Hierarchical Low-Carbon Economic Dispatch with Source-Load Bilateral Carbon-Trading Based on Aumann–Shapley Method

Abstract

Introducing carbon trading is an essential way to decarbonize the power system. Many existing studies mainly consider source-side unilateral carbon trading (UCT). However, there are still rare studies considering source-load bilateral carbon trading (BCT). The effect of source-load BCT on system-wide carbon mitigation is worth studying. To fill this research gap, a hierarchical low-carbon economic-dispatch model with source-load BCT based on the Aumann–Shapley method was proposed. In the first layer, economic-dispatch was conducted to minimize the power-generation costs and source-side carbon-trading costs. Then, based on the carbon-emission flow (CEF) theory, the actual load carbon emissions can be obtained and passed to the second layer. At the second layer, the demand-response optimization was performed to minimize the load-side carbon-trading costs. Finally, the proposed model was tested on the modified New England 39-bus and IEEE 118-bus systems using the MATLAB/YALMIP platform with the Gurobi solver. The results indicate that the proposed model can effectively facilitate peak-load shifting, wind-power consumption, and carbon mitigation. Furthermore, compared with the models only considering source-side or load-side UCT, the proposed source-load BCT model has obvious advantages in carbon mitigation.

1. Introduction

Since industrialization, the exploitation and utilization of a large number of fossil fuels have made the greenhouse effect increasingly serious [1]. The current global average temperature suggests that meeting the Paris Agreement temperature goals is fraught with challenges [2,3,4,5]. With the continuous development of green energy, the power system has huge potential for decarbonization [6,7,8,9]. The research on carbon-mitigation strategies for the power system have become an international research hotspot [10].

At present, the research on carbon-mitigation strategies for the power system generally include two routes. One is the emerging low-carbon technology route, such as energy storage technologies, carbon capture utilization storage (CCUS) technologies, renewable energy technologies, etc. [11,12,13,14,15]. The other is the economic regulation mechanism route, that is, to guide the dispatch of power-generation and energy-consumption behavior, and the stimulate the development and application of emerging technologies through economic means [13,16]. Carbon trading is one of the most important and effective means of economic regulation [17,18].

The implementation of carbon transaction in the power system has attracted the increasing attention of many scholars recently. Issues pertaining to economic dispatch, considering carbon trading, have been extensively investigated. The study in [19] presented a stochastic dynamic economic-dispatch model considering wind-power uncertainty and carbon-emission rights simultaneously and discussed the effectiveness of carbon transaction to cope with the pressure of carbon mitigation. The optimal-dispatch model under a carbon-emission transaction mechanism for an integrated wind–photovoltaic–thermal power system was researched in [20,21]. In [22], a low-carbon economic operating model with a reward-and-punishment ladder-type carbon-trading mechanism was established for an integrated energy system that considered carbon capture technologies. On the other hand, some scholars have considered carbon trading in planning problems of the power system. In [23], a framework was proposed to optimize the energy–water–emissions nexus for regional power-system planning, and a carbon-emission trading mechanism was adopted to enhance the carbon-mitigation effect. The study in [24,25] introduced carbon trading in the capacity planning of generators and power-to-gas devices in the power system, whereas the above studies [19,20,21,22,23,24,25] only considered source-side unilateral carbon trading (UCT).

Demand response has become a research hotspot in the smart grid. Demand response incentivized by real-time tariffs, time-of-use tariffs, etc. has been extensively studied [26,27,28,29]. In recent years, a few scholars have also paid attention to the combination of load-side unilateral carbon trading and demand response. The environmental benefits of users participating in both the electricity- and carbon-emission transaction markets via active demand-side management were investigated in [30]. In [31], demand-side carbon trading was introduced in robust energy-systems scheduling considering uncertainties. However, source-load bilateral carbon trading (BCT) is a relatively new topic of research. The effect of source-load BCT on carbon mitigation is worth studying.

