AbstractâThis paper focuses on providing an automatic and efficient electric vehicles (EVs) charging management system. (CMS) by exploiting the benefits of ...
2015 IEEE International Conference on Data Science and Data Intensive Systems
Internet of Things for Electric Vehicle: An Improved Decentralized Charging Scheme Leehter Yao, Yu-Qiao Chen, Wei Hong Lim Department of Electrical Engineering, National Taipei University of Technology Taipei 10608, Taiwan
considerable attentions in the smart grid research. It is a network comprised by objects having identities, virtual personalities operating in smart spaces using intelligent interfaces to connect and communicate with the users, social, and environmental contexts [2]. The abilities of IoT to demonstrate the ubiquitous perception and the real-time interactive view in the smart grid system allows it to gather and act on energy and power related information in an automated fashion with the goal to improve the efficiency, reliability, and sustainability of the production and distribution of electricity. This paper focuses on the objective of providing an efficient and interactive CMS to carry out the charging load scheduling of large-scale EVs with the IoT technology.
Abstract—This paper focuses on providing an automatic and efficient electric vehicles (EVs) charging management system (CMS) by exploiting the benefits of Internet of Things (IoT) technology in offering the ubiquitous perception abilities and a real-time interactive view of the physical world by various sensors and radio devices. An improved decentralized charging scheme is also proposed to coordinate the charging of large-scale EVs in multiple residential buildings by leveraging the distributed optimization capability of alternating direction method of multiplier (ADMM). Extensive studies revealed that the proposed work outperforms two other compared decentralized methods by producing higher final mean state-ofcharge (SOC) levels to the connected EVs and incurring less electricity bill paid to the utility. Furthermore, the proposed charging scheme is proven better than the centralized approach because of its ability to consume lower communication overhead and offer better robustness in preserving the user privacy.
As for the charging load scheduling strategy, there are two main approaches, known as the centralized and decentralized charging schemes were reported in the literature [3]. The decentralized approaches are gaining more attentions in recent years than the centralized approach because of the following reasons: First, the decentralized approach is scalable to solve the large-scale EV charging problem due to the its ability decompose this high complexity problem into several less complex sub-problems, while the centralized approach tends to suffer with excessively high computational overhead when a significant amount of EV charging demands are encountered. Second, the decentralized approach has better robustness in preserving the user privacy because it only requires each EV to publicize their charging demands to the CMS during the scheduling process, rather than the private user information as requested by the centralized approach.
Keywords—Alternating direction method of multiplier (ADMM); charging management system (CMS); electric vehicle (EV); internet of things (IoT); smart grid
I. INTRODUCTION Both of the energy crisis and the environmental problems have threatened the sustainable development of human society. Billions of dollar were pledged to fund the research and development (R&D) activities of EVs years because this technology is promising for better energy conversion efficiencies and the reduction of greenhouse gasses emission, by displacing the energy demands from crude oil to electricity. Being an emerging load, the large-scale penetration of EV introduces the new electricity demands and this leads the occurrence of new peak loads to the existing power grid system. For instance, it is reported in [1] that 20% market penetration of EVs could increase the daily peak demand up to 35.8%. These additional charging loads are nontrivial and could be detrimental to the grid system if no EV charging management system (CMS) has been deployed.
Given the advantages offered by the decentralized approach, numerous works were proposed in recent years to solve the large-scale EV charging problems with different objectives. For instance, a decentralized charging strategy was proposed by Ma et al. [4] based on game theory to fill the load valley. The work of Gan et al. [5] required the price signal broadcasted by the utility to update the EV charging profiles iteratively. Wen et al. [6] aimed to maximize the EV user convenience by leveraging the capability of the alternating direction method of multiplier (ADMM) method to solve the charging selection problem in distributed manner. Another on-off based decentralized charging scheme is suggested by Zhan et al. [7], whereby a transition probability inspired by the Markov chain model is used to guide the shifting of charging loads. Inspired by the effectiveness of congestion pricing in the network traffic control researches, a distributed charging framework was proposed by Fan [8] to regulate the EV charging power based
The CMS is essential in mitigating the negative impacts of simultaneous EV charging by shifting these massive charging loads to other off-peak periods. Some notable mechanisms of the CMS include charging, metering and billing, scheduling, etc. In general, an effective CMS is highly automated, intelligent and interactive. It also needs high level information communication technology (ICT) support for information perception, aggregation, interaction and visualization. The Internet of Things (IoT) technology has recently acquired a 978-1-5090-0214-6/15 $31.00 © 2015 IEEE DOI 10.1109/DSDIS.2015.41
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on a load dependent price function and a parameter related to user’s willingness to pay. While the decentralized charging schemes reported in [6] delivered promising performances, a number of scopes for improvement could be observed. First, the charging schedules of [6] is determined by maximizing the user convenience expressed in terms of the state-of-charge (SOC) level of EV and the remaining charging time left. Although it is promising to satisfy the EV charging demands, the monetary expenses paid to the utility is not guarantee to be the minimum since the electricity price factor is not considered during the scheduling process. Second, the charging selection problem formulated in [6] is essentially a combinatorial optimization problem which is nontrivial to be solved because the decision variables to be optimized are the binary values. The on-off strategy employed in [6] tends to produce the suboptimal charging schedule which could either violate the power grid constraints or fail to fully utilize the available capacity allocated for EV charging.
