consider one OLTC in
distribution networks for simplicity as it is just one example
of voltage control resources and it is not the key focus of this
paper. To include multiple OLTCs in the optimization model,
equation (11) is expanded for all buses where each OLTC
locates and the problem can be solved by a distributed algo-
rithm [23]. Equations (12) and (13) present maximum switch-
ing time limits for OLTC tapmax and CBs capikmax, and qik,t
is reactive power output of one capacitor. To reduce the non-
linearity of the original formulation, equations (11)-(13) are
converted to (14)-(16) with linearization and conic relaxation
method [29]–[30].
{
v1,t = ∑2tapk=0
[(
Vs +
(
k − tap)V)2dk,t
]
∑2tap
k=0 dk,t=1
(14)
⎧
⎪⎨
⎪⎩
tapt+1 − tapt ≤ βt
tapt − tapt+1 ≤ βt∑T
t=1 βt ≤ tapmax
(15)
⎧
⎪⎪⎪⎨
⎪⎪⎪⎩
bik,t = cik,t + cik,t+1 − 2aik,t
aik,t ≤ cik,t, aik,t ≤ cik,t+1, aik,t ≥ cik,t + cik,t+1 − 1
∑T
t=1 bik,t ≤ capik,max
QCBi,t = ∑k cik,tqik,t
(16)
where lap is the maximum tap position of OLTC; dk,t is
a binary variable satisfying the constraint (14); β t is an
integer variable within the range [−5, 5]; aik, t=cik, t·cik,
t+1 is a binary variable. By substituting equations (11)-(13)
with new constraints (14)-(16), the reformulated optimization
problem (7)-(10) and (14)-(16) is a mixed-integer second-order
cone programming (MISOCP) model. In this case, the dif-
ficulty in solving the problem may lie in addressing binary
or integer variables, which makes the whole optimization
problem non-convex. Generally, discrete variables can be
relaxed with the branch and cut method while the MISOCP
model could also achieve rapid and effective solutions with
CPLEX solvers [29].
The TOU the charging price is determined based on a rule-
based method. The theoretical foundation could be the demand
theory, which means the quantity demanded of a commod-
ity change in the opposite direction with its own price. For
example, the CS with a higher voltage level is more likely
to violate upper voltage limits considering the uncertainty of
PVs and load. It will set a lower charging price to attract
more charging EVs to reduce local voltages and the potential
voltage violation risk. It is assumed that the basic objec-
tive of the CS is to maximize their profit, and an original
optimal charging price λj,t has been set in advance. The
detailed research of the optimal pricing methods at CS is out
of the scope of this paper and interested readers can refer
to [14] for more information. Thereafter, the TOU charging
price in this paper is modified based on both λj,t and the
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4756 IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 6, NOVEMBER 2021
calculated voltage levels in (17).
cpj,t =
⎧
⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎩
λj,t − 2δ, V > 1.04
λj,t − δ, 1.02 < V ≤ 1.04
λj,t, 0.98 < V ≤ 1.02
λj,t + δ, 0.96 < V ≤ 0.98
λj,t + 2δ, V < 0.96
(17)
where cpj,t is the modified TOU charging price at CS j at
time t; δ is a positive constant used to regulate the price.
The modified charging prices are calculated based on volt-
age profiles in the day-ahead optimization and will be used
to estimate the charge cost of EVs in the charging navigation
process. Note that the day-ahead prediction errors will lead
to variations in the voltage at CS, but may not cause changes
in charging prices based on the proposed rule-based pricing
method. Moreover, the advanced power prediction methods
can also improve the accuracy of the modified TOU charging
price. Therefore, the charging navigation in layer 2 is not sen-
sitive to prediction errors with the proposed pricing method
and acceptable prediction accuracy.
D. Layer 2: EV Dispatch With Optimal Route Planning
In the intra-day dispatch process, each EV will make
a charging route planning based on the customized charg-
ing navigation introduced in Section II-B. For EVs in each
preference mode, the optimal charging route selection can be
determined by formulating and solving a mixed-integer lin-
ear programming (MILP) problem. Except for the objectives
defined in each mode, several constraints are also included and
introduced as following.
(1) Charging time estimation:
Tci,j =
(
SOCmax − SOCai,j
)
Eev
Pchη
(18)
where SOCai,j is the SOC of EV i arriving at CS j and should
be larger than zero; SOCmax is the maximum SOC value and
equals to 0.8; Eev is the capacity of EV battery; Pch is the
rated charging power, which represents fast charging power
in Mode 1 and slow charging power in Mode 2-5; η is the
charging efficiency. Note that in battery swap charging mode,
Tci,j is relatively short and only takes several minutes.
