Optimization for Charge Station Placement in Electric Vehicles Energy Network

Transcription

1 Optimization for Charge Station Placement in Electric Vehicles Energy Network Yu Sui, Ping Yi, Xin Liu, Wei Wang, Ting Zhu School of Electronic, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, , China Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, MD, 21250, USA Abstract Energy Network allows energy flow flexibly for and distribution. Energy Network using electric vehicles (EVs) can transfer and distribute energy to every energy user contributing to the mobility of EVs. Energy Network using EVs is what we call EV energy Network. The main idea of this paper focus on the optimization problem of how to deploy energy routers in an EV energy Network. We develop a branch solution. Simulations using real-world transporting data in Manhattan and the Pioneer Valley Transit Authority(PVTA) show that this method is efficient. I. INTRODUCTION Traditionally, power grid system allows energy flow from power stations to energy users. Nowadays, as related technology develops, a new power system called Energy Network is presented. Energy Network allows energy flow from one place to another flexibly as information is allowed to transfer from one place to another in Internet. Energy users in traditional power grid system can only receive energy and use energy while they can transfer surplus energy to other users in Energy network. Hence Energy network allows energy flow more efficiently and total energy cost can be reduced. Nowadays, electric vehicles(evs) become more and more popular as people want to cut down the usage of traditional vehicles for saving traditional energy. EVs equipped with can store a lot of energy and may be used for energy storage. The mobility of EVs allows energy in the network can be transferred from one place to another. This network mentioned above is what we called EV Energy Network. As more and more traditional vehicles will be replaced by EVs, the amount of energy stored in EVs will become so tremendous that the Energy Network based on EVs is of great potential. The main advantage of EV Energy Network is the energy loss of EV Energy Network is less than that of the traditional power grids system in ideal situation, which is proved in Section II. EVs can charge from renewable energy sources and travel to other places for discharge. If EVs can charge and discharge in an ideal situation, there is little energy loss. The energy loss of EV Energy Network can be much lower than that of the traditional power grids system. What is the ideal situation is will be discussed later. To make EV Energy Network work, it is necessary to deploy charge stations on right places. At preliminary stage of the problem, the cost of construction of charge stations is considerable. Some charge stations have to be built in order to make the network operate properly. In other words, the energy from source should be able to be transmitted to every bus stop. The bus stop where can charge and discharge energy must be charge station. The less charge stations are indispensable, the less cost must be paid. Although energy loss could be lower as there are more charge stations, the number of charge station is more important at preliminary stage of the problem. The cost of building a charge station is tremendous after all. Hence, we study the optimization problem of how to deploy charge stations in previous work [1]. Previously, a algorithm is presented to minimize the number of charge stations while it provides full coverage for all bus lines. Meanwhile, the energy loss also should be reduced small enough as a large energy loss is not endurable. In this paper, we focus on how to find a better method minimizing the number of charge stations than previous algorithm. Our main contributions are as follows. Develop a branch algorithm to solve the problem of minimizing the number of charge stations while providing full coverage for all bus lines. The branch algorithm firstly gets the locations of energy sources and then works on the map of bus lines for finding the best point for the construction of a charge station connecting to points that have already been chosen. The previous algorithm finds the points for the construction of charge stations at first. Then it connects charge stations with energy sources. The branch algorithm proves to be better than the previous algorithm and other algorithms considered. Test these algorithms mentioned above by real-world transporting data, which is transporting