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Viability of the Business Model of Demand Response Aggregator: Spot Energy Market Based Revenues for an Aggregator under Uncertainty and Contractual Limitation CEEM Paris Dauphine Research Seminar “The Issue of Consumer Participation in the Electricity Markets via Platform Market and Aggregators” 13th December 2016 Antoine VERRIER Ph. D candidate Chaire European Electricity Markets (CEEM) Université Paris-Dauphine

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Page 1: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Viability of the Business Model of Demand Response Aggregator:

Spot Energy Market Based Revenues for an Aggregator under Uncertainty and Contractual

Limitation

CEEM Paris Dauphine Research Seminar

“The Issue of Consumer Participation in the Electricity Markets via Platform Market and Aggregators”13th December

2016

Antoine VERRIERPh. D candidate

Chaire European Electricity Markets (CEEM)Université Paris-Dauphine

Page 2: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Purpose and Outline

Introduction

• Economics of Demand Response

Economic assessment of Demand Response

• Day-ahead energy market:• Economic dispatch under uncertainty

• Demand Response representation:• Storage model with customer-based constraints

Case Study and Results

• DR aggregator annual profits• French power system-based data in 2015

Conclusions

What is the Economic potential of Demand Response

in Electricity Markets ?

Page 3: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economic potential: three key points to consider

Economics of Demand Response

1) Competition with other technologies and the impact on market prices

2) Different markets to value Demand Response

3) Role of Demand Response aggregators

DR marginal cost of activation

Investment cost in the enable infrastructure

Large-scale DR deployment will impact the price

Wholesale market designs are key to large-scale deployment of

Demand Response

Aggregators are enablers, both at wholesale and retail sides

They have to deal with contract-based constraints

Page 4: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

Involuntary load curtailment valued at VoLL are a rough way to clear the market by the demand-side

Power

Prices

VoLL

Dem

and

System C

apacity

Involuntary load curtailment / Brown-out handled by the TSO

VoLL

Zero fixed-cost technology and the highest marginal cost

Page 5: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

DR can reduce peak demand and take part of generation adequacy

Power

Dem

and

System C

apacity

DR as Load-sheddingHigh (marginal) activation cost

Prices

VoLL

VoLL

Zero fixed-cost technology and the highest marginal cost

Page 6: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

DR can also be activated at a lower marginal cost

Power

Dem

and

System C

apacity

DR as Load-shiftingLow (marginal) activation cost

DR as Load-sheddingHigh (marginal) activation cost

Prices

VoLL

VoLL

Zero fixed-cost technology and the highest marginal cost

Page 7: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

DR lowers market prices, especially during peak periods

Power

Prices

Price

Dem

and

System C

apacity

DR as Load-shiftingLow (marginal) activation cost

DR as Load-sheddingHigh (marginal) activation cost

VoLL

Page 8: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

DR provides flexibility and enables the integration of Renewable Energies

Power

Prices

Dem

and

System C

apacity

DR as Load-shiftingLow (marginal) activation cost

DR as Load-sheddingHigh (marginal) activation cost

Page 9: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

DR provides flexibility and enables the integration of Renewable Energies

Power

Prices

Dem

and

DR as Load-shiftingLow (marginal) activation cost

Inflexible power plant

Page 10: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

DR provides flexibility and enables the integration of Renewable Energies

Power

Prices

Dem

and

Inflexible power plant

Page 11: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

The long-run effect

Power

Dem

and

System C

apacity

DR as Load-shiftingLow (marginal) activation cost

DR as Load-sheddingHigh (marginal) activation cost

Prices

VoLL

VoLL

Zero fixed-cost technology and the highest marginal cost

Page 12: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Dynamics of competition in electricity markets regarding Demand Response

The long-run effect

Power

Dem

and

System C

apacity

DR as Load-shiftingLow (marginal) activation cost

High fixed cost

DR as Load-sheddingHigh (marginal) activation cost

Low fixed cost

Competition with Hydro Pumped Storage

and other type of Storages

Competition with peakers

Page 13: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Demand Response Market Valuation – DR can be valued in at least 4 wholesale markets

Day-ahead Market Balancing Market Ancillary Services Capacity Mechanisms

Demand Response

(Large)Consumers

(Small)Consumers

(Small) Consumers

(Small)Consumers

Retail Market

(Small) Consumers

MWhMWh

MWhMWh

€/MWh €/MWh €/MWh €/MW

Wholesale Markets

Page 14: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Demand Response Market Valuation – Market design impedes DR to participatein wholesale markets; retail market design might not incentivize DR

