1. Introduction

• The main contributions of this paper are as follows:

2. Framework for VPP Operation with Hydrogen Storage and Carbon Trading

2.1. Composition of Virtual Power Plant (VPP)

A Virtual Power Plant (VPP) integrates various energy sources such as wind power, solar photovoltaic (PV), thermal power, hydropower, and natural gas within a specific region. It establishes a unified virtual control center to manage and dispatch energy resources. In a broader sense, by incorporating technologies like demand response, energy storage, electric vehicles, as well as communication and control systems, the integration of supply and demand sides can be achieved. This enables flexible coordination between power generation and consumption, and orderly integration of distributed energy sources. However, traditional VPPs heavily rely on coal-fired or combined heat and power (CHP) units, resulting in high carbon emissions and low utilization efficiency of clean energy, which hinders the implementation of China's 30-60 plan. In contrast, a combined system of carbon capture and storage (CCS) and hydrogen energy storage can effectively sequester a large amount of carbon dioxide and convert it into methane, thereby promoting a zero-carbon-oriented energy planning at the level of the power supply chain. This provides a feasible pathway for emission reduction, improving energy utilization efficiency, and implementing carbon neutrality strategies. Therefore, integrating CCS and hydrogen storage systems into the VPP can effectively control carbon emissions.

The proposed framework for the VPP, as illustrated in the figure below, includes PV, wind power, CHP, carbon capture, hydrogen storage systems, and electric boilers. By introducing hydrogen storage and electric boilers into the VPP, a portion of the CO₂ emitted from the combustion of coal in CHP units can be captured and stored using carbon capture devices. Additionally, hydrogen produced by the hydrogen storage system can be converted into methane through a methanation reactor. The generated methane can be directly sold. Furthermore, the hydrogen fuel cells can generate electricity and heat by burning hydrogen, which can be operated in conjunction with electric boilers. This further decouples the CHP units from thermal-based electricity generation, leading to a reduction in carbon emissions, lowering system energy costs, and improving economic benefits.

Figure 1. Topological Structure of Virtual Power Plant (VPP).

Figure 1. Topological Structure of Virtual Power Plant (VPP).

3. Virtual Power Plant Low-carbon Economic Dispatch Model

3.2. Constraint conditions

3.2.1. The constraint on wind and solar power output

$$0\le P_{wind0}(t)\le P_{wind,N}$$

(37)

$$0\le P_{pv0}(t)\le P_{pv,N}$$

(38)

In the equation, $P_{wind,N}$ and $P_{pv,N}$ are the rated installed capacity of wind farms and solar power plants, respectively

3.2.2. The constraint of electricity balance

$${\displaystyle \sum _{i\in \theta }{P}_{CHP}^i}(t)+P_{pv}(t)+P_{wind}(t)+P_{grid,buy}(t)+P_{HFC,e}(t)=P_{load}(t)+P_{el}(t)+P_{EH}(t)+P_{CCS}(t)$$

(39)

$$0\le P_{grid,buy}(t)\le P_{grid,buy}^{\max }$$

(40)

In the equation, $P_{grid,buy}(t)$ is the purchasing power from VPP to the higher-level power grid during time period t. $P_{HFC,e}(t)$ is the power input of hydrogen fuel cells during time period t. $P_{load}(t)$ is the electric load power during time period t. $P_{el}(t)$ is the power of the electrolyzer during time period t. $P_{EH}(t)$ is the power of the electric boiler during time period t. $P_{CCS}(t)$ is the power of the carbon capture and storage (CCS) system during time period t. $P_{grid,buy}^{\max }$ is the upper limit of purchasing power.