map data using Manhattan bus lines and the bus map of the Pioneer Valley Transit Authority(PVTA). The paper is organized as follows. We introduce the problem of charge stations in Section II. We formulate the chargestation deployment problem in Section III, and provide solutions in Section IV. Section V presents the simulations and analysis. Section VI concludes the paper. II. PROBLEM DESCRIPTION Besides EVs ability to store energy, EVs also have flexible mobility so EVs can be used in EV Energy Network to transfer and distribute energy from energy sources to energy users. EV Energy Network has three main parts:energy generation,energy transportation and energy consumption. Energy generation consists of power plants of different energy which hopefully

2 are renewable energy. Energy consumption concludes any people using electricity. Energy transportation is composed of EVs and EV charge stations. The paper describes the concept of Energy Network and presents some algorithms to calculate the number of charge stations needed. To achieve the assumption, the charge speed is important. The battery only can charge and discharge during stop time at the stop. Hence, there are few minutes to charge or discharge. The technology named Ultra-fast Chargers creates the conditions for working of EV Energy Network [2]. A. EV Energy Network is used to transport the power from solar energy stations to charge stations. The battery discharge 0.03% of the total power per day [10]. The third is similar to the first. The loss of it is about 5% [9]. The total energy loss of the process is about 10%. Comparing to the energy loss in power through grid, it is clear that the energy loss is less in EV energy network if the times of charge and discharge are less than 3. Hence, the time of the battery charging and discharging is an important target. In ideal situation, we can get a such small energy loss that EV energy network is worthy of design. Solar energy Charge station Fig. 1. DC/AC Converter DC/AC efficiency:91% AC/DC efficiency:85% Power line Power through grid Power line efficiency:93.5% Power through grid is one of the way to transmit the solar energy, which is shown in Fig. 1. There are three s to transmit energy from solar energy stations to charge stations in the scheme. The first is to convert DC power created by the solar panels into grid-ready AC power, which loses about 10% of the total power [5]. The second is by power lines. It loses about 6.5% [7]. The last that is to convert AC energy to DC energy leads to 15% energy loss [8]. It is for charging rechargeable in charge stations. The total energy loss of the scheme is up to 28%. The simple way causes large energy loss. III. PROBLEM FORMULATION To make the model simple, we assume all energy routers as charge stations are located at bus stops. The simple way of making Energy Network is to have charge stations located at all bus stops. However, it may incur prohibitive costs. To cut down the investment of charge stations, it may be of great importance to reduce the number of charge stations as less as possible. Then we discuss the charge station deployment problem formally. To make the problem simple, we assume that the energy capacity of the charge stations is large enough. In addition, the bus is an example of EVs. It can be replaced by the train as well. L 1 L 2 L 3 A 1 A 2 A 3 B 1 B 2 B 3 C 1 C 2 C 3 A B Solar energy DC/DC Converter C Charge station Fig. 2. DC/AC efficiency:95% DC/DC efficiency:95% Electric bus Electric bus efficiency: 99.97% Power through EV Energy Network EV energy network is a new way of power, which has been shown in Fig. 2. The process contains three s from solar energy stations to charge stations as well. Charging EVs by DC power doesn t need to convert DC power to AC power, of which the efficiency is 95% [9]. Then EVs Fig. 3. Schematic diagram of bus lines We define some terms as follows: Definition 1: Energy router is EV charge station with. The function of energy router is to charge power from EVs and discharge power to EVs. EV charge stations can receive energy and forward energy just like router in the communication network. Definition 2: Energy source is power station supplying electricity. As urban space is restricted, energy sources are normally located in rural area. EVs can charge power from an energy source when passing by it. Definition 3: Energy capacity is the energy can be stored by one charge station at most. When energy capacity is larger, the energy network can work more efficiently.

