Comparison of Incentive Policies for Renewable Energy in an Oligopolistic Market with Price-Responsive Demand

This article compares different incentive policies to encourage the development of renewable energy (RE). These incentive policies (carbon tax, feed-in tariff, premium payment and quota system) are modeled in a simpliﬁed radial power network, using price-responsive demand. Most results are derived assuming an oligopolistic Cournot competitive framework and that the costs of subsidies are covered by the government (i.e., customers do not directly pay back for the sub-sidies). We compare the different RE incentive schemes at different congestion levels in terms of energy prices, RE generation, CO 2 emissions, and social welfare. Weﬁnd that the effectiveness of the different incentive schemes varies signiﬁ-cantly depending on the market structure assumed, the costs of renewable energy, and the subsidy recovery method considered. Subsidy policies (FIT and premium payments) are more cost effective in reducing CO 2 emissions than those policies that apply penalties or taxes, when assuming oligopoly competition and that customers do not directly pay back for the subsidies. Quota and carbon tax policies are more cost effective when assuming that either a perfectly competitive electricity market takes place or customers directly pay back for the subsidies. Additionally, we show that, in the feed-in tariff system, there is an interaction among incentive levels for renewable energy technologies. Given a certain feed-in tariff price to be set for a particular renewable technology, this price inﬂuences the optimal feed-in tariff price to be set for another technology.


INTRODUCTION
Due to the great concern worldwide about reducing carbon dioxide (CO 2 ) emissions, different policies have been implemented to incentivize the development of renewable energy (RE) sources, such as wind, solar and geothermal, among others.In 2009, power and heat generation from conventional sources was responsible for 41% of the CO 2 emissions worldwide (IEA, 2011a).In 2009, 3% of the electricity generation came from non-hydraulic renewable energy sources (IEA, 2011b).According to the International Energy Agency (2011b), this percentage could reach 15% by the year 2035, through the implementation of annual subsidies of 180 billion dollars.

BASE POWER-MARKET MODEL
In order to study the RE incentive policies, we model the electricity market using game theory, analogously to Downward (2010).Our objective is to analyze the behavior and interaction of power generation firms, which are able to generate through both conventional and RE sources.
A simplified radial (two-node) power network is modeled, assuming generation firms compete a `la Cournot.In this Cournot game, each player (generation firm) has some degree of market The dispatch problem considers operating, maintenance and fuel cost, assuming generation capacity is fixed for all sources.Accordingly, a RE power plant, which has a marginal cost close to zero, should always be dispatched at its maximum available capacity.Then, in order to incorporate the generation capacity investment decision, another optimization problem should be formulated.A bilevel formulation is usually employed for solving the generation investment and dispatch problems (Pozo et al., 2013a).However, a simpler manner to model this (although with some limitations) is formulating the problem just as a dispatch problem, but replacing the marginal cost of generation by the levelized cost, which includes both investment and operations costs in a per-MWh basis (Becker et al., 2014;Moiseyev et al., 2014;Eichman et al., 2013;Crane et al., 2011;Park et al., 2011;Nicholson et al., 2011).In our problem, we follow this last approach since we are interested in jointly evaluate both the investment in RE capacity and the dispatch decisions, but incorporating later other complexities, like the consideration of market power in an oligopoly framework, while keeping the problem computationally tractable.power.As in Downward (2010), we assume constant marginal costs and linear price-responsive demand functions.
The power network considered in this work is shown in Figure 1.There are two nodes linked by a transmission line with capacity K.The flow through the transmission line is designated by f.In each node i, there is a generation firm, which can produce power from a RE source at a levelized cost of and/or from a conventional source at a levelized cost of . 1 The total amount r c c c i i of energy injected into node i is , which corresponds to the sum of the conventional ( ) and c q q i i renewable ( ) power generation in node i. r q i At each node, we consider an inverse demand curve, given by , where p (y ) = ab ⋅ y i i i i i and are both strictly positive constants, is the power demand satisfied at node i, and is a b y p i i i i the price at node i.
We consider that the generation firm located at node 1 owns two power plants: a (conventional) coal power plant and a (renewable) wind power plant.Maximum generation capacities are and , respectively.In turn, the generation firm located at node 2 owns two power plants: one c r K K 1 1 using natural gas (conventional source) and the other using solar energy (renewable source).Maximum generation capacities are and , respectively.
We model the market as a Cournot game, where each generation firm maximizes its profit making rational expectation of its rival decisions, in anticipation of the dispatch 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 The game considered here is as follows: in the first stage, both generation firms simultaneously commit to a specific level of generation for a given period.Then, in the second stage, the ISO solves the dispatch problem by determining the energy flowing through the line and the energy consumption levels (and hence nodal prices) that maximize the total gross surplus.Accordingly, generation firms are able to anticipate the ISO's dispatch decisions, so that it is possible to infer how their actions affect line congestion and prices (Yao et al., 2008).Naturally, transmission constraints in the dispatch problem also have an influence on generation firms trying to maximize their own profit.
Generation firm i's problem is as follows: Maxq ⋅ (pc ) + q ⋅ (pc ) (5) and the optimality conditions of the ISO's problem where is the Lagrangian multiplier (shadow price) of the energy balance constraints, (2) and (3).p i Constraints in (5) relate to generation capacity limits of both conventional and RE power plants, as well as the optimality conditions of the ISO's problem.
To formulate this two-stage problem as a single optimization program (for each firm), the Karush-Kuhn-Tucker (KKT) conditions of the problem in (1)-( 4) are considered as constraints of the problem of each generation firm in (5).Accordingly, the complete formulation of the problem for generation firm i is presented in Appendix A (see base model in Appendix A).In this formulation, the objective function reflects the profit of generation firm i when there is no RE incentive scheme in place.Energy balance constraints represent the balance between supply and demand for nodes 1 and 2. Transmission capacity constraints have an influence on nodal prices through the Lagrangean multipliers and .

