A tripartite equilibrium for carbon emission allowance allocation in the power-supply industry

Energy Policy 82 (2015) 62–80

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Energy Policy journal homepage: www.elsevier.com/locate/enpol

A tripartite equilibrium for carbon emission allowance allocation in the power-supply industry Jiuping Xu a,b,n, Xin Yang a,b, Zhimiao Tao a,b a b

Low Carbon Technology and Economy Research Center, Sichuan University, Chengdu 610064, PR China Business school, Sichuan University, Chengdu 610064, PR China

H I G H L I G H T S








A three-level decision model is proposed for allowance allocation policy-making. The relationship between the regional authority, power plants and grid company is considered. GA is combined with KKT conditions to search for the tripartite equilibrium. Appropriate emission limits have a great effect on achieving the reduction target. Power plants with lower carbon intensity should be allocated more allowances.

art ic l e i nf o

a b s t r a c t

Article history: Received 6 November 2014 Received in revised form 9 January 2015 Accepted 25 February 2015

In the past decades, there has been a worldwide multilateral efforts to reduce carbon emissions. In particular, the “cap-and-trade” mechanism has been regarded as an effective way to control emissions. This is a market-based approach focused on the efficient allocation of initial emissions allowances. Based on the “grandfather” allocation method, this paper develops an alternative method derived from Boltzmann distribution to calculate the allowances. Further, with fully considering the relationship between the regional authority, power plants and grid company, a three-level multi-objective model for carbon emission allowance allocations in the power-supply industry is presented. To achieve tripartite equilibrium, the impacts on electricity output, carbon emissions and carbon intensity of the allocation method, allocation cap, and emission limits are assessed. The results showed that the greatest impact was seen in the emission limits rather than the allocation cap or allocation method. It also indicated that to effectively achieve reduction targets, it is necessary to allocate greater allowances to lower carbon intensity power plants. These results demonstrated the practicality and efficiency of the proposed model in seeking optimal allocation policies. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Carbon emission allowance allocation Power-supply industry Tripartite equilibrium Emission limits

1. Introduction The Fifth Assessment of the Intergovernmental Panel on Climate Change (IPCC) has shown that the climate is changing (IPCC, 2013). For example, global mean surface air temperatures over land and oceans have increased over the last 100 years, and the extreme weather and climate events have an increasing trend (WMO-No.1119; Xu et al., 2014a). Rapid carbon emissions growth (short for GHG emissions) is regarded as one of the largest contributors to these changes, having risen by 30% between 2000 and 2010 (Peters, 2013; IEA, 2012). In particular, fossil fuel burning for n Corresponding author at: Low Carbon Technology and Economy Research Center, Sichuan University, Chengdu 610064, PR China. Fax: þ 86 28 85415143. E-mail address: [email protected] (J. Xu).

http://dx.doi.org/10.1016/j.enpol.2015.02.029 0301-4215/& 2015 Elsevier Ltd. All rights reserved.

electricity purposes has been one of the major contributors to human activity carbon increases over the last 20 years. Because of the harmful impact brought by excessive carbon emissions, several policy instruments have been developed to attempt to mitigate climate change and reduce carbon emissions, such as carbon taxes, command-and-control, and cap-and-trade (Keohane, 2009; Cong and Wei, 2010b; Hahn, 2009). The cap-andtrade mechanism, also known as the emission trading scheme (ETS), is an application of Coase (1960) Theorem, and has proved to be effective in controlling emissions and has been successfully put into practice (Clo, 2009). In this mechanism, the initial carbon emission allowances are defined and allocated for free or at auction or a combination of both (Cong and Wei, 2012; Zhang and Li, 2011). Free allocations presently dominate and are expected to continue to play an important role to 2020 (Hong et al.,

J. Xu et al. / Energy Policy 82 (2015) 62–80

2014). Research on free carbon emission allowance allocations has attracted significant attention in the last few decades, with many scholars having conducted in-depth studies on international carbon emission allowance allocations. Grubler and Nakicenovic (1994) proposed that all countries should be assigned a consistent emissions reduction rate, which ignored the inherent relationship between emissions and population or human activities. The per capita emission-based allocation, signifying that everyone possesses equal emission rights, was suggested by Grubb (1990). This concept has received considerable attention but opposed by several high per capita emission countries. The per unit GDP-based allocation, in which all countries are assumed to have equal emissions per GDP, is another efficient method (Phylipsen et al., 1998). At the same time, some attention has been paid to allocating emission allowances within a specific country. For instance, Yi et al. (2011) introduced a carbon emission intensity-based allocation method, which was applied to the allocation of reduction targets for provinces in China. An improved zero sum gains data envelopment analysis optimization model was proposed by Wang et al. (2013) to realize China's national mitigation targets through a regional allocation of emission allowances. Yu et al. (2014) put forward an approach based on the PSO algorithm, fuzzy c-means clustering algorithm, and Shapley decomposition to determine carbon emission reduction target allocation. Besides these approaches, other allocation approaches have been proposed at the sector level, such as “grandfathering”, allowances based on historical emissions and "benchmarking", allowances based on energy input or product output (Hong et al., 2014). Chang and Lai (2013) proposed carbon emission reduction models for the transportation industry using carbon allowance allocation policies. In addition, a series of more comprehensive and complex allocation models have been developed. Phylipsen et al. (1998) presented a Triptych sector approach which included per capita emissions, per capita GDP, and carbon emissions per unit GDP. Park et al. (2012) introduced the Boltzmann distribution in the physical sciences to allocate emission allowances. These studies have contributed to the improvement of viable solutions to the carbon emission allowance allocation problem (CEAAP) significantly, but these existing allocations are only based on the entity's historical behaviors and have not often considered its possible reactions for the allowances. In fact, under the “cap-andtrade” mechanism, each entity's actual emissions may not be equal to the allowances it receives. The achievement of controlling and reducing emissions depends on the user performance. Therefore, it is necessary to include user opinions in the allocation process. This paper analyzes the CEAAP in the power-supply industry, particularly. As large carbon emitters, power plants must be considered when seeking to mitigate carbon emissions (Chappin, 2006; Cong and Wei, 2010a; Chen et al., 2010, 2013; Zhu et al., 2013). They are in charge of electricity generation, which is influenced by the regional authority's allocation policy. At the same time, when they estimate and seek to maximize profits, it is often difficult to estimate electricity sale revenues because these are decided by the grid company under the “bidding on power net” mechanism. In turn, power plants can also have an impact on the decision-making of regional authority and grid company through carbon emissions and their sale pricing decisions, respectively. Therefore, the allocation involves the regional authority, power plants, grid company and depends on the interactive relationship. With this in mind, the CEAAP in the power-supply industry is presented as a three-level problem with three decision-makers: the regional authority, power plants and grid company. In addition, since there are many uncertainties in the allocation system (Cong and Wei, 2010a; Zhu et al., 2013), fuzzy random theory is used to describe the practical problems (Kwakernaak 1978a,b; Xu and Tao, 2012; Xu

63

et al., 2014b). To deal with the multi-level model, KKT optimization conditions (Sinha and Sinha, 2002) are used to transform this tripartite arrangement to a game between the regional authority and power plants. And a KKT-based interactive genetic algorithm (Hejazia et al., 2002) is followed to search for the points of equilibrium. Finally, practical examples are discussed to seek an efficient allocation policy for emissions control. These results indicated that an appropriate emissions limit and allocating more allowances to power plants with lower carbon intensity are advisable. It is proved that our optimization method was very practical and efficient in solving the CEAAP in the power-supply industry. The remainder of this paper is organized as follows. Section 2 is the methodology part, including description of the key problem statement for CEAAP in the power-supply industry, the formulation of a three-level mathematical model and the search of an efficient solution approach. In Section 3, an application in Shenzhen ETS is presented to explore useful results. To confirm the generality of these results, a general case and some further discussions are shown in Section 4. Finally, Section 5 gives our conclusions and policy implications.

2. Methods 2.1. Key problem statement The power-supply industry CEAAP is a complex system (Fig. 1) comprising a carbon trading market, an electricity generation market, a fuel supply market, consumers, the government, regional authority, power plants and grid company (Ottino, 2004; Zhu et al., 2013). Therefore, efficient allocation policies are required, as unsuitable allocations may not only fail to achieve emissions control targets, but also result in local electricity supply shortages or even system collapse (Wang et al., 2013; Yu et al., 2014). In the allocation system, as the regional authority is directly responsible for the allowances allocation, it has a close relationship with the power plants. The regional authority seeks to control and reduce carbon emissions with limited allowances, but the power plants desire greater allowances and emissions levels for the sake of themselves. Besides, the ETS often means that each plant's emissions could not be equal to its allowances, the regional authority's emissions mitigation target is heavily dependent on the performance of the power plants. There also exists an interesting and close relationship between the power plants and the grid company. Power plant electricity generation costs and sales prices increase when carbon emissions are controlled and treated as assets (Cong and Wei, 2010). Consequently, the grid company decides on each power plants electricity sales with the primary goal of minimizing purchase costs under the “bidding on the power net” mechanism. Therefore, power plant generation plans are influenced by decisions beyond their control. In summary, the power-supply industry CEAAP is a tripartite game between the regional authority, power plants and grid company. In an attempt to find an equilibrium, this paper uses a multi-level analysis to develop a hierarchical structure which simulates this tripartite interaction (Fig. 2). The regional authority is appeared in the “Authorities level” to make allocation policies, including decisions on allowances allocation and emissions limitation. It attempts to maximize the minimal allocation satisfaction and the overall carbon efficiency, while meeting each plant's allowances demand. After obtaining the allowances, the power plant focuses on economic profits maximization with optimal output decision, which must satisfy the capacity and emissions

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J. Xu et al. / Energy Policy 82 (2015) 62–80

Fig. 1. The allocation system in the power-supply industry.

constraints. The grid company shown in "Grid company level" decides on purchase volume with the primary goal of minimizing costs. The decisions are restricted by each plant's output and must meet the electricity demand. It can be observed that there exist allowances flow from the regional authority to power plants and electricity flow from power plants to the grid company. In turn, there are capital flow from the grid company to the power plants and emissions flow from the power plants to the regional authority. Consequently, there is a “Leader–Follower” relationship between the government and power plants because of the allowances allocation, and it is also between the power plants and the grid company due to the electricity sales.

2.2. Model formulation In this section, a three-level programming for the power-supply industry CEAAP is constructed. The mathematical description is given as follows. 2.2.1. Assumptions For the model construction, the following assumptions were made: 1. This is a single period allocation problem, and, at the beginning of the next period, the allowances for each power plant are reset. 2. The carbon emission allowances bank is not considered here.

J. Xu et al. / Energy Policy 82 (2015) 62–80

65

Fig. 2. Concept model for the power-supply industry CEAAP.

