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Auc2Charge: An Online Auction Framework forElectric Vehicle Park-and-Charge
Qiao Xiang1, Fanxin Kong1, Xue Liu1,Xi Chen1, Linghe Kong1 and Lei Rao2
1School of Computer Science, McGill University2General Motors Research Lab
July 16th, 2015
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Introduction Electric Vehicles
Introduction
Electric Vehicles(EV)
Crucial component of Intelligent TransportationSystem(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 stationsA 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 utilizationof 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-useFlat 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 stationrevenue 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 socialwelfare.
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Motivation and Challenges Motivation
Motivation
Future market deployment of park-and-chargedesires 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 forpark-and-charge
Auc2Charge: an online auction framework
Understanding system benefits via numericalsimulation
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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 maximizationTruthfulness and individual rationality
What enables Auc2Charge?
Budget-constrained online auction and randomizedauction theory
Auc2Charge can be extended to other operation modes ofcharging stations, e.g., fast charging reservation.
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System Settings and Problem Formulation
System Settings and Problem Formulation
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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
AllocaK
on and
Pay De
cision
AllocaKon and
Pay Decision
EVs arrive, park-and-charge, and leave
Users send bids on how much to charge, when to charge andhow much to pay, i.e., {bkj (t), ckj (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 : maximizeT∑t=1
M∑j=1
K∑k=1
bkj (t)y
kj (t) Social Welfare
subject toK∑
k=1
T∑t=1
bkj (t)y
kj (t) ≤ Bj , ∀j , Users Budget
M∑j=1
K∑k=1
ckj (t)ykj (t) ≤ R(t), ∀t, Station Supply
K∑k=1
y kj (t) ≤ 1, ∀j and t, No Double Wins
K∑k=1
ckj (t)ykj (t) ≤ Cj(t), ∀j and t, Unit-Time Charging Capacity
y kj (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 computationallyefficient
PNC is stochastic→ The auction must be online
Users may bid strategically→ The autcion must be truthful and individualrational
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Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell
Auc2Charge in a Nutshell
1. Decompose PNC into smaller auctions via bidsupdate 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 Adwordsauction1, and extended to resource auction in cloudcomputing.2
Intuition: adjust reported valuation in PNCone(t) basedon 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 fullycharged
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.
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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
ωkj (t)y
kj (t), Social Welfare
subject toM∑j=1
K∑k=1
ckj (t)ykj (t) ≤ R(t), Station Supply
K∑k=1
y kj (t) ≤ 1, ∀j No Double Wins
K∑k=1
ckj (t)ykj (t) ≤ Cj(t), ∀j Unit-Time Charging Capacity
y kj (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 approximationalgorithm3
1 Perform a fractional VCG auction for PNCone(t)2 Decompose fractional solutions to PNCone(t) into a
polynomial number of feasible solutions3 Randomly select one feasible solution as the allocation
decision4 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.
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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 forPNCone(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 approximationratio of α and an integrality gap of α to problem PNCone(t)in polynomial time.a
aα = 1 + ε(e − 1) θθ−1
.
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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 ofAuc2Charge online auction framework.a
aRmax : the maximal per-timeslot bid-to-budget ratio.
Theorem
Using Aucone as the one-shot auction, the Auc2Charge frameworkis truthful, individual rational, computationally efficient and(1 + Rmax)(α(1 + Rmax) + 1
ϕ−1)-competitive on the social welfarefor 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, 500 EVs
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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 5000
0.5
1
1.5
2
2.5
3
Number of Electric Vehicles
Rat
io o
f Offl
ine/
Onl
ine
Soc
ial W
elfa
re
Auc2ChargeOffOptimal
T = 12 Hours
12 18 240
1
2
3
Number of Time SlotsR
atio
of O
fflin
e/O
nlin
e S
ocia
l Wel
fare
Auc2ChargeOffOptimal
M = 100 Electric Vehicles
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Performance Evaluation Evaluation Results
Evaluation Results
User Satisfaction
100 200 300 400 5000
0.2
0.4
0.6
0.8
1
Number of Electric Vehicles
Ave
rage
of U
ser
Sat
isfa
ctio
n R
atio
T=12T=18T=24
User Satisfaction Ratio
100 200 300 400 5000
0.1
0.2
0.3
0.4
0.5
Number of Electric VehiclesA
vera
ge o
f Uni
t Pay
men
t
T=12T=18T=24
Unit Charging Payment
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Performance Evaluation Evaluation Results
Evaluation Results
User Satisfaction - Cont’d
100 200 300 400 5000
1
2
3
4
Number of Electric Vehicles
Ave
rage
of T
otal
Pay
men
t
T=12T=18T=24
Total Charging Payment
100 200 300 400 5000
0.1
0.2
0.3
0.4
Number of Electric Vehicles
Ave
rage
of B
udge
t Util
izat
ion
Rat
io
T=12T=18T=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 EVcharging stations
Propose Auc2Charge, an online auction framework for EVpark-and-charge
Demonstrate system benefits in terms of social welfareand user satisfaction
Future Work
Include other realistic constraints, e.g., V2G transmissionand ramp-up/down generation cost
Investigate privacy-preserving auctions for EV charging
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