bi-level providers - consumers competition model

Bi-level providers -consumers

competition model

CUI Yaheng,BEAUDE Olivier,LE DU Marc,

ZORGATI Riadh

Decentralizing inelectricity systems

Bi-levelcompetition model

Consumer model

Nonflexible consumer

Flexible consumer

Flexible consumerwith RE and storage

Providers model

Yearly dynamics

Simulation

Preliminar simulationsetting: only 2providers

Simulations:convergence of thedynamics?

Simulations: analysisof the obtainedequilibrium

Conclusion andperspectives

Bi-level providers - consumers competitionmodel

CUI Yaheng, BEAUDE Olivier, LE DU Marc,ZORGATI Riadh

EDF R&D OSIRIS department

Smart Energy and Stochastic Optimization thematicweek - June 2, 2016


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Outline

1 Decentralizing in electricity systems

2 Bi-level competition model

3 Simulation

4 Conclusion and perspectives


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Outline


2 Bi-level competition modelConsumer model


Flexible consumer

Flexible consumer with RE and storage

Providers modelYearly dynamics

3 SimulationPreliminar simulation setting: only 2 providersSimulations: convergence of the dynamics?Simulations: analysis of the obtained equilibrium



competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Decentralizing in electricity systems: big picture

Legislator

regulatory rules, constraints

Global / local network manager

responsible for the global / local supply - demand balance

Wholesale producertraditional / virtual power plants

Minimize his global costown supply - demand eq. + risk

Productionplanning

Adjustmentrequest

Other producerslocal, intermittent

Minimize his global costlocal supply - demand eq. + risk

Productionplanning

ElectricitymarketS

Buy

Sell

Buy

Sell

Providers / traders

Buy Sell

Nonflexible consumers

traditional fixed

electrical appliances

Calculate his Bill

Flexible consumersfixed applis + flexible ones

(water-heaters, electric veh.)

Minimize his bill

Flexible cons. withlocal productionfixed applis + flexible ones+ local (intermittent) prod.

Min. his billMax. his self-cons. / prod.

Sell

1st subproblem Providers / traders

Buy Sell

Nonflexible consumers

traditional fixed

electrical appliances

Calculate his Bill

Flexible consumersfixed applis + flexible ones

(water-heaters, electric veh.)

Minimize his bill

Flexible cons. withlocal productionfixed applis + flexible ones+ local (intermittent) prod.

Min. his billMax. his self-cons. / prod.

Sell


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Decentralizing in electricity systems: a few main

ingredients

Decentralize = a few reasons / needs

emergence of local actors → new (local) decision-takers

⇒ coordinate local VS global with prices, incentivesNatural framework for bilevel models + mechanismdesign [4, 9]

huge and complex problems

⇒ (stochastic) decomposition = ”fictively” decentralize

local data / information (privacy concerns...)

⇒ Design of (strategic) information exchange scheme[2, 5]


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Outline




Flexible consumer






competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Bi-level competition model

Bi-level competition game (Stackelberg multiple-leaders /multiple-followers game):

Leaders (upper level): electricity providers f ∈ F

Followers (lower level): electricity consumers c ∈ C

Provider1 Provider2 · · · ProviderF

Non-flexible

consumers

Flexible

consumers

Flexible

consumers withRE and storage

Electricityprice

Providerchoice


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Consumer electricity bill and provider profit

Yearly price for provider f is a sequence of size D ∗ T withindices j ∈ J day and t ∈ T time-slot.

Price [6]:

pfj(t) = gfjt(∑

c∈C

ℓcj(t))

Consumer bill:

∑

j∈J

∑

t∈T

pfj(t)× ℓcj(t)

Provider profit:

∑

c∈Cf

∑

j∈J

∑

t∈T

pfj(t)× ℓcj(t)

with Cf set of consumers choosing f as provider.


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation






Nonflexible consumption profile: ℓ0c = (ℓ0cj (t))j∈J ,t∈T

Pb = provider choice

minf ∈F

∑

j∈J

∑

t∈T

pf j(t)× ℓ0cj (t)


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Flexible consumer

Fixed consumption profile: ℓ0c = (ℓ0cj (t))j∈J ,t∈T

+ Flexible consumption profile: ℓ1c = (ℓ1cj (t))j∈J ,t∈T

Pb = flexible consumption scheduling + provider choice

minf ∈F

∑

j∈J

minℓ1cj∈R

T+

∑

t∈T

pf j(t)× (ℓ0cj(t) + ℓ1cj(t))

s.t.