(2) Waiting time estimation: The waiting time can be esti-
mated by two parameters, i.e., the number of EVs arriving
at CS
j,t and the number of EVs charging at CS μj,t [17].
Assume that each CS is equipped with sufficient slow chargers
and limited fast chargers, and EVs will wait in queue when
the sum of
j,t and μj,t is larger than total number of EV
fast chargers sj. According to the queue model in [31], the
probability for the kth arriving EVs charging at CS j at time
t is
Pk,j,t =
⎧
⎪⎨
⎪⎩
1
k!
(
φj,t
μj,t
)k
P0,j,t, k ≤ sj
1
sj(sj!)k−s
(
φj,t
μj,t
)k
P0,j,t, k > sj
(19)
where P0,j,t can be estimated in (20).
P0,j,t =
⎡
⎣
sj−1∑
k=0
1
k!
(
φj,t
μj,t
)k
+ 1
sj!
μj,t
μj,t − φj,t
(
φj,t
μj,t
)sj
⎤
⎦
−1
(20)
Thus, the average length of queue Lq,j,t is expressed in an
expected format in (21).
Lq,j,t =
∞∑
k=sj
(
k − sj
)
Pk,j,t =
(
φj,t
μj,t
)sj φj,t
sjμj,t P0,j,t
sj!
(
1 − φj,t
sjμj,t
)2 (21)
The average wait time at CS j Twi,j is also given in (22).
Twi,j =
{
0, φj,t + μj,t ≤ sj
Lq,j,t/φj,t, φj,t + μj,t > sj (22)
(3) Charge cost estimation:
Ci,j = Pslow/fast
∫ tai,j+Twi,j+Tci,j
tai,j+Twi,j
cpj,tdt + CVRSi,j (23)
tai,j = ti + Tdi,j (24)
where tai,j is the arrival time of EV i at CS j. CVRSi,j is the
extra economic compensation of EVs in VRS, which is esti-
mated in EV dispatch process and adjusted in real-time voltage
control.
(4) SOC and charging selection constraints:
SOCai,j = SOC0i − eDi,j/Eev (25)
NC∑
j=1
ωij = 1 (26)
where SOC0 i is the initial SOC of EV i before going to CS;
e is the driving consumption power.
(5) Service number constraints: This constraint is designed
to limit the total number of EVs in VRS for each CS to find
a trade-off between voltage control effect and regulation cost
in ADN.
{
0 ≤ NSj,t ≤ NSmax j,t
NSj,t+1 = NSj,t + ∑i∈4 ωij
(27)
where NSj,t is the number of EVs in VRS at CS j at time t.
In the formulated optimization problem with
objectives (1)-(6) and route planning constraints (18)-(27),
variables Tdi,j and Di,j can be represented by the shortest
time and distance of EV i to CS j, which are then transferred
to constant values at each snapshot to reduce the binary
variables in optimization. This is regarded as the shortest path
problem and solved by the well-known Dijkstra method [32].
With a weighted graph G and a starting point S as inputs,
the method could find the shortest (lowest weight) path
from S to any nodes in G. Fig. 2 presents the optimal path
search process and the Dijkstra algorithm is also shown in
Algorithm 1, where W is the weighted matrix indicating the
time cost or travel distance between two nodes; Dis(p) is the
shortest distance between start point S and node p; Path is
a set used to restore the shortest path from S to any other
node p. Note that the weights between two nodes are different
with regard to the time and distance. The relationship between
travel time and distance along the road in TN is formulated
in (28).
Tpq = Dpq
v¯pq,t
(28)
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Fig. 2. Process of path search by Dijkstra method, where I is the starting
point; number in green indicates distance from I to other nodes; number in
black indicates weight value of the edge.
Algorithm 1 Dijkstra algorithm
1: Initialize Graph G; starting point S; nodes number N;
weight matrix W; Path(p)= undefined
2: for p=1,2. . . N, do
3: if S and p are disconnected
4: Dis(p)= infinity
5: else
6: Dis(p)= W(S,p)
7: end if
8: end for
9: Define sets Z1= [], Z2= { p|p∈ G}
10: while Z2
= [] do
11: u= argmin(Dis(p)) and u
= S
12: Z1= Z1∪{ u}, Z2= Z2\{ u}
13: for node q=1,2. . . N, do
14: if Dis(q)> Dis(u)+W(u,q)
15: Dis(q)= Dis(u)+W(u,q)
16: Path(q)= u
17: end if
18: end for
19: end while
20: Backtracking nodes in Path set to obtain shortest path
where Tpq and Dpq are travel time and distance between node
p and q; pq,t is the average driving velocity. The value of pq,t
can be estimated by crowd sensing technology, which is well
explained in [17]. In practice, the formulated charging naviga-
tion model can also be implemented in an application (APP)
on mobile phones to provide customized charging suggestions
for EV users.
