## 2 IGDT-Based Optimization Model for Industrial Parks
### IGDT Stochastic Scheduling for Industrial Parks with Multiple Transformers  
When addressing uncertainty in the industrial park optimization model, two common approaches are robust optimization and stochastic optimization. However, robust optimization tends to be overly conservative in handling uncertain variables, while stochastic optimization requires a significant number of samples for effective optimization. In contrast, IGDT offers a more favorable solution by imposing less information requirements on uncertain variables and not relying heavily on their probability distribution [24]. In view of the above discussions, this paper adopts IGDT as the chosen method to handle the uncertainties associated with PV and load. IGDT provides a robust and practical framework for dealing with uncertainty in the optimization model, allowing for more reliable and efficient decision making in the industrial park setting. The general optimization problem can be described as:  
\[ \begin{array}{c}\min F(x,l)\\ \text{s.t.}\left\{\begin{array}{l}H_{i}(x,l)\leq 0,i\in\rho_{\text{ineq}}\\ G_{j}(x,l)=0,j\in\rho_{\text{eq}}\end{array}\right.\end{array}  \tag{7}\]  
where \(F\) is the objective function. \(x\) and \(l\) are the decision variable and uncertainty variable, respectively. \(H_{i}(x,l)\) and \(G_{j}(x,l)\) are the inequality constraints and equality constraints, respectively. \(\rho_{\text{ineq}}\) and \(\rho_{\text{eq}}\) are the sets of inequality constraints and equality constraints, respectively. Based on the risk aversion strategy, a general IGDT robust optimization model can be constructed as follows [25]:  
\[ \begin{array}{c}\max\varphi\\ \text{s.t.}\left\{\begin{array}{l}\max F(x,l)\leq F_{\text{c}}\\ F_{\text{c}}=(1+\beta)F_{0}\\ H(x,l)\leq 0\\ U(\varphi,\widetilde{x})\end{array}\right.\end{array}  \tag{8}\]  
where \(\varphi\) is the uncertainty. \(F_{0}\) is the optimal solution in the deterministic environment. \(\beta\) is the cost deviation factor for the IGDT model. \(U(\varphi,\widetilde{x})\) is the fluctuation range of uncertain variables. Equation (8) shows that the IGDT robust optimization model solves for the maximum value of the uncertainty in the upper layer and the maximum value of the objective function in the lower layer. Nevertheless, as the number of uncertain variables increases, the IGDT model transitions from a single-objective problem to a multi-objective problem, significantly intensifying the complexity of solving the model. To address this challenge, this paper employs the concept of net load shown by Equation (9) to describe the uncertainty within the optimization model, thereby reducing the complexity of the problem. Net load, in this context, refers to the difference between the forecasted load and the forecasted PV generation. By utilizing the net load, the uncertainty associated with PV and load can be effectively characterized within the optimization model. This simplification facilitates the resolution of the model and enables more efficient decision making in real-world scenarios. \[\Delta P_{j,\text{L}}=P_{i,\text{load}}-P_{i,\text{pv}} \tag{9}\]  
To provide a more accurate representation of the uncertainty variables, this paper employs the envelope model as a means to describe the variability and uncertainty associated with these variables [26]. The envelope model is chosen due to its effectiveness in capturing the range of potential values for uncertain variables. It provides a concise and flexible representation allowing for a comprehensive analysis of the uncertainty within the optimization model. The specific form of the envelope model adopted in this paper is as follows:  
\[U\Big{(}a_{i},\Delta\widetilde{P}_{i,\text{L}}\Big{)}=\left\{a_{i}:\left| \frac{\Delta P_{i,\text{L}}-\Delta\widetilde{P}_{i,\text{L}}}{\Delta\widetilde {P}_{i,\text{L}}}\right|\leq a_{i}\right\} \tag{10}\]  
where \(\Delta\widetilde{P}_{i,\text{L}}\) is the predicted value of net load and \(a_{i}\) is the radius of uncertainty.