Scheduling for Wireless Energy Sharing Among Electric Vehicles

Transcription

1 Scheduling for Wireless Energy Sharing Among Electric Vehicles Zhichuan Huang Computer Science and Electrical Engineering University of Maryland, Baltimore County Ting Zhu Computer Science and Electrical Engineering University of Maryland, Baltimore County Abstract To be able to create a sustainable system for electric vehicles, charging facilities are used as energy providers for these cars and scheduling is done using simple algorithms such as FIFO or EDF. However, these algorithms may not provide the best performance for charging cars and energy is lost during wired transmission. On the contrary to these solutions, our aim is to develop an algorithm for scheduling wireless energy sharing among electric vehicles. We give an optimal offline solution for the scheduling problem. Besides we develop an online algorithm which is based on shortest job first. We conduct system evaluation with simulator that we implemented. Results show our algorithm achieves better throughput than FIFO, EDF and our proposed online algorithm have close performance with optimal solution. I. INTRODUCTION Carbon dioxide emissions of vehicles that run with gas to are very high. With development in technology, vehicles that use electricity become popular. However, since the battery in electrical vehicle is limited, thus how to charge them becomes an important problem. Most common approach for charging these cars is to use charging facilities and charge the vehicles through wires. However, it limits the application of electrical vehicles and makes electrical vehicles difficult for ordinary people to purchase for daily usage. Doing charging wirelessly started to surpass this idea since it is more convenient and easy. Instead of using charging facilities to charge vehicles, our proposed approach is to share energy between electric vehicles wirelessly. In particular, we study the possibility of sharing energy in electrical vehicles among different vehicles when they are parked in parking lot. To apply energy sharing of electrical vehicles in parking lot, we need to investigate how to scheduling the wireless charging among electrical vehicles. Previous works are mostly based on charging electric vehicles over wires using charging facilities and these previous approaches use simple algorithms similar to FIFO or EDF for scheduling charging. In our work, our aim is to have a system in a parking lot for electric vehicles so that they will share energy wirelessly in order to be charged. However, the problem is how to schedule charging. This is important because development in wireless technology is increasing and reusability of energy is a concern. Electric vehicles are green compared to vehicles using gas and without using charging facilities for charge is flexible. However, vehicles need to be parked in parking lots designed for this wireless charging. No need to worry about running out of charge because another car with surplus energy can arrive in the future. We first formulate our problem and define our design goal. Then we analyze the possible optimal solution with given assumptions and provide proof the optimal solution for wireless charging scheduling. The basic idea of our proposed solution is to split problem to sub problems; then find an optimal solution for sub problems, then we prove optimal solution for whole problem is achieved. In addition, we develop an online solution for practical scenarios. The algorithm is based on shortest job first algorithm. However, we add some situation checking to improve the performance of algorithm. To evaluate the performance of our proposed scheduling algorithm, we conduct simulations for 100 electrical vehicles in parking lot with different scenarios. The main contribution of our paper is summarized as follows: To our knowledge, this is the first work to develop a scheduling algorithm for sharing energy wirelessly between electric vehicles. We implement the algorithm and the simulator to run our algorithm and compare it with existent algorithms. Our evaluation indicates that our proposed optimal solution provides better throughput than FIFO, EDF and Shortest Job First. For three online algorithms, our proposed Online Shortest Job First performs better than other two algorithms. The rest of the paper is organized as follows: the problem is formulated in Section II; the detailed design for scheduling charging vehicles is described in Section III; implementation and simulations are provided in Section IV; related work are discussed in Section V; finally, we conclude the paper in Section VI. II. MODEL Electric vehicles are becoming more popular. However, how to charge them is an important problem. In our work, our aim is to have a system in a parking lot for electric vehicles so that they will share energy wirelessly in order to be charged. However, the problem is how to schedule charging. This is important because development in wireless technology is increasing and reusability of energy is a concern. Electric vehicles are green compared to vehicles using gas and without using charging facilities for charge is flexible. However, vehicles need to be parked in parking lots designed for this wireless charging (shown in Figure 1). A. Problem Formulation Let the set of vehicles be N = {1, 2,, n} and D and S are demander set and supplier set with energy shortage and

