Renewable Energy Transmission through Multiple Routes in a Mobile Electrical Grid

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1 Renewable Energy Transmission through Multiple Routes in a Mobile Electrical Grid Ping Yi, Yixiong Tang, Yijie Hong, Yuzhe Shen, Ting Zhu, Qingquan Zhang, Miroslav M. Begovic Shanghai Jiao Tong University, Shanghai, , China; Binghamton University, Binghamton, NY, 13905, USA University of Minnesota, MN, 55455, USA; Georgia Institute of Technology, 30332, Georgia, USA Abstract Vehicle-to-Grid (V2G) technology utilizes the stored energy in electric vehicle batteries to contribute electricity back to the grid. The energy in batteries can move with electric vehicles (EVs). Combining V2G and the mobility of vehicles, EVs can provide a natural energy transmission architecture called mobile electrical grid. The main idea of this paper focuses on multiple energy transmission route in mobile electrical grid from solar energy sources to places as capacity of every energy route is limited. The features of energy route in mobile electrical grid are analyzed and a minimum cost flow algorithm is presented. Simulations using real-world transporting data in Manhattan. Simulations show that this method is efficient. I. INTRODUCTION Vehicle-to-Grid (V2G) is a technology that makes clean and efficient electric-powered transportation possible by allowing electric vehicles (EVs) to power and be powered by the grid [1]. A large number of EVs can become a large energy storage system with V2G. For instance, those power capacity in EVs is 24 times that of the entire electric generation system in the United States, if all light vehicles become EVs [2]. Meanwhile, the energy in EVs also is moved from place to place with EVs movement. Combining V2G and mobility of the vehicles, we present an EV energy transmission model that use EVs to transmit energy from renewable energy sources to energy users [3]. In previous works on mobile electrical grid, we analyse the problem on charging station placement [3], schedule and allocation of energy [4], energy route algorithm [5], and robustness analysis [6]. In this paper, the main idea in this paper is how to search multiple energy routes from the energy sources to energy demander with limit of energy transmission in energy route. The main contributions are as follows: Introduce the mobile electrical grid, and analyse the features for energy transmission from multiple energy sources to multiple charging stations with limit of energy transmission in energy route. A network flow model is introduced to analyze the multiple energy route problem, and a minimum-cost flow algorithm is designed to minimize the cost of energy route while transmit energy from energy sources to destinations. Test the algorithm by real-world transporting data, which is transporting map date using Manhattan bus map in New York city. Compare our algorithm with random algorithm with different number of sources. Results show our algorithm is efficient. The rest of the paper is organized as follows. Related works are discussed in Section II. The problem about how to transmit energy with minimum cost in mobile electrical grid is introduced in Section III. The problem is formulated in Section IV and a solution is provided in Section V. Section VI presents the simulations and analysis. Section VII concludes the paper. II. RELATED WORK V2G is a very promising research area in EV applications. The concept of Vehicle-to-Grid is presented in 2005 [1]. Authors proposed that EVs can generate or store electricity, and with appropriate connections EVs can feed power back to the grid. They thought that V2G can help the storage and backup of renewable energy, since the vehicle fleet has 24 times the power capacity of the entire electric generation system in USA [2]. An aggregator is developed for V2G frequency regulation regarding the optimal control strategy [7]. This paper adopts a dynamic programming algorithm to compute the optimal charging control for each vehicle. An optimization method developed to design power transmission networks with the aim of balancing network efficiency versus the cost of building the network [8]. The above papers are mainly related to the V2G technology, which is focused on some technology to feed energy stored in EVs back to the power grid. We first present the energy transmission model by EVs and do some research on charging station placement, schedule and allocation of energy, energy route algorithm, and robustness analysis. For charging station placement, we mainly study the optimization problem of how to deploy charging stations in an mobile electrical grid. We formulate the optimization problem with the objective of minimizing the number of charging stations while providing full coverage for all bus lines and minimizing the loss of transmission energy in an mobile electrical grid [3]. A hypergraph model is introduced to analyze the EV energy network, and an optimization problem is discussed to minimize the hops of energy route while transmit energy from energy sources to all charging stations [4]. For energy route algorithm, energy route is discussed when some paths are clogged by traffic jam. The problem is formulated by bipartite graph, and then two algorithms are presented /14/$ IEEE

