Valuing demand response controllability: a system and ... · Introduction & motivation I Many research/policy papers on ‘the value of demand response’: 0 50 100 112 73 52 35 (e

Valuing demand response controllability:a system and aggregator perspective

K. Bruninx

Thanks to: D. Patteeuw, C. Protopapadaki, A. Arteconi, G. Reynders, L. Helsen,D. Saelens, H. Le Cadre, H. Pandzic, Y. Dvorkin, D. Kirschen, W. D’haeseleer &

E. Delarue

Zagreb, Croatia – June 19, 2018

Context

I Thermal inertia allows decoupling the electrical & thermal demand without loss of comfort→ opportunity for demand response!

1/31

Introduction & motivation

I Many research/policy papers on ‘the value of demand response’:

0

50

100

112

73

52

35

Co

stsa

vin

gs

(e/

year

/h

h)

5 25 50 10098.5

99

99.5

100

ADR penetration rate (%)

Op

erat

ing

cost

(%)

Source: A. Arteconi et al., Active demand response with electric heating systems: Impact of marketpenetration, Applied Energy, Vol. 177, 2016, pp. 636–648.

2/31

Limiting assumptions in current modeling efforts

I Representation of physical/technical characteristics of the DR resource;

I Non-disruptive end-energy service (e.g. guaranteed thermal comfort);

I Perfectly controllable DR;

I Objective DR provider perfectly aligned with system/aggregator objective;

I Limited heterogeneity in the representation of the DR resource;

I . . .

3/31

Limiting assumptions in current modeling efforts

I Representation of physical/technical characteristics of the DR resource;

I Non-disruptive end-energy service (e.g. guaranteed thermal comfort);

I Perfectly controllable DR;

I Objective DR provider perfectly aligned with system/aggregator objective;

I Limited heterogeneity in the representation of the DR resource;

I . . .

3/31

Research questions

1. The system perspective:I How can we study the system value (arbitrage & operating reserves) of demand response with

thermostatically controlled loads?I What is the impact of requiring thermal comfort at all times?I What is the impact of limited controllability on the system value?I Source: K. Bruninx et al., ‘Valuing Demand Response Controllability via Chance Constrained

Programming’, IEEE Trans. Sustain. Energy, vol. 9, no. 1, 2018.

2. The aggregator perspective:I How can we study the strategic participation of an aggregator in a market while guaranteeing that all

user-defined comfort constraints are met?I . . . interaction between an aggregator and its demand response providers?I . . . if demand response providers are limitedly controllable?I Source: K. Bruninx et al., On the Interaction between Aggregators, Electricity Markets and

Residential Demand Response Providers, submitted to IEEE. Trans. Power Syst., 2018.

4/31

PART 1: The system perspective

Demand response & unit commitment models

Minimize E[Total Operating Cost]

Subject to

I D + DR = generation + RES;

I Technical constraints of power plants andenergy storage systems;

I Limited predictability wind and solar→ Probabilistic reserve requirements;

I Physical demand side model.

Source: D. Patteeuw et al., Integrated modeling ofactive demand response with electric heatingsystems coupled to thermal energy storage systems,Applied Energy, Vol. 151, 2015, pp. 306–319.

Heating system models

Building (stock) models

User behavior and weather data

6/31

Demand response & unit commitment models


Subject to

I D + DR = generation + RES;

I Technical constraints of power plants andenergy storage systems;



Source: D. Patteeuw et al., Integrated modeling ofactive demand response with electric heatingsystems coupled to thermal energy storage systems,Applied Energy, Vol. 151, 2015, pp. 306–319.

Minimize∑t∈T

λAh,t ·dHh,t

subject to

dHh,t = pHP,SH

h,t +pHP,HWh,t +pAH,SH

h,t +pAH,HWh,t

pHP,SHh,t +pHP,HW

h,t ≤PHPh , pAH,SH

h,t +pAH,HWh,t ≤PAH

h∑s∈S

qSHh,s,t =COPSHh ·p

HP,SHh,t +pAH,SH

h,t

qHWh,t =COPHW

h ·pHP,HWh,t +pAH,HW

h,t

TSHh,p,t =ASH

h,p · TSHh,p,t−1 +

∑s∈S

BSHh,p,s ·q

SHh,s,t+ESH

h,p,t

TSHh,p,t≤TSH

h,p,t≤TSHh,p,t

THWh,t =AHW

h ·THWh,t−1 + BHW

h · qHWh,t +EHW

h,t

THWh,t ≤THW

h,t ≤THWh

7/31

Endogenous probabilistic reserve sizing and allocation in UC models

RES

D

Time

Pow

er

p(RES)

RES

Power

Pro

bab

ility

Source: Bruninx, K., Delarue, E., Endogenous probabilistic reserve sizing and allocation in unitcommitment models: cost-effective, reliable and fast, IEEE Transactions on Power Systems, vol. 32,no. 4, 2017.

