## 4 Tiered Carbon Emissions Trading Model  
The traditional carbon trading modality has inherent flaws in its pricing mechanism, particularly due to its static pricing and lack of sufficient constraints on carbon emissions. To impose further limits on carbon emissions, this paper introduces a tiered carbon trading pricing mechanism. The mechanism segments carbon prices based on the difference between the IEMG's actual carbon emissions and its allocated carbon emissions quota. This approach compensates for the limitations of the traditional methodology. Additionally, the multidimensional energy IEMG can obtain a certain economic reward by selling extra quotas on the carbon market. The lower the carbon emissions, the larger the carbon interval corresponding to the difference between the quota and the actual emissions--the higher the sales price for the carbon quota, and thereby the higher the revenue generated. Conversely, a higher amount of carbon emissions would result in the opposite scenario.  
On this basis, by considering the actual carbon emissions from the \(i-\text{th IEMG}\) and the size of the carbon emissions quota allocated gratuitously, it can ascertain the actual amount of carbon emission quotas for the IEMG to trade within the carbon marketplace:  
\[\left\{\begin{array}{l}E_{\text{v.buy}}=\sum\limits_{t=1}^{24}\tau_{\text{buy} }P_{\text{buy}}^{t}+\tau_{g}H_{\text{buy}}^{t}\\ E_{\text{v.g}}=\sum\limits_{t=1}^{24}\tau_{\text{v.g}}(\eta_{\text{CCHP}}P_{ \text{CCHP},t}+H_{\text{CCHP},t,t})-Q_{\text{CO}_{2},t}^{\text{CCS}}\\ E_{p,i}=E_{\text{v.buy}}+E_{\text{v.g}}\\ E_{R,i}=E_{p,i}-E_{C,i}\end{array}\right. \tag{44}\]  
wherein \(E_{C,i}\) presents the actual carbon emission trading amount of the \(i-\text{th IEMG}\), \(E_{p,i}\) is the carbon emission of IEMG, \(E_{R,i}\) is the actual carbon emission, \(\tau_{buy}\) is the parameter for calculating carbon emissions from purchased electricity, \(\tau_{g}\) is the parameter for calculating carbon emissions from natural gas, \(\eta_{CCHP}\) is the energy equivalence coefficient, and \(\tau_{\text{v.g}}\) is the carbon emission quota per natural gas unit.  
When \(E_{R,i}<0\), it indicates that the carbon emissions of the IEMG are lower than the carbon emission quota, resulting in certain profits. The smaller the carbon emission range, the higher the corresponding carbon trading price, which is to say the following:  
\[F_{\text{CO2},i}=\left\{\begin{matrix}-cd-c(1+\alpha)(-E_{R,i}-d)&E_{R,i}\leq- d\\ -c\cdot(-E_{R,i})&-d<E_{R,i}\leq 0\end{matrix}\right. \tag{45}\]  
wherein \(F_{\text{CO2},i}\) represents the stepwise carbon trading cost of the IEMG; \(c\) is the benchmark price for IEMG's carbon emission rights trading; \(d\) is the carbon emission interval for the IEMG.  
When \(E_{R,i}>0\), it indicates that the carbon emissions of the IEMG exceed the carbon emission quota, necessitating the purchase of carbon emission allowances from the carbon trading market. The larger the carbon emission range, the higher the corresponding carbon trading price, which is to say the following:  
\[F_{\text{CO2},i}=\begin{cases}cE_{R,i}&0<E_{R,i}\leq d\\ c(1+\alpha)(E_{R,i}-d)+cd&d<E_{R,i}\leq 2d\\ c(1+2\alpha)(E_{R,i}-2d)+c(2+\alpha)d&2d<E_{R,i}\leq 3d\\ c(1+3\alpha)(E_{R,i}-3d)+c(3+3\alpha)d&3d<E_{R,i}\leq 4d\\ c(1+4\alpha)(E_{R,i}-4d)+c(4+6\alpha)d&E_{R,i}>4d\end{cases} \tag{46}\]  
wherein \(\alpha\) represents the growth coefficient of the carbon trading price for IEMG.  
Based on the aforementioned theoretical analysis, the tiered carbon trading mechanism can be represented in Figure 3.