3. If the actual emissions are inconsistent with the allowances a power plant obtains, the difference in value is dealt with through trading on the carbon emissions trading market, where the buying and selling of allowances takes place. At the end of this period, the allowances and emissions at each plant must be offset. 4. Grid loss is added to electricity demand, and not considered separately. 5. Each CEAAP decision maker fully understands the objective functions and inherent constraints and behaves rationally.

ei

ρi ai ri p0

θ

(3) Uncertain parameters

∼ oi ∼ vi

2.2.2. Notations To facilitate the problem description, the following notations are introduced. (1) Subscripts

∼ p D͠

i l

γ

index for the power plants, i = 1, 2, … , I . index for power conversion technologies, l = 1, 2, … , L . (2) Certain parameters

si Ei dimin dimax

the the the the

maximum available output at power plant i carbon emissions per output at power plant i minimum allowances demand at power plant i maximum allowances demand at power plant i

the emission coefficient at power plant i the capacity price at power plant i the power consumption rate at power plant i the profit rate at power plant i the electricity sale price in other regions the adjustment coefficient for supply–demand relationship

the annual fixed operating and maintenance costs for power plant i the unit variable operating and maintenance costs for power plant i the carbon emission allowance price the electricity demand (4) Variables and decision variables

β xi zi yi Bi Pi

the excess emission level permitted, decided by the regional authority the allocation index determined by the regional authority the output decision at power plant i purchasing decision of the grid company the carbon emission allowances allocated to power plant i the bidding price of power plant i the sale price of power plant i

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J. Xu et al. / Energy Policy 82 (2015) 62–80

⎧1 power plant i is using power conversion technology l εil = ⎨ , ⎩ 0 otherwise

⎧ 0, yi ≤ dimin, ⎪ ⎪ ⎪ y − dimin gi (yi ) = ⎨ i , dimin < yi < dimax. ⎪ dimax − dimin ⎪ ⎪ yi ≥ dimax. ⎩1,

L

satisfying ∑l = 1 εil = 1, ∀ i = 1, 2, … , I .

2.2.3. Model formulation The complete allocation problem involves the regional authority allocations decisions, the power plants output decisions and the grid company purchasing decisions. Therefore, the complete model includes first, second and third level objectives and constraints, all of which are discussed in detail in the following. Regional authority's carbon emission allowances allocation: First, an alternative method using the Boltzmann distribution is introduced to calculate the allowance allocations for each plant (Park et al., 2012). Suppose that the total emission allowances E⁎ = αN , where α is the unit allowance and N is the quantity. Because of the differences in the maximum available output of different power-conversion technologies, the allowances cap for each I I technology is given by the equation Nl = N ( ∑i = 1 siεil / ∑i = 1 si). Then the unit allowance quantity allocated to the jth available output at plant i (Nij) using conversion technology l satisfies I

si

∑ ∑ Nijεil = Nl

−βEi

where Nij = Ae

following the maximum entropy principle provided by the Boltzmann distribution (Wannier, 1987). A is a constant and is forI mulated by A = Nl/ ∑i = 1 siεile−βEi using Eq. (1). Ei is the sub-state energy of a physical system (Reif, 1965; Wannier, 1987), and is replaced by the “ potential energy allocation per output” of plant i in this paper. The simplest form is determined by the actual carbon emissions per output at each power plant. Therefore, the probability that a unit emissions allowance allocated to power plant i is expressed as s

s

Pi =

Nl

=

∑ ji= 1 Aεile−βEi I

s

∑i = 1 ∑ ji= 1 Aεile−βEi

=

I

∑i = 1 siεile−βEi (2)

Then the amount of emission allowances allocating to plant i is

siεile−βEi I ∑i = 1 siεile−βEi

I

= E⁎

for i = 1, 2, …, I , l = 1, 2, …, L.

siεile−βEi ∑i = 1 siεil I I ∑i = 1 si ∑i = 1 siεile−βEi

(3)

Therefore, the allowances calculation has been converted into a determination of β value, which is called the allocation index (AI) in this paper. It follows from Eq. (1) that β value is directly related to the potential allocation energy per output at a plant (Ei). It can be concluded that plants with relatively low carbon intensities in their class (i.e. with the same conversion technology) prefer a larger β value, while those with relatively high carbon intensities prefer a smaller value. Consequently, no single β value is able to satisfy all plants and its determination needs further consideration. In this paper, a useful reference β value is suggested, which is based on the three key allocation principles of equity, efficiency, and sustainability (Cong and Brady, 2012). The objective function is established by considering the allocation satisfaction at each plant and the overall carbon efficiency; namely, the electricity output per emissions unit. Allocation satisfaction: The regional authority defines the allocation satisfaction for each plant using the following function (Xu et al., 2014b):

(5)

Carbon efficiency: As previously mentioned, the carbon emissions allowance allocation is designed to reduce carbon intensity, which could also be explained by improvements in carbon efficiency. Therefore, an effective allocations policy needs to maximize the overall carbon efficiency in the power-supply industry, which, in turn, depends on the power plants performance; i.e. I

∑i = 1 zi I ∑i = 1 xi ei

. (6)

Nonnegative constraints: The allowances calculation is converted into a determination of β value, which should be in a nonnegative region (Park et al., 2012), so is considered an excess emissions level:

β ≥ 0,

γ ≥ 0.

(7)

Demand constraints: To ensure allocations sustainability, the allowances allocated to each power plant cannot be less than the minimum demand:

yi ≥ dimin.

siεile−βEi

for i = 1, 2, …, I , l = 1, 2, …, L.

yi = αNlPiεil = αNl

max G = min{gi (yi )}

(1)

i=1 j=1

∑ ji= 1 Nijεil

This satisfactory function assumes that for each power plant there is a basic (minimal) allowances demand dimin and a maximal demand dimax. If the allowances are less than dimin, the degree of satisfaction for that plant is reduced to zero, and if they are more than dimax, the degree of satisfaction for that plant cannot increase to greater than one. As a result, to equally allocate and satisfy each power plant's demand to a maximal degree, the objective function is used to maximize the minimal allocation satisfaction:

max U =

for l = 1, 2, …, L

(4)

(8)

Power plant's electricity generation plan: The regional authority allocations policy restricts the power plant performance, as the power plant affects the achivement of regional authority's objective for maximizing the overall carbon efficiency. Each plant performance depends on its respective electricity generation plan, which is designed to maximize profit. Generation costs: The introduction of an ETS has had a noticeable effect on the power-supply industry, as it has influenced the relative costs for the different power generation technologies and increased the average electricity price (Cong and Wei, 2010a). A power plant's generation costs are made up of carbon related costs and operating costs (Zhou et al., 2014). The carbon related costs are the emission allowances trading costs, which have a mathematical description whereby a positive value indicates that the initial allowances allocated are not sufficient and a negative value indicates that there are extra allowances (Zhu et al., 2013), i.e. ∼ (x iei − yi )Ed(p ). The operating costs are divided into fixed operating ∼ costs and maintenance costs Ed(oi), which include depreciation expenses and variable operating and maintenance costs, such as fuel costs, material expenses and others, all of which are related to ∼ the generation quantity, x iEd(vi). So, the crisp equivalent for total generation costs is given as

∼ ∼ ∼ Ed(Ci) = (xi ei − yi )Ed(p ) + xi Ed(vi) + Ed(oi ).

(9)

Here, the fixed and variable operating costs at each plant are addressed as uncertain parameters due to the intrinsic fluctuations in the factors (e.g. cash flow and energy price) (Zhu et al., 2013). The

J. Xu et al. / Energy Policy 82 (2015) 62–80

allowances price, therefore, is also affected by multiple factors such as the economic situation, market volatility and government interference (Zhou et al., 2014). When comparing the two main uncertain approaches, it is not hard to find that fuzzy approaches are suitable for subjective uncertainty and can be used in modeling past experience, while the random approaches is appreciate for objective uncertainty, which describes the impersonal uncertainty by the historical data and statistical methods. Since there are not enough historical data of fixed and variable annual operating costs for each plant (less than 30), it is difficult to determine the probability distribution accurately. Human behaviors have a significant influence on the allowance price, because the government guides it to fluctuate within a rational range. Some similar uncertain parameters were estimated by experienced experts with interval values in many recent studies (Chen et al., 2010; Zhu et al., 2013; Zhou et al., 2014). In this study, the collected data for uncertain parameters (e.g., fixed and variable annual operating costs, allowance price) are also established by close consultation with many experienced experts, who describe the parameters as an interval (i.e. [lw,rw]), with a most possible value (i.e. mw). Since different experts may come to different conclusions, the fluctuation of the most possible value can be characterized by a stochastic distribution. For example, the most possible value of the allowance price can be regarded as a random variable (i.e. ξ). By comparing the most possible values (i.e. mw for w = 1, 2, … , W ), it is found that approximately follows a normal distribution (i.e., ξ ∼ N(μ, σ 2)), whose parameters can be estimated by some statistical methods like the maximum likelihood method. Besides, the minimum value of all lw and maximum value of all rw (for w = 1, 2, … , W ) are expressed by l and r , respectively. Thus, each uncertain parameter can be recognized as a fuzzy random variable (l, ξ, r), where ξ ∼ N(μ, σ 2). The fuzzy random theory, proposed by Kwakernaak (1978a,,b), is proved to be effective in modeling and analyzing imprecise values associated with the sample space of a random experiment through the use of fuzzyset functions (Gil, 2006). It has a higher validity than random theory to prevent the effect of uncertainty when there is only imprecise data or no-stationary data, particularly when human behavior can impact the operations (Zeng et al., 2014). Meanwhile, the fuzzy random approach has a higher accuracy than simple fuzzy method thanks to the different conclusions from quite a few expert consultations. Finally, It is noted that a double expected value [i.e. Ed(·)] of fuzzy random variable is employed: the first is the fuzzy expected value to convert the fuzzy random variable to a fuzzy number (Kruse and Meyer, 1987), and the second is employed to transform the fuzzy number into a deterministic value using the theory proposed by Heilpern (1992). Economic benefits: Power plant revenues generally come from electricity sales. Based on a Two-Part Pricing System, the sales price is composed of a capacity price and an electricity price (Cong and Wei, 2010a). The former is used to compensate for the fixed investments and is therefore relatively stable and is determined by the power-conversion technology of plant i expressed by ρi. The latter, because the main aim is to gain profits, is determined by the market and each plant's bidding price, with the expected value for∼ θ[E (D ) −∑iI xi(1 − ai)]

, where Ed(Bi) = (1 + ri)[(x iei − yi )Ed mulated by Ed(Bi)e ∼ ∼ (p ) + x iEd(vi)]/x i(1 − ai) is the expected value of plant i's bidding price. Thus, the actual sale price received for electricity produced by ͠

I

power plant i is Ed(Pi) = ρi + Ed(Bi)e θ[Ed(D ) −∑i xi(1 − ai)]. The uncertain electricity demand is also estimated through fuzzy random approach. Because it is unreasonable to determine the probability distribution with no-stationary data of electricity demand, which increases with the rapid growth of economy. Finally, the power plant's economic benefits is ziEd(Pi). The objective function for each power plant is to measure and

67

maximize economic profits, so the benefits should be maximized and costs be minimized. The expected value of the objective function can be calculated as follows (Chen et al., 2010):

⎡ z (1 + r ) ⎤ I ͠ i Ed(Fi) = ziρi + ⎢ i e θ[Ed(D ) − ∑i = 1 xi(1 − ai)] − 1⎥ ⎣ xi (1 − ai) ⎦ ⎡ ∼ ∼⎤ ∼ ⎢(xi ei − yi )Ed(p ) + xi Ed(vi)⎥ − Ed(oi ). ⎣ ⎦

(10)

Production constraints: Due to capacity limits and equipment maintenance needs, the electricity output cannot exceed the maximum possible value si (Zhou et al., 2014). Besides, electricity generation cannot be negative:

0 < xi (1 − ai) ≤ si ,

∀ i = 1, 2, …, I .

