VANET Based Online Charging Strategy for ... - Semantic Scholar
VANET Based Online Charging Strategy for Electric Vehicles Miao Wang∗ , Hao Liang∗ , Ruilong Deng†∗ , Ran Zhang∗ , Xuemin (Sherman) Shen∗ ,
∗ Department † State
of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China
Abstract—An online charging strategy is an efficient approach to provide charging plans for electric vehicles (EVs) from a global point of view, aiming to improve energy efficiency while avoiding overloading of an electric power system. However, designing an efficient online charging strategy to achieve optimal energy utilization remains a challenging problem, especially when the coordinated behaviors of both EVs and charging stations are taken into consideration. In this paper, we first introduce an intelligent power distribution system which utilizes vehicular adhoc networks (VANETs) to enable communication among EVs on roads, road-side units (RSUs), and a vehicle-traffic server. Then, we propose a globally optimal online EV charging strategy, which not only improves energy utilization of the whole system but also prevents charging stations from overloading, which may cause a voltage drop in the power distribution system. Lagrange duality optimization techniques are exploited to address the associated optimal EV charging problem. The performance of our proposed strategy is evaluated by extensive simulations, and the results are compared with that of the traditional autonomous offline charging strategy.
I. I NTRODUCTION Electric vehicles (EVs), as a crucial component of a sustainable and environmentally-friendly transportation system, have received considerable attention in many countries across the world. By adopting EVs into the transport sector, conventional energy consumption can be significantly lessened, so can environmental pollution (e.g., greenhouse gas emissions). For instance, battery-powered EVs, which completely depend on rechargeable batteries and produce no emissions, have the protential to cut down overall emissions from the transport sector by 70% [1]. According to the Electric Power Research Institute (EPRI), the EV penetration level can reach 35%, 51%, and 62% by 2020, 2030, and 2050, respectively [2]. However, the widespread implementation of EVs into a transportation system would lead to EV charging problems. Much research has been conduct on designing EV charging profiles for individual EVs, but conventional charging strategies [3]–[9] have not fully resolved the overloading problems of charging stations; on the contrary, the conventional approaches still face a number of challenges. Among them, one particular research challenge to our field of interest is to obtain real-time EV traffic information and electric load information and to use the collected information for global EV charging planning and charging overload avoidance. Thanks to the emergence of vehicular ad-hoc networks (VANETs), the challenge above can have a promising res-
olution through equipping transportation systems with enhanced functionalities. Specifically, VANETs support both vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications [10]–[13], enabling efficient information collection/reporting of traffic updates from/to neighboring vehicle nodes as well as road-side units (RSUs). As a result, the collected real-time traffic information can be utilized for traffic flow management [14], individualized vehicle path planning [15], vehicle localization [16], etc. Nevertheless, how to accomplish the globally optimal EV charging functionality for individual vehicles with the avoidance of overload charging is still an unsolved problem. To be specific, it is still unclear (1) how to efficiently and reliably transmit real-time information of traffic statistics and electric loads in order to guide vehicles to perform charging planning decisions in an online fashion; and (2) how to perform globally optimal online EV charging functionalities based on the above collected EV-traffic and electric load information. In this work, to address the challenge, we integrate VANETs into a power distribution system and propose an online globally optimal EV charging strategy to avoid overloading of charging stations. Under the strategy, a vehicle-traffic server is in charge of collecting real-time information and doing EV charging planning from a global perspective, rather than doing the charging planning in an individual offline charging planner installed in each vehicle which makes the decision in an uncoordinated manner. Then, the centralized EV charging decisions are further delivered to EVs in need of charging via V2V and V2I communications. Our centralized EV charging strategy can improve energy utilization from a global point of view as well as prevent the overloading of the power distribution system. The contributions of this paper are fourfold: •
•
first, we propose a VANET-assisted power distribution system framework with the enhanced functionalities of online EV charging planning; specifically, VANETs enable efficient communication between vehicles and RSUs to deliver useful information for EV charging planning in a real-time manner; second, we design an online globally optimal EV charging strategy to improve the overall energy utilization. Much more than this, with our proposed EV charging strategy, a vehicle intelligently avoids from overloading charging stations using the received charging decision
from a vehicle-traffic server; third, Lagrange duality optimization techniques are exploited to solve the optimization problem corresponding to the proposed EV charging strategy; and • finally, we carry out extensive simulations to validate the effectiveness and efficiency of our proposed EV charging strategy. Simulation results confirm that our proposed EV charging algorithm is able to find alternative EV charging decisions to bypass heavily-loaded charging stations in a timely, efficient and globally coordinated way. The remainder of the paper is organized as follows: Section II provides an overview of the network architecture. In Section III, the proposed EV charging strategy is presented. Section IV demonstrates the performance of the proposed strategy by simulations. Section V concludes this paper. •
II. N ETWORK A RCHITECTURE Aiming to provide an online EV charging strategy for EVs from a global perspective, we introduce a VANETenhanced power distribution system architecture to efficiently perform centralized EV charging control, followed by a power distribution system model to explain the detailed constraints of EV charging in a corresponding power distribution system. A. VANET-Enhanced Power Distribution System Architecture Fig. 1 shows the components of the architecture in a considered VANET-enhanced power distribution system, consisting of four charging stations (i.e., parking lots along the roads), a vehicle-traffic server, access points on road sides (i.e., RSUs), and electric vehicles. A power distribution system, including a basis electric supplying bus, supports charging for all EVs in parking lots. Based on power flow of electric supplying buses, the voltage at each charging station for a certain time duration in the power system can be estimated. For example, a voltage at one charging station is lower during a peak-load time duration (e.g., from 7pm to 9pm) than a voltage in an off-peak duration. The voltage can decide how much load a bus can support, i.e., its capacity. Then, the capacity limits of the maximal power supplied for each charging station can be obtained and delivered to the vehicle-traffic server based on wired communication. Furthermore, a set R of RSUs are deployed in the network. RSUs, also wired connected to the vehicle-traffic server, can obtain and relay the charging decisions to individual EVs in need of charging in a multi-hop manner based on DedicatedShort-Range-Communication (DSRC) protocol [17]. Here, DSRC protocol supports both RSU-to-vehicle (R2V) communications and vehicle-to-vehicle (V2V) transmissions. On the other hand, based on V2V and V2R communications, EV traffic flow information can be collected and shared among RSUs. Consider that a large number of EVs V move around in the area following map-based pathes; and within a certain transmission range these EVs can communicate with each other or RSUs. As soon as an EV moving on a road receives a charging decision from either neighboring EV relays or an
Vehicle-Traffic Sever R2V R2V
Wired connected
RSU Wired connected
RSU
V2V
: Parking lots, i.e., Charging stations : Wired connected : R2V communication : V2V communication
Fig. 1: A VANET-enhanced power distribution system.
