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
1
Introduction
 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.
2
Introduction
 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!
A storage-assisted smart grid
3
Why Online Procurement Auction?
 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).
4
Our Contributions
 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
5
Model
Auction includes T time slots; M agents, each agent m ∈ [M]
submits a set of K bids. Each bid is a pair:
Social cost
XOR bidding rule
Cover power shortage
Capacity limit
6
Online Problem
 What difficulties could the capacity bring?
 Greedy vs Optimal
Agent A C=10
Agent B C=10
Round 1 $2 4
Round 2 $6 5
Round 3 $3 6
Round 1 $4 4
Round 2 $7 5
Round 3 $9 10
7
Online Problem
 What difficulties could the capacity bring?
 Greedy
Agent A C=10
Agent B C=10
Round 1 $2 4
Round 1 $4 4
Remaining
Capacity=6
D1=4
8
Remaining
Capacity=10
Online Problem
 What difficulties could the capacity bring?
 Greedy
Agent A C=10
Agent B C=10
Round 1 $2 4
Round 2 $6 5
Round 1 $4 4
Round 2 $7 5
Remaining
Capacity=1
D2=5
9
Remaining
Capacity=10
Online Problem
 What difficulties could the capacity bring?
 Greedy social cost=2+6+9=17
Agent A C=10
Agent B C=10
Round 1 $2 4
Round 2 $6 5
Round 3 $3 6
Round 1 $4 4
Round 2 $7 5
Round 3 $9 10
Remaining
Capacity=1
D3=6
10
Remaining
Capacity=0
Online Problem
 What difficulties could the capacity bring?
 Optimal social cost=2+7+3=12.Greedy social cost=17
Agent A C=10
Agent B C=10
Round 1 $2 4
Round 2 $6 5
Round 3 $3 6
Round 1 $4 4
Round 2 $7 5
Round 3 $9 10
11
Our solution
 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
12
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
13
Example
 Simulate Aonline on the previous example
 Two bids, Aone select the agent with smallest cost.
Agent A C=10
Agent B C=10
Round 1 $2 4
Round 1 $4 4
Remaining
Capacity=6
D1=4
14
Remaining
Capacity=10
Example
 Simulate Aonline on the previous example
 Two bids, Aone select the agent with smallest cost.
Agent A C=10
Agent B C=10
Round 1 $2 4
Round 2 $6 5
adjust: $7.2 5
Round 1 $4 4
Round 2 $7 5
adjust: $7 5
Remaining
Capacity=6
D2=5
15
Remaining
Capacity=5
Example
 Greedy algorithm: social cost $17
 Optimal solution: social cost $12
 Aonline : social cost $12
Agent A C=10
Agent B C=10
Round 1 $2 4
Round 2 $6 5
Round 3 $3 6
adjust: $10.2 6
Round 1 $4 4
Round 2 $7 5
Round 3 $9 10
adjust: $12.6 10
Remaining
Capacity=0
D3=6
16
Remaining
Capacity=5
One-round Auction Design
 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
17
One-round WDP
Increased cost of supply
XOR bidding
Cover power shortage
18
One-round WDP
 We augment the original one-round WDP: introduce
a number of redundant inequalities.
 Introducing dual variables y , z.
Primal ILP
Dual ILP
19
One-round Auction Mechanism
Initialize the primal and
dual variables
While loop: updates the primal
and dual variables
Find the threshold bid,
Calculate the payment
Once a dual constraint becomes tight,
the bid corresponding to that
constraint is added to the set A
20
Performance Evaluation
 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
21
Performance of One-round WDP
Algorithm
 Approximation ratio approaches 1 towards the bottomright corner of the surface
 A downward trend as the number of bids per agent grows
600
EL=10GWh
EL=20GWh
EL=30GWh
EL=40GWh
EL=50GWh
550
500
450
Total cost
Approximation Ratio
1.2
1.15
1.1
1.05
400
350
300
250
200
12
150
10
1
0
8
100
6
1000
4
2000
50
2
3000
4000
0
k
0
1
2
3
4
5
6
7
Number of bids per agent
Number of Agents
22
8
9
10
Performance of Online Algorithm
 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
5000
1.45
Round 1
Round 2
Round 3
Round 4
4000
Total Cost
3500
1.35
3000
2500
2000
1500
1.3
1.25
1.2
1.15
1000
1.1
500
1.05
0
1000
1400
1800
2200
2600
k=1
k=2
k=4
1.4
Competitive Ratio
4500
1
3000
Number of Agents
2
4
6
8
Number of Rounds
23
10
12
Conclusions
 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
24
Thank you!
 Questions?
25