8/31


RES

D

Time

Pow

er

RES

D−1

D−2

D−3

D−4

D−5

D+1

D+2

D+3

D+4

D+5

Power

Pro

bab

ility


8/31


RES

D

Time

Pow

er

RES

D−1

D−2

D−3

D−4

D−5

D+1

D+2

D+3

D+4

D+5

P−2

Power

Pro

bab

ility


8/31


RES

D

Time

Pow

er

RES

D−1

D−2

D−3

D−4

D−5

D+1

D+2

D+3

D+4

D+5

P+1 P

−2

Power

Pro

bab

ility


8/31


+ Approximation of expected deploymentcosts, hence endogenous reserve sizingpossible and close to optimal UC schedules;

+ Fast;

+ Ensured feasibility of real-time deployment ofenergy storage and DR-based regulation;

− Conservative, especially for energy storageand DR-based regulation services.

RES

D

Time

Pow

er

RES

D−1

D−2

D−3

D−4

D−5

D+1

D+2

D+3

D+4

D+5

Power

Pro

bab

ility

8/31

Value of controllable DR

I DR-arbitrage → more cost-efficient upwardreserve provision;

I DR-reserves → higher uptake RES-basedgeneration, while guaranteeing thermalcomfort.

5 10 15 2018

20

22

Time (h)

Tem

per

atu

re(

C)

TSH TSH,+

(a) No DR0

3

6

Tes

t

SR NSR ES RES SH DHW Φ+

(b) DR - arbitrage0

3

6

Upw

ard

flex

ibili

ty(G

W)

(c) DR - arbitrage & reserves

5 10 15 200

3

6

Time (h)T

est

9/31


I DR-arbitrage → more cost-efficient upwardreserve provision;

I DR-reserves → higher uptake RES-basedgeneration, while guaranteeing thermalcomfort.

5 10 15 2018

20

22

Time (h)

Tem

per

atu

re(

C)

TSH TSH,+

(a) No DR0

3

6

Tes

t


(b) DR - arbitrage0

3

6

Upw

ard

flex

ibili

ty(G

W)

(c) DR - arbitrage & reserves

5 10 15 200

3

6

Time (h)T

est

9/31


No DR Arb. Reg. No DR Arb. Reg. No DR Arb. Reg.80

90

100-6% -7% -4%

-6% -7%

-4%

-6% -7%

SR SR & NSR SR, NSR & ESE

[TO

C]

(%)

Average W7 W9 W15 W25

10/31

Challenging the guaranteed thermal comfort-assumption

5 10 15 2018

20

22

Time (h)

Tem

per

atu

re(

C)

TSH TSH,+, ∆T = 0

TSH TSH,+, ∆T = 1

(c) DR - arb. & reg. - ∆T = 00

3

6

Upw

ard

flex

ibili

ty(G

W)


(d) DR - arb. & reg. - ∆T = 1

5 10 15 200

3

6

Time (h)

tess

t11/31

Challenging the guaranteed thermal comfort-assumption

5 10 15 2018

20

22

∆T

Time (h)

Tem

per

atu

re(

C)

TSH TSH,+, ∆T = 0

TSH TSH,+, ∆T = 1

(c) DR - arb. & reg. - ∆T = 00

3

6

Upw

ard

flex

ibili

ty(G

W)


(d) DR - arb. & reg. - ∆T = 1

5 10 15 200

3

6

Time (h)

tess

t11/31

Value of thermal discomfort

0 1 2 0 1 2 0 1 285

90

95

100-2% -3% -3.5%

-2% -3%

-3.5%

-2% -3%

SR SR & NSR SR, NSR & ES

∆T (K)

E[T

OC

](%

TO

C(D

R&

SR

,∆

T=

0K

))

Average W7 W9 W15

12/31

Challenging the perfectly controllability-assumption


Subject to

I D + DR = generation + RES

→ Pr(D + DR ≤ generation + RES) ≥ 1− ε;