MODELING INCENTIVE POLICIES FOR THE DEVELOPMENT OF RE
We modify the base model presented before depending on the incentive policy to be considered.For each one of the incentive schemes, the ISO's problem in the second stage of the game is modeled in the same way as in the base case, represented by ( 1) -(4).Later on Section 4, we modify the ISO's problem to account for the direct recovery of subsidies from end consumers, in the case of the RE policies providing subsidies. 3

Carbon Tax Policy
A carbon tax policy consists of establishing an additional cost to generation firms associated to their CO 2 emissions.Mathematically, the generation firm i's problem (first stage) is:

Set of constraints of the base model
The tax to be imposed and the CO 2 emissions factor are identified as (in $/ton of CO 2 ) and c c α γ i (in tons of CO 2 /MWh), respectively.We use for coal power plants and for natural gas power plants.
The complete formulation of the generation firm i's problem, anticipating the ISO dispatch, is presented in Appendix A. Note that, with this incentive scheme, firms are still exposed to variations in market prices.

Feed-in Tariff
A feed-in tariff policy consists of the payment of a fixed price for the power generated by means of RE.This mechanism reduces the firm's risk associated to market price volatility.The generation firm i's problem is formulated as: Set of constraints of the base model where is the fixed price that is paid to the generation firm for each unit of energy generated FIT p i by means of RE.The complete formulation of the generation firm i's problem, anticipating the ISO dispatch, is presented in Appendix A.
As mentioned before, the reader should note that this formulation assumes that the cost of the subsidy is covered by the government (i.e., customers do not directly pay back for the subsidy).Although this is the case in some countries, there are also some other countries where customers directly pay back for the subsidy.In Section 4.6.4,we reformulate this policy to evaluate the effect of directly including the subsidy in the demand curve.

Premium Payment
A premium payment policy consists of a fixed payment that is added to the market price, as a premium for power generated by means of RE sources.The generation firm i's problem is formulated as: Set of constraints of the base model where is the premium, in addition to the market price, that it is paid to the generation firm PREM i i for generating electricity from RE sources.The complete formulation of the generation firm i's problem, anticipating the ISO dispatch, is presented in Appendix A.
As in the case of the feed-in tariff, this formulation assumes that the cost of the subsidy is covered by the government.In Section 4.6.4,we reformulate this policy to evaluate the effect of directly including the subsidy in the demand curve (i.e., customers directly pay back for the subsidy).

Quota Obligation
A quota obligation policy consists of setting a percentage of the total power generation over a given period that must be produced by means of RE only.If generation firms (or whoever is obligated to comply with the quota) fail to comply with this obligation, a penalty is applied to them.The generation firm i's problem is formulated as: Set of constraints of the base model In this model, an additional variable is added to the base case, .This variable corresponds penalty q i to the amount of power failing to comply with the RE quota.This amount of power has associated a penalty, C penalty , which is the same for both generation firms.The parameter β establishes the compliance percentage of the quota.Thus, constraints (10) and ( 11) are added to the base model.Constraint (10) establishes that must take a non-negative value.Constraint (11) establishes penalty q i the correct relationship among , and .In this formulation, we assume that the money penalty c r q q q i i i collected from penalties goes to the government (i.e., it is not directly recovered by end consumers).
The complete formulation of the generation firm i's problem is presented in Appendix A.

CASE STUDY AND RE POLICY ANALYSIS
In order to study carbon tax, feed-in tariff, premium payments and quota obligation policies, we implement the proposed models in Matlab᭧ (2012) for the radial network shown in Figure 1.First, we analyze the results for each one of the modeled policies and, then, we perform a comparative analysis among them.

Data
The models were first calibrated with data provided by Downward (2010) and then adjusted by using cost data obtained from the Chilean power market.

Generation costs
Information from the Chilean Ministry of Energy (2011) was used as reference for levelized costs, which reflect the cost of capacity investment, operation and maintenance incurred to produce energy, temporarily discounted at a rate of 10%.These costs are presented in Table 1.As explained before, by using levelized costs, we incorporate the decision of the optimal level of investment in RE under different incentive policies into the dispatch problem.

Demand data
In each node, a linear demand function was considered, given by the equation: where corresponds to the power consumed at node i.The values utilized for the parameters y a i i and are detailed on Table 2. b i Demand curves represent the consumption of cities of similar size, but where there is a group of consumers in node 2 willing to pay more than any consumer in node 1 and where consumption at node 2 is more inelastic than at node 1.

Generation capacity and transmission network data
The transmission line capacity (K) was initially assumed to be 200 MW, although sensitivities are made with K = 60 MW to analyze the effect of congestion in the transmission line.
We assume the actual power generation capacity for conventional sources is 250 MW and the actual power generation capacity for RE sources is 80 MW (based on a 0.32 capacity factor and a nominal installed capacity of 250 MW).

Table 3: Range of Parameters Used for Analyzing the Considered Policies
Carbon tax The tax level varies between 0 and $300/ton of CO 2 .

