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) 15 th IAEE European Conference 06.09.2017
Content Main drivers for multinational TEP 0 - More renewables -> need for flexibility Motivation: Impact of grid investments 1 - Analytical examples Methodology: An efficient allocation method 2 - Shapley Value (cooperative game theory) Case Study: North Sea Offshore Grid 3 - Traditional allocation vs Shapley Value 4 Conclusions North Sea Link Viking NordLink 2
Main drivers for TEP Provide flexibility for large-scale integration of variable generation
More renewables into the system Quarterly Investments by Assets (ex. R&D) ..causes a more volatile net-load Ref: NREL, Holttinen (VTT) 4
…and the renewable resources are geographically located Wind Speeds Solar Irradiation Ref: Tobias Aigner, PhD Thesis, NTNU 5
… yielding a demand for infrastructure and flexibility Increasing demand for spatial and temporal flexibility North Sea Offshore Grid (NSOG) 6
Impact of grid expansion How multinational welfare is affected when a congested network is expanded
Consider two disconnected price areas Two markets 𝐿 1 2 Price Price 𝑑 2 = 𝑑 0 + 𝑏 2 𝑒 2 𝑞 2 𝑑 1 = 𝑑 0 + 𝑏 1 𝑒 1 𝑞 1 𝑒 1 𝑒 2 Demand Demand Consumer Surplus (CS) Producer Surplus (PS) Generation Costs (GC) 9
… capacity expansion yields a system re-dispatch Capacity Two markets Expansion Price Price 𝐿 ∗ 𝑞 2 ∗ 𝑞 1 𝑒 1 (𝑒 2 −𝐿) 𝑒 2 Demand (𝑒 1 +𝐿) Demand Consumer Surplus (CS) Producer Surplus (PS) Congestion Rent (CR) Aggregated benefits are always positive for efficient capacity expansion of a congested line, but the distribution of benefits can be asymmetric . 10
…and an assymetric distribution of benefits 𝑋 𝑗 = 𝐷𝑇 𝑗 + 𝑄𝑇 𝑗 Welfare: Capacity Market Two markets Expansion effects 𝑋 𝑗 = 𝐷𝑇 𝑗 + 𝑄𝑇 𝑗 + 𝛽 𝑗 ⋅ 𝐷𝑆 Net welfare: Price Price 𝑒𝐷𝑇 1 𝑒𝐷𝑇 2 𝑒𝐿 < 0 𝑒𝐿 > 0 𝐿 ∗ 𝑞 2 𝑒𝑄𝑇 1 𝑒𝑄𝑇 2 ∗ 𝑞 1 𝑒𝐿 > 0 𝑒𝐿 < 0 𝑒 1 (𝑒 2 −𝐿) 𝑒 2 Demand (𝑒 1 +𝐿) Demand Consumer Surplus (CS) Producer Surplus (PS) Congestion Rent (CR) 𝑒𝑋 𝑒𝐿 = 𝑒𝐷𝑇 𝑗 𝑒𝐿 + 𝑒𝑄𝑇 𝑗 𝑒𝐿 + 𝛽 𝑗 ⋅ 𝑒𝐷𝑆 𝑒𝑋 𝑒𝐿 = 𝑒𝐷𝑇 𝑒𝐿 + 𝑒𝑄𝑇 𝑗 𝑒𝐿 𝑒𝐿 𝑒𝑋 𝑒𝐿 > 𝑒𝑋 Nonnegative Nonnegative 2 1 for all K<K*c for K<K^M 𝑒𝐿 Negative K^M<K<K* Aggregated benefits are always positive for efficient capacity expansion of a congested line, but the distribution of benefits can be asymmetric . 11 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 Low price High price Medium price 𝐿 3 1 2 Price Price Price 𝑞 2 𝑞 3 𝑞 1 𝑒 2 𝑒 3 𝑒 1 Demand Demand Demand Consumer Surplus (CS) Producer Surplus (PS) Generation Costs (GC) Although aggregated system benefits are nonnegative, nodal benefits might in some cases be negative 12
Summary - Potentional impact of line expansion Shapley Value Aggregated benefits are always positive for efficient capacity expansion of a congested line, but the 1 distribution of benefits can be asymmetric . For investments close to system optimal (K*), varying the ownership has limited impact on welfare 2 reallocation . 3 Considerable nodal incentives to deviate from system-optimal investment levels. Although aggregated system benefits are nonnegative, nodal benefits might in some cases be negative . 4 Expanding a line in a system might have negative impact on other existing lines. Hence, the sequence of 5 investments has an impact on estimated nodal benefits . 13
Reallocating unevely distributed benefits Using side-payments to bridge the gap
Cooperative game theory Game Theory Cooperative Game Theory Collect decisions Collect outcome/solution 15
A cooperative game 𝐻 = (𝑂, 𝑤) : A cooperative game 𝑂 : Finite set of players indexed by 𝑗 𝑤 ∶ 2 𝑂 → 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) 16
Shapley value 1 𝜚 𝑗 𝑂, 𝑤 = 𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇 𝑂 ! 𝑇 ⊆𝑂\{𝑗} Weight different ways where 𝑗 can add value to a coalition 𝑇 17
Shapley value 1 𝜚 𝑗 𝑂, 𝑤 = 𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇 𝑂 ! 𝑇 ⊆𝑂\{𝑗} Weight different ways where 𝑗 can add value to a coalition 𝑇 , using: Marginal contributions of player 𝑗 for different sequences 18
Shapley value 1 𝜚 𝑗 𝑂, 𝑤 = 𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇 𝑂 ! 𝑇 ⊆𝑂\{𝑗} 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 19
Shapley value 1 𝜚 𝑗 𝑂, 𝑤 = 𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇 𝑂 ! 𝑇 ⊆𝑂\{𝑗} 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. 20
Shapley value 1 𝜚 𝑗 𝑂, 𝑤 = 𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇 𝑂 ! 𝑇 ⊆𝑂\{𝑗} 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 orderings/sequences of all players, 𝑂 ! . 21
Shapley value 1 𝜚 𝑗 𝑂, 𝑤 = 𝑇 ! 𝑂 − 𝑇 − 1 ! 𝑤 𝑇⋃𝑗 − 𝑤 𝑇 𝑂 ! 𝑇 ⊆𝑂\{𝑗} 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 orderings/sequences of all players, 𝑂 ! . 22
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: A kon would have to pay 80, B eyonce 56, and C linton 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 23
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 24
North Sea Offshore Grid Case Study Considering three already planned interconnectors
North Sea Offshore Grid Case Study North Sea Link Viking NordLink 29
The impact of investment sequence Impact of NSL Cost savings : €18.9bn Reduced CO2 emissions : 82000ton/yr Impact of NSL Cost savings : €17.6bn Reduced CO2 emissions : 73000ton/yr 30
Marginal contribution to system benefits € € € …for all possible sequences and combinations 31
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 2 6 = 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 North Sea Link Viking NordLink 32
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