Additionally, the implementation of carbon transaction in the power system generally faces two issues that need to be addressed [18,32,33,34,35,36]. The first is that in the process of formulating the carbon-trading mechanism, it is necessary to reasonably allocate the allowance of carbon-emission responsibilities of the participants in carbon transaction [18,32]. Usually, the Shapley value method and the prenucleolus method are used to allocate the carbon allowances of carbon-trading participants [33]. The second issue is that the actual carbon emissions of participating entities need to be measured during the carbon-trading process [34]. Since generators have fixed carbon-emission intensities, the actual carbon emissions can be directly measured through the output power. However, the carbon-emission intensities of load nodes will change with a change in the power-flow dispatch, so it is difficult to directly calculate the carbon emissions of loads. The proposal of the carbon-emission flow (CEF) theory provided a great solution for the measurement of the actual carbon emissions on the load side [35,36].

To summarize, this paper considers the carbon-emission responsibilities of generators and loads simultaneously and focuses on the impact of the participation of both the source and load in carbon trading on carbon mitigation in the power system. The key contributions of the article are threefold:

(1)

A hierarchical economic-dispatch model considering source-load bilateral carbon trading is proposed in the article. The first layer conducted economic dispatch to minimize the costs of power generation and source-side carbon trading. Then, based on the CEF theory, the actual carbon emissions of the loads were measured. In the second layer, demand-response optimization was carried out to minimize the load-side carbon-trading costs.

(2)

Using the Aumann–Shapley method, the carbon-emission responsibilities of the participants in carbon trading were reasonably allocated, and thus, a source-load bilateral ladder-type carbon-trading mechanism was constructed.

(3)

Based on the modified New England 39-bus and IEEE 118-bus test system, the effectiveness of the proposed model in peak shaving and valley filling, wind-power consumption, and carbon mitigation was verified. Moreover, compared with the source-side and load-side unilateral carbon-trading models, the proposed source-load bilateral carbon-trading model has obvious advantages in carbon mitigation.

The structure of the article is as follows: Section 2 illustrates the formation of the source-load BCT mechanism; Section 3 introduces the hierarchical low-carbon economic-dispatch model with source-load BCT; the case results and discussion are presented in Section 4; and Section 5 concludes the article.

2. Source-Load Bilateral Carbon-Trading Mechanism Based on the Aumann–Shapley Method and CEF Theory

To fully promote the low-carbon transformation on the power production and consumption side, it is necessary to implement carbon trading on both the source side and load side. The carbon-trading mechanism mainly consists of two parts: the allocation of carbon allowances and the measurement of carbon-emission responsibilities.

2.1. The Carbon-Allowance Allocation of Source-Side and Load-Side Based on the Aumann–Shapley Method

Carbon allowance is an effective way to decarbonize the power system. For each member of the power system, carbon allowance can be regarded as a resource with a fixed total amount, and therefore, can be allocated by a cooperative game method, such as the Shapley value method and prenucleolus method. Between them, the Shapley value method is more fair, reasonable, and rigorous [33]. However, the traditional Shapley value method faces the problem of the sub-alliance explosion, resulting in a huge amount of calculation. Hence, the Shapley value method is impractical for application in an alliance that contains too many members. The Aumann–Shapley method, as a derivative of the Shapley value method, overcomes the shortcomings of the Shapley value method regarding the large-scale membership problem [37]. Therefore, the Aumann–Shapley method was adopted to allocate the carbon allowance in this paper. On the basis of the discretized form of the Aumann–Shapley method in [37], the Aumann–Shapley value of carbon-emission responsibility for member $i$ in the power system, $X_{ASV,i}$, can be expressed as (1)

$$X_{ASV,i}=P_i{\displaystyle \sum }_{k=1}^M\frac{c\left(\frac{k}{M}\mathit{P}+∆P_i\right)-c\left(\frac{k}{M}\mathit{P}\right)}{M∆P_i}$$

(1)

where $\mathit{P}$ denotes the vector of power of source-side or load-side members; $P_i$ represents the actual power of member $i$; $c\left(\mathit{P}\right)$ denotes the calculation function of total system carbon-emission responsibilities; and $M$ denotes the number of segments for discretization. To better formulate a ladder-type carbon-trading mechanism based on the Aumann–Shapley values, the Aumann–Shapley values in period $T$ are averaged to obtain the carbon allowances, as in (2).

$$R_{ALL,i}={\propto }_{ALL}{\displaystyle \sum }_{t=1}^T{X}_{ASV,i,t}/T$$

(2)

where ${\propto }_{ALL}$ represents the rate of free carbon allowance, and $R_{ALL,i}$ represents the carbon allowance of member $i$.