Day-ahead Market Balancing Market Ancillary Services Capacity Mechanisms

Demand Response

(Large)Consumers

(Small)Consumers

(Small) Consumers

Minimum bid-size Minimum bid-size

Response time

Minimum bid-size

Response time

Ramping rates

Commitment of availability

Commitment of availability

(Small)Consumers

Retail Market

(Small) Consumers

Time-based rates

Wholesale Markets

Page 15: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

Demand Response Market Valuation – Consumers’ constraints can hinder DR to participate in wholesale markets

Day-ahead Market Balancing Market Ancillary Services Capacity Mechanisms

Demand Response

(Large)Consumers

(Small)Consumers

(Small) Consumers

Minimum bid-size Minimum bid-size

Response time

(Small)Consumers

Retail Market

(Small) Consumers

Time-based rates

Market monitoring

Complexity to respond

Wholesale Markets

Minimum bid-size

Response time

Ramping rates

Commitment of availability

Commitment of availability

Page 16: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand ResponseThe role of Demand Response aggregators – DR aggregators are enablersremoving the barriers by contracting with consumers and make the link withwholesale markets

Day-ahead Market Balancing Market Ancillary Services Capacity Mechanisms

Demand ResponseAggregator

(Large)Consumers

(Small)Consumers

(Small) Consumers

(Small)Consumers

(Small) Consumers

Contract 1 Contract NContract 2 ……

Energy€

Enabling technologies

Page 17: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

The role of Demand Response aggregators – The contract terms shouldreflect consumers’ willingness to participate in the DR program

Contract

Contract terms Description UnitCapacity Max. amount of curtailable power MW

Cost of activation Compensation the consumer gets €/MWhDuration Max. time the load capacity can be shed/shifted hFrequency Max. number of events over a period N/yearNotice time Time before the event is actually triggered hRecovery time Max. time energy has to be recovered h

Page 18: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Economics of Demand Response

The role of Demand Response aggregators – Frequency constraint and Uncertainty together creates an Opportunity Cost of using DR

Contract

Contract terms Description UnitCapacity Max. amount of curtailable power MW

Cost of activation Compensation the consumer gets €/MWhDuration Max. time the load capacity can be shed/shifted hFrequency Max. number of events over a period N/yearNotice time Time before the event is actually triggered hRecovery time Max. time energy has to be recovered h

When will the aggregator use its DR resource on the wholesale markets ?

Market Uncertainty and Frequency => Opportunity Cost to use a DR resource

Page 19: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Outline

Introduction

• Dynamics of competition in electricity markets regarding DR

• The impact on market designs on DR valuation

• The role of Demand Response aggregators

Economic assessment of Demand Response

• Day-ahead Energy market:• Economic dispatch under uncertainty

• Demand Response representation:• Storage model with customer-based constraints

Case Study and Results

• DR aggregator annual profits• French power system-based data in 2015

Conclusions

Page 20: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

What is the Economic potential of Demand Response in Electricity

Markets ?

The business case of a DR aggregator on the Day-ahead Market

Economic assessment of Demand Response

Market-based revenues and compare those to the investment cost of enabling

technologies

Contributions

1. Competition with other technologies

2. DR impact on the market price

3. Market uncertainty

4. Customer-based constraints specified in contracts

Page 21: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Day-ahead Energy Market model

An optimization-based economic dispatch model under uncertainty is used

– Minimize the total operational cost of the system

– Exogenous electricity mix: no investments

– The dispatch is performed

• Over one year

• On a hourly basis

hours

January December

Hourly Residual Electricity Demand

For the 8760 hours

Main OutcomesPower generated by each technologyMarket prices

Page 22: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Day-ahead Energy Market model

Focus on the UncertaintyResidual Demand Scenarios

– Uncertainty:

• Electricity Demand and Renewable production

– Modelling:

• 20 Residual Demand Scenarios ; Weekly time steps

hours

January December

Residual Electricity Demand scenarios

Page 23: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Day-ahead Energy Market model

Focus on the UncertaintyWhen does the Uncertainty “hits” the system ?

– Uncertainty:

• Electricity Demand and Renewable production

– Modelling:

• 20 Residual Demand Scenarios ; Weekly time steps

hoursJanuary

Residual Electricity Demand scenarios

Week 1 Week 2 Week 4 Week 5

Page 24: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Day-ahead Energy Market model

Focus on the UncertaintyWhen does the Uncertainty “hits” the system ?

