Active Distribution System Reinforcement Planning With EV Charging Stations-Part I: Uncertainty Modeling and Problem Formulation
Active Distribution System Reinforcement Planning With EV Charging Stations-Part I: Uncertainty Modeling and Problem Formulation
Active Distribution System Reinforcement Planning With EV Charging Stations-Part I: Uncertainty Modeling and Problem Formulation
2, APRIL 2020
Abstract—Due to the associated uncertainties, the large-scale EVCS Electric vehicle charging station
deployment of electric vehicles (EVs) and renewable distributed HMM Heuristic moment matching
generation is a major challenge faced by the modern distribu- OEV Other-purpose electric vehicle
tion systems. The first part of this two-paper series proposes a
scenario-based stochastic model for the multistage joint reinforce- PV Photovoltaic
ment planning of the distribution systems and the electric vehicle SoC State-of-charge
charging stations (EVCSs). The historical EV charging demand Markov Model Related Parameters and Variables
is first determined using the Markovian analysis of EV driving
patterns and charging demand. A scenario matrix, based on the Ec EV energy consumption per kilometer
heuristic moment matching method, is then generated to char- (kWh/km)
acterize the stochastic features and correlation among historical Cb Maximum battery capacity (kWh)
wind and photovoltaic generation, and conventional loads and EV Sn ch EV normal charging state
demands. The scenario matrix is then utilized to formulate the ex- Sf ch EV fast charging state
pansion planning framework, aiming at the minimization of the
investment and operational costs. The proposed expansion plan Sd EV driving state
determines the optimal construction/reinforcement of substations, Sp EV parking state
EVCSs, and feeders, in addition to the placement of wind and Pn Typical power of normal charging (kW)
photovoltaic generators, and capacitor banks over the multi-stage Pf Typical power of fast charging (kW)
planning horizon. In the second companion paper, the effective- tm d Departure time in the morning of CEV
ness and scalability of the proposed model is assessed through case
studies in the 18-bus and the IEEE 123-bus distribution systems, tm a Arrival time in the morning of CEV
respectively. ted Departure time in the evening of CEV
tea Arrival time in the evening of CEV
Index Terms—Distribution system, distributed generation,
electric vehicle charging stations, multistage expansion planning,
td Departure time of OEV
heuristic moment matching. ta Arrival time of OEV
Nd Valid samples generated by Monte-Carlo sim-
NOMENCLATURE ulation
SoC(t) SoC in the existing time slot
Abbreviations SoC(t + 1) SoC in the next time slot
CEV Commuting electric vehicle v EV average driving speed (km/h)
DG Distributed generation P Markov model of EV
DSEP Distribution system expansion planning ti ith time slot
EV Electric vehicle Sni ch Probability of normal charging in ith time slot
Sfi ch Probability of fast charging in ith time slot
Sdi Probability of driving in the ith time slot
Manuscript received November 15, 2018; revised March 2, 2019; accepted
May 4, 2019. Date of publication May 7, 2019; date of current version March Spi Probability of parking in the ith time slot
23, 2020. This work was supported in part by the National Key Research and P ev EV charging demand
Development Program of China under Grant 2018YFB0904800, in part by the
National Natural Science Foundation of China under Grant 51777183, and in HMM Method Related Parameters and Variables
part by the Major Scientific Project of Zhejiang Lab under Grant 2018FD0ZX01. ai , bi , ci , di Transforming coefficients
Paper no. TSTE-01132-2018. (Corresponding author: Qiang Yang.)
A. Ehsan is with the College of Electrical Engineering, Zhejiang University,
i = 1, 2, 3 Indices for wind generation, PV generation,
Hangzhou 310027, China, and also with the Department of Electrical Engi- conventional load and EV demands
neering, COMSATS University Islamabad, Sahiwal 57000, Pakistan (e-mail:, k = 1, 2, 3, 4 Expectation, standard deviation, skewness and
aliehsan@zju.edu.cn).
Q. Yang is with the College of Electrical Engineering, Zhejiang University,
kurtosis
Hangzhou 310027, China, and also with the Zhejiang Lab, Hangzhou 310058, L Lower-triangle matrix of R
China (e-mail:,qyang@zju.edu.cn). Mi,k N T , Mi,k T
kth normalized target moment and kth target
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
moment of ith column vector
Digital Object Identifier 10.1109/TSTE.2019.2915338 Mi,k (Z i ) Moments of target scenarios
1949-3029 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information.