2.2. The Measurement of Source-Load Bilateral Carbon-Emission Responsibilities

The carbon dioxide of the power system is completely emitted in the stage of power generation. However, the source side and load side are interdependent in carbon-emission responsibility, and with the absence of either side, the carbon emissions will not exist. Therefore, in this study, it was assumed that the source side and load side play an equivalent role in carbon-emission mitigation, and therefore, undertake equivalent carbon-emission responsibilities.

2.2.1. The Measurement of Source-Side Carbon-Emission Responsibilities

According to the above assumption in this paper, the source-side carbon-emission responsibilities are half of their actual carbon emissions:

$${\mathit{R}}_G=0.5{\mathit{e}}_G{\mathit{P}}_G$$

(3)

where ${\mathit{R}}_G$, ${\mathit{e}}_G$, and ${\mathit{P}}_G$ denote the vectors composed of carbon-emission responsibilities, carbon intensities, and actual output power of generators, respectively.

2.2.2. The Measurement of Load-Side Carbon-Emission Responsibilities via the CEF Theory

The load side is responsible for the other half of the system’s total carbon emissions. The carbon responsibilities of each load depend on the composition of the electricity it consumes. Via the CEF theory, the carbon-emission responsibilities of each load can be obtained [35,36].

According to the method introduced in [38,39], the allocation matrix ${\mathit{T}}^{gross}$ denotes the allocation of carbon responsibilities from the source side to the load side:

$${\mathit{T}}^{gross}={\mathit{B}}^{gross}{\left({\mathit{E}}^{gross}-{\mathit{A}}^{gross}\right)}^{-1}$$

(4)

where ${\mathit{A}}^{gross}$ and ${\mathit{B}}^{gross}$ are distribution matrixes and can be obtained via (5) and (6). ${\mathit{E}}^{gross}$ is an identity matrix.

$$A_{ij}^{gross}=\{\begin{array}{c}{P}_{ji}^{gross}/P_{B,i}^{gross} j\in i^{+}\\ 0 else\end{array}$$

(5)

$$B_{ij}^{gross}=\{\begin{array}{c}{P}_{L,i}/P_{B,i}^{gross} i=j\\ 0 i\ne j\end{array}$$

(6)

$P_{ji}^{gross}$ is the gross flow, which is defined as: $P_{ji}^{gross}=P_{ji}+P_{ji}^{loss}$; $P_{ji}^{loss}$ and $P_{ji}$ are the power transmission losses and active power on branch $j-i$; $P_{L,i}$ denotes the power load of node $i$; $i^{+}$ denotes a set of beginning nodes of all the branches that inject into bus $i$; and $P_{B,i}^{gross}$ is the gross power flux and can be obtained via (7).

$$P_{B,i}^{gross}={\displaystyle \sum }_{j\in i^{+}}{P}_{ji}^{gross}+P_{G,i}$$

(7)

The load-side carbon-emission responsibilities ${\mathit{R}}_L^{gross}$ can be obtained via (8).

$${\mathit{R}}_L^{gross}={\mathit{T}}^{gross}{\mathit{R}}_G$$

(8)

2.3. Source-Load Bilateral Carbon-Trading Mechanism

The reward-and-punishment ladder-type carbon-trading mechanism is more conducive to stimulating the carbon-mitigation potential of the system [25]. Therefore, reward-and-punishment ladder-type carbon trading was adopted in the proposed source-load bilateral carbon-trading mechanism in this paper. The member participating in the carbon trading will obtain profits when their carbon emissions are lower than their carbon allowance. With their carbon emissions increasing, the price of purchasing carbon allowance will also increase. The total carbon-trading costs $C_{i,t}^{CT}$ of member $i$ can be expressed as (9).

