Auc2Charge: An Online Auction Framework for Electric Vehicle Park-and-Charge Qiao Xiang 1, Fanxin Kong 1, Xue Liu 1, Xi Chen 1, Linghe Kong 1 and Lei Rao 2 1 School of Computer Science, McGill University 2 General Motors Research Lab July 16th, 2015 Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 1/ 26
Introduction Introduction Electric Vehicles Electric Vehicles(EV) Crucial component of Intelligent Transportation System(ITS) Shift energy load from gasoline to electricity Cause high penetration of power grid Require large-scale deployment of charging stations Various charging stations Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 2/ 26
Introduction Park-and-Charge Park-and-Charge An up-and-coming mode for charging stations A parking lot equipped with Level 1 and Level 2 chargers EVs get charged during parking, e.g., a few hours Slow charging, inexpensive hardware and high utilization of space A Controller A C B Charging Points C B Parking Lot Figure: An illustration of park-and-charge Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 3/ 26
Introduction Current Field Deployment Park-and-Charge Workplace, airport, military base and etc. Pricing policies Pay-per-use Flat rate Boston University Seattle-Tacoma Airport Sources:bu.edu and plugincars.com Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 4/ 26
Motivation and Challenges Pay-Per-Use and Flat-Rate Pricing Motivation Advantages Simple and straightforward Helpful for early market expanding Limitations Overpricing and underpricing Undermined social welfare i.e., sum of station revenue and user utilities Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 5/ 26
Motivation and Challenges Motivation Social Welfare in Park-and-Charge: An Example Pay-per-use and flat-rate: allocate 15kWh to each EV A SOC: 20/40 B SOC: 5/25 Park and Charge +15 +15 A SOC: 35/40 B SOC: 20/25 However, Marginal utilities of EVs are different Lower arriving SOC Higher marginal utility Ignorance of such difference Undermined social welfare Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 6/ 26
Motivation and Challenges Motivation Social Welfare in Park-and-Charge: An Example To maximize social welfare: Allocate electricity to low SOC vehicle as much as possible A SOC: 20/40 B SOC: 5/25 Park and Charge +10 +20 A SOC: 30/40 B SOC: 25/25 Pay-per-use and flat-rate focus on station revenue, not social welfare. Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 7/ 26
Motivation Motivation and Challenges Motivation Future market deployment of park-and-charge desires an efficient market mechanism to Avoid overpricing and underpricing Maximize social welfare Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 8/ 26
Our Focus Motivation and Challenges Our Focus Our Focus Investigate auction as market mechanism for park-and-charge Auc2Charge: an online auction framework Understanding system benefits via numerical simulation Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 9/ 26
Motivation and Challenges Related Work Related Work Auctions has been widely studied in Internet Adwords, cloud computing and smart grid. Social welfare maximization Truthfulness and individual rationality What enables Auc2Charge? Budget-constrained online auction and randomized auction theory Auc2Charge can be extended to other operation modes of charging stations, e.g., fast charging reservation. Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 10/ 26
System Settings and Problem Formulation System Settings and Problem Formulation SOC: 60% Bid 1 Lose 2-3pm, $0.50, 5kWh Bid 2 Win 3-4pm, $2.00, 9kWh... Bids AllocaKon and Pay Decision.... AllocaKon and Pay Decision Bids SOC: 30% Bid 1 Win 2-3pm, $1.50, 6kWh Bid 2 Win 3-4pm, $3.00, 8kWh... EV Customer 1 EV Customer N EVs arrive, park-and-charge, and leave Users send bids on how much to charge, when to charge and how much to pay, i.e., {bj k(t), ck j (t)}, to the charging station Auctions are conducted every time slot, and users get notified Users can adjust future bids anytime during parking, Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 11/ 26
System Settings and Problem Formulation A Binary Programming Formulation PNC : subject to K k=1 t=1 M K j=1 k=1 K k=1 T maximize T M K t=1 j=1 k=1 b k j (t)y k j (t) Social Welfare b k j (t)y k j (t) B j, j, Users Budget c k j (t)y k j (t) R(t), t, Station Supply K k=1 y k j (t) 1, j and t, No Double Wins c k j (t)y k j (t) C j (t), j and t, Unit-Time Charging Capacity y k j (t) {0, 1}, j, k and t. Winning Indication Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 12/ 26
System Settings and Problem Formulation Challenges Challenges PNC is NP-hard The auction must be computationally efficient PNC is stochastic The auction must be online Users may bid strategically The autcion must be truthful and individual rational Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 13/ 26
Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell Auc2Charge in a Nutshell 1. Decompose PNC into smaller auctions via bids update process. PNCone(1) PNCone(2) PNC PNCone(t) Bids Update Process PNCone(T) Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 14/ 26
Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell Auc2Charge in a Nutshell Bids Update Process: Originally proposed in budget-constrained online Adwords auction 1, and extended to resource auction in cloud computing. 2 Intuition: adjust reported valuation in PNC one (t) based on the results from PNC one (t 1) Users not getting electricity in t 1 No adjust in t Users getting electricity in t 1 Reduce reported valuation in t based on remaining budget Rationale: avoid user depleting budget fast without fully charged Result: the overall budget constraint is dropped. 1 Buchbinder, Niv, et al. Online primal-dual algorithms for maximizing ad-auctions revenue. Algorithms-ESA 2007. 2 Shi, Weijie, et al. An online auction framework for dynamic resource provisioning in cloud computing. ACM SIGMETRICS 2014. Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 15/ 26
Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell A Binary Programming Model without Budget Constraint PNC one(t) : maximize p(t) = subject to M K cj k (t)yj k (t) R(t), j=1 k=1 K k=1 K k=1 M K j=1 k=1 ω k j (t)y k j (t), Station Supply y k j (t) 1, j No Double Wins Social Welfare c k j (t)y k j (t) C j (t), j Unit-Time Charging Capacity y k j (t) {0, 1}, j and k. Winning Indication Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 16/ 26
Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell Auc2Charge in a Nutshell 2. Execute randomized auction for PNC one (t) PNCone(1) Aucone PNCone(2) Aucone PNC PNCone(t) Aucone PNCone(T) Aucone Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 17/ 26
Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell Auc2Charge in a Nutshell Randomized Auction Auc one Basic idea: design truthful mechanism via approximation algorithm 3 1 Perform a fractional VCG auction for PNC one (t) 2 Decompose fractional solutions to PNC one (t) into a polynomial number of feasible solutions 3 Randomly select one feasible solution as the allocation decision 4 Compute the corresponding pricing decision 3 Lavi, Ron, et al. Truthful and near-optimal mechanism design via linear programming. Journal of the ACM (JACM) 58.6 (2011): 25. Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 18/ 26
Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell Auc2Charge in a Nutshell How to find a polynomial number of feasible solutions? Use a greedy primal-dual approximation algorithm for PNC one (t) as a separation oracle Greedy approximation algorithm Drop bids exceeding the unit-charging capacity Select the bid with highest unit-value, one at a time, while supply and demand lasts Theorem The greedy algorithm provides a close-form approximation ratio of α and an integrality gap of α to problem PNC one (t) in polynomial time. a a α = 1 + ɛ(e 1) θ θ 1. Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 19/ 26
Auc2Charge: An Online Auction Framework Properties of Auc2Charge Properties of Auc2Charge Theorem Auc one is computationally efficient, truthful, individual rational, and α(1 + R max )-competitive in the one-shot auction of Auc2Charge online auction framework. a a R max: the maximal per-timeslot bid-to-budget ratio. Theorem Using Auc one as the one-shot auction, the Auc2Charge framework is truthful, individual rational, computationally efficient and (1 + R max )(α(1 + R max ) + 1 ϕ 1 )-competitive on the social welfare for the EV park-and-charge system. a a ϕ = (1 + R max) 1 Rmax. Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 20/ 26
Performance Evaluation Simulation Settings Simulation Settings Park-and-charge Facility: 500 spots EV battery capacity: 40kWh Arriving SOC (0, 0.7] Parking time [2, 6] hours Budget: [8, 12] dollars Number of bids/hour: 5 Simulated time T = 12, 18, 24 hours Simulated scale M = 100, 200, 300, 400, 500 EVs Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 21/ 26
Performance Evaluation Simulation Settings Simulation Settings Metrics Social Welfare Approximation ratio over offline optimum User Satisfaction User Satisfaction Ratio Unit Charging Payment Total Charging Payment Budget Utilization Ratio Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 22/ 26
Performance Evaluation Evaluation Results Evaluation Results Approximation Ratio on Social Welfare Ratio of Offline/Online Social Welfare 3 2.5 2 1.5 1 0.5 Auc2Charge OffOptimal 0 100 200 300 400 500 Number of Electric Vehicles T = 12 Hours Ratio of Offline/Online Social Welfare 3 2 1 Auc2Charge OffOptimal 0 12 18 24 Number of Time Slots M = 100 Electric Vehicles Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 23/ 26
Performance Evaluation Evaluation Results Evaluation Results User Satisfaction Average of User Satisfaction Ratio 1 0.8 0.6 0.4 0.2 0 T=12 T=18 T=24 100 200 300 400 500 Number of Electric Vehicles User Satisfaction Ratio Average of Unit Payment 0.5 0.4 0.3 0.2 0.1 0 T=12 T=18 T=24 100 200 300 400 500 Number of Electric Vehicles Unit Charging Payment Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 24/ 26
Performance Evaluation Evaluation Results Evaluation Results User Satisfaction - Cont d Average of Total Payment 4 3 2 1 0 T=12 T=18 T=24 100 200 300 400 500 Number of Electric Vehicles Total Charging Payment Average of Budget Utilization Ratio 0.4 0.3 0.2 0.1 0 T=12 T=18 T=24 100 200 300 400 500 Number of Electric Vehicles Budget Utilization Ratio Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 25/ 26
Concluding Remarks Conclusion and Future Work Conclusion and Future Work Conclusion Explore auctions as efficient market mechanisms for EV charging stations Propose Auc2Charge, an online auction framework for EV park-and-charge Demonstrate system benefits in terms of social welfare and user satisfaction Future Work Include other realistic constraints, e.g., V2G transmission and ramp-up/down generation cost Investigate privacy-preserving auctions for EV charging Qiao Xiang et al. (McGill) ACM e-energy 15 07/16/2015 26/ 26