Fig. 1. The proposed architecture of decentralized charging system for M residential buildings.
This paper aims to overcome the difficulties of [6] by proposing an improved decentralized charging scheme to tackle the large-scale EV charging problem involves with multiple residential buildings. The innovations employed to refine the work of [6] are described as follows. First, the proposed work attempts to modulate the EV charging power in continuous power instead of employs the on-off strategy to schedule the EV charging. The selection probability introduced in [6] is redefined by current work as the charging ratio with respect to the maximum charging power of EV. Under this new perspective, the EV charging problem could be formulated as a convex optimization problem, whereby the associated optimal charging schedule could be solved efficiently. The charging schedule with continuous charging power is also anticipated to be more promising for being able to fully utilize the available grid capacity without violating the grid constraints. Second, this paper considers the influences of both user convenience and electricity prices in solving the EV charging optimization problem. In contrast to [6], the proposed work offers the merits of being able to simultaneously maximize the user convenience level and minimize the electricity bill paid to the utility. Third, another parameter known as the membership parameter as inspired from [8] is included in deriving the user convenience. This enables the EV drives that willing to pay more can get more allocation of charging powers and thus meet the charging demand with shorter waiting time.
Fig. 2. IoT architecture for EV charging system
central CMS is connected with the M local CMS installed in each residential building according to Fig. 1. The local CMS of each i-th parking station is connected with Ni charging gateways and each of them is used to coordinate the EV charging of each household. The IoT architecture of EV employs the information sensing equipment coupled with the wired or wireless communications to implement the information extraction, transmission, and the scheduling for a EV charging system. From Fig. 2, it consists of three layers: physical layer, network layer, and application service layer. The description of each layer is provided as follows:
The rest of this paper is organized as follows. Section II describe the system model of multiple residential building and the IoT based EV charging architecture. This is followed by Section III which presents the formulation of the centralized EV charging scheduling problem. The employment of ADMM method in deriving the decentralized EV charging scheduling problem is demonstrated in Section IV. Section V presents the experimental settings and simulation results, and finally the conclusion are drawn in Section V.
• Physical layer: The information sensing equipment such as sensor, in-car terminals, and RFID tags are deployed in this layer. These equipment are used to collect different types of perception information such as battery status, EV identification, EV arrival and departure times, and etc. For instance, the charging gateway can acquire the EV battery status parameters from battery management system (BMS) through the CAN interface before the charging process is initiated. These perception information are then transmitted through the charging gateways to the network layer.
II. SYSTEM MODEL AND IOT ARCHITECTURE The system model of a decentralized charging system for the M residential buildings and the IoT based EV charging architecture are illustrated in Figs. 1 and 2, respectively. A
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• Network layer: Wired (e.g., power cable, RS-485) and wireless communications (e.g., Wifi, GPRS/3G/4G) are used to complete the perception information transmission between the components of EV charging network. The main concern of this layer includes the data routing and proactive information push mechanisms.
introduced in this paper to guide the charging power allocated of each active charging gateway.
