Bi-Level Emission Reduction Model of the Hybrid Power Market Based on Carbon Emission Flow Theory and Source–Load Coordination

Abstract

Limited by the influence of network topology and other factors, the theory of carbon emission flow is unreasonable in the allocation of carbon responsibility on the user side, which leads to the low enthusiasm of users to respond to emission mitigation. The emergence of bilateral transactions provides users with the freedom to choose the type of power supply which is of great significance to exploring the potential of users to reduce emissions and promote the consumption of new energy. For this reason, this paper proposes a bi-level emission reduction model of the hybrid electricity market considering carbon emission flow and source–load coordination. The upper level aims to maximize the revenue of wind, photovoltaic, and thermal power generators and establishes a market-clearing model based on the trading rules of the hybrid electricity market to obtain the bid-winning power of each generator and the hybrid market electricity price. After the market is cleared, the carbon emission liability of the user side is calculated by using the carbon emission flow theory. The lower level takes the minimum cost of electricity consumption as the target and uses electricity price and carbon responsibility as incentives to establish a decision-making model for users to purchase electricity and guide users to actively choose green energy for consumption. The results of the example show that compared with the single pool market trading model the carbon emissions of the system are reduced by 11.9% while the income of the new energy power generations is increased by 9.84% and the electricity cost of the user is reduced by 21.2%, which underlines a mutually beneficial outcome for all stakeholders in the market.

1. Introduction

The environmental problems caused by carbon emissions in today’s world are becoming increasingly serious. In 2020, China proposed a “dual carbon” goal, aiming to reach a carbon peak by 2030 and carbon neutrality by 2060 [1]. According to statistics, carbon emissions from China’s major power industry account for about 40% of the total carbon emissions from the energy industry; the power system is facing severe pressure regarding carbon emission reduction [2]. Under this trend, the concept of carbon has been gradually integrated into all aspects of power market construction. In particular, with the continuous development of the smart grid, the information interaction between source and load has been strengthened [3,4,5,6]. Based on this, designing a flexible and efficient market mechanism to both optimize the allocation of source and load resources and promote carbon mitigation has become one of the important ways to achieve the goal of carbon neutrality. Therefore, it is crucial to address the urgent problem of implementing low-carbon power market dispatch at multiple levels, including source and load coordination [7], carbon responsibility allocation [8], and market mechanism design [9], all from the perspective of carbon [10].

At present, the coordination of source and load has become an important way to realize the optimal scheduling of a power system: to coordinate the generation side and user side dispatchable resources to realize their combined participation and optimize the system operation so as to obtain the best economic and environmental benefits [11]. Typically, source–load coordination is achieved through a demand response. It was found that the demand side response can improve the consumption rate of new energy through load regulation to maximize the benefits of participants in the market [12]. However, before carbon trading was paid great attention to in the market, the most optimal scheduling was from the perspective of a penalty incentive which reduces the output of thermal power units by imposing the cost of wind and light abandonment; there is a lack of research on carbon incentives for the market players to actively reduce their own carbon responsibility in response to emission reduction.

The carbon emission flow theory (CEF) of power systems is often used in the calculation of carbon responsibility allocation of load nodes. In this theory, carbon emissions will not be considered as a type of greenhouse gas but as a type of network flow which represents the flow of carbon from one node to another along network branches or paths in an energy network with visible structures and facilities. Based on this concept, the carbon emission flow theory tracks carbon emission from the generation side to the user side and closely links source–load with carbon emission flow as a bond so as to realize the allocation of carbon responsibility [13,14]. In [15], the theory of carbon emission flow and the power flow information of the electric energy transmission network were used to determine the transfer amount of carbon emissions on the power generation side at each node of the system, thus accurately tracking the carbon emission trajectory and clarifying the carbon responsibility of user nodes which laid the foundation for subsequent research. From the “carbon perspective”, the low-carbon demand response mechanism was investigated in [16,17,18]; based on the carbon emission flow theory, dynamic carbon emission factors were used as guidance signals for users to actively change their electricity consumption behaviors which shows that under carbon incentive users had a more obvious tendency to actively choose green generators through the demand response. The study by [19] implemented the incentive policy of time-of-use electricity price and carbon quota based on netload power and the results showed that this mechanism increased the effort of absorbing new energy, reduced the phenomenon of abandoning wind and solar power, and improved the on-site absorption capacity and the interests of both grid and load.

Based on the theory of carbon emission flow, the above literature combined carbon trading and source–load coordination which is of great significance to the study of low-carbon scheduling of power systems. However, the carbon responsibility allocation based on the carbon emission flow theory is irrational due to the topology of the power grid and the heterogeneity of carbon emissions from power sources. This is because the matrix of the power injected into nodes and the carbon intensity matrix of each generator are involved in the process of solving the carbon intensity matrix of the user node using the carbon emission flow theory [20,21]. For this reason, the user’s carbon responsibility is not only related to electricity consumption. In the pool market environment, the carbon responsibility allocation based on the carbon emission flow theory is unfair to users with a higher carbon intensity of nodes. In order to reduce carbon responsibility, users respond to emission reduction by reducing or transferring load which will lead to a decrease in user satisfaction with electricity consumption [22,23].

With the gradual opening of the electricity sales side market [24,25,26], the bilateral transaction mode emerges, providing a new way for demand side resources to participate in the power market. From the perspective of game theory, the literature [27,28] pertaining to studies on the bilateral transaction modes between multiple power generators and large users provides references for the formulation of bilateral transaction mechanisms. The studies in [29,30] analyzed the energy-saving and emission reduction benefits of four bilateral trading modes, including power generation rights trading, trans-regional and trans-provincial power trading, and direct power purchasing trading for large users, providing a theoretical basis for the bilateral market to help the low-carbon construction of the market. In [31], the impact of pricing strategies of generators participating in spot and bilateral markets on other market participants was discussed, maximizing the benefits of each power generator participating in the market under the game environment and achieving the economic objectives of the market. To sum up, bilateral transactions promote new energy consumption and carbon emission reduction by introducing competitive power sellers and gradually opening up the user’s right to choose [32,33]. Therefore, bilateral trading realizes the direct interaction between the two sides of the source and load, creates a place of free trade for users and power generators, and provides a new way for users to reduce their own carbon responsibility through market means.