3 Definition 4: Energy network is an area that allows energy flow from one place to another flexibly as data can flow flexibly in the Internet. The flexibility makes the areas energy flow like a network. Definition 5: Energy loss happens every time the battery charges or discharges. In previous work, we know that energy loss is about 10 percents in one time of charge and discharge. As energy loss is not wanted, we should try to make the times of charge and discharge as few as possible. Suppose S = {s 1,, s n } denote the set of bus stops, L = {L 1,, L m } denote the set of bus lines, D denote energy sources, D S. For simplicity, assume that all energy sources are located at bus stops so buses can be charged when they arrive at these bus stops. Fig.3 shows an example. There is one bus stop at any crosses of two streets, denoted as A i, B i or C i, i = 1, 2, 3. Assume six bus lines: l 1 : (A 1, A 2, A 3 ), l 2 : (B 1, A 1, A 2, B 2, B 3 ), l 3 : (C 1, C 2, C 3 ), l 4 : (A 1, B 1, C 1 ), l 5 : (A 2, B 2, C 2 ), and l 6 : (A 3, B 3, C 3 ). There are two renewable energy sources, A 1 and C 3.The relationship refers to Fig.4. To solve problems, a bipartite graph G is introduced to analyse the energy transportation network graph. The edge set E S L reveals the relationship between the two vertex sets. In particular, an edge (s i, l j ) E reveals the bus stop is along the bus line. Let L S denote the set of bus lines that passes bus stop s. Apparently, L S = {l (s, l) E}. For simplicity, we also say L S is the set of bus lines that are covered by bus stop s. For simplicity, we assume all charge stations are located at bus stops. When a charge station is placed at bus stop s, it can be used by all the bus lines in L S. A1 A2 A3 B1 B2 B3 C1 L1 L2 L3 L4 L5 L6 C2 C3 Algorithm 1: Algorithm for CSC Problem input : Bus lines and bus stops. Renewable energy stations output: Charge station cover set 1 Initialization: Build bipartite graph for bus lines and bus stops; 2 L 1 adjacency matrix of bipartite graph; 3 S = busstops; 4 L = buslines; 5 D = renewableenergystations; 6 C = Chargestationcoverset; 7 n = 0; 8 while L 1 do 9 Calculate degree of all nodes in adjacency matrix stop-line; 10 select the largest degree node s i S; 11 L s are the lines connected with s i; 12 L 1 = L 1/L s; 13 n = n + 1; 14 C = C s i; 15 for S i C do 16 for s j D do 17 find the shortest path between S i and s j; 18 record the shortest number of the paths P ; 19 C = C P ; 20 Return C The algorithm has come up to solve the CSC problem. The process of greed algorithm will be showed in 1. It is the best algorithm for most of the bus route map before the branch algorithm is put forward. The branch algorithm is to be explained in IV. The complexity of the followed heuristic is O(mn+ n 3 ), where m is the number of bus lines and n represent the quantity of bus stops. It is refered to 1. The running complexity of line 9 to line 14 is O(mn). The running complexity of line 9 to line 14 is O(n 3 ). As the consequence of that, the total running complexity is O(mn + n 3 ). It is clear that CSC problem is what the paper wants to discuss. It equals to the minimum set cover problem. So, it is Non-deterministic Polynomial (NP) hard, which means the complexity of the problem is non-deterministic. It has been previously proved in the. Fig. 4. The bipartite graph for bus lines and bus stops A. Coverage Problem The problem we discuss is how to get the minimum number of charge stations to cover all the bus lines, referred to as the charge station cover(csc) problem. Let C S denote the set of charge stations. So the CSC problem is Subject to min C C S (1) L s = L (2) IV. PROBLEM SOLUTION In Section II, we know that the CSC problem is NP-hard and previously solved by a algorithm. In this section, we present a branch algorithm to solve the CSC problem. It aims to use a minimum number of charge station while covering all bus lines. In the previous paper [1], they compared the algorithm and the algorithm to make a conclusion that the algorithm gives the best possible performance. Therefore, we introduce and contrast the four kinds of algorithms in detail, which are algorithm, algorithm, algorithm and branch algorithm. The method of building a bus-lines model has been introduced in section III, then we will accomplish the pseudocode