2 which are multi-source shortest route and multi-source edgedisjoint route for computing minimum energy metric route [5]. For robustness analysis, we analyse the impact of traffic congestion on the mobile electrical grid [6]. The paper discuss another problem on energy route, which focuses on energy route algorithm from multiple energy sources to multiple charging stations with limit of energy transmission in energy route. III. PROBLEM DESCRIPTION Fig. 1. Some bus lines in Manhattan The main idea of an mobile electrical grid is that EVs transfer energy from renewable energy (solar or wind) plants to users that need energy (e.g., charging stations and houses). The Fig.1 shows topology of some rectangular city blocks in Manhattan interconnected by streets traversed by bus lines. There are 23th street, 14th street, 8th street and so on from west to east. There are Park Ave, 5 Ave and 6 Ave from north to south. There is a solar power station to generate energy in the southwestern corner. There are multiple charging stations in intersection of bus lines. The mobile electrical grid is comprised of charging stations and EVs and its function is transmit energy from the solar power station to all charging stations. In our previous work, we analyse energy route when some paths are clogged by traffic jam. We presented multi-source shortest energy route algorithm [5]. We assume every energy route can transmit unlimited energy from energy source to energy user in this paper. The hypothesis may not be realistic. Because batteries in EVs are limited, energy that can be transmitted by EVs is limited in any finite time frame. In other words, the bandwidth of energy transmission route in mobile electrical grid is limited. When the bandwidth of energy route is limited, the classical algorithms such as shortest route may not be used in mobile electrical grid. Suppose there is a shortest energy route from some energy source to one energy user. But for the bandwidth of this energy route is less than energy requirement of the user. Another energy route may be found to transmit more energy to supply the user. There are multiple energy sources to generate energy. And there are multiple energy users to require energy in mobile electrical grid. The key problem in this paper is how to find energy routes from all energy sources to all energy users with minimum cost in mobile electrical grid. IV. PROBLEM FORMULATION To clearly illustrate this problem, we take an electric bus company as an example for mobile electrical grid. Let us suppose that there is an electric bus company in a city. All buses in the company are electric. Some buses have access to solar energy stations in rural area, and most of charging stations are placed in the city. Electric buses can transmit renewable power from energy sources in rural area to charging stations in the city. Since the space is limited, most of the renewable energy sources (i.e. solar energy and wind energy) are placed in rural area. One way is to connect the renewable sources in rural area to charging station in urban areas via transmission or distribution lines. It is need to increase power transmission capacity. It will cost many money to invest to build transmission lines, substations and so on. On the other hand, renewable energy cannot be easily connected to the power grid due to its unstable and intermittent nature [9]. The charging of a large number of EVs will have potential impact on the power grid. Since mobile electrical grid can bridge between renewable energy system and EV charging system, mobile electrical grid using electric vehicles may be a good solution to transmit and distribute power from renewable energy system to EV charging system. To build a mobile electrical grid to support electric buses, the problem is how to transmit the energy from renewable energy sources in the outskirts of the city to charging stations in city. In the application scenario for the electric bus company, some renewable energy stations provide power to supply the electric buses to charge. Not all electric buses pass the renewable energy sources. The buses, which go through the renewable energy sources, also do not pass by all charging stations. Supposed we have built many charging stations in city and there are one charging station in one bus stop. Charging stations can store energy from one electric bus and forward the energy to another bus like router. By this way, the energy from renewable energy sources can be transmitted to all charging stations. Fig.2 shows the schematic diagram of bus lines and bus stops transformed from Fig.1. Assume there is one bus stop at every intersection of two bus lines, named S 1,S 2,... Let us suppose there are n intersecting bus stops. Let us set up one charging station in one bus stop S i and its energy demand is demand Si. Let us suppose the number of renewable energy sources is m. Any energy source is E j, 0 <j<mand its energy supply is supply Ej. we assume the model is scaled up in size to represent a realistic rectangular set of city blocks interconnected by bus lines traversing the matrix of mutually orthogonal streets.