I Technical constraints of power plants and energy storagesystems;



DR(µ, σ)

DRHeating demand

Pro

bab

ility

13/31

Challenging the perfectly controllability-assumption


Subject to

I D + DR = generation + RES→ Pr(D + DR ≤ generation + RES) ≥ 1− ε;

I Technical constraints of power plants and energy storagesystems;



DR(µ, σ)

DR

ε

Heating demand

Pro

bab

ility

13/31

Value of limitedly controllable DR-based arbitrage

0.99 0.9 0.8 0.7 0.6 0.590

100

110

1− ε (-)

E[T

OC

](%

)

0.99 0.9 0.8 0.7 0.6 0.575

80

85

90

1− ε (-)

E[W

UF

](%

)

σNP = 50 MW σNP = 100 MW σNP = 250 MW

0.99 0.9 0.8 0.7 0.6 0.50

100

200

300

400

500

1− ε (-)

E[E

NS

](M

Wh

/w

eek)

14/31

Concluding remarks - the system perspective

A novel unit commitment model considering a physical demand response model & RES forecastuncertainty allows illustrating that

I significant operating cost reductions may be attained by leveraging demand response withelectric heating systems for arbitrage & ancillary services;

I this value can be increased if thermal discomfort is allowed to a limited extent;

I imperfectly controllable demand response may hold limited value for a risk-averse powersystem operator.

15/31

PART 2: The aggregator’s perspective

The aggregator perspective

I How can we study the strategic participation of an aggregator in a market while guaranteeing thatall user-defined comfort constraints are met?

I . . . interaction between an aggregator and its demand response providers?

I . . . if demand response providers are limitedly controllable?

AGGREGATOR

OF: Profit Maximization

MARKET CLEARING

OF: Social Welfare Maximization

DEMAND RESPONSE PROVIDER

OF: Energy Costs Minimization

17/31

Literature review

Interaction DR aggregator – electricity markets

I Price-taking agent → optimization models (Xu et al., 2017, Mathieu et al., 2015, Zugno et al.,2013);

I Strategic price-maker → Stackelberg Game → bilevel optimization problem/MPEC (Kazempouret al., 2015, Kardakos et al., 2016).

Interaction DR aggregator – DR provider

I Leader-follower → Stackelberg Game → bilevel optimization problem/MPEC (Li et al., 2016, Yuet al., 2016, Zugno et al., 2013);

I Collaboration → Nash Bargaining Game → optimization problem (Contreras et al., 2017, Hoa etal., 2016, Ye et al., 2017)

Limited controllability

I System studies/non-strategic aggregators → chance constrained programming;

I Uncertain availability of DR resources (Li et al., 2015, Zhang et al., 2017);

I Limited controllability (Bruninx et al., 2017).

18/31

Methodology: Aggregator’s perspective

Objective: maximize operating profit

Maximize ΠA =∑t∈T

[RA(λA

h,t ,DHt )−

∑ω∈Ω

πω ·λt,ω ·qaggt,ω

]

I Revenue RA(λAh,t ,D

Ht ), based on retail rate λA

h,t and DR load DHt ;

I Expenses in whole-sale market∑

ω∈Ωπω ·λt,ω ·qaggt,ω , with λt,ω the market clearing price.

subject toP(Qagg

t ≥DHt , ∀t∈T

)≥1−ε

I Chance constraint: procure sufficient electricity to cover the limitedly controllable DR load DHt

with a probability of (1− ε)·100%;

DHt =(1 + δP) ·

∑h∈H

NBh ·dHh,t +δNP, ∀t∈T

I Assume δP and δNP follow a Gaussian distribution → SOC19/31

Methodology: Market operator’s perspective

Objective: maximize total surplus w.r.t. the bids and offers of the market participants

Maximize∑t∈T

[Pd ·dt,ω+Pagg ·qagg

t,ω −∑i∈I

Pgi · gi,t,ω

]Subject to:

− wt,ω−∑i∈I

gi,t,ω+dt,ω + qaggt,ω = 0 (λt,ω)

0 ≤ gi,t,ω ≤ Gi

0 ≤ dt,ω ≤ Dt

0 ≤ wt,ω ≤Wt,ω

0 ≤ qaggt,ω ≤ Qagg

t

Market clearing condition (price)

Generation limit (conventional)

Demand

Generation limit (RES)

Aggregator bid limit

20/31

Methodology: Demand Response Provider’s perspective

Objective: minimize the cost of electric space heating and hot water production

Minimize∑t∈T

λAh,t ·dH

h,t

subject to

θh,t − θh,t−1 = G(dHh,t ,Ch,Ph,Ah,Eh,t)

θh,t≤θh,t≤θh,t , ∀t∈T

Source: D. Patteeuw et al., Integrated modeling of active demand

response with electric heating systems coupled to thermal energy

storage systems, Applied Energy, Vol. 151, 2015, pp. 306–319.

