An analysis of a feed-in tariff in Taiwan’s electricity market
Ming-Chung Chang
a,⇑, Jin-Li Hu
b, Tsung-Fu Han
ca
Department of Banking and Finance, Kainan University, Taiwan
b
Institute of Business and Management, National Chiao Tung University, Taiwan
c
Department of Business Administration, Tungnan University, Taiwan
a r t i c l e
i n f o
Article history: Received 12 March 2012
Received in revised form 14 August 2012 Accepted 19 August 2012
Available online 27 September 2012 Keywords:
Power plant Renewable resources Stackelberg game
a b s t r a c t
For the earth’s sustainable development, the proportion of power generated by renewable resources has risen, whereas the proportion of power generated by fossil fuel has fallen. Many small-sized power plants that generate power through renewable resources sell power to large-size traditional power plants that generate power using fossil fuel. In this study we employ the Stackelberg framework to analyze the feed-in tariff (FIT) regime feed-in which a traditional power plant purchases power from a small-size green power plant. We conclude that such a FIT regime causes social welfare to decrease when the marginal cost of the public power plant decreases and the public power plant purchases too much renewable power.
Ó 2012 Published by Elsevier Ltd.
1. Introduction
Economic growth brings about a rapid increase in electricity consumption. However, traditional fossil fuel power plants emit a lot of greenhouse gases that cause global warming and climate change. For the earth’s sustainable development, many countries’ governments are actively developing green power generated by renewable resources. Generation expansion planning (GEP) deter-mines which kind of power plants should be constructed and when they should start to operate[25]. In recent years, because of energy shortages, many governments have encouraged private enterprises to build independent power plants[24]. Independent power pro-ducers (IPPs) can sell the electricity power to the traditional fossil fuel power plant. It is proved that IPPs will generate more profits in a cooperative game than in a non-cooperative game[15]. In other words, IPPs usually do not generate profits only by using their ex-cess generation capacity, but by using their full generation capacity. Since the Kyoto Protocol has asked member states to decrease their greenhouse gas emissions for the earth’s sustainable develop-ment, the traditional generation method using fossil fuel is now viewed in an environmentally unfriendly way. On the other hand, the green power generated by using renewable resources such as solar and wind is taken to be environmentally friendly energy. Ameli et al.[3] study the optimal proportion of green power in overall electricity consumption and the economic advantage of green power. They present some models in which the power plants have different production cost functions to discuss the problem of augmenting power networks with solar power plants and find
their optimal production point. Many countries have started to emphasize the generation of green power, such as the United Kingdom’s (UK) target for the proportion of green power in overall electricity consumption to be 15% in 2015 and rise to 20% in 2020
[22]. The European Union set the target of green power supply to be 12% in 2010[18]. In 2010, the European Commission published the Communication ‘‘Energy 2020 – A strategy for competitive, sustainable and secure energy’’, which mentions that the European Union will promote the target of the renewable energy supply to 20% in 2020 by introducing a legislative framework design. Some studies also discuss the operational risk of power generation by using renewable energy[13].
In order to encourage the adoption of renewable energy tech-nology, many countries have established the feed-in tariff (FIT) re-gime in which the government asks the electricity utility companies to purchase the power at the price decided by a long-term contract. The FIT regime has been adopted by 20 countries in the European Union. For example, France offers a FIT price of 8.2 €cents/kW h for wind electricity power for the first 10 yr of operation. Portugal provides a FIT price for hydro-power ranging from 5.91 €cents/kW h (30 MW in capacity) to 7.04 €cents/kWh (10 MW in capacity). In Germany, the FIT price for a new installa-tion has been cut by 1% for wind power plants and by 10% for pho-tovoltaic systems in order to encourage technology improvements to the plant. In Ireland, since there are favorable wind conditions, the FIT price of wind electricity power ranges from a low of 5.6 €cents/kW h to 5.8 €cents/kW h. Taiwan’s Legislative Yuan in 2009 passed the Renewable Energy Development Act as a basis for Taiwan’s FIT regime. The most important issue in regard to Taiwan’s FIT regime is to design a reasonable FIT price. In 2011, the Taiwan government announced a cut in the FIT price with
0142-0615/$ - see front matter Ó 2012 Published by Elsevier Ltd.
http://dx.doi.org/10.1016/j.ijepes.2012.08.038
⇑Corresponding author. Tel.: +886 3 341 2500x6212; fax: +886 3 341 2228. E-mail address:changmc@mail.knu.edu.tw(M.-C. Chang).
