Research on Day-Ahead Optimal Scheduling Considering Carbon Emission Allowance and Carbon Trading

Abstract

In the context of the marketization of carbon trading in the power system, it is of great theoretical and practical significance to study a scientific and effective carbon emission quota allocation strategy. To solve this problem, under the current situation of large-scale access to new energy, considering the limitations of the carbon emissions from different emission subjects plus the construction of a carbon trading model among the emission subjects, a day-ahead optimal scheduling method that takes carbon emission quotas and carbon trading into account is proposed. Firstly, carbon transaction cost models of thermal power and wind power are constructed, respectively, and a carbon emission quota allocation strategy based on the entropy method is proposed to redistribute the weights of baseline emission factors for the regional power grid. Then, considering the additional carbon emissions of conventional thermal power units caused by wind power access, the carbon trading costs of different types of generation units are calculated on the basis of carbon trading price prediction. Thereafter, a day-ahead optimal scheduling model considering carbon emissions trading is constructed with the objective of minimizing the total cost of the system in the scheduling period. The model is solved as an MINLP problem based on MATLAB 2016a software utilizing CPLEX 12.4. Simulation results verify the correctness and effectiveness of the proposed method.

1. Introduction

As the world’s second largest economy [1], China’s carbon emissions have continued to grow in recent years, from 489 million tons in 1965 to 9.123 billion tons in 2016, an increase of nearly 20 times [2,3]. Among them, more than 40% of its carbon emissions are caused by fossil fuel combustion in the process of power generation [4]. Therefore, it is necessary to introduce the Carbon Emission Trading (CET) mechanism in the power industry to limit its carbon emissions. As an important part of power system operation decision making, day-ahead optimal dispatch is bound to be affected by the introduction of carbon emission trading mechanism. Therefore, it is of great theoretical and practical significance to study the day-ahead optimal dispatch method of power system considering the carbon emission trading mechanism.

At present, the research on unit commitment considering energy saving, carbon reduction, and synergy mainly originates from the perspective of carbon emissions and carbon transaction costs, and constructs the corresponding decision making model. Reference [5] proposes a low-carbon economic dispatch model for power systems considering the combination of generalized energy storage and carbon capture equipment to increase the deep peak regulation margin of units and reduce carbon emissions during peak load hours. In reference [6], based on the calculation of carbon emissions, a multi-objective generation dispatching optimization model based on carbon emissions was established, and an interactive minimax stepwise tolerance constraint method is proposed to solve the model. Reference [7] established a multi-objective mixed chance-constrained unit commitment model with random variables by considering the impact of carbon emissions in both the objective function and the priority index of unit start-up and shutdown. Reference [8] designed a day-ahead scheduling framework for demand-side reserve and established an optimal scheduling model considering carbon emission constraints. Taking carbon emission as the optimization target has improved the economy and environmental protection of power system optimal dispatch to a certain extent. However, with the advancement of the electricity market, it is not in line with the current situation of the carbon trade market to only add a carbon reduction target to the dispatch decision model. Therefore, some studies have proposed considering carbon trading mechanisms in the process of power system optimal dispatch, so as to achieve the goal of energy saving and carbon reduction. Reference [9] introduced carbon transaction costs into the planning model of integrated energy system (IES), proposed a reward-penalty ladder carbon trading model, and analyzed the impact of carbon transaction costs on IES planning and operation. Reference [10] studied the low carbon and economy of IES under the stepped carbon trading mechanism considering the two-stage operation of electricity to gas. Reference [11] compared the traditional carbon trading mechanism with the stepped carbon trading mechanism and explained the rationality of introducing the stepped carbon trading mechanism into IES. In reference [12], an economic dispatch problem including wind power and carbon transaction cost was proposed on the assumption that wind power prediction follows the Weibull distribution. Taking CO2 emission as a dispatchable resource and considering low-carbon power technology, carbon transaction cost, and carbon constraint, a preliminary model of low-carbon power dispatching decision, was established in reference [13] to coordinate “power balance” and “carbon balance” in power dispatching. The above optimal dispatch method of power systems considering carbon trading mechanism improves the effectiveness of decision making to a certain extent, but it does not consider the impact of allocating carbon emission quotas on day-ahead optimal dispatch and overall system emissions.

At present, the allocation of carbon emission quotas in domestic power systems mostly adopts the free quota mechanism, and the existing free quota mechanism mainly includes the historical method and the baseline method [14]. However, the historical emission method is based on the enterprise’s own historical emission situation to issue quotas. This method is directly based on the emission reduction results, which is more mandatory, and cannot take into account production efficiency. Compared with the historical method, the baseline method allocates quotas from the perspective of carbon emissions per unit of electricity, which avoids the problem of “whipping fast cattle” in the historical method. The allocation method is more flexible and reasonable, but the weighted average of marginal emission factors of electricity and marginal emission factors of capacity is too subjective [15,16]. Therefore, although the above literature considers the impact of carbon emission quotas, there are still some limitations in the model of quota allocation.

To summarize, in the context of large-scale access to new energy, this paper proposes a day-ahead optimal scheduling method considering carbon emission quota and carbon trading, also considering the restriction of carbon emissions of emission subjects and the establishment of carbon trading model among emission subjects. Firstly, the carbon transaction cost models of thermal power and wind power are constructed, respectively, and a carbon emission quota allocation strategy based on the entropy method is proposed to redistribute the weights of the baseline emission factors of regional power grid. Then, considering the additional carbon emissions of conventional thermal power units caused by wind power access, the carbon trading costs of different types of units are calculated on the basis of carbon trading price prediction. Thereafter, a day-ahead optimal scheduling model considering carbon emission trading is constructed with the optimization objective of minimizing the total cost of the system in the scheduling period. The model is solved as a MINLP problem based on MATLAB 2016a software utilizing CPLEX 12.4. Compared with the existing research, the main contributions of this paper include:

(1)

The carbon emission quota allocation strategy based on the entropy method, to a certain extent, avoids the subjective processing method of the weighted average of the marginal emission factor of electricity and the marginal emission factor of capacity, and reduces the carbon emission of the system by limiting the quota of high-emission units within a certain range;

(2)

Considering the calculation of the hidden carbon emission of wind power after the wind power is connected enables the wind power to participate in carbon trading to obtain benefits to offset a part of the carbon trading cost of a thermal power unit and preferentially dispatch the unit with a low carbon emission factor in a dispatching model, thereby reducing the total operation cost of the system.