Heating system models

Building models

Consumer behavior21/31

Methodology: Aggregator – Market Interaction

Maximize Operating profit

subject to

Chance constraints: P(Qagg

t ≥DHt , t∈T

)≥1−ε

Market clearing: (λt,ω, qaggt,ω ) = argmaxTotal surplus s.t. market clearing conditions

I Assume: aggregator (leader) decides on bid in the wholesale market (follower);

I Bilevel optimization problem → KKT conditions market clearing problem → MPEC → MIQCP

22/31

Methodology: Aggregator – Demand Response Provider Interaction

Retailer ∼ Stackelberg Game

I flat retail rate λAh,t = λA → Consumers minimize their energy demand;

I dHh,t : parameter in the retailer’s problem

I Assume: best possible case for consumer → profit-neutral retailer:∑h∈H

NBh ·RRh =

∑t∈T

∑ω∈Ω


Aggregator ∼ Nash Bargaining Game, S(Stackelberg Game) ∈ S(Nash Bargaining Game)

I DR providers collaborate with the aggregator;

I Total benefit of this collaboration:

B =∑h∈H

NBh · RRh −

∑t∈T

∑ω∈Ω

πω · λt,ω ·qaggt,ω

I Division of benefit → Nash Bargaining Game, i.e., contract, not on day-to-day basis;

I Aggregator can only influence∑

t∈T∑

ω∈Ωπω ·λt,ω ·qaggt,ω on day-to-day basis;

I No restrictions on formation retail rate & guaranteed thermal comfort? → S(Stackelberg Game)∈ S(Nash Bargaining Game)!

23/31

Equivalent MIQCP

RetailerMaximize −

∑t∈T

∑ω∈Ω


s.t. Chance constraint: P(Qagg

t ≥DHt , t∈T

)≥1−ε

Profit neutrality:∑

h∈HNBh ·RRh =

∑t∈T∑

ω∈Ωπω ·λt,ω ·qaggt,ω

dHh,t assumed given

Market clearing constraints

Aggregator

Maximize −∑t∈T

∑ω∈Ω


s.t. Chance constraint: P(Qagg

t ≥DHt , t∈T

)≥1−ε

Demand response model

Market clearing constraints

24/31

Case study

We’ll show how . . .

I the aggregator shifts heating demand from high to low price periods, without jeopardizing thethermal comfort of its consumers;

I the benefit of the aggregator - consumer collaboration decreases if demand response loads becomeless controllable. Liquid intraday and balancing markets limit impact limited controllability.

Data & assumptions

I ∼ isolated Belgian power system, additional gas-fired generation to cover electrified heatingdemand;

I Wind energy ∼ 50% of the annual energy demand (excl. electric space heating);

I Number of DR providers∑

h∈H NBh = 106 → average 2030 low-energy building;

I Stochastic occupancy model → equivalent comfort constraints;

I Reference case: retailer serving a perfectly controllable/predictable heating demand;

I Most results for 316th day of the calendar year (abundant wind power during first hours of theday, median of heating season conditions).

25/31

Optimal bidding strategies – Perfectly controllable heating loads

I Aggregator avoids high λDAt period by shifting heating demand DH

t to the night;I Significant pre-heating (space heating) and pre-charging (hot water tanks), but day-zone & hot

water temperatures remain within user-specified comfort constraints.