E. Layer 3: Local Voltage Control With Power Allocation
Although the dispatch process of EVs has improved the
voltage profile in ADN, real-time local voltage control is also
necessary considering the following two aspects. On the one
hand, EV users have their own preferences in charging selec-
tion, which will lead to variation and uncertainty in charging
demand at CS. On the other hand, the fast fluctuation of PVs
will also cause unexpected voltage violations without the con-
trol of fast-response voltage regulation devices. Moreover, the
regulation of charging power and its allocation process is only
performed among EVs in VRS. Considering the difference in
Fig. 3. Local voltage control and power allocation among EVs.
arrival time for each EV, the power allocation is dynamic and
updated minutely corresponding to control steps. Since we
only focus on voltage violation in real-time control, a local
voltage control scheme is adopted and presented in Fig. 3.
Once voltage violation occurs, the local controller at CS
measures local voltage value Vm and regulates charging power
with P(V) control curve. The curve has a dead-band within the
range [Vmin,Vmax], and the slope can be calculated based on
V-P sensitivity as following.
⎧
⎨
⎩
[
P
Q
]
=
[
JPθ JPV
JQθ JQV
]
·
[
θ
V
]
SVP = ∂V∂P = (JPV − JPθJ−1Qθ JQV)−1
(29)
where P and Q are the vectors of nodal active and reactive
power injection to the grid; θ and V are the vectors of phase
angle and node voltage; SVP is the V-P sensitivity matrix. Take
CS at node j as an example, the charging power regulation Pr,t
is expressed in (30).
Pr,t =
⎧
⎨
⎩
(Vmin − Vm)/SVP(j, j), Vm < Vmin
0, Vmin ≤ Vm ≤ Vmax
(Vm − Vmax)/SVP(j, j), Vm > Vmax
(30)
PCS,t = PCS,t−1 − Pr,t (31)
The Pr,t is then allocated to each EV in VRS considering
their present SOC levels. The charging power of EV i at time
t is
PEVi,t = PEVi,t−1 − SOCi,t∑
i∈VRS SOCi,t
Pr,t (32)
{
SOCi,t = SOCi,t−1 + PEVi,t−1ηt/Eev
SOCmin ≤ SOCi,t ≤ SOCmax (33)
where PEV i,t is the charging power of EV i at time t; “t-1”
is a time index indicating the snapshot one minute ahead of
the current time step. Note that PEVi,0 is the initial charging
power once EV arrives at the CS and can be determined by
the selection of fast or slow chargers. equation (33) is the
SOC constraints in the charging process and SOCmin is the
minimum value of SOC and set at 0.1 in this paper. If an EV
participates in the VRS, the extra service time can be expressed
as follows.
Tei,j = tsi,j − tai,j − Twi,j − Tci,j (34)
where Tei,j is the extra service time of EV i at CS j; tsi,j is the
actual leaving time of EV i at CS j. Thus, the CVRSi,j in (23)
is then adjusted and calculated as follows.
CVRSi,j =
{
0, 0 C0 + α
(
Tei,j − 0.5
)
, 0.5 ≤ Tei,j ≤ 2 (35)
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4758 IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 6, NOVEMBER 2021
where C0 is a constant; α is a compensation factor and can be
calculated based on EV’s V2G contract in [33]. According to
(35), EVs can obtain economic compensation only when their
extra service time is larger than 0.5 h. They are also required
to leave the CS once Tei,j exceeds 2 h. In this paper, EVs in
VRS are assumed to have enough time for charging and will
not actively interrupt the voltage regulation process. Therefore,
they are supposed to stop the charging process when the Tei,j is
larger than 0.5 h and SOC reaches the requirement (e.g., 0.8).
Moreover, the distribution system operator should also com-
pensate for the potential economic loss of the CS. According
to (17), the maximum profit of the CS can be estimated by
multiplying λi,t and the expected charging demand under this
price. If the actual income of CS is lower than the maximum
profit due to the modification of charging prices, the economic
difference will also be compensated by the system operator to
ensure the benefit of the CS. Finally, two conditions should be
met to facilitate the proposed economic compensation mech-
anism in this paper: (1) The CS are willing to participate in
ancillary services in distribution networks by adjusting their
charging prices. (2) The compensation mechanism is avail-
able to make up for the financial losses of CS caused by
participating in VRS.
