Charge Station Placement in Electric Vehicle Energy Distribution Network

Transcription

1 Charge Station Placement in Electric Vehicle Energy Distribution Network Jianwen Xu, Ping Yi, Tiantian Xie, Wei Wang, Xin Liu, Ting Zhu School of Information Security Engineering, Shanghai Jiao Tong University, Shanghai, 00, China Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, MD, 21250, USA Abstract Energy internet is now an industry hot spot which enables the interconnection and sharing of energy just like the Internet. Inspired by the concept of energy internet, this paper will focus on a designed energy distribution network, using city bus lines running Electric Vehicles (EV) to achieve electric power storage and transmission. This network is made of renewable energy sources providing power, charge stations for power exchange and bus lines as delivery, electric buses serving as the carriers of flowing power in network. This paper will mainly discuss and solve the problem of placing charge stations on city bus map to compose the network framework. Our work includes two optimization algorithms using some ideas of graph theory, simulating with real-world transporting data of different city maps and analyzing the results to evaluate efficiency as well as advantages and disadvantages on algorithms and data sets. I. INTRODUCTION Nowadays, energy internet, the idea of building relationship between energy industry and Internet of Things (IoT), has drawn more and more attention. Aiming at taking the advantages of both uniformity & mobility of electric power and interconnectivity & sharing property of IoT, a whole network connecting all energy need and supply may reconstruct our cognition about power generation and consumption to a certain extent. clean energy from photovoltaic power, terrestrial heat and wind, energy internet can ensure the improvement of our living environment. Electric vehicle, together with Vehicle-to-Grid (V2G) technology, is playing an important role in energy internet. As fast charging/discharging and large capacity battery have been widely applied, we realize that using EVs to storage and transmit electric power can be achieved. Energy distribution network is a designed power storage and transmission system based on city bus lines running EVs. This network includes three main parts: renewable energy sources providing power, charge stations for power exchange between EVs passing by and EV bus lines as power delivery. To ensure the normal operation of the system, several problems like determining the position of energy sources and charge stations, energy scheduling and allocation, dealing with traffic incidents need to be solved. This paper may focus on the charge stations placement, that is, using as small number as possible of charge stations to cover the whole network that every EV bus line can get energy replenishment when needed, as well as reduce the energy loss on the process of charging/discharging. In this paper, we will focus on the optimization algorithm of placing charge stations. The main contributions are as follows. Build up mathematical model based on basic graph theory, collect and pretreat the bus maps of three cities, some special modifications are needed to cater to the follow-up work; Design two optimizations using idea of Breadth-First Search (BFS) and shortest path method, some further modifications are aimed at resolving the particularity of energy distribution network. Compare the performance among different algorithms and cities data, analyze the stimulation results to evaluate efficiency as well as advantages and disadvantages on algorithms and data sets. Fig. 1. A schematic of energy internet As shown in Fig. 1, energy internet mainly includes power generation from traditional source and renewable source to power transmission and consumption processes like Power Line Communication (PLC), smart home devices, EV (bus, car, bicycle and even newcome unicycle). Especially with the There are six sections in this paper to state the overall details of the research. In Section I, the introduction. Second II will be the problem of analysis, elaborate process from initial idea to formation of algorithm. Section III uses real-world data to simulate the algorithm. Section IV gives results of simulation and some analysis. Section V summarizes the previous work and draw conclusions. Section VI are the acknowledgements /17/$ IEEE

2 II. RELATED WORKS As the technical basis of energy internet, V2G provide the core technology of power exchange. The research group led by Dr. Willett Kempton in University of Delaware has focused on V2G for more than ten years. From initial conception about how an EV market be like in the future in 00s to establishing cooperation with vehicle manufacturing companies like Toyota and also power department like PJM which serves as the leading experimental unit in United States. Other countries such as Japan, Denmark, UK, South Korea also actively build up infrastructure collaborated with University of Delaware [1]. Key technologies of V2G have also inspired a lot on urban traffic improvement like smart charging [2], Bus Rapid Transit (BRT) system [3]. Early in 04, planning ideas like with the help of V2G, large-scale of renewable energy can be supported, which caused great concern. Actually