## 2 IGDT-Based Optimization Model for Industrial Parks  
### Economic Model of Industrial Parks  
An industrial park comprises multiple interconnected microgrids under a multi-transformer topological structure which facilitates the efficient consumption of renewable energy and enhances the overall stability and security of the system. Moreover, the integration of distributed ES systems offers additional benefits by increasing the penetration of renewable energy and reducing transformer losses. In line with real-world operational scenarios, this paper establishes an economic optimization model for the industrial park. The model incorporates various components, including a two-part tariff structure [21] consisting of a time-of-use tariff, on-grid tariff, and demand tariff. Additionally, it considers the operational and maintenance costs associated with the ES and micro-turbine (MT). The economic optimization model for the industrial park is formulated as follows:  
\[\min f=f_{1}+f_{2}+f_{3} \tag{1}\]  
where \(f\) is the cost of microgrids. \(f_{1}\), \(f_{2}\), and \(f_{3}\) are the cost of MT, the cost of electricity consumption, and the cost of using ES, respectively. For users, MT can help cope with emergencies and alleviate the peak of ES or power grid. Moreover, the high efficiency and reliability of the MT are suitable for application to the smart grid with multiple transformers. Therefore, this paper considers the use of the square equation to describe the cost of MT [22]:  
\[f_{1}=\sum_{t=1}^{T}\left\{\sum_{i=1}^{N}\alpha_{i}\big{(}P_{i,g}(t)\Delta t \big{)}^{2}+\beta_{i}P_{i,g}(t)\Delta t+c_{i}\right\} \tag{2}\]  
where \(\alpha_{i}\), \(\beta_{i}\), and \(c_{i}\) are cost coefficients of MT and \(P_{i,g}(t)\) is the MT power. \(T\), \(N\), and \(\Delta t\) are the optimization time, the number of microgrids, and time interval, respectively. For users, they need to pay electricity according to the maximum monthly demand and actual electricity consumption. Therefore, this paper uses a two-part tariff to charge users. \[f_{2}=\sum_{t=1}^{T}\{c_{\rm b}(t)P_{\rm b}(t)\Delta t+c_{\rm dec}P_{\rm dec}(t )-c_{\rm s}(t)P_{\rm s}(t)\Delta t\} \tag{3}\]  
where \(c_{\rm b}(t)\), \(c_{\rm dec}\), and \(c_{\rm s}\) are the time-of-use tariff, demand tariff, and on-grid tariff, respectively. \(P_{\rm b}(t)\), \(P_{\rm dec}(t)\), and \(P_{\rm s}(t)\) are the buying power, demand power, and on-grid power, respectively. ES can transfer the user demand in time and space, charging in the flat and valley period of time-of-use tariff, and discharging in the peak period, thus reducing user costs. Therefore, the operation and maintenance cost of ES needs to be considered. \[f_{3}=\sum_{t=1}^{T}\{c_{\rm v}(P_{i,c}(t)+P_{i,d}(t))\Delta t\} \tag{4}\]  
where \(c_{\rm v}\) denotes operation and maintenance cost of ES and \(P_{i,c}(t)\) and \(P_{i,d}(t)\) are, respectively, the charging and discharging power of ES. To enhance the solution efficiency and effectiveness of the proposed economic optimization model for the industrial park, this paper introduces two categories of constraints: distributed generator constraints and power balance constraints. 1. Operation constraints of distributed generators [6; 23] \[\begin{cases} \begin{aligned} & p_{i,\mathbf{g}}^{\min}\leq P_{i,\mathbf{g}}(t)\leq p_{i, \mathbf{g}}^{\max}\\ &\mu_{1}p_{i,c}^{\min}\leq P_{i,c}(t)\leq\mu_{1}p_{i,c}^{\max}(t)\\ &(1-\mu_{1})p_{i,\mathbf{d}}^{\min}(t)\leq P_{i,\mathbf{d}}(t)\leq(1- \mu_{1})p_{i,\mathbf{d}}^{\max}(t)\\ & SOC(t)=SOC(t-\Delta t)+(\eta_{c}\Delta tP_{i,c}(t)-P_{i,\mathbf{d}}(t) \Delta t/\eta_{\mathbf{d}})/E\\ & SOC(0)=SOC(T)\\ & 0.2\leq SOC(t)\leq 1\end{aligned} \] (5) where \(p_{i,\mathbf{g}}^{\max}\) and \(p_{i,\mathbf{g}}^{\min}\) are the upper and lower generation limits of MT, respectively. \(p_{i,\mathbf{c}}^{\max}\) and \(p_{i,\mathbf{c}}^{\min}\) are the upper and lower limits of the charging power, respectively. \(p_{i,\mathbf{d}}^{\max}\) and \(p_{i,\mathbf{d}}^{\min}\) are the lower and upper limits of the discharging power, respectively.