Feed-in tariff
The fixed tariff varies between 0 and $350/MWh.

Premium payments
The premium varies between 0 and $300/MWh.

Quota obligation
For the case of a penalty of $32/MWh, the obligation compliance varies between 0 and 100%.

Range of parameters
Table 3 shows the range of parameters for which the results are analyzed under each policy.Next, in subsections 4.2 -4.5, we present an analysis by type of policy, following the assumptions made in Section 3. To safeguard the integrality of the results, we use the same assumptions in all these cases.

Carbon Tax Policy Outcome
Under the carbon tax policy, in the case of a transmission line with 200 MW of capacity, the results show a decongested line for all carbon tax scenarios considered.As it is shown in Figure 2, the tax implies a monotonic decrease in the power supplied from the conventional technology at node 1, reaching a level of zero for a tax of $60/ton of CO 2 .In the case of the conventional technology at node 2, the power supply increases as the tax level increases up to $60/ton of CO 2 4. For a feed-in tariff between 0 and $164/MWh, the firm located at node 1 does not produce RE because the difference between the FIT and the nodal price ($138.31/MWh) is smaller than the difference between coal and natural gas ($26/ (since the effect of the tax is more than compensated/offset by the increase of the energy price in that node).Once the tax level exceeds $60/ton of CO 2 , the supply of such technology starts to decrease, as expected, until the tax level reaches $129/ton of CO 2 .In the tax range between $129/ ton and $158/ton the conventional energy supply gets fixed at 60 MWh due to the fact that the cheap renewable generation capacity is fully utilized and demand at node 1 reaches zero.
On both nodes, for tax levels between 0 and $129/ton of CO 2 , demand decreases, as a consequence of an increase in the price level.Demand falls to zero at node 1 and to 140 MWh at node 2, for tax values larger than $129/ton of CO 2 (values which remain fixed for tax levels larger than $129/ton of CO 2 ).With respect to RE, only the firm at node 1 finds profitable to generate power (at maximum capacity, effective 80 MWh), for tax levels larger than $32/ton of CO 2 .
Accordingly with the previous results, CO 2 emissions (at an aggregate level) decrease as the tax increases, see Figure 3. Neververtheless, it is interesting to note that emissions at node 2 grow in the tax range of 0 to $60/ton of CO 2 .
Assuming a carbon tax level of $32/ton of CO 2 (which is the lowest tax level needed to encourage RE generation of 80 MWh), we determine the existence of a single market equilibrium, resulting in a single nodal price of $153.24/MWh.From the best response functions of both firms in the Cournot model (resulting with these levels of tax and nodal prices), a power supply of 157.25 MWh at node 1 and 121.89MWh at node 2 is reached at the market equilibrium, as shown in Appendix C (Figure 24).

Feed-in Tariff (FIT) Policy Outcome
Under FIT policy, in the case of a transmission line with 200 MW of capacity, the results show a decongested line for all feed-in tariff scenarios considered.As illustrated in Figure 4, the power supplied takes a step-wise form in the FIT model (the same occurs in the premium-payments model).This is because the subsidy is not directly included into the demand curve, but only applied directly to the supply of RE, which always varies from zero to full capacity. 4In this sense, a rebound MWh).At FIT = $165/MWh, nodal prices turn out to be $133.18/MWhat both nodes, which makes the difference between FIT and nodal price larger than $26/MWh, meaning that the firm at node 1 produces its maximum capacity of RE. 5. Verma and Kumar (2013) find a similar effect (i.e., an increase in power generation) when applying a FIT policy.
effect is produced by the subsidy when RE is generated (consumers increase electricity consumption due to the artificial price reduction). 5Indeed, when incorporating the cost of the subsidy back into the demand curve (simulation results are reported in Section 4.6.4),we observe that the rebound effect is eliminated and power supply, the flow through the line, and demand at the market equilibrium vary smoothly as FIT increases (i.e., the step-wise form of the curves in Figure 4 disappears).
In the cases of carbon tax and quota, on the contrary, payments/costs are directly applied into conventional power supply, which are internalized by consumers through the resulting price levels, implying that the rebound effect is not produced.
Figure 4 shows that, for a feed-in tariff level of $165/MWh applied to both nodes, there is a decrease in the supply of energy from conventional sources on both nodes, which is more than offset by an increase in the supply of RE sources on node 1.The same situation is repeated for a level of feed-in tariff of $312/MWh, applied to both nodes, but this time the decrease in the supply of conventional energy of both nodes is more than offset by an increase in renewable energy supply on node 2.
Remarkably, on both nodes, for feed-in tariff levels of $165/MWh and $312/MWh, demand for energy is spurred (rebound effect), as a consequence of a decrease in the price level, resulting at levels of $133.18/MWh and $128.05/MWh,respectively.In this particular example, the totality of the additional demand due to the rebound effect is supplied from RE sources.Accordingly with these results, CO 2 emissions decrease at each node for feed-in tariff levels of $165/MWh and $312/ Assuming a feed-in tariff of $165/MWh, we determine the existence of a single market equilibrium, resulting in a price of $133.18/MWh on both nodes.From the best response functions of both generators in the Cournot model (resulting with these levels of feed-in tariff and nodal prices), a power supply of 299.34 MWh at node 1 and 84.12 MWh at node 2 is reached at the market equilibrium, as shown in Appendix C (Figure 25).A single equilibrium for a feed-in tariff of $312/MWh and a price of $128.05/MWh on both nodes is also found, reaching a total power supply amount of 272.67 MWh at node 1 and 137.47 MWh at node 2.