3.2.2. The constraint of thermal balance

$${\displaystyle \sum _{i\in \theta }{H}_{CHP}^i}(t)+H_{EH}(t)+H_{HFC,h}(t)=H_{load}(t)$$

(41)

In the equation, $H_{EH}(t)$ is the thermal power converted by electric boilers in time period t, $H_{HFC,h}(t)$ is the thermal power input by hydrogen fuel cells in time period t, and $H_{load}(t)$ is the thermal load power in time period t

3.2.3. The constraint of hydrogen power balance

$$P_{el,H_2}(t)=P_{H_2,MR}(t)+P_{H_2,HFC}(t)+P_{ES}^{H_2}(t)$$

(42)

In the equation, $P_{el,H_2}(t)$ is the hydrogen production power of the electrolyzer. $P_{H_2,MR}(t)$ is the hydrogen consumption power of the methane reactor. $P_{H_2,HFC}(t)$ is the hydrogen consumption power of the hydrogen fuel cell. $P_{ES}^{H_2}(t)$ is the hydrogen storage power in the hydrogen storage tank.

3.2.4. The constraints of the hydrogen energy storage system

EL, MR, HFC, and HST can be described by equations (1) to (15).

3.2.5. The constraints on carbon capture quantity for CCS

To ensure the utilization and regular maintenance of CCS, a minimum capture rate must be set. Therefore, the constraint on the carbon capture quantity for CCS can be expressed as follows[34],

$${\eta }_{\min }{E}_{CHP}(t)\le E_{CCS}(t)\le {\eta }_{\max }{E}_{CHP}(t)$$

(43)

In the equation, where ${\eta }_{\max }$ and ${\eta }_{\min }$ are the upper and lower bounds of the carbon capture rate for CCS devices, respectively.

3.2.6. Capacity constraint of electric boilers

$$0\le H_{EH}(t)\le H_{EH}$$

(44)

In the equation, $H_{EH}$ is the capacity for configuring electric boilers.

3.2.7. Constraint on electric-thermal conversion of electric boilers

$$H_{EH}(t)={\eta }_{EH}{P}_{EH}(t)$$

(45)

In the equation, ${\eta }_{EH}$ is electric-thermal conversion efficiency during the operation of electric boilers.

3.2.8. Constraints on thermal and electric output and ramping of CHP units

(46)

In the equation, $P_{CHP}^{i,\max }$ and $P_{CHP}^{i,\min }$ are the lower and upper limits of electric power for the i-th CHP unit, $H_{CHP}^{i,\max }$ and $H_{CHP}^{i,\min }$ are the lower and upper limits of thermal power for the i-th CHP unit, $R_{CHP}^{i,up}$ and $R_{CHP}^{i,down}$ are the lower and upper limits of ramping rate for the i-th CHP unit.

3.2.9. Operational Region Constraints for Combined Heat and Power Generation

• Due to the thermoelectric coupling characteristics and the unique operation mode of heat-driven electricity generation, there exist specific thermoelectric operating ranges for two types of heat-driven electricity generation units[35].

For backpressure CHP units, the electrical output and heat output need to maintain a certain proportional relationship. This is represented by the slope of the line in Figure 2(a). When operating in a "heat-led" mode, this type of unit has only one operational state, namely.

$$P_{CHP}^i(t)={\gamma }_{CHP}{H}_{CHP}^i(t)=\frac{P_{CHP}^{\max }-P_{CHP}^{\min }}{H_{CHP}^{\max }-H_{CHP}^{\min }}{H}_{CHP}^i(t)$$

(47)

In the equation, $P_{CHP}^{\max }$ and $P_{CHP}^{\min }$ are the maximum and minimum electric output of the i-th CHP unit, respectively, $H_{CHP}^{\max }$ and $H_{CHP}^{\min }$ are the maximum and minimum thermal output of the i-th CHP unit, respectively.