{ℓ1cj (t) ≤ ℓmax, ∀j ∈ J ,∀t ∈ T ,∑

t∈T ℓ0cj (t) + ℓ1cj(t) = Lcj , ∀j ∈ J


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Flexible consumer with renewable energy (RE)

and storage

Fixed consumption ℓ0c + flexible consumption ℓ

1c

RE generation profile w

storage charging /discharging profile s

→ storage energy level ecj(t) = ecj (t − 1) + scj (t)

Pb = consumption/storage scheduling + provider choice

minf ∈F

∑

j∈J

minℓ1cj∈RT+,

s∈RJ×T

∑

t∈T

pf j(t)× [ℓ0cj(t) + ℓ1cj (t)− wcj(t) + scj(t)]+

s.t.

ℓ1cj(t) ≤ ℓmax, ∀j ∈ J ,∀t ∈ T ,∑

t∈T ℓ0cj (t) + ℓ1cj(t) = Lcj , ∀j ∈ J ,

0 ≤ ecj (t) ≤ Ec , ∀j ∈ J ,∀t ∈ T ,

where [x ]+ = max(x , 0).


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Providers model

For provider f ∈ F

Πf (pf ,p−f ) =∑

c∈Cf (pf ,p−f )

∑

j∈J

∑

t∈T

pfj(t)× ℓcj(t)

where p−f the prices proposed by alternative providers

p−f = (p1, · · · ,pf−1,pf+1, · · · ,pF )

Pb = profit maximization

maxpf ∈P f

Πf (pf ,p−f )


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Consumer’s/provider’s decisions update: a yearly

dynamics

Consumer’s choices 6= perfect rationality → Discretechoice models [8]

1. Class choiceProportions in different classes for the year to come

γyi =

e−αconsCyi

∑i∈{0,1,2} e

−αconsCyi

with y index of year, i index of the classes (0 non-flexible, 1flexible, 2 flexible with RE and storage), Ci cost, αcons pricesensibility for consumers.

2. Provider’s choiceSame model with αprov


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Consumer’s/provider’s decisions update: a yearly

dynamics

Provider f ’s price-update → best-response strategy [3]

pf ,y ∈ arg maxpf ∈P f

Πf (pf ,p−f ,y−1)

with y year index,

−f = (1, · · · , f − 1, f + 1, · · · ,F ) alternative providers.


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Outline




Flexible consumer






competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Simulation setting: only 2 providers

Two providers: F = {1, 2}

Two classes of consumers: non-flexible, flexible

Consumers daily energy need → ”Recoflux” ERDF data:nonflexible consumption = base consumptionflexible consumption = water-heating

No yearly evolution of energy needs

Daily exogenous on/off peak fare:

pf = (t fon, tfoff , p

fon, p

foff )

0am 5am 10am 3pm 8pm

Time

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Price

(€/kWh)

ton toff

pon

poff

On/off time fare

Off peak fare choices On peak fare choices

Other parameters: αprov, αcons, ℓmax max. flexible load,

γy=0flex

initial proportion of flexible consumers


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Pseudo-code for the yearly dynamics simulation

Initial year pf ,y=0 randomly chosen

Calculate initial consumers consumption+ provider choice

while∑

f ∈F ‖pf ,y − pf ,y−1‖ >= ǫ and y ≤ Y do

Next year y = y + 1

for f ∈ F do

for pf ∈ Pf do

Simulate consumers consumption+ provider choice

Calculate Πf (pf , p−f ,y−1)

end for

Choose pf ,y maximizing Πf (·, p−f ,y−1)end for

end while


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Simulations: convergence of the dynamics

1 2 3 4 5

Year

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Bill (p.u.)

Dynamic bills for flexible consumer

Provider 1

Provider 2

αprov=αcons=1

1 2 3 4 5

Year

0

20

40

60

80

100

Proportion (%)

Dynamic proportions for flexible consumer

Total

Provider 1

Provider 2

αprov=αcons=0.05

Figure: γy=0flex

= 100% and ℓmax = 3kW


Time

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Price

(€/kWh)

maximal on/off allowed prices minimum off-peak duration

On/off time fare

Initial fare provider 1 Initial fare provider 2 Final fare

⇒ same final fare for both providers with minimumoff-peak duration and maximum prices levels


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Convergence: impact of discrete choice models

αcons ∈ {0.01, 0.05, 0.1, 0.2, 0.4, 0.6, 0.8, 1}αprov ∈ {0.01, 0.05, 0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, 4}

0.0 0.2 0.4 0.6 0.8 1.0α_cons

0

1

2

3

4

5

α_prov

Convergence of the dynamics

Convergence

Divergence

1 2 3 4 5

Year

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Bill (p.u.)