Simulation results verify the correctness and effectiveness of the proposed method.

2. Carbon Emission Quota Allocation Method Based on the Entropy Method

2.1. Traditional Carbon Credit Allocation Method

In the power system carbon trade market, if the initial allocation of carbon emissions is too low it will limit the enthusiasm of power generation enterprises, which is not conducive to social or economic development. However, if the carbon emission quota is too high, the corresponding emission reduction effect cannot be achieved, which is not in line with the medium and long-term development goals of carbon peak and carbon neutrality proposed by the country [13]. In order to mobilize the enthusiasm of emission reduction on the power supply side, the allocation of carbon emission quotas in the power system mostly adopts the free quota mechanism, which mainly includes the historical method and the baseline method [14].

(1)

Historical method

The historical method is based on the historical average carbon emissions of generating units, and then determines the carbon emission credits allocated to the units in the future so that the carbon emission credits allocated to the units are proportional to their historical carbon emissions [15]. The carbon emission quota of unit i according to the historical method is:

$$Q_i=\frac{E_i^b}{E^b}\times Q$$

(1)

where: $E_i^{\mathrm{b}}$ is the carbon emissions of unit i; $E_i^{\mathrm{b}}$ is in the benchmark case; $Q$ is the total amount of carbon credits that can be allocated.

However, the historical method has the following problems: Firstly, it is difficult to obtain valuable historical emission data for new units or units taking emission reduction measures (such as carbon capture power plant units); Secondly, the carbon emission quota obtained by the unit is positively correlated with historical emissions [16]. The higher the historical emission, the more the carbon emission quota of the unit is. In the long run, the emission reduction effect of the historical method is not obvious.

(2)

Baseline method

The baseline method determines the allocation quota of each unit according to the unit capacity and fuel type [17] and allocates the quota according to actual power generation. The carbon emission quota Q_i of unit i according to the baseline method is:

$$Q_i=\eta P_i\Delta t$$

(2)

where: $\eta$ is the carbon emission factor of unit electricity of the unit; $P_i$ indicates the output of unit i; $\Delta t$ is the time step.

The baseline method generally uses the regional grid baseline emission factors (electricity marginal emission factor and capacity marginal emission factor) as the basis for the allocation of credits, where the electricity marginal emission factors are calculated based on total net power generation, fuel type and total fuel consumption of all units (excluding units with low operating costs and units that must be operated) [18,19]. The specific calculation formula is:

$$E{F}_{OM}=\frac{{\displaystyle {\sum }_i\left(F{C}_i\times NC{V}_i\times E{F}_i\right)}}{EG}$$

(3)

where: i is the type of fuel; $EG$ is the total electricity except for the low operating cost and the units that must be operated; $F{C}_i$ indicates the total consumption of fuel i by the unit; $NC{V}_i$ represents the average net calorific value of fuel i; $E{F}_i$ is the emission factor of fuel i.

The capacity marginal emission factor is obtained from the weighted average of the power supply emission factors of the selected m new units with the power quantity as the weight, and the calculation formula is as follows:

$$E{F}_{\mathrm{BM}}=\frac{{\displaystyle {\sum }_m(E{G}_m\times E{F}_{EL,m})}}{{\displaystyle {\sum }_{m}E{G}_m}}$$

(4)

where: $E{G}_m$ represents the net power generation of the m-th newly added unit; $E{F}_{EL,m}$ indicates the emission factor per unit of electricity of the m-th newly added unit.

Compared with the historical method, the baseline method allocates quotas from the perspective of carbon emissions per unit of electricity, avoiding the problem of “whipping fast cattle” in the historical method, and the allocation method is more flexible and reasonable.

2.2. Carbon Emission Quota Allocation Strategy Based on the Entropy Method

The baseline method avoids the problems of the historical method and is more conducive to emission reduction than the historical method. However, the weighted average of marginal emission factors of electricity consumption and capacity is too subjective. Therefore, this section proposes a carbon emission quota allocation strategy based on the entropy method. The entropy method is essentially an objective weighting method, and its core concept is to determine the weight of different indicators from the data.

For n units, m emission factors, using $x_{i,j}$ represents the j-th emission factor of unit i ($i=1,2,\cdots ,n$, $j=1,2,\cdots ,m$), determining the carbon emission quota based on the entropy method, the specific steps are as follows:

Step 1: Acquiring an electric quantity marginal emission factor and a capacity marginal emission factor of i units;

Step 2: Before calculating the carbon emission quota coefficient, it is necessary to perform normalization processing; that is, to convert the absolute value of the index into a relative value, specifically.

$$r_{i,j}=\frac{x_{i,j}-\min (x_{1,j},x_{2,j},\cdots ,x_{n,j})}{\max (x_{1,j},x_{2,j},\cdots ,x_{n,j})-\min (x_{1,j},x_{2,j},\cdots ,x_{n,j})}$$

(5)

here: $r_{i,j}$ express $x_{i,j}$ normalized value.

Step 3: Calculating the proportion of the i-th unit in the j-th emission factor.

$$p_{i,j}=\frac{r_{i,j}}{{\displaystyle \sum _{i=1}^n{r}_{i,j}}}$$

(6)

where: $p_{i,j}$ is the proportion of the i-th unit in the emission factor j under the j-th emission factor.