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Electrical Power and Energy Systems
respect to solar energy generators, because of the falling cost of installation equipment [5,6]. Similar actions such as reducing energy subsidies and cutting the FIT price have also been initiated in Germany, Greece, the UK, and Switzerland[21].
The model structure in this paper depends on the real story in Taiwan’s electricity market. Taiwan Power Company (Taipower) is the only domestic public electricity company whose main power source is fossil fuels. There are many private electricity companies that use renewable resources to generate power. Since Taipower is a public electricity company, it not only needs to set a suitable power price for maximizing social welfare, but it must also buy the green power according to the FIT regime in order to encourage the renewable energy industry. Since the electricity market is a typical oligopoly competition, game theory is widely applied to the topic, especially in auctions for the purchase and sale of elec-tricity[4,10,11,14,17]. Some studies on the electricity market have focused on generation expansion planning[8], transmission con-strained networks[9], and power plant behavior in the short term
[20].
The basic concept of the Stackelberg model is that at least one of the players in the market is able to pre-commit itself to a particular level of supply before other players have fixed their level of supply. The other firms observe the leader’s supply decision and respond with their output decision. The players able to initially pre-commit their level of output are called the market leaders and the other players are the followers[19]. In this study, the renewable power plant is promised that all its power output will be purchased by the public power plant in the FIT regime. Even if the renewable power output, such as wind and solar production, is non-manage-able, all renewable power output produced by the renewable power plant will be purchased by the public power plant. In other words, the renewable power plant firstly pre-commits an output level that depends on the natural condition and that this output level will be purchased by the public power plant, and later the public power plant decides its output level. In Taiwan’s electricity market case, Taipower has an obligation to purchase all green power generated by private power companies, and thus Taipower is a Stackelberg fol-lower and many private power companies are Stackelberg leaders.
The emergence of a green power plant causes the traditional monopoly of the electricity market structure to change. Ackermann
[1]defines distributed generation as an electric power source that directly connects to a distribution network or on the customer side of the meter. The author analyzes the effect of distributed genera-tion on market power by applying the cases of combined heat & power and wind power in western Denmark. He concludes that the distributed generation can reduce a power plant’s market power. Peças Lopes et al.[18]mention that the integration forces of distributed generation include the environment, regulatory is-sues, and commerce. They also conclude that distributed genera-tion will benefit the power plant located in a large industrial area or residential area since the power plant does not invest too much in infrastructure.
The concept of distributed generation is not to replace the cur-rent power system, but to integrate it into the system operation. Strbac et al.[22]assess the costs and benefits of wind generation in the UK electricity system and conclude that the system will be able to accommodate a significant increase in wind power genera-tion with relatively small increases in overall costs of supply. Akhmatov and Knudsen[2]point out that although there is a large penetration of distributed generation in the Danish power system, the central large-size power plants still control the voltage and fre-quency of the grid. However, the trend is changing and large wind farms are playing an important role in supporting the services.
Some distributed generation business models have been discussed by Gordijn and Akkermans [12]. They survey cases in various countries, including Spain, Norway, the UK, and The
Netherlands, and highlight some novel ideas. For example, the small-size local producer business model for renewable distributed generation is profitable. In many countries the reserve power gen-eration capacity is decreasing due to deregulation, creating new opportunities for distributed generation.
The remainder of this paper is organized as follows. Section2
shows the model set-up. Section 3presents the model analysis. Section4provides the numerical analysis. Section5concludes.
2. The model set-up
The basic setting in this study is based on two power plants: one is the public power plant that generates power by using tradi-tional fossil fuel, and the other one is a private power plant that generates power by using renewable resources. The relationship between the power market price (p) and the power demand (Q) takes a linear form:
p ¼ a ¼ bQ: ð1Þ
The parameter a > 0 represents the power market size, and the parameter b < 0 indicates that there is a negative relationship be-tween the power price and power demand. Since an equilibrium status requires that the power demand be equal to the power sup-ply, Q = x + y, where x is the power output of the public power plant by using traditional resources; y is the power output of the private power plant by using renewable resources, where x
e
R+ andy 2 ½0; y; and y refers to the non-zero output level of the private power plant that depends on weather conditions.
The marginal costs of outputs x and y are cxand cy, respectively.