$$C_{i,t}^{CT}=\{\begin{array}{c}\begin{array}{c}{\lambda }_1\left(R_{ALL,i}-R_{i,t}\right), 0\le R_{i,t}<R_{ALL,i};\\ {\lambda }_2\left(R_{i,t}-R_{ALL,i}\right), R_{ALL,i}\le R_{i,t}<\left(1+a\right)R_{ALL,i};\end{array}\\ \begin{array}{c}{\lambda }_{2}a{R}_{ALL,i}+{\lambda }_3\left(R_{i,t}-\left(1+a\right)R_{ALL,i}\right), \left(1+a\right)R_{ALL,i}\le R_{i,t}<\left(1+2a\right)R_{ALL,i};\\ ({\lambda }_2+{\lambda }_3)a{R}_{ALL,i}+{\lambda }_4\left(R_{i,t}-\left(1+2a\right)R_{ALL,i}\right), R_{i,t}\ge \left(1+2a\right)R_{ALL,i}\end{array}\end{array}$$

(9)

where ${\lambda }_1~{\lambda }_4$ denotes the carbon-trading prices as (10); $a$ represents the step of carbon-emission responsibilities; and $R_{i,t}$ denotes the actual carbon-emission responsibilities of member $i$, as in (11).

$${\lambda }_{1~4}=\{\begin{array}{c}{\lambda }_{1~4}^{Load}, i\in {\Omega }_L;\\ {\lambda }_{1~4}^{Gen}, i\in {\Omega }_G\end{array}$$

(10)

$$R_{i,t}=\{\begin{array}{c}{R}_{L,i}^{gross}, i\in {\Omega }_L;\\ R_{G,i}, i\in {\Omega }_G\end{array}$$

(11)

where ${\Omega }_L$ and ${\Omega }_G$ represent the sets of loads and generators, respectively, and ${\lambda }_{1~4}^{Load}$ and ${\lambda }_{1~4}^{Gen}$ represent the load-side and source-side carbon-trading prices, respectively.

3. Hierarchical Optimal-Dispatch Model Considering the Source-Load Bilateral Carbon-Trading Mechanism and Load-Side Electrical Energy Storage

3.1. Hierarchical Model Framework

Figure 1 presents the framework of the proposed hierarchical dispatch model. The first layer performs economic dispatch considering source-side carbon trading and obtains the power flow. Using the CEF theory, load-side carbon-emission responsibilities are obtained according to the power flow and passed to the second layer. The second layer conducts the carbon-oriented demand-response optimization with the electrical energy storage (EES). Then, the optimal EES operation of each load is obtained and sent back to the first layer for the next iteration until the computation tends to converge.

3.2. First-Layer Optimization

3.2.1. Objective

The first-layer optimization conducts an economic dispatch of the entire power network. The objective function includes two parts: power-generation costs and source-side carbon-transaction costs. The specific expression is as follows:

$$min{\displaystyle \sum }_{t=0}^T\left({\displaystyle \sum }_{g=1}^{N_G}{c}_g{P}_{g,t}+{\displaystyle \sum }_{g=1}^{N_G}{C}_{g,t}^{CT}\right)$$

(12)

where $c_g$ is the generation cost coefficient of generator $g$; $P_{g,t}$ denotes the output power of generator $g$ at time $t$; $N_G$ and $T$ denote the number of generators in the system and the calculation period, respectively; and $C_{g,t}^{CT}$ represents the source-side carbon-trading costs, as in (9)–(11).

3.2.2. Constraints

To be more accurate, the DC power-flow model considering transmission losses was adopted in this paper [40]. Constraints (13)–(19) denote the system-operating constraints. Inequality (13) denotes the maximum and minimum constraints of the generator output. Equations (14) and (15) denote the power flow and transmission losses of the branches. Inequality (16) denotes the maximum and minimum limits of the branch transmission capacity. Equation (17) is the constraint of the bus power balance. Inequality (18) denotes the constraint of the phase-angle difference. Equation (19) denotes the constraint of the slack-bus phase angle.