3 TABLE I TERM AND NOTATION FOR MOBILE ELECTRICAL GRID Term Description Example Notation Energy Router Energy Link Energy Route Energy Transmission Bandwidth Energy Demand Energy Transmission Loss It is an EV charging station with batteries, which can store energy. It can discharge EVs to charge itself and then release the energy to other EVs. It can store energy and forward energy like routers in the communication network. It is energy transmission link between two energy routers. It is composed of road between energy router and EV running on road. Road and EV are similar to cable and communication signal in data networks. It is the combination of energy links from energy source to the destination that accepts energy. One energy route may contain many energy links. It is maximum amount of energy which can be transmitted in one energy route within one time unit. It is similar to network bandwidth in computer network EV charging stations not only act as energy routers, but also provide power energy for electric buses. For buses that have fix schedules and routes, we can obtain the power consumption of every bus for a round trip. Therefore, we can obtain the power requirement of every charging station through the power consumption of the buses. There is energy loss in process of charging and discharging batteries. In our previous work, we have discuss energy loss in one time of charging and discharging batteries and it is about 10% [3]. There is one time process of charging and discharging batteries when energy is forwarded at energy route. Energy router S 5 can accept energy from E 1 and forward it to S 6. S 1 S 2 is one energy link between energy router S 1 and energy router S 2. Energy route S 9 S 6 contains energy links S 9 S 5 and S 5 S 6 and names R 9,6. The maximum amount of energy transmission in R i,j within one hour is nkwh. The energy transmission bandwidth in R i,j is n. Charging station in S 1 need energy nkwh to charge EVs. Energy is transmitted by R 9,6 and is forwarded at S 5. Energy will lose 10% at S 5. S i L i,j R i,j B Ri,j D Si C Ri,j Fig. 2. Schematic diagram of bus lines Charging stations in the mobile electrical grid is different from charging stations for EVs. Charging stations for EVs get energy from the power grid and charge it to EVs immediately, as no energy storage is provided in them. The charging stations in the mobile electrical grid are equipped with an energy storage unit, which can receive energy from EV and store energy in the energy storage unit. They can also charge EVs by their energy storage. In other words, the charging stations in the mobile electrical grid can receive energy from one EV, store and then forward it to another EV. Their functions are similar to routers in the communication network. Charging stations in the mobile electrical grid are called as energy routers. The router in the communication network only forwards packets. Energy routers, however, do not only forward energy but also charge EVs. At this point, energy routers are more similar to nodes in mobile ad hoc network, which are both routers and terminal users. For clarity, we define some terms and notations in Table I. Let us suppose one charging station S i need energy D Si. There is one energy route R 1 from energy source to S i and its energy transmission bandwidth B R1.IfB R1 <D Si, it means S i can received enough energy by energy route R 1. The second energy route R 2 need to be find to transmit energy to R 1.If B R1 + B R2 >D Si, S i can receive enough energy by these routes. Otherwise, we must find the third or fifth energy route to transmit energy for S i. For example, supposed charging station S 10 needs power energy 1000 KwH every hour Fig.2. Renewable energy source E 1 have also enough energy to support S 10. However, EVs in bus line 8 can not transmit those enough energy from E 1 to S 10. Because batter capacity in EVs is limited and the number of EVs to transmit energy is limited, energy can be transmitted in one bus line is limited. To support S 10 enough energy, we may find other energy routes: R 1 : E 1 S 5 S 6 S 10,R 2 : E 1 S 1 S 2 S 10,... There are many energy routes from energy sources to the charging station. There is different energy transmission loss in every energy route. To reduce energy loss, the total number of energy forward for all energy route should be minimized. V. PROBLEM SOLUTION To solve the above problem, it is to minimize energy loss when energy is transmitted through multiple energy routes from energy source to charging station. There are different energy loss in every energy route, for the number of energy forward is different. One time of energy forward is one time that charging station charges energy from one EV and discharge this energy into another EV. In the previous research [3], we know energy loss is about 10% under one time of energy charge and discharge. We may find one combination