2 Fig. 1. Parking Lot With Wireless Chargers Algorithm 1 Optimal Scheduling Input: D, S Output: Energy transmission set Q 1: Fetch the vehicle i in D which leaves first; 2: if i is chargeable then 3: Charge i with the energy provided in S in order of latest departure time; 4: else 5: for vehicle j is charged before do 6: if i becomes chargeable after remove j then 7: Recalculate the solution with largest future energy available; 8: end if 9: end for 10: Select the case between Q m and (i, ( Q m - 1) vehicles in Q m ) with largest future energy available; 11: end if 12: Go to Step 1 until the all vehicle in D is processed; Fig. 2. An Example of Scheduling energy surplus. And all the vehicles are parked in the same parking lot. Each vehicle arrives and leaves at a specific time and can supply or need a certain amount of energy. An example is given in Figure 2. Five cars are given in the example. For vehicle 1, it can supply 60kW h energy for other vehicles; for vehicle 2, it needs 40kW h energy; and for vehicles 3-5, they all need 20kW h energy. And the block shows the arriving and leaving time. Then our goal is to maximize the number of vehicles can get enough energy before they leave. In this example, vehicle can either decide to charge vehicle 2 and vehicle 3 or charge vehicles 3-5. To maximize the throughput, we should assign vehicle 1 to charge vehicles 3-5 even vehicle 2 arrives and leaves early. There are other complex cases of charging and the detailed analysis and design in described in latter sections. III. DESIGN With the problem formulation in previous section, we detailed describe our design in this section. We first analyze the possible optimal solution with given assumptions and provide proof the optimal solution. Then we propose an online shortest job first design to solve the problem in real-time. A. Optimal Solution To analyze the possible optimal solution for electrical vehicle charging scheduling, we first give some assumptions to simplify the problem. Assumption 1: Arrival time to parking lot and departure time from parking lot of vehicles are known Assumption 2: Charge status of each car is known. Either demander or supplier. Assumption 3: The charging speed between vehicles is fast enough for energy transmission. In reality, the assumption 2 can be implemented by devices deployed in each vehicle to collect charging status. Then when each vehicle entering the lot sends a charging request to a base station and informs it about its status (demander or supplier). For assumption 3, with the development of charging technology, we believe it can be achieved in near future. For assumption 1, it is generally not possible to predict accurate future information, thus it is only used for analysis of optimal solution. Our proposed approach is to develop a scheduling algorithm that achieves maximum amount of cars with enough charge to reach their destinations. Then with those assumptions, we propose an dynamic programming algorithm to find the optimal scheduling. Firstly, overlaps between cars are generated. An overlap is a time period and starts with a car arrival which makes number of cars in the lot at least 2 and end with a car departure or a new car arrival. Basic idea is for each demander car with earliest departure time in an overlap it is checked if it can be charged. If yes then this is sub-optimal solution. If not, sub-optimal solution is tried to be found either using previous sub-optimal solution without new car or replacing one of the old cars in the previous sub-optimal solution with the new demander car. The detailed algorithm is described in Algorithm 1. We first fetch the vehicle i in D which leaves first (Line 1). Then if i is chargeable, we decide to charge i with the energy provided in S in order of latest departure time (Line 2-3). Otherwise, for vehicle j is charged before, if i becomes chargeable after remove j, we recalculate the solution with largest future energy available (Lines 4-9). After checking for all vehicles charged before, we select the case between Q m and (i, ( Q m - 1) vehicles in Q m ) with largest future energy available (Lines 10-11). Finally, The algorithm goes to Line 1 until the all vehicle in D is processed (Line 12). To prove Algorithm 1 is optimal solution, we first suppose