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EHSAN AND YANG: ACTIVE DISTRIBUTION SYSTEM REINFORCEMENT PLANNING WITH EV CHARGING STATIONS 971
G d d
Mik kth moment of ith column vector of target sce- Pi,u ,h , Qi,u ,h Active (kW) and reactive (kvar) power de-
narios mands
N (0, 1) Normal distribution Ra , Xa , Za Resistance, reactance and impedance per
Nh , N u Number of scenarios & uncertainty factors length of conductor type a (Ω)
Phw t , Phpv , Phd Generated (target) scenarios of wind genera- V ,V Lower and upper bus voltage limits (V)
tion, PV generation and load α Number of hours in one year
R Target correlation matrix of historical scenarios φl , φs Load factor and loss factor
Ril G Correlation matrix of generated scenarios φm
soc
ax
Upper limit on EV state-of-charge
Ril N T Target correlation matrix of historical scenarios θij,a Binary parameter for initial state of feeder at
Xi, Zi Independent column vectors of randomly gen- the beginning of the planning horizon
su b
erated scenarios and target scenarios θs,q Binary parameter for initial state of substation
X N h ×N u n-dimensional matrix of randomly generated at start of planning horizon
sq r sq r
scenarios Iij,a,u , Vi,u Square of branch current (A) and bus
Y N h ×N u n-dimensional matrix obtained via matrix voltage (V)
transformation PmD,u
G
Active power supplied by DG units, i.e., wind
Z N h ×N u n-dimensional matrix of normalized scenarios and photovoltaic generators (kW)
obtained via cubic transformation Pij,a,u ,h , Active (kW) and reactive (kvar) power flows
εc , εm Correlation error and moment error Qij,a,u ,h in the feeders
εc , εm Upper limits on correlation error and moment ss
Pi,u ss
,h , Qi,u ,h Active (kW) and reactive (kvar) power supplied
error by substation (kW)
ΩH Uncertainty matrix wt
Pi,u pv
,h , Pi,u ,h Active power supplied by wind and photo-
DSEP Problem Related Parameters and Variables voltaic generators (kW)
QD G
i,g ,u Reactive power supplied by DG unit, i.e., wind
a, b, c Index for conductor types
and photovoltaic generators (kvar)
e Index for charger types
Qcb Reactive power supplied by capacitor bank
g Index for DG units, i.e., wind and photovoltaic
(kvar)
i Index for buses
Vj,u Estimated voltage at bus j (V)
ij, kj Index for feeders
φsoc EV state-of-charge at arrival
m Index for DG unit buses
nchi
p,e,u Integer variable for EVCS chargers
p Index for EVCS buses
ncbi
i,u Integer variable for capacitor units
q, t, r Index for substation alternatives
s Index for substation buses xcb
i,u Binary variable for the installation of capacitor
u, k Index for stages banks
v Index for EV types xcs
p,u Binary variable for installing EVCS chargers
ccij,a,b Cost of feeder using conductor type b, assum- xdg
m ,g ,u Binary variable for DG installation, i.e., wind
ing initial type a ($) and photovoltaic
ccb Installation cost of capacitor banks ($) xcir
ij,a,b,u Binary investment variable for feeder construc-
ccs , cce Installation cost of EVCS and chargers ($) tion/reinforcement using type b, assuming ini-
cdg Installation cost of DG units, i.e., wind and tial type a
g
photovoltaic ($) xsu b
s,q ,t,u Binary variable for substation construction/ re-
ce Cost of electricity supplied by substation ($) inforcement using substation type t, assuming
cedg Cost of electricity generated by DG units, i.e., initial type q
g cir
wind and photovoltaic ($) yij,a,u Binary variable for operation/connection status
c mod Cost per module of capacitor banks ($) of a feeder using conductor type a
su b
css,q ,t Cost of substation using substation type t, as- ys,q ,t,u Binary variable for substation operation using
suming initial type q ($) only one investment type in a stage
cvs Operational costs of substation ($)
Cp Upper limit on number of chargers I. INTRODUCTION
dwcs Operating time of chargers HE primary objective of distribution system expansion
Evr eq
Ia
Energy required by EV of type v
Upper limit on current in conductor type a
T planning (DSEP) is to provide enabling solutions that en-
sure the security, reliability and quality of electricity supply
K, τ Number of years in a stage and interest rate to customers at minimum cost [1]. One of the upcoming chal-
lij Conductor length (km) lenges faced by distribution systems is the unexpected uptake of
neve,v ,u Number of EVs assigned to charger type e electric vehicles (EVs), driven by advances in power electronics
NvE,uV Number of type v EVs that require charging and battery technologies. The rapid adoption of EVs provides
Pech Rated power of EVCS charger type e (kW) a promising solution for reducing greenhouse gas emissions,
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972 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 11, NO. 2, APRIL 2020
mitigating global warming issue [2], and utilizing renewable scenario generation method is proposed in [7] to deal with the
distributed generation (DG); however, this is accompanied by EV uncertainty. In [9], [10], the EV demand uncertainty is char-
an uncertain electricity demand growth. Therefore, adequate acterized through probabilistic factors and probability distribu-
DSEP methodologies should be developed for the explicit char- tion functions pertaining to the EV arrival and state-of-charge
