2015 48th Hawaii International Conference on System Sciences
Multiple Equilibria in Oligopolistic Power Markets with Feed-in Tariff
Incentives for Renewable Energy Generation
Enzo Sauma
Pontificia Universidad Católica
de Chile
[email protected]
Miguel Pérez de Arce
Pontificia Universidad Católica
de Chile
[email protected]
reach 15% by the year 2035, through the
implementation of incentive policies based on
subsidies that reached 101 billion dollars in 2012 and
should be increased to 220 billion dollars by 2035.
Among the policies, the most commonly used are:
carbon taxes, feed-in tariffs, premium payments, quota
systems, auctions and cap and trade systems, as it is
pointed out by Munoz et al. [4]. Each policy has
advantages and disadvantages, but, in general terms,
there is evidence that the policies mentioned have
allowed large penetration of RE and reductions of
greenhouse gas emissions [5-11].
Feed-in-tariff (FIT) policies have been implemented in
several countries. Menanteau et al. [12], suggest that a
FIT policy is more efficient than a bidding system, but
recognize that theoretically may be more efficient the
implementation of a quota system with green
certificate. Palmer and Burtraw [13] find that a quota
obligation can be a good policy to promote RE and
reducing emissions, and that it is more cost-effective
when considering tax credit. Rowlands [14]
recommends a policy of FIT because it would allow
diversifying the supply of renewable energy, compared
to a quota system. Mitchell et al. [15] also indicate that
FIT policy is more effective that quota system. Lewis
and Wiser [16] analyze different incentive policies and
identify the FIT as a successful policy, from a
qualitative perspective. Green et al. [17] indicate that
carbon tax policy could help to reduce emissions
associated with conventional energy. Lipp [18] found
evidence that FIT policy is more cost-effective than the
quota system. Wiser et al. [19], emphasize the
experience and success of the quota system in United
States and give some recommendations to be applied at
the federal level. Butler and Neuhoff [20] found that, in
practice, the FIT applied in Germany has allowed
achieving lower prices for wind energy, greater
competition and more deployment, in comparison with
the UK´s quota system and the auction mechanisms.
Fouquet and Johansson [21] recommend implementing
a FIT instead of a quota system with tradable green
certificates, as it allows greater competition in the
Abstract
Different policies have been implemented to
incentivize the development of renewable energy
generation. One of these policies is the feed-in tariff
mechanism. When evaluating this policy, the typical
approach is to look at the social welfare and the
carbon emission reductions obtained in the optimal
dispatch solution. However, in the context of
oligopolistic competition in power markets, multiple
market equilibria may take place. Under such a
paradigm, there is generally no information about the
consequences of actually occurring an equilibrium that
is different than the one obtained from the optimization
algorithm. Thus, a relevant question is whether the
implementation of a feed-in-tariff policy decreases
social welfare for all possible market equilibria or not.
This paper analyzes the existence of multiple
equilibria within the context of oligopolistic
competition in power markets and studies the social
welfare resulting in each one of them. We find that
there may be equilibria for which the feed-in tariff
policy increases social welfare, but also there may be
equilibria for which this policy reduces social welfare.
Moreover, carbon emission reductions vary from
equilibrium to equilibrium, significantly varying the
cost-effectiveness of the feed-in-tariff policy in
reducing emissions.
1. Introduction
Many countries have committed to reduce greenhouse
gas emissions. According to US-EIA [1], European
OECD countries have committed to reduce greenhouse
gas emissions to 20% (base year 1990) by 2020 and
between 80% and 95% (base year 1990) by 2050. To
meet these goals, the integration of renewable energy
(RE) in the energy matrix has been identified as a key
[2]. According to the IEA [3], in 2011, 4% of the world
electricity generation came from non-hydraulic
renewable energy sources and this percentage could
1530-1605/15 $31.00 © 2015 IEEE
DOI 10.1109/HICSS.2015.305
Javier Contreras
Universidad de Castilla – La
Mancha
[email protected]
2540
market. Laird and Stefes [22] argue that the FIT policy
successfully applied in Germany may fail in the US
model because of institutional and social factors.