3 first m vehicles solution Q m with throughput Q m is optimal solution, then we prove that solution Q m+1 produced by Algorithm 1 for first m +1 vehicles solution is also optimal solution. Condition 1: i is chargeable. In this case, Q m+1 = Q m + 1. If i is not in Q m+1, then we can have the contradiction that Q m = Q m + 1, thus i is in the solution. Since the other vehicles are the optimal solution of first m vehicles, they should be in the Q m+1 too. We only need to select the way of charging i with largest future energy, which is shown in Line 3 in Algorithm 1. Thus, under this condition, our proposed algorithm is optimal solution. Condition 2: i is chargeable if remove one of the vehicles in Q m. Select the optimal solution of m vehicles or ( Q m 1) vehicles in Q m and i as optimal solution. Then we prove our proposed algorithm is optimal solution under Condition 2. a) Select the optimal solution of m vehicles. Since optimal solution of m vehicles is better than ( Q m 1) vehicles in Q m and i, thus we only need to prove optimal solution of m vehicles is better than i and other ( Q m 1) vehicles which are not all in Q m. Suppose i and other ( Q m 1) vehicles which are not all in Q m is optimal solution of Q m+1, then we can have a subset of Q m with ( Q m 1) vehicles except vehicle k have lower future energy than ( Q m 1) vehicles which are not all in Q m, otherwise ( Q m 1) vehicles which are not all in Q m and k is the optimal solution of Q m. However, the subset of Q m with ( Q m 1) and i should be optimal solution, which contradicts with the assumption. b) Select Q m 1 vehicles in Q and i. Since optimal solution of m vehicles is worse than (Q m 1) vehicles in Q m and i, thus we only need to prove optimal solution of m vehicles is better than i and other ( Q m 1) vehicles which are not all in Q m. Suppose i and other ( Q m 1) vehicles which are not all in Q m is optimal solution of Q m+1, then we can have a subset of Q m with ( Q m 1) vehicles except vehicle k have lower future energy than ( Q m 1) vehicles which are not all in Q m, otherwise ( Q m 1) vehicles which are not all in Q m and k is the optimal solution of Q m. However, the subset of Q m with ( Q m 1) and i should be optimal solution, which contradicts with the assumption. For both two cases a) and b), we can also prove that our proposed algorithm is the optimal solution. Combined with analysis of Condition 1, we can prove that in all scenarios, our proposed algorithm is the optimal solution. B. Online Solution Though optimal solution can be obtained by dynamic programming, it needs whole future information, which is not applicable in reality. In this section, we propose an online algorithm to do the scheduling. Since we want to maximize the throughput, thus we should rather charge cars which need less energy. Thus shortest job first algorithm is our first choice. However, in some case, the shortest job first algorithm fails, shown in Figure 2. When car 2 enters parking lot, we will charge car 2 with car 1. Then when car 4 and 5 enters in, we dont have enough energy to charge the car. Thus we make some revision on shortest job first algorithm for better performance. Algorithm 2 Online Shortest Job First Input: D i, S i in overlap i Output: Energy transmission set Q 1: Find list L of cars which require energy and will arrive soon after overlap; 2: for each vehicle in L do 3: if required energy of car C j is less than car with least required energy in D i then 4: Reserve energy C j needs in supplier in S i which leaves first; 5: end if 6: end for 7: Follow the same process as traditional shortest job first. The basic idea of online shortest job first algorithm is to use short term future information. If we know the information of car 3, 4 and 5, we can skip car 2 and charge other three cars, which performs high throughput. The detailed algorithm is in Algorithm 2. We first find list L of cars which require energy and will arrive soon after overlap (Line 1). Then for each vehicle in L, we check if required energy of car C j is less than car with least required energy in D i. If yes, we reserve energy C j needs in supplier in S i which leaves first (Lines 2-6). After processing each vehicles in L, we follow the same process as traditional shortest job first for scheduling charging vehicles (Line 7). However, we need short term future information to do online shortest job first algorithm. Currently, we use accurate short term future information. In future, we can use GPS in car to predict cars which will arrive soon. For example, if the location of one car is close to parking lot, we can predict its highly possible this car will enter parking lot very soon. IV. EVALUATION To evaluate the performance of online shortest job first algorithm, we implement a simulator to test the performance of four algorithms. Four algorithms are: Online Shortest Job First, Earliest Job First, FIFO and optimal solution. Note that Online Shortest Job First is the Algorithm 2 instead of traditional Shortest Job First. We then do some simulations on three different scenarios. All the results in simulations are the average result of 100 simulations. For each simulation, each electrical vehicle will be randomly assigned to be demander or supplier with specific amount of energy. A. Random Scenario We first do the simulations in a random scenario, in which arrive time and departure time of all vehicles are random generated with uniform distribution. The results are shown in Figure 3. From Figure 3, we can find optimal solution is best algorithm as proved. And online shortest job first algorithm is close to optimal solution. And the advantage of online shortest job first algorithm increases with the increase of number of cars. When there is 100 vehicles in simulation, we can find that the performance of different algorithms are various. Optimal solution performs best and EOF performs worst. And our