RSU directly, that EV moves to a particular charging station following the received charging decision. Only one type of EVs is considered in this work, namely electric taxis, which are constantly in-motion most of the time and likely in need of charging at any time. When individual electric taxis require charging, they would be dispatched to particular charging stations using Global Positioning System (GPS). Note that a GPS device is supposed to be equipped on each EV which has ordered the service of shortest paths. With the collected estimated capacities of all charging stations and real-time EV traffic information, the vehicle-traffic server is capable of performing online charging strategies to provide globally optimized charging decisions for EVs in need of charging. Note that the detailed technologies of real-time EV traffic information collection are not discussed, but can be referred to in [18]. Therefore, as shown in Fig. 1, communications in the considered VANET-enhanced power distribution system can be divided into three layers: wired communication between charging stations and a vehicle-traffic server, wired communication between a vehicle-traffic server and RSUs, and wireless V2R/R2V and V2V communications based on DSRC protocol. To disseminate decisions as quickly as possible among vehicles until the decisions reach the destined EVs, similar to [18], the EVs with large mobility differentiation from the source EV, (i.e., the first EV receiving the decisions from an RSU), are responsible for relaying the decisions based on multi-hop transmissions within a certain decision lifetime, e.g., through a downlink, i.e., a server - an RSU/vehicle relay - the vehicle in need of charging. That is, the EVs whose mobility characteristics (i.e., moving direction and velocity) are different from the source EV beyond a threshold are selected as relays. Based on this forwarding scheme: i) a decision can be delivered towards destination EVs as efficiently as possible, thus reducing transmission delay; ii) forwarding collisions can be reduced due to strategically selected relaying EVs; and iii) the delivery ratio of decisions can be guaranteed due to multiple EVs forwarding.
B. Power Distribution System Model In order to implement charging control for EVs in the VANET-enhanced power distribution system, there exists relationships among power flow on the feeders (i.e., buses), the bus voltages and phases, and the load demand (i.e., EV charging demand). That is, a power flow analysis including voltage deviations and power losses as well as the number of customers, should be performed to facilitate the centralized online charging strategy for EVs. In the following, a power distribution system model is described aiming to estimate the electric-supply capability (i.e., capacity) of individual buses to propose a centralized EV charging strategy. Based on the network architecture as shown in Fig. 1, consider a power distribution system which is an N -bus system as depicted in Fig. 2(a), where N denotes the set of buses in the system. Take N = 12 as an example. The equivalent power distribution system model is shown in Fig. 2(b). The power is supplied through the traditional substation at Bus0 . Four EV charging stations are located at Bus2 , Bus6 , Bus9 and Bus12 , respectively. An EV charging station can impose a certain maximum load to the corresponding connected bus according to the voltage limits. For instance, consider one EV charging station located at Bus2 can accommodate 1000 standard EVs for simultaneous charging; each EV imposes a maximum electrical load of 4kW on the bus, which makes up for a total of a maximum additional load of 4M W at Bus2 if all EVs had with the same charging capabilities. In this paper, it is considered that each EV will be connected to the network via a standard single-phase Alternating-Current (AC) connection. Although the concept of vehicle-to-grid for local system exists [8], bi-directional flow of electricity or the directional flow from an EV battery to the grid is left for our further work. To summarize this section, based on the defined network architecture and established power distribution system model, the proposed online EV charging framework above is exploited to: a) collect the estimated voltage and power supply information at each bus in the power distribution system; b) transmit all the collected information to the vehicle-traffic server; c) do information fusion and work out the charging decisions for EVs in the vehicle-traffic server; and d) send the charging decisions back to the individual EVs in need of charging. III. C ENTRALIZED O NLINE EV
CHARGING
S TRATEGY
In this section, we first present the power flow equations in the predefined power distribution system. Based on the power flow equations, a voltage profile can be estimated for calculating the maximal loading at each bus and the relationship among loading capacities of different buses. Finally, an optimization problem is formulated to maximize the overall energy utilization while preventing system overloading. A. Power Flow Equation The power demand-supply balance on a bus Busi (i ∈ N ), at hour k, is calculated as
Bus1
V0
V1
V2
Bus3
Bus4
Bus5
V6
Bus2
Bus7
Bus8
V9
Pload 3
Pload 2
Pload 1 Vehicle Parking Lot (Charging Station)
Bus10 Bus11 V12 Bus12
Bus9
Bus6
Pload 4
... ...
(a) Illustrated Power system model. Bus1
V0
V1
V2
Bus3
Bus4
Bus2
Bus5 Bus7 V Bus6
Bus8
V9 Bus9
6
Pload 1
Bus10 Bus11 V12 Bus12
Pload 3
Pload 2
Pload 4
(b) Equivalent Power system model.
Fig. 2: Power distribution system model.
Vi ,k Pij ,k
Rij + jX ij
V j ,k
Qij ,k Fig. 3: The relationship between voltages and active (reactive) power flow in a 2-bus system.