4 Algorithm 2: Algorithm that find the cover node like branch input : Bus lines and bus stops. Renewable energy stations output: Charge station cover set 1 Initialization: Build bipartite graph for bus lines and bus stops; 2 L 1 adjacency matric of bipartite graph; 3 S = bus stops; 4 L = bus lines; 5 D = renewable energy stations; 6 C = charge station cover set; 7 array = charge station connected with node; 8 n = 0; 9 max = 0; 10 v n = 0; 11 for s i D do 12 put the stops which is located at the same bus lines as s i in array; 13 L s is the lines connected with s i; 14 Calculate degree of the nodes which is in array in adjacency matrix stop-line; 15 for n i array do 16 if degree of nodes in array larger than max, max is the degree and v n is the node; 17 for l L s do 18 L 1 = L 1/l; 19 C = C v n; 20 n = n + 1; 21 max = 0; 22 while L 1 do 23 Calculate degree of the nodes which is located at the same bus lines as array in adjacency matrix stop-line; 24 put the stops which is located at the same bus lines as v n in array; 25 for n i array do 26 if degree of nodes in array larger than max, max is the degree and v n is the node; 27 L s is the lines connected with v n; 28 for l L s do 29 L 1 = L 1/l; 30 n = n + 1; 31 C = C max; 32 v n = max; 33 max = 0; 34 Return C; by different algorithms according to the model instruction which has been mentioned before. The first one to be introduced is branch algorithm 2. In all algorithms, array is created to put the nodes which current node can arrive directly, which means that the stops in array are located in the same bus lines as the bus stops arrived. Then, the degree of the stops should be calculated in array to determine which node to choose next. At the beginning of the algorithm, all the nodes in D are put into the array. After that, the degree of the nodes that are connected with the node in D, which means that the stops in array are located in the same bus lines as the bus stops arrived, would be calculate to find the largest one. It is called v n. Then the nodes connected with v n are added into array. After deleting the covered lines, the degrees of all nodes in array are calculated again to find the node with the largest degrees. We could call it max. Then the nodes connected with max are add into array to delete the covered lines. Those s are repeated until all bus lines are deleted. The covered nodes will be record by C. To explain branch algorithm specifically, there is an example. The used graph is proposed in section III. According to above method, the nodes in D is A 1 and C 3. We put them in array and find the covered bus lines. They are l 1,l 2,l 3,l 4,l 6. Then we put the connected nodes into array and delete the covered lines from the graph. The connected nodes are A 2,A 3,B 1,B 2,B 3,C 1,C 2. After that, the degree of all the nodes in array should be calculated to find the largest one. The degree of nodes A 2,B 2 and C 2 are both one, while the other nodes degree is zero. Thus, anyone of the nodes with the degree of one can be selected as max. max covers the last bus line l 5, so that the algorithm is over. Because the network is mesh, it is convenient to find the cover node list C. The second one to be introduced is algorithm. This algorithm is used to find the key nodes by. The function of it is similar to branch algorithm in some ways. However, there are significant differences in property. It is possible that the algorithm has worse property than algorithm. It is to be discussed in detail by showing the simulation results. One of the greatest difference is that it must find the next node connected with the node in max, which limits the property of the algorithm seriously. Technically, the branch algorithm is modified from algorithm. Then, the algorithm to be discussed is algorithm [1], which has been described in the pervious paper. In this algorithm, the node with the largest degree would be found out in the whole graph and be put into C as the covered node. Then the bus lines connected with the found node should be deleted. Then we calculate the nodes degree in the whole new graph. Those s are repeated until all the bus lines are deleted. After that, the shortest path between all the covered nodes and every nodes in D should be found and put into C. The algorithm seems to be the best one. Nevertheless, compared to the algorithm, the better algorithm is branch algorithm. It will be proved in the section V as well. Finally, the last algorithm is algorithm. The function of it is to add the nodes to C at, until every line is covered. This algorithm is very easy to achieve. However, it is the worst algorithm for the most of time. There is no advantage in property for the algorithm. It is used to compare with the better algorithm merely. V. SIMULATION AND ANALYSIS In this section, we evaluate the performance of our algorithms with data from real world. A. Experiment Setup The evaluation is done by data from really world. In particular, the evaluation bases on two maps. One is the Manhattan bus map in New York with 41 bus lines and about 400 bus stops [12]. As charge stations transfer energy among