Step 4: Calculating the information entropy of each emission factor.

$$s_j=-\frac{1}{\ln n}{\displaystyle \sum _{i=1}^n{p}_{i,j}}\ln p_{i,j}$$

(7)

where: $s_j$ represents the information entropy of the j-th emission factor.

Step 5: Determining the weight corresponding to each emission factor.

$$w_j=\frac{1-s_j}{{\displaystyle \sum _{j=1}^m\left(1-s_j\right)}}$$

(8)

where: $w_j$ is the weight corresponding to the j-th emission factor.

Step 6: Calculating the carbon emission quota coefficient corresponding to group i.

$$e_i={\displaystyle \sum _{j=1}^m{w}_j{r}_{i,j}}$$

(9)

where: $e_i$ is the carbon emission quota coefficient corresponding to the i-th unit.

Step 7: Calculating the carbon emission quota of the group according to the carbon emission quota coefficient obtained in step 6. For thermal power units participating in carbon trading, the allocated carbon emission credits are shown in formula (10):

$$Q_{\mathrm{G}i,t}=e_i{P}_{\mathrm{G}i,t}△t$$

(10)

where: $\Delta t$ is the time step.

In addition, under the development trend of clean energy systems, the study of initial carbon emission quota allocation mechanisms oriented by intermittent energy generation has a positive effect on promoting clean energy consumption [20], but the volatility of intermittent energy output leads to essential differences in carbon emission quota allocation between intermittent energy generation and thermal power units [21]. Taking wind power as an example, this section calculates the carbon emission quota $Q_{\mathrm{W},t}$ of wind power by combining the carbon emission quota coefficient per unit electricity of thermal power and the prediction error of wind power, specifically:

$$Q_{\mathrm{W},t}=e_i(P_{\mathrm{W},t}+{\xi }_t)\Delta t$$

(11)

where: $P_{\mathrm{W},t}$ is the predicted value of wind power in time interval t; ${\xi }_t$ represents the wind power forecast error in time interval t.

Wind power forecast error ${\xi }_t\sim N(0,{\delta }_{\mathrm{W},t}^2)$, the calculation formula of Standard deviation ${\delta }_{\mathrm{W},t}$ is [14]:

$${\delta }_{\mathrm{W},t}=0.2P_{\mathrm{W},t}+0.02P_{\mathrm{WT}}$$

(12)

where: $P_{\mathrm{WT}}$ is the total installed capacity of wind power.

3. Construction of Day-Ahead Optimal Scheduling Model Considering Carbon Emission Trading

3.1. Carbon Trading Costs for Different Types of Power Generation

(1)

Thermal power carbon transaction cost

The participation of thermal power in carbon trading incurs additional costs, specifically:

$$F{C}_{\mathrm{G}i,t}=p_t\left(E_{\mathrm{G}i,t}-Q_{\mathrm{G}i,t}\right)$$

(13)

where: $F{C}_{\mathrm{G}i,t}$ represents the carbon transaction cost of thermal power unit i in time period t; $E_{\mathrm{G}i,t}$ is the actual carbon emission of unit i in time period t, specifically, $E_{i,t}={\mu }_i{P}_{i,t}{}^2+{\nu }_i{P}_{i,t}+{\omega }_i$, in which ${\mu }_i$, ${\nu }_i$, ${\omega }_i$ is the carbon emission coefficient of unit i; $p_t$ represents the carbon trading price in time period t.

(2)

Carbon transaction cost of wind power

In the actual power generation process, the intermittent energy represented by wind power, and photovoltaics does not produce carbon emissions, but the large-scale access of intermittent energy brings great uncertainty to the power generation side of the power system, so it is necessary for conventional thermal power units to provide more reserve capacity to weaken the impact of intermittent energy power fluctuations, which makes the carbon emissions of thermal power units increase. Therefore, in this section, the increase in the carbon emissions of thermal power units due to the uncertainty of wind power is considered as the carbon emissions of wind power, specifically:

$$E_{\mathrm{W},t}={\mu }_i{({\zeta }_{\mathrm{W}}{P}_{\mathrm{W},t})}^2+{\nu }_i({\zeta }_{\mathrm{W}}{P}_{\mathrm{W},t})+{\omega }_i$$

(14)

where: $E_{\mathrm{W},t}$ is the latent carbon emission of wind power in time period t; ${\zeta }_{\mathrm{W}}$ is the wind power reserve capacity factor, and it is assumed that the reserve is provided by unit i in time period t.

It can be seen that the cost of wind power participating in carbon trading is:

$$F{C}_{\mathrm{W},t}=p_t(E_{\mathrm{W},t}-Q_{\mathrm{W},t})$$

(15)

where: $F{C}_{\mathrm{W},t}$ is the carbon trading cost of wind power in time period t.

On this basis, the carbon emission balance or surplus of different types of units is coordinated through the carbon trade market mechanism. As shown in Figure 1, thermal power units can purchase insufficient carbon emission credits from the carbon trade market, and wind power units can sell the remaining carbon emission credits through the carbon trade market to obtain profits [22].

3.2. Day-Ahead Optimal Scheduling Model Considering Carbon Emission Trading

(1)

Objective function

The day-ahead optimal dispatching model in this paper takes the minimum total cost of the system in the dispatching period as the optimization objective, including the operation cost of thermal power units, the carbon transaction cost of thermal power units, the spinning reserve cost generated by wind power access, and the carbon transaction cost of wind farms.

$$\min F=\min (F_{\mathrm{G}}+F{C}_{\mathrm{G}}+F_{\mathrm{R}}+F{C}_{\mathrm{W}})$$

(16)

$$\min F_{\mathrm{G}}(U_{\mathrm{G}i,t},P_{\mathrm{G}i,t})=\min {\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^{N_{\mathrm{G}}}\left[U_{\mathrm{G}i,t}(1-U_{\mathrm{G}i,t-1})\cdot S{U}_{\mathrm{G}i,t}\right.}}+\left.U_{\mathrm{G}i,t-1}(1-U_{\mathrm{G}i,t})\cdot S{D}_{\mathrm{G}i,t}+U_{\mathrm{G}i,t}{R}_{\mathrm{G}i,t}(P_{\mathrm{G}i,t})\right]$$

(17)

where: $F_{\mathrm{G}}(U_{\mathrm{G}i,t},P_{\mathrm{G}i,t})$ represents the total operating cost; t is the scheduling period; $N_G$ is the total number of thermal power units; $U_{\mathrm{G}i,t}$, $U_{\mathrm{G}i,t-1}$ respectively indicate the start-up and shutdown status of the i-th unit during t and t − 1, 0 indicates shutdown, and 1 indicates start-up; $P_{\mathrm{G}i,t}$ is the active power output of Unit i in time period t.

