Efficient Allocation of Benefits from Multinational Grid Investments - - PowerPoint PPT Presentation

Efficient Allocation of Benefits from Multinational Grid Investments North Sea Offshore Grid 2030

Presentation by: Martin Kristiansen Co-authors: Francisco Muñoz (Universidad Adolfo Ibáñez, Chile) Shmuel Oren (UC Berkeley, USA) Magnus Korpås (NTNU, Norway) 15th IAEE European Conference 06.09.2017

Content

2

North Sea Link Viking NordLink

Motivation: Impact of grid investments

• Analytical examples

1

Methodology: An efficient allocation method

• Shapley Value (cooperative game theory)

2

Conclusions

4

Case Study: North Sea Offshore Grid

• Traditional allocation vs Shapley Value

3

Main drivers for multinational TEP

• More renewables -> need for flexibility

Main drivers for TEP

Provide flexibility for large-scale integration of variable generation

More renewables into the system

4

Ref: NREL, Holttinen (VTT)

..causes a more volatile net-load Quarterly Investments by Assets (ex. R&D)

…and the renewable resources are geographically located

5

Ref: Tobias Aigner, PhD Thesis, NTNU

Solar Irradiation Wind Speeds

…yielding a demand for infrastructure and flexibility

6

Increasing demand for spatial and temporal flexibility North Sea Offshore Grid (NSOG)

Impact of grid expansion

How multinational welfare is affected when a congested network is expanded

Consider two disconnected price areas

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2 1 𝑞2 𝑞1 𝑒1 𝑒2 𝑑1 = 𝑑0 + 𝑏1𝑒1 𝑑2 = 𝑑0 + 𝑏2𝑒2 Price Price Demand Demand 𝐿 Consumer Surplus (CS) Producer Surplus (PS) Generation Costs (GC)

Two markets

…capacity expansion yields a system re-dispatch

10 Two markets Capacity Expansion

𝑞2

∗

𝑒1 𝑒2 Price Price Demand Demand Consumer Surplus (CS) Producer Surplus (PS) Congestion Rent (CR) 𝐿 𝑞1

∗

(𝑒2−𝐿) (𝑒1+𝐿)

Aggregated benefits are always positive for efficient capacity expansion of a congested line, but the distribution of benefits can be asymmetric.

…and an assymetric distribution of benefits

11 Two markets Capacity Expansion

𝑞2

∗

𝑒1 𝑒2 Price Price Demand Demand Consumer Surplus (CS) Producer Surplus (PS) Congestion Rent (CR) 𝐿 𝑞1

∗

(𝑒2−𝐿) (𝑒1+𝐿)

Market effects

𝑋

𝑗 = 𝐷𝑇𝑗 + 𝑄𝑇𝑗 + 𝛽𝑗 ⋅ 𝐷𝑆

Net welfare: Welfare: 𝑋

𝑗 = 𝐷𝑇𝑗 + 𝑄𝑇𝑗

𝑒𝑋 𝑒𝐿 = 𝑒𝐷𝑇 𝑒𝐿 + 𝑒𝑄𝑇 𝑒𝐿 𝑒𝐷𝑇1 𝑒𝐿 < 0 𝑒𝑄𝑇1 𝑒𝐿 > 0 𝑒𝐷𝑇2 𝑒𝐿 > 0 𝑒𝑄𝑇2 𝑒𝐿 < 0 𝑒𝑋

2

𝑒𝐿 > 𝑒𝑋

1

𝑒𝐿

Aggregated benefits are always positive for efficient capacity expansion of a congested line, but the distribution of benefits can be asymmetric.

𝑒𝑋

𝑗

𝑒𝐿 = 𝑒𝐷𝑇𝑗 𝑒𝐿 + 𝑒𝑄𝑇𝑗 𝑒𝐿 + 𝛽𝑗 ⋅ 𝑒𝐷𝑆 𝑒𝐿

Nonnegative for all K<K*c Nonnegative for K<K^M Negative K^M<K<K* Incremental net benefits might not always be nonnegative for K’s above merchant investment level (under ideal conditions) due to the concave congestion rents

Expansion could also yield negative welfare externalities

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Consumer Surplus (CS) Producer Surplus (PS) Generation Costs (GC) 𝑞2 𝑞1 𝑒1 𝑒2 Price Price Demand Demand 𝑞3 𝑒3 Price Demand 2 1 𝐿 3

Low price High price Medium price

Although aggregated system benefits are nonnegative, nodal benefits might in some cases be negative

Summary - Potentional impact of line expansion

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Aggregated benefits are always positive for efficient capacity expansion of a congested line, but the distribution of benefits can be asymmetric.

1

For investments close to system optimal (K*), varying the ownership has limited impact on welfare reallocation.

2

Although aggregated system benefits are nonnegative, nodal benefits might in some cases be negative.

