2. * Motivation * Objective Find out proper fairness schemes/metrics to meet the customers’ needs to a great extent. Customer : various energy requirement & desired departure time Available Energy : limited for some time Fairly distribute energy?

3. * Use Switch to control power supply (5 min interval) * Information : Energy requirement, desired departure time, battery level, energy available * Cars come to charge in a queue with Poisson dist.. * Each 5 min can only charge limited cars. * Different fairness schemes : Decide who will be charged, update charging queue for every 5 min. * When energy requirement is satisfied, remove the car from the queue.

4. Charged Not Charged New Arrivals Beginning of the queue

5. 8 units10 units5 units Beginning of the queue

6. Current time Desired departure time Units of energy required Spare time-N

7. ParametersData /Distribution Arrival of EV’s Poisson Distribution Arrival rate -> real world data Desired Plug-in time Gaussian distribution [6, 22]: Mean(μ)=14 hrs, StDev(σ)=4 hrs Desired Departure timeArrival time + Desired Plug-in time

8. ParametersData /Distribution Desired distance Fitting real world data to Exponential dist. [20, 90] R (Supply and demand ratio) Energy Available Function of energy consumption (real world data) and R Current battery level (%) Uniform dist. 0%-30% of full battery level Energy Requirement Calculated from desired distance 100 mile = 28 kwh 1 kwh = 6.67 Units of 5 min Full battery level = 100 miles = 186.7 Units of 5 min

11. * MMER fairness scheme does not work well in terms of the metrics we applied because it takes no advantage of the information of departure time. It performs even worse than the baseline Round Robin. * MMDT fairness scheme generally achieves the best performance. * To ensure 95% cars departing without delay, Round Robin: R > 1.8 MMDT: R < 1.1

12. * MMER shows the worst performance in comparison to other charging schemes.

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14. * MMER shows the worst performance in comparison to other charging schemes. zoom out

15. * MMER shows the worst performance in comparison to other charging schemes.

16. * Compare Round Robin with two schemes which take the information of departure time into account. * It turns out that using the additional information can improve the performance.

17. * Compare Round Robin with two schemes which take the information of departure time into account. * It turns out that using the additional information can improve the performance.

18. * Compare Round Robin with two schemes which take the information of departure time into account. * It turns out that using the additional information can improve the performance.

19. * In comparison to FDFS, MMDT fairness scheme achieves better performance when the available power is a little bit more than the required energy.

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21. * In comparison to FDFS, MMDT fairness scheme achieves better performance when the available power is a little bit more than the required energy.

22. Car A (Unit of 5 minute)Car B (Unit of 5 minute)Car ACar B Required Energy Desired Depart Time - Current Time Required Energy Desired Depart Time - Current Time MMDT Metric 3.5322-0.50 2.5221-0.5 2.5110-1.5 Car A (Unit of 5 minute)Car B (Unit of 5 minute) Required Energy Desired Depart Time - Current Time Required Energy Desired Depart Time - Current Time 3.5322 211 100 FDFS:

23. * MMDT fairness scheme achieves the best performance when the available power is a little bit more than the required energy.

25. * 1. Lie about Time (2 methods) * a. punish with extra time b. punished by fine DayClaimActuallyPunishDesired departure time 18am10am(10-8)+1=38am 27am10am(10-7)+2=510am 35am10am(10-5)+3=810am 42am10am(10-2)+4=1210am 5…….. * 2. Lie about Distance (2 methods) * a. punish with extra time (convert distance to time) 1 mile = 10 min * b. punished by fine

26. WeekTasks 1, 2, (Jan 30 – Feb 10)Background reading and literature review. √ 3,4, (Feb 13 – Feb 24)Simulate a baseline charging system. √ 5, 6 (Feb 27 – Mar 9) 8, (Mar 19 – Mar 23) Implement different types of fairness; Each of us is responsible for one specific fairness scheme. √ 9,10, 11 (Mar 26 – Apr 13)Compare the results and make some conclusions. Discuss about lies. √ 12,13, (Apr 16 – Apr 27)Write a technical paper.