before EV that only consume energy from battery (Battery EV, BEV) coming into view, EV using hybrid power(hybrid EV, HEV) as a transitional product also brought impact on research about distribution network [4] [5]. The idea of electric vehicle energy distribution network was first raised in 12, a paper about energy transmission network using EV described what the blueprint may look like [6], [7]. The authors also proposed ideas on energy routing [8], [9], [10], energy scheduling and allocation [11], [12] and robustness analysis [13]. Follow-up works paid more attention to some preliminary conception like conceptual framework of integrating EV into power system, establishing connection between EV and new source to develop green economy [15]. III. PROBLEM DESCRIPTION Fig. 2. A schematic of energy distribution network Energy distribution network mainly researches on the EV and charge station part circled with dotted line in Fig. 1. As shown in Fig. 2, the network here is made up of city bus lines and motivated electric power from renewable energy sources. Just like fuel vehicles, we drive to gas station to fill up the gasoline tank before running out of fuel, EV s battery also needs charging in the charge station. In consideration of some restriction like battery capacity and energy loss on electricity migration, we may drive battery cars to charge stations more often than refueling gasoline ones. City buses using electric power and charge stations providing power supplement together build up the energy distribution network. Therefore, to organize a city bus network entirely relying on electric power, we need charge stations to play the role of routers in ethernet. That is, charge stations provide energy for low power buses and get supplying from high power ones. All power comes from renewable energy sources, bus lines directly passing by can get full charged and carry power to charge stations also in their fixed routes. Then bus lines passing by these charge stations can get charged while there exists a percentage energy loss rate, which means percentage power carried by bus lines going through energy sources is wasted. In comparison with routing in ethernet, we don t want multiple forwarding since there can be more possibilities for packet loss. What s more, building charge station itself may cost a lot as well as occupying urban area. As a result, the priority target of energy distribution network is choosing optimal location to place as few charge stations as possible to make sure all bus lines can get charged in time. This paper will propose solutions for the charge station placement problem, using the least charge stations to cover all the bus lines, since the cost of building charge stations may sharply increase spend on infrastructure construction. Moreover, after placing fixed number of charge stations, choosing which charge station to supply power for which bus line also need deliberate arrangement that every bus line can get charged when running out of power. Also, we dont want situation that one charge station always overloads and the other one adjacent to it sometimes left unused. Graph theory is a mathematics field studying the structures of graphs, which used to model pairwise relations in objects like nodes, lines, arcs, etc. In relation to our target, some ideas about connecting isolated vertexes with edges. One basic problem in graph theory, the graph search or graph traversal problem, to visit each vertex in a graph, which is similar to the charge station placing problem and has already been widely applied in many subjects or fields. Since problems in any field may have their own characteristics, aiming ar traversing the bus lines rather than bus stops, while mathematics modeling we have to apply some definition on variables. An undirected graph G =(V,E), in which V stands for vertexes and E for edges that connect the vertexes. To build the relationship between this model and our target, vertexes are going to be the bus lines and edges stand for bus stops located at intersections of bus lines, which can be some kind of unusual, however, is necessary for the follow-up work. Algorithms may still start at bus stops with nearby energy sources, which can be regarded as algorithms actually starting at bus lines that stop over energy sources. Algorithm 1: Modified Breadth-First Search Algorithm Our first idea may consider BFS, which is used to find graph data in a tree map starting at tree root and continuing until any nodes or leaves been found. Accordingly, one energy station as one tree root, all these roots may share one First In