(11)

Emissions constraints: Because of the limitation on excess emissions set by the regional authority, no plant can generate extra emissions:

xi ei ≤ yi (1 + γ),

∀ i = 1, 2, …, I .

(12)

Grid company's electricity purchase plan. As a direct buyer and transmitter of electricity, the grid company connects the power plants and customers. The influence of the ETS on the electricity prices transfers to the grid company, thereby increasing the electricity purchase costs (Cong and Wei, 2010a). Since the impact on each plant's bidding price is different, it is necessary to optimize the electricity purchase plan so as to minimize costs while satisfying electricity demand. Electricity purchase cost: Based on the argument that the bidding price determines the capacity sold, the grid company decides on the quantity of electricity to be purchased from plant i acI cording to its bidding price, which incurs a cost ∑i = 1 ziEd(pi ). To satisfy demand, it is possible to import electricity from other regions at a price p0 (Zhu et al., 2013). Therefore, the total purchase cost is as shown below: E d (W ) =

I

⎡

i =1

⎣

∑ z i⎢⎢ρi +

∼ ∼ ⎤ ∼ I (1 + ri)[(x iei − yi )Ed (p ) + x iEd (vi)] θ[E (D ) − ∑ x i(1 − ai)]⎥ e + p0 z 0 . i ⎥ x i (1 − a i) ⎦

(13)

Demand-supply balance: Regardless of the purchase plans, the grid company must satisfy electricity demand (Zhu et al., 2013; Zhou et al., 2014): I

∑ zi + z0 ≥ Ed(D͠ ). i=1

(14)

Capacity constraint: The quantity purchased from each local plant cannot exceed its maximum output:

zi ≤ xi (1 − ai),

∀ i = 1, 2, …, I .

(15)

Nonnegative constraints: Each purchase quantity cannot be negative:

zi ≥ 0,

∀ i = 0, 1, 2, …, I .

(16)

Global model: To control carbon emissions, the government employs a “cap-and-trade” mechanism, in which the initial carbon emissions allowances allocation is of significant importance. The regional authority is responsible for the allocations policy-making, and, as the major emitters, the power plants are focus of those allocations. Based on the traditional “grandfather” allocation, an alternative method combining the Boltzmann distribution is applied to guide the change in allowances. However, “carbon intensity” replaces “historical emissions”, which considers both historical outputs and emissions. When making allocations decisions, the regional authority first considers the equity principle and attempts to maximize the minimum allocation satisfaction

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J. Xu et al. / Energy Policy 82 (2015) 62–80

formulated by Eq. (4). More importantly, the allocation must be helpful for emissions mitigation, which can be achieved by maximizing carbon efficiency, which depends on the overall performance of the power plants. Aimed at profit maximization, the power plants then develop power generation plans based on the allowances obtained. However, they are unable to make decisions regarding the sales quantities as these decisions are made by the grid company, whose objective is to minimize purchase costs. At the same time, the grid company makes purchase decisions based on each plant's bidding price. Therefore, the power-supply industry CEAAP gives rise to an interactive relationship between the regional authority, power plants and the grid company, which is too complex relationship for a simple allocation formula. Therefore, in this paper, a three-level model is developed to describe this relationship as follows:

proposed by Karush, developed by Kuhn and Tucker, are necessary conditions for solving an optimization problem with differentiable objective and constraint functions which satisfies a strong duality (Stephen and Lieven, 2004). In particular, when the primal problem is convex, the KKT conditions are also sufficient. Naturally, this term can be satisfied because the objective functions and constraints in the third level of model (17) are both convex. Thus, it is suitable to adopt KKT conditions to transform the three-level mode into a bi-level model. By applying the KKT conditions, the third level in model (17) has the same solution as the following constraint conditions:

⎧min G = min{g (y )} i i ⎪ I ⎪ ∑i = 1 zi ⎪min U = I ⎪ ∑i = 1 xi ei ⎪ ⎧ I ⎪ −βEi ∑i = 1 siεil ⎪ y = E⁎ siεile ⎪ , i = 1, 2, …, I; l = 1, 2, …, L. i I I ⎪ ⎪ ∑i = 1 si ∑i = 1 siεile−βEi ⎪ ⎪ ⎪ y ≥ d min, i = 1, 2, …, I . ⎪ i ⎪ i ⎪ ⎪ β ≥ 0, ⎪ ⎪ ⎪ ⎪ γ ≥ 0, ⎪ ⎪ ⎪ ⎡ ⎤⎡ I ⎪ ∼⎤ ∼ ⎪max E (F ) = z ρ + ⎢ zi(1 + ri) e θ[Ed(D͠ ) − ∑i = 1 xi(1 − ai)] − 1⎥⎢(x e − y )E (∼ ⎨ p ) + xi Ed(vi)⎥ − Ed(oi ) d i i i i i i d ⎪ ⎣ xi (1 − ai) ⎦⎣ ⎦ ⎪ ⎪ ⎪ ⎪ ⎧ 0 < x (1 − a ) ≤ s , i = 1, 2, …, I . ⎪s. t. ⎨ i i i ⎪ ⎪ ⎪ ≤ + γ x e y i = 1, 2, …, I . (1 ), ⎪ i i i ⎪ ⎪ ⎪ ⎪ ∼ ∼ ⎪ I ⎡ ⎪ (1 + ri)[(xi ei − yi )Ed(p ) + xi Ed(vi)] θ[E(D∼) − ∑ I x (1 − a )]⎤ ⎪ ⎪ i ⎥ + p z ⎢ρ + i =1 i = E W z e min ( ) ∑ ⎪ d i 0 0 i ⎪ ⎪ xi (1 − ai) ⎢⎣ ⎥⎦ ⎪ = i 1 ⎪s. t. ⎨ ⎪ ⎪ ⎪ ⎧ I ⎪ ⎪ ⎪ ⎪∑ z ≥ E (D͠ ), ⎪ i d ⎪ ⎪ ⎪ ⎪ i=0 ⎪ ⎪ ⎪s. t. ⎨ ⎪ ⎪ zi ≤ xi (1 − ai), i = 1, 2, …, I , ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ zi ≥ 0, i = 1, 2, …, I . ⎩ ⎩ ⎩

2.3. Solution approach

(17)

The proposed model (17) is a multi-objective three-level decision making problem, which reflects the interactive relationship between the regional authority, power plants and grid company. However, there are few algorithms available to solve three-level programming. Through a rethinking of the CEAAP, it can be seen that the decision conflicts between the power plants and grid company essentially originate from competition between the power plants for increased market share, and the grid company power purchase plan is the result of that competition. Therefore, in reality, the game between the power plants and the grid company is actually a game between the power plants (Jiang et al., 2014). Accordingly, the three-level model (17) can be converted into a bi-level model with additional constraints, which can be realized using the KKT optimality conditions in mathematics (Sinha and Sinha, 2002).

⎧ E (P ) − λ − μ + ν = 0, i = 1, 2, …, I . i i ⎪ d i ⎪ p0 − λ − μ 0 + ν0 = 0, ⎪ I ⎪ ͠ ⎪ λ[Ed(D ) − ∑ zi] = 0, ⎪ i=0 ⎪ I ⎪ z ≥ E (D͠ ), d ⎪∑ i ⎨i = 0 ⎪ νi[zi − xi (1 − ai)] = 0, i = 1, 2, …, I , ⎪ ⎪ zi ≤ xi (1 − ai), i = 1, 2, …, I , ⎪ ⎪ μi zi = 0, i = 0, 1, 2, …, I . ⎪ z ≥ 0, i = 0, 1, 2, …, I . ⎪ i ⎪ μi , νi ≥ 0, i = 1, 2, …, I . ⎪ ⎩ λ ≥ 0, μ 0 ≥ 0, ν0 = 0.

2.3.1. KKT optimality conditions KKT (short for Karush–Kuhn–Tucker) optimality conditions,

where λ, μi , νi(i = 0, 1, 2, … , I) are Lagrange multipliers associated with the problem, λ is the supply-demand multiplier, μi and νi are

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J. Xu et al. / Energy Policy 82 (2015) 62–80

the coupled purchase multipliers, at least one of which is zero. Eq. (18) I suggests λ > 0 and ∑i = 0 zi = Ed(D͠ ). Because if λ = 0, then μ0 = p0 > 0 and μi − νi = Ed(Pi) > 0 (∀ i = 1, 2, … , I ), which implies μi > 0 and νi = 0, leading to zi ¼0 for all i = 0, 1, 2, … , I . It does not satisfy the I constraint ∑ z ≥ E (D͠ ) and is impossible in practice. In addition, it i=0 i

d

͠

I

can be concluded that if Ed(Pi) = ρi + Ed(Bi)e θ[Ed(D ) −∑i xi(1 − ai)] satisfies Ed(P1) ≤ Ed(P2) ≤ … ≤ Ed(PI) ≤ p0 , then , and if there exists Ed(Pi) > p0 then zi ¼0. This indicates that power plants compete with each other for market share through their sales price. Therefore, the bi-level model transformed from (17) by employing KKT conditions is as follows:

finally attained at the points where the behavior of all power plants satisfies the Cournot–Nash equilibrium conditions and the regional authority realizes its Pareto optimal based on the knowledge of the reactions of power plants in response to its own. This is called Stackelberg–Nash–Cournot equilibrium (Nash, 1951; Hansif et al., 1983). Considering the complexity, an interactive genetic algorithm (Majumdar and Bhunia, 2007; Xu et al., 2014b) based on KKT conditions (KKT-IGA) is developed to search for the equilibrium points. Framework of KKT-IGA: The framework for the overall KKT-IGA is shown in Fig. 3, which is dived into three parts: the data part,