The operational range of an absorption-type CHP unit, considering both thermal and electric output, is depicted in Figure 2(b). The constraints on the operational range of the absorption-type CHP unit, considering both thermal and electric output, can be represented by the following equation.

$$\{\begin{array}{l}{P}_{CHP}^{i,\min }-c_{v2}^i{H}_{CHP}^i(t)\le P_{CHP}^i(t)\le P_{CHP}^{i,\max }-c_{v1}^i{H}_{CHP}^i(t) 0\le H_{CHP}^i\le H_{CHP}^{\mathrm{m}ed}\\ c_m^i(H_{CHP}^i(t)-H_{CHP}^{i,\mathrm{m}ed})+P_{CHP}^{i,\min }\le P_{CHP}^i(t)\le P_{CHP}^{i,\max }-c_{v1}^i{H}_{CHP}^i(t)H_{CHP}^{imed}\le H_{CHP}^i\le H_{CHP}^{i,\max }\end{array}$$

(48)

In the equation, $P_{CHP}^{i,\max }$ and $P_{CHP}^{i,\min }$ are the maximum and minimum electric output of the i-th CHP unit, respectively. $H_{CHP}^{i\max }$ and $H_{CHP}^{i\min }$ are the maximum and minimum thermal output of the i-th CHP unit, respectively. $H_{CHP}^{i\mathrm{m}ed}$ is the thermal output corresponding to the minimum electric output of the i-th CHP unit. $c_{v1}^i$ and $c_{v2}^i$ are the decrease in maximum and minimum output under constant turbine intake when extracting a unit of heat for the i-th unit. $c_m^i$ is the coefficient of the ratio between electric output and thermal output when the i-th CHP unit operates under back pressure conditions.

4. Case study analysis

4.3. Analysis of Scheduling Results under Different Scenarios

The predicted data for wind power, photovoltaic power, electric load, and heat load for the cooling season, transition season, and heating season are shown in Figure 5. By comparing the VPP's electricity and heat sales revenue, fuel costs, wind and solar curtailment costs, and carbon emissions under the three scenarios set in the three seasons, the optimal scheduling strategy was selected and analyzed.

4.3.1. Analysis of Scheduling Results during the Cooling Season

The analysis of scheduling results during the cooling season is shown in Figure 6, which displays the electric power and heat power balance in three different scenarios. The parameter comparison of VPP revenue under different scenarios is presented in Table 4.

Combining Figure 6 and Table 3, it can be observed that due to the "heat-driven electricity" constraint, the output power of the combined heat and power (CHP) units cannot be reduced, resulting in a large amount of curtailed wind and solar power in Scenario 1. This leads to significant curtailment costs. In Scenario 2, the introduction of a hydrogen energy storage system allows for greater integration of wind and solar power during periods of high generation. During peak load periods, the system can release electricity and heat, reducing the output of CHP units and thus lowering fuel costs. As a result, the fuel cost in Scenario 2 is reduced by 24.25%. However, the introduction of the hydrogen energy storage system leads to a 4.7% decrease in revenue from selling electricity, heat, and gas due to considerations of its operation and maintenance costs. In order to reduce carbon emissions, the purchasing cost of electricity increases by 26%. Additionally, the costs and emissions associated with carbon trading decrease by 28.43% and 9.04% respectively. Despite the decrease in revenue from selling electricity, heat, and gas, the net profit increases by 29.71%. In Scenario 3, an optimized carbon trading mechanism is introduced based on Scenario 2, which further reduces the fuel cost by 11.55% and increases the integration of wind and solar power, leading to a 4.27% reduction in curtailment costs. The purchasing cost of electricity decreases by 38.62%, and the costs and emissions associated with carbon trading decrease by 43.67% and 36.64% respectively. Although there is a 0.87% decrease in revenue from selling electricity, heat, and gas, the overall net profit increases by 15.6%. Therefore, under cooling season conditions, it can be concluded that the proposed model in this paper can increase the integration of wind and solar power, reduce carbon emissions, and improve the economic benefits of the virtual power plant (VPP), demonstrating its practicality.