In summary, from the perspective of emission reduction, this paper introduces the bilateral trading mode between generators and users and proposes a bi-level emission reduction model of the hybrid electricity market incorporating source–load coordination and carbon emission flow. Finally, the multi-case comparison verifies that the user response mechanism under the hybrid electricity market has the benefit of emission reduction. The main contributions of this paper are as follows:

(1)

Based on the source–load coordination and the carbon emission flow theory, this paper proposes a bi-level emission reduction model of the hybrid electricity market;

(2)

Introducing the bilateral trading mode, the trading mechanism of the hybrid electricity market is constructed, and thus, a new way for users to respond to emission reduction is provided;

(3)

Based on the IEEE9-node system, the effectiveness of the emission reduction model in the hybrid electricity market is verified. In addition, compared with the trading mode of the pool market and the allocation of carbon responsibility on the generation side, the carbon responsibility allocating on the user side in the hybrid electricity market proposed in this paper has obvious carbon emission reduction advantages.

The structure of this paper is arranged as follows: Section 2 introduces the trading rules and carbon responsibility allocation method of the hybrid electricity market, Section 3 introduces the hybrid electricity market emission reduction model considering carbon emission flow and source–load coordination, case studies are carried out in Section 4, and Section 5 serves as the concluding section of this article, summarizing the key findings.

2. Market Transaction Rules and the Carbon Responsibility Apportioning Method

2.1. Hybrid Electricity Market Trading Model

As the marginal clearing mode of the pool market is a large number of uncertain centralized clearing among generators [34,35], the bid-winning power of new energy generators cannot be guaranteed, while bilateral trading can guide users to achieve preferential consumption of clean energy in the market through carbon responsibility incentive measures; so, this paper proposes a model that could potentially enable user’s choice regarding power generators. Generators are encouraged to give priority to bilateral transaction needs.

As indicated in Figure 1, in the hybrid electricity market, users, and generators can engage in both pool and bilateral transactions. In the pool market, users and generators trade through the Independent System Operator (ISO) which is an independent body responsible for regulating the electricity market and the electricity transmission and distribution grid. Under this trading mechanism, each generator submits the quotation strategy and each user declares the demand for electricity. After that, ISO announces the market clearing price and bid-winning power. In the bilateral market, the users and the generators trade directly. Generators quote prices to user and users report the bilateral demand, finally reaching a bilateral contract.

2.1.1. Bilateral Market Trading Model

The trading methods in the bilateral market are divided into bilateral trading, centralized matching trading, centralized bidding trading, etc. [36,37]. This paper focus on the bilateral transaction mode between multiple generators and multiple large users under the background of the spot market. Large users can freely choose multiple generators for trading and the same generators can be selected by multiple large users. The generator gives the corresponding quotation within the quotation range according to its own cost, and the large user accepts the bilateral quotation given by the generator and selects the generator that is suitable for its own transaction demand.

Suppose there are J generators and I large user in the market. First of all, the generator j gives the quotation strategy ${\mathit{P}}_{\mathit{b},\mathit{j}}^{\mathit{t}}$ for all large users, where ${\mathit{P}}_{\mathit{b},\mathit{j}}^{\mathit{t}}=[{\mathit{P}}_{\mathit{b},\mathit{j},\mathbf{1}}^{\mathit{t}},{\mathit{P}}_{\mathit{b},\mathit{j},\mathbf{2}}^{\mathit{t}},\dots {\mathit{P}}_{\mathit{b},\mathit{j},\mathit{i}}^{\mathit{t}}]$ is the set of bilateral transaction quotations for the generator t period.

After obtaining the quotation from each generator, a large user i determines the contract electricity quantity ${\mathit{Q}}_{\mathit{b},\mathit{j}}^{\mathit{t}}$ signed with each generator according to its own electricity demand, where ${\mathit{Q}}_{\mathit{b},\mathit{j}}^{\mathit{t}}=[{\mathit{q}}_{\mathit{b},\mathit{i},\mathbf{1}}^{\mathit{t}},{\mathit{q}}_{\mathit{b},\mathit{i},\mathbf{2}}^{\mathit{t}},\dots {\mathit{q}}_{\mathit{b},\mathit{i},\mathit{j}}^{\mathit{t}}]$ is the set of bilateral electricity transactions between large user i and generator j during the period t.

As a result of the opening of the market on the electricity-selling side, each power generator participates in the market competition as an independent power seller. Compared with the traditional pool market, the mode of user participation in the market has changed from only purchasing power through ISO to directly trading with each power producer, which improves the flexibility of the market trading mechanism and increases the competition among power producers.

2.1.2. Pool Market Trading Model

After meeting the demand of the bilateral market, the generators will participate in the pool market bidding with the remaining capacity as the upper limit and submit the quotation strategy to ISO. Subsequently, ISO determines the final market clearing price and the bid-winning power of each generator according to the quotation strategies. In this paper, the clearing price of each generator is settled according to the marginal price mechanism, namely, the Market Clearing Price (MCP) which corresponds to the highest bid among the participating generators.

2.2. Carbon Emission Model Based on Carbon Emission Flow Theory

After the hybrid electricity market is cleared, the carbon emission flow theory is used to share the carbon responsibility on the user side and the allocated carbon responsibility will be used as an incentive signal to guide the user to actively choose clean energy consumption.