Convergent dynamics

Provider 1

Provider 2

αprov=αcons=0.05

2 4 6 8 10 12 14 16 18 20

Year

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Bill (p.u.)

Divergent dynamics

Provider 1

Provider 2

αprov=αcons=0.05


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Consumer’s bill / provider’s profit at equilibrium

1 2 3 4 5

Year

0.0

0.5

1.0

1.5

2.0

2.5

Bill (p.u.)

Bill dynamics

Nonflexible

Flexible

αprov=αcons=0.05

1 2 3 4 5

Year

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Profit (p.u.)

Profits dynamics

Provider 1

Provider 2

αprov=αcons=0.05

⇒ nonflexible consumer’s bill > flexible consumer’s bill

⇒ providers’ profit nearly doubled (strongly depends on themin./max. prices allowed to the providers)


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Estimated impact on the electricity network

metrics


Time

0

1

2

3

4

Consu

mption (kW

)

Daily consumptionInitial

Finalαprov=αcons=0.05

PARy=1 : 1.34PARy=5 : 2.03

⇒ Peak-to-Average-Ratio PAR = max(ℓ)mean(ℓ) almost doubled!


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Consumers interest for flexibilityFlexible x%: consumer with x% of flexibility (SAME TOTALENERGY NEED)

ex Flexible 0% = nonflexible / Flexible 100% = flexible

1 2 3 4 5

Year

0.0

0.2

0.4

0.6

0.8

1.0

Bill (p.u.)

Dynamic cost with different level of flexiblity (%)

γ 0flex = 0%

γ 0flex = 25%

γ 0flex = 50%

γ 0flex = 75%

γ 0flex = 100% αprov=αcons=0.05


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Sensibility to initial consumer pool

1 2 3 4 5 6 7 8 9 10

Year

0.0

0.2

0.4

0.6

0.8

1.0

Bill (p.u.)

γ 0flex = 10%

γ 0flex = 20%

γ 0flex = 30%

γ 0flex = 40%

γ 0flex = 50%

γ 0flex = 60%

γ 0flex = 70%

γ 0flex = 80%

γ 0flex = 90%

γ 0flex = 100%

αprov=αcons=0.05

⇒ no effect of initial pool on the obtained (final)equilibrium


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Outline




Flexible consumer






competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





Conclusion and perspectives

generic bilevel model to analyze providers - consumerscompetition

intuitive preliminary simulation results on a simplesetting→ to be enriched with sourcing part (end of good timesfor providers...)

theoretical study of a simplified Stackelberg modelwith

only F = 2 providersonly nonflexible and flexible consumersendogenous polynomial prices (link with existing resultsin routing games [7, 1]).


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





References I

Eitan Altman, Tamer Basar, Tania Jimenez, and NahumShimkin.Competitive routing in networks with polynomial costs.Automatic Control, IEEE Transactions on, 47(1):92–96,2002.

Vincent P Crawford and Joel Sobel.Strategic information transmission.Econometrica: Journal of the Econometric Society,pages 1431–1451, 1982.

Drew Fudenberg and Jean Tirole.Game Theory.MIT Press, Cambridge, MA, 1991.


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





References II

L. Gkatzikis, I. Koutsopoulos, and T. Salonidis.The role of aggregators in smart grid demand responsemarkets.IEEE Journal on Selected Areas in Communications,31(7):1247–1257, July 2013.

B Larrousse, O Beaude, and S Lasaulce.Crawford-sobel meet Lloyd-Max on the grid.In Acoustics, Speech and Signal Processing (ICASSP),2014 IEEE International Conference on, pages6127–6131, 2014.

A. H. Mohsenian-Rad, V. W. S. Wong, J. Jatskevich,R. Schober, and A. Leon-Garcia.Autonomous demand-side management based ongame-theoretic energy consumption scheduling for thefuture smart grid.


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





References III

IEEE Transactions on Smart Grid, 1(3):320–331, Dec2010.

Ariel Orda, Raphael Rom, and Nahum Shimkin.Competitive routing in multiuser communicationnetworks.IEEE/ACM Transactions on Networking (ToN),1(5):510–521, 1993.

Kenneth Train.Qualitative choice analysis: Theory, econometrics, andan application to automobile demand, volume 10.MIT press, 1986.


competition model


ZORGATI Riadh



Consumer model


Flexible consumer


Providers model

Yearly dynamics

Simulation





References IV

W. Tushar, J. A. Zhang, D. B. Smith, H. V. Poor, andS. Thibaux.Prioritizing consumers in smart grid: A game theoreticapproach.IEEE Transactions on Smart Grid, 5(3):1429–1438, May2014.

bi-level providers - consumers competition model

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