$$P_{g,min}\le P_g\le P_{g,max}$$

(13)

$$P_{ij}=\frac{{\theta }_{ij}}{x_{ij}}$$

(14)

$$P_{ij}^{loss}=g_{ij}{\theta }_{ij}^2$$

(15)

$$P_{ij,min}\le P_{ij}\le P_{ij,max}$$

(16)

$$P_g={\displaystyle \sum }_{j\in {\mathsf{\Omega }}_i}{P}_{ij}+{\displaystyle \sum }_{j\in {\mathsf{\Omega }}_i}\frac{1}{2}{P}_{ij}^{loss}+P_i^{load}$$

(17)

$${\theta }_{ij,min}\le {\theta }_{ij}\le {\theta }_{ij,max}$$

(18)

$${\theta }_{ref}=0$$

(19)

where $P_g$, $P_{g,max}$, and $P_{g,min}$ represent the generator output power and its maximum and minimum values, respectively; ${\theta }_{ij}$, ${\theta }_{ij,max}$, and ${\theta }_{ij,min}$ are the phase-angle differences of branches $i-j$ and their maximum and minimum values, respectively; $x_{ij}$ and $g_{ij}$ denote the line reactance and conductance, respectively; $P_{ij}$, $P_{ij,max}$, and $P_{ij,min}$ represent the transmission power and its maximum and minimum values, respectively; $P_{ij}^{loss}$ denotes the transmission losses of branches $i-j$; $P_i^{load}$ is the node power load; ${\mathsf{\Omega }}_i$ is the set of nodes adjacent to node $i$; and ${\theta }_{ref}$ is the phase angle of the slack node.

3.3. Second-Layer Optimization

3.3.1. Objective

The second-layer optimization performs the carbon-oriented EES optimal operation on the demand side. The problem is solved based on the following objective function:

$$min{\displaystyle \sum }_{t=0}^T\left({\displaystyle \sum }_{i=1}^{N_L}{C}_{i,t}^{CT}\right)$$

(20)

where $C_{i,t}^{CT}$ represents the load-side carbon-trading costs as in (9)–(11), and $N_L$ denotes the number of loads in the system.

3.3.2. Constraints

The load-side EES operation constraints can be expressed as (21)–(29). Specifically, constraint (21) represents the EES state-of-charge (SOC) constraint considering charge–discharge efficiency and self-discharge rate. Equation (22) represents the SOC returns to the initial state after the optimization is over. Inequality (23) denotes the maximum and minimum limits of the SOC. Equations (24) and (25) are the nominal capacity and power-rating constraints. Constraints (26)–(29) denote the EES charge and discharge constraints.

$$E_{t+1}=\left(1-{\gamma }_{loss}\right)E_t+\left({\eta }_{cha}{P}_t^{cha}-P_t^{dis}/{\eta }_{dis}\right)·∆t$$

(21)

$$E_0=E_T$$

(22)

$${\alpha }_{min}{E}_N\le E_t\le {\alpha }_{max}{E}_N$$

(23)

$$E_N={\mathsf{\tau }}_{cfg}{P}_{max}^{load}$$

(24)

$$P_N={\mathsf{\phi }}_{resp}{P}_{max}^{load}$$

(25)

$$0\le P_t^{cha}\le B_t^{cha}{P}_N$$

(26)

$$0\le P_t^{dis}\le B_t^{dis}{P}_N$$

(27)

$$0\le B_t^{cha}+B_t^{dis}\le 1$$

(28)

$$B_t^{cha},B_t^{dis}\in \left\{0,1\right\}$$

(29)

where $E_0$, $E_T$, and $E_t$ represent the SOC at the start time, end time, and time $t$, respectively; ${\gamma }_{loss}$, ${\eta }_{cha}$, and ${\eta }_{dis}$ represent the self-discharge rate, charging efficiency, and discharging efficiency of the EES, respectively; $P_t^{cha}$ and $P_t^{dis}$ represent the EES charging and discharging power, respectively; $∆t$ is the time step of the calculation; ${\alpha }_{max}$ and ${\alpha }_{min}$ represent the maximum and minimum limits of EES operation depth, respectively; $E_N$ and $P_N$ denote the EES nominal capacity and power rating; $P_{max}^{load}$ is the maximum power of the load; ${\mathsf{\tau }}_{cfg}$ and ${\mathsf{\phi }}_{resp}$ denote the nominal capacity coefficient and power-rating coefficient in the EES configuration; and $B_t^{cha}$ and $B_t^{dis}$ are binary variables representing the state of charge and discharge, respectively.

