## 4 Case Studies  
### Case and Parameter Settings  
To verify the effectiveness of the model proposed in this paper, a robust control model of the automatic load commutation device considering the uncertainties of the source and load is established using MATLAB R2019b. Then, the commercial optimization solver CPLEX 12.9.0 is employed to solve the optimization model. The test environment utilizes an Intel Xeon Gold 5117 CPU with a clock speed of 2.00 GHz and 64 G RAM.  
The topology of the modified IEEE 33-bus power system, used in this paper, is illustrated in Figure 2. The system comprises 33 nodes, 32 branches, a voltage level of 12.66 kV, and an installed capacity of 1 MVA. The photovoltaic systems have an installed capacity of 250 kVA and are installed at nodes 6 and 27 connected to phase A. Additionally, a photovoltaic system with an installed capacity of 250 kVA is installed at node 20 connected to phase C. Wind turbines with an installed capacity of 300 kVA are positioned at nodes 15 and 24 connected to phase B. The power factor for renewable energy sources is set at 0.8. The branch parameters and reference load data are based on information from reference [29] as presented in Table 1. The total active power and reactive power of the standard system are measured at approximately 3635 MW and 2265 Mvar, respectively. The difference in active power carried by each phase of the system's load can reach up to a maximum difference of 30 kW, indicating the presence of a three-phase imbalance phenomenon.  
Figure 1: Solving process of robust control model for three-phase automatic load regulation device considering the uncertainties of both source and load.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Branch** & **Head Node** & **End Node** & \multicolumn{6}{c}{**Branch Impedance/C**} & \multicolumn{6}{c}{**Load of End Node/(WX,box)**} \\ \cline{3-13}
**Branch** & **Head Node** & **End Node** & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Za**} & \multicolumn{6}{c}{**Phase B**} & \multicolumn{6}{c}{**Phase C**} \\ \hline  
The optimization period in this paper spans 24 h, which is divided into 24 equal time periods. The values of renewable energy and load demand at the beginning of each period are used as the numerical input. The unit price of active power consumption for distribution network loss and the cost coefficient for switching once are set to USD 0.8/kW-h and USD 1/time, respectively. The variation curves of the predicted output for the three-phase load and renewable energy are shown in Figure 3. To simulate the load demand and renewable energy output over the 24 h period, the original load at the node is multiplied by the corresponding change rate, and the capacity of renewable energy is multiplied by the same rate. It is worth noting that different change rates can be used without compromising the effectiveness of the proposed method.  
Figure 3: Forcasted output of load and renewable energy.  
Figure 2: Structure of the modified IEEE 33-bus power system.