Falconett and Nagasaka [23] conclude that FIT policies
are the best mechanism to promote solar PV systems
and wind energy projects. They also show that green
certificate mechanisms stimulate the most competitive
technology as hydropower. In addition, they argue that
governmental grants and carbon credits are secondary
support mechanisms compared to FIT and renewable
certificates. Fischer [24] recognizes that a quota system
with renewable certificates combines the benefits of
both a subsidy and an implicit tax. However, the price
impacts can be ambiguous. Woodman and Mitchell
[25] indicate that a quota system has limitations that
make it less efficient than a FIT. Limpaitoon et al. [26]
indicate that not necessarily carbon tax policy would
reduce emissions in the presence of strategic behavior
of market players. Wood and Dow [27] identify
weaknesses in the quota system applied in the UK,
concluding that it definitely needs to be renovated or it
must go for a FIT. Woodman and Mitchell [25]
mentioned that one of the main differences between a
quota system and a FIT is that the latter has the
advantage of managing market risk. Dong [28]
detected that policies such as FIT would be more
efficient than the quota system. Verbruggen and
Lauber [29] conclude that the FIT policy has better
performance than a system of tradable green
certificates. In [30], the author highlights the
significant role played by the FIT in Germany. Martin
and Rice [31] identify that was important for the
development of RE the implementation of a carbon tax
policy in Australia. Kitzing [32] identifies, using meanvariance portfolio theory, that the FIT requires lower
subsidy levels than the premium payment policy.
When identifying pros and cons of RE encouraging
policies, it becomes very relevant the market structure
that it is assumed [33-34]. In this paper, we consider a
power market where agents compete as Cournot
oligopolistic firms. This framework is rather common
in power markets [33-38]. The model used in this study
is based on a Cournot duopoly power market with
transmission constraints, uncertainty on the availability
of renewable resources, and variability of both
renewable resources and demand.
Within the context of the oligopolistic competition, the
potential existence of multiple equilibria makes the
analysis more complex. In particular, it would be
interesting to know whether the implementation of a
FIT policy would decrease social welfare for all
possible market equilibria or not. To face this question,
in this paper we analyze the existence of multiple
equilibria within the context of oligopolistic
competition in power markets and studies the social
welfare resulting in each one of them. In particular, we
look for the possibility of finding equilibria for which
the FIT policy is relatively efficient in reducing
greenhouse gas emissions and other equilibria in which
this policy is less efficient. Some studies, such as [3941] have identified ways to search for Nash equilibria,
as in the case of the relaxation algorithm applying
Nikaido-Isoda function [42]. An interesting approach
to identify all equilibria is proposed in [43], which we
use in this paper to identify all the equilibria of our
model in the case of the FIT policy.
2. Basic market model
The basic model used in this paper is an extension of
the model proposed by Downward [44]. Differently
than Downward’s model, our model incorporates
uncertainty and the variability of both renewable
resources and demand, which are very relevant features
of real power systems.
Our model considers two nodes (indexed by i) linked
by a transmission line, as shown in Figure 1. In each
node i, there is a generation firm, which can invest in a
conventional-source power plant and/or in a
renewable-source power plant.
Our model considers n scenarios of demand, wind
availability and solar availability. Each scenario is
indexed by h and it has an occurrence probability of φh.
We can think about scenarios as realizations for sample
hours during a year, where φh would represent the
number of hours occurring similar demand and wind
and solar availability than that hour during the year
divided by 8760. In the case that each scenario is
equally probable to occur in a particular hour during
the year, this probability is 1/n.
The main decision variables of the models are the total
amount of energy injected into node i in scenario h, qih
(which corresponds to the sum of the conventional,
qcih, and renewable, qrih, power generation in node i in
scenario h), the demand satisfied in node i in scenario
h, yih, the flow through the transmission line in scenario
h, fh, the nodal price (i.e., the Langrangean multiplier
of the energy balance constraint) in node i in scenario
h, pih, the Langrangean multiplier of the transmission
capacity constraints in node i in scenario h, ηih, the
conventional-generation capacity installed in node i,
Kci, and the renewable-generation capacity installed in
node i, Kri.