The local voltage control only aims at mitigating fast voltage
violations, which cannot achieve globally optimal operation
of the distribution networks. Moreover, voltage violations can
occur at some buses at the end of the feeder even the voltage
at CS lies within operation limits. In this case, several critical
buses are selected and equipped with voltage measurements.
The voltage at the critical bus is then sent to the neighboring
CS and voltage violations can also be mitigated with the local
control strategy.
F. Interaction Between Layers
Based on the mathematical models formulated for three
layers in Sections II-D and II-E, the interaction between lay-
ers with different timescales is further clarified in Fig. 4.
Layer 1 sends modified charging price (cpj,t) to layer 2 to
estimate the charge cost in (23), and also sends dispatch
results (tapt, QCBi,t) to OLTC and CBs in layer 3 to regulate
the voltage. Since the centralized optimization in layer 1 has
already been performed and completed ahead of the day, the
information flow between layer 1 and the other two layers is
unidirectional without any feedback control.
The dynamic interaction occurs between layer 2 and
layer 3 with a bidirectional information flow. The customized
charging navigation is solved in layer 2 to obtain the charg-
ing selections (ωij) and preference modes (Mode 1-6) of EVs.
These decisions will influence the total charging demand at
each CS (PCS,t) and the extra service time (Tei,j) calculated
in (29)-(35) in layer 3. It is worth mentioning that the real-
time control in layer 3 also has feedback on the optimization
process in layer 2. Specifically, the number of EVs charging
(μj,t), arriving (
j,t) and participating in VRS (NSj,t) at CS
are all sent back to layer 2 every 15 minutes to calculate the
wait time in (19)-(22) and evaluate the availability for EVs to
participate in VRS in (27).
Fig. 4. Interaction between layers in the proposed hierarchical framework.
Fig. 5. Coupled 33-bus distribution network and 24-bus transportation
network.
III. CASE STUDY
The simulations were conducted using MATLAB on a 64-bit
laptop with 2.60 GHz CPU and 16GB RAM. The optimization
models are programmed on GAMS, where the MISOCP and
MILP are solved by the CPLEX solver.
A. Test System and Parameters Settings
We consider a modified IEEE 33-bus distribution network
coupled with a 24-bus transportation network in Sydney to ver-
ify the effectiveness of the proposed three-layer hierarchical
voltage control strategy [29]. Fig. 5 shows the network topol-
ogy and bus coupling relationship between ADN and TN. The
data of TN can be obtained from Google Map and are listed
in Table I. The OLTC is with ±5% tap range and 10 tap posi-
tions, while the CBs have a unit adjusting of 100 kVar and
a maximum of 400kVar. Each CS has 8 fast chargers and suf-
ficient slow chargers, and also a maximum number of 20 EVs
in VRS. Fig. 6(a) presents hourly forecasted PV, EV and load
data in day-ahead optimization, which is calculated as the aver-
age value of minute real data within each hour. Fig. 6(b) shows
PV and load data with 1-min resolution during 13:00 and
14:00 in real-time voltage control [34]–[35]. Note that we
consider a typical 24-hour commercial load curve in simu-
lation, while other types of load like residential and industrial
loads can also be included. All the loads are uncontrollable
and will remain constant in the optimization process. It means
the varying load types differ only in load curves and may
change the modified charging prices in numerical values, but
will not impose challenges on the hierarchical control strategy
and loss minimization process. We also consider an emergency
condition for PV systems, i.e., a sudden active power drop at
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SUN AND QIU: HIERARCHICAL VOLTAGE CONTROL STRATEGY IN DISTRIBUTION NETWORKS 4759
Fig. 6. Data of PV, EV and load: (a) day-ahead prediction, (b) real-time
control.
TABLE I
DATA OF THE 24-BUS TRANSPORTATION NETWORK
about 13: 35 caused by cloud coverage. For simplicity, there
are only three starting points in TN during this hour, and the
dispatch process is performed every 15 minutes with 50 EVs.
In the test, the operational voltage range is [Vmin, Vmax] =
[0.95, 1.05] p.u. Eev, e and η equal to 30 kWh, 0.15kWh/km
and 0.9 respectively [11]. The fast and slow charging power at
CS are 60kW and 10kW, while the constant C0 and coefficient
α equal to 1.5 and 0.54 respectively. Note that the charac-
teristics of different types of EVs like battery capacity and
charging speed are assumed to be the same in this paper. The
variation in EV’s characteristics will not significantly influ-
ence the charging selection but may lead to different charging
time and cost. The proposed method can also be expanded to
include EV characteristics by introducing charging parameters
found in [17].