The profit functions of the public power plant and private power plant are, respectively:
p
1¼ ðp cxÞx þ ðcx wÞy;p
2¼ ðw cyÞy;ð2Þ
where w is a price whereby the public power plant purchases power from the private power plant. We define w as the electricity buy-back price. In short, the public power plant is only one power supplier by generating power x and purchasing power y from the private power plant. The term (w cy) in Eq.(2)is an avoided cost
mentioned by Xing and Wu[24]in which the public power plant es-capes by purchasing the renewable power for resale instead of building a new plant. It consists of the capital cost and operating cost of the foregone power plant. The term (w cy) in Eq.(2)is also
the FIT price.
The social welfare function is composed of a consumer’s sur-plus, a producer’s surplus (
p
1+p
2), and the environmental damagefunction of green house gas (GHG) emission. Under the assumption of a linear demand function, the consumer’s surplus can be re-duced to (b/2)Q2(the proof is inAppendix A). The environmental
damage function is assumed to be convex in the GHG emission le-vel. A convex environmental damage function implies that the marginal environmental damage increases with increased emis-sions. This functional form is used as D(x) = (k/2)x2 by Chang
et al.[7], where k is the increment in marginal environmental dam-age due to the GHG emission, and the functional form implicates that one unit power output of the public power plant by using tra-ditional resources generates one unit GHG emission; however, the power output of the private power plant by using renewable re-sources does not generate any GHG emission. The social welfare function is described by:
W ¼ ðb=2ÞQ2
þ ð
p
1þp
2Þ ðk=2Þx2: ð3ÞThis is a three-stage game. In stage 1, the social planner chooses the optimal power price pto maximize social welfare. In stage 2,
price w according to the FIT regime established by the
govern-ment. In stage 3, the two power plants choose the optimal outputs xand y. Since the public power plant must purchase all
renew-able power generated by the private power plant, the public power plant is a Stackelberg follower and the private power plant is a Stackelberg leader. We shall examine the following question: Would an FIT regime and the private power plant as a Stackelberg leader cause low social welfare?
3. Analytical results
In this section we try to compare the social welfare under the FIT regime with that in the benchmark model.
3.1. Benchmark model
In the benchmark model, we assume that the public power plant is a monopolist for supplying the power, i.e., Qm= x, where
superscript m represents the monopoly case. The social welfare function in this case is composed of the consumer’s surplus, i.e., (b/2)Qm2, the producer’s surplus, i.e.,
p
m= (p cx)Qm, and the
envi-ronmental damage of GHG emission, i.e., D = (k/2)Qm2. The social planner sets the optimal power price to maximize the social wel-fare function, i.e., pm¼ a bðacxÞ
bþk . Given the optimal power price
pm, the consumer’s surplus is bðacxÞ2
2ðbþkÞ2, the producer’s surplus is kðacxÞ2
ðbþkÞ2, the environmental damage is kðacxÞ2
2ðbþkÞ2, and the maximized
so-cial welfare isðacxÞ2
2ðbþkÞ.
3.2. The FIT regime
According to our basic model setup, the public power plant is a monopoly selling power in the market, and it not only generates power by itself, but also purchases power from the private power plant. We employ backward induction to obtain the optimal solu-tion in this scenario.
(i) The case of 0 < cy< cx
The decision making for the private power plant, i.e., the Stac-kelberg leader, in stage 3 is as follows:
y ¼ y; if w P cy;
0; if w < cy:
ð4Þ
Eq.(4)means that if the electricity buy-back price makes the profit of the private power plant positive (negative), i.e., w cyP(<)0,
then the private power plant will (not) sell all (any) power to the public power plant. According to Eq. (2), the public power plant chooses the output to maximize the profit as follows:
x ¼a cx
2b
y
2: ð5Þ
In stage 2, the public power plant decides the optimal electricity buy-back price according to the FIT regime established by the gov-ernment. From the profit function of the public power plant, we find @
p
1/ow < 0. Based on the concept of the avoided cost and theFIT regime, the optimal electricity buy-back price for the public power plant is:
w¼ c
x; ð6Þ
whererepresents the case of 0 < c
y< cx. Referring back to Eq.(4),
we realize that the private power plant will sell all power, i.e., y¼ y, to the public power plant.
In stage 1, the social planner decides the optimal power price to maximize social welfare. Because of w= c
x, the social welfare
function in Eq.(3)can be rewritten as follows:
W ¼ ðb=2ÞQ2þ ½ðp cxÞx þ ðcx cyÞy ðk=2Þx2; ð7Þ
where Q ¼ x þ y. By the first-order condition of the social welfare function, we obtain the optimal quantity of power production for the public power plant as:
x¼a cx
b þ k: ð8Þ
The optimal market total output, the power price, and social welfare are, respectively:
Q ¼a cx b þ kþ y; p¼ a b a cx b þ kþ y ; W¼ða cxÞ 2 2ðb þ kÞþ by 2 þ cx cy y > 0: ð9Þ
From Eq.(9), we find that there is a positive social welfare in this case.