4. Test Results and Discussion

To illustrate the validity of the proposed model, case research was conducted on the modified New England 39-bus and IEEE 118-bus test systems. All test program codes were performed on a laptop with an 11th Gen Intel^® Core^TM i7 3.00 GHz CPU and 16 GB memory. The case-optimization models were developed based on a MATLAB R2021a environment with the YALMIP toolbox and were solved using a Gurobi 9.5.0 optimization solver. The optimization period was one day, and the time step was set to 1 h.

4.1. The Modified New England 39-Bus Test System

4.1.1. Basic System Parameters

The modified New England 39-bus test system is shown in Figure 2 [41]. The system contains 10 generators, including 5 coal generators, 2 gas generators, and 3 wind turbines. The specific parameters of the installed capacities, power-generation cost coefficients, and carbon-emission intensities of the generators are given in

Table 1. Parameters of generators.

Generator No.	Type	Capacity /(MW)	Cost Coefficient /(USD/MWh)	Carbon Intensity /(tCO2/MWh)
G1	Coal-fired	900	30	1.31
G2	Gas-fired	400	62	0.58
G3	Coal-fired	760	40	0.92
G4	Gas-fired	400	62	0.58
G5	Wind turbine	720	32	0
G6	Coal-fired	680	42	0.85
G7	Wind turbine	720	32	0
G8	Wind turbine	720	32	0
G9	Coal-fired	850	38	1.15
G10	Coal-fired	900	30	1.31

[41,42]. The actual power generated by the wind turbine is largely affected by the ambient wind speed. Typical forecast curves are usually used to describe wind-power outputs in related research [43,44]. The predicted wind-power output curve adopted in this paper is shown as a black line in Figure 3. There are 21 loads in the system, as indicated by the arrows on the buses in Figure 2. The trend of the load for 24 h is marked as a red line in Figure 3. The benchmark parameters for 21 loads are listed in

Table 2. Parameters of loads.

Load No.	Bus	Load Power /(MW)	Load No.	Bus	Load Power /(MW)	Load No.	Bus	Load Power /(MW)
L1	1	97	L8	12	8	L15	23	247
L2	3	322	L9	14	9	L16	24	308
L3	4	500	L10	15	320	L17	25	224
L4	7	233	L11	16	329	L18	26	139
L5	8	522	L12	18	158	L19	27	281
L6	9	6	L13	20	280	L20	28	206
L7	11	450	L14	21	274	L21	29	283

. Each load is equipped with EES devices to support demand response. The specific parameters of the EES devices are shown in

Table 3. Parameters of load-side EES devices.

Item	Parameter	Item	Parameter
${\eta }_{cha}$$/{\eta }_{dis}$	95%	${\alpha }_{max}$	90%
${\mathsf{\phi }}_{resp}$	25%	${\alpha }_{min}$	10%
${\gamma }_{loss}$	2%/month	${\mathsf{\tau }}_{cfg}$	2 h

. There are 46 branches in the system, and their reactance and conductance parameters refer to MATPOWER [41].

4.1.2. Parameters of the Source-Load Bilateral Ladder-Type Carbon-Trading Mechanism

To formulate a source-load bilateral ladder-type carbon-trading mechanism, the carbon-emission responsibility ranges of the generators and loads should be divided reasonably. Using the Aumann–Shapley method mentioned in Section 2, the Aumann–Shapley values of 10 generators, i.e., the rational allocations of carbon-emission responsibilities, can be calculated under economic dispatch as shown in Figure 4. Due to the small power-generation cost coefficient, the coal-fired generators G1 and G10 continue to generate electricity at full capacity, resulting in a constant high carbon-emission responsibility. On the contrary, due to the large power-generation cost coefficient, the gas-fired generators G2 and G4 continue to generate electricity with the minimum lower limit, resulting in a constant low carbon-emission responsibility. With zero carbon intensity, wind turbines G5, G7, and G8 always have zero carbon-emission responsibility. The carbon-emission responsibilities of coal-fired generators G3, G6, and G9 vary substantially with the power output.

