[PPT] - Auc2Charge: An Online Auction Framework for Electric Vehicle PowerPoint Presentation

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Auc2Charge: An Online Auction Framework for Electric Vehicle Park-and-Charge

Qiao Xiang1, Fanxin Kong1, Xue Liu1, Xi Chen1, Linghe Kong1 and Lei Rao2

1School of Computer Science, McGill University 2General Motors Research Lab

July 16th, 2015

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Introduction Electric Vehicles

Introduction

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

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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

f space

Parking Lot Charging Points A B C A B C

Controller

Figure: An illustration of park-and-charge

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Introduction Park-and-Charge

Current Field Deployment Workplace, airport, military base and etc. Pricing policies Pay-per-use Flat rate

Boston University Seattle-Tacoma Airport

Sources:bu.edu and plugincars.com

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Motivation and Challenges Motivation

Pay-Per-Use and Flat-Rate Pricing 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

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Motivation and Challenges Motivation

Social Welfare in Park-and-Charge: An Example

Pay-per-use and flat-rate: allocate 15kWh to each EV

A B A B

SOC: 5/25 SOC: 20/40 SOC: 35/40 SOC: 20/25 +15 +15 Park and Charge

However,

Marginal utilities of EVs are different Lower arriving SOC → Higher marginal utility Ignorance of such difference → Undermined social welfare

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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 B A B

SOC: 5/25 SOC: 20/40 SOC: 30/40 SOC: 25/25 +10 +20 Park and Charge

Pay-per-use and flat-rate focus on station revenue, not social welfare.

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Motivation and Challenges Motivation

Motivation Future market deployment of park-and-charge desires an efficient market mechanism to Avoid overpricing and underpricing Maximize social welfare

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Motivation and Challenges Our Focus

Our Focus Our Focus Investigate auction as market mechanism for park-and-charge Auc2Charge: an online auction framework Understanding system benefits via numerical simulation

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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.

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System Settings and Problem Formulation

Bid ¡1

2-‑3pm, ¡$0.50, ¡5kWh ¡ ¡ Bid ¡2 3-‑4pm, ¡$2.00, ¡9kWh SOC: ¡60% . ¡. ¡. Win Lose

EV ¡Customer ¡1

Bid ¡1 2-‑3pm, ¡$1.50, ¡6kWh ¡ ¡ Bid ¡2 3-‑4pm, ¡$3.00, ¡8kWh SOC: ¡30% . ¡. ¡. Win Win

EV ¡Customer ¡N

. ¡. ¡. ¡.

Bids Bids AllocaKon ¡and ¡ Pay ¡Decision A l l

c

a K

n

¡ a n d ¡ P a y ¡ D e c i s i

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., {bk

j (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,

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System Settings and Problem Formulation

A Binary Programming Formulation

PNC : maximize

T

t=1

M

j=1

K

k=1

bk

j (t)y k j (t)

Social Welfare

subject to

K

k=1

T

t=1

bk

j (t)y k j (t) ≤ Bj,

∀j,

Users Budget

M

j=1

K

k=1

ck

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

K

k=1

ck

j (t)y k j (t) ≤ Cj(t),

∀j and t,

Unit-Time Charging Capacity

y k

j (t) ∈ {0, 1},

∀j, k and t. Winning Indication

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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

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Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell

Auc2Charge in a Nutshell

1. Decompose PNC into smaller auctions via bids

update process.

PNC PNCone(1) PNCone(2) PNCone(t) PNCone(T) Bids ¡Update ¡ Process

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Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell

Auc2Charge in a Nutshell

Bids Update Process: Originally proposed in budget-constrained online Adwords auction1, and extended to resource auction in cloud computing.2 Intuition: adjust reported valuation in PNCone(t) based

n the results from PNCone(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.

1Buchbinder, Niv, et al. ”Online primal-dual algorithms for maximizing ad-auctions revenue.” Algorithms-ESA 2007. 2Shi, 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

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Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell

A Binary Programming Model without Budget Constraint

PNCone(t) : maximize p(t) =

M

j=1

K

k=1

ωk

j (t)y k j (t),

Social Welfare subject to

M

j=1

K

k=1

ck

j (t)y k j (t) ≤ R(t),

Station Supply

K

k=1

y k

j (t) ≤ 1,

∀j

No Double Wins

K

k=1

ck

j (t)y k j (t) ≤ Cj(t),

∀j

Unit-Time Charging Capacity

y k

j (t) ∈ {0, 1},

∀j and k. Winning Indication

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Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell

Auc2Charge in a Nutshell

2. Execute randomized auction for PNCone(t)

PNC PNCone(1) PNCone(2) PNCone(t) PNCone(T) Aucone Aucone Aucone Aucone

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Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell

Auc2Charge in a Nutshell

Randomized Auction Aucone Basic idea: design truthful mechanism via approximation algorithm3

1 Perform a fractional VCG auction for PNCone(t) 2 Decompose fractional solutions to PNCone(t) into a

polynomial number of feasible solutions

3 Randomly select one feasible solution as the allocation

decision

4 Compute the corresponding pricing decision 3Lavi, 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

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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 PNCone(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 PNCone(t) in polynomial time.a

aα = 1 + ǫ(e − 1) θ θ−1. Qiao Xiang et al. (McGill) ACM e-Energy’15 07/16/2015 19/ 26

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Auc2Charge: An Online Auction Framework Properties of Auc2Charge

Properties of Auc2Charge

Theorem Aucone is computationally efficient, truthful, individual rational, and α(1 + Rmax)-competitive in the one-shot auction of Auc2Charge online auction framework.a

aRmax: the maximal per-timeslot bid-to-budget ratio.

Theorem Using Aucone as the one-shot auction, the Auc2Charge framework is truthful, individual rational, computationally efficient and (1 + Rmax)(α(1 + Rmax) +

1 ϕ−1)-competitive on the social welfare

for the EV park-and-charge system.a

aϕ = (1 + Rmax)

1 Rmax .

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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, 500EVs

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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

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Performance Evaluation Evaluation Results

Evaluation Results Approximation Ratio on Social Welfare

100 200 300 400 500 0.5 1 1.5 2 2.5 3 Number of Electric Vehicles

Ratio of Offline/Online Social Welfare

Auc2Charge OffOptimal

T = 12 Hours

12 18 24 1 2 3 Number of Time Slots

Ratio of Offline/Online Social Welfare

Auc2Charge OffOptimal

M = 100 Electric Vehicles

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Performance Evaluation Evaluation Results

Evaluation Results User Satisfaction

100 200 300 400 500 0.2 0.4 0.6 0.8 1

Number of Electric Vehicles

Average of User Satisfaction Ratio

T=12 T=18 T=24

User Satisfaction Ratio

100 200 300 400 500 0.1 0.2 0.3 0.4 0.5

Number of Electric Vehicles

Average of Unit Payment

T=12 T=18 T=24

Unit Charging Payment

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Performance Evaluation Evaluation Results

Evaluation Results User Satisfaction - Cont’d

100 200 300 400 500 1 2 3 4

Number of Electric Vehicles

Average of Total Payment

T=12 T=18 T=24

Total Charging Payment

100 200 300 400 500 0.1 0.2 0.3 0.4

Number of Electric Vehicles

Average of Budget Utilization Ratio

T=12 T=18 T=24

Budget Utilization Ratio

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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

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