In which that cost of generate electricity $R_{\mathrm{G}i,t}(P_{\mathrm{G}i,t})$, start-up costs $S{U}_{\mathrm{G}i,t}$ and downtime costs $S{D}_{\mathrm{G}i,t}$ are:

$$R_{\mathrm{G}i,t}(P_{\mathrm{G}i,t})=a_i+b_i\cdot P_{\mathrm{G}i,t}+c_i\cdot {(P_{\mathrm{G}i,t})}^2$$

(18)

$$S{U}_{\mathrm{G}i,t}={\alpha }_i+{\beta }_i(1-{\mathrm{e}}^{{\tau }_{\mathrm{G}i,t}/{\gamma }_i})$$

(19)

$$S{D}_{\mathrm{G}i,t}=\lambda P_{\mathrm{G}i,t}$$

(20)

where: ${\tau }_{\mathrm{G}i,t}$ indicates the time that unit i has been shut down continuously at time t; $a_i$, $b_i$, $c_i$ is the unit power generation cost parameter; ${\alpha }_i$ represents the turbine start-up and maintenance costs for unit i; ${\beta }_i$ is the start-up cost of the boiler of unit i in the cooling environment; ${\gamma }_i$ represents time constant representing the cooling rate of unit i; $\lambda$ is the incremental downtime cost parameter.

Among them, the operation cost $F_{\mathrm{G}}$ of the thermal power unit is referred to formulas (17) to (20), and the carbon trading costs for thermal power units $F{C}_{\mathrm{G}}$ is calculated as:

$$F{C}_{\mathrm{G}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^{N}F{C}_{\mathrm{G}i,t}}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^N{p}_t(E_{\mathrm{G}i,t}-Q_{\mathrm{G}i,t})}}$$

(21)

where N is the number of thermal power units in the system.

In addition, the randomness of wind power output leads to additional spinning reserve cost $F_{\mathrm{R}}$, and the specific calculation is [17]:

$$F_{\mathrm{R}}={\displaystyle \sum _{t=1}^T{C}_{\mathrm{R}}(1-{\epsilon }_t)P_{\mathrm{W},t}}$$

(22)

where: $C_{\mathrm{R}}$ is the price of the spinning reserve capacity; ${\epsilon }_t$ is the reliability level of the predicted output of wind power in time period t.

Carbon trading $F{C}_{\mathrm{W}}$ of wind power is:

$$F{C}_{\mathrm{W}}={\displaystyle \sum _{t=1}^{T}F{C}_{\mathrm{W},t}}={\displaystyle \sum _{t=1}^T{p}_2(E_{\mathrm{W},t}-Q_{\mathrm{W},t})}$$

(23)

where: $p_2$ is the carbon price at the time the allowance is sold.

(2)

Constraints

(a)

Unit constraint

Unit output constraint, minimum continuous start-up/shutdown time constraint, and unit creep/landslide constraint of conventional thermal power are shown in formulas (24)–(26), respectively.

$$P_{\mathrm{G}i}^{\min }\le P_{\mathrm{G}i,t}\le P_{\mathrm{G}i}^{\max }$$

(24)

$$\left\{\begin{array}{l}\left(X_{\mathrm{G}i,t-1}^{\mathrm{on}}-T_{\mathrm{G}i}^{\mathrm{on}}\right)\left(U_{\mathrm{G}i,t-1}-U_{\mathrm{G}i,t}\right)\ge 0\hfill \\ \left(X_{\mathrm{G}i,t-1}^{\mathrm{off}}-T_{\mathrm{G}i}^{\mathrm{off}}\right)\left(U_{\mathrm{G}i,t}-U_{\mathrm{G}i,t-1}\right)\ge 0\hfill \end{array}\right.$$

(25)

$$\left\{\begin{array}{l}{P}_{\mathrm{G}i,t}-P_{\mathrm{G}i,t-1}\le R{U}_i\\ P_{\mathrm{G}i,t-1}-P_{\mathrm{G}i,t}\le R{D}_i\end{array}\right.$$

(26)

where: $P_{\mathrm{G}i}^{\min }$ and $P_{\mathrm{G}i}^{\max }$ respectively represent the lower limit and upper limit of active power output of unit i; $X_{\mathrm{G}i,t}^{\mathrm{on}}$ and $X_{\mathrm{G}i,t}^{\mathrm{off}}$ respectively represent the continuous start-up time and shutdown time of the i-th unit in time period t; $T_{\mathrm{G}i,t}^{\mathrm{on}}$ and $T_{\mathrm{G}i,t}^{\mathrm{off}}$ respectively represent the minimum continuous start-up and shutdown time of unit i; $R{U}_i$ and $R{D}_i$ are the maximum climbing capacity and the maximum sliding capacity of the active power of unit i in time period t.

The wind farm shall meet the following constraints during operation:

$$P_{\mathrm{W},t}+{\xi }_t\le P_{\mathrm{W}}^{\max }$$

(27)

where: $P_{\mathrm{W}}^{\max }$ is the maximum power of the wind farm, that is, the installed capacity of wind power.