As shown in Figure 6, the power balance diagram for Scenario 3 is as follows: From 1:00 to 5:00, when the photovoltaic (PV) power is zero and the wind power is relatively low while the heat demand and electricity load are high, wind power is fully absorbed. The absorbed wind power is used for heat generation through an electric boiler and supplied by a combined fuel cell to reduce the heat output of the CHP units. This not only reduces the fuel cost but also enhances the flexibility and peak shaving capability of the system. The remaining wind power is consumed through electrolyzers and carbon capture devices to maintain a low-carbon level. Due to the need to maintain the power balance, the VPP purchases a small amount of electricity from the main grid. From 6:00 to 14:00, the heat demand decreases sharply and reaches a low point, while the electricity load increases rapidly and enters a peak period. At this time, due to the low heat demand and the constraint of "heat-driven electricity," the fuel cell and electric boiler outputs are limited by the minimum heat output of the CHP units. As a result, the heat output of the CHP units is low, leading to a decrease in electricity output and a reduction in carbon emissions. The carbon capture output decreases, and the electrolyzer output increases to consume the remaining wind and solar power. Additionally, more hydrogen gas is produced for methane synthesis to improve the profitability of selling gas. In order to maintain the power balance, the VPP experiences occasional curtailment and purchases a small amount of electricity. From 15:00 to 20:00, the electricity load decreases rapidly, and the heat demand gradually increases. At the same time, the power output of PV and wind decreases. This leads to an increase in the heat output of the CHP units. The electric boiler and fuel cell increase their heat outputs to reduce the heat output of the CHP units, resulting in a decrease in carbon capture output. The electricity output of the CHP units increases, and to maintain the power balance, the VPP has to purchase electricity from the main grid. This occurs during a period of high electricity prices, resulting in higher purchasing costs. From 21:00 to 24:00, the electricity load continues to decrease, the heat demand increases, and the wind power also increases. The PV power is zero at this time. The fuel cell bears most of the remaining heat demand, and the VPP has high electricity and heat outputs, leading to higher carbon emissions. Therefore, the carbon capture device output increases, while the electrolyzer output decreases. There is no wind curtailment, but there are occasional small amounts of electricity purchases. Although this reduces the economic efficiency, the purchasing cost is still lower compared to Scenarios 1 and 2, resulting in overall higher net economic benefits. Based on the above analysis, it can be concluded that the proposed model in this paper can increase the integration of wind and solar power, reduce carbon emissions, and improve the economic benefits of the VPP under cooling season conditions.

4.3.2. Analysis of Scheduling Results during the Transition Season.

The analysis of scheduling results during the transition season is shown in Figure 7, which displays the electric power and heat power balance in three different scenarios. The parameter comparison of VPP revenue under different scenarios is presented in Table 5.