⎧min G = min{g (y )} i i ⎪ I ⎪ ∑i = 1 zi ⎪min U = I ⎪ ∑i = 1 xi ei ⎪ ⎧ I ⎪ −βEi ∑i = 1 siεil ⎪ y = E⁎ siεile ⎪ , i = 1, 2, …, I; l = 1, 2, …, L. i I I ⎪ ⎪ ∑i = 1 si ∑i = 1 siεile−βEi ⎪ ⎪ ⎪ y ≥ d min, i = 1, 2, …, I . ⎪ i ⎪ i ⎪ ⎪ β ≥ 0, ⎪ ⎪ ⎪ ⎪ γ ≥ 0, ⎪ ⎪ ⎪ ⎡ ⎤⎡ I ∼⎤ ∼ ⎪max E (F ) = z ρ + ⎢ zi(1 + ri) e θ[Ed(D͠ ) − ∑i = 1 xi(1 − ai)] − 1⎥⎢(x e − y )E (∼ ⎪ p ) + xi Ed(vi)⎥ − Ed(oi ) d i i i i i i d ⎪ ⎪ ⎣ xi (1 − ai) ⎦⎣ ⎦ ⎪ ⎪ ⎧ 0 < x (1 − a ) ≤ s , i = 1, 2, …, I . ⎪ ⎪ i i i ⎪ ⎪ ⎪ ⎨ ⎪ xi ei ≤ yi (1 + γ), i = 1, 2, …, I . ⎪ ⎪ ⎪ ⎪ ∼ ∼ ⎪ ⎪ (1 + ri)[(xi ei − yi )Ed(p ) + xi Ed(vi)] θ[E (D͠ ) − ∑ I x (1 − a )] ⎪ i − λ − μ + ν = 0, i = 1, 2, … , I . ⎪s. t. ⎨ i =1 i ρi + e d ⎪ i i ⎪ ⎪ xi (1 − ai) ⎪ ⎪ ⎪ ⎪ p − λ − μ = 0, ⎪ ⎪ 0 ⎪ 0 ⎪ ⎪ I ⎪ ⎪ ⎪ ∑ zi = Ed(D͠ ), ⎪s. t. ⎪ ⎪ ⎨ ⎪ ⎪ ⎪i = 0 ⎪ ⎪ ⎪ νi[zi − xi (1 − ai)] = 0, i = 1, 2, …, I , ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ zi ≤ xi (1 − ai), i = 1, 2, …, I , ⎪ ⎪ ⎪ μ z = 0, i = 1, 2, …, I . ⎪ ⎪ ⎪ i i ⎪ ⎪ ⎪ zi ≥ 0, i = 0, 1, 2, …, I . ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ μi , νi ≥ 0, i = 0, 1, 2, …, I . ⎪ ⎪ ⎪ λ > 0, μ ≥ 0. ⎪ ⎪ ⎩ 0 ⎩ ⎩

The KKT conditions have successfully switched the electricity sales from a game between the power plants and grid company to a game between the power plants and other power plants. The game can finally achieve an equilibrium called the Cournot–Nash equilibrium, at which point each plant has no incentive to change its output as its current output maximizes profits if other plants do not alter their production levels (Nash, 1951; Hansif et al., 1983). The power plants must strive to reduce the sales price to less than p0 to establish or expand market share. The grid company makes the purchase decisions based on a sales price sort order that reflects the competition results. 2.3.2. KKT-based interactive GA After employing the KKT conditions, the three-level model (17) has been successfully transformed to a bi-level model (19) with Lagrange multipliers, which describes the game between regional authority and power plants with Cournot competition. The interaction of their decisions influences each player and balance is

69

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the regional authority level and the power plants level. The data part, including the input of various parameters and the definition of chromosome representation, is preparatory work. KKT-IGA starts from the initialization. The authority's decision variables (i.e. β and γ) are initialized first, following are the plants' decision variable (i.e. xi) and Lagrange multipliers (i.e. λ), finally the sales (i.e. zi) are initialized. The search for optimal solutions in the power plants level begins with the initialization, which must satisfy the KKT conditions to ensure feasibility. When generating the offsprings with genetic operators, the KKT conditions also must be satisfied and if not repair strategies are applied immediately. If the stopping criteria in plant level are met, the optimal chromosomes are sent back to the authority level for further optimization till the stopping criteria are satisfied. Finally, the best optimal chromosome is output. Though the KKT-IGA technological process is roughly similar to a standard GA, there are inherent differences, especially the chromosome representation, initialization, crossover, and mutation in the power plants level because of the

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J. Xu et al. / Energy Policy 82 (2015) 62–80

particularity of KKT conditions. The details for each step are discussed below. Interactive evolutionary mechanism: An interactive evolutionary mechanism is employed to find the Stackelberg solution (Sakawa and Nishizaki, 2009) for this bi-level model. The regional authority first specifies an allocation strategy, and then each power plant specifies its own strategy so as to optimize the profits maximization objective with full knowledge of the actions of the regional authority and the other plants. Then the optimal response from all

power plants is fed back to regional authority as a baseline to adjust the strategies for optimal objectives. Chromosome representation in the KKT-IGA: The chromosome representation should meet three principles: completeness, soundness, and non-redundancy (Goldberg, 1989). It can be seen that there is close relationship between Lagrange multipliers and decision variables at power plants level due to the KKT conditions, i.e. after KKT conditions, the Lagrange multipliers are intimately linked decision variables on power plants level, i.e. p0 − λ − μ0 = 0;

Fig. 3. Overall procedure for the KKT-IGA.

(0.2929, η4, 0.3389) η4 ∼ N(0.3248, 0.0072)

(0.2946, η3, 0.3409) η3 ∼ N(0.3266, 0.0065)

(0.2223, η2, 0.2421) η2 ∼ N(0.2322, 0.0046)

(0.2152, η1, 0.2258) η1 ∼ N(0.2247, 0.0041)

∼ Unit variable operating and maintenance costs vi (RMB/KWh)

(0.9378, ξ4, 0.9834) ξ4∼N(0.9606,0.0289)

(0.8743, ξ3, 0.9175) ξ3∼N(0.8974,0.0225)

(1.8474, ξ2, 1.9314) ξ2∼N(1.8834,0.0441)

(3.7401, ξ1, 3.9079) ξ1∼N(3.7343,0.0841)

(10 RMB )

30

25

22

23

0.045

0.045

0.037

0.037

8

Profit rate ri (%)

∼ Annual fixed operating and maintenance costs oi

G

max

−G

min

,

T′ =

T − T min T

max

− T min

.

(20)

Let w1 and w2 be the weight of the objective functions G (i.e., minimal allocation satisfactory) and T (i.e., overall carbon efficiency), respectively. They are determined according to the decision makers opinion, reflecting the importance of each objective in the decision makers' mind. Then the fitness function for regional authority can be expresses as

(21)

KKT conditions based initialization: Since there exists inherent relationship between the gens (i.e., between λ, xi and zi) in a chromosome, it is unreasonable to randomly generate all the genes like the stand GA. Therefore, a KKT conditions-based initialization is designed to initialize the chromosomes to guarantee the feasibility of the initial population. Step 1: Set t¼1. Step 2: Initialize β and γ by generating random real numbers [0, 1], [0, β0] and respectively, then within I

I

I

yi = E⁎siεile−βEi ∑i = 1 siεil / ∑i = 1 si ∑i = 1 siεile−βEi . Step 3: Initialize λ by generating a random real number within (0, p0]. If λ < p0 , then initialize z0 = 0, otherwise initialize z0 by generating a random real number within [0, E (D͠ )].

47.9706

45.7026

373.0860

721.2240

d

(104Tonnes )

Emissions baseline

G − G min

fupper = w1G′ + w2T ′.

Capacity price ρi (RMB/ KWh)

650.8299 336.6714 98.7661 103.6674 540.1889 269.3372 79.0128 82.9339

Step 4: Set i¼1. Step 5: Initialize xi by generating a random real number and calculate within (0, min(si /(1 − ai), yi (1 + γ)/ei)], ∼ ∼ Ed(Pi) = ρi + ((1 + ri)[(x iei − yi )Ed(p ) + x iEd(vi)]/x i(1 − ai)).

85.2120

41.4225

10.2903

10.8686

i¼ 2

i¼ 3

i¼ 4

Power supply baseline

Power plant index i

(108 KWh )

Coal Coal LNG LNG i¼ 1 i¼ 2 i¼ 3 i¼ 4

͠

i¼ 1

801.36 829.08 434.32 431.88 2  600 2  300 2  250 2  260

71

∀ i , if Ed(Pi) − λ > 0, then μi = Ed(Pi) − λ , νi = 0, and zi ¼0; if Ed(Pi) − λ < 0, then μi = 0 , νi = λ − Ed(Pi), and zi = x i(1 − ai); if Ed(Pi) − λ = 0, then μi = νi = 0, zi ∈ (0, x i(1 − ai)]. Therefore, only λ and all decision variables (i.e., β, γ, xi and zi) are considered in the chromosome representation, so as to improve the efficiency of GA. They are represented as real number strings of the floating-point numbers, and the structure is shown in Fig. 3. Handling multiple objectives: A weight-sum approach (Gen and Cheng, 2000) is adopted to deal with the two objective functions in the regional authority level. The aggregated objective in the form of a weighted-sum makes it possible to find the optimal Pareto solutions only when the solution set is convex (Xu and Tao, 2012). Naturally, this term can be satisfied, as the constraints in regional authority level are convex. To ensure the validity of the conformity in the multi-objectives, the dimensions must be divided out and the order of magnitude unified before the weightedsum procedure. The regret function formulation method is proved to be a good choice (Xu and Yao, 2011). Suppose that Gmax (Tmax) and Gmin (Tmin) are the maximal and minimal values of objective function G (T) in each generation, respectively, then the regret values are defined as

G′ =

5.32 7.95 2.21 2.15

0.8464 0.9007 0.4441 0.4414

85.2120 41.4225 24.6431 26.0281

Maximum demand dimax

(104 Tonnes)

Minimum demand dimin

Emission coefficient ei (g/ KWh) Capacity (MW) Fuel type

Description Power plant index i

Table 1 The basic information of the power plants.