(b)

The power balance constraint is:

$${\displaystyle \sum _{i=1}^N{U}_{\mathrm{G}i,t}{P}_{\mathrm{G}i,t}=}{P}_{\mathrm{L},t}-P_{\mathrm{W},t}$$

(28)

where: $P_{\mathrm{L},t}$ is the forecast the load for the system.

(c)

The system reserve constraints are:

$$\left\{\begin{array}{l}{\displaystyle \sum _{i=1}^N(P_{\mathrm{G}i}^{\max }}-P_{\mathrm{G}i,t})\ge {\zeta }_{\mathrm{L}}{P}_{\mathrm{L},t}+{\zeta }_{\mathrm{W}}{P}_{\mathrm{W},t}\\ {\displaystyle \sum _{i=1}^N(}{P}_{\mathrm{G}i,t}-P_{\mathrm{G}i}^{\min })\ge {\zeta }_{\mathrm{L}}{P}_{\mathrm{L},t}+{\zeta }_{\mathrm{W}}{P}_{\mathrm{W},t}\end{array}\right.$$

(29)

where: ${\zeta }_{\mathrm{L}}$ indicates the load reserve factor.

(d)

Network security constraints:

The network security constraints after wind power access are as follows:

$$P_{l,\min }\le {\displaystyle \sum _{i=1}^N{G}_{l,i}}{P}_{\mathrm{G}i,t}+{\displaystyle \sum _{j=1}^{N_{\mathrm{W}}}{G}_{l,j}{P}_{\mathrm{W}j,t}}-{\displaystyle \sum _{d=1}^D{G}_{l,d}}{P}_{\mathrm{L}d,t}\le P_{l,\max }$$

(30)

where: $P_{l,\min }$ and $P_{l,\max }$ in that ground state case respectively represent the minimum and maximum transmission capacity allowed by the line in the case of the ground state; $G_{l,i}$ is the power transfer distribution factor of unit i to line l; $G_{l,d}$ and $G_{l,i}$ are also power transfer distribution factors; $P_{\mathrm{W}j,t}$ is the load value of node d in time period t; $N_{\mathrm{W}}$ is the number of wind farms; $P_{\mathrm{W}j,t}$ represents the power of the j-th wind farm; $G_{l,j}$ is the power transfer distribution factor.

4. Simulation Verification

4.1. Simulation and Analysis Based on IEEE-30 Bus System

4.1.1. Example Parameters

Firstly, the IEEE-30 node system connected to the wind farm is taken as an example for simulation analysis, and the system wiring diagram is shown in Figure 2. It includes six conventional thermal power units, which are connected to a wind farm with an installed capacity of 150 MW at 22 nodes. The predicted values of load and wind power in each period are shown in Figure 3, and the parameters of six conventional thermal power units are shown in reference [23]. The marginal emission factors of electricity and capacity of each unit are shown in

Table A1. Energy Marginal Emission Factor and Capacity Marginal Emission Factor of Each Unit of IEEE-30 System.

Unit Number	Marginal Emission Factor of Electricity (ton/MW·h)	Capacity Marginal Emission Factor (ton/MW·h)
G1	0.9419	0.4819
G2	0.9316	0.3467
G3	0.9229	0.3071
G4	1.0826	0.2399
G5	1.0925	0.2631
G6	0.9316	0.3467

of Appendix A and other parameters are given in reference [24]. Considering the allocation of carbon emission credits and the calculation of carbon trading costs, the time step is taken as 1 h, and the scheduling period T is 24 h [25]. In addition, the load reserve coefficient is 0.1, and the wind power reserve coefficient is 0.14. In this chapter, the predicted carbon price of days 401 to 424 is selected to simulate the 24 h carbon trading price in the scheduling period.

The related calculation is based on MATLAB 2016a software and CPLEX 12.4, and the hardware configuration is Windows 10 64-bit operating system with CPU i5-7500 and 8G running memory [27].

4.1.2. Simulation Results

According to the calculation method in Section 4.2, the weights of marginal emission factor of electricity and marginal emission factor of capacity are 0.65 and 0.35 [28], respectively, and the corresponding carbon quota coefficient of each unit is shown in

Table 1. Carbon Quota Coefficients for IEEE-30 System.

Unit	G1	G2	G3	G4	G5	G6
Quota factor $e_i$(t/MW·H)	0.7809	0.7269	0.7074	0.7877	0.8022	0.7269

.

It can be seen from Table 1 that thermal power unit G3 has the lowest quota coefficient, while unit G5 has the highest quota coefficient. If other factors are not taken into account [29], the carbon emissions of the system can be reduced by giving priority to dispatching unit G3 when the system needs the same output level.

In addition, the day-ahead optimal scheduling results in this paper are shown in Figure 4.

It can be seen from Figure 4 that thermal power units G1, G2 and G3 bear the basic load of the system, and G3 is always in full load state during the dispatching period. In the period from t = 1 to t = 6, due to the reduction of load demand, the system adapts to reduce the output of G2 to balance the load constraint; while in the period from t = 6 to t = 12, the system constraint is satisfied by increasing the output of G2.

4.1.3. Comparative Analysis

In order to verify the correctness and effectiveness of the method proposed in this chapter, the following three scenarios are set up:

Scenario 1: Day-ahead optimal scheduling without considering carbon emissions trading;

Scenario 2: Considering the carbon emission trading of the power system, the carbon emission quota allocation method based on the weighted average of the electricity marginal emission factor and the capacity marginal emission factor is used;

Scenario 3: Considering the carbon emission trading of the power system, and using the carbon emission quota allocation method based on the entropy method; that is, the model in this paper.

(1)

Considering the necessity of the verification of carbon emission trading

In order to verify the necessity of incorporating carbon trading into the day-ahead optimal scheduling model, the total carbon emissions of Scenario 1 and Scenario 3 are calculated and analyzed. Firstly, the output plan of each unit under Scenario 1 and Scenario 3 in the dispatching period is shown in Figure 5.