A. User Convenience During the scheduling process, different EVs have different values charging parameters and this leads to different charging priorities. Intuitively, the active charging gateways connected by the EVs with higher charging priorities need to be allocated with more charging power and vice versa. Given this fact, the notion of user convenience is introduced to quantify the charging priority of each EV at any time step. Unlike [6], the attributes used to formulate the user convenience wnji of EV
• Application service layer: All perception information obtained from the network layer are stored, processed, and analyzed in this layer. For instance, the EV driving parameters uploaded by each charging gateway are stored in the database platform. Meanwhile, the charging scheduling process is performed at the application platform. The latest charging instructions could be transmitted to each charging gateway through the Ethernet.
connected to the ni-th charging gateway are the current SOC level of EV ( γ nji ), the remaining charging time ( Tnij = κ ndep − j ), i and the membership ranking ( Ξ ni = {high, medium, low} ).
A discrete-time system is used in this paper to approximate the continuous EV charging model. Let H and Ts be the total available time period for charging during a day and the interval lengths between two successive time steps, respectively. The number of time intervals for charging in one day is thus computed as J = H / Ts .
Mathematically, the user convenience of EV is computed as: wnji =
B. Preference on Electricity Price While it is essential to satisfy the EV charging demands by drawing as much charging power as possible to the connected EVs, it is economically desirable to minimize the monetary expenses by leveraging the real time pricing (RTP) scheme of electricity price. Intuitively, more charging powers should be drawn for EV charging when electricity prices are relatively low and vice versa. A new parameter ρ nji is thus introduced to
arrival and departure time steps of EV connected to the ni-th charging gateway. Different with [6], the charging power Pnij allocated to the EV connected to the ni-th charging gateway is semi-continuous value that can either be zero or take values between a threshold Pnthres and the maximum charging power Pnmax , i.e., Pnij ∈ 0 ∪ i i [ Pnthres , Pnmax ] . Let snthres be the minimum charging ratio used to i i i
quantify the preference of the ni-th active charging gateway on the electricity price α j at the j-th time step. Let
= snthres Pnmax , each charging gateway produce the threshold Pnthres i i i needs to determine a charging ratio snji in the range of[ snthres ,1] i to obtain the associated charging power Pni = s P
(1)
i
needs because they need to be charged as much as possible prior to their departures. Notably, the EVs with higher membership ranking are also given higher priority due to their willingness to pay for getting more power allocation.
as 1 if it is occupied by an EV and 0 for otherwise. Two and κ ndep are also used to denote the parameters known as κ narr i i
max ni
, ∀j ∈ [1, J ], ∀ni ∈{N i j δ nji = 1}, ∀i ∈ [1, M ]
From (1), the EVs with lower SOC have higher charging priority because more remaining battery level needs to be filled. The EVs with shorter Tnij also have more urgent charging
connection status of each ni-th charging gateway at the j-th time step for ∀ni = 1,..., N i and ∀j = 1,..., J . Notably, δ nji is set
j ni
γ nj Tnj i
Assume that each i-th residential building consists of Ni charging gateways to provide the EV charging service, where ∀i = 1,..., M . The binary variable δ nji is used to denote the
j
Ξ ni
αnmax = max{α j κnarr ≤ j ≤κndep} and αnmin = min{α j κnarr ≤ j ≤κndep} be the i
drawn.
i
i
i
i
i
maximum and minimum electricity prices perceived by the nith active charging gateway, the associated ρ nji is computed as:
III. CENTRALIZED CHARGING SCHEME
ρnj =
The centralized EV charging problem is first formulated in this section. Let the number of active charging gateway that are connected with EV at the i-th residential building is N i j ≤ N i for ∀j = 1,..., J , ∀ni = 1,..., N i , and ∀i = 1,..., M . The total active charging gateway occupied with EVs in the M
i
αnmax − α j , ∀j ∈[1, J ], ∀ni ∈{Ni j δ nj = 1}, ∀i ∈[1, M ] αnmax − α nmin i
i
i
(2)
i
From (2) that ρ nji returns a higher preference value when electricity price α j is low at the j-th time step and vice versa.
residential buildings are thus computed as N j = ¦ i =1 Ni j . M
C. Problem Formulation Recall that the EV charging problem of current work considers multiple optimization objectives, i.e., to maximize the charging power allocated to the connected EVs and minimize the electricity bill paid to utility. The objective function to be optimized at each j-th time step is formulated in
The EV charging problem considered in this paper aims to simultaneously maximize charging power allocated to each EVs and minimize the monetary expenses without violating the power constraints. Two criteria known as the user convenience and the preference of electricity price are
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(3), whereby the first term of aims to maximize the sum of user convenience, while the second term maximizes the sum of preference on electricity price. The decision variables to be optimized in (3) are the real-value charging ratios snji assigned
privacy because it requires the disclosure of private user information to the central CMS. The efficiency of the approach in solving the large scale charging problem is also degraded because these significant amount of EV charging demands could lead to the high problem dimensionality of (3) and the tremendous amounts of constraints (4)-(6).
