## 2 IGDT-Based Optimization Model for Industrial Parks
### IGDT Stochastic Scheduling for Industrial Parks with Multiple Transformers
The proposed IGDT stochastic optimization model for industrial parks, based on the industrial park economic model and the envelope constraint model, can be expressed as follows:  
\[ \begin{array}{c}\max[a_{1},a_{2},\ldots,a_{i}]\\ \text{s.t.}\left\{\begin{array}{l}\max C\leq(1+\beta)C_{0}\\ \Delta P_{i,\text{L}}\in U\big{(}a_{i},\Delta\widetilde{P}_{i,\text{L}}\big{)} \\ \text{s.t.}(1)\sim(3)\end{array}\right.\end{array}  \tag{11}\]where \(C_{0}\) and \(C\) are the costs of the industrial park in deterministic and uncertain environments, respectively. The IGDT stochastic optimization model of industrial parks is a bi-level optimization model which is difficult to solve directly. Therefore, this paper uses the idea of robust optimization to transform \(\max[a_{1},a_{2},\ldots,a_{i}]\) into \(\max\)min\([a_{1},a_{2},\ldots,a_{i}]\). In addition, when the fluctuation of net load reaches the maximum fluctuation, it can be written as Equation (12). The second formula of Equation (6) can be written as Equation (13). \[\Delta P_{i,\text{L}}=(1+a_{i})\Delta\widetilde{P}_{i,\text{L}} \tag{12}\]  
\[P_{i,\text{out}}(t)+P_{i,\text{ex}}(t)+P_{i,\text{c}}(t)+(1+a_{i})\Delta \widetilde{P}_{i,\text{L}}=P_{i,\text{g}}(t)+P_{i,\text{d}}(t)+P_{i,\text{in}} \tag{13}\]  
At this time, the cost of the proposed IGDT model is the highest. The \(\max C\leq(1+\beta)C_{0}\) of the lower model can be written as:  
\[C\leq(1+\beta)C_{0} \tag{14}\]  
The development of such a method is of the utmost importance to address the practical challenges associated with PV and load uncertainties. By incorporating it into the industrial park optimization model, the proposed approach seeks to provide a comprehensive solution that encompasses both economic efficiency and operational robustness. In summary, the IGDT stochastic optimization model of industrial parks can be expressed as:  
\[ \begin{array}{l}\max\min[a_{1},a_{2},\ldots,a_{i}]\\ \text{s.t.}\left\{\begin{array}{l}C\leq(1+\beta)C_{0}\\ \Delta P_{i,\text{L}}=(1+a_{i})\Delta\widetilde{P}_{i,\text{L}}\\ \text{s.t.}(1)\sim(3)\end{array}\right.\end{array}  \tag{15}\]  
We calculate \(\max\min[a_{1},a_{2},\ldots,a_{i}]\) according to the enumeration method mentioned in [27]. The enumeration method is essentially based on a property [28]: if D is a closed convex set and F is a convex function, if F has a maximum value on D then the maximum value will be obtained at a certain pole of D.  
By formulating this economic optimization model, the paper aims to provide a comprehensive framework that maximizes the economic benefits of the industrial park while considering various tariff structures, operational costs, and renewable energy integration. The optimization model serves as a valuable tool for decision makers in the industrial park to make informed choices regarding tariff selection, ES utilization, and MT operation, thus contributing to the sustainable and cost-effective operation of the industrial park. In summary, the flow of IGDT-based stochastic optimization for smart microgrids with multiple transformers in this paper is shown in Figure 1.  
Figure 1: Flowchart of stochastic optimization based on IGDT. When we solve the MILP problem according to Figure 1, we divide the problem into a deterministic environment and an uncertain environment. Firstly, we solve the model in a deterministic environment and obtain the cost in a deterministic environment. Then, the cost in the deterministic environment is brought into the IGDT model to solve the IGDT stochastic optimization model.