– Uncertainty:

• Electricity Demand and Renewable production

– Modelling:

• 20 Residual Demand Scenarios ; Weekly time steps

hoursJanuary

Residual Electricity Demand scenarios

Uncertainty Uncertainty Uncertainty Uncertainty Uncertainty Uncertainty

Week 1 Week 2 Week 4 Week 5

Page 25: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Day-ahead Energy Market model

Focus on the UncertaintyWhen does the Uncertainty “hits” the system ?

– Uncertainty:

• Electricity Demand and Renewable production

– Modelling:

• 20 Residual Demand Scenarios ; Weekly time steps

hoursJanuary

Residual Electricity Demand scenarios

Uncertainty Uncertainty Uncertainty Uncertainty Uncertainty Uncertainty

Week 1 Week 2 Week 4 Week 5

Scenario realisation

Hourly Dispatch

Deterministic setting

Scenario realisation

Hourly Dispatch

Deterministic setting

Scenario realisation

Hourly Dispatch

Deterministic setting

Scenario realisation

Hourly Dispatch

Deterministic setting

Scenario realisation

Hourly Dispatch

Deterministic setting

Page 26: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Outline

Introduction

• Dynamics of competition in electricity markets regarding DR

• The impact on market designs on DR valuation

• The role of Demand Response aggregators

Economic assessment of Demand Response

• Day-ahead Energy market:• Economic dispatch under uncertainty

• Demand Response representation:• Storage model with customer-based constraints

Case Study and Results

• DR aggregator annual profits• French power system-based data in 2015

Conclusion

Page 27: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Demand Response: modelling approach

We use a storage representation for Demand ResponseContract terms define constraints for using DR

Load-shifting

Modelled as Hydro pumped storage

Load-shedding

Modelled as Hydro reservoir

Turbining

Capacity

[W]

Pumping

Capacity

[W]

Turbining

Capacity

[W]

Reservoir Size

[Wh]

Contract terms Description UnitCapacity Max. amount of curtailable power WCost of activation Compensation the consumer gets €/MWhDuration Max. time the load capacity can be shed/shifted hFrequency Max. number of events over a period N/yearNotice time Time before the event is actually triggered hRecovery time Max. time energy has to be recovered h

Co

ntr

act

Page 28: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Demand Response: modelling approach

We use a storage representation for Demand ResponseTime availability is an important constraint

0

5000

10000

15000

20000

MW

Residential electric heating annual load profile – France (RTE data)

Residential electric Heating can’t provide DR during summer

Summer period

Load-shifting

Modelled as Hydro pumped storage

Load-shedding

Modelled as Hydro reservoir

Turbining

Capacity

[W]

Pumping

Capacity

[W]

Turbining

Capacity

[W]

Reservoir Size

[Wh]

Page 29: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Outline

Introduction

• Dynamics of competition in electricity markets regarding DR

• The impact on market designs on DR valuation

• The role of Demand Response aggregators

Economic assessment of Demand Response

• Day-ahead Energy market:• Economic dispatch under uncertainty

• Demand Response representation:• Storage model with customer-based constraints

Case Study and Results

• DR aggregator annual profits• French power system-based data in 2015

Conclusions

Page 30: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Case study: French power system data (2015)

Thermal units

Nuclear63 100 MW23 € / MWh

Coal 2 900 MW35 € / MWh

Gas CCGT5 700 MW75 € / MWh

Hydro units

Demand Response

Hydro Reservoir9 100 MW8 € / MWh

Residential Heating17 500 MW11 € / MWh

Tertiary Heating8 700 MW11 € / MWh

Tertiary Cooling2 800 MW11€ / MWh

Industry Cement272 MW20 € / MWh

Industry Paper87 MW20 € / MWh

Industry Cross-tech402 MW16€ / MWh

The Supply-side In addition to the existing French electricity mix, DR is integrated

Source: RTE bilan prévisionnel 2015; Gils 2014; IEA projected cost of generating electricity 2015; Gruber 2014

Pumped Storage 5 000 MW9 € / MWh

Fuel-Oil5 100 MW100 € / MWh

Gas Turbine1 900 MW120 € / MWh

Other peakers3 000 MW150 € / MWh

Renewables

Production added to make up the ResidualDemand

Load-shifting

Load-shedding

Industry Steel272 MW411 € / MWh

Industry Aluminium87 MW164 € / MWh

Industry Chemicals402 MW100 € / MWh

Page 31: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Case study: French power system data (2015)