≤ snji ≤ 1 . Given to the active charging gateways, where snthres i that the first and second terms of (3) are both linear, it is feasible to reduce the sum of ( wnji + ρ nji ) as a single term ϑnji .
IV. DECENTRALIZED CHARGING SCHEME
This implies that for each j-th time step, the amount of charging power allocated to each ni-th active charging gateway is dictated by either the user convenience or the preference on electricity prices. M
Ni j
M
N ij
M
Compared with the centralized approach, the decentralized charging scheme offers better scalability and robustness in preserving the user privacy. The decentralized approach also allows each charging gateway to locally adjust the charging powers in iterative manner without needing much intervention from the central CMS. In this paper, the alternating direction method of multiplier (ADMM) [9] is used to decompose the high dimensionality centralized charging problem into several sub-problems with low complexity because it does not impose the strict convexity condition of objective function. The improved decentralized charging scheme based on ADMM is formulated as follow.
Ni j
Ψ = ¦¦ w s + ¦¦ ρ s = ¦¦ ( wnji + ρ nji ) snji j
i =1 ni =1 M
j j ni ni
i =1 ni =1
j ni
j ni
i =1 ni =1
Ni j
= ¦¦ ϑnji snji i =1 ni =1
(3) The optimization constraints related to the power limits of charging gateway, local, and primary distribution transformers j are given in (4)-(6), respectively. Denote PTotal and ϕTotal as the capacity of primary distribution transformer to serve the area covering all M residential buildings and the proportion of available capacity used for EV charging at the j-th time step, respectively. Constraint (4) prevents the total charging load of all M residential buildings at any j-th time step to exceed the j available capacity ϕTotal PTotal . Constraint (5) is the local version
Denote the charging ratios of Nji active charging gateway in the i-th parking station as a vector form sij = [ s1j ,..., snji ,...sNj j ]T , i
where s ∈ ℜ j i
j
s j ∈ ℜ N .The available power capacities of primary and local distribution transformers for EV charging at the j-th time step j j j j T is denoted as Plimit = [ϕTotal Ptotal , ϕTotal ,1 Ptotal ,1 ,..., ϕTotal , M Ptotal , M ] , j where Plimit ∈ ℜ( M +1) . The power constraints of (4) and (5) can thus be represented in a matrix form as follow: j P j s j ≤ Plimit
(7)
j
The matrix P j ∈ ℜ( M +1)× N of (7) denotes the maximum charging power that can be drawn by each EV from the associated charging gateway and it is derived in (8) based on the architecture of distributed charging system illustrated in Fig. 1. A vector p ni ∈ ℜ( M +1) with two nonzero entries is
and exceed 1. Based on the maximum charging power Pnmax i aforementioned descriptions, the centralized EV charging optimization to be solved at each j-th scheduling period can therefore be formulated as: max
. The overall charging vector of all M parking
stations can thus be expressed as s j = [s1j ,..., sij ,...s Mj ]T , where
j of (4), where PTotal ,i and ϕTotal , i refer to the capacity of local distribution transformer for the i-th residential building and the proportion of available capacity for EV charging, respectively. Constraint (6) ensures that the charging power drawn from each ni-th active charging gateway cannot be lower than snthres of i
snj , ni =1,..., Nij ,i =1,..., M
Ni j
defined to denote each column of (8) for ∀ni ∈ N i j and ∀i ∈M .