4

Considerable nodal incentives to deviate from system-optimal investment levels.

3

Expanding a line in a system might have negative impact on other existing lines. Hence, the sequence of investments has an impact on estimated nodal benefits.

5

Shapley Value

Reallocating unevely distributed benefits

Using side-payments to bridge the gap

Cooperative game theory

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Game Theory Cooperative Game Theory Collect decisions Collect outcome/solution

A cooperative game

𝐻 = (𝑂, 𝑤) : A cooperative game 𝑂 : Finite set of players indexed by 𝑗 𝑤 ∶ 2𝑂 → ℝ : Characteristic function for each subset 𝑇 ⊆ 𝑂 𝑇 : A coalition formation 𝑤(𝑂) : Value of the grand coalition that the members can distribute among themselves 𝑤(𝑇) : Value of a coalition that the members can distribute among themselves 𝑤 Ø = 0 : Value of an empty set We use this to answer: 1. Which coalitions will form? (the grand coalition) 2. How should that coalition allocate its value among the members? (fair-Shapley or stable-Core)

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Shapley value

𝜚𝑗 𝑂, 𝑤 = 1 𝑂 ! ෍

𝑇 ⊆𝑂\{𝑗}

𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇

17

Weight different ways where 𝑗 can add value to a coalition 𝑇

Shapley value

𝜚𝑗 𝑂, 𝑤 = 1 𝑂 ! ෍

𝑇 ⊆𝑂\{𝑗}

𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇

18

Weight different ways where 𝑗 can add value to a coalition 𝑇, using: Marginal contributions of player 𝑗 for different sequences

Shapley value

𝜚𝑗 𝑂, 𝑤 = 1 𝑂 ! ෍

𝑇 ⊆𝑂\{𝑗}

𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇

19

Weight different ways where 𝑗 can add value to a coalition 𝑇, using: Marginal contributions of player 𝑗 for different sequences, and weight it by the 𝑻 ! ways the coalition could be formed prior to 𝑗 joining

Shapley value

𝜚𝑗 𝑂, 𝑤 = 1 𝑂 ! ෍

𝑇 ⊆𝑂\{𝑗}

𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇

20

Weight different ways where 𝑗 can add value to a coalition 𝑇, using: Marginal contributions of player 𝑗 for different sequences, and weight it by the 𝑻 ! ways the coalition could be formed prior to 𝑗 joining and by the 𝑶 − 𝑻 − 𝟐 ! ways the remaining players could be added.

Shapley value

𝜚𝑗 𝑂, 𝑤 = 1 𝑂 ! ෍

𝑇 ⊆𝑂\{𝑗}

𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇

21

Weight different ways where 𝑗 can add value to a coalition 𝑇, using: Marginal contributions of player 𝑗 for different sequences, and weight it by the 𝑻 ! ways the coalition could be formed prior to 𝑗 joining and by the 𝑶 − 𝑻 − 𝟐 ! ways the remaining players could be added. Finally, sum over all combinations 𝑻 ⊆ 𝑶\{𝒋} and average over all possible

• rderings/sequences of all players, 𝑂 !.

Shapley value

𝜚𝑗 𝑂, 𝑤 = 1 𝑂 ! ෍

𝑇 ⊆𝑂\{𝑗}

𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇

22

Weight different ways where 𝑗 can add value to a coalition 𝑇, using: Marginal contributions of player 𝑗 for different sequences, and weight it by the 𝑻 ! ways the coalition could be formed prior to 𝑗 joining and by the 𝑶 − 𝑻 − 𝟐 ! ways the remaining players could be added. Finally, sum over all combinations 𝑻 ⊆ 𝑶\{𝒋} and average over all possible

• rderings/sequences of all players, 𝑂 !.

Shapley Value: Three friends sharing a meal

• Characterisitc functions: Three friends share a meal
• The bill ended at 90, but they don’t know who ate/drank what
• If they went alone: Akon would have to pay 80, Beyonce 56, and Clinton 70
• Marginal value: based on coalitions entering towards GC
• If A enters 80, then B (v({A,B})=80) add 0, and then C (v({A,B,C})=90) add 10
• If A enters 80, then C (v({A,C})=85) add 5, and then B (v({A,B,C})=90) add 5
• ….
• Then take the average off all marginal contributions
• Shapley Value
• (39.2, 20.7, 30.2) sums to 90.1, i.e. the total costs for grand coaltion

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Shapley Value: The airport problem

• Airport needs to be built for a range of different flights
• Each flight has different run-way-length requirements
• How to distribute the costs to each aircraft-company?
• Shapley Value ensures
• Everyone are better off
• Those who need a long runway, pays more
• Those who need a shorter, pays less
• No one pays as much as they would have needed to do alone, or in smaller coalitions