€-

€2 000 000

€4 000 000

€6 000 000

Aluminium Steel Chemicals

Market revenues per scenario

€-

€200 000

€400 000

€600 000

€800 000

€1 000 000

€1 200 000

Cross-Indutrial Cement Paper

Market revenues per scenario

Market revenues in the Industrial Sector

Load-shifting

Load-shedding

Average

700 000€

Average

56 000€

Average

1 500 000€ Average

1 000 000€

Average

88 000€

Average

175 000€

Scenarios with veryhigh demand

Revenues = 0 for mostof the scenarios

Page 32: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Case study: French power system data (2015)

Market revenues in Tertiary and Residential Sectors

Load-shifting

€-

€2 000 000

€4 000 000

€6 000 000

€8 000 000

€10 000 000

€12 000 000

Residential_Heating Tertiary_Heating Tertiary_Cooling

Market revenues per scenario

Average

1 500 000€

Average

1 600 000€Average

350 € !

More scenarios withactivation: seems less risky

Time availability Constraint(Cooling during summer)

Page 33: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Case study: French power system data (2015)

Average Market revenues by CapacitySort by Demand Response categories

Load-Shifting Load-shedding

Residential Heating 90 € / MW / year

TertiaryHeating 180 € / MW / year

Cooling 0 € / MW / year

Industry

Cross-tech 220 € / MW / year

Cement 650 € / MW / year

Paper 650 € / MW / year

Aluminium 5 100 € / MW / year

Steel 3 600 € /MW / year

Chemicals 5 500 € / MW / year

Page 34: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Case study: French power system data (2015)

What is the investment cost in DR enabling technologies ?

Investment Cost Source

Industry (Load-shedding) [200 ; 8 000] € / MW Stede 2016

Tertiary 200 000 € / MW Frontier and Formaet 2014

Residential

500 € / meter Prüggler 2013

25 € / meter / year Léautier 2012

6 € / kW / year Steurer et al. 2015

Investment Cost Source: Calculation based on

Industry (Load-shedding) [16 ; 640] € / MW / year Stede 2016

Tertiary 16 000 € / MW / year Frontier and Formaet 2014

Residential

10 000 € / MW / year Prüggler 2013

6 250 € / MW / year Léautier 2012

6 000 € / MW / year Steurer et al. 2015

Assuming:

20-years lifetime;

a 5% rate of return;

a meter in the residential sector controls 4 kW

Page 35: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Case study: French power system data (2015)

Comparison between Annual Market Revenues and Investment Costs

Avearge Market Revenues Investement Costs

Residential Heating 90 € / MW / year [ 6000; 10 000]€/MW/year

TertiaryHeating 180 € / MW / year

16 000 € /MW/year

Cooling 0 € / MW / year

Industry Load-shifting

Cross-tech 220 € / MW / year

Cement 650 € / MW / year No data found

Paper 650 € / MW / year

Industry Load-sheddingAluminium 5 100 € / MW / year

[16; 640] € / MW / yearSteel 3 600 € /MW / year

Chemicals 5 500 € / MW / year

Page 36: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Outline

Introduction

• Dynamics of competition in electricity markets regarding DR

• The impact on market designs on DR valuation

• The role of Demand Response aggregators

Economic assessment of Demand Response

• Spot Energy market:• Economic dispatch under uncertainty

• Demand Response representation:• Storage model with customer-based constraints

Case Study and Results

• DR aggregator annual profits• French power system-based data in 2015

Conclusions

Page 37: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Conclusions

What is the Economic potential of Demand Response in Electricity

Markets ?

A. What can we say about the business case of a DR aggregator, using French power

system data ?

B. Consequences regarding Market Designs and Business model of aggregators

1) What class customers to contract with ? (Only Small Consumers / Industrial ; or a

mix of both ? )

2) DR should have access to ancillary serives and/or Capacity Mechanisms

A. Further Research

1) Tertiary: no business case for DR based on cooling (time availability constraint)

2) Tertiary and Residential: Heating based DR isn’t viable but show more

promising results

3) Industrial DR: is a viable business because installed Capacities are lower.

However it looks more risky (DR is only activated during high demand

scenarios)

1) Only Day-ahead has been modeled: can the revenues from other wholesale

markets change the business case ?

2) What would be the dynamics of Investment in Demand Response ?