Power consumption rate ai (%)

Emissions per output Ei (Tonne/ Maximum output si GWh) (108 KWh)

(104 Tonnes)

J. Xu et al. / Energy Policy 82 (2015) 62–80

I

e θ[Ed(D ) −∑i xi(1 − ai)] If Ed(Pi) − λ > 0, initialize zi ¼0; if Ed(Pi) − λ < 0, initialize zi = x i(1 − ai); if Ed(Pi) − λ = 0, initialize zi by generating a random real number within (0, x i(1 − ai)]. Then let i = i + 1. Step 6: If i < I + 1, return to Step 5, and if i = I + 1 and I ∑i = 0 zi = Ed(D͠ )], go to Step 7, otherwise return to Step 3. Step 7: If t¼T, the stopping criterion is met, if t < T let t = t + 1, return to Step 2. Genetic operators in the KKT-IGA: The genetic operators include selection, crossover, and mutation. In the KKT-based interactive GA, changes are made in crossover and mutation. 1. Crossover operations: The KKT-based crossover is similar to the initialization of the KKT-based IGA. The crossover operation in the power plant level is actually done in the previous two parts

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J. Xu et al. / Energy Policy 82 (2015) 62–80

Table 2 The parameters involved in the three-level model proposed. Weights for multiple objectives

Supply-demand adjustment coefficient θ

Electricity price p0 (RMB/KWh)

E⁎(104Tonnes )

w1 = 0.6 , w2 = 0.4

0.001

0.45

1260.38

Total allowances

(i.e. λ and xi) of each chromosome with the rest (i.e., zi) derived under the KKT conditions, which guarantees the feasibility of the child chromosomes. If the child chromosomes do not satisfy the KKT conditions, the sales variables zi are reproduced using new xi and λ in the same child chromosomes through the method discussed in initialization. Otherwise, the terminal condition feasiI bility ∑i = 0 zi = Ed(D͠ ) is checked. If both children are feasible, the parents are replaced, otherwise, the child chromosomes are reproduced. On the other hand, to fully search the feasible region for all possible solutions, the crossover operations in both authority level and power plant level are conducted in the two sections (β and γ, x and λ) of the chromosomes, respectively (Xu et al., 2013). Taking the gens of the authority level as an example. Let pa , pb ∈ (0, 1) be the probability of crossover operation. Generate two random numbers a and b from (0, 1), a < pa and b < pb . Suppose that J1 = (β1, γ1) and J2 = (β2, γ2) are selected as parents, then the crossover operation on J1 and J2 produces two children H1 and H2 satisfying H1 = (aβ1 + (1 − a)β2, bγ1 + (1 − b)γ2) and H2 = (aβ2 + (1 − a)β1, bγ2 + (1 − b)γ1) . 2. Mutation operations: The KKT-based mutation is also different from the operation in the standard GA. Its operation follows KKT conditions. In the standard GA, the mutation can occur in any genes in the whole chromosome, whereas the KKT-based mutation only occurs in the previous two parts (i.e. λ and xi) of each chromosome on power plant level, with the rest (i.e., zi) derived under the KKT conditions to guarantee the offspring be feasible. Let pm be the probability of the crossover operation. Generate a random number m from [0, 1], and m < pm . Suppose that the chromosome J is selected as a parent, then a mutation operation on J produces child H by randomly selecting a mutation direction as follows:

⎧ p1 = 0.5; ⎪1, d=⎨ ⎪ ⎩ 0, p2 = 0.5.

(22)

For each chromosome, a gene is randomly selected. Then let M be a relatively large positive number, and the child chromosome H = J + Md . It is seen that β, γ, xi, and λ all have upper bound, i.e., β ∈ [0, β0], γ ∈ [0, 1], x i ∈ (0, si /(1 − ai)] and λ ∈ (0, p0]. So take

Allowances allocated (10 4 Tonnes) 0.4

900

0.35

700 600 500 400 300

Allowance price ∼ p (RMB/Tonne)

(150.05, ρ, 170.45), where ρ ∼ N(159.85, 24.75)

(50,ζ,90), where ζ ∼ N(65, 23.04)

these bound as the value of M when the relevant gene is selected as the mutation point. If H1 is out of the feasible space, reset M as a random number between 0 and M until a feasible one is found or a given number of cycles are completed. 2.3.3. Multi-round negotiations for allowance allocation The three-level model (17) simulating the power-supply industry CEAAP is transformed to a bi-level model (19) with KKT conditions, and finally solved using a KKT based interactive GA. The tripartite game between the regional authority, power plants and the grid company because of allowances allocation is converted into a Stackelberg game between the regional authority and the power plants with Cournot competition. Inspired by the KKTIGA, an innovative mechanism for multi-round negotiations is used to deal with the power-supply industry CEAAP. This negotiation focuses on the interaction between the regional authority and power plants, both of which must understand their own responsibilities. The regional authority's role is to develop an allocations policy, formulate game rules and organize game procedures, while the plants need to obey the game rules and make rational decisions. The key game rules are as follows: (1) the allocation cap is given; (2) each power plant's information is known by others; (3) historical information and projected generation plans are submitted by a plant to compete with other plants for allowances; (4) plants with a higher historical intensity are required to receive larger reductions; (5) all parties in the game must act as promised. This multi-round negotiation has the following steps. Step 1: The regional authority calculates allowances with a reasonable β value using Eq. (3). The power plants are also notified of the excess emissions level γ . Step 2: Each power plant develops a production plan based on its allowances under the Cournot assumption that other plants maintain output at existing levels to maximize economic profits. Step 3: The regional authority calculates the current overall carbon efficiency according to the data submitted by the plants. If the authority is satisfied with the results, the game is over and the allocations are completed. Otherwise, the authority makes adjustments to the last allocations policy and then Step 2 is repeated in a new game round.

650 600 550

0.3

Power plant 1 Power plant 2 Power plant 3 Power plant 4

500

0.25

450

0.2

400

100

0.05

0

0

value

Power plant 1 Power plant 2 Power plant 3 Power plant 4

350

0.15

300

0.1

200

Allowances allocated (104 Tonnes)

Mimimu degree of satisfaction

1000 800

∼ Electricity Demand D (108KWh)

250

2.3902 value

Fig. 4. The allowances change with the allocation index.

200 150

0

2.3902 value

J. Xu et al. / Energy Policy 82 (2015) 62–80

Carbon emissions (104 Tonnes)

Electricity generation (108 KWh) 85

700

75

600

Power plant 1

65

1.3793

500 400

Power plant 3 Power plant 4

45

200

25

100

value

Power plant 1

1.3791

Power plant 2

1.3789

Power plant 3 Power plant 4

300

35

Electricity output per emission (KWh/Kg) 1.3795

Power plant 2 55

73

1.3787 1.3785 1.3783 1.3781 1.3779 1.3777 1.3775

value

value

Fig. 5. The plants' reactions when no excess emission is allowed.

Step 4: The game is over after finite repeats set in advance. The regional authority chooses a satisfactory allocations policy from all results. In summary, this method makes better use of scattered information and subjective plant initiatives to obtain relatively satisfactory results.

In this section, the Shenzhen ETS is taken as a practical application to explore carbon emission allowance allocation policies and demonstrate the practicality of our optimization method.

average income of 136 422.67 CNY per capita in 2013. On 8 July 2013, the Shenzhen carbon emissions trading market was officially launched, being the first “cap-and-trade” pilot scheme in China. Jiang et al. (2014) gave an overview of the Shenzhen ETS and mentioned that the regulated entities for emissions reductions were industry, public building and the transport sectors. Power plants, as the biggest emitters, are inevitably included. Compared with other ETSs in developed economies, the Shenzhen ETS sets an intensity-based cap on emissions because of the rapid economic growth and the accelerated structural adjustment. The intensity reduction targets for the electricity-supply sector are set at 2%, which is used to determine the allowance cap. Additionally, initial free allowances are allocated using benchmarking.

3.1. Presentation of case problem

3.2. Data collection

With rapid economic development, China's energy consumption, especially electricity consumption, has increased rapidly. Since 2010, China has been the greatest consumer of energy and the greatest emitter of carbon in the world, and has faced enormous pressure in the international negotiations on carbon emissions control and climate change mitigation (Wang et al., 2013). At the Copenhagen climate conference in 2009, the Chinese government pledged that China would reduce carbon emissions intensity (i.e. carbon emissions per unit GDP) by 40–45% based on 2005 levels by 2020. To achieve this target, several regional pilot ETSs have been launched in China, including Beijing, Tianjin, Shanghai, Guangdong, Shenzhen, Chongqing and Hubei, as a trial for a possible national ETS (Wang et al., 2014; Jiang et al., 2014). The seven pilot sites vary from each other but all face allowances allocations. In this part, the Shenzhen ETS is used as an application case to explore the problem. Shenzhen, the first special economic zone in China, is located on the China's south eastern coast, adjoining Hong Kong. It covers an area of 1953 km2 and has a population of 10.63 million, with an

Four power plants were considered which have 2 different power-conversion technologies: plants 1 and 2 are coal-fired plants, and 3 and 4 are LNG-fired plants. Plant 1 is equipped with 2  600 MW supercritical units, plant 2 with 2  300 MW subcritical units, plant 3 with a 2  250 MW S209E gas turbine and plant 4 with a 2  260 MW S209F gas turbine. The basic information for these plants, such as emission coefficients, power consumption rates and operating and maintenance costs, is shown in Table 1. Other parameters involved in the model are shown in Table 2. Most data in Table 1 were obtained from the power plants, except the fixed and variable operating and maintenance costs, which were estimated based on expert consultations as well as the electricity demand and allowance price in Table 2. The electricity price in Table 2 was from the survey for China Southern Grid Company, and the “allocation cap” was calculated to be 1260.38 × 104 Tonnes, according to the total electricity output (i.e., 147.79 × 108 KWh ), total emissions (i. e ., 1187.9833 × 104 Tonnes), and the intensity reduction target (i.e., 2%).

3. Application and results

Electricity generation (108 KWh)

Carbon emissions (104 Tonnes)

Electricity output per emission (KWh/Kg)

790

90

1.3447

690

80

Power plant 1

70

Power plant 1

590

Power plant 2 60

Power plant 3

50

Power plant 4

Power plant 2

490

Power plant 3

390

Power plant 4

1.3445 1.3443 1.3441

40

290

1.3439

30

190

1.3437

20

value

90

value

1.3435

Fig. 6. The plants' reactions when 10% excess emissions is allowed.

value

74

J. Xu et al. / Energy Policy 82 (2015) 62–80

Electricity generation (108 KWh)

Carbon emissions (104 Tonnes)

Electricity output per emission (KWh/Kg)

770

98 88

670

78

Power plant 1

68

Power plant 2 Power plant 3

58

1.3146

Power plant 2

1.3126

470

Power plant 3

1.3106 1.3086

Power plant 4

370

Power plant 4

48

Power plant 1

570

1.3066 1.3046

270

38 28

170

18

70

1.3026 1.3006 1.2986

value

value

value

Fig. 7. The plants' reactions when 20% excess emission is allowed

Electricity generation (108 KWh)

Carbon emissions (10 4 Tonnes)

95

Electricity output per emission (KWh/Kg)

850 750

85

650 75

550

Power plant 1 Power plant 2 Power plant 3 Power plant 4

65 55

1.302 1.3 1.298 1.296 1.294 1.292 1.29 1.288

Power plant 1 Power plant 2 Power plant 3 Power plant 4

450 350 250

45

150

35

50

value

value

value

Fig. 8. The plants' reactions when 30% excess emission is allowed.

Carbon emissions (10 4 Tonnes)

Electricity generation (10 8KWh) 95

800

85

700

Power plant 1 Power plant 2 Power plant 3 Power plant 4

75 65 55

600 500 400

45

300

35

200

25

100

15

1.288221

Power plant 1 Power plant 2 Power plant 3 Power plant 4

1.2882205 1.28822 1.2882195 1.288219 1.2882185

0

value

Electricity output per emission (KWh/Kg)

1.288218

value

value

Fig. 9. The plants' reactions when 40% excess emission is allowed.