P i,k − P Di,k − P chi,k =
N ∑ [Vi,k Vj,k Yi,j j=1
· cos(θi,j + δj,k − δi,k )]
(1)
where P i,k is the active power injected into the system at Busi at hour k; P Di,k is the active power demand at Busi at hour k; P chi,k , the active power load introduced by the charging of EVs batteries at Busi at hour k, is a continuous variable, determined from the given charging solution; Vi,k and Vj,k are voltages at the points of Busi and Busj at hour k, and j ∈ N ; Yi,j is the admittance of line i-j; δi,k and δj,k are the voltage phases of Busi and Busj at hour k; and θi,j is the corresponding angle. Note that these above variables are originally defined in the power flow analysis. Voltage Drop Estimation Given the power injected by the generation buses, voltage drops between generation buses and demand buses at hour k, e.g., Vi,k and Vj,k respectively, as depicted in Fig. 3, can be written as Vi,k − Vj,k =
Pij,k · Rij + Qij,k · Xij Vj,k
(2)
where Pij,k and Qij,k are the active and reactive power flow from Busi to Busj at hour k. R + jX is the impedance of feeder line i-j. And these variables are used for power flow analysis in a power system as well. In per unit, (2) is usually approximated in the power flow analysis as [19] Vi,k − Vj,k = Pij,k · Rij + Qij,k · Xij .
(3)
Take a summation on both sides of (3) over all bus pairs, we
can get V12,k in Fig. 2(b) V12,k = V0,k −
11 ∑
(Pij,k · ri + Qij,k · xi ).
(4)
i=0
B. Network Sensitivity: Voltage versus Load Based on the analysis of power flow in the system, voltages and the power supply ability of the points of buses can be obtained. Subject to the loading of EVs, the voltage of one bus can decrease with the increased load [19]. However, voltages of points of buses should fluctuate within a certain range. If voltage sags out of thresholds at points of buses, they cannot be corrected efficiently by injecting reactive power. In other words, voltage magnitudes at each bus (e.g., Busj ) at hour k, are constrained by their respective upper and lower limits min max Vj,k ≤ Vj,k ≤ Vj,k . To keep the voltage within a certain range, it is efficient to reduce the load or to inject an active power. Therefore, an additional load conversely determines a change in voltage and loading levels at all the points of demand buses, and there exists a tradeoff between voltages and load sensitivities. Load-Capacity Estimation: In our work, load sensitivity valuing for the voltage and loading assigned to one bus is the summation of all voltages and loading sensitivities at the charging points of EVs on the feeder. This takes account of the impact that multiple EV loads, charging simultaneously, can be served by a particular demand bus. With a given charging rate, the sensitivity value is used in conjunction with the EV charging voltage and served loading measurements at each time to determine an optimal charging number of EVs. For each EV v (∈ V), consider the EV charger active power constraint is as max P chmin vj ,k ≤ P chvj ,k ≤ P chvj ,k
P chmin vj ,k
(5)
P chmax vj ,k
where and are predefined charger active power constraints of continuous charging power P chvj ,k by Busj at hour k. And the total charging active power during a period is limited by the EV battery capacity, i.e., init max Pv,k + P chvj ,k ≤ Cbattery
EV charging-related loading is given, e.g., heating power supplying to the resident. Then, the total power supplying to EV charging stations can be calculated; furthermore the power supplied to individual charging station has a reciprocal and linearly relationship with other charging stations. Proof: For all buses, voltages should be no less than the minimal required voltage Vmin , e.g., Vmin = 0.9 per unit voltage [20]. For instance, from (4), the lowest voltage is at Bus12 , i.e., V12,k . Then, V12,k = V0,k −
11 ∑
(Pij,k · ri + Qij,k · xi ) ≥ Vmin .
(9)
i=0
Namely, 11 ∑
(Pij,k · ri + Qij,k · xi ) ≤ V0,k − Vmin .
(10)
i=0
In addition, we denote jj the sorted number of the buses which are without EV loading, and JJ is the set of these buses jj ∈ JJ(∈ N ); we consider jw being the sorted number of the buses with EV loading, and JW is the set of those buses jw ∈ JW (∈ N ). Then, (10) can be represented by ∑
(Pjj,k rjj + Qjj,k xjj ) +
∑
jw−1 ∑
(Pl,k rl + Ql,k xl )
jw∈JW l=0
jj∈JJ
≤ V0,k − Vmin .
(11) Consider the loads of the buses which are without EV loading are known as a constant, ∑
jw−1 ∑
(Pl,k · rl − Ql,k · xl ) ∑ (Pjj,k · rjj − Qjj,k · xjj ). ≤ V0,k − Vmin −
jw∈JW l=0
(12)
jj∈JJ
The inequality (12) implies that the summation of power supplying to EV charging stations is related to the locations of charging stations and the total number of charging stations.
(6)
init where Pv,k is the initial active power stored in EV v at hour k. And, ∑ P chj,k = P chvj ,k (7)
C. Optimization Objectives
v∈V
where P chvj ,k is non-negative when vehicle v is served by the certain charging station Busj at hour k, otherwise 0. The capacity of loading at Busj at hour k is defined as P chmax j,k , P chj,k ≤ P chmax j,k .
(8)
Furthermore, we give the relationship among the loadcapacities of buses in Theorem 1, and the proof is given based on power flow analysis in the power system. Theorem 1: (Linearly Reciprocal-Related Load-Capacities of Buses) Consider the total supplied power on one power supplying bus is constant, and the power demand for non-
Once the vehicle-traffic server receives the collected estimated capacities of all charging stations from the power system, charging decisions are operated by the vehicle-traffic server to guide EVs in need of charging and balance EV charging cost evenly in the whole network, based on real-time EV traffic information. Let χ(.) be a non-decreasing function on the charging active power for EVs on one charging bus at hour k. Then, our objective is to maximize the overall energy utilization with the guarantee of power system stability. The overall utilization problem is given as follows
∑∑
max
k j P chmin vj ,k ≤
s.t.
χ(
∑
Then, let Lagrangian dual function D(λv , ιv , γk ) be the maximum value of Lagrangian L(.) over P chvj ,k .
v∈V P chvj ,k )
D(λv , ιv , γk ) ∑ k ∑ init max D (λv , γk ) + λv [Pv,k − Cbattery ] v k ∑ init + ιv [Pv,k − 0].