Ψj
i
ªP11max « «P11max « Pj = « 0 « « # « «¬ 0 = ªp11 ¬
Subject to M
N ij
¦¦ s i =1 ni =1 Ni j
¦s ni =1
j ni
j ni
j Pnmax ≤ ϕTotal PTotal , ∀ni ∈ [1, Ni j ], ∀i ∈ [1, M ] (4) i
j Pnmax ≤ ϕTotal ∀ni ∈ [1, N i j ], ∀i ∈ [1, M ] , i PTotal , i , i
snthres ≤ snji ≤ 1, ∀ni ∈ [1, Ni j ], ∀i ∈ [1, M ] i
(5)
(6)
The centralized EV charging problem described in (3)-(6) is a convex optimization problem because the objective function (3) is concave and the constraints (4)-(6) are linear. While (3)(6) can be solved efficiently using the linear programming, this centralized approach tends to compromise the user
P12max " PNmax " PNmax " P1Mmax " PNmax j j j º 1 2 M » max 0 " 0 " 0 " 0 » " PN j 1 » " 0 P12max " PNmax " 0 " 0 » j 2 » % # % " 0 " 0 " 0 » » 0 " 0 " P1Mmax " PNmax " 0 j » M ¼ " p N j p12 " p N j " p1 j " p N j º M M ¼ 1 2
(8)
The ADMM form of (3) is formulated by introducing the auxiliary vector z nji = p ni snji ∈ ℜ( M +1) , denoting the charging demand of the ni-th active charging gateway in the i-th parking
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j , r . The vector p j , r +1 ∈ ℜ M +1 in (16) could be calculated by
station at the j-th time step. Meanwhile, the average charging demands of z j ∈ ℜ( M +1) and p j ∈ ℜ( M +1) are computed as:
pj =
M
1 Nj
zj =
Ni
¦¦ z i =1 ni =1
M
1 Nj
Ni
averaging the latest charging demands p ni snji, r +1 using (10). Finally, the updated value of j , r +1 in (17) is determined by
j
j ni
(9)
employing the updated primal variables ( s j , r +1 , z j , r +1 ) and the
j
¦¦ p i =1 ni =1
j ni ni
s
gradient ascent method to solve the dual problem of max Lρ (s j , z j , j ) . j
(10)
j − N j z j ) with non-negative real An indicator function I + (Plimit value is also defined in (11) to satisfy the power constraints of (4) and (5).
j limit
I + (P
j °0, if N j z j ≤ Plimit −N z )=® °¯∞, otherwise j
j
° § M Nij s j , r +1 := arg min ®− ¨ ¦¦ ϑnji snji ¨ sthres ≤ s j ≤1 ° ¯ © i =1 ni =1
j
(11)
j
N z
j ≤ Plimit
2
}
½° ¾ ¿°
snthres ≤ snji ≤ 1, ∀ni ∈ [1, Ni j ], ∀i ∈ [1, M ] i
(15) (16) (17)
At this stage, the s-minimization problem in (15) is not decomposable with respect to each active charging gateway due to the unknown value of p j .To overcome this difficulty, our work uses the previous states of each charging gateway (i.e., p ni snji, r ) to estimate p j . The state deviation of each active
· j j j ¸ − I + (Plimit − N z ) ¸ ¹
pj − z j = 0
charging gateway needs to be as small as possible for more accurate estimation of p j . For this reason, the estimation of
(12)
p j is formulated as a minimization problem as shown in (18),
For the ease of derivation using the procedures of [9], the objective function (12) can be equivalently expressed as: j
j
2
j , r +1 := j , r + (p j , r +1 − z j , r +1 )
Subject to
§ M Ni j j − min ¨ ¦¦ ϑni sni ¨ i =1 n =1 s j ,z j i ©
{
z j , r +1 := arg min z j − p j , r +1 − j , r
Based on (9)-(11), the ADMM form of (3) is formulated as:
§ M Ni j j max ϑni sni ¨ j j ¨ ¦¦ s ,z © i =1 ni =1
· ρ j j ,r j ,r ¸+ p − z + ¸ 2 ¹
where p ni snji is defined as the current state of each ni-th active charging gateway for ∀ni ∈ N i j and ∀i ∈ M .