Total electricity output (108KWh)

Total carbon emissions (104Tonnes)

161

1260

160

1240

1200

158 157 156

AI=0

1180

AI=2.3902

1160

benchmarking

155 154

1.38

1220

159

1.36

AI=0 AI=2.3902 benchmarking

1140

10

20

30

40

50

1100

AI=0

1.34

AI=2.3902

1.32

benchmarking

1.3

1120 0

Electricity output per emission (KWh/Kg)

1.4

0

10

20

30

40

50

1.28

0

10

20

30

40

50

Fig. 10. The comparative analysis in Shenzhen ETS.

3.3. Parameter selection for the KKT-IGA Many scholars such as Zouei (2002), Dimou and Koumousis

(2003), and Grefenstette (1986) have given suggestions on the proper parameters for GA, including the population size (N), iteration number (I), crossover probability (pc) and mutation

J. Xu et al. / Energy Policy 82 (2015) 62–80

75

Fig. 11. The allocation policy and results for Shenzen ETS.

probability (pm). For example, Liu and Gao (2009) advised that it is suitable that pc ∈ [0.6, 1]. For the population size, there is a tradeoff between it and the evaluation. When a problem has nontrivial evaluation times, a very limited number of search generations evolved at a large population size can take significant computational time. Through a comparison of several sets of parameters, the most suitable parameters in the KKT-IGA in this case were identified as follows: population size N ¼100; iteration number for upper level Iu ¼ 75; iteration number for lower level Iu ¼ 100; mutation probability Pmo = 0.04 , four segmental probabilities of crossover probability are Pa ¼ 0.55 and Pb ¼0.65 for upper level, and Pe ¼ 0.6 and Pd ¼0.5 for lower level. 3.4. Results and analysis To verify the practicality and efficiency of the optimization method for the power-supply industry CEAAP presented in this paper, the proposed KKT conditions and KKT-based interactive genetic algorithm (KKT-IGA) were applied and run on MATLAB 7.0. The focus was to determine the equilibrium points and to summarize the efficient allocation policies. The changes in the allowances each plant obtained and the minimum degree of satisfaction as the allocation index β grows are shown in Fig. 4. It can be seen that only when 0 ≤ β ≤ 2.3902 do the allowances satisfy each plant's minimum demand. For γ, the excess emissions level allowed, consider the following 5 scenarios. 3.4.1. Scenario 1: γ ¼0 In this scenario, the emissions cannot be more than the allowances. Fig. 5 presents each plant's optimal generation strategy

and the actual emissions against a changing allowances level. To maximize economic profits, all power plants strive to gain higher market share and finally reach an equilibrium, at which point plants 1 and 2 have used up the allowances while plants 3 and 4 achieve maximum output. It follows from Fig. 5 that the total electricity output is around 155 × 108 KWh with a gap of 5  108 KWh to meet the demand, and the total emissions are around 1124.5119 × 104 Tonnes. Thus, the carbon efficiency is improved by about 10.8% compared with the baseline (i.e. 1.2441 KWh/kg). 3.4.2. Scenario 2: γ ¼10% Fig. 6 shows each plant's optimal reactions to the changing allowances level when 10% excess emissions are allowed. In contrast to Scenario 1, plants 1 and 2 increase production to generate the maximum allowable emissions, while plants 3 and 4 reduce output to ensure a supply-demand balance. Plants 3 and 4 bid the same price at their respective output levels. It can be concluded from Fig. 6 that as β rises, the total electricity output remains equal to the demand 160 × 108 KWh , the total emissions change little being at around 1190  104 Tonnes, which improves carbon efficiency by around 8.00%. 3.4.3. Scenario 3: γ ¼20% Each power plant's optimal response to the changing allowances level when 20% excess emissions are allowed is presented in Fig. 7. This excess emissions level is enough for power plant 1 to achieve maximum output, but not enough for plant 2. Therefore, plant 1 chooses to achieve maximum output, while plant 2 continues to generate the maximum allowable emissions. Plants 3 and

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Table 3 The comparison results of two allocation methods. Allocation method

Plant type

Plant index

Allowances yi (104 Tonnes )

Degree of satisfaction

Generation xi (108 KWh )

Sales zi (108 KWh )

Emissions ei (104 Tonnes )

Profits Fi (108 RMB )

G

T (KWh/kg)

γ¼ 5% β¼ 0

Coal

i¼ 1 i¼ 2 i¼ 3 i¼ 4 Total

605.7308 294.4524 175.1757 185.0211 1260.3801

0.5924 0.3730 1 1

75.1449 34.3267 24.6431 25.8853 160.0000

636.0173 309.1751 109.4486 114.2499 1168.8910

4.9586 1.8465 1.7457 1.8840 10.4348

0.3730

1.3688

–

79.3672 37.2913 25.2000 26.4541 168.3127

i¼ 1 i¼ 2 i¼ 3 i¼ 4 Total

726.6871 353.2507 87.7551 92.6872 1260.3801

1 1 0.4426 0.4704

85.2120 39.2203 17.4581 18.1098 160.0000

721.2240 353.2507 77.5376 79.9311 1231.9430

6.0695 2.3551 1.0190 1.0760 10.5196

0.4426

1.2988

–

90.0000 42.6076 17.8526 18.5077 168.9679

LNG

Benchmarking (γ ¼ 0)

Coal LNG

Unit index i

Description Maximum demand dimax

Capacity (MW)

Emission coefficient ei (g/KWh)

Power consumption rate ai Emissions per output Ei (Tonne/ GWh) (%)

(10 KWh)

(10 Tonnes)

(104 Tonnes)

i¼ 1 i¼ 2 i¼ 3 i¼ 4 i¼ 5 i¼ 6 i¼ 7

Coal Coal Coal Coal Coal LNG LNG

1000 600 600 300 200 190 390

778.68 808.92 821.52 841.68 888.89 429.44 380.64

5.4 75.00 5.20 7.00 10.00 2.20 2.10

70.95 42.75 42.66 20.92 13.45 13.01 26.73

425.6206 265.2897 269.4220 138.0168 97.1728 41.6252 75.7320

532.0258 331.6122 336.7775 172.5210 121.4660 52.0315 94.6650

Unit index i

Power supply baseline

Emissions baseline

(108 KWh )

(104 Tonnes )

Capacity price ρi (RMB/ KWh)

Profit rate ri (%)

i¼ 1

70.95

584.01

0.045

32

i¼ 2 i¼ 3 i¼ 4 i¼ 5 i¼ 6 i¼ 7

42.75 42.66 20.50 13.00 4.64 10.50

364.01 369.68 185.53 128.40 20.37 40.82

0.8231 0.8514 0.8666 0.9050 0.9877 0.4391 0.3888

0.045 0.045 0.045 0.045 0.037 0.037

30 28 25 25 24 28

Maximum outputsi

Minimum demand dimin

Fuel type

8

4

∼ Annual fixed operating and maintenance costs oi 8

(10 RMB)

∼ Unit variable operating and maintenance costs vi (RMB/KWh)

(3.014, ξ1, 3.154)

(0.1749, η1, 0.2623)

ξ1 ∼ N(3.084, 4.41 × 10−4)

η1 ∼ N(0.2186, 1.69 × 10−4 )

(1.841, ξ2, 1.925)

(0.1814, η2, 0.2721)

ξ2 ∼ N(1.883, 3.24 × 10−4 )

η2 ∼ N(0.2267, 1.75 × 10−4 )

(1.767, ξ3, 1.851)

(0.1841, η3, 0.2762)

ξ3 ∼ N(1.809, 3.24 × 10−4

η3 ∼ N(0.2302, 1.75 × 10−4 )

(0.895, ξ4, 0.939)

(0.1884, η4, 0.2828)

ξ4 ∼ N(1.8834, 2.56 × 10−4 )

η4 ∼ N(0.2356, 1.88 × 10−4

(0.594, ξ5, 0.622)

(0.1825, η5, 0.2738)

ξ5 ∼ N(0.608, 1.21 × 10−4 )

η5 ∼ N(0.2281, 1.78 × 10−4 )

(0.449, ξ6, 0.472)

(0.2584, η6, 0.3876)

ξ6 ∼ N(0.461, 1.21 × 10−4 )

η6 ∼ N(0.3230, 2.25 × 10−4 )

(0.904, ξ7, 0.951)

(0.2297, η7, 0.3446)

ξ7 ∼ N(0.927, 1.42 × 10−4 )

η7 ∼ N(0.2872, 2.59 × 10−4 )

J. Xu et al. / Energy Policy 82 (2015) 62–80

Table 4 Detailed data about basic information of the power units.

J. Xu et al. / Energy Policy 82 (2015) 62–80

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Table 5 The comparison among different allocation policies. Reduction target

1.00% (1716.78) (0.8175) 2.00% (1699.44) (0.8093) 3.00% (1682.10) (0.8010) 4.00% (1664.76) (0.7927) 5.00% (1647.42) (0.7845)

Description

Allocation method

γ ¼5%

γ ¼ 10%

γ = 15%

γ ¼ 20%

γ¼ 25%

γ¼ 30%

β¼ 0 Benchmarking β¼ 0 Benchmarking β¼ 0 Benchmarking

208.22 210.00 1593.32 1681.68 0.7652 0.8008

210.00 210.00 1635.96 1700.29 0.7790 0.8097

210.00 210.00 1674.18 1708.42 0.7972 0.8135

210.00 210.00 1686.75 1711.99 0.8032 0.8152

210.00 210.00 1687.76 1715.27 0.8035 0.8168

210.00 210.00 1687.44 1716.88 0.8035 0.8176

210.00 210.00 1687.44 1716.88 0.8035 0.8176

Output (108 KWh) Emissions (104 Tonnes) Intensity (Tonne/GWh)

β¼ 0 Benchmarking β¼ 0 Benchmarking β¼ 0 Benchmarking

206.60 210.00 1579.04 1676.76 0.7643 0.7985

210.00 210.00 1628.55 1698.56 0.7755 0.8088

210.00 210.00 1665.75 1706.61 0.7932 0.8123

210.00 210.00 1686.23 1711.23 0.8030 0.8149

210.00 210.00 1687.76 1714.47 0.8037 0.8164

210.00 210.00 1687.76 1716.88 0.8037 0.8176

210.00 210.00 1687.76 1716.88 0.8037 0.8176

Output (108 KWh) Emissions (104 Tonnes) Intensity (Tonne/GWh)

β¼ 0 Benchmarking β¼ 0 Benchmarking β¼ 0 Benchmarking

204.87 210.00 1564.62 1670.98 0.7637 0.7957

210.00 210.00 1621.13 1695.65 0.7720 0.8075

210.00 210.00 1657.18 1704.79 0.7891 0.8118

210.00 210.00 1685.21 1710.46 0.8025 0.8145

210.00 210.00 1687.83 1713.66 0.8037 0.8160

210.00 210.00 1687.83 1716.87 0.8037 0.8176

210.00 210.00 1687.83 1716.87 0.8037 0.8176

Output (108 KWh) Emissions (104 Tonnes) Intensity (Tonne/GWh)