With respect to the parameters used, K is the capacity
of the transmission line, Kci’ is the maximum
conventional-generation capacity that can be installed
in node i, Kri’ is the maximum renewable-generation
capacity that can be installed in node i, Ici is the hourlyequivalent
per-MW
conventional-generation
2541
investment cost in node i, Iri is the hourly-equivalent
per-MW renewable-generation investment cost in node
i, MCci is the marginal cost of the conventional unit in
node i, MCri is the marginal cost of the RE unit in node
i, PR is the unit price for reserves , Esolarh is the
maximum generation capacity factor of the solar power
plant in scenario h, Ewindh is the maximum generation
capacity factor of the wind power plant in scenario h,
Edemandh is a factor accounting for the variability of the
peak demand in scenario h, and ai and bi are positive
constants of the price-responsive demand curve in node
i.
the energy demand levels (and hence nodal prices) that
maximize the total gross surplus in each scenario.
In agreement with the formulated game, marginal costs
of generation are not included in the ISO’s dispatch
problem (in the same way they are not included in
[44]) because they are fixed quantities as seen by the
ISO (recall that the marginal costs of generation
depend on qih, which are seen as fixed parameters by
the ISO in our formulation).
We assume power plants generating RE require power
reserves. In particular, we assume: (i) the total installed
generation capacity of RE plants cannot exceed the
sum of the installed generation capacities of
conventional power plants and (ii) reserves from
conventional power plants are paid a fixed price PR.
Being a two-stage game, generation firms are able to
anticipate individual rationality prices. Then, the firm
i’s profit-maximization problem is as follows:
­ ª qihc ⋅ ( pih − MCic ) − K ic ⋅ I ic º ½
° «
»°
+
° «
»°
n
°
» °¾
Max ¦ ®ϕ h « PR ⋅ ( K ic − qihc )
«
»°
h =1 °
+
«
»°
° «
r
r
r
r »
° ¬« qih ( pih − MCi ) − K i ⋅ I i ¼» °
¯
¿
s.t.
Figure 1: Two-node power network
We assume price-responsive demand curves, given by
the inverse demand curve: pih = ai ⋅ Edemandh – bi ⋅ yih , in
node i in scenario h.
We model the market as a Cournot game, assuming
generation firms maximize their expected profit and
make rational expectation of their rival firm’s outcome
and the subsequent dispatch outcome performed by an
independent system operator (ISO).
The optimal dispatch of electric power is determined
by the ISO, who indirectly decides on nodal prices and
on the energy flowing through the line with the goal of
maximizing social surplus at each hour. The
formulation of the ISO problem follows the
formulation in [44], but incorporating, in every hour,
scenarios associated with the availability of the
renewable resources and with demand. The ISO’s
problem at hour h is formulated as (1) – (4).
Max
1
1
a1h y1h − b1 y12h + a2 h y2 h − b2 y22h
2
2
(2)
(3)
fh ≤ K
(4)
0≤q ≤ K
, ∀i, h
r
i
0≤K ≤K '
c
i
0≤K ≤K '
, ∀i
r
i
K +K ≤K +K
r
1
r
2
n
¦ϕ
h
(5)
, ∀i
c
i
r
i
c
1
c
2
=1
h =1
and the optimality conditions of ISO's problem ∀i, h
Constraints in (5) relate to both conventional and
renewable maximum generation capacity investments,
the required energy reserves, and the optimality
conditions of the ISO problem. To formulate this twostage problem as a single optimization program (for
each firm), the Karush-Kuhn-Tucker (KKT) conditions
of the problem in (1) to (4) are implemented as
constraints to each firm’s problem. Consequently, the
problem for generation firm i is formulated in the
following way:
s.t.
y2 h − f h = q2 h , with q2 h = q2r h + q2ch
, ∀i, h
r
ih
(1)
y1h + f h = q1h , with q1h = q1rh + q1ch
0 ≤ qihc ≤ K ic
We assume generation firms are able to anticipate the
ISO dispatch decision. Thus, the game considered here
is as follows: in the first stage, generation firms
simultaneously commit to a specific level of generation
for a given hour in each scenario. These decisions have
implicit the simultaneous decisions of the generation
capacity to be installed in every node. Then, in the
second stage, the ISO solves the dispatch problem by
determining the energy flowing through the line and
2542
­ ª qihc ⋅ ( pih − MCic ) − Kic ⋅ I ic º ½
° «
»°
+
° «
»°
n
°
» °¾
Max¦ ®ϕh « PR ⋅ ( Kic − qihc )
«
»°
h =1 °
+
«
»°
° «
° «¬ qihr ( pih − MCir ) − Kir ⋅ I ir »»¼ °
¯
¿
s.t.
y1h + f h = q1ch + q1rh
the firm’s risk associated to market price volatility.
