- Deregulated electricity markets and investments in
intermittent generation technologies -
Silvia Concettini
Universitá degli Studi di Milano
and
Université Paris Ouest Nanterre La Défense
IEFE Seminars - December 10 2013
Introduction
The model
Conclusions
Outline
1
Introduction
Policy framework
Background
Original contribution
Which model?
2
The model
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
3
Conclusions
Extensions
Conclusions
Silvia Concettini
IEFE Seminars - December 10 2013
2/30
Introduction
The model
Conclusions
Policy framework
1
Policy framework
Background
Original contribution
Which model?
Third Energy Package (2009): full liberalization of electricity industry
Unbundling of transmission/distribution from generation and retail
Introduction of competition in generation and retail
Creation of spot electricity markets
Objective: Optimal level of aggregate generation capacity and optimal
technological mix
2
Climate and Energy Package (2009): commitment to low-carbon economy
Reduction in greenhouse gas emissions
Increase in the share of EU energy consumption produced from renewable
resources
Improvement in energy eciency
Objective: A 20% share of EU energy consumption produced from
renewable sources by 2020
Silvia Concettini
IEFE Seminars - December 10 2013
3/30
Introduction
The model
Conclusions
Background
1
Policy framework
Background
Original contribution
Which model?
A variety of models of competition for power generators:
Spot market design and bidding behaviours:
Green and Newbery, 1992
von der Fehr and Harbord, 1993
Fabra et al., 2006
Bidding behaviours and investment incentives:
Murphy and Smeers, 2005
Milstein and Tishler, 2009
Fabra et al., 2011
=⇒
However competition in generation seems to be animated by new
entrants investing in renewable technologies
2
A lack of models of competition between traditional and renewable
generators
Silvia Concettini
IEFE Seminars - December 10 2013
4/30
Introduction
The model
Conclusions
Original contribution
Policy framework
Background
Original contribution
Which model?
Dene a theoretical model of competition between traditional and
renewable generators which embeds the following features:
Production from some renewable power sources is subject to randomness
Electricity from renewable sources is the rst to be brought on-line in spot
markets because of merit order rule
Investment and production from renewable sources are supported through
publicly nanced schemes
Use the model as an eective and easy-to-manage tool for assessing the
impact and the desirability of incentives to production and investment in
green technologies
Silvia Concettini
IEFE Seminars - December 10 2013
5/30
Introduction
The model
Conclusions
Literature review
Policy framework
Background
Original contribution
Which model?
Imperfect competition for power generation preceded by an investment stage:
1
Capacity choice and Bertrand-Edgeworth competition (Kreps and
Scheinkman, 1983)
2
Capacity choice and Supply function approach (Green and Newbery, 1992)
3
Capacity choice and Auction approach (Fabra et al., 2011)
4
Capacity choice and Quantity competition (Murphy and Smeers, 2005;
Milstein and Tishler, 2012)
=⇒
Strategic base-load investments may modify short run competition
Silvia Concettini
IEFE Seminars - December 10 2013
6/30
Introduction
The model
Conclusions
Which model and why?
Policy framework
Background
Original contribution
Which model?
A modied version of the Dixit model for entry deterrence (1980) with Cournot
competition in the post entry stage:
Given the favourable merit order rule the renewable producer has a rst
mover advantage in the investment game
In the post entry stage a renewable and a traditional producers compete
in quantities rather than in prices
In quantity competition both rms are paid the same price as in a uniform
price auction of real spot markets
Randomness of electricity production from renewable source can be easily
introduced
Silvia Concettini
IEFE Seminars - December 10 2013
7/30
Introduction
The model
Conclusions
Overview of main results
Policy framework
Background
Original contribution
Which model?