β¼ 0 Benchmarking β¼ 0 Benchmarking β¼ 0 Benchmarking

203.20 210.00 1550.27 1663.26 0.7629 0.7920

210.00 210.00 1613.77 1691.85 0.7685 0.8056

210.00 210.00 1648.67 1702.96 0.7851 0.8109

210.00 210.00 1680.50 1709.69 0.8002 0.8141

210.00 210.00 1688.03 1712.86 0.8038 0.8156

210.00 210.00 1688.03 1716.04 0.8038 0.8172

210.00 210.00 1688.03 1716.86 0.8038 0.8176

Output (108 KWh) Emissions (104 Tonnes) Intensity (Tonne/GWh)

β¼ 0 Benchmarking β¼ 0 Benchmarking β¼ 0 Benchmarking

203.20 208.15 1535.92 1647.422 0.7622 0.7915

210.00 210.00 1606.42 1686.27 0.7650 0.8030

210.00 210.00 1640.16 1701.16 0.7810 0.8101

210.00 210.00 1677.24 1708.92 0.798 0.8138

210.00 210.00 1688.24 1712.06 0.8039 0.8153

210.00 210.00 1688.24 1715.20 0.8039 0.8168

210.00 210.00 1688.24 1716.85 0.8039 0.8176

1740 1720 1700 1680 1660 1640 1620 1600 1580 1560

AI=0 AI=0.186 benchmarking

20

30

Electricity output per emission (KWh/Kg)

Total carbon emissions (104Tonnes)

Total electricity output (10 8KWh)

10

γ¼0 Output (108 KWh) Emissions (104 Tonnes) Intensity (Tonne/GWh)

210.5 210 209.5 209 208.5 208 207.5 207 206.5 206

0

Excess emission level

40

1.32 1.3

AI=0 AI=0.186

1.28

benchmarking

1.26

AI=0 AI=0.186 benchmarking

1.24 1.22 1.2

0

10

20

30

40

0

10

20

30

40

Fig. 12. The comparison between different allocation policies.

4 reduce output as in Scenario 2 to maintain equilibrium (i.e. the same bidding prices and supply-demand balance). Fig. 7 implies that with an increasing β value, there is a decrease in total emissions from 1231.9864 × 104 Tonnes to 1216.6613 × 104 Tonnes, which is a carbon efficiency improvement of between 4.39% and 5.71%. 3.4.4. Scenario 4: γ ¼30% Fig. 8 shows each plant's optimal response to the changing allowances level when 30% excess emissions are permitted. This condition makes it possible for plant 2 to achieve maximum output when β < 0.7. On this occasion, both plants 1 and 2 choose to operate at maximum output when β < 0.7, as when β rises plant 2 reduces output to satisfy the emissions constraint. Regardless of the β value, plants 3 and 4 provide the remaining electricity needed to meet the demand with equal bidding prices. Under this scenario, total emissions fall from 1242.0249 × 104 Tonnes to

1230.3558 × 104 Tonnes with the growth of β, leading to carbon efficiency increases of between 3.55% and 4.53%. 3.4.5. Scenario 5: γ ¼40% If a 40% excess emissions level is allowed, all power plants are able to achieve maximum output in spite of the β value, which is equivalent to a no emissions cap. Each plant's optimal actions as the allowances levels change are shown in Fig. 9. Despite the level of the β value, plants 1 and 2 remain at maximum production level, while plants 3 and 4 develop generation plans to satisfy the remaining electricity demand with the same bidding price. It should be noted that the results under γ > 40% are consistent with those shown in Fig. 9. Therefore, when γ ≥ 40% (or no emissions limits), the total emissions are about 1242.0245 × 104 Tonnes, and the carbon efficiency is improved by 3.55% compared to the baseline.

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J. Xu et al. / Energy Policy 82 (2015) 62–80

Fig. 10 compares the allocation results from the different methods under different excess emissions levels. It suggests that the influence of the emissions limitations dominates the results in contrast to the allocation index. When γ < 5% , the total electricity output is unable to satisfy demand, but increases as γ rises until the demand is met. At the same time, the total carbon emissions increase until γ = 40% , and the greatest gap is reached at 117 × 104 Tonnes. The carbon efficiency decreases accordingly but is still improved compared with the baseline. In summary, when γ ¼5%, the electricity demand is satisfied and total emissions are relatively low, leading to a higher carbon efficiency. Further, as the weights considered here are w1 ¼0.6 and w2 ¼0.4, the importance is put on the allocation satisfaction, as the equality principle is more important in the beginning of emissions control. Beside, the changes in the β value have little influence on carbon efficiency, so β ¼ 0 is appreciated. Therefore, γ ¼ 5% and β ¼0 are chosen as the optimal solutions(see Fig. 11). 3.5. Effectiveness analysis Free allowances are allocated using benchmarking for power plants in the Shenzhen ETS at present (Jiang et al., 2014). The allocation results based on this method under different excess emission levels can be found in Fig. 10. It suggests that the electricity demand can be satisfied regardless of the emissions limitation levels, but total emissions are minimized when no excess emissions are allowed, which indicates that the emissions limitations make a difference in the benchmarking method. In particular, when comparing the optimal results from γ ¼ 0 with those in this paper, the latter is more optimal (shown in Fig. 10 and Table 3), because of the nearly 63 × 104 Tonnes fewer emissions at the same output level. This proves the superiority and effectiveness of the allocation model proposed in this paper. Comparing the two allocation methods in Table 3, it can be seen that the LNG-fired power plants could obtain more allowances using the allocations method proposed in this paper (called plan 1) in contrast with benchmarking allocations (called plan 2), while for the coal-fired plants, the situation is the reverse. This affects the electricity generation distribution and the market share. Under capacity and emissions constraints, the electricity generation and sales from LNG-fired plants in plan 1 are greater than those in plan 2, but for the coal-fired plants the situation is the opposite. As a result, the total emissions in plan 1 are less than those in plan 2, leading to a higher carbon efficiency. This is because of the low carbon intensity of LNG-fired power plants and the high carbon intensity of coal-fired power plants. Therefore, including emissions limitations is appropriate for the allocation of relatively more allowances to LNG-fired power plants to lower carbon intensity.

4. Discussion The above results indicate that emissions limitations play a vital role in emissions mitigation, and allocating additional allowances to a plant with lower carbon intensity could increase its output and improve carbon efficiency. Therefore, a combination of the two policies would be able to balance electricity output and carbon emissions, i.e. emissions are effectively controlled while guaranteeing output to meet demand. This conclusion was derived from a specific case. To verify the generality, another set of more general data (Table 4) were applied check the viability. The data were estimated based on published papers (Zhou et al., 2014; IPCC, 2013) and actual surveys for power plants in China, except the fixed and variable operating costs, which were based on expert

consultations. In this example, power plants were replaced by power units and 7 different units were considered. They were a 1000 MW ultra supercritical (USC) coal-fired unit, a 600 MW USC coal-fired unit, a 600 MW supercritical coal-fired unit, a 300 MW subcritical coal-fired unit, a 200 MW circulating fluidized bed (CFB) coal-fired unit, a 190 MW S209E LNG-fired unit, and a 390 MW S209F LNG-fired unit. The present carbon intensity was calculated at 0.82577 Tonne/GWh. The fuzzy random variable was (201.55, ρ , 221.34), where for electricity demand D͠ ∼ ρ ∼ N(210.69, 9). The fuzzy random variable for allowances price p was (25, ζ , 90), where ζ ∼ N(55, 25). In this case, 5 intensity reduction targets (i.e. 1%, 2%, 3%, 4% and 5%) and 7 allowable excess emissions levels (i.e. γ ¼0, γ ¼5%, γ ¼10%, γ ¼ 15%, γ ¼20%, γ ¼25%, and γ ¼30%) were considered. The 5 different intensity reduction targets led to 5 different allocation caps, as shown in Table 5. By applying the same proposed solution approach, Table 5 lists the allocations results for the two allocation methods (allocation index β ¼ 0 and benchmarking) under 35 scenarios. Regardless of the allocation method, the total emissions decreased as the intensity reduction target rose under the same emissions constraints, and increased when the emissions limitations were loosened under the same reduction target. The changes in total emissions resulting from the emissions limitations were all significant despite the allocation caps. The differences because of the reduction targets, however, varied little when the emissions limitations were too unconstrained to be of no limit. Therefore, it can be seen that emissions limitations are important for emissions reduction. When comparing the two allocation methods, we found that there were less total emissions and higher carbon intensities in β ¼ 0 than in the benchmarking allocation under the 35 scenarios. This implies that the allocation method proposed in this paper is more successful because of the greater allowances given to LNG-fired power plants. Further, the results of β ¼ 0, β ¼ 0.186 and the benchmarking allocation under different excess emissions levels when a reduction target was 2% are presented in Fig. 12, which also indicates that an appropriate emissions limitation is a smart strategy, and allocating additional allowances to a plant with a lower carbon intensity is helpful. Note that β was limited within [0, 0.186] so as to satisfy each power unit's minimum allowances demand. Therefore, the results from the Shenzhen case can be more widely applied. In fact, these results were due to the competition for greater profits between the power plants, so can be generally extended. Under the “bidding on the power net” mechanism, coalfired power plants have a competitive advantage because of their lower generation costs. As a result, they are able to maximize electricity generation and gain maximum profits as long as they abide by the capacity and emissions allowable. LNG-fired power plants, however, have a disadvantageous position because of their higher generation costs. Under a supply-demand relationship, they are only able to maximize profits by providing the remaining electricity to satisfy demand. Therefore, establishing emissions limitations restricts coal-fired plant activities and allows for the allocation of additional allowances to LNG-fired plants to improve their market share. Consequently, total emissions are controlled, electricity demand is satisfied, and carbon intensity achieves the reduction targets. All in all, the game between the power plants has a significant impact on the allocation results, which needs to be considered when regional authorities decide on allocations policies.