acterization of uncertainties related to conventional loads and (SoC) data. Furthermore, a non-Gaussian multivariate stochas-
EV demands, and non-dispatchable wind and photovoltaic (PV) tic model based on copula functions is examined in [13] to
generation. approximate the hourly EV charging demand. However, the un-
In the existing literature, several research works have inves- certainties associated with the conventional loads, and the wind
tigated a wide range of mathematical models and solution tech- and photovoltaic generation have not been investigated.
niques pertaining to the DSEP problem. The authors in [3]–[6] In the existing literature, several methodologies have been
have employed the evolution algorithms, along with the mixed- proposed to deal with these uncertainties. In general, these
integer linear programming (MILP) for the solution of DSEP methods can be classified as stochastic optimization [14], ro-
problem considering EV integration. In [3], the optimal place- bust optimization [15], Monte Carlo simulation [16], Latin Hy-
ment of the electric vehicle charging stations (EVCSs) is studied bercube Sampling technique [17], Taguchi’s orthogonal array
for the minimization of costs associated with expansion. A mul- testing [15] and probability statistical methods [18]–[20]. How-
tistage DSEP problem is examined in [4], which determines the ever, it should be noted that these methods may not always
optimal siting and sizing of EVCSs. Similar methodologies are guarantee computational accuracy and efficiency; for example,
presented in [5] and [6], which investigate the joint expansion the Monte Carlo simulation in [16] produces unnecessary sce-
planning of distribution system and EVCSs. A multi-objective narios that results in computational intractability. Moreover, the
planning model is presented in [5] for the distribution sys- scenarios provided by Taguchi’s orthogonal array testing in [15]
tem with EVCSs; however, the random behavior of EV drivers exhibit inadequate occurrence probabilities, whereas the selec-
and the various charging modes are not studied. Furthermore, tion of a suitably-sized uncertainty set is problematic in robust
the yearly electricity demand growth, and the time-intervals optimization [15]. Different from these techniques, the heuris-
of normal-charging and fast-charging modes are disregarded. tic moment matching (HMM) method [21] utilizes a signifi-
In order to address these inadequacies, a stochastic multistage cantly reduced number of scenarios for the characterization of
planning model is presented in [6] for a distribution network uncertainties, providing an improved computational efficiency
with EVCSs considering different charging modes and bat- [22]. The HMM method reduces the complications related to
tery swapping; however, the proposed metaheuristic algorithm- the high-dimensional discrete variables, involved in the con-
based solution cannot ensure the solution optimality. Moreover, ventional moment matching method [21]. The HMM method
the studies in [3]–[6] have neglected the placement of DG units has earlier been employed in [22] to consider the stochastic
and capacitor banks. wind generation in transmission network planning; however,
Although the siting and sizing of EVCSs is investigated ex- the uncertainties of PV generation and load demand have been
tensively in the prevailing literature, such as [7]–[13], the joint disregarded. The HMM method is also adopted in [23]–[25] to
expansion planning of distribution systems and EVCSs is not address the uncertainties of wind and PV generation, and load
addressed considerably. The EVCS model proposed in [7], con- demand, whilst determining the optimal siting and sizing of DG
siders the exchanges between the reserve market and energy units. The DG planning method in [23] aims at the minimization
market, and DG operation, using a two-stage method; however, of power losses and voltage deviation in the distribution systems,
the primary focus of this work is EVCS operation planning. whereas the DG investment planning model in [24], maximizes
Another two-stage technique proposed in [8], addresses the op- the distribution network operator’s profit. The investment plan-
timal EVCS planning problem under the consideration of dif- ning model in [25], exploits the optimal DG integration and
ferent charger types, environmental aspects and service area; storage arbitrage benefit to maximize the distribution network
however, the operation of DG units and capacitor banks, and operator’s profit. However, the allocation of EVCSs and EV
the different EV types are not studied. Moreover, metaheuris- demand uncertainty, and the reinforcement of substations and
tic algorithms, such as the genetic algorithms in [9], [10] and feeders is not investigated in these works. Although the op-
the particle swarm optimization in [12], have been employed timal EVCS allocation is investigated within the DSEP prob-
for the solution of EVCS allocation problem; nevertheless, the lem in [26], the uncertainties of wind and PV generation are
operation of DG units has not been considered. disregarded.