· j j j ¸ + I + (Plimit − N z ) ¸ ¹
M
Ni j
min ¦¦ p ni snji − p ni snji, r
2
(18)
i =1 ni =1
Subject to
The solution of (18) can be obtained if the condition of p ni snji − p j = p ni snji, r − p j , r is fulfilled. The unknown value of
pj − z j = 0 snthres ≤ snji ≤ 1, ∀ni ∈ [1, Ni j ], ∀i ∈ [1, M ] i
(13)
p j can therefore be estimated as:
M +1
A Lagrange multiplier vector ∈ ℜ and a non-negative scalar penalty parameter ρ > 0 are subsequently introduced in (14) to derive the augmented Lagrangian Lρ of (13) for solving the EV charging problem in decentralized manner. j
§ M Ni Lρ (s j , z j , j ) = − ¨ ¦¦ ϑnji snji ¨ i =1 n =1 i © j
+
ρ
2
· j − N jz j) ¸ + I + (Plimit ¸ ¹ p − z + j
j
j 2
−
ρ 2
p j = p ni snji − p ni snji, r + p j , r
(19)
By substituting (19) into (15), the s-minimization problem can be implemented separately in parallel at each ADMM iteration to update the charging ratio snji, r +1 of each ni-th individual active charging gateway as follow:
(14)
{
snji,r +1 := argmin −ϑnji snji +
j 2
thres
s
≤snj i
≤1
ρ 2
2½ pni snji − pni snji,r + p j ,r − z j ,r + j,r ¾ ¿
(20)
Let (p j , r − z j , r + j , r ) in (20) to be simplified as q j , r ∈ ℜ M +1 ,
To compute the near-optimal charging schedules of each charging gateway for each j-th time step, the ADMM method is employed to update the primal variables ( s j , z j ) and the
the closed form solution χ nji, r +1 of each ni-th active charging gateway at each (r+1)-th ADMM iteration can be determined from (21) by finding the stationary point of snji in (20):
j
scaled dual variable alternatively through (15)-(17), where r represents the iteration index of ADMM. The updated value of s j , r +1 in (15) is obtained by minimizing (14) based on the previous values of z j , r and j , r . Similarly, (16) states that the
χ nj , r +1 = i
ρ pTn (p n snj , r − q j , r ) + ϑnj i
i
i
i
ρ pTn p n i
latest z j , r +1 is computed from the updated s j , r +1 and the previous
(21)
i
The closed form solution χ nji, r +1 obtained from (21) denotes
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the updated charging ratio of each ni-th active charging gateway. It is possible violate the power limit of charging gateway as described in (6) if no restriction is imposed. Since the charging power drawn from each ni-th active charging = snthres Pnmax and exceed gateway cannot be lower than Pnthres i i i
Pnmax , the actual charging ratio snji, r +1 of each active charging i gateway at the (r+1)-th iteration of ADMM is thus bounded as:
snji, r +1
0, < χ nji, r +1 snthres i °° j , r +1 = ® χ ni , snthres ≤ χ nji, r +1 ≤ 1 i ° χ nji, r +1 > 1 °¯1,
(22)
Meanwhile, the global and local aggregated charging demands stored in the vector z j , r +1 are updated by taking the minimum j / N j ) and values between the average charging demands (Plimit
Fig. 3. The communication structure of the proposed decentralized charging scheme.
the stationary point of (18), i.e., (p j , r +1 + j , r ) as follow: j z j , r +1 := min{Plimit / N j , p j , r +1 + j , r }
V. (23)
The communication structure of the proposed decentralized charging scheme is illustrated in Fig. 3 and the associated implementation is described as follow:
A. Simulation Settings In this paper, the sampling length of Ts = 15 minutes is set. The 24-hour baseload curve for a residential distribution network which consists of M residential buildings were generated based on the smart meter data provided by the Réseau de transport d'électricité (RTE) in France [10].
1) At each j-th scheduling period, the ϑ term of each EV is j ni
computed using (1) and (2). The primal variable vector z j and the dual variable vector j are also initialized. 2) At each r-th iteration of ADMM, the updated charging ratio of each active charging gateway snji, r +1 is computed
Three types of EVs with different battery capacities, i.e., 16kWh, 24kWh, and 32kWh, are considered and the associated proportions are set as 30%, 50%, and 20% of the total EVs, respectively. All connected EVs are charged with the normal charge mode and thus the maximum charging power drawn are assumed to be 7 kW. The minimum charging ratio snthres of each i
using (21). The updated charging demand snji, r +1 Pnmax is i reported by each charging gateway to the associated local CMS installed in each i-th parking station. The average charging demand p j , r +1
= 1/ Ni j ¦ n i=1 p ni snji, r +1 Nj
i
PERFORMANCE EVALUATION
Extensive simulations are conducted to evaluate the performance of the proposed work. The simulation settings are first described, followed by the simulation results.