4 Fig. 3. Fig. 4. Throughput in Random Scenario Throughput in Mall Scenario proposed online shortest job first algorithm is more than 30% better than EOF. B. Mall Scenario Then we do the simulation under mall parking lot scenario. To simulate the arrive time of departure time of cars in mall parking lot, we first use normal distribution to generate arrive time of cars. And the mean of arrive time is 6PM mostly range from 4PM to 8PM. Then we generate interval of arrive time and departure time with normal distribution. The mean of interval is 2 hours and mostly range from 1 hour to 3 hours. Then we get the departure time of cars by adding arrive time and interval. The simulation result under these data are shown in Figure 4. From Figure 4, we can find optimal solution is best algorithm as proved. And online shortest job first algorithm is better than other algorithms especially when number of cars is large. When there is 100 vehicles in simulation, we can find that the performance of different algorithms are various. Optimal solution performs best and EOF performs worst. And our proposed online shortest job first algorithm is more than 20% better than EOF. C. Commercial Building Scenario We also do the simulation in building scenario. To simulate the arrive time of departure time of cars in an office building, Fig. 5. Throughput in Building Scenario we first use normal distribution to generate arrive time of cars. And the mean of arrive time is 9AM mostly range from 7AM to 11AM. Then we generate departure time with normal distribution. The mean of departure time is 5PM and mostly range from 3PM to 7PM. The simulation result under these data are shown in Figure 5. From Figure 5, we can find optimal solution is best algorithm as proved. However, the difference among four algorithms are very close. A reasonable explanation is in building scenario, all cars stay in parking lot for a long time, thus when decide which car to charge, we have enough information about most of cars. And with more information, each algorithm performs similar throughput. When there is 100 vehicles in simulation, we can find that the performance of different algorithms are various. Optimal solution performs best and EOF performs worst. And our proposed online shortest job first algorithm is more than 10% better than EOF. In summary, for all three scenarios, optimal solution always performs best since it is proved to be optimal. For other three online algorithms, our proposed shortest job first always performs better than other two algorithms. The possible explanation is because our design goal is to maximize the throughput, thus if we finish shortest job first, it provides more time for vehicles with surplus energy to share energy with vehicles need energy. V. RELATED WORK Our work focuses on scheduling wireless charging of electrical vehicles in the parking lot. The related work contains three part: i) energy efficient system; ii) Vehicle-to-Grid; and iii) electrical vehicle charging. Energy efficient systems are widely studied to save energy cost in different areas. In [2], models of HVAC operation, building manager and owner are analyzed to design incentive scheme for energy savings. In [6], local energy storage is colocated with DC appliances to save energy conversion loss. Local generation and renewable energy are investigated to reduce energy cost [12]. A novel architecture is proposed to utilizing existing home resources to reduce energy consumption [8]. Efficient power allocation in AC electrical systems is analyzed with a new variation of knapsack problem [14]. In [5], optimal power flow problem in distributed network is solved with SOCP relaxation of the problem. In [15],

5 different types of energy storage devices are investigated to reduce energy cost in datacenters. [3] evaluates the effect of storage on the electrical grid under different electricity pricing schemes and discusses possible pricing schemes under which storage adoption is profitable for homeowners. [1] analyzes the hourly aggregate load data to study whether the choice of TOU parameters adequately reflects the aggregate load, and to study whether TOU pricing has actually resulted in a decrease in the mean peak-to-average ratio. In [13], a novel demand response mechanism is proposed to exploits appliance elasticity to decrease peak loads, a fuzzy-logic based controller for appliances and a signal generator for the utility are designed to reduce the power consumed by appliances. Vehicle-to-Grid (V2G) is a very promising research area in EV applications. In [10], authors proposed that electrical vehicles can get electricity from power grid and feed power back to the power grid in some conditions. They thought that V2G can help the storage and backup of renewable energy, since the battery in electrical vehicles is large and can supply for daily usage in residential buildings [11]. In [7], authors developed techniques for V2G frequency regulation to better control strategy. The above papers are mainly related to the V2G technology, which is focused on technology to feed energy stored in electrical vehicles back to the power grid. Different from V2G, our work is to share energy among electrical vehicles by wireless charging. Compared to V2G, our approach can be more flexible since we do not restrict the electrical vehicles to get