In addition to the consideration of aforementioned aspects, Different from the aforementioned works, this work investi-
the uncertainties related to the growth of conventional loads and gates the optimal EVCS siting and sizing within DSEP problem,
EV demands must be explicitly examined to mitigate the risks, whilst considering the uncertainties of wind and PV generation,
prevent underinvestment, and avoid operational issues. The pre- and conventional and EV demands. To this end, we propose a
vious studies in [3], [7], [9], [13] have investigated the uncer- scenario-based stochastic model for the multistage joint expan-
tainty related to EV demands and the operational constraints of sion planning of distribution networks and EVCSs, aiming at the
distribution network, while only the EV demand uncertainty is minimization of investment and operational costs. The solution
examined in [10]. In [3], the EV demand uncertainty is tackled provides the optimal construction/reinforcement of substations,
by means of a geometric Brownian motion method, whereas feeders and EVCSs, and optimal placement of DGs and capac-
a two-stage stochastic programming model combined with a itor banks.
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EHSAN AND YANG: ACTIVE DISTRIBUTION SYSTEM REINFORCEMENT PLANNING WITH EV CHARGING STATIONS 973
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974 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 11, NO. 2, APRIL 2020
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EHSAN AND YANG: ACTIVE DISTRIBUTION SYSTEM REINFORCEMENT PLANNING WITH EV CHARGING STATIONS 975
given in (11).
Z i = ai + bi Y i + ci Y i 2 + di Y i 3 (10)
Mi,k (Z i ) = Mi,k T , i = 1, 2, 3; k = 1, 2, 3, 4 (11)
5) The moment errors (εm ) and the correlation error (εc ) are
calculated, as given in (12) and (13), respectively, and the
upper limits on these errors are set in (14).
Nh
G 4
G
εm = NT
Mi1 − Mi1 + NT
Mik − Mik /Mik NT
i=1 k =2
(12)
Nh
w N N
2 w
G 2
εR = Ril − Ril N T
i=1
Nu (Nu − 1) i=1 i=1
(13)
εm = 5%, εc = 5% (14)
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976 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 11, NO. 2, APRIL 2020
IDG = cdg dg
g xm ,g ,u (20) Qk j,a,u ,h − sq r
Qij,a,u ,h + Xa lij Iij,a,u ,h
m g kj a ij a
ICB = ccb xcb
i,u +c mod
ncbi
i,u (21) + ncbi cb ss wt pv d
i,u ,h Q + Qi,u ,h + Qi,u ,h + Qi,u ,h = Qi,u ,h ∀u, h, i
i (27)
ICS = ccs xcs c chi
p,u + ce np,e,u (22) 2
Vj,u sq r
,h Iij,a,u ,h = f (Pij,a,u ,h , V I a , Γ)
p e
+ f (Qij,a,u ,h , V I a , Γ) ∀ij, a, u, h
The electricity costs (EC) and the substation operational
(28)
costs (OS) are determined by (23) and (24), respectively, where
ζ(τ, K) evaluated the present value of annualized costs, as de- 2 (Ra Pij,a,u ,h + Xa Qij,a,u ,h ) lij
sq r sq r
fined in (25). The function f (ρ, ρ, Γ) provides the piecewise Vi,u ,h − Vj,u ,h −
a
2 sq r
+Za2 lij Iij,a,u ,h
linearization of the square value of a variable ρ, described in
2
terms of its maximum value (ρ) and number of discretization ≤ V −V2 1 − yij,a,u
cir
∀ij, u, h (29)
,h
intervals (Γ), as discussed in [28]. a
V ≤
2 sq r
Vi,u ,h ≤V
2
∀u, h, i (30)
e S edg D G
EC = aϕl c Ps,u + cg Pm ,u ζ (τ, K)
sq r 2
s m g 0 ≤ Iij,a,u ,h ≤ I a yij,a,u ,h
cir
∀ij, a, u, h
(23) (31)
f Ps,uS
, St , Γ
OS = αϕs cvs ζ (τ, K) 2) Logical Constraints for the Substations: The set of con-
s t +f QSs,u , St , Γ straints (32)–(36) ensure the coordination of the investment and
(24) the operation of substations over the planning horizon. The in-