EV is set as 0.2. The initial SOC of each EV is randomly generated from a uniform distribution in the intervals of 0.1 to 0.5. The Gaussian model is used to model the plug-in and plugout times of the EVs. Specifically, the EV arrival times are generated from a normal distribution centered at μ = 6.00PM with a standard deviation of σ = 1 hour, whereas the departure time of EV follows a normal distribution with μ = 6.00AM and σ = 2 hours.
i
of each i-th parking station is computed by the respective local CMS and then submitted to the central CMS. 3) Based on the average charging demands p j , r +1 received i
from the M local CMSs, the central CMS computes the vector p j , r +1 using (12). Both vectors of z j , r +1 and j , r +1 are also updated using (25) and (19), respectively. 4) The control signal vector q j , r +1 := p j , r +1 − z j , r +1 + j , r +1 , is computed and broadcasted by the central CMS to each local CMS, followed by the active charging gateways, to determine the appropriate charging power ratio allocated to each connected vehicle. 5) The charging schedules of each connected EV is revised based on the control signal by repeating steps 2) to 4) until the termination condition of ADMM is met. A few tens of iterations is sufficient for ADMM to achieve the reasonable good solutions according to [9]. 6) Repeat steps 1) to 5) for each j-th scheduling period until the J-th time step is reached.
Two test cases are considered in the following simulation studies to evaluate the scalability of the proposed work, i.e., (a) the scheduling of 2,000 EVs randomly partitioned into M = 40 residential buildings and (b) the scheduling of 5,000 EVs randomly partitioned into M = 100 residential buildings. B. Performance Comparisons The scheduling capability of the proposed decentralized ADMM charging scheme is compared with: (a) decentralized ADMM charging scheme with binary decision variable without considering the preference on electricity price (ADMM-1) [6], (b) decentralized ADMM charging scheme with continuous decision variable without considering the
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preference on electricity price (ADMM-2), and (c) centralized linear programming charging scheme with continuous decision variable without considering the preference on electricity price (LP). All compared methods are evaluated through the Monte-Carlo simulation with 103 trials. The simulation results are elaborated as follows. While EV is fundamentally used as a transportation tool, one main concern would be the travelling distance offered after the vehicle is plugged-out from the charging gateway. Given this fact, the final mean SOC level ( γ f ) of EVs when they leave is employed as a useful metric to evaluate this criteria. The values of γ f produced by the ADMM-1, ADMM-2, ADMM, and LP in scheduling the 2,000 and 5,000 EVs are presented in Tables I and II, respectively. The values of γ f gained by the EVs with high, medium, and low membership rankings are also summarized in these two tables. Simulation results revealʳ that the γ f values produced by all compared methods are slightly decreased with the increasing of EVs. Among the three compared decentralized charging scheme, the proposed work designated as ADMM delivers the best performance because it produces the highest overall γ f in scheduling the charging of 2,000 and 5,000 EVs, followed by the ADMM-1 and ADMM-2. Although all decentralized methods produce the comparable γ f values in charging the EVs with high and medium membership rankings, ADMM demonstrates the most significant improvement on the γ f values gained by the EVs with low membership ranking. On the other hand, the centralized LP charging scheme outperforms all decentralized methods by producing higher γ f values for all categories of EVs. This observation is anticipated because the central CMS of LP method has the complete information of all connected EVs, thus can better utilize the available capacity of power system during the scheduling process.
Fig. 4. Charging load arrangements with all compared methods (2,000 EVs).
Apart from γ f , the normalized electricity bill (in NTD/kW) incurred by the ADMM, ADMM-1, ADMM-2, and LP methods in scheduling the charging of 2,000 and 5,000 EVs are also computed and presented in Table III to evaluate the financial feasibility of each compared methods. Accordingly, ADMM is the most economically feasible charging scheme for incurring the least monetary expenses during the scheduling process, followed by the LP, ADMM-1, and ADMM-2 methods. The charging load profiles produced by all compared charging schemes in scheduling the 2,000 EVs are presented in Fig. 4 to justify how the charging load arrangement with ADMM-1, ADMM-2, ADMM, and LP methods affect the normalized electricity bills. The charging load profiles produced by both ADMM-1 and ADMM-2 are insensitive to the electricity price variable because these two methods schedule the EV charging based only the user convenience defined in (1). The charging load peaks of the ADMM-1 and ADMM-2 concentrate at the peak departure time steps of EVs (i.e., around j = 60 to 70), which coincidently have more expensive electricity prices. This explains the high normalized electricity bills incurred by these two methods. In contrary, the charging behavior of ADMM is induced by both of the user convenience and preference on electricity prices defined in (1) and (2), respectively. Fig. 6 reveals that the ADMM method is able to move majority of the charging loads into the time steps with cheaper electricity prices. This mechanism is effective in reducing the excessive charging at the times when electricity prices are high, and thus incurs lower monetary expenses. Although the load profiles produced by the LP and ADMM methods share some similarities at the earlier time steps, the charging behavior of the LP is benefited through the capability of its central CMS to fully utilize the available capacity instead of the lower electricity prices. The insensitive of LP towards the variation of electricity prices is proven at the time steps around j = 50, when the electricity prices are not financially favorable for charging. The charging loads of ADMM are significantly reduced in response to the expensive electricity prices at these scheduling periods, whereas no notable charging load reductions have been demonstrated by the LP method.