P chvj ,k ≤ P chmax vj ,k ,
=
∀v ∈ V, ∀j ∈ JW, ∀k; ∑ ∑ init max 0 < Pv,k + ( P chvj ,k − pkcons ) ≤ Cbattery , j
k
j
P chj,k
To minimize the Lagrangian dual function over dual variables, λv , ιv , and γk , we get
∀v ∈ V; k ≤ Ptotal , ∀j ∈ JW, ∀k
min D(λv , ιv , γk )
(13) where pkcons is the average power cost for each individual k vehicle at hour k. Ptotal is defined as the supplying power upper bound of the whole power system at hour k, which can be obtained from (12). The optimization problem (13) can be solved by applying Lagrange Duality [21] techniques. The basic idea is to take the constraints of (13) into account by argumenting the objective function with a weighted sum of the constraint functions. We define the Lagrangian L(.) associated with the problem (13) as L(P chvj ,k ) ∑∑ ∑ ∑ ∑∑ k χ( P chvj ,k ) + γk [ P chvj ,k − Ptotal ] v v j j k k ∑ ∑ ∑ init max + ( P chvj ,k − pkcons ) − Cbattery ] + λv [Pv,k v j k ∑ ∑ ∑ init + ( P chvj ,k − pkcons ) − 0]. + ιv [Pv,k
=
v
k
j
we refer to γk as the Lagrange ∑ multiplierk associated with the k th inequality constraint P chj,k ≤ Ptotal . The vectors j
{λv }, {ιv }, and {γk } are called dual variables or Lagrange multiplier vectors associated with the problem (13). Rearranging the equation (14), it can be expressed as L(P chv ,k ) ∑ ∑ ∑ j∑ ∑ = { χ( P chvj ,k ) + λv ( P chvj ,k − pkcons ) v j∑ ∑ j∑ v k ∑ k P chvj ,k − Ptotal ]} + ιv ( P chvj ,k − pkcons ) + γk [ v v j j ∑ ∑ init max init + λv [Pv,k − Cbattery ] + ιv [Pv,k − 0]. v
v
(15) We further degrade the problem into a series of uncoupling subproblems by means of dual decomposition [21], and denote Dk (λv , ιv , γk ) be the maximum value of Lagrangian L(.) over P chvj ,k at hour k. Dk (λv , ιv , γk ) ∑ ∑ ∑ ∑ = max { χ( P chvj ,k ) + λv ( P chvj ,k − pkcons ) P ch v v j ∑ vj ,k∑ j ∑∑ k + ιv ( P chvj ,k − pkcons ) + γk [ P chvj ,k − Ptotal ]}. v
j
λv ,ιv ,γk
j
v
(16)
(18)
s.t.λv > 0, ιv > 0, γk > 0.
The intrinsic philosophy behind the solution, which can still be guaranteed globally optimal even after decoupling, is that the objective utility function is convex; all the inequality constrains are linear. IV. P ERFORMANCE E VALUATION In this section, we evaluate the performance of our proposed EV charging strategy, using a custom simulator built in Matlab. And Kitchener-Waterloo (K-W) downtown region is used in the simulation; and the power system data is obtained from Waterloo North Hydro [22]. The performance metric is Total EV charging Power (TECP) which is used as a representation for an electric power utilization. Specifically, TECP is defined as the total charging power of EVs charged up in charging stations for each hour.
j
(14) We refer λv and ιv as the Lagrange multipliers assoinit ciated with the v th inequality constraint 0 ≤ Pv,k + ∑ ∑ k max ( P chvj ,k − pcons ) ≤ Cbattery , for vehicle v; similarly, k
v
250
Total EV-charging Power / KW
∑
(17)
Based on the proposed charging strategy Without EV-charging scheduling Upper bound of power-supplying
200 150 100 50 0 0
5
10 15 Time slot / hour
20
25
Fig. 4: TECP of EVs for each hour. Fig. 4 shows the TECP with and without implementing the proposed charging strategy. We can observe that the TECP with charging strategy is much higher than that without charging strategy. For example, at 5pm, the TECP reduction under no charging strategy is about 40%. That is because without the charging strategy, overloading on a power-supply bus may happen with high probability during the electricconsuming peak time. Once an overloading happens, the corresponding bus can be cut down without supplying electric power any more, resulting in the decreased TECP at that time. Furthermore, the TECP during day time is higher than that at night on average; however, the TECP in the early morning is not that high. This can be explained as that 1) during the day time, there is less electric power required for routine life (e.g., heating demand for the resident), and so that the power
capacity supplied for EV charging during the day time is much higher than that at night; 2) in the early morning, usually the demand for EV charging is not that much, and therefore the TECP is relatively low. In addition, the TECP with charging planning is slightly smaller than the power capacity; however, it approaches asymptotically towards the capacity. Therefore, effective charging strategy not only improves network TECP performance, i.e., the spatial utilization, but also benefits the stability of the power system to avoid the overloading.
Total Number of charged EVs
60 Based on the proposed charging strategy Without EV-charging scheduling
50 40 30 20 10 17
18
19
20 Time slot / hour
21
22
23
Fig. 5: Illustration of balancing EV loads among charging stations. Fig. 5 illustrates the effect of load balance among charging stations. It is shown that when the total supplied power to charging stations is relatively low while the routine power demand is high correspondingly (e.g., during the time duration from 6pm to 11pm), the TECP under proposed charging strategy increases, compared to the case without charging strategy. The reason is that some particular charging stations have no capabilities to load any more EVs due to limited load capacities; then, with the predicted charging strategy, some EVs may find an alternated charging station to be charged which results in the increased TECP. Thus, it implies that our proposed charging strategy is with a good adaptability to an electric-consuming peak time duration. V. C ONCLUSIONS In this paper, we have developed a VANET-enhanced online EV charging strategy to prevent the charging failure caused by overloading. In specific, we first propose a VANETenhanced power-supply framework with the functionalities required for an EV charging strategy, involving wireless V2V and V2R communications to forward messages efficiently. Then, a globally optimal online EV charging strategy is designed to deal with the electric power utilization problem, maximizing the overall power utilization and avoiding to overload electric charging stations, by means of Lagrange Duality optimization techniques. Extensive simulations have been conducted to demonstrate that the proposed EV charging strategy can achieve a better performance than the offline individual charging strategy, in terms of the total EV charging power as well as the adaptability to the power-consuming peak duration. In our future work, we intend to collect large-scale real-world vehicle traffic traces, in order to further validate the benefits of the proposed algorithm in practical scenarios; the
design of the charging strategy in a distributed manner will be integrated to reduce the implementation complexity of our strategy. ACKNOWLEDGEMENT
This research work is financially supported by Natural Sciences and Engineering Research Council of Canada Collaborative Research and Development Grants, Canada.