It can be seen from Figure 5 that compared with Scenario 1, the output level of units G1 and G2 bearing the basic load of the system in Scenario 3 is obviously reduced for the whole dispatching period, in which the output of G1 is reduced most obviously, while the output of units G3, G4, G5 and G6 is significantly increased. This is because the carbon emissions of thermal power units are positively correlated with the unit output. For units G1 and G2, with large active power output and high carbon emission levels, in order to reduce the system carbon emissions in each dispatching period, the Scenario 3 model reduces the output of G1 and G2. For units G3, G4, G5 and G6, with small output and low carbon emission levels, the corresponding active power output is increased. Therefore, incorporating carbon trading into the day-ahead optimal dispatching model is mainly to reduce carbon emissions in each dispatching period by reducing the output of units with higher carbon emission levels, while increasing the output of units with lower carbon emission levels to ensure power supply balance.

Furthermore, in order to analyze the change of the total cost of the system in the scheduling period after considering the carbon trading, the total cost of each period under the two scenarios is calculated, and the comparison chart is shown in Figure 6.

It can be seen from Figure 6 that in the period from t = 1 to t = 5, compared with Scenario 1, the system cost of Scenario 3 is reduced, mainly because the carbon trading income of wind power is greater than the carbon trading cost of thermal power units, thus offsetting part of the cost. In the period from t = 10 to t = 24, the dispatching cost of Scenario 3 is higher than that of Scenario 1, which is mainly due to the increase in output of G3, G4, G5 and G6 in the corresponding period, resulting in the carbon trading cost of thermal power exceeding the carbon trading income of wind power. For the whole dispatching period, the total cost of Scenario 3 is 18,700 yuan higher than that of Scenario 1. Combined with Scenario 3 in Figure 5, although the output of G1 and G2 is reduced to limit carbon emissions, the total cost will eventually increase to a certain extent. Therefore, incorporating carbon emissions trading into the day-ahead scheduling model is essentially to reduce the total carbon emissions of the system by reducing the output of high-emission units while increasing the output of low-emission units at the cost of a small increase in the total cost.

Then, the total carbon emissions of the system in each scheduling period under Scenario 1 and Scenario 3 are calculated, as shown in Figure 7.

It can be seen from Figure 7 that the carbon emissions of Scenario 3 are significantly lower than those of Scenario 1. In the whole scheduling period, the total carbon emission from the Scenario 1 system is 5616.36 tons, while the total carbon emission of Scenario 3 is 5262.33 tons, which reduces carbon emissions by nearly 354 tons compared with Scenario 1. Therefore, incorporating carbon emission trading into the day-ahead scheduling model can effectively reduce the total carbon emission of the system.

(2)

Validity verification of the carbon emission quota allocation method based on the entropy method

The output results of each unit under Scenario 2 and Scenario 3 are shown in

Table A2. Output Result of Each Unit in IEEE-30 System under Scenario 2.

	G1	G2	G3	G4	G5	G6
T = 1	50.00	77.78	50.00	10.00	30.00	12.22
T = 2	50.00	56.39	50.00	10.00	20.56	12.22
T = 3	50.00	53.06	50.00	10.00	13.06	12.22
T = 4	50.00	35.56	50.00	10.00	10.28	22.78
T = 5	50.00	26.67	50.00	10.00	10.28	30.00
T = 6	50.00	30.56	50.00	10.00	10.28	33.06
T = 7	50.00	51.39	50.00	10.00	10.28	31.94
T = 8	60.83	80.28	50.00	10.00	10.28	40.00
T = 9	64.17	80.28	50.00	10.00	10.28	40.00
T = 10	89.17	80.28	50.00	11.67	19.72	40.00
T = 11	93.33	80.28	50.00	26.94	10.28	40.00
T = 12	103.89	80.28	50.00	20.00	10.28	40.00
T = 13	84.72	80.28	50.00	34.72	10.28	40.00
T = 14	103.89	80.28	50.00	19.72	10.28	40.00
T = 15	107.78	80.28	50.00	10.28	20.00	40.00
T = 16	123.89	80.28	50.00	10.28	30.00	23.89
T = 17	148.89	80.28	50.00	12.78	30.00	12.50
T = 18	146.94	80.28	50.00	10.28	30.00	13.89
T = 19	122.22	80.28	50.00	24.72	30.00	12.22
T = 20	111.67	80.28	50.00	20.00	30.00	26.67
T = 21	110.56	80.28	50.00	34.72	30.00	13.06
T = 22	85.28	80.28	50.00	19.44	30.00	24.17
T = 23	60.83	80.28	50.00	10.00	20.00	38.06
T = 24	50.00	55.83	50.00	10.00	30.00	23.61

and

Table A3. Output Result of Each Unit in IEEE-30 System under Scenario 3.

	G1	G2	G3	G4	G5	G6
T = 1	50.00	74.16	50.00	10.00	29.97	12.14
T = 2	50.00	49.35	50.00	10.00	23.26	17.31
T = 3	50.00	24.55	50.00	10.00	22.48	32.04
T = 4	50.00	20.16	50.00	10.00	14.47	33.07
T = 5	50.00	20.16	50.00	10.00	11.89	34.37
T = 6	50.00	25.58	50.00	10.00	11.63	36.43
T = 7	50.00	49.87	50.00	10.08	10.08	35.40
T = 8	50.00	75.45	50.00	24.81	10.08	40.05
T = 9	50.00	80.10	50.00	24.81	10.08	40.05
T = 10	64.08	80.00	50.00	34.88	19.90	40.05
T = 11	84.75	80.00	50.00	34.88	10.08	40.05
T = 12	88.63	80.00	50.00	34.88	10.08	40.05
T = 13	84.75	80.00	50.00	34.88	10.08	40.05
T = 14	88.63	80.00	50.00	34.88	10.08	40.05
T = 15	82.95	80.00	50.00	34.88	19.64	40.05
T = 16	80.36	80.00	50.00	34.88	29.97	40.05
T = 17	96.90	80.00	50.00	34.88	29.97	40.05
T = 18	94.06	80.00	50.00	34.88	29.97	40.05
T = 19	81.91	80.00	50.00	34.88	29.97	40.05
T = 20	82.17	80.00	50.00	34.88	29.97	40.05
T = 21	79.07	80.00	50.00	34.88	29.97	40.05
T = 22	54.26	79.85	50.00	31.27	29.20	40.05
T = 23	50.00	74.16	50.00	24.81	19.38	40.05
T = 24	50.00	50.00	50.00	10.08	29.20	25.06

of Appendix A, respectively. In order to verify the effectiveness of the carbon emission quota allocation method based on the entropy method, the total carbon emission quota of each unit in Scenario 2 and Scenario 3 is calculated, and the specific results are shown in

Table 2. Carbon emission quota for each unit in Scenarios 2 and 3.