The renewable producer strategically exploits merit order rule to behave as
a sort of Stackelberg leader crowding out the production of its rival
Including considerations about the average availability of installed capacity
does not change preferences over strategies of renewable producer for most
of the parameters' value
The strategy chosen by renewable producer may benet consumers too
depending on the value of average capacity availability
The incentives for strategic behavior may be stronger even for small errors in
the forecasting of the true value of capacity availability factor
Silvia Concettini
IEFE Seminars - December 10 2013
8/30
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Introduction
The model
Conclusions
Assumptions
Two rms:
Capacities:
S
(photovoltaic power plant) and
(combined cycle gas turbine plant)
ki , i = s, g
Investment cost per unit of capacity:
Ii > 0, i = s, g
Production cost per unit of electricity:
Average cost:
Is > c + Ig
Available capacity: xks , where
whose expected value is E[x] =
Inverse demand function:
ci , i = s, g ,
with
0 = cs < cg = c
(cft. levelised cost of energy)
Amount of electricity produced:
G
G
qi , i = s, g
x is
x∗
the realization of a random variable
p(Q) = a − bQ,
where
Q = qs + qg ∈ [0, xks + kg ]
makes positive prots in any post entry equilibrium:
Silvia Concettini
X ∈ [0, 1]
a > 2(c + Ig )
IEFE Seminars - December 10 2013
9/30
Introduction
The model
Conclusions
Timing of the game
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
The structure of the game is the following:
1
In the rst stage:
Firm
S
chooses its capacity,
ks
The investment is irreversible
2
In the second stage:
Firm
G
selects simultaneously capacity,
kg ,
and production,
Firm
S
can increase capacity prior to choose production,
qg
qs
Solve the game by backward induction to nd the sub-game perfect Nash
equilibrium
Since
qs
and
qg
are strategic substitute,
S
never installs excess capacity in
the rst stage (Bulow et al., 1985)
Silvia Concettini
IEFE Seminars - December 10 2013
10/30
Introduction
The model
Conclusions
Strategy A - Small capacity
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
The renewable rm instals a small capacity in the rst stage:
x∗ (a + c + Ig ) − 2Is
A
ks 6
3bx∗2
x∗ (a + c + Ig ) − 2Is
A
qs =
A
qg =
A
p
qg
3bx∗
x∗ [a − 2(c + Ig )] + Is
3bx∗
Ȓs (qg)
∗
=
x (a + c + Ig ) + Is
3x∗
A
qgA
Rs (qg)
A
Πs =
A
Πg =
[x∗ (a + c + Ig ) − 2Is ]2
9bx∗2
{x∗ [a − 2(c + Ig )] + Is }2
x*ks
Rg (qs)
qsA
qs
Figure : Equilibrium in case A
9bx∗2
Silvia Concettini
IEFE Seminars - December 10 2013
11/30
Introduction
The model
Conclusions
Strategy B - Large capacity
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
The renewable rm instals a large capacity in the rst stage:
B
ks >
B
qs =
B
qg =
p
B
Πs =
B
a + c + Ig
3bx∗
qg
a + c + Ig
3b
a − 2(c + Ig )
3b
=
Ȓs (qg)
a + c + Ig
3
(a + c + Ig )((a + c + Ig )x − 3Is )
B
Rs (qg)
Rg (qs)
qsB
9bx∗
Πg =
B
qgB
∗
[a − 2(c + Ig )]2
x*ks
qs
Figure : Equilibrium in case B
9b
Silvia Concettini
IEFE Seminars - December 10 2013
12/30
Introduction
The model
Conclusions
Strategy C - Intermediate capacity
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
The renewable rm instals an intermediate capacity in the rst stage:
x∗ (a + c + Ig ) − 2Is
∗
ks =
2bx∗2
x∗ (a + c + Ig ) − 2Is
C
qs =
C
qg =
C
p
2bx∗
qg
Ȓs (qg)
x∗ [a − 3(c + Ig )] + 2Is
4bx∗
Rs (qg)
∗
=
x (a + c + Ig ) + 2Is
A
B
4x∗
Rg (qs)
C
Πs =
C
Πg =
[x∗ (a + c + Ig ) − 2Is ]2
8bx∗2
{x∗ [a − 3(c + Ig )] + 2Is }2
x*ks
qs
Figure : Equilibrium in case C
16bx∗2
Silvia Concettini
IEFE Seminars - December 10 2013
13/30
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Introduction
The model
Conclusions
Optimal strategy
1
Strategy C is preferred to A if:
C
Πs =
2
[x∗ (a + c + Ig ) − 2Is ]2
>
8bx∗2
[x∗ (a + c + Ig ) − 2Is ]2
9bx∗2
A
= Πs
∀ x∗
⇒
For
⇒
Firm S prefers to anticipate investments
Strategy C is preferred to B if:
C
Πs =
[x∗ (a + c + Ig ) − 2Is ]2
8bx∗2
>
(a + c + Ig )((a + c + Ig )x∗ − 3Is )
9bx∗
⇒
Case 1: for
∀ x∗
⇒
Case 2: for
6Is
x∗ 6= a+c+I
g
when
B
= Πs
a + c + Ig < 6Is
when
a + c + Ig ≥ 6Is
Functional relation between prots and x∗ is
dierent
⇒
Silvia Concettini
IEFE Seminars - December 10 2013
14/30
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Introduction
The model
Conclusions
Comparative statics
How does the pay-o of strategies B and C change with respect to the average
availability of capacity?
For strategy B:
∂
∂ΠB
s
=
∗
∂x
h
(a+c+Ig )((a+c+Ig )x∗ −3Is )
9bx∗
i
∂x∗
=
(a + c + Ig )Is
>0
3bx∗
For strategy C:
∂ΠC
s
=
∂x∗
∂
[x∗ (a+c+Ig )−2Is ]2
8bx∗2
=
∂x∗
⇒
2Is
a+c+Ig
< x∗ < 1
Silvia Concettini
Is (a + c + Ig )
2Is2
−
>0
2bx∗2
2bx∗3
and
2Is < a + c + Ig
IEFE Seminars - December 10 2013
15/30
Introduction
The model
Conclusions
Results
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Proposition
The renewable producer is strategic and exploits merit order rule to behave as a
Stackelberg leader.