The Aumann–Shapley value represents a reasonable allocation of carbon-emission responsibility. Thus, according to (2), the carbon-allowance values of 10 generators can be obtained, and the results are given in Figure 5.

Similar to the above, the 24 h carbon-emission responsibilities of 21 loads under economic dispatch with the Aumann–Shapley method are presented in Figure 6. Figure 7 presents the carbon-allowance values of 21 loads obtained according to (2).

According to Section 2.3, the parameters of the source-load bilateral ladder-type carbon-trading mechanism are set as seen in

Table 4. Bilateral ladder-type carbon-trading parameters.

Carbon-Responsibility Range/tCO2	Carbon-Trading Price/(USD/tCO2)
	Source-Side	Load-Side
$0~R_{ALL,i}$	${\lambda }_1=-10$	${\lambda }_1=-2$
$R_{ALL,i}~\left(1+\mathrm{a}\right)R_{ALL,i}$	${\lambda }_2=15$	${\lambda }_2=5$
$\left(1+a\right)R_{ALL,i}~\left(1+2\mathrm{a}\right)R_{ALL,i}$	${\lambda }_3=25$	${\lambda }_3=8$
$\left(1+2\mathrm{a}\right)R_{ALL,i}$	${\lambda }_4=40$	${\lambda }_4=10$

. The step of carbon-emission responsibility is $a=1/3$.

4.1.3. Optimization Results of the Proposed Source-Load BCT Mechanism

After performing the hierarchical optimal-dispatch model considering the proposed source-load BCT mechanism, the output power of each generator before and after optimization is shown in Figure 8.

As shown in Figure 8, the different colors represent different types of units. Orange, blue, and green represent the coal generators, gas generators, and wind turbines, respectively. The top edge of the colored area denotes the total power demand of the system. Comparing Figure 8b with Figure 8a, the total power-demand curve after optimization is flatter and more wind power is consumed, especially at night. Stimulated by the source-load BCT mechanism, load-side EES tends to charge at night and discharge during the day, and meanwhile, the wind turbines are encouraged to produce greater outputs. Therefore, it can be verified that the proposed mechanism can effectively increase wind-power consumption and reduce the peak-valley difference in power demand.

Figure 9 presents the bus carbon-intensity results before and after optimization. Comparing Figure 9b with Figure 9a, most bus intensities become lower, which means the electricity that flows through the buses becomes cleaner. The bus intensities of some buses, such as bus 8 and bus 9, are not substantially changed. This is because the bus intensity is influenced by the relative location to the wind turbines. The total carbon emissions of the system before and after optimization are 96,470.3 tCO₂ and 81,054.5 tCO₂, a reduction of 16.0%.

To summarize, it can be proven that the proposed source-load BCT mechanism can effectively increase the wind-power consumption, decrease the power peak-valley difference, and therefore, significantly promote carbon-emission mitigation.

4.1.4. Comparative Analysis of the UCT Mechanism and the Proposed BCT Mechanism

To illustrate the superiority, the proposed mechanism was compared with two other carbon-trading mechanisms in relevant studies. As seen in

Table 5. Three cases with different carbon-trading mechanisms.

Case	Carbon-Trading Mechanism			Reference
	Source-Side	Load-Side	Type
Case 1		✔	UCT	[31]
Case 2	✔		UCT	[22]
Case 3	✔	✔	BCT	Proposed in this study

, Case 1 is the economic dispatch considering the load-side UCT mechanism [31]; Case 2 is the economic dispatch considering the source-side UCT mechanism [22]; and Case 3, proposed in this study, is the economic dispatch considering the source-load BCT mechanism.

The three cases were performed in the modified New England 39-bus test system. The output power of each generator after optimization in Case 1 and 2 was obtained, as presented in Figure 10. The output power of each generator after optimization in Case 3 is shown in Figure 8b above. Compared to Figure 8, in Case 1, load-side UCT can promote wind-power consumption and reduce the load peak-valley difference by scheduling the EES. In Case 2, source-side UCT can facilitate wind-power consumption by increasing the generation costs of thermal-power generators. Hence, it can be noticed from the comparison that the proposed source-load BCT mechanism takes into account the advantages of both the load-side UCT mechanism and the source-side UCT mechanism.