10 200

20

40

60

Time (h)

λDA

t(e

/M

Wh

)

RET AGG-PC

(a) Day-ahead electricity price

10 200

2

4

6

Time (h)

DH t

(GW

)

RET AGG-PC

(b) Heating demand

10 20

20

22

Time (h)

Tem

per

atu

re(

C)

DRP A DRP B

50

60

(c) Day-zone (solid) and hot water(dashed) temperatures (AGG)

26/31

Optimal bidding strategies – Limitedly controllable heating loads

I Risk-averse aggregator is able to maintain day-ahead price profile λDAt , but more procurement

during the high price period;I Procured demand DH

t during the night remains approximately the same, but part of this procuredquantity is ‘reserved’ to deal with unexpected real-time deviations;

I Excess/deficits can be sold/bought in intraday markets: risk-averse aggregator is more likely tosell, but sees lower prices λID

t .

10 200

20

40

60

Time (h)

λDA

t(e

/M

Wh

)

ε = 0.5 ε = 0.1

(a) Day-ahead electricity price

10 200

2

4

6

Time (h)

DH t

(GW

)

ε = 0.5 ε = 0.1

(b) Heating demand

10 200

20

40

60

Time (h)

λID t

(e/

MW

h)

ε = 0.5 ε = 0.1

(c) Intraday electricity price 27/31

Sensitivity analysis w.r.t. ε, δP ∼ N(0, σP) and δNP ∼ N(0, σNP)

.5 .6 .7 .8 .9 .99

0

1

2

1− ε (-)

B(Me

)

σNP =50MW, σP =0.05 σNP =100MW, σP =0.1 σNP =150MW, σP =0.15

Figure: Change in benefit B of the consumer-aggregator cooperation for different ε, δP ∼ N(0, σP) andδNP ∼ N(0, σNP) values for the 316th day of the calendar year.

28/31


.5 .6 .7 .8 .9 .99

0

1

2

1− ε (-)

B(Me

)



28/31


.5 .6 .7 .8 .9 .99

0

1

2

1− ε (-)

B(Me

)



28/31

Sensitivity analysis w.r.t. heating demand

.5 .6 .7 .8 .9 .99

0

1

2

3

1− ε (-)

B(Me

)

D16 (1%) D40 (10%) D92 (25%) D316 (50%)

D262 (75%) D105 (90%) D295 (99%)

Figure: Change in benefit B of the consumer-aggregator cooperation for different days of the heating season.σP was set to 0.1, σNP equals 100 MW.

29/31

Concluding remarks - the aggregator’s perspective

Model

I Strategic interaction aggregator – wholesale market ∼ Stackelberg game;

I Cooperation aggregator – DR provider ∼ Nash Bargaining game on division benefits,solution equivalent Stackelberg game ∈ set outcomes of Nash Bargaining Game;

I Limited controllability of DR providers → chance constraints.

Case study

I Aggregator may lower wholesale prices by actively managing limitedly controllable resources,respecting consumer’s comfort constraints;

I As the DR resource becomes less controllable and the aggregator becomes more risk-averse → theaggregator’s profit decreases, but impact is limited if intraday markets are sufficiently liquid.

30/31

Concluding remarks

To sum up:

I Two different perspective, both illustrating significant benefits in DR with TCLs;

I Violating thermal comfort leads to system-wide savings, but compensation available to consumersmay be insufficient;

I Impact limited controllability depends on perspective & model assumptions: system perspectivemay be too conservative, whereas intraday markets may be represented as too liquid.

Future work:

I Consumer-centric perspective;

I Sub-rational consumer behavior;

I Other aggregator strategies - e.g., risk-aversion;

I . . .

31/31

Contact: [email protected]

Publications: www.mech.kuleuven.be/en/tme/research/energy_environment

References:

I K. Bruninx et al., ‘Valuing Demand Response Controllability via Chance ConstrainedProgramming’, IEEE Trans. Sustain. Energy, vol. 9, no. 1, 2018.

I K. Bruninx, E. Delarue, Endogenous probabilistic reserve sizing and allocation in unit commitmentmodels: cost-effective, reliable and fast, IEEE Trans. Power Syst., vol. 32, no. 4, 2017.

I D. Patteeuw et al., Integrated modeling of active demand response with electric heating systemscoupled to thermal energy storage systems, Applied Energy, Vol. 151, 2015, pp. 306–319.

I K. Bruninx et al., On the Interaction between Aggregators, Electricity Markets and ResidentialDemand Response Providers, submitted to IEEE. Trans. Power Syst., 2018.

mailto:[email protected]

www.mech.kuleuven.be/en/tme/research/energy_environment

Documents

Valuing demand response controllability: a system and ... · Introduction & motivation I Many research/policy papers on ‘the value of demand response’: 0 50 100 112 73 52 35 (e