(ii) The case of 0 < cx< cy
In this case, based on the FIT regime, the optimal electricity buy-back price is:
W¼ c
y; ð10Þ
whererepresents the case of 0 < c
x< cy. Referring back to Eq.(4),
we realize that the private power plant will sell all its power, i.e., y¼ y, to the public power plant.
In stage 1, the social planner decides the optimal power price. Because w= c
y, the social welfare function in Eq. (3) can be
rewritten as follows:
W ¼ ðb=2ÞQ2þ ½ðp cxÞx ðcy cxÞy ¼ ðk=2Þx2; ð11Þ
where Q ¼ x þ y. By the first-order condition of the social welfare function, we obtain the optimal quantity of power production for the public power plant as:
x¼a cx
b þ k: ð12Þ
The optimal market total output, the power price, and social welfare are, respectively:
Q ¼a cx b þ kþ y; P¼ a b a cx b þ kþ y ; W¼ða cxÞ 2 2ðb þ kÞþ by 2 cyþ cx y: ð13Þ
From Eq.(13), because of the term cy+ cx< 0, there is an uncertain
sign on the social welfare.
The optimal solutions under various scenarios are arranged in
Table 1.
Table 1shows that the FIT regime improves social welfare when 0 < cy< cx; however, the FIT regime causes lower social welfare
when 0 < cx< cyand cyis larger than cxby too much. We also find
that the FIT regime must cause the consumer’s surplus to increase. The result is caused by the electricity market becoming more com-petitive in the FIT regime than in a monopolistic market. When the market structure is a monopoly, the profit of the public power plant is necessarily larger than zero; however, the FIT regime may cause the profit of the public power plant to be negative. On the other hand, since the aim of the FIT regime is to encourage the develop-ment of a renewable power plant, the profit of the renewable power
plant is non-negative. A more interesting result is that the environ-mental damage of GHG emission is the same no matter in the monopoly regime or in the FIT regime. Finally, we conclude with some important findings in Proposition 1 as follows:
Proposition 1. In the FIT regime,
(i) the consumer’s surplus will be improved;
(ii) the profit of the public power plant may be negative; how-ever, the profit of the private power plant is non-negative; (iii) social welfare is lower when cyis larger than cxby too much.
3.3. Discussions
InTable 1, it is obvious that a decrease in the marginal cost of the public power plant will cause an increase in the consumer’s surplus regardless of the kind of market structure. This result is from the public power plant being a monopoly selling power in the market.
We next concern ourselves about the effect of a change in the marginal costs of the private power plant and public power plant on social welfare. To arrive at the answer, we show some compar-ative statistical results as follows:
@W @cy ¼ @W @cy ¼ y < 0; ð14Þ @W @cx ¼@W @cx ¼ ða cxÞ ðb þ kÞþ y > 0 if y > ða cxÞ ðb þ kÞ: ð15Þ
From Eq.(14)we find that a decrease in the marginal cost of the pri-vate power plant will cause social welfare to increase. This result is because the profit of the private power plant increases if cy< cx, or a
loss suffered by the public power plant decreases if cy> cx. On the
contrary, an increase in the marginal cost of the private power plant will cause social welfare to decrease. More importantly, a decrease in the marginal cost of the public power plant may cause social wel-fare to decrease when the purchased amount of power by the public power plant is too much, i.e., y > ða cxÞ=ðb þ kÞ. The reason for the
result is that a decrease in cx causes a relatively high renewable
power price cy. If the public power plant purchases too much
renewable power y, then it will cause the social welfare to decrease. The results in this subsection are concluded in Proposition 2 as follows.
Proposition 2. In the FIT regime,
(i) an increase in the marginal cost of the private power plant will cause social welfare to decrease;
(ii) if the marginal cost of the public power plant decreases and the public power plant purchases too much renewable power, then the social welfare will decrease.
Table 1
The optimal solutions under various scenarios.