Mathematically, the firm i’s problem may be
represented as follows:
(6)
­ ª qihc ⋅ ( pih − Cmgic ) − Kihc ⋅ CFi c º ½
° «
»°
+
°
«
»°
n
° «
c
c
» °¾
Max ¦ ®ϕh PR ⋅ ( K ih − qih )
«
»°
h =1 °
+
«
»°
° «
r
FIT
r
r
r»
° ¬« qih ⋅ ( pi − Cmgi ) − K ih ⋅ Fi ¼» °
¯
¿
s.t.
∀h
(7)
∀h
(8)
∀h
(9)
p2 h + b2 ⋅ y2 h = a2 ⋅ E
∀h
(10)
p1h − p2 h + η1h − η2 h = 0
∀h
(11)
η1h ⋅ ( f h − K ) ≤ 0
η2 h ⋅ (− f h − K ) ≤ 0
∀h
(12)
where pi
∀h
(13)
firm i for each unit of RE generated.
fh − K ≤ 0
∀h
(14)
− fh − K ≤ 0
∀h
(15)
y2 h − f h = q + q
c
2h
r
2h
p1h + b1 ⋅ y1h = a1 ⋅ E
Demand
h
Demand
h
K1r + K 2r ≤ K1c + K 2c
∀h
0≤q ≤K
∀h
(17)
∀h
(18)
0 ≤ q ≤ K ⋅E
∀h
(19)
0 ≤ q2r h ≤ K 2r ⋅ EhSolar
∀h
(20)
c
1h
c
1
0 ≤ q2ch ≤ K 2c
r
1h
r
1
Wind
h
(21)
0≤ K ≤ K '
(22)
0≤ K ≤ K '
(23)
0≤ K ≤ K '
(24)
r
1
c
2
r
2
c
1
r
1
c
2
r
2
0 ≤ p1h , 0 ≤ y1h , 0 ≤ η1h
∀h
(25)
0 ≤ p2 h 0 ≤ y2 h 0 ≤ η2 h
∀h
(26)
n
¦ϕ
h
=1
(7) − (27)
FIT
is the fixed price that is paid to generation
4. Case study
(16)
0≤ K ≤ K '
c
1
(25)
We implement the proposed models in a radial (twonode) network.
4.1 Data
The data used here are presented below. They were
obtained mostly from the U.S. Energy Information
Administration and International Energy Agency’s
webpage.
4.1.1 Scenarios of availability of renewable
resources and high demand. We consider 20
scenarios (i.e., n = 20), indexed by the subscript h,
taken from [4]. The variability of the availability of RE
resources is represented by the factors Esolarh and Ewindh
(presented in Appendix A). The variability of the peak
demand at each node is modeled by applying the factor
Edemandh (see Appendix A) on the positive constant ai.
(27)
h =1
The objective function in (6) maximizes the firms’
profit from generating energy and providing reserves,
without considering any RE incentive scheme. The
energy balance constraints (7) and (8) represent the
balance between supply and demand for nodes 1 and 2,
respectively. Transmission capacity constraint,
represented in (14) and (15), have an influence on
nodal prices, as represented in (11) to (13). Investment
capacity constraints for conventional and RE are
represented by constraints (21) to (24) and (16).
Maximum generation limits of both conventional and
RE plants are represented by constraints (17) to (20).
4.1.2 The emission factors. In the cases of power
generation using coal and natural gas, the emission
factors considered are 1 ton of CO2/MW and 0.4 ton of
CO2/MW, respectively, taken from [4].
4.1.3 Costs of renewable and conventional power
generation. Information from the U.S. Energy
Information Administration [45] and International
Energy Agency [46-47] was used as reference for fixed
and marginal cost, which reflects the cost of
investment, operation and maintenance incurred to
produce energy. These costs are presented in Table 1
and 2. By using fixed and marginal costs, we
incorporate the decisions of the optimal level of both
investment and operation in conventional and RE
production.