3 Algorithm 1: Algorithm 1 R Relation matrix of bus lines; 2 x number of renewable energy sources; 3 S n all the bus lines passing by any x energy Sources; 4 m = length(r), FLAG =0, A LIST = ; 5 Q =, Q.HEAD = Q.T AIL =1, HOP = zeros(m); 6 put S n into Q; 7 Q.T AIL = Q.T AIL + n; 8 while Q.HEAD Q.T AIL do 9 i = Q(Q.HEAD); 10 for j =1to m do 11 if can t find j in FLAG && R(i, j) == 1 then 12 Q(Q.T AIL) =j; 13 Q.T AIL Q.T AIL +1; HOP(j) HOP(i)+1; 15 push j into FLAG; push [i, j] into A LIST ; 17 Q.HEAD Q.HEAD +1; First Out (FIFO) queue and check whether the next vertex (bus line) has been visited already. Actually, as we know, the BFS itself may not be so efficient when meeting a quite large tree map that contains thousands of bus lines and countless stops, since both time and space complexity which can be briefly expressed as O( V + E ) show that the augment of data quantity can bring an linear increase on calculating cost. Further optimization based on it would exponentially suffer more. To solve this hidden trouble to some extent and cater to what energy distribution network require, a few modifications on details are also necessary. The steps and pseudo codes are as follow. i. Bring all tree roots into a queue before algorithm begins, use a head and a tail to as marks; ii. Start searching, judge if a vertex has not been visited yet and there is 1-relation in the relation matrix with queue head, then put this vertex into queue tail; iii. Build adjacency list to save connecting edge between newcome vertex and queue head, head mark comes to the next and go back to step ii; iv. Anytime if the queue is empty (head equals tail), algorithm ends. First let R be the relation matrix for all bus lines and x stands for tree roots (energy sources). Then choose fixed number of bus stops to place energy sources and build S n to save all the bus lines stopping over energy sources. Then, let FLAG records the bus lines that have been visited and HOP marks the present the depths of nodes in trees. Q has a head Q.HEAD and a tail Q.T AIL to guarantee the FIFO rule. A simple example is given to describe what actually the algorithm works. In Fig. 3, there are 9 vertexes stands for 9 bus lines waiting to be visited. What we have explained in last paragraph about line 6 in pseudo codes of Algorithm 1, the gray dot ES in Fig. 3 stands for an energy source, node B and F are stop-over bus lines. Line of HOP shows the depth of ES tree which records how many times of charging/discharging processes are needed before reach current bus ES A F D H B G C E I HOP QUEUE B F A D E G H C A-LIST B A B D B E F G F H E C G I Fig. 3. An example of the Algorithm line. The 9 vertexes are pushed into Q in order from the first B to the last I, at the same time A LIST orderly save the pathfinding processes (black edge double arrows) as adjacency list. Arrows in figure have no meaning of directed graph. Then we can get charge station number and energy loss rate from Formula (1) and (2). R E LOSS = 1 m m i=1 3 I [ HOP(i)] (1) R E LOSS stands for average energy loss rate based on charging/discharging times when EVs stop by charge stations. The efficiency of charging or discharging for EVs using DC is about 95% [], which means 5% may just waste on energy exchange. Therefore, we take 90% (actually 90.25%) as the energy efficiency for a complete charging/discharging process. N C STAT = length[unique(c STAT)] (2) C STAT contains bus stops located at intersections between pairs of bus lines in A LIST as shown in Fig. 3. The adjacency list records all the edges building up the tree map, some of them may be repeated which means more than one bus lines using the same charge station. Algorithm 2: Preferred Algorithm The second thought we are going to lay more emphasis on the energy loss. To approach this, an idea easily come into mind that why not each bus line just seek help from its nearest energy source to reduce the percentage loss on delivery, which means we want shortest connections between every bus line and energy source. Another classical problem in graph theory, finding shortest path between two vertexes or nodes in a graph while the sum of the weights of its constituent edges is minimized. Usually the edges in shortest path problem have different weights even negative ones, to deal with this several functional algorithms perform separately with advantages and disadvantages. We only pay attention to one special condition, undirected singlepair shortest path problem without weights on edges. The steps and pseudo codes are as follow. i. Divide all vertexes into two groups, the source group and destination group; ii. Take turns in destination group polling source group to find the shortest path to get connected with any source vertex;

4 Algorithm 2: Algorithm 1 R m Relation matrix of bus lines; 2 x number of renewable energy sources; 3 S n all the bus lines passing by any x energy Sources; 4 A LIST =, Q =, S PATH = zeros(m, 10); 5 put S n into Q; 6 for i =1to m do 7 if i/ Q then 8 for j =1to length(q) do 9 find shortest path between R i,1 and Q i; 10 if shorter than S PATH i S PATH i == 0 then 11 push it into S PATH i; ES A B C E D F C D E F C A D C A E C A C E B F E C B D C E B E B F E B Fig. 4. An example of the Algorithm iii. Build adjacency list to save all the edges in shortest paths. Variables used here are almost the same with Algorithm 1, except S PATH, which stands for a container of all bus lines shortest paths. Also a simple example explains the steps and pseudo codes above. In Fig. 4, there are 6 vertexes stands for 6 bus lines waiting to be visited. Two of them, A and B stand for bus lines that stop by renewable energy source. Then our target here turns into finding path to connect other bus lines to A or B. Algorithm 2 may just try all possibility to build connections between energy source stop-over bus lines and all the others, then record the full path of the shortest one, with least power exchange times, that is, least energy loss. Then bus line C, D, E, F separately choose