vestment types represent the available apparent power capacities
ζ (τ, K) = 1 − (1 + τ )−K τ −1 (25) for the construction or reinforcement of the substations, where
the substation types are arranged according to the ascending
order of their power capacities and investment costs. The im-
B. The Constraints
plementation of more than one investment type in the same
The fundamental constraints of the distribution system, along stage is prevented by the constraint (32). The constraint (33)
with the logical constraints of the substations, the feeders and the ensures that a certain substation investment can be made only
EVCSs, based on [26], are modified to incorporate the scenario once over the planning horizon. The constraint (34) guarantees
matrix. Moreover, piecewise linearization is employed to repre- that the substation reinforcement using an initial type q can
sent the square of active and reactive powers in the constraints only be carried out if the type q has been employed for the sub-
that model the steady-state operation of distribution system, as station construction/reinforcement in the previous stages. The
discussed in [28]. The constraints for the operational limits of constraint (35) assures that the substation operation is allowed
the DG units and capacitor banks, and the radiality conditions only if the associated investment has been made. The constraint
are not discussed here due to limited space. A detailed descrip- (36) ensures that the substation operation is carried out using
tion of these constraints can be found in [28]. only one investment type in each stage.
1) Fundamental Constraints of the Distribution System: The
s,q ,t,u ,h ≤ 1
xsu ∀s, u, h
b
set of constraints (26)–(29) represents the Kirchhoff’s laws and (32)
signifies the radial operation of distribution system. The ac- q t
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EHSAN AND YANG: ACTIVE DISTRIBUTION SYSTEM REINFORCEMENT PLANNING WITH EV CHARGING STATIONS 977
in (32)–(36). Here, the investment types represent the conductor scenario-based stochastic model for the multistage joint expan-
capacities available for the construction or reinforcement of the sion planning of the distribution systems and the electric vehicle
feeders. charging stations. The EV charging demand was firstly deter-
mined using the Markov-based temporal SoC analysis of the EV
ij,a,b,u ,h ≤ 1
xcir ∀ij, u, h
driving patterns and charging demand. Then, the scenario ma-
a b
(37) trix was obtained using the heuristic moment matching method,
which guaranteed the explicit representation of the stochastic
xcir
ij,a,b,u ,h ≤1 ∀ij, a, b, h features and the correlation among the historical wind and pho-
u
tovoltaic generation, and conventional loads and EV demands.
(38)
The scenario matrix was employed to develop the stochastic ex-
u −1
pansion planning formulation, aiming at the minimization of the
ij,a,b,u ,h ≤ θi,j,a +
xcir ij,c,a,k ,h ∀ij, a, b, u, h
cir
xcir
investment and operational costs. The optimal expansion plan-
k =1 c
(39) ning solution determined the construction/reinforcement of sub-
u −1 stations, EVCSs and feeders, along with the placement of dis-
tributed generators and capacitor banks over the planning hori-
,h ≤ θij,b + ij,a,b,u ,h ∀ij, b, u, h
cir su b
yij,b,u xcir
k =1 a zon. Numerical results and detailed discussions are presented
(40) in the Part II of this two-paper series. The 18-bus distribution
system is used to test the developed model and its scalability is
cir
yij,b,u ,h ≤1 ∀ij, u, h
further assessed in the IEEE 123-bus distribution system.