4 of multiple energy routes to minimize energy loss as charging station can receive enough energy from energy sources. We transform bus line graph in Fig.2 to network graph G(V,E). V stands for the bus stop at cross of bus lines, such as S 1,S 2. E stands for energy route. We may introduce network flow model to describe the problem. Each edge(i, j) has an associated cost c i,j that denotes the energy loss per unit energy flow on the edge. We know that the energy flow cost varies linearly with the amount of energy flow. We also associate with each edge(i, j) route bandwidth B i,j that denotes the maximum amount that can transmit energy on the edge. We associate with each node i V an integer number k(i) representing its supply or demand. If k(i) > 0, node i is a supply node, such as an energy source. If k(i) < 0, node i is a demand node, such as an charging station. If k(i) =0, node i is a transshipment node, such as an energy route. The decision variables in the problem are energy flows and we represent the energy flow on an edge(i, j) E by x i,j. The minimum-cost flow problem is an optimization model formulated as follows: Subject to: min (i,j) E c i,j x i,j (1) xi,j x j,i = k(i), all i V (2) x i,j B i,j, all(i, j) E. (3) There are one or several renewable energy sources to supply energy in mobile electrical grid. There are also many charging stations to receive energy. EVs in bus lines transmit energy and energy routers forward energy in mobile electrical grid. There are multiple energy routes from sources to charging stations. The key problem is to find the minimum-cost routes within multiple energy routes. We design a multi-source multidestination minimum-cost energy flow algorithm as follows: The main idea of the algorithm is to convert multiple sources and multiple destinations into single source and single destination. There are several classical algorithms on minimum-cost flow [10], such as cycle canceling algorithm or successive shortest path algorithm, but they are all minimum-cost flow algorithm on single source and single destination. There are multiple energy sources and multiple energy demanders in mobile electrical grid. Therefore, we must transform the graph before we use the classical algorithms. We add a virtual source node and a virtual destination node in line 7 as single source and single destination. We add the link from the virtual source node to every source in line 9. We assign cost of this link is 0 in line 10 and setup capacity of the link by the supply amount of this source in line 11. By the way, the previous source nodes are converted into energy routers. They can only provide its previous supply amount, for their input amount is the same as their previous supply amount. Similarly, we add the link from the virtual destination node to all energy demander and assign their cost as 0 and capacity of energy link by their demand amount. Then, we search minimum-cost energy flow from the Algorithm 1: multi-source multi-destination minimumcost energy flow algorithm 1 Line all bus lines; 2 Destination all charging stations and energy demand; 3 Source all energy sources and energy supply; 4 Cost cost of energy route; 5 Bandwidth bandwidth of energy transmission route; 6 construct network graph G by transportation and bus line; 7 add a virtual source node s 0 and a virtual destination node d 0 in graph G; 8 while s i Source do 9 add an edge(s 0,s i ) in graph G ; 10 cost s0,s i =0 ; 11 Bandwidth s0,s i = supply si ; 12 while d i Destination do 13 add an edge(d i,d 0 ) in graph G ; 14 cost di,d 0 =0 ; 15 Bandwidth di,d 0 = demand di ; 16 find minimum-cost energy flow from s 0 to d 0 in graph G using minimum-cost flow algorithm ; 17 return minimum-cost, maximum flow ; source to the destination using classical minimum-cost flow algorithm. VI. SIMULATION AND ANALYSIS A. Experiment Setup To evaluate the performance of the algorithm, two kinds of bus system are adopted. One is the bus map of Manhattan in New York [11]. There are 37 bus lines and about 400 bus stops in Manhattan. Select bus stops which are in the intersecting point between two or more bus lines as charging stations. After pre-processing bus map data, 159 bus stops are obtained. The cost of energy route is proportional to total hops. The number of total hops, which is the sum of all route hops from energy