Based on Figure 7 and Table 4, it can be seen that due to the "heat-first, electricity-second" principle, the output of the CHP unit cannot be reduced, which leads to a large amount of wind and solar power being wasted during periods of low electricity demand. In particular, there is a long period of wind power curtailment during the transition season, resulting in high costs for wind and solar power curtailment, as well as high fuel costs and carbon emissions in Scenario 1.Scenario 2 introduces a hydrogen energy storage system, which can absorb excess wind and solar resources, increase the consumption of wind and solar power, and reduce the electricity and heat output of the CHP unit, thereby reducing the carbon emissions of the VPP. Compared with Scenario 1, the fuel costs, wind and solar power curtailment costs, carbon trading costs, and carbon emissions are reduced by 21.82%, 33.31%, 33.85%, and 10.28%, respectively, while the revenue of the VPP increases by 24.02%.In Scenario 3, an optimized CHP output is achieved through a stepped carbon trading mechanism, resulting in a further reduction in fuel costs, carbon emissions, carbon trading costs, wind and solar power curtailment costs, and electricity purchases, while net income increases by 12.24%.The electric heat power balance diagram in Scenario 3 shows that during the 1:00-8:00 period, the PV output is almost zero, wind power gradually decreases, and the heat load fluctuates within a small range at a high level. The electric boiler consumes some of the wind power and converts it into heat energy, while the rest of the wind power is consumed by the carbon capture and electrolysis facilities. To maintain heat power balance and reduce the heat output of the CHP unit, the fuel cell output is high, generating a large amount of heat and electricity to meet the demand. However, due to the high electric and heat output, the carbon emissions of the VPP remain high, which requires the carbon capture and electrolysis facilities to increase their output to reduce carbon emissions, resulting in insufficient wind and solar power to meet the electricity demand. Therefore, the VPP has to purchase electricity from the main grid, increasing its purchase cost. During the 9:00-16:00 period, the electricity demand continues to decrease and remains at a low level throughout the day. The PV output slowly increases, but wind power rapidly increases and remains at a high level. The heat load still fluctuates within a small range, and the electric boiler output increases, while the fuel cell output decreases and the electrolysis output increases to consume more wind and solar power. However, due to the "heat-first, electricity-second" principle of the CHP unit and the capacity constraints of the electrolysis equipment, wind and solar power curtailment occurs, increasing the cost of wind and solar power curtailment. During the 17:00-24:00 period, the electricity demand rapidly increases again, while the heat load still fluctuates within a small range. The PV output gradually decreases to zero, and wind power also decreases. At this time, the electric boiler output decreases, and the fuel cell burns a large amount of hydrogen to provide heat and electricity, increasing the flexibility and adjustability of the CHP unit's electricity output. However, due to the high output of the CHP unit, the carbon emissions of the VPP remain high. To maintain a low level of carbon emissions, the carbon capture facility output increases, while the hydrogen storage tank and electrolysis output supply more hydrogen to promote CO₂ methanation, reducing carbon emissions while also increasing gas sales revenue. In some periods, wind and solar power curtailment and electricity purchases still occur, but compared with Scenario 2, the amount of wind and solar power curtailment and electricity purchases is smaller, resulting in higher net income. In conclusion, the VPP low-carbon economic dispatch model established in this paper still has high economic benefits and carbon emission reduction capabilities when used as input during the transition season.

4.3.3. Analysis of Scheduling Results during the Heating Season

The analysis of scheduling results during the heating Season is shown in Figure 8, which displays the electric power and heat power balance in three different scenarios. The parameter comparison of VPP revenue under different scenarios is presented in Table 6.

Figure 8. Power Balance Chart of Electricity and Heat during the Cooling Season.

Figure 8. Power Balance Chart of Electricity and Heat during the Cooling Season.