Unit	G1	G2	G3	G4	G5	G6
Scenario 2 Total carbon Emission Allowance/ton	1436.65	1068.45	738	241.72	315.93	423.45
Scenario 3 Total Carbon Emission Allowance/ton	1259.23	1150.96	848.88	476.12	386.18	629.99

.

It can be seen from Table 2 that the carbon emission quota of G1 in Scenario 3 is higher than that in Scenario 2. By comparing the output results of G1 in the two scenarios, the carbon emission quota is actually reduced by lowering its output. Compared with Scenario 2, the output of G4 and G6 units with lower carbon emission intensity in Scenario 3 increases significantly, and their corresponding carbon emission quotas also increase accordingly. In addition, the carbon emission quota of thermal power units G2, G3 and G5 is higher than that of Scenario 2. This is because the method of calculating the carbon quota coefficient based on the entropy method takes into account the carbon emission characteristics of different units. Compared with the method of directly averaging carbon emission factors, the increase of the carbon quota coefficient leads to a corresponding increase of the carbon emission quota.

In addition, in order to analyze the impact of the carbon emission quota allocation method in this paper on different units, the carbon emission quotas of each unit in Scenario 2 and Scenario 3 are compared in detail. The carbon emission quotas of six thermal power units in the dispatching period are shown in Figure 8.

It can be seen from Figure 8 that for unit G1 bearing the base load, compared with Scenario 2, the carbon emission quota of Scenario 3 from t = 14 to t = 23 is significantly reduced. The main reason is that the output level of unit G1 is more stable, and the total active output is significantly reduced in Scenario 3. For unit G2, the carbon emission quota under Scenario 3 is significantly higher than that under Scenario 2 from t = 8 to t = 24, and the output levels of the two scenarios are basically the same. The main reason for the increase of the G2 quota is that the quota coefficient of Scenario 3 is higher than that of Scenario 2. For unit G3 with unchanged unit output under the two scenarios, the quota of Scenario 3 is higher than that of Scenario 2, which is also caused by the increase of the quota coefficient. For units G4, G5 and G6, their quotas under Scenario 3 are higher than those under Scenario 2. The common reason for the increase of their carbon emission quotas is that they are affected by the increase of the quota coefficient. In addition, the output of G4 and G6 increases significantly and remains within a certain range due to their undertaking the reserve required for wind power access. These two reasons make the quotas of G4 and G6 increase under Scenario 3. Therefore, this method not only optimizes the carbon emission quota of each unit, but also makes the output level of the unit more stable.

4.2. Simulation and Analysis Based on IEEE-118 Bus System

4.2.1. Example Parameters

The effectiveness of the proposed method is further verified in a large-scale power system, and the IEEE-118 bus system connected to wind farms is used for simulation analysis. Among them, nodes 36, 69 and 77 are connected to wind farms with installed capacities of 100 MW, 200 MW and 250 MW, respectively. The load forecast value and wind power forecast value of each period are shown in Figure 9. In addition, the load reserve coefficient is 0.1, and the wind farm reserve coefficient is 0.14. The carbon price prediction results in Chapter 3 are also used to simulate the carbon price changes in the dispatching period. See reference [18] for other relevant parameters.

4.2.2. Simulation Results

According to the carbon emission quota allocation method based on the entropy method in this chapter, the corresponding weights of the two emission factors are calculated to be 0.55 and 0.45, respectively, and the corresponding quota coefficients of each unit are obtained as shown in

Table 3. Comparison of specific SEC indicators for solutions 2882 and 2703.

Unit Number	$\mathbf{Quota}\mathbf{Factor}{\mathit{e}}_{\mathit{i}}(\mathbf{t}/\mathbf{MW}·\mathbf{H})$
27, 28	0.6432
42	0.6474
50, 54	0.6565
7, 14, 16, 19, 22, 23, 26, 30, 34, 35, 37, 47, 48, 51–53	0.6699
4, 36	0.6915
20, 21, 24, 25, 40	0.6937
5, 10, 11, 29, 39, 43–45	0.6959
6	0.7214
1–3, 8, 9, 12, 13, 15, 17, 18, 31, 38	0.7270
32, 33, 41, 46, 49	0.7359

.

It can be seen from Table 3 that the quota coefficients of units 27 and 28 are the lowest, while the quota coefficients of units 32, 33, 41, 46 and 49 are the highest, of which the units with quota coefficients of 0.6699 tons/MW · H and 0.6915 tons/MW · H account for 61.4% of the total installed capacity of thermal power units. In addition, for the units with a small characteristic difference in the system, the difference of their quota coefficients is very small or even the same.

Combined with the model in this chapter, the calculated start-stop scheme of each unit of IEEE-118 system is shown in

Table 4. Carbon Quota Coefficients for IEEE-118 Systems.