Based on the principle of “who uses, who bears” [17], this paper distributes the carbon responsibility in the environment of the hybrid electricity market. In the bilateral market, the power supply of the user is the generator with which the bilateral transaction is made and the source and sink of carbon emission flow are determined. In the pool market, the power distribution in the network can be defined only after the power flow analysis and the carbon emission flow theory can be used to apportion the carbon responsibility on the user side according to the results of the power flow calculation. Therefore, when calculating the corresponding carbon emission of each transaction, bilateral transactions and pool transactions should be dealt with separately [38].

2.2.1. Carbon Emission Flow Concept

According to the carbon emission flow theory of power systems, the carbon dioxide generated during power generation flows to the user side along with the virtual “carbon flow” of power flow. In this paper, the concepts of carbon emission flow rate R and carbon flux density ρ are introduced to quantitatively calculate carbon emission.

The carbon emission flow rate represents the carbon emission flow energy F passing through network nodes or branches in unit time and its unit is tCO₂/h, as shown in Equation (1):

$$R=\frac{dF}{dt}$$

(1)

The branch carbon flow density ρ represents the carbon emission value of the generation side caused by the unit power consumption of branch transmission in tCO₂/kWh, as shown in Equation (2):

$$\rho =\frac{R}{P}$$

(2)

where P is the branch power and the unit is kWh.

2.2.2. User Side Carbon Emission Model of Hybrid Power Market

In the hybrid electricity market, according to the carbon emission flow theory, the carbon emission allocated by users at node i consists of two parts. The specific expression is as follows:

$$R_i=R_{b,i}+R_{p,i}$$

(3)

where $R_{b,i}$ is the carbon emission allocated by users at node i in the bilateral market and $R_{p,i}$ is the carbon emission allocated by users at node i in the pool market.

The carbon emission assigned by users at node i in a bilateral market can be calculated directly according to the carbon intensity of the power supply, that is:

$$R_{b,i}={\displaystyle \sum _{j=1}^M{q}_{b,i,j}{e}_j}$$

(4)

where $q_{b,i,j}$ is the bilateral transaction electricity between the user i and generator j and e_j represents the carbon intensity of generator j, which is obtained according to the power generation characteristics.

The carbon emission allocated by users at node i in the pool market can be calculated via Equations (5) and (6):

$$e_i=\frac{{\displaystyle \sum _{i=1}^I{P}_i{\rho }_i}+P_j{e}_j}{{\displaystyle \sum _{i=1}^I{P}_i+P_j}}$$

(5)

where e_i is the carbon intensity of node i which represents the equivalent carbon emission caused by the unit electricity consumed by the node. P_i is the power injected into node i, P_j is the generator output power at node j, and ${\mathsf{\rho }}_i$ is the branch carbon flow density injected into node i. I indicates the number of branches that inject power to node i. The branch carbon flow density i can be replaced by the carbon intensity of the node at the beginning of the branch. After the carbon intensity e_i of the user at node i is obtained, the carbon responsibility of the user at node i can be calculated according to the following equation:

$$R_{p,i}=e_i{D}_{p,i}$$

(6)

where $D_{p,i}$ is the electricity purchased by user i in the pool market.

According to Equations (5) and (6), when sharing carbon responsibility in the pool market, the carbon responsibility of the user is affected by the carbon intensity of the unit and the network topology. Even the user with the same electricity demand will have different carbon emission R_p,i. From the perspective of the bilateral market, the users’ carbon responsibilities are not constrained by the network topology but are directly determined by the generators. On the basis of Equation (4), when users purchase clean energy to meet part of their electricity demand through bilateral transactions, the carbon intensity e_j of new energy is 0 and its assigned carbon emission R_i will be greatly reduced. Therefore, the introduction of bilateral markets provides an effective way to reduce carbon responsibility for users with large carbon flow rates.

3. Hybrid Electricity Market Emission Reduction Model Considering Carbon Emission Flow and Source–Load Coordination

3.1. Bi-Level Model Interaction Framework

In this paper, the bilateral market is introduced to establish a hybrid electricity market emission reduction model considering carbon emission flow and source–load coordination. The framework is shown in Figure 2 and is described as follows:

The upper layer is the clearing layer of the hybrid electricity market. In the pool market, the mode of centralized bidding and unified liquidation is adopted, and all the power generators quote to ISO, where the wind power and photovoltaic power generators consider uncertainty factors in the quotation and ISO determines the market clearing price and the bid-winning power of each generator with the minimum procurement cost as the goal. Meanwhile, the bilateral market refers to the bilateral negotiation mode under the background of the direct purchase of electricity by large users. Generators determine the quotation of both parties according to the declared power of the user. The pool market and bilateral market were cleared at the same time; according to the cleaning result, the carbon intensity of each user node is calculated using the carbon emission flow theory and the electricity price is sent to the user.

The lower layer is the decision-making level of the users’ electricity consumption. According to the electricity price and carbon responsibility allocation results, users decide the power purchasing strategy for each period with the goal of minimizing the cost of electricity.

After constructing the double-layer model, the paper uses the idea of double-layer iterative optimization to solve it so as to obtain the optimal power purchase strategy scheduling of users every day (24 h). The model is divided into two optimization levels: upper optimization and lower optimization. Among them, the optimization of the upper layer is solved by an improved genetic algorithm, the optimization of the lower layer is solved by Yalmip/Gurobi solver and the upper and lower layers are iteratively optimized through interactive decision variables. It is important to note that the parameter setting of the genetic algorithm has a great influence on the performance and effect of the algorithm. The increase in the population will lead to the expansion of the search space but the calculation time will also increase. Therefore, the general setting range is 50–200. Furthermore, the crossover rate determines the number of individuals required for each generation. A high crossover rate may lead to early convergence so the experience value is 0.6–0.9. In addition, the number of iterations should be optimized according to the space size of feasible solutions. The main steps are as follows:

Step 1

Input data such as the output parameters of wind, light, and fire generators; user load; scalar constraint; and market clearing price constraint in generators.

