2nd ESIC-HARPS Workshop on Smart Grid andRenewable Energy

Power Profile Markets: Power Profile Balancing under
Large-Scale Penetration of Battery Storage

Takayuki Ishizaki (Tokyo Institute of Technology)
Masakazu Koike, Asami Ueda, Tu Bo, Jun-ichi ImuraIntroduction
Large-scale penetration of battery storage• improve dispatchability of renewables

power

timeISOtime

Agg 1
Consumerpower• power profile control is necessary to regulate unpredicted battery usebalance

Agg 2
Producer
profile = vector

Power profile market for competitive aggregators
2/18

Ways to Market Clearingfor efficientuse of battery

Present: time point market clearing

Prospect: time period market clearing

11:30 12:00 12:30 13:00 13:30 14:00

11:30 12:00 12:30 13:00 13:30 14:00

Market mechanism = Math program:
Bidding strategies: offline programs

Dynamical pricing: online iterations

ISOISO

Agg 1

Agg 2

- simple market clearing by bid funs
/ valid only for scalar-valued products

Agg 1

Agg 2

- applicable to vector-valued products/ premise of strictly convex problem

Goal: Clearing scheme for non-strictly convex power profile markets

Contents
Introduction of Market Mechanisms
Difficulty of Power Profile Market Clearing
Clearing Scheme Based on Particular Property of Electricity Markets
Numerical Verification
Concluding Remarks

4/18

Math Tools from Convex Analysis
strictly convex&smoothnot strictly
convexnot smooth
jump
jump

Subdifferential:

map to set-values if F is not smoothmonotone increasing

Conjugate transformation:
conjugateinverse
5/18

Links to Market Mechanisms
Profit function:

focus on a time point

incomebothandare scalars

Maximum profit:

timecost

12:00 12:30 13:00 13:30 14:00

Maximizer:
bid function

producer

Lagrangianconsumer6/18

Bidding Strategy for Profile Markets?
Profit function:

focus on a time period

incomebothandcost

are vectors (profiles)

time
12:00 12:30 13:00 13:30 14:00

Market clearing with bid functions:
Bid function:
Too hard to plot!!
aggregator α

Bidding strategy is practical only for scalar-valued products
7/18

Contents
Introduction of Market Mechanisms
Difficulty of Power Profile Market Clearing
Clearing Scheme Based on Particular Property of Electricity Markets
Numerical Verification
Concluding Remarks

8/18

Cost Function of Power Profiles
Power profile of Aggregator :: load profile (constant): generation profile

profiles in: constraints: battery charge & discharge profiles
Generation cost (convex):

Battery usage cost (convex):

including evaluation of final SOC:

【Lemma】

is convex.

uncertain renewables can be involved as robust/stochastic optimization
9/18

Conjecture from Numerical Simulations
Producer:
Consumer:Market clearing:when varying the degree of battery penetration:

PriceClearing price

Lagrangiansmall

battery penetration

large

time label

Large-scale battery penetration leads to price leveling-off?
10/18

Mathematical Deduction【Definition】 A power profile

is said to be shiftable between

time points i and j ifpower

battery!
shiftshifttime【Theorem】

shiftability withoutchanging costnon-strict convexity

There exists some aggregatorsuch thatis shiftable between time points i and j iff
Price levelling-off deduced from battery capacity margin
11/18

Pricing via Energy Bid Functions
Power profile profit function:

pricelevelling-off

Energy profit function:

Profit maximum energy:

energy producer

plottable bid function
for energy trade!
bid functions = offline programs

energy consumer

Levelling-off price can be found via offline programs
12/18

profile shift

powerpower

From Energy Balance to Profile Balance

timetimebutand

Profile imbalance minimization:
whereEnergy profit function

is maximized

Decentralized scheme by ADMM:
imbalance【Theorem】

In particularISOAgg 1

Agg 2

if

Contents
Introduction of Market Mechanisms
Difficulty of Power Profile Market Clearing
Clearing Scheme Based on Particular Property of Electricity Markets
Numerical Verification
Concluding Remarks

14/18

scale is not yet adjusted to real situation

Numerical Verification
ISO
Agg 1Consumers

Agg 2(load + battery)Agg 3

Producer(generator)

Clearing pricewhen varying the degree of battery penetration:

priceprice levelling-off

Small

Middletime label (time length n = 12)

Large
15/18

Pricing by Energy Bid Functions
trading amount

Total bid functions:

Small

MiddleLarge

trading amount

Bid functions in the large battery case:discharge
price sensitive

chargeBid function 1

Bid function 2
price

Bid function 3
16/18

Profile Imbalance Minimization
imbalance [%]Profile imbalance minimization by ADMM:
Smallpower

Resultant power profiles:

MiddleLarge

iteration step

Agg 3

Agg 3

Agg 3

imbalanceimbalance

imbalance

Aggs 1 & 2Aggs 1 & 2Aggs 1 & 2time label

17/18

Concluding Remarks

for efficientuse of battery

Present: time point market clearing

Prospect: time period market clearing

11:30 12:00 12:30 13:00 13:30 14:00

11:30 12:00 12:30 13:00 13:30 14:00

Power profile markets for competitive aggregatorslarge-scale battery penetration leads to price levelling-off
profile shiftability owing to battery capacity margin
non-strictly convex programs

levelling-off price is found by energy bid functions (offline programs)
decentralized profile imbalance minimization by ADMM

Future works
analysis on the best length of time periods

Thank you for your attention!