Premium Payment Policy Outcome
Under the premium payment policy, in the case of a transmission line with 200 MW of capacity, the results also show a decongested line for all payment scenarios considered.As illustrated in Figure 6, for a premium level of $32/MWh, there is a decrease in power supply coming from conventional sources in node 1, which is offset by an increase of equal magnitude in the supply of RE sources on the same node.The same situation is repeated for a premium level of $181/MWh, but this time the reduction of conventional energy supply occurs on node 2, which again is offset by an increase of equal magnitude in RE supply on that node.On both nodes, energy demand remains constant as the premium increases and firms are incentivized to produce RE at maximum capacity (80 MWh) for premium levels larger than $32/MWh and $181/MWh, respectively.
Assuming a premium of $32/MWh, we determine the existence of a single market equilibrium, resulting in a price of $138.31/MWh on both nodes.From the best response functions of both generators in the Cournot model (resulting with these levels of premium tariff and nodal prices), a power supply of 246 MWh at node 1 and 110.8 MWh at node 2 is reached at the market equilibrium, as shown in Appendix C (Figure 26).
Accordingly with the previous results, CO 2 emissions (at an aggregate level) decrease in each node for the premium levels of $32/MWh and $181/MWh, see Figure 7.

Outcome of Quota Obligation Policy
Under the quota policy, in the case of a transmission line with 200 MW of capacity, the results show a decongested line for the different quota scenarios considered.As illustrated in Figure 8, with a penalty of $32/MWh, the supply of conventional energy in both nodes decreases as the required quota increases.On both nodes, energy demand is reduced as quota obligation increases, which is a result of the increase in the price level due to the RE obligation.Regarding RE generation, the firm at node 1 produces RE at maximum capacity (80 MWh) for quota obligations larger than 36%, while in the case of node 2, there is no RE supply for any of the quota obligations.
Assuming a quota obligation of 36%, we determine the existence of a single market equilibrium, resulting in a price of $145.99/MWh on both nodes.From the best response functions of both generators in the Cournot model (resulting with these levels of quota obligation and nodal prices), a power supply of 226.03 MWh at node 1 and 90.83 MWh at node 2 is reached at the market equilibrium, as shown in Appendix C (Figure 27).
Accordingly with the previous results, CO 2 emissions decrease at each node as the quota obligation increases, see Figure 9.

Comparative Analysis of the Policies
In this section, we compare the different RE incentive schemes in terms of energy prices, RE generation, CO 2 emissions, and social welfare, when considering a certain level of RE penetration, when considering a determined target for carbon emissions, when considering different market structures, and when varying the methods to recover subsidy costs.

Analysis Based on RE Penetration
A first comparative analysis was conducted on the results obtained for a total renewable penetration of 80 MWh (this means, a total RE production of 80 MWh).Tables 4 and 5 show the detailed results for each of the policies.From Table 4, we observe that we obtain the highest social welfare (without considering the base case) with feed-in tariff policy followed by premium payments, quota and tax policies.It is important to recall that here we are assuming oligopoly competition and that customers do not directly pay back for the subsidy.As demonstrated in later sections, these results change when assuming that either a perfectly competitive electricity market takes place or customers directly pay back for the subsidies.
The subsidy, in the case of the FIT policy, is computed as the difference between the value of the FIT and the nodal price at the market equilibrium ($165/MWh minus $133.2/MWh is equal to $31.8/MWh, as seen later on Table 6).In Tables 4 and 5, the total subsidy cost (which corresponds to the before-mentioned value of the subsidy multiplied by the amount of RE generated) is presented.At the equilibrium, the value of the FIT subsidy ends up being similar to the value of the subsidy in the case of the premium ($32/MWh).
On the other hand, the calculation of the producer surplus associated with the RE generation (REPS as seen in Table 4) is determined based on the difference between the value of the FIT and the cost of RE generation ($165/MWh minus $122/MWh is equal to $43.0/MWh), in the case of the FIT policy.In the case of the premium payment, the REPS is computed based on the value of the nodal price plus the premium minus the cost of RE generation (i.e., $138.3/MWhplus $32/ MWh minus $122/MWh, which is equal to $48.3/MWh).
Note that, in agreement with these results, firms have incentives to invest in RE capacity (i.e., generate RE in our model using levelized costs) because their profits are larger than the profits obtained by producing with the coal power plant (In the FIT case, $43.0/MWh is larger than $42.2/MWh, which is $133.2/MWhminus $91/MWh; and in the premium payment case, $48.3/MWh is larger than $47.3/MWh, which is $138.3/MWhminus $91/MWh).
The second row of Table 4 presents the social welfare and RE participation when carbon tax level is $32/ton of CO 2 and nodal price is $153.24/MWh.Similar results, but in the case that the transmission line has a capacity of 60 MW, are shown in Table 5.In the case that the transmission line has a capacity of 60 MW, the line becomes congested for a tax level larger than $32/ton of CO 2 , resulting in higher prices (i.e., $160.9/MWh and $174.9/MWh for nodes 1 and 2, respectively).show the effect of congestion on social welfare in each type of policy.Independently of the incentive policy, social welfare is always higher in the uncongested case, which is explained by the lower nodal prices obtained.
As a result of this congestion, social welfare decreases (from $22,233 to $18,278), as it is shown in Tables 4 and 5, respectively.Notwithstanding the foregoing, the congestion favors producers, which is reflected in the increase of their surplus from $7,693 (Table 4) to $8,738 (Table 5).This situation (congestion produced when K = 60MW reduces social welfare, favoring producers) also occurs in the case of the other RE policies.
Table 6 shows the minimum incentive levels that are required in each policy to achieve the penetration of 80 MWh of RE, when the transmission line is congested and when it is uncongested.Under a carbon tax policy, this condition is satisfied with a tax of $32/ton of CO 2 , which is the same independently of the transmission congestion.A similar situation is observed under premium payment and quota obligation policies.The incentive levels required with FIT policy are different, depending on the congestion of the network.
Table 7 shows nodal prices, at the market equilibrium, in the case of a penetration of 80 MWh of RE.Naturally, prices are the same in both nodes for the uncongested line (K = 200 MW) and they are different when there is congestion (K = 60 MW).As expected, nodal prices are lower when there is no congestion in the line, yielding larger social welfare, as shown in Figures 10 to 13. 6 As observed in Table 7, equilibrium price levels differ among the RE policies.