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∗ Department † State
of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China
Abstract—An online charging strategy is an efficient approach to provide charging plans for electric vehicles (EVs) from a global point of view, aiming to improve energy efficiency while avoiding overloading of an electric power system. However, designing an efficient online charging strategy to achieve optimal energy utilization remains a challenging problem, especially when the coordinated behaviors of both EVs and charging stations are taken into consideration. In this paper, we first introduce an intelligent power distribution system which utilizes vehicular adhoc networks (VANETs) to enable communication among EVs on roads, road-side units (RSUs), and a vehicle-traffic server. Then, we propose a globally optimal online EV charging strategy, which not only improves energy utilization of the whole system but also prevents charging stations from overloading, which may cause a voltage drop in the power distribution system. Lagrange duality optimization techniques are exploited to address the associated optimal EV charging problem. The performance of our proposed strategy is evaluated by extensive simulations, and the results are compared with that of the traditional autonomous offline charging strategy.
I. I NTRODUCTION Electric vehicles (EVs), as a crucial component of a sustainable and environmentally-friendly transportation system, have received considerable attention in many countries across the world. By adopting EVs into the transport sector, conventional energy consumption can be significantly lessened, so can environmental pollution (e.g., greenhouse gas emissions). For instance, battery-powered EVs, which completely depend on rechargeable batteries and produce no emissions, have the protential to cut down overall emissions from the transport sector by 70% [1]. According to the Electric Power Research Institute (EPRI), the EV penetration level can reach 35%, 51%, and 62% by 2020, 2030, and 2050, respectively [2]. However, the widespread implementation of EVs into a transportation system would lead to EV charging problems. Much research has been conduct on designing EV charging profiles for individual EVs, but conventional charging strategies [3]–[9] have not fully resolved the overloading problems of charging stations; on the contrary, the conventional approaches still face a number of challenges. Among them, one particular research challenge to our field of interest is to obtain real-time EV traffic information and electric load information and to use the collected information for global EV charging planning and charging overload avoidance. Thanks to the emergence of vehicular ad-hoc networks (VANETs), the challenge above can have a promising res-
olution through equipping transportation systems with enhanced functionalities. Specifically, VANETs support both vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications [10]–[13], enabling efficient information collection/reporting of traffic updates from/to neighboring vehicle nodes as well as road-side units (RSUs). As a result, the collected real-time traffic information can be utilized for traffic flow management [14], individualized vehicle path planning [15], vehicle localization [16], etc. Nevertheless, how to accomplish the globally optimal EV charging functionality for individual vehicles with the avoidance of overload charging is still an unsolved problem. To be specific, it is still unclear (1) how to efficiently and reliably transmit real-time information of traffic statistics and electric loads in order to guide vehicles to perform charging planning decisions in an online fashion; and (2) how to perform globally optimal online EV charging functionalities based on the above collected EV-traffic and electric load information. In this work, to address the challenge, we integrate VANETs into a power distribution system and propose an online globally optimal EV charging strategy to avoid overloading of charging stations. Under the strategy, a vehicle-traffic server is in charge of collecting real-time information and doing EV charging planning from a global perspective, rather than doing the charging planning in an individual offline charging planner installed in each vehicle which makes the decision in an uncoordinated manner. Then, the centralized EV charging decisions are further delivered to EVs in need of charging via V2V and V2I communications. Our centralized EV charging strategy can improve energy utilization from a global point of view as well as prevent the overloading of the power distribution system. The contributions of this paper are fourfold: •
•
first, we propose a VANET-assisted power distribution system framework with the enhanced functionalities of online EV charging planning; specifically, VANETs enable efficient communication between vehicles and RSUs to deliver useful information for EV charging planning in a real-time manner; second, we design an online globally optimal EV charging strategy to improve the overall energy utilization. Much more than this, with our proposed EV charging strategy, a vehicle intelligently avoids from overloading charging stations using the received charging decision
from a vehicle-traffic server; third, Lagrange duality optimization techniques are exploited to solve the optimization problem corresponding to the proposed EV charging strategy; and • finally, we carry out extensive simulations to validate the effectiveness and efficiency of our proposed EV charging strategy. Simulation results confirm that our proposed EV charging algorithm is able to find alternative EV charging decisions to bypass heavily-loaded charging stations in a timely, efficient and globally coordinated way. The remainder of the paper is organized as follows: Section II provides an overview of the network architecture. In Section III, the proposed EV charging strategy is presented. Section IV demonstrates the performance of the proposed strategy by simulations. Section V concludes this paper. •
II. N ETWORK A RCHITECTURE Aiming to provide an online EV charging strategy for EVs from a global perspective, we introduce a VANETenhanced power distribution system architecture to efficiently perform centralized EV charging control, followed by a power distribution system model to explain the detailed constraints of EV charging in a corresponding power distribution system. A. VANET-Enhanced Power Distribution System Architecture Fig. 1 shows the components of the architecture in a considered VANET-enhanced power distribution system, consisting of four charging stations (i.e., parking lots along the roads), a vehicle-traffic server, access points on road sides (i.e., RSUs), and electric vehicles. A power distribution system, including a basis electric supplying bus, supports charging for all EVs in parking lots. Based on power flow of electric supplying buses, the voltage at each charging station for a certain time duration in the power system can be estimated. For example, a voltage at one charging station is lower during a peak-load time duration (e.g., from 7pm to 9pm) than a voltage in an off-peak duration. The voltage can decide how much load a bus can support, i.e., its capacity. Then, the capacity limits of the maximal power supplied for each charging station can be obtained and delivered to the vehicle-traffic server based on wired communication. Furthermore, a set R of RSUs are deployed in the network. RSUs, also wired connected to the vehicle-traffic server, can obtain and relay the charging decisions to individual EVs in need of charging in a multi-hop manner based on DedicatedShort-Range-Communication (DSRC) protocol [17]. Here, DSRC protocol supports both RSU-to-vehicle (R2V) communications and vehicle-to-vehicle (V2V) transmissions. On the other hand, based on V2V and V2R communications, EV traffic flow information can be collected and shared among RSUs. Consider that a large number of EVs V move around in the area following map-based pathes; and within a certain transmission range these EVs can communicate with each other or RSUs. As soon as an EV moving on a road receives a charging decision from either neighboring EV relays or an
Vehicle-Traffic Sever R2V R2V
Wired connected
RSU Wired connected
RSU
V2V
: Parking lots, i.e., Charging stations : Wired connected : R2V communication : V2V communication
Fig. 1: A VANET-enhanced power distribution system.