5 Number of covered charge station Number of covered charge station bus lines, we calculate the number of bus stops which are placed on two or more lines. After calculating, we know that there are 159 bus stops in Manhattan satisfying the request. The bus lines in Manhattan are organized highly densely. The other map is from Pioneer Valley Transit Authority(PVTA) in Massachusetts [13]. This map has 34 bus lines and about 200 bus stops. After the same calculation as before, we get 116 bus stops in PVTA. The reason why we choose these two bus maps is that they have different features. Comparing to dense bus lines in Manhattan, the PVTA bus lines are sparsely distributed as a star network. Because the problem is proposed recently, the algorithms to deal with it is few. Before branch algorithm, the best algorithm is algorithm. Then the algorithm can solve the problem as well. B. Experiment Results Firstly, Fig.5 shows the Manhattan simulation. Clearly, branch algorithm is the best algorithm among all these algorithms considering stability and the number of charge stations. When the number of sources comes to 13, the number of covered charge stations becomes 6 in the branch algorithm. The performance is really good in the Manhattan map because more sources allow the branch algorithm to find a bus station with a bigger degree. The map of the city is messy so that it is easy to find a node which links many bus lines. Then the number of reached nodes increase greatly. The more nodes reached, the greater possibilities there are to found another good node. It forms a virtuous circle. Several good node could be key point of the city which can cover all of the lines. Hence, the property of branch is better than expected. Although the algorithm also tries to find the bus station with a biggest degree, its performance loses against the branch algorithms performance when the number of sources become larger. The reason why it happens is that the algorithm usually needs extra charge stations for connecting to sources while the branch algorithm does not need that branch 5 Fig. 5. The number of cover node in Manhattan The algorithm and the algorithm are also worse than the branch algorithm. The algorithm hardly does anything when the number of sources changes. The algorithm is the easiest strategy but also the worst in performance. Whats more, the algorithm also performs not well. As Fig.5 shows, the algorithm sometimes performs extremely terribly ( eg: when the number of source is 8 ). Whether it performs well greatly depends on the choice of its start. When the algorithm finds a good start, it performs well. However, its performance will not be good when the choice of the start is not good. The reason why the algorithm is so unstable is that this algorithm chooses a bus station with the biggest degrees at the beginning, but it is uncertain whether it can make good choices of bus stations later. In the other words, the when the number of source is 8, the start point is bad enough to cause a enormous energy loss. Although the start point has a max node number, it performs badly when the next chosen node is bad. Because it choose next node locally, the algorithm doesn t care about whether the function of next node is useful to the global map. As a consequence of that, the final chosen nodes would form a loop, which terribly effect the efficiency of the algorithm. Due to the instability of the algorithm, it can not be a suitable algorithm branch 0 Fig. 6. The number of cover node in PVTA Performances in PVTA as showed in Fig.6 somehow resembles that in Manhattan. The branch algorithm still has a superior performance. The algorithm is also still not good and the algorithm barely satisfies the request. Reasons for the performances of these algorithms are generally the same as reasons mentioned in Manhattan. It should be noticed that the performance of the algorithm in PVTA becomes rather worse. This is mainly because sparse routes make it difficult to make effective choices. The reason that leads to the awful performance of algorithm is not hard to wonder. PVTA is a thin state with sparse routes. Once the nodes is chosen by, it is frequent to chose a node located in the edge of the city. When the current chosen node is located in the urban edge and there is many nodes not reached, the next node should be chosen backward. The phenomenon leads to the chosen node form many loops. Even the nodes are chosen ly, there may not be such a large number of redundant nodes. Some people may focus on what are the differences between