Given the organization of spot electricity market, rm
S
is able to manipulate
short run market outcomes:
it installs a larger capacity than the one resulting from a one stage Cournot
game
it partially crowds out
G
production (and investments if already sunk)
it does not take advantage of its position to its maximum extent
Lemma
For most of the parameters' values the average availability of installed capacity
does not change
S 's
preferences between strategies.
Silvia Concettini
IEFE Seminars - December 10 2013
16/30
Introduction
The model
Conclusions
Producer vs consumers
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
The strategy with the lowest price
guarantees the larger consumer surplus (the
demand is monotone)
Firm S
C
x*
∗
The value of x determines which strategy
leads to the lower price
=
C
B
C
6𝐼𝑠
x =
𝑎 + 𝑐 + 𝐼𝑔
∗
0
1
Strategy C is preferred by consumers if:
x∗ >
Consumers
6Is
a+c+Ig
B
C
x*
While strategy C is preferred by
x∗ 6=
S
if:
∗
0
x =
6𝐼𝑠
𝑎 + 𝑐 + 𝐼𝑔
1
6Is
a+c+Ig
Figure : Preferences over strategies
Silvia Concettini
IEFE Seminars - December 10 2013
17/30
Introduction
The model
Conclusions
Producer and consumers
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Proposition
Merit order rule may lead to an equilibrium which benets both the renewable
producer and consumers.
Strategy C benets both consumers and producer if:
investment cost in renewable capacity is relatively low (Case 2)
the average capacity availability factor is larger than a certain threshold
Lemma
A public intervention which reduces
S
investment cost increases the likelihood of
this outcome.
The average availability of capacity depends on technology and weather conditions
and cannot be exogenously increased
A reduction in S investment cost decreases the threshold that
6Is
∗
consumers to prefer strategy C (x > a+c+I
)
x∗
must exceed for
g
Silvia Concettini
IEFE Seminars - December 10 2013
18/30
Introduction
The model
Conclusions
Ex post prots
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Investment choices are taken on the basis of the average value of capacity
∗
availability, x
Production of
The
ksB
S
may be adjusted according to the realized value of
x
ex post prots are the pay-o of S when it has invested in capacities ksC or
and it produces according to the real value of
B,C
Πs = (a − bqg
B,C
− bxks
x:
B,C
)xks
B,C
− Is ks
produces the lower quantity between its installed capacity and its optimal
production given the electricity supplied by S :
G
B,C
qg
=
a − b max (x, x∗ )ksB,C − c − Ig
2b
The ex post prots are random because they depend on
x
which is a random
variable
Silvia Concettini
IEFE Seminars - December 10 2013
19/30
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Introduction
The model
Conclusions
Expected value of ex post prots
To calculate the expected value of ex post prots let us use a generic probability
density function for x, P (x) for x ∈ [0, 1], such that:
1
Z
E[f ] =
f (x)P (x)dx
0
The expected values of ex post prots are then:
B,C
E[Πs
1
Z
]=
ΠB,C (x)P (x)dx
0
B
E[Πs ] =
AIs
A2
A2
∗2
2
−
+
(2x − 2E[x ] + M )
18b
3bx∗
18bx∗2
C
E[Πs ] =
where:
B2
∗2
2
(2x − 2E[x ] + M )
8bx∗4
1
Z
M =
∗
x max (x, x )P (x)dx
0
A = a + c + Ig
B = 2Is − Ax
Silvia Concettini
∗
IEFE Seminars - December 10 2013
20/30
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Introduction
The model
Conclusions
Ex post analysis of strategies
Recalling that
E[x] = x∗
and Var[x]
= E[x2 ] − E[x]2
we rewrite ex-post
expected prots as:
E[ΠB
s ]=
A2
AIs
A2
−
+
(M − 2Var[x])
18b
3bx∗
18bx∗2
E[ΠC
s ]=
B2
(M − 2Var[x])
8bx∗4
The condition for strategy C to be ex-post preferred to strategy B may be
reduced to (after some manipulation):
x̂2 s(s − 1) <
where
I = 6Is , x̂ =
I
and
A
s=
1 − 6s + 5s2
(M − 2Var[x])
4s2
x∗
x̂
Silvia Concettini
IEFE Seminars - December 10 2013
21/30
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Introduction
The model
Conclusions
An example
Consider the probability density function of a uniform distribution dened as:
P (x) =


1
2
for

0
otherwise
x∗ − ≤ x ≤ x∗ + The inequality which determines the optimal ex post choice of renewable
producer becomes:
x̂2 s(s − 1) <
1
(s − 1)(5s − 1)(4x̂2 s2 + x̂s − 22 )
4
How does the optimal strategy of
S
Silvia Concettini
change ex post?