their shortest paths to A/B. Four paths may be recorded in S PATH, charge station number and energy loss rate are easily to calculate afterwards. The formulas of both are the same with Algorithm 1, we only need to replace the HOP in Formula (1) by the length of each whole path (number of edges) in S PATH. For example, in Fig. 4 bus line D has the shortest path D to C to A, so the power on the energy efficiency (0.9) is 3, which means even bus line A or B have a process of charging/discharging to get energy from energy source ES. Arrows in figure also have no meaning of directed graph. R E LOSS = 1 m m i=1 [ length(s PATHi)+1] (3) IV. SIMULATION AND ANALYSIS In this section, we will compare the performance of the two algorithms using ideas of graph theory and make simulation about the possible effects on metrics from real-world city bus maps. The length of the bus line or number of stops it contains, the density of bus lines and stops and other potential factors may just get different simulation results. There are two city bus maps that available to everyone for study usage through the Internet, Manhattan of New York [17] and Pioneer Valley Transit Authority (PVTA) of Western Massachusetts [], which are already widely used in researches about urban transportation. Recent years in China, as one of the largest and most modern cities worldwide, Shanghai plays important roles in frontiers of science and technology, so do new energy and V2G technology. Electric vehicles such as cars, buses or bicycles and charging/discharging facilities are easy to find all around the city. New energy industry like the photovoltaic power generation is already put into civil use in some area [19] []. Therefore we choose a district of Shanghai, Minhang as the third real-world data set for simulation and analysis, which may also receive some practical significance. City Map Bus Lines Bus Stops Stops on Line Lines Pass Stop Manhattan PVTA Minhang total TABLE I DATA SHEET OF THREE CITY MAPS In TABLE I, while the number of bus lines are alike, Minhang has much more bus stops, which means we can test the performance of algorithms with much longer bus lines. Moreover, Minhang has more than half of the bus stops that are isolated, that is, only one bus line come across these stops, which is also an extra designed condition for testing. The 2 nd and 3 rd columns show the number of bus lines and stops in city maps, 4 th stands for the averages of one bus line containing how many stops, 5 th means the average number of bus lines passing by each bus stop. The last two columns are obtained from parts of algorithms, we list them here to help explaining the simulation results below. After some necessary screening and pretreatment, we get three data sets in special forms which show not only the names of all lines/stops, but the sequences of bus stops in each line and number of bus lines each bus stop is involved. Regard average percentage of energy loss and number of needed charge stations as the metrics to simulate the Algorithm 1, 2 and compare with algorithm in [6] (Charge Station Placement Algorithm, in Fig. 5 and 6). Randomly choose 1 to 10 renewable energy sources at the beginning, each condition repeat 50 times to reach an average result. Simulation environment is MATLAB Ra. Fig. 5 shows the percentage of energy loss of distributing electricity from energy sources to each bus line in three data sets. The broken lines are very close to each other under the real-world data of all three city maps which means two

5 Percentage of energy loss rate (%) Simulation of Manhattan (a) Percentage of energy loss rate (%) Simulation of PVTA (b) Percentage of energy loss rate (%) Simulation of Minhang District, Shanghai (c) Fig. 5. Percentage of energy loss rate in three city maps algorithms using ideas of graph theory may not raise the observable performance of energy loss. It is possible that percentage of energy loss mostly rely on the data set itself rather algorithm. Whether reasonable or not, we still can draw some conclusion from the scope of y axis to analyze the influence of different features in three data sets. Fig. 5-b has both the maximum and the largest scope of percentage of energy loss rate, with the smallest number of bus stops as options to be chosen to place charge stations, paths connecting energy sources and bus lines can be longer with more adjacent edges. Fig. 6 shows how many charge stations are needed to cover all the bus lines in three data sets. From the whole point of view, along with the increase in number of renewable energy sources, all broken lines in three figures show clear downward trends. Since energy sources themselves also can take the function of charging/discharging EVs, there exists negative correlation between number of energy sources and charge stations. While there are more energy sources, EVs can get power supply directly from sources instead of charge stations, nevertheless in fact, the number of energy sources can never be large, even 10 is too large, we only take the range of energy source numbers as research purpose to see extreme situation that may enhance algorithms improvement. Algorithm in [6] () performs obviously poor to two algorithms designed here in all three city maps with different gaps. Algorithm 1 takes advantage of raising up usage