Analysis Based on Emission reduction Performance
We previously compared the performance of RE policies by looking at the social welfare when reaching 80 MWh of RE generation.However, we must be careful in using this comparison to make a conclusion about the policy performance in reducing CO 2 emissions (because CO 2 emission levels are different in each case).To adequately compare the CO 2 emission abatement performance of the RE encouraging policies, we set the same level of emissions achieved with every policy.That is, we modify the level of incentives in each policy in order to achieve 253 tons of CO 2 in emissions (value arbitrary chosen) for the case of a line with 200 MW of capacity and 174 tons of CO 2 for the case of a line with 60 MW of capacity, as shown in Tables 8 and 9, respectively.Then, the performance of each policy to reduce CO 2 emissions is determined based on the ratio between emission abatement from base case (37 tons of CO 2 for the case of a line with 200 MW of capacity and 40 tons for the case of a line with 60 MW of capacity) and the difference W Base- Case minus W Policy .This index is presented in Tables 8 and 9 (see PERP in Tables 8 and 9).Through this index, Tables 8 and 9 allow establishing a ranking of policies regarding the cost effectiveness in reducing CO 2 emissions, in the case of assuming oligopoly competition and that consumers do not directly pay back for subsidies.
Figures 14 and 15 compare the social welfare in the base case (W Base-Case ) with the social welfare under each policy (W Policy ), when having the same level of CO 2 emissions.
Both subsidy policies (FIT and premium payments) are the most cost effective in reducing CO 2 emissions, as seen in Figure 14 (case K = 200 MW, uncongested) and Figure 15 (case K = 60, congested MW).This means that subsidy policies, under the assumptions made here, reduce more CO 2 emissions per each dollar of social welfare that is forgone with respect to the base case.In the particular case analyzed here, this result is explained because subsidies generate two combined effects.First, the subsidy in FIT or premium payment reduces the price of electricity that consumers face, as seen in Figure 16, which leads to increments in energy consumption (rebound effect).While, in general, it is expected that the rebound effect leads to higher emissions, in our case, the      increment in the energy consumption (rebound effect) produced in the FIT policy is fully met with RE supplied from node 1, which leads to an emission reduction (recall from Figure 4 that, under FIT policy, the reduction on conventional energy production is more than compensated by an increment in the RE supply).Secondly, the subsidy contributes to mitigate the generation firms' market power in the case of the FIT policy.In general terms, oligopolistic generation firms wish reducing generation to increase price with respect to the perfectly-competitive equilibrium.When Copyright ᭧ 2016 by the IAEE.All rights reserved.
7. Recall that, in order to include both investment and operations costs in a per-MWh basis into the dispatch problem, we used levelized-cost formulations in previous sections, as done in (Becker et al., 2014;Moiseyev et al., 2014;Eichman et al., 2013;Crane et al., 2011;Park et al., 2011;Nicholson et al., 2011).Accordingly, in order to correctly compare each RE policy under perfect competition and oligopoly, we keep a levelized-cost formulation in the perfect-competition framework -as in (Oak et al., 2014), although we recognize the levelized-cost model is less appropriate for perfectly-competitive markets.
subsidizing RE through the FIT, only conventional energy is sensitive to the market price.Thus, generation firms exercise market power only through controlling (reducing) the conventional power production.Accordingly, the under-FIT subsidized RE production artificially reduces electricity prices and increases demand, mitigating the market power of generation firms.In this manner, social welfare may be higher under FIT than under other policy due to the market-power mitigation effect of the subsidized RE.We must remark that this result holds only as long as the increase in demand due to the rebound effect is met with RE generation (i.e., as long as there is a "green" rebound effect).In the case of premium payment policies, these effects are more moderate.In fact, as it can be observed in Figure 16, market power is larger for premium payment policies than for FIT policies since premium payments increase the amount of inframarginal technologies in the system (and therefore the incentive for exerting market power).
These two effects are not present in the case of penalty or tax policies, where the price of conventional energy gets higher levels, as seen in Figure 16, which leads to a relative reduction in energy consumption that is not compensated with increasing RE.Recall that here we are assuming oligopoly competition and that customers do not directly pay back for the subsidy.These results change when assuming that either a perfectly competitive electricity market takes place or customers directly pay back for the subsidies.
These differences of the performance on reducing CO 2 emissions among RE policies are even more significant when the network is congested, which is shown in Figure 15.In this case, the subsidy leads to the fact that conventional energy generated at node 2 replaces some conventional energy generated at node 1 due to the congestion, yielding fewer emissions under FIT.
In agreement with the previous results, the level of RE penetration is higher in the case of feed-in tariff, as shown in figures 18 and 19.In the case of a carbon tax policy, for the considered levels, it does not encourage the production of RE.

