## Appendix A The Constraints, Related Parameters, and Output Results of Mixed Game Model
Wind and photovoltaic output power curtailment penalty cost is  
\[E^{ss}(1)=E^{sss}(24) \tag{2}\]8  
where \(\varphi_{cur}\) is the wind and photovoltaic curtailment penalty cost factor; \(P_{t}^{cur}\) is the curtailment power of VPP at time \(t\). The demand response cost is  
\[E^{ss}(1)=E^{sss}(24) \tag{2}\]9  
where \(c_{e}^{\text{\tiny p,cut}}\), \(c_{h}^{\text{\tiny p,cut}}\), and \(c_{e}^{\text{\tiny p,t}ran}\) are, respectively, the cost coefficient of thermal load reduction and the cost coefficient of electric load transfer of VPP at time \(t\). In the model proposed in this paper, the main sources of carbon emissions are co-generation units, gas boilers, and the purchase of electricity from superiors, so the carbon emission quota of VPP can be quantified as  
\[E^{ss}(1)=E^{sss}(24) \tag{3}\]0\[E^{ss}(1)=E^{sss}(24) \tag{3}\]1  
\[E^{ss}(1)=E^{sss}(24) \tag{3}\]2  
\[E^{ss}(1)=E^{sss}(24) \tag{3}\]3  
where \(E^{\prime}\), \(E^{\prime}_{CHP}\), \(E^{\prime}_{GB}\), and \(E^{\prime}_{buy}\) are the non-cost carbon emission quotas of VPP, cogeneration system, and gas boiler, respectively; \(\beta^{\prime}_{h}\) is the amount of free carbon emission per unit heat; \(H^{CHP}_{t}\) and \(P^{CHP}_{t}\) are, respectively, the thermal and electrical output power of the cogeneration system in the \(t\)th hour period. Symbol \(\varphi_{e,h}\) is the conversion coefficient of heat output of cogeneration equipment; Symbol \(H^{GB}_{t}\) is the heating power of gas boiler in the \(t\)th hour period. Considering CCS's ability to capture CO\({}_{2}\), the actual carbon emissions of VPP are  
\[E^{ss}(1)=E^{sss}(24) \tag{3}\]4  
\[E^{ss}(1)=E^{sss}(24) \tag{3}\]5  
where \(E\), \(E_{CHP}\), \(E_{GB}\), and \(E_{buy}\) are, respectively, the non-cost carbon emission quota of VPP system, cogeneration system, gas boiler, and power purchase from the superior power grid; \(E_{P2G}\) is the amount of CO\({}_{2}\) consumed by the conversion of power to gas. The calculation method of \(E_{CHP}\), \(E_{GB}\), and \(E_{buy}\) is basically consistent with Equations (102)-(103). The difference is that the carbon emissions per unit of electricity \(\beta_{h}\). \[C^{\text{CO}_{2}}= \begin{cases}\lambda E,E\leq l\\ \lambda(1+\alpha)(E-l)+\lambda l,l<E\leq 2l\\ \lambda(1+2\alpha)(E-2l)+(2+\alpha)\lambda l,2l<E\leq 3l\\ \lambda(1+3\alpha)(E-3l)+(3+3\alpha)\lambda l,3l<E\leq 4l\\ \lambda(1+4\alpha)(E-4l)+(4+6\alpha)\lambda l,4l<E\end{cases} , \tag{105}\]  
where the symbol \(\lambda\) represents the basic price of carbon trading, the symbol \(l\) represents the length of the interval of carbon emission, and \(\alpha\) is the price growth rate. (2) Constraints related to VPPs  
(i) Price restraint  
In order to ensure the fair and reasonable operation of the market, the purchase price between VPP and PVP alliance should meet the following constraints:  
\[c^{\text{ss}}_{\text{min}}\leq c^{\text{rs}}_{t}\leq c^{\text{es}}_{\text{ max}}, \tag{106}\]  
\[c^{\text{ls}}_{\text{min}}\leq c^{\text{bs}}_{t}\leq c^{\text{ls}}_{\text{ max}}, \tag{107}\]  
\[\sum_{t=1}^{24}c^{\text{rs}}_{t}/24\leq c^{\text{es}}_{\text{ave}}, \tag{108}\]  
\[\sum_{t=1}^{24}c^{\text{bs}}_{t}/24\leq c^{\text{hs}}_{\text{ave}} \tag{109}\]  
where \(c^{\text{es}}_{\text{ave}}\) and \(c^{\text{hs}}_{\text{ave}}\) are, respectively, the average constraints of PVP alliance's purchase price from VPP. (ii) CHP constraints  
Gas turbines generate electric energy and heat energy by burning natural gas at the same time.