5. Conclusions and policy implications This paper studied the power-supply industry CEAAP and proposed a three-level multi-objective mathematical model based

J. Xu et al. / Energy Policy 82 (2015) 62–80

on a consideration of reactions from the power plants, and even the grid company. Compared with the traditional allocation model, this model can reflect the interaction of mutual restriction of these decision makers at different levels, and help decision makers to adjust decisions according to the changes from other decision makers. The KKT conditions were introduced to transform the three-level model to a bi-level model, which also converted the tripartite collaborative competition into a game between the regional authority and the power plants. Then a KKT-based interactive genetic algorithm was applied to simulate the interaction between the regional authority and the power plants to find the equilibrium. The model and solution approaches are derived from the allocation problem and in turn to solve the problem. Besides, fuzzy random theory is employed to deal with the uncertainties during the allocation, which has a higher validity than random approach and a higher accuracy than fuzzy method, generating high cost. A case study at the Shenzhen ETS demonstrated that the proposed method has better results compared to the “benchmarking” method. The effects of carbon emissions allowance allocation policies, such as emission limitations, allocation methods, and allocation caps, on total electricity output, total emissions and carbon efficiency were also examined in this work. The results showed that emissions limitations had the greatest impact compared to allocation methods and caps. Further, it was demonstrated that under the same allowable excess emissions levels, allocating increased allowances to lower carbon intensity plants was useful for emissions reduction. These results contribute to the literature by assisting regional authorities to determine optimal carbon allowances allocation policies. From this research it can be concluded that policies targeting emissions limitations should be strengthened. If there were no emissions constraints or the constraints were too loose, high carbon intensity power plants would maximize output with no regard for the level of emissions as the lower generation costs would assist these plants gain greater market share when “bidding on the power net”. However, if the limitations are too tight, there could be a shortage of electricity because the capacity of the low carbon intensity plants may be not great enough to meet demand. When considering the competitive relationship between the power plants, it is crucial to set an appropriate emissions limit, with an excess emissions level between 5% and 15% allowed. Second, allocations policies could be biased toward those plants with lower carbon intensity, such as LNG-fired plants. Under the same emissions limitations levels, providing lower carbon intensity plants with more allowances could enhance their output and increase their market share, thus improving overall carbon efficiency. An efficient allocation of carbon emissions could control coal-fired plants and help improve supplies from LNG-fired plants, which would not only benefit the environment protection, but also contribute to the balanced development of the electricity market. The competitiveness of power plants could be protected against the adverse impact of allocation policies in the following ways. Coal-fired power plants dominate the market because of their low generation costs, yet their high carbon intensity means that these plants are inferior in the competition for allowances. For this reason, coal-fired plants need to reduce their carbon emissions intensity by investing in advanced technologies such as coal pretreatment and stable-combustion technology, or employing carbon capture methods such as pre-combustion capture, oxygenenriched combustion and post-combustion capture. For LNG-fired power plants, however, the situation is the opposite. These plants need to reduce generation costs and, as the high LNG price is beyond their control, they need to develop management efficiencies such as strict supervision of the production process, reducing waste or a flexible use of the workforce. In a word, both technical improvements and efficiency management are necessary

79

for power plants to gain competitive advantage. Further, while there is a need for the development of a comprehensive plan for a low carbon electricity-supply system, for existing power plants, an efficient carbon emissions allowance allocations policy is essential. However, the future of the electricity generation market lies in a new focus on renewable energies such as solar, wind, and wave power. Therefore, management control and technical innovation must be combined to build future low carbon electricity-supply systems.

Acknowledgments This research was supported by the Programs of NSFC (Grant nos. 70831005, 71401114) and 985 Program of Sichuan University Innovative Research Base for Economic Development and Management, and the Research Foundation of Ministry of Education for the Doctoral Program of Higher Education of China (Grant no. 20130181110063). The authors would like to give our greatest appreciation to the editors and anonymous referees for their helpful and constructive comments and suggestions, which have helped to improve this paper.

References Chang, C.C., Lai, T.C., 2013. Carbon allowance allocation in the transportation industry. Energy Policy 63, 1091–1097. Chappin, E.J.L., 2006. Carbon Dioxide Emission Trade Impact on Power Generation Portfolio, Agent-based Modelling to Elucidate Influences of Emission Trading on Investments in Dutch Electricity Generation (Master Thesis). Delft University of Technology, Delft. Chen, W.T., et al., 2010. A two-stage inexact-stochastic programming model for planning carbondioxide emission trading under uncertainty. Appl. Energy 87, 1033–1047. Chen, C., et al., 2013. An inexact robust optimization method for supporting carbon dioxide emissions management in regional electric-power systems. Energy Econ. 40, 441–456. Clo, S., 2009. The effectiveness of the EU emission trading scheme. Clim. Policy 9, 227–241. Coase, R.H., 1960. The problem of social cost. J. Int. Econ. 3, 1–44. Cong, R.G., Brady, M., 2012. How to design a targeted agricultural subsidy system: efficiency or equity?. PLoS One 7, e41125. Cong, R.G., Wei, Y.M., 2010a. Potential impact of (CET) carbon emissions trading on Chinas power sector: a perspective from different allowance allocation options. Energy 35, 3921–3931. Cong, R.G., Wei, Y.M., 2010b. Auction design for the allocation of carbon emission allowances: uniform or discriminatory price? Int. J. Energy Environ. 1, 533–546. Cong, R.G., Wei, Y.M., 2012. Experimental comparison of impact of auction format on carbon allowance market. Renew. Sustain. Energy Rev. 16, 4148–4156. Dimou, C.K., Koumousis, V.K., 2003. Genetic algorithms in competitive environments. J. Comput. Civil Eng. 17, 142–149. Gen, M., Cheng, R.W., 2000. Genetic Algorithms and Engineering Optimization. John Wiley & Sons, New York; USA. Gil, M.Á., 2006. Overview on the development of fuzzy random variables. Fuzzy Set Syst. 157, 2546–2557. Goldberg, D., 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Boston, USA. Grefenstette, J., 1986. Optimization of control parameters for genetic algorithms. IEEE Trans. Syst. Man Cybern. 16, 122–128. Grubb, M., 1990. The greenhouse effect: negotiating targets. Int. Aff. 66 (1), 67–89. Grubler, A., Nakicenovic, N., 1994. International Burden Sharing in Greenhouse Gas Reduction. International Institute for Applied Systems Analysis, Laxenburg, Austria. Hahn, R.W., 2009. Greenhouse gas auctions and taxes: some political economy considerations. Rev. Environ. Econ. Policy 3 (2), 167–188. Hansif, D.S., et al., 1983. Stackelberg–Nash–Cournot equilibria: characterizations and computations. Oper. Res. 31, 253–276. Heilpern, S., 1992. The expected value of a fuzzy number. Fuzzy Set Syst. 47, 81–86. Hejazia, S.R., et al., 2002. Linear bilevel programming solution by genetic algorithm. Comput. Oper. Res. 29, 1913–1925. Hong, T., et al., 2014. Benchmarks as a tool for free allocation through comparison with similar projects: focused on multi-family housing complex. Appl. Energy 114, 663–675. IEA, 2012. Key World Energy Statistic.〈http://www.iea.org/publications/freepublications/ publication/name31287,en.html〉 (Retrieved Date November 25, 2012). IPCC, 2013. Summary for Policy Makers, Concentrations of Atmospheric Greenhouse Gases IPCC TAR WG1. Jiang, J.J., et al., 2014. The construction of Shenzhen's carbon emission trading scheme. Energy policy 75, 17–21. Keohane, N.O., 2009. Cap and trade, rehabilitated: using tradable permits to control U.S. greenhouse gases. Rev. Environ. Econ. Policy 3 (1), 42–62. Kruse, R., Meyer, K.D., 1987. Statistics with Vague Data. Reidel D Publishing Company, Dordrecht, Netherlands.

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Kwakernaak, H., 1978a. Fuzzy random variables-I. Definitions and theorems. Inf. Sci. 15, 1–29. Kwakernaak, H., 1978b. Fuzzy random variables-II, Algorithms and examples for the discrete case. Inf. Sci. 17, 253–278. Liu, L.Z., Gao, X., 2009. Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm. Appl. Math. Model. 33, 3926–3935. Majumdar, J., Bhunia, A.K., 2007. Elitist genetic algorithm for assignment problem with imprecise goal. Eur. J. Oper. Res. 177, 684–692. Nash, J.F., 1951. Non-cooperative games. Ann. Math. 54, 286–295. Ottino, J.M., 2004. Engineering complex systems. Nature 427, 399. Park, J.W., et al., 2012. Permit allocation in emissions trading using the Boltzmann distribution. Physica A 391, 4883–4890. Phylipsen, G.J.M., et al., 1998. A Triptych sectoral approach to burden differentiation; GHG emissions in the European bubble. Energy Policy 26 (12), 929–943. Peters, G.P., et al., 2013. The challenge to keep global warming below 2 °C. Nat. Clim. Change 3, 4–6. Reif, F., 1965. Fundamentals of Statistical and Thermal Physics. McGraw-Hill, New York, USA. Sakawa, M., Nishizaki, I., 2009. Cooperative and Noncooperative Multi-Level Programming. Springer, New York, USA. Sinha, S., Sinha, S.B., 2002. KKT transformation approach for multi-objective multi-level linear programming problems. Eur. J. Oper. Res. 143, 19–31. Stephen, B., Lieven, V., 2004. Convex Optimization. Cambridge University Press, London, England. Wang, K., et al., 2013. Regional allocationof CO2 emissions allowanceoverprovincesin China by 2020. Energy Policy 54, 214–229. Wang, D., et al., 2014. Emissions trading in China: progress and prospects. Energy Policy 75, 9–16. Wannier, G.H., 1987. Statistical Physics. Dover Publications, New York. WMO–The World Meteorological Organisation, 2013. The Global Climate 2001–2010: A Decade of Climate Extremes Summery Report. 〈https://www.wmo.int/pages/media centre/press_releases/pr_976_en.html〉.

Xu, J.P., Yao, L.M., 2011. Random-like Multiple Objective Decision Making. Springer-Verlag, Berlin, German. Xu, J.P., Tao, Z.M., 2012. A class of multi-objective equilibrium chance maximization model with twofold random phenomenon and its application to hydropower station operation. Math. Comput. Simul. 85, 11–33. Xu, J.P., et al., 2013. Bilevel optimization of regional water resources allocation problem under fuzzy random environment. J. Water Resour. Plan. Manag. 139, 246–264. Xu, J.P., et al., 2014a. Innovative Approaches Towards Low Carbon Economics-Regional Development Cybernetics. Springer-Verlag, Berlin, Germany. Xu, J.P., et al., 2014b. Water Allocation Modelling and Policy Simulation for the Min River Basin of China under Changing Climatic Conditions. Research Presentation, July 16, 2014, Spain, Barcelona, INFORMS. Yi, W., et al., 2011. How can China reach its CO2 intensity reduction targets by 2020: a regional allocation based on equity and development. Energy Policy 39, 2407–2415. Yu, S.W., et al., 2014. Provincial allocation of carbon emission reduction targets in China: an approach based on improved fuzzy cluster and Shapley. Energy Policy 66, 630–644. Zeng, et al., 2014. Antithetic method-based particle swarm optimization for a queuing network problem with fuzzy data in concrete transportation systems. Comput. Aided Civil Infrastruct. Eng. 29, 771–800. Zhang, Z.X., Li, Y.L., 2011. The impact of carbon tax on economic growth in China. Energy Proc. 5, 1757–1761. Zhou, Y., et al., 2014. Integrated modeling approach for sustainable municipal energy system planning and management: a case study of Shenzhen, China. J. Clean. Prod. 75, 143–156. Zhu, Y., et al., 2013. Planning carbon emission trading for Beijings electric power systems under dual uncertainties. Renew. Sustain. Energy Rev. 23, 113–128. Zouei, P.P., 2002. Genetic algorithm for solving site layout problem with unequal-size and constrained facilities. J. Comput. Civil Eng. 16, 143–151.