Analysis of the Effect of Market Power and the RE cost
An interesting question concerns the influence of market power on the performance of the RE policies.To bring some insights into this, we now compare each RE policy under two market structures: perfect competition and oligopoly, in the context of the results presented in Table 8.The perfect-competition model formulations are presented in Appendix B. 7 To produce comparable scenarios, the same level of demand, resulting from applying the oligopolistic model in each of the policies (Table 8), is used in the perfect-competition models.The results of this comparative analysis are shown in Table 10.
Table 10 suggests that, under a perfectly-competitive market structure, there is relatively large RE penetration for the cases of establishing subsidies or carbon tax.The lower cost of RE at node 1 (due to the subsidies or the tax) compared to conventional energy cost at node 2 contributes to these increasing RE penetrations.On the other hand, CO 2 emissions are higher under perfect competition than under oligopoly for all policies other than carbon tax because of the lower energy consumption produced due to the exercise of market power by generation firms.As the information in Table 10 suggests, the performance in reducing CO 2 emissions is different comparing the equilibria under oligopoly and perfect-competition market structures.To adequately compare RE policies under the two different market structures, we set the incentives in all policies in order to achieve the same CO 2 emission level (253 tons of CO 2 ).The results are presented in Table 11.11), when assuming that consumers do not directly payback for subsidies.From Table 11, we observe that the performance of each RE policy significantly depends on the market structure.While FIT is the most cost-effective RE policy in reducing CO 2 emissions when assuming oligopoly, the quota system is the most cost-effective RE policy in reducing CO 2 emissions when assuming perfect competition.Notation is as in Table 8.  Figure 20 shows the RE penetration and Figure 21 shows the PERP index for both oligopoly and perfect competition.From Figure 21, we observe that the magnitude of the PERP index (determined as the ratio between emission abatement, 37 tons for the case of oligopoly and 40 tons for the case of perfect-competition, and the difference W Base-Case minus W Policy ) significantly depends on the market structure.
In Table 11 (and Figures 20 and 21), the subsidy for solar energy in the case of the FIT is determined as the difference between the value of the FIT and the nodal price (i.e., $312/MWh minus $133.2/MWh, which is equal to $178.8/MWh) and the RE producer surplus (REPS as seen in Table 11) is determined based on the difference between the value of the FIT and the cost of RE (i.e., $312/MWh minus $297/MWh, which is equal to $15.0/MWh).The subsidy in the case of the premium payment is $181/MWh and the REPS is the value of the nodal price plus premium minus the cost of RE (i.e., $138.3/MWhplus $181/MWh minus $297/MWh, which is equal to $22.3/ MWh).
Accordingly, the results obtained not only depend on the market structure assumed, but also on the cost of RE.In particular, if we consider a levelized cost for solar power of $130/MWh, we obtain the results presented in Table 12.
In agreement with the results in Table 12, Asano (2013) points out the existence of a negative effect that the cost of solar power would have in the application of the FIT policy in Japan.Asano (2013) makes a comparison between the FIT and the quota system, finding that the application of the FIT policy has excessively raised prices, which is mainly explained due to the high cost of solar energy.

Influence of the subsidy's recovery method on the performance of RE policies
Although our analysis up to this point assumes that RE subsidies (under premium payment and feed-in tariff policies) are governmental contributions, these subsidies are directly paid back by customers through the electricity tariff in several countries, like Germany (Bo ¨hringer and Lo ¨schel, 2006).
In this section, we study the effect of considering that customers directly pay back for the subsidies on the performance of the RE policies.To reformulate our model assuming that the subsidies are paid back by customers through the electricity tariff, we must modify the base model so that demand constraints ( ) are replaced by ( 12) and ( 13) in the case of the premium payment policy and by ( 14) and ( 15) in the case of the FIT policy.
To adequately compare RE policies (quota, tax, premium payments and feed-in tariff) in this case, we set the same level of emissions achieved with every policy.Accordingly, we modify the incentive levels in each policy in order to achieve 210 tons of CO 2 emissions (value arbitrary chosen), for the case of an uncongested transmission line.Then, the performance of each policy to reduce emissions is determined as before based on the ratio between emission abatement from base case and the difference W Base-Case minus W Policy .We analyze the performance of the RE policies considering both oligopoly and perfect competition.Table 13 presents the results obtained when assuming that the subsidies are paid back by customers through the electricity tariff.
From Table 13, we observe that the quota policy yields to different outcomes than the other policies (this is true even if we vary the incentive levels so that the same amount of RE is generated).This is a non-intuitive result because one might expect to have the same outcomes for     quota and feed-in tariff (or premium payment) policies when assuming that the subsidy is directly paid back by consumers.However, this difference occurs because we have assumed that the money collected from penalties in the quota system goes to the government and it is not directly recovered by consumers.Accordingly, although the money collected from the penalties partially goes to end consumers through the electricity price (depending on the demand elasticity), retail prices do not completely capture the potential effect of penalties in the consumers' behavior because, in our model, generation firms are assumed to anticipate dispatch decisions.In the feed-in tariff policy analyzed in Table 13, instead, the whole subsidy is paid back by consumers, directly influencing the consumers' behavior.Something similar occurs in the case of the carbon tax policy, where we have assumed that the money collected from taxes goes to the government and it is not directly recovered by the consumers.
Looking at the PERP index in Table 13 (which is graphed in Figure 23), the cost-effectiveness ranking is headed by the quota system followed by tax, premium payments and FIT policies, in that order.From Figure 23, we observe that, as before, the PERP index depends on the market structure.Interestingly, from Figure 23, we also observe that, in the case of considering that the subsidies are directly paid back by customers, both market structures (oligopoly and perfect competition) yield the same cost-effectiveness ranking of the RE policies.That is, by incorporating the subsidy recovery directly into the customers' tariff, we obtain more consistent results about the cost effectiveness of the RE policies.This is mainly because the fact that customers directly pay back for the subsidies significantly reduces the rebound effect.
From the results (as seen in Figures 21, 22 and 23), it is concluded that the ranking of the PERP index is significantly conditioned by the market structure-which is relevant due to some evidence of the presence of market power in some markets, as mentioned by Yenita and Kirschen (2012)-the cost level of renewable energy, and who bears the cost of the subsidy.