6 The radio of charge station in PVTA The radio of charge station in Manhattan branch algorithm and algorithm which make branch algorithm possess such good property. The major difference between them is that branch can select from a larger nodes group nonetheless the algorithm s is smaller. The nodes group of the branch are all the nodes which connected with all of the selected nodes. However the only select the nodes connected with present node. It seems that the two algorithm are similar. Actually, there are crucial difference in property. The linear method of algorithm determines that it is easy to form loops. All the nodes selected by algorithm is a zigzag line. However, the nodes selected by branch algorithm seems like a tree with many branches, which is why it is called branch algorithm. Every selected nodes could grow a branch that is formed by many nodes. It can choose nodes map without forming loops and it is why it need extraordinarily few nodes Fig. 7. The radio of charge station in Manhattan Fig.7 and Fig.8 represent the number of covered stations of three algorithms dividing by that of the branch algorithm. We can directly see how much other algorithms are worse than the branch algorithm. Comparatively, these two figures also show the superiority of the branch algorithm Fig. 8. The radio of charge station in PVTA Clearly, the more the value of the y label is close to 1, the more the performance of the algorithm closes to that of the branch algorithm. In Manhattan, the algorithm performs well when the number of sources comes close to 1 while the algorithm performs well, but instability. The performance of the algorithm is not related to the number of source. It just relies on where to begin. The performance of the algorithm is still bad. When the number of sources increases to 15, the and algorithm are nearly four times worse than branch algorithm. These three algorithms are rather bad in PVTA, comparing to that in Manhattan. PVTA is a city with sparse bus lines. Among these three algorithms, the algorithm performs best while the algorithm performs worst. However, these three algorithms are all rather worse than the branch algorithm. Hence, the branch algorithm is considerably necessary for a asteroid bus route map. VI. CONCLUSIONS The energy problem is one of the greatest problems of all mankind. Researchers have proposed various approaches to either reduce energy consumption, or efficiently and securely utilize energy. In this paper, we discuss about a novel concept called EV energy network, for energy and distribution using EVs. We study how to deploy a minimum number of charge stations in an EV energy network. We know that it is NP-hard problem and develop a branch algorithm and some others for comparison. Simulation use real-world data to demonstrate that the branch algorithm has a good performance. VII. ACKNOWLEDGEMENTS National Natural Science Foundation of China( , , , ), the Natural Science Foundation of Shanghai (15ZR ), NSF under grant CNS REFERENCES [1] Ping Yi, Ting Zhu, Bo Jiang, Bing Wang, Don Towsley, An Energy Transmission and Distribution Network Using Electric Vehicles, IEEE ICC2012 [2] fast chargers [3] T.Zhu and M.Yu. A Dynamic Secure QoS Routing Protocol for Wireless Ad Hoc Network. In Proceedings of the 29th IEEE Sarnoff Symposium,2006 [4] T. Zhu, Z. Zhong, T. He and Z.-L. Zhang. Exploring link correlation for efficient flooding in wireless sensor networks. In em Proceedings of the 7th USENIX conference on Networked Systems Design and Implementation(NSDI), [5] center/pdf/xantrex XW-Hybrid-inverter11-07.pdf. [6] Y.Gu, T.Zhu and T.He. Esc:Energy Synchronized Communication in Sustainable Sensor Networks. In ICNP, [7] U.S. Energy Information Administration, Where can I find data on electricity and distribution losses? Frequently Asked Questions - Electricity, [8] ds pdf [9] Y. Du, X. Zhou, S. Bai, S. Lukic, and A. Huang, Review of nonisolated bi-directional DC-DC converters for plug-in hybrid electric vehicle charge station application at municipal parking decks, 25th IEEE APEC Conference. 2010, pp , Feb 2010 [10] [11] T.Zhu, Z. Zhong, Y. Gu, T.He, and Z. Zhang. Leakage-aware energy synchronization for wireless sensor network. In MobiSys, [12] [13]