Step 2

Initialize the generator parameters and select the most suitable parameters for the genetic algorithm after several simulation tests according to the above rules. Set the population number m to 55, the number of iterations to 80, the scaling factor to 0.5, the crossover probability to 90%, and the convergence error. The improved adaptive genetic algorithm is used to generate the initial quotation quantity strategy group of power generators. ISO determines the market clearing price and the bid quantity according to the strategies of power generators and feed them back to each power generator. The selection and variation of the improved adaptive genetic algorithm are used to generate a new optimal quotation strategy for power generators.

Step 3

Determine whether the number of upper iterations meets the convergence condition. If yes, output; if no, return to Step 2.

Step 4

Use the carbon emission flow theory to calculate the users’ carbon responsibility.

Step 5

The clearing price and node carbon intensity are substituted into the lower-level user model and solved using Yalmip/Gurobi on the MATLAB platform.

Step 6

According to the solution result in Step 5, judge whether the change amount of the user’s power purchase strategy is less than or equal to ε, which is the allowable error of the change in the user’s power purchase strategy and generally a very small value used to judge whether convergence occurs. If yes, output the optimal solution; otherwise, return to Step 2.

3.2. Upper Level Optimization

3.2.1. Cost of Generator

Under the market background of this paper, new energy power generators and thermal power generators participate in market bidding fairly and their costs are expressed in the form of quadratic functions [39]. The cost factor is discussed as follows:

$$C_{\cos t}=a{p}^2+bp+c$$

(7)

where a and b are variable cost coefficients. The variable cost of a thermal power generator mainly refers to the cost of coal consumption and the variable cost of new energy generators includes power generation operation cost and unbalanced cost. c is the fixed cost factor which refers to the investment and construction costs of power generators. p is the output of the unit.

The existence of the variable cost coefficients a and b indicates that this part of the cost will vary with the change in the quantity of generation when the generator participates in the bidding. According to the actual situation, since the new energy generator does not consume fuel in the power generation process, the fuel cost is often far less than the thermal power generator. However, after considering the randomness of new energy outputs [40,41], in order to suppress this part of unbalanced power, new energy needs to take into account the high unbalanced cost [42,43,44] so its variable cost coefficient is generally greater than the thermal power cost. This phenomenon reflects the real situation that new energy generators affected by the randomness of output lack competitiveness when bidding with thermal power generators. In addition, as coal and oil are non-renewable resources, the rising trend of variable cost coefficients of thermal power generators will continue in the future.

Moreover, since the installed capacity of the power plant is fixed after the investment in power generation, it will not change for a long period of time and the cost of this part of the power plant does not vary with the change in the power generation. In the context of the spot market studied in this paper, the fixed costs incurred for the already built generation side are not considered so item c is often assigned a value of 0.

3.2.2. Objective of the Wind Power Generator

The maximum revenue of the wind power generator takes into consideration the bilateral market, the pool market sales revenue, and the generation cost and is described by Equation (8). Specifically, the revenue from the bilateral market is the sum of revenue from bilateral contracts between the generator and each user and in the pool market, the revenue of the generator is settled at the market-clearing price. In addition, the cost is calculated based on the total amount of electricity sold by the generator in the hybrid market, as shown in Equations (9)–(11).

$$\max C_w=\max [C_{b,w}^{sell}+C_{p,w}^{sell}-C_{\cos t,w}]$$

(8)

$$C_{b,w}^{sell}={\displaystyle \sum _{t=1}^{24}{\displaystyle \sum _{i=1}^N{P}_{b,i,w}^t{q}_{b,i,w}^t}}$$

(9)

$$C_{p,w}^{sell}={\displaystyle \sum _{t=1}^{24}{q}_w^t{\lambda }^t}$$

(10)

$$C_{\cos t,w}={\displaystyle \sum _{t=1}^{24}a}{({\displaystyle \sum _{i=1}^N{q}_{b,i,w}^t}+q_w^t)}^2+b({\displaystyle \sum _{i=1}^N{q}_{b,i,w}^t}+q_w^t)+c$$

(11)

where N is the number of large users, $C_{b,w}^{sell}$ is the electricity sales revenue of wind power generator in the bilateral market, $C_{p,w}^{sell}$ is the electricity sales revenue of wind power generator in the pool market, and $C_{\cos t,w}$ is the generation cost of the wind power generator. $q_w^t$ is the bid-winning power of wind power generator in the pool market and ${\lambda }^t$ is the market clearing price in the pool market during the period t. $P_{b,i,w}^t$ is the bilateral transaction price between the wind power generator and user I and $q_{b,i,w}^t$ is the bilateral transaction electricity between the wind power generator and user i.

3.2.3. Constraints on Wind Power Generator

In the process of market clearing, considering the increase in power generation cost caused by the randomness, the new energy power generators are encouraged to make reasonable quotations and the upper and lower limits of the quotations are set so that the quotations of the market main members can only be within the set range. The quotation constraints can be expressed as (12) and (13), where Inequality (12) denotes the quotation constraint of wind power generators in the bilateral market and Inequality (13) denotes the constraint in the pool market. In addition, considering that the bid-winning power cannot exceed the bid power, Inequality (14) is used to describe the bid-winning power constraint in the pool market.

$$P_{w,\min }\le P_{b,i,w}^t\le P_{w,\max }$$

(12)

$$P_{w,\min }\le P_{p,w}^t\le P_{w,\max }$$

(13)

$$0\le q_w^t\le G_w^t-{\displaystyle \sum _{i=1}^N{q}_{b,i,w}^t}$$

(14)

where $P_{p,w}^t$ is the quotation of wind power generator in the pool market and $P_{w,\max }$ and $P_{w,\min }$ are, respectively, the upper and lower limits of the quotation of wind power generator in the market. $G_w^t$ is the maximum power generated by wind power at time t.