energy from traditional power grid. Large scale charging of electric vehicles [4] is one of the works that has been done for schedule charging for electric vehicles. However, proposed approach is to use a charging facility and an operator to manually schedule charging. Also in order be charged vehicle, owners have to make payment and the most profitable vehicles have priority over others. Dynamic Energy-Oriented Scheduling (DEOS) [16] is similar to our case. Proposed approach is to make scheduling according to real time available energy and energy consumptions by each task. Like in our system energy changes dynamically however, this scheduling is for tasks in wireless sensor networks. Previous works are mostly based on charging electric vehicles over wires using charging facilities and these previous approaches use simple algorithms similar to FIFO or EDF for scheduling charging. In our work, our aim is to have a system in a parking lot for electric vehicles so that they will share energy wirelessly in order to be charged. VI. CONCLUSION To sum up, using electric vehicles is the very convenient compared to vehicles that use gas or fuel. It is cheaper compared to large facilities, green and more flexible. But to create a sustainable system for electric vehicles, there should be an efficient way to charge them. In order to achieve this, an efficient scheduling algorithm is necessary to charge maximum amount of cars to reach their destinations in a parking lot. After couple of researches we came up with two particular papers that are similar to our approach in some ways. But these approaches are for either using wires and facilities or for tasks. Existent scheduling algorithms do not give the optimal solution for our case. Therefore, we developed our own algorithms. First algorithm uses dynamic programming to charge maximum amount of cars in a parking lot. We also proved this algorithm. However, in order to implement it, future information should be known. In reality, this is not true all the time. Therefore, we developed a second algorithm that uses shorter term future information and prediction. We compared our algorithms with FIFO, Shortest Job First and Earliest Deadline First algorithms. In our simulation results we find that FIFO and EDF never reach the maximum output that our algorithms have reached. On the other hand, we realize that Shortest Job First almost reached optimal solution but never as high as our dynamic programming. Our goal for future is to expand the scale of parking lots to bigger parking lots. ACKNOWLEDGMENT This work was supported by NSF CNS REFERENCES [1] A. Adepetu, E. Rezaei, D. Lizotte, and S. Keshav. Critiquing time-ofuse pricing in ontario. In IEEE International Conference on Smart Grid Communications, [2] A. Aswani and C. Tomlin. Incentive design for efficient building quality of service. In 50th Annual Allerton Conference on Communication, Control, and Computing, [3] T. Carpenter, S. Singla, P. Azimzadeh, and S. Keshav. The impact of electricity pricing schemes on storage adoption in ontario. In e-energy, [4] S. Chen and L. Tong. iems for large scale charging of electric vehicles: Architecture and optimal online scheduling. In Smart Grid Communications (SmartGridComm), 2012 IEEE Third International Conference on, pages , Nov [5] L. Gan, N. Li, U. Topcu, and S. H. Low. Optimal power flow in distribution networks. In IEEE Conference on Decision and Control, [6] S. K. Ghai, Z. Charbiwala, S. Mylavarapu, D. P. Seetharamakrishnan, and R. Kunnath. DC picogrids: A case for local energy storage for uninterrupted power to DC appliances. In e-energy, [7] S. Han, S. Han, and K. Sezaki. Development of an optimal vehicle-togrid aggregator for frequency regulation. Smart Grid, IEEE Transactions on, 1(1):65 72, [8] H. Hlavacs, K. Hummel, R. Weidlich, A. Houyou, A. Berl, and H. Meer. Energy efficiency in future home environments: A distributed approach. Home Networking, 256:69 84, [9] J. K. Johnson and M. Chertkov. A majorization-minimization approach to design of power transmission networks. In Decision and Control (CDC), th IEEE Conference on, pages IEEE, [10] W. Kempton and J. Tomić. Vehicle-to-grid power fundamentals: calculating capacity and net revenue. Journal of power sources, 144(1): , [11] W. Kempton and J. Tomić. Vehicle-to-grid power implementation: From stabilizing the grid to supporting large-scale renewable energy. Journal of Power Sources, 144(1): , [12] L. Lu, J. Tu, C.-K. Chau, M. Chen, and X. Lin. Online energy generation scheduling for microgrids with intermittent energy sources and co-generation. In SIGMETRICS, [13] P. Srikantha, S. Keshav, and C. Rosenberg. Distributed control for reducing carbon footprint in the residential sector. In 2012 IEEE Third International Conference on Smart Grid Communications, [14] D. Wang, C. Ren, A. Sivasubramaniam, B. Urgaonkar, and H. Fathy. Energy storage in datacenters: What, where, and how much? In SIGMETRICS, [15] L. Yu and C.-K. Chau. Complex-demand knapsack problems and incentives in AC power systems. In AAMAS, [16] T. Zhu, A. Mohaisen, Y. Ping, and D. Towsley. Deos: Dynamic energy-oriented scheduling for sustainable wireless sensor networks. In INFOCOM, 2012 Proceedings IEEE, pages , March 2012.