source to charging stations, is calculated to test the algorithm. This metric represents the energy loss for transmission from energy source to charging stations in the mobile electrical grid. The smaller the number of total hops, the smaller will be the energy loss in the transmission process. The number of route hops on each route from renewable energy node to charging station is calculated. The total route metric is the sum of route hops in all routes. B. Experiment Results In the simulation, the number of renewable energy sources varies from 1 to 10. The number of energy demand node is 10. Suppose the amount of energy demand of every demander is 100. Therefore, the sum of energy demand is Suppose the capacity of every energy route, i.e. bus line, is 90. When there are two bus line in one edge, the capacity of this edge is 180. For each case, place the renewable energy sources on the bus map randomly using independent random seeds to obtain

5 Max Flow Max Flow Total Cost 4 x Random Cost Cost/Flow /Flow Random Cost/Flow (a) Cost under maximum flow 0 (b) Cost under per flow (a) Maximum flow (b) Minimum-cost Fig. 3. The maximum flow and minimum-cost under different number of energy sources in Manhattan bus map Fig. 4. Compare minimum-cost flow algorithm with random algorithm under different number of energy sources in Manhattan bus map the results. The process is repeated for 1000 times to obtain averages. The proposed algorithm is implemented in Matlab R2010b. Compare the performance with the random algorithm. Random Algorithm: For each energy source and destination, arbitrarily selects a sequence of energy routes from these sources to these destination. Then we calculate the sum of cost of these routes. Fig. 3(a) shows maximum flow from all energy sources to all destinations in Manhattan with different numbers of energy sources. It can be observed that sum of total cost increases with the increasing number of energy sources. Because capacity of energy transmission of bus line is limited, energy demanders can not get enough energy as the number of energy sources is less than 6. The number of energy route is increase with increment of number of sources. When the number of sources is 6, network graph G gets its maximum flow. Fig. 3(b) shows minimum-cost from all energy sources to all destinations in Manhattan bus map with different numbers of energy sources. It can be observed that sum of minimumcost increases with the increasing number of energy sources as the number of source is less than 6. The minimum-cost start to decrease after the number of source is less than 6. It is because the network flow does not get its maximum flow before the number of source is less than 6. When a new energy source is added, some energy routes are added to transmit more energy. Therefore, total cost will increase with increment of energy source. When the number of source reaches six, the network flow assumes its maximum value. After this time, network flow can not increase with increment of the number of source. The algorithm will find some shorter energy routes with increment of more sources. Therefore, minimum cost will start to decrease when the number of sources is larger than six. We compare our algorithm with random algorithm under different number of energy sources in Manhattan bus map in Fig. 4. Fig. 4(a) shows total cost from all energy sources to all destinations under maximum flow. In other words, we calculate total cost for all flows. The cost of random algorithm is about 7-10 times more than that of our algorithm. For example, the cost of our algorithm is 3200 and the cost of random algorithm is Fig. 4(b) shows cost of two algorithm under per flow. The cost of per flow is that total coat / total flow. The cost of random algorithm is about times more than that of our algorithm. We observe that the cost in our algorithm is more stable than that of random algorithm, especially when considered as normalized per flow. Simulations show that our algorithm is efficient. VII. CONCLUSIONS This paper discusses the energy transmission through multiple route in the mobile electrical grid. A network flow model is used to analyze the transportation map, and then a minimumcost flow algorithm is adopted to find multiple route from energy sources to users. The bus map data of Manhattan in New York city is used to test the algorithm. Simulations show that the algorithm is efficient. VIII. ACKNOWLEDGEMENTS This work was supported by National Natural Science Foundation of China ( , , ), the NSF grant CNS REFERENCES [1] W. Kempton, J. 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