3.2.4. Objective of Photovoltaic Power Generator

The maximum revenue of the photovoltaic power generator takes into consideration the bilateral market, the pool market sales revenue, and the generation cost and is described by Equation (15).

$$\max C_{pv}=\max [C_{b,pv}^{sell}+C_{p,pv}^{sell}-C_{\cos t,pv}]$$

(15)

$$C_{b,pv}^{sell}={\displaystyle \sum _{t=1}^{24}{\displaystyle \sum _{i=1}^N{P}_{b,i,pv}^t{q}_{b,i,pv}^t}}$$

(16)

$$C_{p,pv}^{sell}={\displaystyle \sum _{t=1}^{24}{q}_{pv}^t{\lambda }^t}$$

(17)

$$C_{\cos t,pv}={\displaystyle \sum _{t=1}^{24}a}{({\displaystyle \sum _{i=1}^N{q}_{b,i,pv}^t}+q_{pv}^t)}^2+b({\displaystyle \sum _{i=1}^N{q}_{b,i,pv}^t}+q_{pv}^t)+c$$

(18)

where $C_{b,pv}^{sell}$ is the electricity sales revenue of photovoltaic power generator in the bilateral market, $C_{p,pv}^{sell}$ is the electricity sales revenue of photovoltaic power generator in the pool market, and $C_{\cos t,pv}$ is the generation cost of the photovoltaic power generator. $q_{pv}^t$ is the bid-winning power of photovoltaic power generator in the pool market and ${\lambda }^t$ is the market clearing price in the pool market during the period t. $P_{b,i,pv}^t$ is the bilateral transaction price between the photovoltaic power generator and user I and $q_{b,i,pv}^t$ is the bilateral transaction electricity between the photovoltaic power generator and user i.

3.2.5. Constraints on the Photovoltaic Power Generator

Similarly to the wind power generator, the quotation constraints can be expressed as (19) and (20), where Inequality (19) denotes the quotation constraint of photovoltaic power generators in the bilateral market and Inequality (20) denotes the constraint in the pool market. Inequality (21) is the constraint of bid-winning power in the pool market.

$$P_{pv,\min }\le P_{b,i,pv}^t\le P_{pv,\max }$$

(19)

$$P_{pv,\min }\le P_{p,pv}^t\le P_{pv,\max }$$

(20)

$$0\le q_{pv}^t\le G_{pv}^t-{\displaystyle \sum _{i=1}^N{q}_{b,i,pv}^t}$$

(21)

where $P_{p,pv}^t$ is the quotation of photovoltaic power generator in the pool market and $P_{pv,\max }$ and $P_{pv,\min }$ are, respectively, the upper and lower limits of the quotation of photovoltaic power generator in the market. $G_{pv}^t$ is the maximum power generated by photovoltaic power at time t.

3.2.6. Objective of the Thermal Power Generator

The maximum revenue of the thermal power generator takes into consideration the bilateral market, the pool market sales revenue, and the generation cost and is described by Equation (22).

$$\max C_f=\max [C_{b,f}^{sell}+C_{p,f}^{sell}-C_{\cos t,f}]$$

(22)

$$C_{\cos t,f}={\displaystyle \sum _{t=1}^{24}a}{({\displaystyle \sum _{i=1}^N{q}_{b,i,f}^t}+q_f^t)}^2+b({\displaystyle \sum _{i=1}^N{q}_{b,i,f}^t}+q_f^t)+c$$

(23)

3.2.7. Constraints on the Thermal Power Generator

The quotation constraints can be expressed as (24) and (25), where inequality (24) denotes the quotation constraint of thermal power generator in the bilateral market and Inequality (25) denotes the constraint in the pool market. Inequality (26) is the constraint of bid-winning power in the pool market.

$$P_{f,\min }\le P_{b,i,f}^t\le P_{f,\max }$$

(24)

$$P_{f,\min }\le P_{p,f}^t\le P_{f,\max }$$

(25)

$$0\le q_f^t\le G_{f,\max }-{\displaystyle \sum _{i=1}^N{q}_{b,i,f}^t}$$

(26)

where $P_{p,f}^t$ is the quotation of thermal power generator in the pool market and $P_{f,\max }$ and $P_{f,\min }$ are, respectively, the upper and lower limits of the quotation of thermal power generator in the market. $G_{f,\max }$ is the installed capacity of thermal power unit.

3.2.8. Objective of ISO

In the pool market, ISO takes the quotation of the last winning unit as the market clearing price; all generators settle according to the clearing price and its objective is the minimum power purchasing cost C_P as

$$\min C_P={\displaystyle \sum _{t=1}^{24}{q}_w^t{P}_{p,w}^t+}{q}_{pv}{P}_{p,pv}^t+q_f^t{P}_{p,f}^t$$

(27)

3.2.9. Constraint

The actual power market clearing rules state that ISO needs to arrange unit scheduling under the premise of satisfying load constraints and network security constraints. According to this, Formulas (28)–(30) are formed to describe relevant constraints. Specifically, Equation (28) denotes the load balance constraint and Inequalities (29) and (30) are the network constraints where Inequality (29) is the line power flow constraint and Inequality (30) is the node voltage constraint.

$$q_w^t+q_{pv}^t+q_f^t={\displaystyle \sum _{i=1}^N{D}_{p,i}^t}$$

(28)

$$P_{l,\min }^t\le P_l^t\le P_{l,\max }^t$$

(29)

$$U_{i,\min }^t\le U_i^t\le U_{i,\max }^t$$

(30)

where $D_{p,i}^t$ refers to the electricity purchased by user I in the pool market during the period t. $P_l^t$ is the active power transmitted by line l; $P_{l,\max }^t$ is the maximum active power allowed to be transmitted by line l, and $P_{l,\min }^t$ is the minimum active power allowed to be transmitted by line l. $U_i^t$ is the voltage of the user node and $U_{i,\max }^t$ and $U_{i,\min }^t$ are the upper and lower limits of the voltage of user node I, respectively.