TABLE I COMPARISON OF FINAL MEAN SOC LEVELS (2,000 EVS) Membership Ranking High Medium Low Overall
γ ADMM-1 0.9458 0.9316 0.8886 0.9088
f
ADMM-2 0.9334 0.9215 0.8091 0.8581
ADMM 0.9319 0.9296 0.9296 0.9164
LP 0.9408 0.9406 0.9413 0.9410
TABLE II COMPARISON OF FINAL MEAN SOC LEVELS (5,000 EVS) Membership Ranking High Medium Low Overall
γ ADMM-1 0.9468 0.9232 0.8775 0.9006
ADMM-2 0.9365 0.9124 0.8005 0.8523
f
ADMM 0.9356 0.9250 0.8931 0.9084
LP 0.9412 0.9415 0.9405 0.9409
TABLE III COMPARISON OF NORMALIZED ELECTRICITY BILLS Normalized Electricity Bill (NTD/kW) EV Numbers ADMM-1 ADMM-2 ADMM LP 2,000 3.56 3.65 3.40 3.41 5,000 3.59 3.66 3.45 3.47
The ability of all compared methods to preserve the global schedulable load constraint bounded by the central CMS in (4) is also examined. The normalized load patterns produced by
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VI. CONCLUSION
the ADMM-1, ADMM-2, ADMM, and LP charging schemes in scheduling the 5,000 EVs are illustrated in Fig. 5. It is observed that the charging load profiles produced by all compared methods did not violate the global constraint. Furthermore, Fig. 5 also reveals that both of the ADMM and LP charging schemes demonstrate the more notable valley filling characteristic on the original base load. Apart from the global constraint, it is also essential to investigate if any of the compared charging schemes violate the local schedulable load constraint bounded by the local CMS installed in each residential building. A random snapshot that illustrates the total local constraints and the total charging loads produced by the four compared methods in 20 randomly selected residential building in scheduling the 5,000 EVs is depicted in Fig. 6. Accordingly, the total charging loads produced by ADMM-1 on the parking stations 11, 12 and 17 exceed the local schedulable load constraints and this undesirable behavior could be detrimental to the power system. Compared with the three other compared methods, ADMM-1 is prone to overload the local power constraints because it employs the probabilistic selection mechanism [6] to randomly decide which EVs should be charged with the maximum charging power.
Given the environmentally friendly and cost effective nature of EV, this technology is anticipated to revolutionize the personal transport section in the coming decades. The development of an EV charging management system (CMS) thus becomes necessary to coordinate these massive charging demands. The abilities of IoT to demonstrate the ubiquitous perception and the real-time interactive view in the smart grid system allows it to gather and act on the EV and power related information in an automated fashion with the goal to develop an effective, highly automated, intelligent, and interactive CMS. An improved ADMM-based decentralized charging scheme is also developed in this paper to coordinate the simultaneous charging of large-scale EVs in multiple residential buildings. Different with the previous reported work, the charging behavior of the proposed method is induced by three factors, namely the user convenience, variation of electricity prices, and the willingness of EV driver to pay. Extensive simulation studies reveal that the proposed decentralized charging scheme demonstrates the promising charging performance by producing higher final mean SOC levels and incurring lower electricity bills. ACKNOWLEDGMENT The authors would like to thank the editor and anonymous reviewers for their detailed and constructive comments that help us to enhance the quality of this work. REFERENCES [1]
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Fig. 5. The normalized load curves for 5,000 EVs.
Fig. 6. A random snapshot of local load demands in 20 selected parking station in scheduling 5,000 EVs.
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