RSU directly, that EV moves to a particular charging station following the received charging decision. Only one type of EVs is considered in this work, namely electric taxis, which are constantly in-motion most of the time and likely in need of charging at any time. When individual electric taxis require charging, they would be dispatched to particular charging stations using Global Positioning System (GPS). Note that a GPS device is supposed to be equipped on each EV which has ordered the service of shortest paths. With the collected estimated capacities of all charging stations and real-time EV traffic information, the vehicle-traffic server is capable of performing online charging strategies to provide globally optimized charging decisions for EVs in need of charging. Note that the detailed technologies of real-time EV traffic information collection are not discussed, but can be referred to in [18]. Therefore, as shown in Fig. 1, communications in the considered VANET-enhanced power distribution system can be divided into three layers: wired communication between charging stations and a vehicle-traffic server, wired communication between a vehicle-traffic server and RSUs, and wireless V2R/R2V and V2V communications based on DSRC protocol. To disseminate decisions as quickly as possible among vehicles until the decisions reach the destined EVs, similar to [18], the EVs with large mobility differentiation from the source EV, (i.e., the first EV receiving the decisions from an RSU), are responsible for relaying the decisions based on multi-hop transmissions within a certain decision lifetime, e.g., through a downlink, i.e., a server - an RSU/vehicle relay - the vehicle in need of charging. That is, the EVs whose mobility characteristics (i.e., moving direction and velocity) are different from the source EV beyond a threshold are selected as relays. Based on this forwarding scheme: i) a decision can be delivered towards destination EVs as efficiently as possible, thus reducing transmission delay; ii) forwarding collisions can be reduced due to strategically selected relaying EVs; and iii) the delivery ratio of decisions can be guaranteed due to multiple EVs forwarding.
B. Power Distribution System Model In order to implement charging control for EVs in the VANET-enhanced power distribution system, there exists relationships among power flow on the feeders (i.e., buses), the bus voltages and phases, and the load demand (i.e., EV charging demand). That is, a power flow analysis including voltage deviations and power losses as well as the number of customers, should be performed to facilitate the centralized online charging strategy for EVs. In the following, a power distribution system model is described aiming to estimate the electric-supply capability (i.e., capacity) of individual buses to propose a centralized EV charging strategy. Based on the network architecture as shown in Fig. 1, consider a power distribution system which is an N -bus system as depicted in Fig. 2(a), where N denotes the set of buses in the system. Take N = 12 as an example. The equivalent power distribution system model is shown in Fig. 2(b). The power is supplied through the traditional substation at Bus0 . Four EV charging stations are located at Bus2 , Bus6 , Bus9 and Bus12 , respectively. An EV charging station can impose a certain maximum load to the corresponding connected bus according to the voltage limits. For instance, consider one EV charging station located at Bus2 can accommodate 1000 standard EVs for simultaneous charging; each EV imposes a maximum electrical load of 4kW on the bus, which makes up for a total of a maximum additional load of 4M W at Bus2 if all EVs had with the same charging capabilities. In this paper, it is considered that each EV will be connected to the network via a standard single-phase Alternating-Current (AC) connection. Although the concept of vehicle-to-grid for local system exists [8], bi-directional flow of electricity or the directional flow from an EV battery to the grid is left for our further work. To summarize this section, based on the defined network architecture and established power distribution system model, the proposed online EV charging framework above is exploited to: a) collect the estimated voltage and power supply information at each bus in the power distribution system; b) transmit all the collected information to the vehicle-traffic server; c) do information fusion and work out the charging decisions for EVs in the vehicle-traffic server; and d) send the charging decisions back to the individual EVs in need of charging. III. C ENTRALIZED O NLINE EV
CHARGING
S TRATEGY
In this section, we first present the power flow equations in the predefined power distribution system. Based on the power flow equations, a voltage profile can be estimated for calculating the maximal loading at each bus and the relationship among loading capacities of different buses. Finally, an optimization problem is formulated to maximize the overall energy utilization while preventing system overloading. A. Power Flow Equation The power demand-supply balance on a bus Busi (i ∈ N ), at hour k, is calculated as
Bus1
V0
V1
V2
Bus3
Bus4
Bus5
V6
Bus2
Bus7
Bus8
V9
Pload 3
Pload 2
Pload 1 Vehicle Parking Lot (Charging Station)
Bus10 Bus11 V12 Bus12
Bus9
Bus6
Pload 4
... ...
(a) Illustrated Power system model. Bus1
V0
V1
V2
Bus3
Bus4
Bus2
Bus5 Bus7 V Bus6
Bus8
V9 Bus9
6
Pload 1
Bus10 Bus11 V12 Bus12
Pload 3
Pload 2
Pload 4
(b) Equivalent Power system model.
Fig. 2: Power distribution system model.
Vi ,k Pij ,k
Rij + jX ij
V j ,k
Qij ,k Fig. 3: The relationship between voltages and active (reactive) power flow in a 2-bus system.
P i,k − P Di,k − P chi,k =
N ∑ [Vi,k Vj,k Yi,j j=1
· cos(θi,j + δj,k − δi,k )]
(1)
where P i,k is the active power injected into the system at Busi at hour k; P Di,k is the active power demand at Busi at hour k; P chi,k , the active power load introduced by the charging of EVs batteries at Busi at hour k, is a continuous variable, determined from the given charging solution; Vi,k and Vj,k are voltages at the points of Busi and Busj at hour k, and j ∈ N ; Yi,j is the admittance of line i-j; δi,k and δj,k are the voltage phases of Busi and Busj at hour k; and θi,j is the corresponding angle. Note that these above variables are originally defined in the power flow analysis. Voltage Drop Estimation Given the power injected by the generation buses, voltage drops between generation buses and demand buses at hour k, e.g., Vi,k and Vj,k respectively, as depicted in Fig. 3, can be written as Vi,k − Vj,k =
Pij,k · Rij + Qij,k · Xij Vj,k
(2)
where Pij,k and Qij,k are the active and reactive power flow from Busi to Busj at hour k. R + jX is the impedance of feeder line i-j. And these variables are used for power flow analysis in a power system as well. In per unit, (2) is usually approximated in the power flow analysis as [19] Vi,k − Vj,k = Pij,k · Rij + Qij,k · Xij .