3.3. Lower-Level Optimization

3.3.1. Objective of User

Since users need to comprehensively consider their electricity purchasing costs in the hybrid power market and carbon emission costs to formulate power purchasing strategies, therefore, the minimum cost of the user is described by Equation (31).

$$\min C_i=\min [C_{b,i}^{pay}+C_{p,i}^{pay}+C_{C{O}_2,i}]$$

(31)

where $C_i$ represents the total cost of electricity for user I, $C_{b,i}^{pay}$ is the cost of electricity purchased by the user in the bilateral market, $C_{p,i}^{pay}$ is the cost of electricity purchased by the user in the pool market, and $C_{C{O}_2,i}$ is the cost of carbon responsibility for the user.

According to the trading rules, the power purchasing cost of the bilateral market includes the expenditure of transactions between the user and each power producer. For the pool market, the cost of power is the electricity demand consumption settled at the market clearing price. And the carbon emission cost is the product of its carbon responsibility and carbon price. Based on the analysis above, Equation (31) is expanded as follows:

$$C_{b,i}^{pay}={\displaystyle \sum _{t=1}^{24}(P_{b,i,w}^t{q}_{b,i,w}^t}+P_{b,i,pv}^t{q}_{b,i,pv}^t+P_{b,i,f}^t{q}_{b,i,f}^t)$$

(32)

$$C_{p,i}^{pay}={\displaystyle \sum _{t=1}^{24}{D}_{p,i}^t{\lambda }^t}$$

(33)

$$C_{C{O}_2,i}={\displaystyle \sum _{t=1}^{24}(e_i{D}_{p,i}^t+e_f{q}_{b,i,f}^t}){\lambda }_{c{o}_2}$$

(34)

Here, e_i represents the carbon intensity of user node I, e_f is the carbon intensity of the thermal power generator, and ${\lambda }_{c{o}_2}$ is the market carbon price.

3.3.2. Constraints

The formulation of the power purchase strategy of the user should not only meet its power demand but also be within the scope of the maximum allowable output of the generator so it needs to be constrained. Based on this, Equation (35) is formed to represent the load balance constraints and Inequalities (36) and (37) denote the user demand constraints of wind power and photovoltaic power in the bilateral market.

$$q_{b,i,w}^t+q_{b,i,pv}^t+q_{b,i,f}^t+D_{p,i}^t=D_i^t$$

(35)

$$0\le {\displaystyle \sum _{i=1}^N{q}_{b,i,w}^t}\le G_w^t$$

(36)

$$0\le {\displaystyle \sum _{i=1}^N{q}_{b,i,pv}^t}\le G_{pv}^t$$

(37)

Here, $D_i^t$ is the total electricity purchased by user I during the period t.

4. Case Study

4.1. Basic System Parameters

To illustrate the validity of the proposed model, case research was conducted on the IEEE 9-node system [24] and the network structure of the system is shown in the Figure 3. The system includes three generator sets and three large users. Among them, G1 is a thermal power unit belonging to the thermal power generator (unit capacity of 1500 MW), unit G2 belongs to the wind power generator (unit capacity of 500 MW), and unit G3 belongs to the photovoltaic power generator (unit capacity of 300 MW). L1, L2, and L3 are the three large users in the system. Similarly to study [45], the daily forecast output curves of wind and solar power producers are shown in Figure 4a,b. The specific parameters of the power generation cost coefficients, quotation, and carbon emission intensity of the generators are shown in

Table 1. Power producer cost parameters [46].

	a/($/(MW)2)	b/($/MW)	c/$
Thermal power generator	0	25	0
Wind power generator	0	32.86	0
Photovoltaic power generator	0	37.5	0

,

Table 2. Quotation parameters of power producers [47,48].

	${\mathit{P}}_{\mathit{p},\mathbf{min}}$($/MW)	${\mathit{P}}_{\mathit{p},\mathbf{max}}$($/MW)	${\mathit{P}}_{\mathit{b},\mathbf{min}}$($/MW)	${\mathit{P}}_{\mathit{b},\mathbf{max}}$($/MW)
Thermal power generator	25	100	25	100
Wind power generator	33	100	33	100
Photovoltaic power generator	38	100	38	100

and

Table 3. Carbon intensity parameters of power producers [49].

	Carbon Intensity
Wind power generator	0
Photovoltaic power generator	0
Thermal power generator	1.03

[46,47,48,49], respectively. According to the carbon price survey report and other data [50], the annual carbon price is set at 20$/tCO₂. The optimization period was one day and the time step was set to 1 h.

In addition, as a powerful simulation software, MATLAB R2019a has built in a variety of matrix operation function libraries with high computational efficiency. In the implementation of the algorithm, the relatively simple M language is used for programming so it is widely used in power system optimization scheduling [51]. Moreover, Gurobi solver can solve large-scale linear problems, quadratic problems, and mixed-integer linear problems and supports multi-objective optimization with a faster solution speed and accuracy than other solvers. Therefore, based on MATLAB platform, this paper uses its built-in application toolbox Yalmip cooperating Gurobi solver to solve the two-layer model.

4.2. Simulation Analysis

4.2.1. Market Clearing Analysis

Figure 5 and Figure 6 show the power clearance situation of the bilateral market and pool market, respectively.

According to Figure 5 and Figure 6, through the hybrid power market mechanism and combined with carbon responsibility incentive measures, the electricity sold by new energy generators in the bilateral market is more than that in the pool market at any time; this phenomenon is especially obvious when the wind (01:00–11:00; 19:00–24:00) and the light is strong (13:00–18:00). In addition, as can be seen from Figure 6, the bid-winning power of new energy generators in the pool market at any time is much less than that of the thermal power generator. However, Figure 5 shows that the electricity sold by new energy generators in the bilateral market is close to the electricity sold by thermal electricity suppliers and even exceeds it at some moments, such as t = 2, 3, 11, 13. From one perspective, with the characteristics of zero carbon intensity, new energy generators guide users to participate in the bilateral market through carbon responsibility and actively choose green electricity consumption. From another perspective, according to the MCP mechanism in the pool market, the thermal power output is stable and the cost is low, which gives it a competitive advantage. In summary, it can be seen that the introduction of bilateral transactions provides users with a place to consume new energy and solves the problem of new energy bidding difficulties by market means to a certain extent.

