Energy System Model

Linking Energy System and Macroeconomic Growth Models

Is the Supply Curve Enough?

Nico Bauer Ottmar Edenhofer

Contents

• Two Models

• Two Approaches

• Results

• Augmenting the Soft-Link

• Intermediate Conclusions

• Artificial Constraints

Energy System Model

• 2 types of primary energy (fossil, renewable)

• 2 types of final energy (high and low capital costs)

• 2 conversion technologies for each

( )

( )

2

1

&

Min! ;

s.t.: linear equations;

rt

Inv Fuel O M

t

DESC e C C C dt

τ

τ

−

=

=

∫

Macro Growth Model

• Welfare and macro production function

• 2 types of final energy

• 2 capital stocks with depreciation

( )

2

1

Max! ^t ( , , ) ;

t

e U F K L E I EE dt

τ

ρ τ

−

=

=

∫

Macro Growth Model

σ_KLE

σ_KE L

Y

σ_B σ_A

Hard-Link

• Full Integration of ESM into MGM

• Benchmark for comparison EE = CTot

Soft-Link

• 2 energy supply curves in MGM

• Iteration

• Approximation of hard-link result

( ) ( ) ( ) ( )

1,2

c.

i i

i

EE t a t b t E t

=

= +

∑

( )

( , ); a .

E a b E

b

= ⎛ ⎞⎜ ⎟ = M ⎝ ⎠ E

Research Questions

• Soft-link

– Energy prices?

• Hard-link vs. Soft-link

– Energy prices and quantities?

– Capital market?

Results – Soft-Link

Price energy type 1 Price energy type 2

Results – Hard vs. Soft

Rel. quantity differences Rel. price differences

Results – Hard vs. Soft

• Own rate of return r_i is technology specific

• Equilibrium interest rate r*

• Capital market equilibrium

( )

0 0.

0

i i

i i

i i

I r r

r r I

I r r

∗ ∗

∗

≥ ⇔ = ⎫

− =

= ⇔ > ⎭⎬

Results – Hard vs. Soft

r_i for hard-link I_i/Y for hard-link

Results – Hard vs. Soft

r_i for soft-link I_i/Y for soft-link

Results – Hard vs. Soft

Differences of I_i/Y

Results – Hard vs. Soft

Relative differences Y

Improving the Soft-Link

• Extending the information flow

• Considers now capital scarcity

( )

( , ); , .

E a

a b E r

r b

⎛ ⎞ ⎛ ⎞

= =

⎜ ⎟ ⎜ ⎟

⎝ ⎠ M ⎝ ⎠ E

Augmenting the Soft-Link

Original soft-link Augmented soft-link

Augmenting the Soft-Link

Augmented soft-link Augmented soft-link

Intermediate Conclusions

Capital X market

X Energy X

market

Hard-link Soft-link

Intermediate Conclusions

( )

( )

( )

2

1

0 0

, , , ;

, ;

, . 0.

ˆ ;

t

E P E P

t

E E E E E E E

K

Max W e U F L K E K E I I E dt

K I K K

K I K K K K

F

τ

ρ τ

χ δ

δ

λ ρ δ

−

=

= − − −

= −

= − − ≤

= + −

∫

&

&

Artificial Constraints

( )

( )

( )

( )

2

1

0 0

, , , ;

, ;

, , 0.

ˆ ;

ˆ ; 0.

t

E P E P

t

E E E E E E E

K

E

Max W e U F L K E K E I I E dt

K I K K

K I K K K K

F

F E K K

τ

ρ τ

χ δ

δ

λ ρ δ

λ ρ δ μ μ

−

=

= − − −

= −

= − − ≤

= + −

= + − + − =

′

∫

&

&

Artificial Constraints

r_i for hard-link r_i for soft-link

Artificial Constraints

Price of E² in soft-link r_i for soft-link

Artificial Constraints

r_i for hard-link r_i for soft-link

Artificial Constraints

• Illustration of problem‘s origin

• Linear production technologies and bounds

• Question: How to merge diminishing returns and equilibrium conditions in large-scale

( ) ( ) ( )

1

, , .

n

i i

i

x p t p t x t

=

=

∑

H

Conclusions

• Hard-link guarantees simultaneous

equilibrium of capital and energy market

• Soft-link can not approximate

• Augmentation is not successful

Conclusions

• Artificial constraints induce also capital market disequilibrium

• Either capital market dis-equilibrium or flip-flop

• Solving the problem in the linear framework