B. Day-Ahead Optimal Dispatch
Fig. 7 presents the voltage profile in distribution networks
after day-ahead reactive power dispatch in layer 1. It can be
Fig. 7. Voltage profile after day-ahead reactive power dispatch.
Fig. 8. Day-ahead dispatch results of OTLC and CBs.
seen that all the voltage values lie within the range of operation
limits. The maximum voltage reaches 1.05 p.u. at noon when
PV generation is high, while the minimum voltage reaches
0.952 p.u. at night. Compared with the base case without
voltage control of OLTC and CBs, network power loss has
a reduction of 20.8% from 3128kWh to 2477kWh.
Fig. 8 presents the day-ahead dispatch results of OLTC and
CBs. It is observed that the tap position of OLTC switches
from step 3 to step 4 at 19:00 to mitigate voltage drop prob-
lems caused by the increase of load and charging EVs. Since
nodes 16 and 30 are at the end of the feeders and more likely to
occur voltage violation, CB1 and CB3 will provide more reac-
tive power than CB2 in most periods to support voltage and
reduce power loss. However, CBs provide less reactive power
during 12:00 and 15:00 compared with that in other periods.
Since voltage level is higher at noon due to PV generation,
CBs will switch to decrease their reactive power support so as
not to cause voltage rise problems. Moreover, assuming λj,t
equals to 0.97$/kWh and 0.66$/kWh for fast and slow charg-
ing during 13:00 and 14:00, the modified TOU charging prices
are also calculated. The fast charging prices for CS1-3 are
0.76 $/kWh, 0.55 $/kWh and 0.76 $/kWh, while the corre-
sponding slow charging prices are 0.51 $/kWh, 0.36 $/kWh
and 0.51 $/kWh.
C. Customized Charging Selection and Route Planning
Fig. 9 presents the customized charging selection and route
planning under different preference modes. Take the first dis-
patch interval (from 13:00 to 13:15) and starting point 2 as
an example, it is observed that EVs will make different charg-
ing selections with varying preferences. In Preference Mode 1,
EVs select routes in orange and CS3 with the minimum time
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4760 IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 6, NOVEMBER 2021
Fig. 9. Customized charging selection and route planning for S2.
Fig. 10. Charging selection and route planning with single objective for S2.
TABLE II
AVERAGE DISPATCH RESULTS OF EVS IN DIFFERENT PREFERENCE
MODES
cost. In Preference Mode 2, 3 and 6, EVs only cares about
time cost in traveling and select routes in black and CS1. In
Preference Mode 4 and 5, EVs would like to minimize the total
charge cost and select routes in purple and CS2. Fig. 10 also
presents charging selection results without customized charg-
ing navigation for comparison purposes. Generally, EVs only
focus on minimizing total charge cost or travel time, and the
TOU charging price is not modified [12]. It is observed that
EVs only go to CS1 for charging considering the single objec-
tive of minimizing travel time. Similarly, with the objective
of minimizing charge cost, all EVs go to CS1 with a uni-
form charging price and CS2 with a modified charging price.
Such charging navigation neglects the user’s preferences and
is not conducive to mitigating voltage violations. It may also
influence the EV’s driving behaviors and SOC levels without
considering their willingness (preference modes 3 and 5) in
VRS. Note that even EVs in several modes have the same
route planning and charging selection, they will vary in charge
time and total cost.
TABLE III
SENSITIVITY ANALYSIS OF PREFERENCE MODES ON CHARGING DEMAND
Table II compares the detailed dispatch results of EVs under
different preference modes. Note that all the results presented
in Table II are the average values of EVs in each preference
mode. The proportion of each mode selection is predefined
manually, which is based on the actual situation and can be
further investigated with a questionnaire survey. It is observed
that EVs in Mode 1 have a minimum time cost of 0.70 h
(other than Mode 6) and a maximum charge cost of $13.68.
Although EVs in Mode 2 have a shorter drive time than that
in Mode 1, their wait time is much longer and reaches 0.23 h.
EVs in Mode 5 have a minimum charge cost of $5.78, which
includes cost both for charging and economic compensation
in VRS mode. Since we have no idea about the exact charging
time in EV dispatch (layer 2), the extra service time is assumed
to be 0.5 h to estimate the charge cost. Compared with those
in Mode 2 and 4, EVs in Mode 3 and 5 will participate in
VRS to sacrifice charge time for the saving of charge cost.