4.2.2. User’s Carbon Responsibility Analysis

According to the carbon emission flow theory, the node location of users is the main reason affecting their carbon responsibility. Therefore, in order to study the relationship between the result of carbon responsibility allocation and the network topology, three load nodes with different topological locations were set to simulate the users in different geographical locations in the real power system and the carbon potential of their nodes was calculated and analyzed.

Figure 7 shows the carbon intensity of each user node in the pool market calculated according to the carbon emission flow theory after the market is cleared. User 1 represents node 9, user 2 represents node 7, and user 3 represents node 5.

From 16:00 to 23:00, the carbon intensities of users fluctuates greatly. In combination with Figure 6, it can be seen that this is because the proportion of new energy’s bid-winning power in the pool market fluctuates significantly during this period. The above verifies the carbon intensity and can more accurately track the carbon emission of the system.

At the same time, through the comparison between users, it can be seen that the carbon intensity of user 1 is much more affected by the clearing result than that of users 2 and 3. According to the carbon emission flow theory, the allocation of carbon responsibility in the pool market is constrained by the network topology. In view of the market clearing results, the power flow calculation shows that the demand of users 2 and 3 is mainly provided by thermal power units and the slight adjustment of the output structure of generators has little impact on the carbon intensities of their nodes. Moreover, the results show that the different locations of users and generators in the power grid lead to large differences in the carbon responsibility of users in the pool market. However, the carbon responsibility of users in the bilateral market is directly determined by the type of power supply. Therefore, through the hybrid power market mechanism, users with higher carbon responsibility can meet part of their electricity demand through the bilateral market, decrease the proportion of thermal power purchased in the pool market, and reduce their carbon emission costs.

4.2.3. User’s Power Purchasing Strategy Analysis

The power purchasing strategies of users are aimed at minimizing their own total cost of electricity. Taking user 2 as an example, the optimal power purchasing distribution of user 2 is shown in Figure 8.

As can be seen from Figure 8, user 2 has more bilateral electricity transactions with new energy generators during the time when the wind is strong (02:00–11:00; 19:00–24:00) and the light is strong (13:00–18:00). In combination with Figure 7, it can be seen that the carbon intensity of user 2 in the pool market has maintained at a value of 0.9 or slightly lower, which means that the change in user 2’s power purchasing strategy in the pool market has a slight impact on the carbon intensity. For this reason, it mitigates its carbon responsibility by purchasing large amounts of electricity in the bilateral market. In addition, there are bilateral transactions between users and thermal power generators. This is because in order to increase revenue, thermal power generators take the path of reducing the price to sign electricity with users who have failed to win the new energy power producers. Based on the above analysis, it can be seen that the trading mechanism of the hybrid electricity market can timely reflect the market clearance situation and the resulting carbon responsibility to users, so as to further encourage users to adjust the power purchasing strategies and play a positive role in guiding users to choose new energy.

4.2.4. Sensitivity Analysis of Carbon Price

In the power market, the demand response of users is often achieved through price-based incentives. The time-of-use electricity pricing is to guide users to optimize their own electricity consumption behavior by changing the price of power products in each period so as to achieve the purpose of peak cutting and valley filling. With reference to the electricity price incentive, under the background of carbon trading introduced into the electricity market, it is of great significance to take carbon price as a variable and discuss the impact of the price incentive mechanism on carbon emissions caused by the consumption of electricity. Therefore, the sensitivity analysis of carbon price is carried out. Considering that setting a carbon price too low will lose the price incentive effect and setting a carbon price too high is unrealistic, this paper refers to reference [18] and sets the carbon price as 5$/t, 10$/t, 20$/t,30 $/t, and 45 $/t, respectively, and calculates the carbon emission of the system under the two scenarios of calculating carbon responsibility on the user side and on the power generation side, respectively, as shown in Figure 9 below.

As shown in Figure 9, system carbon emissions under both scenarios show a downward trend and when the carbon price is set at $45 the system carbon emissions are all reduced by more than 30% compared with $5. This is attributed to the reason that when the price of carbon rises, the competitiveness of high-carbon emission-generating units decreases while the competitiveness of new energy-generating units rises due to their zero-carbon intensity advantage. Uniquely, according to the comparison of the two cases, it can be seen that the carbon emissions of the system are less when the carbon emissions cost is calculated on the user side. Under the double incentive of “electricity–carbon”, the change in carbon price has a direct incentive effect on the user which is different from the case of calculating the carbon emission cost on the power generation side which indirectly affects the user’s power consumption strategy in the form of electricity price through the quoting strategy of the power producer.

In [18], a ladder-type carbon-trading mechanism of source–load is adopted to conduct a demand response. The results show that with the increase in carbon price, the system achieves cost reduction by reducing the mobilization of high-carbon emission units which further verifies the impact of carbon price on the system emission reduction.

4.2.5. Comparison of the Proposed Mechanism with the Other Two Cases

In order to prove the advantages of the hybrid electricity market trading mechanism and user-side consideration of carbon responsibility, this paper sets three comparison cases; the method proposed in this paper is set as Case II:

• Case I: Open the pool market and consider carbon responsibility on the user side under the single pool market trading mechanism;
• Case II: Add a bilateral market and consider carbon responsibility on the user side under the trading mechanism of the hybrid electricity market;
• Case III: Add a bilateral market and consider carbon responsibility on the generation side under the trading mechanism of the hybrid electricity market.

The sales of electricity by new energy generators in Case I, Case II, and Case III are shown in Figure 10. The electricity sold by new energy generators in Case II and Case III is significantly higher than that in Case I which means the hybrid electricity market mechanism significantly increases the market share of new energy generators. In addition, the electricity sold by new energy in Case II is closest to the maximum output of new energy generators. On the premise of not changing the user’s demand for electricity, Case II transfers the carbon responsibility from the power generation side to the user side on the basis of Case III which has a direct incentive effect on users, prompting users to adjust power purchase strategies so as to increase the electricity sales of new energy.

