## 4 Case Studies
### Result Analysis for Robust Control Implementation in Automatic Load Commutation Devices  
To demonstrate the effectiveness of the robust control model of automatic load commutation device, a user with an active power of 10 kW and reactive power of 4 kVar equipped with an automatic commutation device is added to each load node in the modified IEEE 33-bus system described above. Similarly, the original load is multiplied by the load change rate to obtain the user's load values for changes within a 24 h period, and optimization simulations are conducted for both determinacy and robustness. The maximum deviation rate of active output from photovoltaic and wind power are set as 30%, and the maximum deviation rate of load demand is set as 40% [30]. Meanwhile, the deterministic model for the automatic load commutation device based on the predicted output of load demand and renewable energy used to solve the model is employed. Commutation operation occurs only once within a 24 h period, with the total network loss over one day being minimized. The uncertainty parameters \(\Gamma_{DG}\) and \(\Gamma_{L}\) of renewable energy and load demand are both set as 1. The robust control results of the automatic load commutation device are shown in Table 2, along with the deterministic control results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Commutation**} & \multicolumn{2}{c}{**Robust Control Model**} & \multicolumn{2}{c}{**Deterministic Control Model**} \\ \cline{2-5}  & **Load Phase before** & **Load Phase after** & **Load Phase before** & **Load Phase after** \\  & **Commutation** & **Commutation** & **Commutation** & **Commutation** \\ \hline  
& C & A \\ Three-phase Total & & & & \\ Network Loss & & & & \\ Total Number of & & & & \\ Commutation Times & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of robust control and deterministic control results of automatic load commutation devices. From Table 2, it can be seen that the automatic load commutation devices in the deterministic model only performed one commutation action within a day, while in the robust control model, the automatic commutation device performed commutation actions four times within a day. In the deterministic model of an automatic load commutation device, the considered load demand and renewable energy are both predicted values, and the distribution network operates under ideal conditions. Therefore, its automatic load commutation device only needs a small number of actions to make the three-phase distribution network operate in a more balanced state. In contrast, the robust control model of automatic load commutation devices needs to consider the optimal operation of distribution network under worst-case scenarios for both load demand and renewable energy. The robust control model of automatic load commutation device aims to optimize the operation of the power distribution network under the worst-case scenarios of load demand and renewable energy. The network loss results obtained from the robust control model are the network losses under the worst-case scenarios of the power injections at node, so the total three-phase network loss is higher than that of the deterministic model. In addition, in order to demonstrate that the robust control model with an automatic load commutation device will not significantly affect the economic efficiency of the distribution network, Table 3 compares the objective function values of the deterministic model and robust control model under the predicted power scenario and the worst-case scenario with fluctuating load demand and renewable energy. According to Table 3, when the load demand and renewable energy are in the predicted power output scenario, the objective function value of the robust control model for the automatic load commutation device is slightly higher than that obtained by the deterministic model.