rate of every single charge station by polling the whole bus line pool. Algorithm 2 even behaves better, especially when number of renewable energy sources increases. As shown in TABLE I, the bus stop-line ratios of Manhattan and PVTA are relatively alike comparing to Minhang or total, firstly we will make comparisons between these two. First, the entire quantity of values in y axis, though trends of broken lines in Fig. 6-a/6-b are nearly the same, scopes of y axis are distinct (10 in Fig. 6-a, in Fig. 6-b), which means to achieve the distribution of power in Manhattan, we averagely need to build almost 10 more charge stations to cover just 1 more bus line (35 bus lines in Manhattan and 34 in PVTA as shown in TABLE I). The simulation results infer that some special factor may greatly influence the seemingly abnormal performance. Finally we found it in the 4 th and 5 th columns of TABLE I which providing the information of average numbers of bus stops on each bus line and average bus lines passing by each bus stop. Fig. 7 may just help explaining the phenomenon above. Look at the two parts of graph made from adjacency matrix of bus lines in Fig. 7, bus stop I has three bus lines to choose next and stop II only has two while the same choosing process can be repeated more than once. Thus, independent of algorithm designing, providing that similar numbers of bus lines are waiting to be covered, each bus stop has more passing-by bus lines which further offer chances for other bus stops to choose from. Combined with 4 th and 5 th columns of TABLE I, Manhattan has larger average numbers of bus lines and stops, which means more options in choosing next bus line/stop may bring diversity. Then as more bus lines/stops are involved, we get branch nodes in tree map composed by colorful dots and black edge double arrows in Fig. 3 and 4. However, take a step back to Fig. 5, the decrease of charge station number causes some offset, more percentage of energy loss on PVTA than the other two also suggests that some negative correlation exists, waiting to be proved in further efforts [21]. Second, in Fig. 6-b two designed algorithms almost stay the same while in 6-a Algorithm 2 is obviously superior to other two algorithms. As if Algorithm 2 lost its superiority in PVTA. On the basis of both feature of data set and algorithm theory, compared to Manhattan, similar number of bus lines with rather less bus stops to choose to place charge stations makes it harder to take advantage of finding preferred path for each single bus line. Back to the comparisons among all three city maps. Take data set of Minhang District, Shanghai into account, with features like similar number of bus lines in total, a lot more bus stops both in total and on each bus line. The covering of only dozens of bus lines can be achieved easily through 500 bus stops, even though performances of three algorithms are not so efficient, especially compared to PVTA, since too many options makes local optimization less meaningful, some global and dynamic optimization are needed for improvement. New discoveries can be found with analysis results between Fig. 6-a and 6-b above. Number of bus stops and the effect of Line Pass Stop (5 th column in TABLE I) have some combined action on the charge station number. Quite a lot more bus stops in total (there are 781 bus stops in total while Minhang has 506) and on each bus line averagely (TABLE I 4 th column,

6 Number of charge stations Simulation of Manhattan 10 (a) Number of charge stations Simulation of PVTA 10 (b) Number of charge stations Simulation of Minhang District, Shanghai (c) Fig. 6. Number of charge stations in three city maps Bus line 1 Bus stop Bus line 2 Bus line 3 Bus line 4 Bus stop Bus line 5 Fig. 7. Description of comparison between Fig. 5-a/5-b.83 in Minhang/11.60 in Manhattan) offset the influence of Line Pass Stop (5 th column, in Minhang/2.554 in Manhattan), which make the Fig. 6-c close to 6-a, especially when number of energy sources is small. V. CONCLUSIONS In this paper we put forward two algorithms using ideas of Breadth-First Search and shortest path in graph theory to place charge stations on bus stops providing energy supply for all bus lines in a city bus network. The results proved that we could reduce the number of needed charge stations to a great extent without losing more energy. VI. ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China ( , 9381, , ), Natural Science Foundation of Shanghai (15ZR23600), State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (LAPS010), the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informationization (U ), Priority Development Field Project of Doctoral Fund ( ), Shanghai Municipal Science and Technology Project ( , DZ10702),and NSF under grant CNS REFERENCES [1] W. Kempton and J. Tomic, Vehicle-to-grid Power Implementation: From Stabilizing the Grid to Supporting Large-scale Renewable Energy, Journal of power sources, vol.4, no.1, pp , 05 [2] R. Mehta, D. Srinivasan, A. M. Khambadkone, J. Yang and A. Trivedi, Smart Charging Strategies for Optimal Integration of Plug-in Electric Vehicles within Existing Distribution System Infrastructure, IEEE Transactions on Smart Grid, pp.1-1,. [3] M. T. Sebastiani, R. Lders and K. V. O. 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