Page 38: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Thank you for your attention

The end

Page 39: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

1. Installed Capacity

2. Activation Costs

3. Duration: DR event length (eg 3 hours)

4. Time availability: load profiles (eg load for heating is absent during summer)

5. Frequency: limits on the number of events (eg 20 activations per year)

Demand Response: modelling approach

Load-shifting

Installed Turbining CapacityInstalledPumpingCapacity

DurationReservoir size = Installed Turb Capacity x Duration

Time availabilityTurb Capacity <Installed Capacity x coeff (Time Step)

Time availabilityPump Capacity <Installed Capacity x coeff (Time Step)

FrequencyReservoir size = Turbining Capacityx DurationxFrequency

Installed Turbining Capacity

Contractual Reservoir

Constraints specific to Demand Response

Page 40: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Load Profiles

0

0,2

0,4

0,6

0,8

1

1,2

1

24

47

70

93

11

6

13

9

16

21

85

20

82

31

25

4

27

73

00

32

3

34

63

69

39

2

41

54

38

46

14

84

50

7

53

05

53

57

6

59

96

22

64

5

66

86

91

71

47

37

76

07

83

80

68

29

85

28

75

89

8

92

19

44

96

79

90

10

13

10

36

10

59

10

82

11

05

11

28

11

51

11

74

11

97

12

20

12

43

Availability Turbining (%)

0

0,2

0,4

0,6

0,8

1

1,2

12

44

77

09

31

16

13

91

62

18

52

08

23

12

54

27

73

00

32

33

46

36

93

92

41

54

38

46

14

84

50

75

30

55

35

76

59

96

22

64

56

68

69

17

14

73

77

60

78

38

06

82

98

52

87

58

98

92

19

44

96

79

90

10

13

10

36

10

59

10

82

11

05

11

28

11

51

11

74

11

97

12

20

12

43

Availability Pumping (%)

Appendix- Building the time availability parameter

Page 41: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Toy model

Results

-

10,00

20,00

30,00

40,00

50,00

60,00

70,00

80,00

90,00

100,00

Full DR f1 f2 f3 f4 f5 f6 f7 No DR

NO

RM

ALI

ZED

VA

LUE

DR system value according to Frequency of activation

𝐷𝑒𝑚𝑎𝑛𝑑 𝑅𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑆𝑦𝑠𝑡𝑒𝑚 𝑉𝑎𝑙𝑢𝑒 = 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡𝑁𝑜 𝐷𝑅 − 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡𝐷𝑅𝑟𝑢𝑛 𝑖

𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = 𝔼𝜔

𝑡

𝑇

𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛 (𝑡, 𝜔)

Run i Frequency

Full DR f= 4

F1 f= 3,5

F2 f= 3

F3 f= 2,5

F4 f=2

F5 f=1,5

F6 f= 1

F7 f= 0,5

No DR f = 0

Page 42: Viability of the Business Model of Demand Response ... Prices d Inflexible power plant. Economics of Demand Response ... An optimization-based economic dispatch model under uncertainty

Appendix – Model formulation

𝔼𝜔0 min𝑥0𝑐0𝑥0 + 𝔼𝜔1 min

𝑥1𝑐1𝑥1 +𝔼𝜔2 min

𝑥2𝑐2𝑥2 + 𝔼𝜔3 min

𝑥3𝑐3𝑥3

s.t. K ≥ 𝑥𝑡 ≥ 0 ; 𝑥𝑡 ≥ 𝑑𝑡𝜔𝑡; 𝑅𝑡 = 𝑅𝑡−1 + 𝑥𝑡−1 ∗ ℎ for each time step t

The multi-stage stochastic problem is formulated as follow:

Power production Balancing constraint Reservoir levels evolution

We end up with the following problem where SDDP builds an approximation of the future cost functions 𝑽𝒕 𝑹𝒕, 𝝎𝒕 at each time step

min𝑥0𝑐0𝑥0 + 𝔼𝜔1 𝑉1(𝑅1, 𝜔1)

𝑉1 𝑅1, 𝜔1 = min𝑥1𝑐1𝑥1 + 𝔼𝜔2 𝑉2(𝑅2, 𝜔2)

𝑉2 𝑅2, 𝜔2 = min𝑥2𝑐2𝑥2 + 𝔼𝜔3 𝑉3(𝑅3, 𝜔3)

𝑉3 𝑅3, 𝜔3 = min𝑥3𝑐3𝑥3 + 𝑉4

𝑉4 = 0