3. Modeling feed-in tariff incentive policy
A feed-in tariff policy consists of the payment of a
fixed price to the generation firms for the power
generated by means of RE. This mechanism reduces
2543
Table 1: Electric power generation marginal costs
Node 1 Cost
Node 2 Cost
c
c
Conventional
Coal ( c ):
Natural Gas( c ):
1
53 $/MWh
Renewable
r
Wind( c1 ):
0 $/MWh
Table 4: Results of base case (no Feed-in-tariff)
Variable
Node 1
Node 2
qcih
158.9 MWh
121.4 MWh
qrih
1.6 MWh
0 MWh
129.6 $/MWh
129.6 $/MWh
pih
131.5 MWh
150.5 MWh
yih
0
$/MWh
0 $/MWh
ηih
c
158.9 MW
250 MW
Ki
1.7 MW
0 MW
Kri
29.0 MWh
29.0 MWh
fh
159 ton
49 ton
CO2
$5,824
$3,941
PSi
2
89 $/MWh
r
Solar( c2 ):
0 $/MWh
Table 2: Electric power generation fixed costs
Node 1 Cost
Node 2 Cost
c
c
Conventional
Coal ( c ):
Natural Gas( c ):
1
331,000
$/MW/year
Renewable
r
Wind( c1 ):
283,000
$/MW/year
2
110,000
$/MW/year
As Table 4 indicates, RE is too expensive in general.
Thus, only 1.6 MW of wind power is installed in node
1, when there is no feed-in-tariff incentive. Also, from
the results, we can verify that these results are free of
the congestion effects, since there is no congestion in
the transmission line.
Using the results in Table 4, we can compute the social
welfare obtained in this base case, which is $17,068.
Now, we consider a feed-in tariff of 157 $/MWh,
applied to both nodes. The results obtained using the
data detailed in the previous section, considering a
feed-in tariff of 157 $/MWh applied to both nodes, are
summarized in Table 5.
r
Solar( c2 ):
451,000
$/MW/year
4.1.4 Price of Reserves. We consider a reserve price
(PR) of 22 $/MW/hour.
4.1.5 Power demand data. In each node, a linear
demand function was considered, given by equation:
pih = ai ⋅ Edemandh – bi ⋅ yih , where yih corresponds to the
power consumed in node i in scenario h. The values
utilized for the parameters ai and bi are detailed on
Table 3.
Table 5: Results of applying Feed-in-tariff policy
Variable
Node 1
Node 2
qcih
136.7 MWh
99.4 MWh
qrih
73.2 MWh
0 MWh
124.3 $/MWh
124.3 $/MWh
pih
148.3 MWh
161.0 MWh
yih
0 $/MWh
0 $/MWh
ηih
136.7 MW
250 MW
Kci
75 MW
0 MW
Kri
61.6 MWh
61.6 MWh
fh
137 ton
40 ton
CO2
$8,581
$3,126
PSi
Table 3: Power demand parameters
Node 1
Node 2
ai
250
300
bi
5/16
1/2
4.1.6 Generation and transmission capacities. The
transmission line capacity (K) was assumed to be 200
MW. We also assume that the maximum generation
capacity to be installed in each power plant is 250
MW, for both conventional and RE production.
4.1.7 Feed-in tariff. We first consider a feed-in tariff
of 157 $/MWh, applied to both nodes. Then, we make
a sensitivity analysis varying this price to 127 $/MWh.
These values are arbitrarily chosen, because the
purpose of these simulations is just to illustrate the
effect of the existence of multiple equilibria.
As Table 5 indicates, RE in node 2 is too expensive
and, consequently, firms do not invest in solar
technology. Also, from the results, we can verify that
these results are free of the congestion effects, since
there is no congestion in the transmission line.
Using the results in Table 5, we can compute the social
welfare obtained in this case, which is $17,057. That is,
in this case, the implementation of this feed-in-tariff
policy yields a reduction on social welfare, although
CO2 emissions are reduced from 207 tons of CO2 to
177 tons of CO2.
We performed a sensitivity analysis when varying the
feed-in tariff to 127 $/MWh, applied to both nodes.
The main results obtained are summarized in Table 6.
4.2 Simulation results
We implemented the model in Matlab© software. The
results obtained using the data detailed in the previous
section, when no considering a feed-in tariff, are
summarized in Table 4.
2544
Table 6: Results when varying Feed-in tariff
Variable
Node 1
Node 2
qcih
138.5 MWh
103.1 MWh
qrih
60.9 MWh
0 MWh
125.6 $/MWh
125.6 $/MWh
pih
144.2 MWh
158.4 MWh
yih
0
$/MWh
0 $/MWh
ηih
c
138.5 MW
250 MW
Ki
62.5 MW
0 MW
Kri
55.3 MWh
55.3 MWh
fh
138 ton
41 ton
CO2
$6,490
$3,575
PSi
policy requires the study of the possibility of reducing
the capacity payments for reserves.
