# Flexible Simulation Platform for Generating Realistic Waveforms with Voltage Notches
## 6 Monte Carlo Simulation-Based Data Generation
### Results  
The Monte Carlo simulation approach introduced in this study generates a diverse range of realistic waveforms for voltage notches and associated currents in industrial LV networks. Figure 22 presents exemplary waveforms obtained from this simulation approach, illustrating various scenarios of increasing complexity. Figure 22 comprises six subfigures (a-f), each depicting voltage (top) and total line current (bottom) waveforms for a specific network configuration:  
1. Scenario 1: represents the base case with only the controlled rectifier. The voltage waveform exhibits pronounced notches, while the current shows the characteristic quasi-square wave pattern of a six-pulse rectifier. 2. Scenario 2: introduces linear loads alongside the rectifier. Voltage notches remain visible, but the current waveform appears smoother due to the linear load contribution. 3. Scenario 3 with non-detuned capacitor bank: incorporates a non-detuned capacitor bank. Notches are not clearly observed given a heavy voltage distortion, and the current waveform displays increased high-frequency components due to capacitor effects. 4. Scenario 3 with detuned capacitor bank: similar to (c) but employs a detuned capacitor bank. Voltage notches are clear and distortion-free, and the current waveform exhibits reduced high-frequency oscillations compared to the non-detuned case. 5. Scenario 4 with non-detuned capacitor bank: combines the rectifier, linear loads, and a non-detuned capacitor bank. Notches are less prominent, and the current waveform reflects a complex interaction of rectifier, linear load, and capacitor bank characteristics. 6. Scenario 4 with detuned capacitor bank: similar to (e) but with a detuned capacitor bank. Voltage notches are clearly observed, and the current waveform depicts some low-frequency oscillations. These waveforms effectively illustrate the impact of various network configurations and power factor correction methods on voltage notches and current distortion in industrial LV networks. The progression from scenarios (a) to (f) showcases the increasing system \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Parameter** & **Range** & **Probability** & **Range Probability** \\ \hline \multirow{3}{*}{\begin{tabular}{c} Network \\ equivalent \\ \end{tabular} } & \multirow{3}{*}{\(S_{\text{sc}}\) (MVA)} & [2, 3] & Uniform & 0.25 \\  & & (3, 10) & Uniform & 0.5 \\  & & (10, 15) & Uniform & 0.25 \\ \hline \multirow{9}{*}{\begin{tabular}{c} Rectifier \\ \end{tabular} } & \(S_{r}\) (kVA) & [1, \(S_{r,ratio,max}\)\(\cdot S_{\text{sc}}\)] & Uniform & 1 \\ \cline{2-5}  & \(\alpha\) (\({}^{\circ}\)) & [10, \(\alpha_{max}\)] & Uniform & 1 \\ \cline{2-5}  & \(X_{com}\) (\(\Omega\)) & \(\mu\) = optimal \(X_{com}\), \(\sigma\) = 0.15\(\cdot\mu\) & Normal & 1 \\ \cline{2-5}  & \multirow{3}{*}{\(L_{D}\) (mH)} & [1, 5] & Uniform & 1 for PD \(>\) 100 kW \\  & & (5, 15) & Uniform & 1 for 10 kW \(<\) PD \(\leq\) 100 kW \\  & & (15, 100) & Uniform & 1 for PD \(\leq\) 10 kW \\ \cline{2-5}  & \(U_{rm}\) (V) & [\(U_{rm,rated}\) = 1400, \(\infty\)] & Exponential & 1 \\ \cline{2-5}  & \multirow{3}{*}{Design curve} & 0.2-Cbase & Uniform & 0.1 \\  & & 0.5-Cbase & Uniform & 0.3 \\  & & 1-Cbase & Uniform & 0.5 \\  & & 2-Cbase & Uniform & 0.1 \\ \cline{2-5}  & \(R_{nn}/R_{base}\) & [min \(R_{nn}/R_{base}\), 6] & Exponential & 1 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Linear loads \\ \end{tabular} } & \(S_{ll}\) (kVA) & [5, \(S_{ll,max}\)] & Uniform & 1 \\ \cline{2-5}  & \(PF_{ll}\) & [0.8, 0.95] & Uniform & 1 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Capacitor bank \\ \end{tabular} } & \multirow{3}{*}{\(QF\)} & [5, 20] & Uniform & 0.25 \\  & & (20, 50) & Uniform & 0.5 \\ \cline{1-1}  & & (50, 100) & Uniform & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Range, type of distribution, and range probability for random parameters in the case study. complexity and the corresponding evolution of voltage notch characteristics.