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

9. Integrating models
NLP
QP
LP
Complementarity
ProblemsKKT conditions
TIMES CGE

10. Hard-linked models
NLP
QP
LP
Complementarity
ProblemsKKT conditions
TIMES CGE

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

16. Going further
NLP
QP
LP
Complementarity
ProblemsKKT conditions
TIMES CGE

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