b
(41) Further work will explore the prospects and challenges
brought by the integration of energy storage systems and traf-
4) Logical Constraints for the EVCSs: The set of constraints fic constraints in distribution systems. Research will also be
(42)–(46) represent the modeling of the EVCSs. The constraint carried out to investigate various distributed energy resource
(42) ensures that an EVCS can be placed only once at a bus over technologies, such as the combined-heat-and-power units and
the planning horizon, whereas the constraint (43) permits the gas boilers, to provide enabling solutions towards the realization
installation of chargers only if the associated EVCS has previ- of low-cost and low-carbon multi-energy distribution systems.
ously been placed. The constraint (44) ensures that the number
of chargers operating in each stage cannot surpass the number of
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matching scenario generation,” Comput. Optim. Appl., vol. 24, no. 2/3, Ali Ehsan received the B.Sc. degree in electrical en-
pp. 169–185, 2003. gineering from the University of Engineering and
[22] J. Li, L. Ye, Y. Zeng, and H. Wei, “A scenario-based robust transmission Technology Lahore, Lahore, Pakistan, in 2010, the
network expansion planning method for consideration of wind power M.Sc. degree in renewable energy engineering from
uncertainties,” CSEE J. Power Energy Syst., vol. 2, no. 1, pp. 11–18, 2016. Kingston University London, London, U.K., in 2012,
[23] A. Ehsan and Q. Yang, “Robust distribution system planning consider- and the Ph.D. degree from the College of Electrical
ing the uncertainties of renewable distributed generation and electricity Engineering, Zhejiang University, Hangzhou, China,
demand,” in Proc. IEEE Conf. Energy Internet Energy Syst. Integration, in 2019. From 2013 to 2015, he was a Lecturer with
Beijing, China, Nov. 2017, pp. 1–6. the Department of Electrical Engineering, COM-
[24] A. Ehsan, Q. Yang, and M. Cheng, “A scenario-based robust invest- SATS University Islamabad, Sahiwal, Pakistan. He
ment planning model for multi-type distributed generation under uncer- is currently a Research Associate with The Univer-
tainties,” IET Gener. Transmiss. Distrib., vol. 12, pp. 4426–4434, 2018, sity of Manchester, Manchester, U.K. His research interests include renewable
doi: 10.1049/iet-gtd.2018.5602. distributed generation, multi-energy microgrids, and planning and optimization
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tributed multi-type stochastic generation and battery storage in active
distribution networks,” IEEE Trans. Sustain. Energy, to be published,
doi: 10.1109/tste.2018.2873370.
[26] N. Banol Arias, A. Tabares, J. F. Franco, M. Lavorato, and R. Romero, Qiang Yang (M’03–SM’18) received the Ph.D. de-
“Robust joint expansion planning of electrical distribution systems and gree in electronic engineering and computer science
EV charging stations,” IEEE Trans. Sustain. Energy, vol. 9, no. 2, from the Queen Mary University of London, London,
pp. 884–894, Apr. 2018. U.K., in 2007. From 2007 to 2010, he was with the
[27] S. Sun, Q. Yang, and W. Yan, “A novel Markov-based temporal-SoC anal- Department of Electrical and Electronic Engineering,
ysis for characterizing PEV charging demand,” IEEE Trans. Ind. Inform., Imperial College London, London, U.K. He visited
vol. 14, no. 1, pp. 156–166, Jan. 2018. the University of British Columbia and the University
[28] A. Tabares, J. F. Franco, M. Lavorato, and M. J. Rider, “Multistage of Victoria Canada as a Visiting Scholar in 2015 and
long-term expansion planning of electrical distribution systems consid- 2016. He is currently a Full Professor with the Col-
ering multiple alternatives,” IEEE Trans. Power Syst., vol. 31, no. 3, lege of Electrical Engineering, Zhejiang University,
pp. 1900–1914, May 2016. Hangzhou, China. He has authored/coauthored more
[29] J. Lofberg, “YALMIP: A toolbox for modeling and optimization in MAT- than 170 technical papers, three books, 10 book chapters and applied for 50
LAB,” in Proc. IEEE Int. Conf. Comput. Aided Control Syst. Des., 2004, national patents. His research interests over the years include smart energy sys-
pp. 284–289. tems, intelligent control systems, and large-scale complex network modeling,
[30] IBM ILOG CPLEX, “CPLEX optimizer,” 2012. [Online]. Available: control, and optimization. He is the Senior Member of IET and China Computer
https://www.ibm.com/analytics/cplex-optimizer. Accessed on: Oct. 15, Federation.
2018.
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