From linking to integration of energy system models and computational general equilibrium models
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This document discusses different approaches to linking and integrating energy system models and computational general equilibrium (CGE) models. It finds that: 1. Hard-linking or integrating models to solve for a Nash equilibrium produces the same results, but integrating the models may be faster, solving all equations at once rather than iteratively. 2. Integrating the models as a mixed complementarity problem (MCP) and solving simultaneously finds the solution faster than hard-linking separately. 3. Integrating the models as a nonlinear program (NLP) is even faster, solving large problems with over 2,500 scenarios in just 7 minutes, compared to 10 hours and 10 minutes for other approaches.
From linking to integration of energy system models and computational general equilibrium models
- 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. CGE model Energy system model
- 3. Hybrid models Separate models 1) Soft linked models 2) Hard linked models 3) Integrated model 2 findings
- 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. Linking the models TIMES CGE 2015 Base year2015 Base year
- 6. Linking the models TIMES CGE 2015 Base year 2026 Future equilibrium 2015 Base year Demand
- 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. 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
- 11. Integrated models - MCP NLP QP LP Complementarity ProblemsKKT conditions TIMES CGE
- 12. Model combinations TIMES CGE Linked LP MCP Linked MCP MCP Integrated MCP MCP
- 13. Problem instances 0% Increasing capital availability +30% 0%Increasinglaboravailability20% 61 x 41 = 2501 problem instances
- 14. From linking to integration 2501 problem instances – different assumptions for capital and labor availability Hard-linked Integrated MCP equilibrium Nash equilibrium Linking
- 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
- 17. … from integrated models - MCP NLP QP LP Complementarity ProblemsKKT conditions TIMES CGE
- 18. … to integrated models - NLP NLP QP LP Complementarity ProblemsKKT conditionsTIMES CGE
- 19. Model combinations TIMES CGE Linked LP MCP Linked MCP MCP Integrated MCP MCP Integrated LP NLP Linked LP NLP Linked MCP NLP
- 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. 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. 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. 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. Thank you for your attention! Per.Ivar.Helgesen@Enova.no +47 95307720 Image:NASA