Note that Mode 4 in Table I presents the results both in fast
and slow charging, and Mode 6 is especially for EV buses
which will not be considered in the comparison.
To evaluate the influence on charging demand of the pro-
portion change in preference modes, a sensitivity analysis is
performed. In the proposed six preference modes, Mode 1,
2, 3 and 6 are time-dependent, while Mode 4 and 5 are
cost-dependent. Thereafter, we define γ to be the ratio of cost-
dependent EVs in the total number of EVs. Table III presents
the maximum, minimum and average charging demand at three
CS under different values of γ . With the increasing propor-
tion of cost-dependent users, more EVs will be attracted to
charge at CS 2, and the average charging demand at CS 1
and 3 decreases. This means the larger proportion of cost-
dependent EVs can better improve voltage profiles (lower
violation risks) under the same charging pricing strategy.
Moreover, the increasing proportion of Mode 2 and 5 (EVs
in VRS) can also provide more flexibility and controllability
for CS in real-time control.
D. Dynamic Interaction Between Layer 2 and Layer 3
Since the charging navigation and voltage control processes
are conducted in a dynamic manner, the charging selection
of EVs will have an influence on the charging demand and
related voltage control effect at CS, and vice versa. To ana-
lyze such dynamic interaction between layer 2 and layer 3,
the wait time and average number of EVs in VRS at each CS
between 13:00 and 14:00 are first presented in Fig. 11. It is
observed in Fig. 11(a) that the wait time at CS 1 is longer than
CS 2 and 3 (zero) at 13:00. However, more EVs are motivated
by the lower charging price and will go to CS 2 for charging
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SUN AND QIU: HIERARCHICAL VOLTAGE CONTROL STRATEGY IN DISTRIBUTION NETWORKS 4761
Fig. 11. Wait time and average number of EVs in VRS for each CS.
during this hour, thus lead to a decrease in wait time at CS 1
and a significant increase in wait time at CS 2. In Fig. 11(b),
the average number of EVs in VRS at CS 2 increases while
that at CS 1 fluctuates slightly. Fig. 12 presents the dynamic
charging selection of EVs at node 10 with three different pref-
erence modes. The EVs with preference mode 1 first choose
CS 3 for charging to minimize total time cost, but change their
charging selections to CS 1 at 13:30 due to its relatively lower
wait time (zero) compared with CS 3 (0.13 h). The EVs with
preference mode 2 make a change on charging selection from
CS 1 to CS 3 at 13:45 due to the improved traffic condition
and lower time cost along the route in orange in Fig. 9. As for
EVs with preference mode 5, they only care about the eco-
nomic cost and always choose CS 2 for charging due to its
lowest charging price within this hour. Although the charging
selection for preference mode 5 remains constant, the number
of EVs in VRS at CS 2 is high (18) at 13:45 and is more likely
to reach the upper limit (20). Therefore, it is predicted that the
VRS may be unavailable at CS 2 in the coming periods and
EVs with preference mode 5 will change their charging selec-
tions to CS 1 for more economic benefits. Fig. 13 shows the
EV charging demand at different CS with and without dispatch
during this hour. The charging demand without dispatch is the
base case which means all CS adopt the same optimal slow and
fast charging prices λj,t during this hour. The charging demand
at CS 1 decreases and that at CS 2 increases significantly after
dispatch, while demand at CS 3 is also slightly higher than that
before dispatch. Since CS 2 is more likely to occur voltage rise
problems, it adopts lower charging price to attract more EVs
and reduces the potential voltage violation risk. However, the
charging demand without dispatch is much higher at CS1 than
others and will cause the local voltage to violate the upper lim-
its within this hour. Take CS1 as an example, the CS adopts
modified charging prices to help improve voltage profiles in
distribution networks, and will receive an economic compen-
sation of $253 from distribution system operators. Note that
the results shown in Fig. 13 are under the proportion of pref-
erence mode selection in Table I. It is concluded that both
the charging price and selection of preference modes will
have an impact on the charging demand profiles. The dynamic
interaction between charging navigation and voltage regulation
Fig. 12. Dynamic charging selection of EVs at node 10 with three different
preference modes.
Fig. 13. Charging demand in different CS with/without dispatch.
also introduces uncertainty to the charging demand at each
CS. Therefore, the customized charging selection is hard to
predict and will lead to variation in charging demand even
after dispatch, which may require further voltage regulation in
layer 3.
E. Numerical Results of Real-Time Voltage Control
To demonstrate the advantage of the proposed hierarchical
voltage control strategy, another three existing voltage control
methods and frameworks are studied and compared.