Influence Among Incentives to RE within FIT System
In the case of the FIT policy, the analysis performed in Section 4.3 considered the same price level for RE at both nodes (i.e., for both RE technologies).From that analysis, it was determined that: (i) for a FIT of $165/MWh (applied to both nodes), there would exist incentives for RE supply only at node 1, at maximum capacity, and (ii) for a FIT level of $312/MWh (applied to both nodes), RE on both nodes would be generated at maximum capacity.Recall also that the analysis considered a line capacity of 200 MW, resulting in an uncongested system.
Next, we analyze, for each RE technology (and in the case K = 200 MW), which would be the level of FIT at which firms would be incentivized to produce RE (i.e., incentivized to invest in RE under our levelized-cost approach) when the other technology of RE does not receive enough incentives.The results are summarized in Table 14.
For the case in which the firm at node 1 does not receive enough incentives, a FIT level of $319/MWh would incentivize RE supply at node 2 to produce RE at its maximum capacity.In turn, for the case in which the firm at node 2 does not receive enough incentives, a FIT level of $165/MWh would in fact incentivize RE production in node 1 to its maximum capacity.
Taking into consideration these two FIT levels (i.e., $319/MWh and $165/MWh), it is then determined, separately for each case, the FIT level at which there would be an incentive for the firm at the opposite node (that didn't have incentives before) to produce RE.For the case in which the firm at node 2 receives a FIT of $319/MWh, the firm at node 1 would be incentivized to produce RE at maximum capacity at a FIT level of $161/MWh (that is, $4/MWh below the case in which the firm at node 2 does not receive enough incentives).Similarly, when the firm at node 1 receives a FIT of $165/MWh, the firm at node 2 would be incentivized to produce RE at maximum capacity at a level of $312/MWh (i.e.$7/MWh less than in the case where the firm at node 1 receives insufficient incentives).
Thus, this particular situation illustrates the possibility that the FIT price of a technology can influence the entry price of another technology.Specifically in this case, we observe that fixing a specific incentive (price) for a technology can lower the incentive that must be offered to a second technology so that it becomes economically profitable and can supply power into the network.This interrelationship constitutes an interesting result which suggests that interrelationships among generation firms employing different RE technologies may occur, and that they should be studied carefully before implementing a FIT system in a real power network.
Analyzing the KKT conditions of the optimization problem in the FIT model formulation, we can observe that there is a tight relationship (dependency) among FIT prices and the shadow prices of the RE generation capacity constraints at both nodes, as it is evident in ( 16) and ( 17).Thus, the higher the FIT at node 1, the lower the required FIT at node 2 to satisfy optimality conditions ( 16)-( 18), and vice versa.
Recall that we have assumed that each firm owns two power plants (located at the same node).Thus, as soon as one firm's RE plant becomes viable (due to the FIT), this plant displaces energy from the coal/gas plant of the other generation firm, making it more willing to build RE plants with a lower subsidy.