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North Sea Offshore Grid Case Study

Considering three already planned interconnectors

North Sea Offshore Grid Case Study

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North Sea Link Viking NordLink

The impact of investment sequence

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Cost savings: €18.9bn Reduced CO2 emissions: 82000ton/yr Impact of NSL Cost savings: €17.6bn Reduced CO2 emissions: 73000ton/yr Impact of NSL

Marginal contribution to system benefits

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€ € €

…for all possible sequences and combinations

Map possible coalitions

• Map possible coalitions

Grand coalition: S = N = {NO,DK,DE,BE,NL,GB} 4-player coalition: S= {NO,DK,DE,GB} 3-player coalition: S= {NO,DK,GB}, S= {DE,DK,GB} 2-player coalition: S= {NO, DE}, S= {NO, GB}, S= {GB, DK} No expansion: S = {Ø}

• Calculate 26 = 64 characteristic functions 𝑤(𝑇)
• S depends on sequence of players in all coalitions
• Value-creation with respect to “no expansion”
• Cost-savings, CO2 emissions, renewable generation

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North Sea Link Viking NordLink

From no cooperation towards the grand coalition

33 System costs CO2 emissions/costs Share of renewables in total generation output From “no cooperation” to “full cooperation”

Possible outcomes (for SV’s characteristic function)

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Traditional allocation of benefits

35

…with incentives to deviate from cooperation (non stable)

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…which are non-existing with the “fair” SV allocation

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Everyone are better off cooperating, than forming sub-coalitions or doing nothing.

The SV allocation relies on side-payments

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The SV allocation is stable for our case study

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𝑤 𝑇 ∪ 𝑗 − 𝑤 𝑇 ≤ 𝑤 𝑈 ∪ 𝑗 − 𝑤 𝑈 ∀𝑇 ⊆ 𝑈 ⊆ 𝑂\{𝑗}, ∀𝑗 ∈ 𝑂

..due to supermodularity, also known as «the snowball effect»

Conclusion: “Shapley Value yields a fair allocation”

Multinational investments might yield unevenly distributed benefits and negative externalities. Our method incorporates 1) the sequence of cable constructions, 2) strategic positions among participating countries, and 3) the marginal contribution with assets that benefit the greater good. Incentives for multinational cooperation is essential for market integration and we present a framework to benchmark fair benefit allocations in order to ensure the most cost-efficient system investments. Assuming tradeable utility, we use side-payments to enforce countries to end up with the cost-benefit benchmark calculated with The Shapley Value.

Relevant findings: Shortcomings and future work:

The considered base case can have a large impact on the re-allocation of costs and benefits. The base case should be wisely chosen for real-life applications. We do not investigate market mechanisms for side-payments. Future work should look into the possibility of using e.g. financial products or quotas to fulfill the suggested allocation framework. Develop a three-level strategic expansion model with decentralized objectives to quantify the expected value

• f a fully functioning allocation scheme.

Working paper available online

@ ResearchGate: https://goo.gl/Ba6rSB

41

Thank you for your attention!

One suggestion for side-payments

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BACKUP

£ -> NOK

Same approach for multiple attributes

44

BACKUP

Non-cooperative: PowerGAME

• Decentralized objectives
• Maximize national welfare
• Strategic decisions: domestic generation and/or transmission

capacity

• Advantage
• Take into account regional/national behaviour
• Political boundries
• Model «what we beleive»
• Quantify the value of fully functioning policies

and allocation schemes

• Follow up on our cooperative game theory paper

45

How can we model multiple national expansion plans?

1

Motivation: How does a decentralized expansion plan compare with a centralized expansion plan?

2

Supra-national planner Maximize system welfare

National planner Maximize national welfare National planner Maximize national welfare

Integrated power market Perfect competition

BACKUP

Investment model (PowerGIM)

• Programmed in Python
• Using PYOMO optimization language
• Stochastic
• Perfect competition
• Time-varying capacities (wind, solar,

load)

• Incorporates
• CO2 emissions
• (Energy storage (using storage values))
• (Demand side flexibility)
• Solves for a sampled set of hours (~500

hours)

• Based on sophisticated clustering techniques
• Scenario decomposition: progressive hedging

Philosophy: “keep it simple”

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North Sea 2030: 25 nodes and 30 branches

BACKUP

PowerGIM : Deterministic formulation

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BACKUP

Market simulator (PowerGAMA)

• Programmed in Python
• Using PYOMO optimization language
• Deterministic
• Perfect competition
• Time-varying capacities (wind, solar,

load)

• Incorporates
• DC Load Flow equations
• Energy storage (using storage values)
• Demand side flexibility
• Solves hour-by-hour (8760 hours)

Philosophy: “keep it simple”

48

Europe 2014: 1500 nodes and 2400 branches

BACKUP