(3)
Take a summation on both sides of (3) over all bus pairs, we
can get V12,k in Fig. 2(b) V12,k = V0,k −
11 ∑
(Pij,k · ri + Qij,k · xi ).
(4)
i=0
B. Network Sensitivity: Voltage versus Load Based on the analysis of power flow in the system, voltages and the power supply ability of the points of buses can be obtained. Subject to the loading of EVs, the voltage of one bus can decrease with the increased load [19]. However, voltages of points of buses should fluctuate within a certain range. If voltage sags out of thresholds at points of buses, they cannot be corrected efficiently by injecting reactive power. In other words, voltage magnitudes at each bus (e.g., Busj ) at hour k, are constrained by their respective upper and lower limits min max Vj,k ≤ Vj,k ≤ Vj,k . To keep the voltage within a certain range, it is efficient to reduce the load or to inject an active power. Therefore, an additional load conversely determines a change in voltage and loading levels at all the points of demand buses, and there exists a tradeoff between voltages and load sensitivities. Load-Capacity Estimation: In our work, load sensitivity valuing for the voltage and loading assigned to one bus is the summation of all voltages and loading sensitivities at the charging points of EVs on the feeder. This takes account of the impact that multiple EV loads, charging simultaneously, can be served by a particular demand bus. With a given charging rate, the sensitivity value is used in conjunction with the EV charging voltage and served loading measurements at each time to determine an optimal charging number of EVs. For each EV v (∈ V), consider the EV charger active power constraint is as max P chmin vj ,k ≤ P chvj ,k ≤ P chvj ,k
P chmin vj ,k
(5)
P chmax vj ,k
where and are predefined charger active power constraints of continuous charging power P chvj ,k by Busj at hour k. And the total charging active power during a period is limited by the EV battery capacity, i.e., init max Pv,k + P chvj ,k ≤ Cbattery
EV charging-related loading is given, e.g., heating power supplying to the resident. Then, the total power supplying to EV charging stations can be calculated; furthermore the power supplied to individual charging station has a reciprocal and linearly relationship with other charging stations. Proof: For all buses, voltages should be no less than the minimal required voltage Vmin , e.g., Vmin = 0.9 per unit voltage [20]. For instance, from (4), the lowest voltage is at Bus12 , i.e., V12,k . Then, V12,k = V0,k −
11 ∑
(Pij,k · ri + Qij,k · xi ) ≥ Vmin .
(9)
i=0
Namely, 11 ∑
(Pij,k · ri + Qij,k · xi ) ≤ V0,k − Vmin .
(10)
i=0
In addition, we denote jj the sorted number of the buses which are without EV loading, and JJ is the set of these buses jj ∈ JJ(∈ N ); we consider jw being the sorted number of the buses with EV loading, and JW is the set of those buses jw ∈ JW (∈ N ). Then, (10) can be represented by ∑
(Pjj,k rjj + Qjj,k xjj ) +
∑
jw−1 ∑
(Pl,k rl + Ql,k xl )
jw∈JW l=0
jj∈JJ
≤ V0,k − Vmin .
(11) Consider the loads of the buses which are without EV loading are known as a constant, ∑
jw−1 ∑
(Pl,k · rl − Ql,k · xl ) ∑ (Pjj,k · rjj − Qjj,k · xjj ). ≤ V0,k − Vmin −
jw∈JW l=0
(12)
jj∈JJ
The inequality (12) implies that the summation of power supplying to EV charging stations is related to the locations of charging stations and the total number of charging stations.
(6)
init where Pv,k is the initial active power stored in EV v at hour k. And, ∑ P chj,k = P chvj ,k (7)
C. Optimization Objectives
v∈V
where P chvj ,k is non-negative when vehicle v is served by the certain charging station Busj at hour k, otherwise 0. The capacity of loading at Busj at hour k is defined as P chmax j,k , P chj,k ≤ P chmax j,k .
(8)
Furthermore, we give the relationship among the loadcapacities of buses in Theorem 1, and the proof is given based on power flow analysis in the power system. Theorem 1: (Linearly Reciprocal-Related Load-Capacities of Buses) Consider the total supplied power on one power supplying bus is constant, and the power demand for non-
Once the vehicle-traffic server receives the collected estimated capacities of all charging stations from the power system, charging decisions are operated by the vehicle-traffic server to guide EVs in need of charging and balance EV charging cost evenly in the whole network, based on real-time EV traffic information. Let χ(.) be a non-decreasing function on the charging active power for EVs on one charging bus at hour k. Then, our objective is to maximize the overall energy utilization with the guarantee of power system stability. The overall utilization problem is given as follows
∑∑
max
k j P chmin vj ,k ≤
s.t.
χ(
∑
Then, let Lagrangian dual function D(λv , ιv , γk ) be the maximum value of Lagrangian L(.) over P chvj ,k .
v∈V P chvj ,k )
D(λv , ιv , γk ) ∑ k ∑ init max D (λv , γk ) + λv [Pv,k − Cbattery ] v k ∑ init + ιv [Pv,k − 0].