The bus carbon intensities after optimization in Case 1 and Case 2 are shown in Figure 11. The bus carbon intensities after optimization in Case 3 are presented in Figure 9b above. Comparing Figure 9b with Figure 11, the proposed BCT mechanism can reduce the bus carbon intensities more effectively and widely. Taking the case of economic dispatch without considering the carbon-trading mechanism as a blank control group, the total carbon emissions and carbon-reduction rates of the three cases are presented in Figure 12. The carbon-reduction rates of the three cases are 4.6%, 9.7%, and 16.0%, respectively. The results demonstrate that the proposed source-load BCT mechanism has superiority in carbon mitigation over the other two UCT mechanisms.

4.2. Large-Scale System Testing: A Modified IEEE 118-Bus System

To further verify the validity and superiority of the proposed mechanism in a larger-scale system, the three cases in Section 4.1.4 were also tested on the modified IEEE 118-bus system [41]. The relevant parameter settings are similar to Section 4.1.1. The bus carbon intensities in the IEEE 118-bus system before optimization and in the three cases are presented in Figure 13. The total carbon emissions and carbon-reduction rates of the three cases are given in Figure 14.

As seen in Figure 13, the carbon intensities of some buses become lower in the three cases and the effect is especially obvious in Case 3. Specifically, as presented in Figure 14, the carbon-reduction rates of the three cases are 6.3%, 9.2%, and 16.8%, respectively. Therefore, it can be verified that the proposed source-load BCT mechanism is still effective and superior to the other two UCT mechanisms for carbon mitigation in a large-scale system.

In summary, the specific comparison results in the two test systems are shown in

Table 6. Comparison results of carbon emissions under different carbon-trading mechanisms in the two systems.

New England 39-Bus Test System			IEEE 118-Bus Test System
Carbon-Trading Mechanism	Carbon Emission /(tCO2)	Carbon-Reduction Rate/(%)	Carbon-Trading Mechanism	Carbon Emission /(tCO2)	Carbon-Reduction Rate/(%)
None	96,470.3	/	None	188,586.0	/
Load-side UCT	92,040.0	4.6	Load-side UCT	176,790.0	6.3
Source-side UCT	87,132.9	9.7	Source-side UCT	171,250.5	9.2
Source-load BCT	81,054.5	16.0	Source-load BCT	156,836.7	16.8

. It is obvious from the carbon-reduction-rate data that the proposed source-load BCT mechanism has significant advantages in carbon mitigation compared with the source-side and load-side UCT mechanisms.

5. Conclusions

This paper focused on the impact of the participation of both the source and load in carbon transaction on carbon mitigation in the power system. A hierarchical low-carbon economic-dispatch model with source-load bilateral carbon trading based on the Aumann–Shapley method was proposed. The model took into account both the generators’ and loads’ carbon-emission responsibilities. The first layer of the model conducted an economic dispatch to minimize power-generation costs and source-side carbon-trading costs. The second layer of the model performed demand-response optimization to minimize the load-side carbon-trading costs. To investigate the effectiveness and advantages, the proposed model was tested on the modified New England 39-bus system and the large-scale IEEE 118-bus system. The case results indicated that the proposed hierarchical economic-dispatch model with a source-load bilateral carbon-trading mechanism can effectively achieve load peak shaving and valley filling, promote wind electricity consumption, and decrease system carbon emissions by about 16%. Moreover, compared with the source-side and load-side UCT mechanisms, the proposed source-load BCT mechanism has obvious advantages in carbon-emission mitigation.

This study provides a theoretical reference for the practical application of carbon transaction in the power system to better promote the decarbonization of the system. This paper assumed that the source side and the load side share total-carbon-emission responsibilities equally in the power system. In the future, we can further study the impact of the source-side and load-side carbon obligation-sharing ratios on carbon mitigation and find the optimal sharing ratio.