Method #1: Single-stage centralized voltage control
This approach only regulates OLTC and CBs every hour to
mitigate voltage violations. The dispatch results of OLTC and
CBs are determined by solving the centralized optimization
model with forecast EV, PV and load. Similar centralized
voltage control frameworks can also be found in [5] and [12].
Method #2: Two-stage coordinated voltage control
This control framework formulates a bi-level optimization
model to coordinate both voltage control in ADN and EV dis-
patch in TN [10], [14]. The day-ahead optimization is first
performed to determine the charging prices at CS. Given the
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4762 IEEE TRANSACTIONS ON SMART GRID, VOL. 12, NO. 6, NOVEMBER 2021
settings calculated in the first stage, the optimal charging
navigation is then performed for each EV in the second stage.
Method #3: Combined central and local voltage control
This method combines the advantages of both central-
izedand local voltage control schemes [36]. Different from the
proposed method, the local voltage control curves are tuned
based on the voltage and power references obtained in the
day-ahead optimization in layer 1.
For the fairness of comparison, the proposed customized
charging navigation strategy is embedded in some of these
methods. This means the charging demand without dispatch
in Fig. 13 is adopted in Method #1 and that with dispatch
is adopted in Method #2 and Method #3 in real-time volt-
age control. Fig. 14(a) presents the voltage profile of all buses
with the proposed method, and Fig. 14(b) presents the mini-
mum voltage at bus 18 with different voltage control methods.
It is observed that the voltages vary with different time peri-
ods and buses, but all of them lie within the safe operation
range after control. In Fig. 14(b), both the voltage rise and
voltage drop problems occur in Method #1, which indicates
such discrete voltage regulation of OLTC and CBs with longer
timescales is not sufficient to mitigate fast and unexpected
voltage violations. The voltage rise problems are addressed in
Method #2 with the proposed charging navigation strategy of
EVs, but voltage still violates the lower limits between 13:42
and 13:56. By contrast, both Method #3 and the proposed
method successfully mitigate voltage violations with the three-
layer hierarchical framework of day-ahead optimization, EV
charging navigation and real-time voltage control process.
Table IV shows the detailed voltage control results with
different methods including maximum and minimum volt-
age (MV), voltage violation time (VT), active power loss (PL)
and extra economic compensation (EC) provided by distribu-
tion system operators. It is concluded that the EV dispatch
process in Method #2 could mitigate voltage rise problems
at bus 18 with an increase PL of 95.2 kWh compared
with Method #1 (76.8kWh). However, it may also increase
the potential voltage violation risk considering the sudden
active power drop of PVs and result in the longest VT of
15 min. It is worth mentioning that Method #3 could miti-
gate voltage violations with a lower PL (81.6 kWh) and an
increased voltage margin (in Fig. 14(b)) compared with the
proposed method. It is because the tuned local voltage con-
trol curves in Method #3 have a tighter dead band voltage
range [1.025, 1.045] p.u. compared with the proposed method
[0.95, 1.05] p.u. The CS with the tuned local control curves
will regulate its charging power once voltage violates the
dead band and lead to a more charging curtailment of EVs
in VRS. Therefore, Method #3 also has a higher EC com-
pared with the proposed method. Even if we assume that the
cost for power loss equal to the maximum fast charging price
of 0.76 $/kWh in this hour, the total cost with the proposed
method is still $3.4 lower than that in Method #3. In this case,
the system operator may need to find a trade-off between the
improved voltage profiles and total economic cost. If the distri-
bution networks aim to address the voltage violation problems
with the minimum economic cost, the proposed method will
also be preferred.
Fig. 14. Voltage profiles with different voltage control methods in the
IEEE 33-bus system: (a) Voltage of all buses with the proposed method,
(b) Comparison of voltage at bus 18 with different methods.
TABLE IV
REAL-TIME VOLTAGE CONTROL RESULTS WITH DIFFERENT METHODS
Fig. 15. Number and total curtailed charging power of EVs in VRS.
Take EVs at CS 2 as an example, the number of EVs
and total charging power regulation in VRS are presented
in Fig. 15. Since real-time control is activated when voltage
violation occurs, only the results during 13:42 and 13:56 are
analyzed. It is observed in Fig. 15 that the number of EVs in
VRS changes dynamically with the variation of user’s arrival
time and preferences. The total curtailed charging power (Pr,t)
reaches the peak value at 13:46 and then decreases, which
corresponds to the voltage trend in Fig. 14. Thus, the power
allocation among EVs in VRS should also be performed
dynamically. The charging/discharging of two typical EVs
with higher and lower SOC are shown in Fig. 16. EVs with
higher SOC will reduce more charging power or even work
in V2G mode to inject active power to the grid and support
local voltage. For EVs with lower SOC, they slightly reduce
the charging power due to their limited energy storage. The
power regulation of EVs is consistent with the trend of their
SOC level.