Based on Figure 8 and Table 5, it can be seen that in Scenario 1, which only includes electric boilers and carbon capture, all costs are higher than the other two scenarios. In contrast, Scenarios 2 and 3 incorporate hydrogen energy storage systems, resulting in a higher consumption of wind and solar resources and a decrease in CHP unit's heat and power output. This reduces the cost of curtailed wind and solar energy, as well as fuel costs. Compared to Scenario 1, Scenario 2's fuel costs decreased by 19.42%, while its carbon trading costs and emissions decreased by 34.94% and 23.16%, respectively, and VPP's net income increased by 12.77%. Compared to Scenario 2, Scenario 3 introduces a tiered carbon trading mechanism that optimizes CHP output, reducing carbon emissions and trading costs. Fuel costs decreased by 14.22%, curtailed wind and solar energy costs decreased by 35.3%, and carbon trading costs and emissions decreased by 44.68% and 26.39%, respectively. Although Scenario 3 resulted in an increase in purchased electricity costs by 58.65%, the net income still increased by 5.88%. Therefore, the VPP low-carbon economic dispatch model established in this paper can optimize the output of VPP equipment, reduce operating costs and carbon emissions, and improve economic benefits during the heating season. Figure 8's power balance diagram for Scenario 3 shows that during the 1:00-8:00 period, the electrical load first decreases and then rapidly increases, while the thermal load is in the early peak period and gradually decreases. At this time, the photovoltaic output is almost zero, and wind power output is low and slowly increasing. Due to the high thermal load, the electric boiler converts wind power into heat, while the fuel cell burns hydrogen to generate heat and electricity to meet the demand for electric heat load. However, due to the thermal load being high and electric load being low, a large amount of wind power is curtailed, resulting in high curtailed wind and solar energy costs, although still lower than Scenarios 1 and 2. During the 9:00-13:00 period, the electrical load rapidly increases and is in the first peak period of the day, while the thermal load is at its lowest point. Meanwhile, the photovoltaic power output gradually increases to its peak, and wind power begins to fluctuate and decrease. Due to the reduced thermal load, the capacity for the electric boiler and fuel cell to convert heat into electricity is reduced, limiting their ability to consume wind and solar energy. CHP unit's power output decreases, reducing carbon emissions, and thus carbon capture output also decreases. However, due to the high electrical load, wind and solar energy shortages occur, and VPP has to purchase electricity from the main grid to maintain power balance. During the 14:00-20:00 period, the thermal load rapidly increases and is in the peak period, while the electrical load first decreases and then slowly increases, also in the second peak period. At this time, wind power also starts to increase and is in the peak period of the day, while photovoltaic power gradually decreases to zero. Due to the rapid increase in thermal load, the electric boiler consumes more wind power, and the fuel cell burns more hydrogen to reduce CHP heat output and decouple heat and electricity to maintain CHP unit's flexibility and peak-shaving capabilities. However, CHP unit's heat and power output still slowly increase, resulting in VPP's highest carbon emissions of the day. Carbon capture output and electrolysis cell output increase to reduce carbon emissions, and hydrogen is produced to supply the fuel cell and methane generator to reduce system carbon emissions and increase gas sales revenue. Although wind power is fully consumed at this time, there is still a shortage of electricity, and VPP has to purchase electricity from the main grid, resulting in higher purchased electricity costs during this period. During the 21:00-24:00 period, the thermal load, electrical load, and wind power output all begin to decrease, and the photovoltaic output is zero. The electric boiler output decreases slightly, while the hydrogen fuel cell output increases to reduce CHP heat output and decouple heat and electricity. However, due to the high thermal load, CHP heat output remains high, and there is also a high demand for electricity, resulting in high carbon emissions for VPP. Carbon capture output and electrolysis cell output increase to reduce carbon emissions, and hydrogen is produced to supply the fuel cell and methane generator to reduce system carbon emissions and increase gas sales revenue. Although wind power is fully consumed during this period, there is still a shortage of electricity, and VPP has to purchase electricity from the main grid, resulting in higher purchased electricity costs. However, compared to the first two scenarios, Scenario 3 still has higher net income.

In summary, this section compares three different scenarios with the same load input during the power supply season, transition season, and heating season by establishing a VPP low-carbon economic dispatch model that considers hydrogen energy storage and tiered carbon trading. The results show that the model has high practicality during all three seasons, reducing VPP carbon emissions, increasing wind and solar consumption, and improving net income.

4.4. Sensitivity Analysis of VPP System Parameters

Hydrogen energy plays a crucial role in decoupling the heat and power coupling mode of CHP units, strengthening the coupling of electric and thermal loads, and improving the consumption of new energy sources in this paper. Similarly, different parameters of carbon trading mechanisms can directly affect the internal operation of VPP. Therefore, this section focuses on the impact of these parameters on VPP's carbon emissions and net profits. Using wind and solar load forecasting data for the transition season, simulation analysis was conducted under Scenario 3, and the results are shown in Figure 9 and Figure 10.

4.4.1. Sensitivity Analysis of Hydrogen Energy Storage System Equipment Capacity

The capacity of various hydrogen energy storage system equipment (electrolysis cell and hydrogen fuel cell) on the economic benefits and carbon emissions of VPP were studied, and the results are shown in Figure 8.

Figure 8. The impact of hydrogen energy storage on VPP.

Figure 8. The impact of hydrogen energy storage on VPP.