P chvj ,k ≤ P chmax vj ,k ,
=
∀v ∈ V, ∀j ∈ JW, ∀k; ∑ ∑ init max 0 < Pv,k + ( P chvj ,k − pkcons ) ≤ Cbattery , j
k
j
P chj,k
To minimize the Lagrangian dual function over dual variables, λv , ιv , and γk , we get
∀v ∈ V; k ≤ Ptotal , ∀j ∈ JW, ∀k
min D(λv , ιv , γk )
(13) where pkcons is the average power cost for each individual k vehicle at hour k. Ptotal is defined as the supplying power upper bound of the whole power system at hour k, which can be obtained from (12). The optimization problem (13) can be solved by applying Lagrange Duality [21] techniques. The basic idea is to take the constraints of (13) into account by argumenting the objective function with a weighted sum of the constraint functions. We define the Lagrangian L(.) associated with the problem (13) as L(P chvj ,k ) ∑∑ ∑ ∑ ∑∑ k χ( P chvj ,k ) + γk [ P chvj ,k − Ptotal ] v v j j k k ∑ ∑ ∑ init max + ( P chvj ,k − pkcons ) − Cbattery ] + λv [Pv,k v j k ∑ ∑ ∑ init + ( P chvj ,k − pkcons ) − 0]. + ιv [Pv,k
=
v
k
j
we refer to γk as the Lagrange ∑ multiplierk associated with the k th inequality constraint P chj,k ≤ Ptotal . The vectors j
{λv }, {ιv }, and {γk } are called dual variables or Lagrange multiplier vectors associated with the problem (13). Rearranging the equation (14), it can be expressed as L(P chv ,k ) ∑ ∑ ∑ j∑ ∑ = { χ( P chvj ,k ) + λv ( P chvj ,k − pkcons ) v j∑ ∑ j∑ v k ∑ k P chvj ,k − Ptotal ]} + ιv ( P chvj ,k − pkcons ) + γk [ v v j j ∑ ∑ init max init + λv [Pv,k − Cbattery ] + ιv [Pv,k − 0]. v
v
(15) We further degrade the problem into a series of uncoupling subproblems by means of dual decomposition [21], and denote Dk (λv , ιv , γk ) be the maximum value of Lagrangian L(.) over P chvj ,k at hour k. Dk (λv , ιv , γk ) ∑ ∑ ∑ ∑ = max { χ( P chvj ,k ) + λv ( P chvj ,k − pkcons ) P ch v v j ∑ vj ,k∑ j ∑∑ k + ιv ( P chvj ,k − pkcons ) + γk [ P chvj ,k − Ptotal ]}. v
j
λv ,ιv ,γk
j
v
(16)
(18)
s.t.λv > 0, ιv > 0, γk > 0.
The intrinsic philosophy behind the solution, which can still be guaranteed globally optimal even after decoupling, is that the objective utility function is convex; all the inequality constrains are linear. IV. P ERFORMANCE E VALUATION In this section, we evaluate the performance of our proposed EV charging strategy, using a custom simulator built in Matlab. And Kitchener-Waterloo (K-W) downtown region is used in the simulation; and the power system data is obtained from Waterloo North Hydro [22]. The performance metric is Total EV charging Power (TECP) which is used as a representation for an electric power utilization. Specifically, TECP is defined as the total charging power of EVs charged up in charging stations for each hour.
j
(14) We refer λv and ιv as the Lagrange multipliers assoinit ciated with the v th inequality constraint 0 ≤ Pv,k + ∑ ∑ k max ( P chvj ,k − pcons ) ≤ Cbattery , for vehicle v; similarly, k
v
250
Total EV-charging Power / KW
∑
(17)
Based on the proposed charging strategy Without EV-charging scheduling Upper bound of power-supplying
200 150 100 50 0 0
5
10 15 Time slot / hour
20
25
Fig. 4: TECP of EVs for each hour. Fig. 4 shows the TECP with and without implementing the proposed charging strategy. We can observe that the TECP with charging strategy is much higher than that without charging strategy. For example, at 5pm, the TECP reduction under no charging strategy is about 40%. That is because without the charging strategy, overloading on a power-supply bus may happen with high probability during the electricconsuming peak time. Once an overloading happens, the corresponding bus can be cut down without supplying electric power any more, resulting in the decreased TECP at that time. Furthermore, the TECP during day time is higher than that at night on average; however, the TECP in the early morning is not that high. This can be explained as that 1) during the day time, there is less electric power required for routine life (e.g., heating demand for the resident), and so that the power
capacity supplied for EV charging during the day time is much higher than that at night; 2) in the early morning, usually the demand for EV charging is not that much, and therefore the TECP is relatively low. In addition, the TECP with charging planning is slightly smaller than the power capacity; however, it approaches asymptotically towards the capacity. Therefore, effective charging strategy not only improves network TECP performance, i.e., the spatial utilization, but also benefits the stability of the power system to avoid the overloading.
Total Number of charged EVs
60 Based on the proposed charging strategy Without EV-charging scheduling
50 40 30 20 10 17
18
19
20 Time slot / hour
21
22
23
Fig. 5: Illustration of balancing EV loads among charging stations. Fig. 5 illustrates the effect of load balance among charging stations. It is shown that when the total supplied power to charging stations is relatively low while the routine power demand is high correspondingly (e.g., during the time duration from 6pm to 11pm), the TECP under proposed charging strategy increases, compared to the case without charging strategy. The reason is that some particular charging stations have no capabilities to load any more EVs due to limited load capacities; then, with the predicted charging strategy, some EVs may find an alternated charging station to be charged which results in the increased TECP. Thus, it implies that our proposed charging strategy is with a good adaptability to an electric-consuming peak time duration. V. C ONCLUSIONS In this paper, we have developed a VANET-enhanced online EV charging strategy to prevent the charging failure caused by overloading. In specific, we first propose a VANETenhanced power-supply framework with the functionalities required for an EV charging strategy, involving wireless V2V and V2R communications to forward messages efficiently. Then, a globally optimal online EV charging strategy is designed to deal with the electric power utilization problem, maximizing the overall power utilization and avoiding to overload electric charging stations, by means of Lagrange Duality optimization techniques. Extensive simulations have been conducted to demonstrate that the proposed EV charging strategy can achieve a better performance than the offline individual charging strategy, in terms of the total EV charging power as well as the adaptability to the power-consuming peak duration. In our future work, we intend to collect large-scale real-world vehicle traffic traces, in order to further validate the benefits of the proposed algorithm in practical scenarios; the
design of the charging strategy in a distributed manner will be integrated to reduce the implementation complexity of our strategy. ACKNOWLEDGEMENT
This research work is financially supported by Natural Sciences and Engineering Research Council of Canada Collaborative Research and Development Grants, Canada.
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