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An Online Procurement Auction for Power Demand
Response in Storage-Assisted Smart Grids
Ruiting Zhou†, Zongpeng Li†, Chuan Wu‡
† University of Calgary‡ The University of Hong Kong
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The central problem in a smart grid is the matching between power supply and demand. Supply < Demand, procure from energy
storage devices Demand < Supply , store electricity.
This work studies the demand response problem in storage-assisted smart grids.
Introduction
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Storage crowdsourcing: thousands of batteries co-residing in the same grid can together store and supply an impressive amount of electricity.
How to incentivize storage participation and minimize the cost?
An Online Procurement Auction!
Introduction
A storage-assisted smart grid
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Effectively response to the imbalance Need no estimation Discover the “right price” reduce the cost
Properties: Online: diurnal cycles, and electricity stored at
low-price hours is in finite supply Procurement: multiple sellers (storage
devices) and a single buyer (the grid).
Why Online Procurement Auction?
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Two main modules Translating online auction into a series of one-
round auctions Aonline
Design a truthful auction for one-round demand response problem Aone A polynomial-time approximation algorithm A payment scheme to guarantee truthfulness
Social cost competitive ratio: 2 in typical scenarios
Our Contributions
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ModelAuction includes T time slots; M agents, each agent m ∈ [M] submits a set of K bids. Each bid is a pair:
Capacity limit
Cover power shortage
XOR bidding rule
Social cost
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What difficulties could the capacity bring? Greedy vs Optimal
Online Problem
Agent A C=10
Round 1 $2 4Round 2 $6 5Round 3 $3 6
Agent B C=10
Round 1 $4 4Round 2 $7 5Round 3 $9 10
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Online Problem
Agent A C=10
Round 1 $2 4
RemainingCapacity=6
Agent B C=10
Round 1 $4 4
RemainingCapacity=10
D1=4
What difficulties could the capacity bring? Greedy
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Online Problem
Agent A C=10
Round 1 $2 4Round 2 $6 5
RemainingCapacity=1
Agent B C=10
Round 1 $4 4Round 2 $7 5
RemainingCapacity=10
D2=5
What difficulties could the capacity bring? Greedy
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What difficulties could the capacity bring? Greedy social cost=2+6+9=17
Online Problem
Agent A C=10
Round 1 $2 4Round 2 $6 5Round 3 $3 6 RemainingCapacity=1
Agent B C=10
Round 1 $4 4Round 2 $7 5Round 3 $9 10
RemainingCapacity=0
D3=6
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Online Problem
Agent A C=10
Round 1 $2 4Round 2 $6 5Round 3 $3 6
Agent B C=10
Round 1 $4 4Round 2 $7 5Round 3 $9 10
What difficulties could the capacity bring? Optimal social cost=2+7+3=12.Greedy
social cost=17
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Lesson Learned Do not exhaust battery’s capacity early Lose all the opportunities on this agent
Solution: Higher priority for agent with higher (remaining) capacity adjust the cost in a bid according to its
remaining capacity
Our solution
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The Online Framework Aonline
Increased cost, adjust each round
Run Aone based on the increased cost. Suppose Aone return a good solution For one-round problem.
Update the value of Sm,based on the ratio of consumed power and total capacity
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Simulate Aonline on the previous example Two bids, Aone select the agent with smallest
cost.
Example
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Agent A C=10
Round 1 $2 4
Remaining Capacity=6
D1=4
Agent B C=10
Round 1 $4 4
RemainingCapacity=10
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Simulate Aonline on the previous example Two bids, Aone select the agent with smallest
cost.
Example
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Agent A C=10
Round 1 $2 4Round 2 $6 5adjust: $7.2 5
Remaining Capacity=6
D2=5
Agent B C=10
Round 1 $4 4Round 2 $7 5adjust: $7 5
RemainingCapacity=5
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Greedy algorithm: social cost $17 Optimal solution: social cost $12 Aonline : social cost $12
Example
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Agent A C=10
Round 1 $2 4Round 2 $6 5Round 3 $3 6adjust: $10.2 6
Remaining Capacity=0
D3=6
Agent B C=10
Round 1 $4 4Round 2 $7 5Round 3 $9 10adjust: $12.6 10
RemainingCapacity=5
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Primal-dual approximation algorithm to determine the winners Approximation ratio=2 when each agent submits one
bid only Payment to winners
key in satisfying truthfulness, provide monetary incentives to encourage truthful bidding
Myerson’s characterization: an auction is truthful iff (i) the auction result is monotone (ii) winners are paid threshold payments
One-round Auction Design
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One-round WDP
Increased cost of supply
Cover power shortage
XOR bidding
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We augment the original one-round WDP: introduce a number of redundant inequalities.
Introducing dual variables y , z.
One-round WDP
Primal ILP Dual ILP
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One-round Auction Mechanism
Initialize the primal and dual variables
While loop: updates the primal and dual variables
Once a dual constraint becomes tight, the bid corresponding to that constraint is added to the set A
Find the threshold bid,Calculate the payment
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Simulation setup Demand: [10GWh, 50GWh] , with reference to
information from ieso (Power to Ontario) Battery capacity [60 kWh, 200 kWh] Amount of supple: [0, 100]kWh cost [$0, $20] 1000~ 3000 agents 1~15 rounds 1~10 bids per agent
Performance Evaluation
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Approximation ratio approaches 1 towards the bottom-right corner of the surface
A downward trend as the number of bids per agent grows
Performance of One-round WDP Algorithm
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The larger number of available agents, the better performance in terms of cost can be achieved
Small values in k and T lead to a lower ratio
Performance of Online Algorithm
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One of the first studies on storage power demand response through an online procurement power auction mechanism
The two-stage auction designed is truthful, computationally efficient, and achieves a competitive ratio of 2 in practical scenarios An online framework which monitors each agent’s
capacity A primal-dual approximation algorithm for one-
round problem
Conclusions
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Questions?
Thank you!