IEFE Seminars - December 10 2013
22/30
Introduction
The model
Conclusions
Some simulations
0.2
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
B=C
0.2
0.15
ε
B=C
0.15
0.1
C
ε
0.05
0.1
C
0.05
0
B
0
0.2
0.4
0.6
0.8
0
1
B
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
s
s
Figure :
Figure :
x̂ = 1
0.2
B=C
0.2
0.15
ε
x̂ = 1.25
B=C
0.15
0.1
C
0.05
ε
0.1
C
0.05
0
B
0
0.2
0.4
0.6
0.8
1
1.2
Figure :
0
B
0
s
0.1
0.2
0.3
0.4
0.5
0.6
s
x̂ = 0.75
Silvia Concettini
Figure :
x̂ = 1.5
IEFE Seminars - December 10 2013
23/30
Introduction
The model
Conclusions
Discussion
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
When parameters value are such that strategy B is never preferred ex ante
Case 1 - the capacity cost is relatively large:
For
x̂ = 1.25
For
x̂ = 1.5
⇒
and
and
0.7 < x∗ < 1
0.8 < x∗ < 1
B is ex post preferred to C for relatively large values of x
∗
When parameters value are such that strategy B may be indierent to C
Case 2 - the capacity cost is relatively small:
For
x̂ = 1
For
x̂ = 0.75
⇒
and
0.5 < x∗ < 1
and
0.4 < x∗ < 0.75
B is ex post preferred to C for relatively small values of x
Silvia Concettini
IEFE Seminars - December 10 2013
∗
24/30
Introduction
The model
Conclusions
Results of ex post analysis
Game's overview
Strategies of rm S
Equilibrium
Ex post analysis
Proposition
Renewable producer preferences between strategies can be reversed even for
small errors in the forecasting of the true value of capacity availability factor.
The ex post analysis of pay-o highlights that:
an ex ante analysis of the game must be coupled with an ex post analysis
the negative eect on
G
production is larger if
S
adopt strategy B
ex post analysis may bring renewable producer to take advantage of rst
mover advantage to its maximum extent
Lemma
The strategic eect of spot market design on investment and production choices of
renewable producer may be stronger according to the ex-post analysis of pay-o.
Silvia Concettini
IEFE Seminars - December 10 2013
25/30
Introduction
The model
Conclusions
Extensions
Conclusions
Extension I
Dominant rm-competitive fringe model (Carlton and Perlo, 2000):
A three stage game
The renewable rm is a price taker in the spot market and has a convex
production cost function
The renewable rm chooses among four strategies
qg
Ȓs (qg)
D
A
B
C
Rg (qs)
Rs (qg)
x*k1 x*k2
x*k3
x*k4
qs
The assumptions of the model complicate the calculations
Qualitative insights of the analysis are barely sensitive to changes in the
market power of renewable producer
Silvia Concettini
IEFE Seminars - December 10 2013
26/30
Introduction
The model
Conclusions
Extensions
Conclusions
Extensions II and III
Use the model as a tool for assessing the impact and the desirability of public
policies which promote investment in green technologies:
Feed-in taris
Partial subsidization of capacity costs
Optimize a social welfare function within the model in order to assess:
The optimal feed-in tari
The optimal rate of subsidization of investment cost
Competitive eects of policy measures
Silvia Concettini
IEFE Seminars - December 10 2013
27/30
Introduction
The model
Conclusions
Extensions
Conclusions
Conclusions
A theoretical framework for studying strategic interactions between a
traditional and a renewable power generators in a decentralized electricity
market
The model explicitly accounts for:
the randomness of generation from some renewable power sources
the merit order for ranking oers in spot electricity markets
Competition is modeled as a modied version of the Dixit game (1980) with
Cournot competition in the post entry stage
Silvia Concettini
IEFE Seminars - December 10 2013
28/30
Introduction
The model
Conclusions
Extensions
Conclusions
Conclusions
The renewable producer exploits merit order rule to behave as a Stackelberg
leader crowding out production of its rival
The strategy chosen by the renewable producer may benet consumers too
The ex post analysis of payos reveals that the incentives to strategic
behavior may be even stronger
A tool for assessing the impact and the desirability of public policies
supporting green technologies
Silvia Concettini
IEFE Seminars - December 10 2013
29/30
THANK YOU
FOR YOUR ATTENTION
- Deregulated electricity markets and investments in
intermittent generation technologies -
Silvia Concettini
Universitá degli Studi di Milano
and
Université Paris Ouest Nanterre La Défense
IEFE Seminars - December 10 2013