## 4 Case Studies
### Sensitivity Analysis of Parameters within Uncertainty Sets  
The range of uncertainty in the source and load considered in this paper is influenced by the maximum deviation and fluctuation in the prediction of load demand and renewable energy. To analyze the impact of parameter changes in uncertain sets on model conservatism, this section utilizes a modified IEEE 33-bus power system to conduct the sensitivity analysis. Different deviation and uncertainty parameters are set for load demand and renewable energy, respectively, to compare the effects of robust control model and deterministic model on optimization results. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Model for Solving**} & \multicolumn{2}{c}{**Value of Objective Function/USD**} \\ \cline{2-3}  & **Predictive Output** & **Worst-Case** \\  & **Scenario** & **Scenario** \\ \hline Deterministic Control Model & 297.89 & 665.88 \\ Robust Control Model & 322.75 & 602.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of objective function values between deterministic model and robust control model under different scenarios. For the sake of comparison, only the uncertainty caused by a single factor is considered. Specifically, it assumes that renewable energy remains at its predicted value while load demand varies within a range of 10% to 40% above the predicted value. Alternatively, it assumes that load demand stays at its predicted value while renewable energy varies within a range of 10% to 30% above the predicted value. The corresponding objective function values for the system are presented in Table 4.  
From Table 4, it can be seen that when the deviation of load demand is higher than that of the predicted value, the objective function value of the robust control model is lower than that of the deterministic model. As the uncertainty of load demand increases, the difference in objective function values between the two models increases and the optimization effect of robust control model is better, reflecting its advantage in adverse scenarios. Conversely, when the deviation of renewable energy surpasses the predicted value, the objective function value of the deterministic model is lower than that of the robust control model. This occurs due to the power injections from renewable energy sources having an opposite effect compared to that of load demands. As renewable energy generation increases, simulation conditions shift towards more favorable scenarios rather than worsening ones. The continuous absorption of connected renewable energy by loads reduces three-phase network losses. Consequently, in these situations, the optimization effect of a robust control model is slightly inferior to that of a deterministic model. It can be concluded that a robust control strategy offers better adaptability to harsh conditions without sacrificing significant economic efficiency within milder scenarios. Furthermore, this approach enhances a distribution network's ability to respond effectively to uncertainties of both the source and load within its system. The number of scenarios contained in the uncertainty sets of load demand and renewable energy will be affected by uncertainty. By controlling the uncertainty parameters, certain limitations can be imposed on the situation of load demand and renewable energy, thereby regulating the conservatism of the robust control model for automatic load commutation devices. This paper designs multiple combinations of renewable energy and load demand uncertainty parameters \(I_{DG}\) and \(I_{L}\). The corresponding objective function values of the system under different uncertainty parameters are shown in Table 5. From Table 5, it can be seen that as the uncertainty parameters \(I_{DG}\) and \(I_{L}\) decrease, the range of the uncertainty set gradually becomes smaller, and the worst-case scenario covered by the generated fluctuation scene is reduced.