CONCLUSIONS
This paper compares different incentive policies to encourage the development of RE (carbon tax, feed-in tariff, premium payment and quota system) in terms of energy prices, RE generation, CO 2 emissions, and social welfare.The results obtained by modeling the different policies to incentivize the incorporation of RE to the power network are useful for decision makers in designing RE policies.These results are important because they show different effects in terms of RE penetration, social welfare, and emission reduction efficiency.
The main result of the article is that the cost effectiveness of the different incentive schemes (in terms of RE penetration, social surplus, and emission-reduction effectiveness) varies significantly depending on the market structure assumed, the costs of RE, and the subsidy recovery method considered.Subsidy policies (FIT and premium payments) are more cost effective in reducing CO 2 emissions than those policies that apply penalties or taxes, when assuming oligopoly competition and that customers do not directly pay back for the subsidies.However, quota system and carbon tax policies are more cost effective when assuming that either a perfectly competitive electricity market takes place or customers directly pay back for the subsidies through the electricity tariff.Nonetheless, this latter result may be reversed in the case that the costs of RE dramatically drop.
When considering oligopoly competition and that customers do not directly pay back for the subsidies, the FIT policy achieves the lowest nodal prices and the highest RE penetration for the same level of CO 2 emissions (which is a direct consequence of assuming that the government bears all the cost of the subsidies).In this case, we obtain that FIT and premium payments policies are the most cost-effective policies in reducing CO 2 emissions.This surprising result is explained because subsidies generate two combined effects.First, the subsidy in FIT or premium payment reduces the price of electricity that consumers face, which leads to increments in energy consumption (rebound effect) -which is fully met by RE production in our case study.Secondly, the subsidy in the FIT contributes to mitigate the generation firms' market power.Accordingly, the subsidized RE production artificially reduces electricity prices and increases demand, mitigating the market power of generation firms.Several sensitivity analyses were made with respect to different levels of demand and costs of generation, leading to the same qualitative conclusions.However, our conclusions cannot be generalized because they only hold as long as the increase in demand is covered by RE generation.
We also showed that network congestion affects nodal prices, and thus social welfare, in each of the studied policies.For example, under the quota obligation system, it was observed that power transmission congestion decreases the maximum demand to be reached for a given obligation and the penalty cost, which in turn affects renewable and conventional generation.In addition, after varying the quota obligation while keeping the penalty constant, it is observed that congestion affects the quota obligation percentage that we must demand in order to attain a certain level of RE generation.This is in agreement with the findings in Munoz et al. (2013), suggesting that there should be a higher obligation demanded when there is line congestion to attain the same amount of RE generation than when there is no congestion.
In the case of the FIT policy, it is possible to detect that there is an interrelationship between RE technologies to be encouraged.This means that a FIT for a particular RE technology may influence a second RE technology FIT, resulting in a lower FIT that is needed to allow similar results in the operation of the power network.When applying the proposed formulations to more complex networks, we should expect that these interrelationships among RE technologies encourage even lower required FIT prices.This is due to the multi-nodal and multi-technology relationships that may occur.
When considering that customers directly pay back for the subsidies, we obtain that the quota system and the carbon tax policies are the most cost-effective policies in reducing CO 2 emissions, independently of assuming oligopolistic or perfectly-competitive markets.We also obtain that the quota system and the carbon tax policies are the most cost-effective policies in reducing CO 2 emissions when considering perfectly-competitive markets, independent of who bears the costs of the subsidies.
However, all these results also depend on the costs of the RE.For example, when we consider that the levelized cost of solar energy decreases to 130 $/MWh, we obtain that the most cost-effective RE policy in reducing CO 2 emissions is the FIT policy, even when assuming that the market is perfectly-competitive.
Our results indicate that the best-performing RE policy varies depending on the market structure, the costs of RE, and the subsidy recovery method considered.Accordingly, in order to compare our results with those appearing in the literature, we should first answer the following questions: (1) What is the market structure considered?; (2) What is levelized cost of the RE considered? and (3) Who bears the cost of the subsidy?For example, in Oak et al. (2014), where a perfectly competitive market is modeled assuming levelized costs, the authors find that quota system and premium payment have the best performance.Verma and Kumar (2013) model an oligopolistic market assuming marginal costs, finding that the FIT policy generates an increase in total power generation (conventional and renewable), which coincides with our result for the case of a oligopolistic market in which the cost of the subsidy is assumed by the government.Fisher (2010) develops a model that predicts that a subsidy policy would reaches lower prices, while carbon tax policy would reach higher energy prices, in the short run, which agrees with the results of our oligopolistic model.

Figure 2 :
Figure 2: Power supply, flow and demand at the market equilibrium under the Carbon Tax Policy

Figure 3 :
Figure 3: CO 2 Emissions under the Carbon Tax Policy

Figure 4 :
Figure 4: Power supply, flow and demand at the market equilibrium under the Feed-in Tariff Policy

Figure 5 :
Figure 5: CO 2 emissions under the Feed in Tariff Policy

Figure 6 :Figure 7 :
Figure 6: Power supply, flow and demand at the market equilibrium under the Premium Policy

Figure 8 :
Figure 8: Power supply, flow and demand at the market equilibrium under the Quota Policy

Figure 9 :
Figure 9: CO 2 emissions under the Quota Policy

Table 4 :
Social Welfare at the Equilibrium in the Situation When Just Reaching 80 MWh of RE Penetration (Uncongested, K = 200) a 5 present a detailed calculation of social welfare for each type of policy.Notation is as following: PS: Producer Surplus (PS = CEPS + REPS); CEPS: Conventional Energy Producer Surplus; REPS: Renewable Energy Producer Surplus; CS: Consumer Surplus; CO

Figure 10 :
Figure 10: Case with Tax

Figure 12 :
Figure 12: Case with Premium

Figure 14 :Figure 15 :
Figure 14: Social Welfare when having the same level of CO 2 emissions (K = 200MW)

Figure 18 :
Figure 18: RE penetration for an abatement of 37 ton of CO 2 (K = 200MW)

Table 12 :
Welfare and RE Participation, Assuming That the Levelized Cost of Solar Power is $130/MWh (

Figure 22 :
Figure 22: RE penetration: Perfect Competition and Oligopoly

Table 5 : Social Welfare at the Equilibrium in the Situation When Just Reaching 80 MWh of RE Penetration (Congested, K = 60) a
a Notation is as in Table4.

Table 9 :
Table 11 allows establishing a ranking of policies regarding the cost effectiveness in reducing emissions (see PERP index in Table

Table 11 : Welfare and RE Participation (Uncongested) a
a Notation is as in Table8.

Table 13 : Welfare and RE Participation (Uncongested) a
Notation is as in Table8.As before, the PERP index is computed as the ratio between CO 2 emission abatement -80 tons for the case of oligopoly and 83 tons for the case of perfect- a Policy ).