4.3 Multiple equilibria in feed-in tariff policy
In the previous section, we observe some interesting
interactions between the performance of the feed-intariff policy and both the levels of the RE incentives
and the reserve price levels. However, these
interactions may be different for different market
equilibria.
In this section we explore the existence of multiple
market equilibria, and its implications in terms of the
performance of the feed-in-tariff policy. For doing this,
we use the same method employed in [43], which is
based on generating some kind of “holes” in the
feasible space around the already known Nash
equilibria. The procedure involves making iterative
optimization procedure that searches for different
balances. In each iteration t, the feed-in tariff policy´s
problem, (25), is solved, incorporating the constraints
(26) for each equilibrium, qe(t-1)ih, that has been
obtained in previous iterations for each scenario h.
Comparing tables 5 and 6, we observe that reducing
the feed-in-tariff incentives leads to lower RE
generation and more CO2 emissions. Also, demand
levels at both nodes are reduced. This is meanly
because the reduction in the RE incentive levels also
allows for exercising more market power by generation
firms, which all lead to a lower social welfare of
$16,801.
Now, we performed a sensitivity analysis when
varying the reserve price, PR, to 17 $/MW/hour. In this
case, we kept the feed-in-tariff incentive in 157
$/MWh, applied to both nodes. The main results
obtained are summarized in Table 7.
(q
ih
( t −1)
− qihe
)
2
≥ ε , ∀h = 1,...., 20 , 0 ≤ ε ≤ 1 (26)
By applying this procedure in our case study, we find
multiple market equilibria for a feed-in-tariff level of
157 $/MWh. For each equilibrium, we can compute the
value of all the variables presented in the previous
section. In particular, looking at the social welfare
resulting in each equilibrium, we can compare the
different possible effects of applying the feed-in-tariff
policy in terms of social welfare. Figure 2 shows the
level of social welfare obtained in the different
equilibria found.
Table 7: Results when varying the reserve price
Variable
Node 1
Node 2
qcih
141.1 MWh
103.8 MWh
qrih
73.2 MWh
0 MWh
122.7 $/MWh
122.7 $/MWh
pih
153.7 MWh
164.3 MWh
yih
0 $/MWh
0 $/MWh
ηih
146.3 MW
134.3 MW
Kci
75 MW
0 MW
Kri
60.6 MWh
60.6 MWh
fh
141 ton
42 ton
CO2
$8,211
$2,918
PSi
Figure 2: Social welfare of different equilibria
when having the same feed-in-tariff incentive
Comparing tables 5 and 7, we observe that, by
reducing the reserve price, firms invest less in
conventional generation capacity (conventional
generation capacity installed is lower), but they
produce more energy from these conventional units.
This is because there are fewer incentives to keeping
generation capacity as reserves. With these changes,
CO2 emissions increase and RE remains the same as in
the case with higher reserve price. Moreover, social
welfare is increased in this case because reducing the
reserve price has an effect in mitigating the exercise of
market power by generation firms, which motivate
them to make a more socially optimal use of their
facilities. These results may suggest that a more
socially beneficial implementation of a feed-in-tariff
In Figure 2, social welfare is graphed for the multiple
equilibria found when applying a feed-in-tariff level of
157 $/MWh. The height of the bar indicates the social
welfare under that equilibrium and the number under
each bar corresponds to the level of CO2 emissions (in
tons) under that equilibrium.
A first observation from Figure 2 is that there are
equilibria with larger social welfare than in the base
case and there are equilibria with lower social welfare
2545
than in the base case. This suggests that there may be
market equilibria for which the implementation of a
feed-in-tariff policy increases social welfare, but also
there may be market equilibria for which this policy
reduces social welfare.
This is very important for policy makers because they
cannot ensure a positive effect of the feed-in-tariff
policy due to the existence of multiple equilibria.
Policy makers cannot anticipate which market
equilibrium will occur, but there is some value of being
aware of the different potential effects.
On the other hand, from Figure 2 we can also observe
that CO2 emissions are always reduced with respect to
the base case when applying the feed-in-tariff policy.