As shown in Figure 8(a), when the capacity of the electrolyzer is less than 150MW, as the configured capacity increases, more hydrogen is produced by electrolysis, and the fuel cell burns more hydrogen to generate electricity and heat, increasing the consumption of new energy and rapidly reducing the system's carbon emissions. The benefits generated are greater than the operational costs, resulting in an increase in the VPP's net income. When the capacity exceeds 150MW, although more hydrogen is produced, it cannot be fully utilized due to the limitations of the fuel cell and hydrogen storage tank, resulting in waste of hydrogen resources and electrolyzer capacity, and the rate of carbon emission reduction slows down. Moreover, the operational costs exceed the benefits generated, leading to a decrease in the VPP's net income.

As shown in Figure 8(b), when the capacity of the fuel cell is less than 60MW, as the configured capacity increases, the fuel cell can burn more hydrogen to generate more electricity and heat, reducing the output of the CHP unit and increasing the sales revenue of the VPP for electricity and heat, while also reducing carbon emissions. When the capacity exceeds 60MW, although the configured capacity increases, it is limited by the electrolyzer and hydrogen storage tank, and the operational costs increase significantly, resulting in a decrease in the VPP's net income. Although carbon emissions still decrease, the rate of reduction slows down and gradually approaches saturation.

According to the above analysis, from the perspective of carbon emission reduction and increasing the consumption of new energy, it can be concluded that when the configured capacity of the electrolyzer is greater than 150MW and the hydrogen fuel cell capacity is greater than 60MW, the VPP's net income is maximized, and the carbon emissions are moderate. Further increasing the configured capacity will only lead to a decrease in the system's net income and waste of capacity. Therefore, a reasonable setting of the capacity of the hydrogen energy storage system equipment can effectively guide the VPP's carbon emissions, net income, and consumption of new energy.

4.4.2. Sensitivity Analysis of Carbon Trading Parameters

Now, we mainly analyze the impact of carbon trading benchmark price and carbon emission interval length on system carbon emissions and net income. The results are shown in Figure 9.

As shown in Figure 9(a), when the carbon trading benchmark price is greater than 90 yuan/t, as the carbon trading benchmark price increases, the proportion of carbon emission target cost also increases, and the role of carbon trading cost becomes stronger. VPP has to reduce carbon emissions to reduce carbon trading costs, so the carbon emissions also begin to rapidly decrease, and VPP's profits also rapidly decrease. When the carbon trading benchmark price is less than 90 yuan/t, although the carbon trading price increases, the price is still relatively low, and VPP's carbon emissions increase. However, from the overall trend, the carbon trading price has a relatively large impact on the system's carbon emissions and net income. Therefore, from a long-term perspective, a reasonable carbon trading price will have broader application prospects in reducing carbon emissions.

As shown in Figure 9(b), when the interval length is less than 400t, as the interval length increases, the carbon trading price is at a low level because the increasing interval length reduces the punishment intensity of stepped carbon trading. VPP's carbon emissions also rapidly increase, and VPP's net income also increases. When the interval length is greater than 400t, carbon emissions are traded based on the benchmark price and the first gradient price, and the impact of the interval length on carbon emissions is relatively small. Stepped carbon trading is transformed into fixed carbon trading, and VPP's carbon emissions and net income slowly increase and tend to stabilize.

From the above analysis, it can be concluded that from the perspective of current energy conservation and emission reduction, when the carbon trading benchmark price is greater than 90 CNY/t, VPP's net income reaches its maximum. Although increasing the carbon benchmark price will continue to reduce carbon emissions, it will also lead to a sharp decline in VPP's net income. When the interval length is less than or equal to 400t, VPP's carbon emissions and net income rapidly increase, while when the interval length is greater than 400t, the system's carbon emissions and net income slowly increase and tend to stabilize. Therefore, setting a reasonable carbon trading benchmark price and interval length can reasonably guide the system's carbon emissions, achieve a balance between VPP's low-carbon operation and economic operation.

5. Conclusion

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