Monopoly (cy= cx) FIT regime (0 < cy< cx) FIT regime (0 < cx< cy)
Optimal pricing rule pm¼ a bðacxÞ
bþk p¼ a b acbþkxþ y
p¼ a bacx bþkþ y
Consumer’s surplus bðacxÞ2
2ðbþkÞ2 bðacxÞ2 2ðbþkÞþ bðacxÞ ðbþkÞy þ 2by2 bðacxÞ2 2ðbþkÞþ bðacxÞ ðbþkÞy þb2y2
Producer’s surplus p1 kðacxÞ2
ðbþkÞ2 >0 kðacxÞ 2 ðbþkÞ2 bðacbþkxÞy kðacxÞ 2 ðbþkÞ2 bðacbþkxÞy ðcy cxÞy p2 – ðcx cyÞy > 0 0
Environmental damage of GHG emission kðacxÞ2
2ðbþkÞ2 kðacxÞ
2
2ðbþkÞ2 kðacxÞ
2 2ðbþkÞ2
Social welfare ðacxÞ2
2ðbþkÞ>0 ðacxÞ2 2ðbþkÞþ by 2þ cx cy y > 0 ðacxÞ2 2ðbþkÞþ by 2 cy þ cx y Table 2
The data and parameter estimation of the power industry in Taiwan.
Original data Estimated parameter
Average FIT price (NT$ per kW h)
Output level of private power plant (MW)
Output level of public power plant (MW) Power market price (NT$ per kW h) Market size (MW)
Marginal cost of public power plant (NT$ per kW h) Slope of power demand curve Parameter symbol cx cy y x p a cx b 2010 11.8741 64 19329993.6000 2.6098 603093809.3 1991.1840 30.2 2011 8.7245 70 19863993.0000 2.6001 581961004.5 53990.5240 28.3
Fig. 1. A comparison of the consumer’s surplus, the profit of the power plant, the environmental damage of GHG emission, and social welfare.
4. Numerical analysis
We apply the model results in this paper to perform a numerical analysis. The original data including the average FIT price (cx cy),
the output level of the private power plant ðyÞ, the output level of the public power plant (x), the power market price (p) and the esti-mated parameters including the market size (a), the marginal cost of the public power plant (cx), and the slope of power demand
curve (b) are shown inTable 2(the calculation process of the esti-mated parameters is shown inAppendix B). The data period ex-tends from 2010 to 2011.Fig. 1. shows the results of comparing the consumer’s surplus (CS), the profit of the power plant (
p
1andp
2), the environmental damage function of GHG emission (D) andthe social welfare (W) in 2010 and 2011.
InFig. 1, we find that the profit of the public power plant has a greater loss in 2011 than that in 2010. This result can be confirmed by the financial statements of Taiwan Power Company in 2010 and 2011 where
p
1= 18.1 billion in 2010 andp
1= 43.3 billion in2011 [23]. The profit of the private power plant is positive in 2010, but the profit decreases in 2011. The environmental damage of GHG emission in 2011 is higher than that in 2010. The con-sumer’s surplus and the social welfare are positive in 2010, but both of them decrease in 2011.
5. Conclusion
This study uses the Stackelberg game to analyze the effect of the FIT regime on social welfare. The main findings in this study are as follows: (i) In the FIT regime, the consumer’s surplus will be im-proved. (ii) A surprising finding is that the FIT regime causes the social welfare to decrease when the marginal cost of the public power plant decreases and the public power plant purchases too much renewable power.
Lee et al.[16]simultaneously consider three major types of effi-cient energies, including electricity, coal, and gasoline oil. Their study points out a direction in which our paper can be extended. In our paper, we only have one kind of renewable power plant. However, there are many different kinds of renewable power plants such as solar power plants, wind power plants, and geo-thermal power plants in the market. Each of them faces a different FIT price and production cost. In a future study, we can broaden the range of renewable power plants to various other types.
Appendix A
The size of the consumer’s surplus can be calculated by examin-ing the area below the demand function and above the price. This area can be shown by the figure as follows:
The size of the triangular area is (b/2)Q2.
Appendix B
According to the equilibrium results p¼ a b acx
bþkþ y
in
Table 1and p¼ a bðx þ yÞ in Eq.(1), we obtain x ¼acx
bþk. We
sub-stitute the original data x ¼acx
bþk
and y into the profit function of the public power plant
p
1¼kðacxÞ2
ðbþkÞ2 bðacxÞ
bþk y in Table 1, given
k = 1,
p
1= 18.1 billion in 2010 andp
1= 43.3 billion in 2011 toestimate the parameter b[23]. Based on the estimated parameter b and the equilibrium result p¼ a bðx þ yÞ in Eq.(1), we obtain
the power market size a. Finally, we use x ¼acx
bþk, the estimated
parameters a, and b, and given k = 1 to estimate parameter cx.
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