1

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

2

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

3

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

4

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?

5

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

6

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

7

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

8

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

9

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

10

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

11

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

12

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

13

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

14

Simulate Aonline on the previous example Two bids, Aone select the agent with smallest

cost.

Example

14

Agent A C=10

Round 1 $2 4

Remaining Capacity=6

D1=4

Agent B C=10

Round 1 $4 4

RemainingCapacity=10

15

Simulate Aonline on the previous example Two bids, Aone select the agent with smallest

cost.

Example

15

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

16

Greedy algorithm: social cost $17 Optimal solution: social cost $12 Aonline : social cost $12

Example

16

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

17

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

18

One-round WDP

Increased cost of supply

Cover power shortage

XOR bidding

19

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

20

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

21

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

22

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

23

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

24

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

25

Questions?

Thank you!