Unit Number	Start-Stop Scheme
10, 11, 20, 21, 24, 25, 27–29, 39, 40, 45	111111111111111111111111
43	110001111111111111111111
36, 44	000000111111111111111111
5	000001111111111111111111
7	000000000111111111111111
14	000000000000000001111100
16, 34	000000000111111111111000
19	000000000111111111111100
22, 23, 35, 37, 48	000000000000000000111110
26, 51	000000000000000111111100
30	000000000000000001111000
47	000000000111111111111110
52	000000000000000001111110
53	000000000000000111111000
1–4, 6, 8, 9, 12, 13, 15, 17, 18, 31, 33, 38, 41, 42, 46, 49, 50, 54	000000000000000000000000

.

It can be seen from Table 4 that by taking the two units of No. 26 and No. 51, No. 16 and No. 34 as an example, since their respective parameters are essentially the same, the obtained start-stop schemes are also the same. Combined with Table 3, it can be seen that the quota coefficient of the normally open unit is lower than that of the normally stopped unit. It can be seen that in the case of the same output level required by the system, if other factors are not considered, the units with low carbon emission quota coefficient will be dispatched preferentially in this model.

4.2.3. Comparative Analysis

In order to verify the correctness and effectiveness of the method proposed in this chapter in a larger system, the same three scenarios as Section 4.1 are set for analysis.

(1)

Consider the necessity of the verification of carbon emission trading

In order to verify the necessity of incorporating carbon trading into the day-ahead optimal scheduling model, the system carbon emissions in each period of Scenario 1 and Scenario 3 are first calculated, and the results are shown in Figure 10.

It can be seen from Figure 10 that the carbon emissions of Scenario 3 in each period are significantly lower than those of Scenario 1. During the whole scheduling period, the total carbon emission of Scenario 1 is 57,286.88 tons, and the total carbon emission of Scenario 3 is 53,675.78 tons, which reduces carbon emissions by 3611.10 tons compared with Scenario 1. The main reason is that carbon emission trading is considered in Scenario 3 model, the essence of which is to shut down high-emission units or reduce the output of high-emission units while increasing the output of low-emission units, thus, effectively reducing the total carbon emissions of the system.

Further, the total cost of the system in each time period under Scenario 1 and Scenario 3 is calculated, and the comparison chart is shown in Figure 11.

It can be seen from Figure 11 that in the periods from t = 1 to t = 4 and from t = 20 to t = 24, the system operation cost of Scenario 3 is significantly lower than that of Scenario 1, mainly because the reduction of load demand in this period reduces the carbon trading cost of thermal power. At the same time, the increasing rate of carbon emission quotas of wind power exceeds the increasing rate of its emissions, which makes wind power gain corresponding benefits from participating in carbon emission trading, thus reducing the total cost. In the period from t = 5 to t = 19, the cost is slightly higher than that in Scenario 1. The main reason is that the reduction of wind power output greatly reduces the income of wind power participating in carbon trading. In this period, the carbon trading cost of thermal power exceeds the carbon trading income of wind power, which ultimately leads to an increase in the total cost. In the whole scheduling cycle, the total cost of Scenario 3 is 290,900 yuan higher than that of Scenario 1, and if 40 yuan per ton is taken as the penalty cost for not conducting carbon trading, 3611.10 tons of carbon emissions will be subject to a fine of 1.444 million yuan. It can be seen that incorporating carbon emissions trading into the SCUC model is essentially a small increase in the total cost to reduce the total carbon emissions of the system, which is more economical than paying fines directly without considering carbon trading.

(2)

Validity verification of carbon emission quota allocation method based on the entropy method

In order to verify the effectiveness of the carbon emission quota allocation method based on the entropy method in a large-scale power system, the total carbon emission quota of each unit in Scenario 2 and Scenario 3 in the whole dispatching period is calculated, and the specific results are shown in Figure 12.

It can be seen from Figure 12 that the carbon emission quota of units G11, G20, G21, G24, G25, G27, G28, G39 and G40 in Scenario 3 is significantly higher than that in Scenario 2, among which the change of units G11, G20, G39 and G40 is more prominent, mainly because these units are normally open in the dispatching period. The total output in the dispatching period is correspondingly increased, so that the carbon emission quota is increased; For the units with only output change and no change in start-up and shutdown status, the change of carbon emission quota is not obvious in Scenario 2 or Scenario 3, which indicates that the carbon emission quota allocation method based on the entropy method in this paper is mainly optimizes the carbon emission quota of each unit by adjusting the start-up and shutdown status of the unit. Therefore, this method takes into account the proportion of units with different emission characteristics in the system, and reasonably allocates the carbon emission quota of each unit by adjusting the start-up and shutdown of units, so as to promote the participation of each subject in carbon emission trading.

5. Conclusions

This paper first analyzes the characteristics and problems of existing carbon emission quota methods and proposes a carbon emission quota allocation method based on the entropy method. In addition, considering the additional carbon emissions brought by wind power access to conventional thermal power units, wind power is taken as the main body of carbon trading and a day-ahead optimal scheduling model is constructed. The following conclusions are drawn through the simulation of an example:

(1)

The carbon emission quota allocation strategy based on the entropy method, to a certain extent, avoids the subjective processing method of the weighted average of the marginal emission factor of electricity and the marginal emission factor of capacity, and reduces the carbon emission of the system by limiting the quota of high-emission units within a certain range;

(2)

Considering the calculation of the hidden carbon emission of the wind power after wind power is connected, the wind power can obtain benefits from participating in carbon trading to offset a part of the carbon trading cost of a thermal power unit. In a dispatching model, a unit with a low carbon emission factor is preferentially dispatched, thereby reducing the total operation cost of the system.

This paper constructs a day-ahead optimal scheduling model considering carbon emission quotas and the carbon transaction costs of different types of units. The consideration of clean energy only involves wind power and does not consider the uncertainty caused by photovoltaics and the correlation between wind and light. In addition, the integrated energy system formed by the interactive integration of different forms of energy systems has developed rapidly, and its impact on individuals participating in carbon trading is more complicated. Therefore, it is necessary to carry out further research on the optimal scheduling of multiple energy coupling systems considering carbon trading.