In addition, as can be seen from Figure 11, the carbon emission in Case II and Case III are significantly reduced compared with Case I; Case II has the least carbon emission. In Case III, the reduction in carbon responsibility on the generation side leads to the power generators with high carbon intensity raising their quotation in order not to incur losses. As thermal power generator has the highest carbon intensity, their market competitiveness and their output decreases. In Case II, the reduction in carbon responsibility on the user side can directly stimulate users and promote the transformation of the users’ power purchasing strategies to low-carbon. The carbon emission results verify the emission reduction effectiveness of this model.

As shown in Figure 10, when both Case II and Case III open bilateral markets the electricity sold by new energy power generators in Case II is higher than that in Case III. In order to more accurately convey the enthusiasm of users to actively choose clean energy, the bilateral power purchase situation of users under Case II and III is analyzed. As shown in Figure 12, the amount of new energy power purchased by users in the bilateral market in Case II is greater than that in Case III. This is because under Case II users are motivated by carbon responsibility and purchase new energy power in the bilateral market to reduce carbon responsibility costs following wind power and photovoltaic output. In Case III, in order to achieve the electricity cost objective function, users only consider the preferential transaction with the generator with the lower bid. However, due to the differences in pricing strategies of power generators at different periods, the proportion of users actively purchasing new energy cannot be guaranteed when there is no carbon responsibility constraint. The comparative analysis shows that, compared with the single price incentive, the double incentive of electric carbon is more conducive to tapping the user’s emission reduction potential and promoting the consumption of new energy.

Table 4. Economic comparison under different cases.

	Wind Power Generator Revenue/$	Photovoltaic Power Generator Revenue/$	Thermal Power Generator Revenue/$	User Electricity Cost/$	Carbon Emission Cost/$
Case I	164,000	35,505	1,525,800	3,229,636	561,860
Case II	180,820	38,323	934,951.9	2,544,523	488,594
Case III	164,840	27,470	880,939	2,446,900	504,369

shows the economic comparison in each case. As indicated by the table, under the condition that the total demand of the user side remains unchanged, Case III opens the bilateral market and allocates the carbon emission cost on the power generation side and Case II transfers the carbon responsibility from the generation side to the user side on this basis, both of which reduce the system carbon dioxide emission, making the carbon emission cost of Case II and Case III significantly lower than that of Case I. In Case II, the new energy generator has the largest income because the users have the highest enthusiasm to buy new energy. It is conducive to the new energy generator to sell a large amount of electricity when the outputs of wind and solar power are high to maximize profits.

In addition, the income of thermal power generators in Case II and III has declined. Under the background of considering carbon cost on the generation side of Case III, the thermal power generator increases the quotation to ensure profitability but excessive quotation will lose the bilateral trading power. Moreover, bilateral transactions between users and new energy generators narrow the space for thermal power generators to sell electricity so the revenue drops more; although the electricity sold by thermal power generators in Case II is smaller than that in Case III, the final income is slightly greater than that in Case III because the thermal power generator does not need to consider the cost of carbon responsibility.

From the perspective of users’ electricity cost, Case II decreased by 21.2% compared with Case I. From one perspective, in the pool market, the market clearing price is settled by the highest quotation of the bid-winning generator while the price of the bilateral transaction can both truly reflect the market supply, demand relationship, and the real price of power products and reduce the cost of electricity for users. From another perspective, bilateral trading provides a place for users to consume new energy and users can freely choose the type of power supply in the bilateral market, thereby reducing the cost of carbon responsibility. Case III has the lowest electricity consumption cost for users because Case III does not take into account the cost of carbon emissions on the user side which leads to a reduction in the cost of electricity to the user.

5. Conclusions

This paper uses market means and carbon incentive measures to promote the consumption of new energy and establishes a bi-level model of emission reduction under the hybrid electricity market considering source and load coordination. Cases based on the IEEE9-node system were studied to test the effectiveness and superiority of the proposed bi-level model and the carbon incentive mechanism. The results show that the proposed hybrid electricity market trading mechanism improves the economy of power producers and users participating in the market. More specifically, according to the analysis, the primary findings are as follows:

• The simulation results show that the carbon emissions of the system are closely related to the setting of carbon prices, presenting a trend of decreasing with the increase in carbon prices. Therefore, systematic emission reduction can be achieved by collocating a reasonable carbon price;
• Case I only considers the pool trading mode which limits the approach of new energy power generators and users to participate in the market; the electricity sold by new energy generators is the least among the three cases which leads to the smallest profit for new energy generators;
• Case III introduces the bilateral transaction mode which provides a new way for market players to take part in the market and reduces the carbon emissions of the system by 10.2% compared with the single pool trading mode; the electricity cost of users is reduced by 24.2%;
• On the basis of Case III, Case II adopts the carbon emission flow theory to apportion the carbon responsibility on the user side and guides the user’s electricity consumption behavior to develop in the direction of low-carbon from the perspective of carbon which further reduces the carbon emissions of the system by 1.7%.

Overall, this study provides a theoretical reference for the realization of low-carbon power market dispatch by market means and promotes the market emission reduction process to a certain extent. However, since the development of China’s electricity market is still in the early stage, there are many problems existing in the participation of new energy in the electricity market. The first is that the randomness of new energy output and the continuous increase in new power generators have brought certain challenges to the design of market mechanisms. The second is that the mechanism for new energy to participate in bilateral electricity trading is not mature enough at this stage and the specific implementation methods are different according to the provisions of local market rules. In the future, it is recommended to study the bilateral market trading mode to explore the electricity price that reflects the real supply and demand relationship in the market and find out the most suitable electricity–carbon incentive mechanism for systematic emission reduction.