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From linking to integration of energy system models and computational general equilibrium models

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From linking to integration of energy system models and computational general equilibrium models

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From linking to integration of energy system models and computational general equilibrium models

  1. 1. From linking to integration of energy system models and computational general equilibrium models ETSAP 75th semi-annual meeting Paris 2019-06-07 Per Ivar Helgesen
  2. 2. CGE model Energy system model
  3. 3. Hybrid models Separate models 1) Soft linked models 2) Hard linked models 3) Integrated model 2 findings
  4. 4. Stylized models Hydropower Gasburner GaspowerGas Hydro Resources Technologies Demand for energy services Electric heating Power specific demand Heat demand Thermal heat Electricity Thermal heat Agents Markets Firm 1 Firm 2 Firm 3 Firm 4 Household Natural Gas Commodity Electricity Commodity Manufacturing Commodity Nonmanufacturing Commodity Capital Labor GAS ELE MAN NON L K HOU total GAS 4 2 3 1 10 ELE 1 1 7 8 5 22 MAN 1 3 6 26 2 38 NON 5 10 10 30 92 147 L 1 1 5 53 60 K 2 3 8 27 40 HOU 60 40 100 total 10 22 38 147 60 40 100 TIMES CGE
  5. 5. Linking the models TIMES CGE 2015 Base year2015 Base year
  6. 6. Linking the models TIMES CGE 2015 Base year 2026 Future equilibrium 2015 Base year Demand
  7. 7. Linking the models TIMES CGE 2015 Base year 2026 Future equilibrium 2015 Base year Demand Energy mix 2026 Future energy system Convergence: When all variables have a relative change below 10-6 solvedforeachyear solvedforhorizonyear
  8. 8. How can we integrate the models? Let us look at problem classes NLP QP LP Complementarity ProblemsKKT conditions Equilibrium programming Non-optimization based problems, e.g. Nash-Cournot games. LP = Linear Program QP = Quadratic Program NLP = Non-Linear Program Source: Prof. Steven Gabriel
  9. 9. Integrating models NLP QP LP Complementarity ProblemsKKT conditions TIMES CGE
  10. 10. Hard-linked models NLP QP LP Complementarity ProblemsKKT conditions TIMES CGE
  11. 11. Integrated models - MCP NLP QP LP Complementarity ProblemsKKT conditions TIMES CGE
  12. 12. Model combinations TIMES CGE Linked LP MCP Linked MCP MCP Integrated MCP MCP
  13. 13. Problem instances 0% Increasing capital availability +30% 0%Increasinglaboravailability20% 61 x 41 = 2501 problem instances
  14. 14. From linking to integration 2501 problem instances – different assumptions for capital and labor availability Hard-linked Integrated MCP equilibrium Nash equilibrium Linking
  15. 15. From linking to integration – finding #1 2501 problem instances – different assumptions for capital and labor availability Hard-linked Integrated MCP equilibrium Nash equilibrium Linking 7 hours 10 minutes
  16. 16. Going further NLP QP LP Complementarity ProblemsKKT conditions TIMES CGE
  17. 17. … from integrated models - MCP NLP QP LP Complementarity ProblemsKKT conditions TIMES CGE
  18. 18. … to integrated models - NLP NLP QP LP Complementarity ProblemsKKT conditionsTIMES CGE
  19. 19. Model combinations TIMES CGE Linked LP MCP Linked MCP MCP Integrated MCP MCP Integrated LP NLP Linked LP NLP Linked MCP NLP
  20. 20. From linking to integration 2501 problem instances – different assumptions for capital and labor availability Hard-linked Integrated MCP Integrated NLP equilibrium Nash equilibrium Linking
  21. 21. From linking to integration – finding #2 2501 problem instances – different assumptions for capital and labor availability Hard-linked Integrated MCP Integrated NLP equilibrium Nash equilibrium Linking
  22. 22. From linking to integration – finding #2 2501 problem instances – different assumptions for capital and labor availability Hard-linked Integrated MCP Integrated NLP equilibrium Nash Stackelberg equilibrium Linking equilibrium 7 hours 10 minutes 7 minutes
  23. 23. Conclusions 1. Linking the models produces the same Nash equilibrium as the integrated model that combines the KKT-conditions into one MCP. 2. Solving one integrated model may be faster than iterating between individual models. 3. Combining the models in a leader-follower setting may produce a Stackelberg equilibrium that differs from the Nash equilibrium.
  24. 24. Thank you for your attention! Per.Ivar.Helgesen@Enova.no +47 95307720 Image:NASA

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