However, the level of carbon emission reductions
varies from equilibrium to equilibrium. This implies
that the cost-effectiveness of the feed-in-tariff policy in
reducing emissions significantly varies from
equilibrium to equilibrium. This, again, is not a result
that policy makers can anticipate and control, but this
result helps them to be aware of the range of potential
effects of the application of the feed-in-tariff policy.
It is also interesting to study how different levels of
feed-in-tariff incentives affect the number of market
equilibria found. For doing this analysis, we computed
all Nash equilibria for several values of the feed-intariff incentives in the range between 100 $/MWh and
200 $/MWh. The results show that the number of
market equilibria decreases as the feed-in-tariff
incentives increases. That is, we obtain more equilibria
when the feed-in-tariff level is lower. A possible
explanation of this phenomenon is related to our
findings in the previous section. As we reduce the
feed-in-tariff incentives, there is roughly less RE
generation and less demand satisfied at both nodes.
Additionally, more market power is generally
exercised by generation firms as the feed-in-tariff
incentives decrease. These effects (reduced RE
generation, reduced demand levels, and increased
exercise of market power) frequently lead not only to
lower social welfare in the equilibria, but also to more
possibilities for market agents to satisfy demand and
all other market and physical constraints. In other
words, by reducing the feed-in-tariff incentives (and,
thus, reducing RE generation, reducing demand levels,
and increasing the exercise of market power), it is
relatively easier to clear the market, leading to multiple
equilibria.
of feed-in-tariff policies, within the context of
oligopolistic competition in power markets.
First, we present some interesting interactions between
the performance of the feed-in-tariff policy and both
the levels of the RE incentives and the reserve price
levels. In particular, we find that reducing the feed-intariff incentives generally leads to lower RE
generation, more CO2 emissions, lower demand levels
at both nodes and more exercise of market power by
firms, jointly implying that social welfare is inferior in
these cases with lower feed-in tariffs.
On the other hand, we also find that, by reducing the
reserve price, firms invest less in conventional
generation capacity, but they produce more energy
from these conventional units. This is because there are
fewer incentives to keeping generation capacity as
reserves. These effects generally lead to larger CO2
emissions and larger social welfare because reducing
the reserve price has an effect in mitigating the
exercise of market power by generation firms, which
motivate them to make a more socially optimal use of
their facilities. These results may suggest that a more
socially beneficial implementation of a feed-in-tariff
policy requires the study of the possibility of reducing
the capacity payments for reserves.
Although the previous results are interesting, they are
difficult to be generalized due to the existence of
multiple market equilibria. As a result of this
multiplicity of equilibria, it is possible to find
equilibria for which the implementation of a feed-intariff policy increases social welfare, but it is also
possible to find market equilibria for which this policy
reduces social welfare. This is very important for
policy makers because they cannot ensure a positive
effect of the feed-in-tariff policy due to the existence of
multiple equilibria. Therefore, although policy makers
cannot anticipate which market equilibrium will occur,
these results let them aware of the different potential
effects of the implementation of the feed-in-tariff
policy.
We also found that the number of market equilibria
decreases as the feed-in-tariff incentives increases. A
possible explanation of this phenomenon is that, as we
reduce the feed-in-tariff incentives, there is roughly
less RE generation, less demand satisfied, and more
exercise of market power, which lead to relatively
more possibilities for market agents to satisfy demand
and all other market and physical constraints.
5. Conclusions
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Acknowledgments
The research reported in this paper was partially supported
by the CONICYT, FONDECYT/Regular 1130781 grant.
APPENDIX A: SCENARIOS
Demand
Timeblock (h) Maximum Demand (Eh
1
0.500
2
0.651
3
0.658
4
0.528
5
0.700
6
0.551
7
0.715
8
0.967
9
0.685
10
0.702
11
0.600
12
0.687
13
1.000
14
0.594
15
0.634
16
0.651
17
0.747
18
0.609
19
0.747
20
0.729
2548
solar
) Availability of Solar (Eh
0.000
0.151
0.000
0.000
0.068
0.000
0.004
0.000
0.538
0.000
0.000
0.000
0.000
0.504
0.048
0.612
0.669
0.354
0.306
0.451
Wind
) Availability of Wind (Eh
0.933
0.994
0.615
0.110
0.085
0.148
0.000
0.977
0.971
0.049
0.252
1.000
0.066
0.981
0.581
0.180
0.330
0.603
0.175
0.335
)