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Fig. 16. Charging/discharging of EVs with different level of SOC: (a) higher
SOC, (b) lower SOC.
TABLE V
PARAMETERS OF VOLTAGE REGULATION DEVICES IN THE IEEE 123-BUS
SYSTEM
F. Scalability of the Proposed Voltage Control Method
To verify the scalability and applicability of the proposed
method, simulations are also performed on a modified IEEE
123-bus distribution network. The topology of the network
can be found in [37] while the detailed parameters of OLTC,
CBs and PVs are listed in Table V. The locations of CS1-
3 in the transportation network are the same as that in Fig. 5,
and are also at bus 14, 123 and 66 respectively in the IEEE
123-bus distribution networks. The day-ahead optimal dispatch
of OLTC and CBs is shown in Fig. 17. Since the whole volt-
age level in the IEEE 123-bus system is lower than that in the
IEEE 33-bus system, the OLTC only regulates the voltage at
slack bus between 0.99 p.u. and 1.01 p.u. to achieve the coarse
regulation in the day-ahead schedule. The CBs also provide
more reactive power in the evening to support voltage which
is similar to that in Fig. 7. Fig. 18 presents the voltage pro-
files in the IEEE 123-bus distribution networks with different
voltage control methods. It is observed that only voltage drop
problems occur with Method #1 and Method #2, and similar
conclusions can also be found compared with that in the IEEE
33-bus system. Table VI presents the corresponding numer-
ical comparison results among different methods. Different
from that in the IEEE 33-bus system, Method #2 becomes less
effective than Method #1 both in mitigating voltage violations
and reducing PL considering relatively lower voltage level.
However, the proposed method is still effective in voltage
control and results in a relatively lower PL than Method #1.
Compared with Method #3, it also achieves a more distinct
total economic cost saving of $13.07.
Fig. 17. Day-ahead dispatch of OLTC and CBs in the IEEE 123-bus system.
Fig. 18. Voltage profiles with different voltage control methods in the
IEEE 123-bus system: (a) Voltage of all buses with the proposed method,
(b) Comparison of voltage at bus 18 with different methods.
TABLE VI
REAL-TIME VOLTAGE CONTROL RESULTS WITH DIFFERENT METHODS
IN THE IEEE 123-BUS SYSTEM
IV. CONCLUSION
This paper proposes a three-layer hierarchical voltage con-
trol strategy to mitigate voltage violation in ADN considering
customized charging navigation of EVs. In this method, OLTC
and CBs are dispatched in day-ahead optimization in layer 1.
The optimal charging navigation of EVs is performed in
layer 2 with novel preference modes considering the user’s
benefits and willingness in VRS. The real-time voltage control
and dynamic power allocation among EVs are implemented
in layer 3. Numerical studies conducted on the IEEE 33-bus
distribution network and 24-bus transportation network verify
the effectiveness of the proposed method both in optimized
charging navigation and mitigating voltage violation problems.
Although the charging EV is one of the promising voltage
control resources, it cannot be the only one to address such fast
voltage violation problems. Future research trends may focus
on the coordinated control among different flexible voltage
control resources like inverter-based PVs and portable energy
storage systems.
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Xianzhuo Sun received the B.Eng. degree in elec-
trical engineering from the Taiyuan University of
Technology in 2016, and the M.E. degree in electri-
cal engineering from Shandong University in 2019.
He is currently pursuing the Ph.D. degree with The
University of Sydney, Sydney, NSW, Australia. His
research interests include power system operation
and voltage control, convex optimization, electrical
vehicles, and deep reinforcement learning.
Jing Qiu (Member, IEEE) received the B.Eng.
degree in control engineering from Shandong
University, China, in 2008, the M.Sc. degree in
environmental policy and management, majoring
in carbon financing in the power sector from
The University of Manchester, U.K., in 2010, and
the Ph.D. degree in electrical engineering from the
University of Newcastle, Australia, in 2014. He is
currently a Senior Lecturer of Electrical Engineering
with The University of Sydney, Australia. His areas
of interest include power system operation and plan-
ning, energy economics, electricity markets, and risk management. He is the
Editorial Board Member of IET Energy Conversion and Economics.
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