# Flexible Simulation Platform for Generating Realistic Waveforms with Voltage Notches
## 3 Simulation Platform Design
### Six-Pulse Controlled Rectifier  
Figure 4 illustrates the general model of a six-pulse controlled rectifier connected to a PCC in an LV network. The main components of the model are as follows:  
* Upstream network: modeled as a Thevenin equivalent as described in Section 3.1. * Commutation reactance (\(X_{com}\)): the total reactance between the PCC and the power converter at power frequency. Figure 4: General model of a six-pulse controlled rectifier. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Distortion Level**} & \multicolumn{5}{c}{**Harmonic Voltage (\(\underline{U_{h}}\))**} \\ \cline{2-7}  & \multicolumn{2}{c}{\(\underline{U_{s}}\)} & \multicolumn{2}{c}{\(\underline{U_{7}}\)} & \multicolumn{2}{c}{\(\underline{U_{11}}\)} & \multicolumn{2}{c}{\(\underline{U_{13}}\)} \\ \cline{2-7}  & **RMS Mag.** & **Phase (\({}^{\circ}\))** & **RMS Mag.** & **Phase (\({}^{\circ}\))** & **RMS Mag.** & **Phase (\({}^{\circ}\))** & **Phase (\({}^{\circ}\))** & **Phase (\({}^{\circ}\))** \\ \hline Low & 0.99 & 170 to 200 & 0.91 & 0 to 60 & No data & No data & No data & No data \\ Medium & 3.78 & 170 to 200 & 2.63 & 0 to 60 & 0.82 & \(-\)10 to 20 & 0.56 & 80 to 110 \\ High & 7.62 & 170 to 200 & 6.11 & 0 to 60 & 2.72 & \(-\)10 to 20 & 3.17 & 80 to 110 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Typical harmonic voltages at the LV side of distribution transformers in Germany (data from ref. [19]). Six-pulse controlled rectifier: a three-phase full-wave rectifier that uses six sequentially firing Silicon Controlled Rectifiers (SCRs) (\(T_{1}\) to \(T_{6}\)) arranged in bridge topology. The SCRs draw current in six pulses and produce a variable DC voltage (\(U_{D}\)) controlled by the firing angle. It also includes parallel RC-snubbers to protect SCRs from transients. * DC smoothing reactor (\(L_{D\_link}\)): an inductor at the DC-link to control harmonics and reduce ripple in \(U_{D}\). * DC load: represented as a resistor (\(R_{D}\)) and inductor (\(L_{D}\)) to model various DC loads like motors, drives, heaters, and welders. Modeling Key Parameters of Controlled Rectifiers Affecting Voltage Notches  
This section explores the key parameters affecting voltage notches in controlled rectifiers, highlighting the importance of modeling and sizing these parameters based on rectifier and DC load requirements and technical constraints of the LV network. For instance, [4; 20] provides expressions for the \(d_{com}\) and commutation angle (\(\mu\)) of voltage notches where these dependencies can be theoretically observed according to (2) and (3). \[d_{com}=\frac{L_{s}}{2\cdot(L_{com}+L_{s})}\cdot\sqrt{2}\cdot U_{s}\cdot\sin( \alpha), \tag{2}\]  
\[\mu=\alpha-\cos^{-1}\bigg{(}\frac{4\cdot\pi\cdot f_{s}\cdot I_{D}\cdot(L_{com }+L_{s})}{\sqrt{2}\cdot U_{s}}+\cos(\alpha)\bigg{)}, \tag{3}\]  
where \(L_{s}\) is the source inductance, \(L_{com}\) is the commutation inductance, \(U_{s}\) is the source RMS phase-to-phase voltage, \(f_{s}\) is the fundamental power frequency of the system, and \(I_{D}\) is the output DC current of the rectifier. To generate realistic synthetic voltage notch waveforms using the scheme depicted in Figures 3 and 4, these key modeling parameters are analyzed below, and relevant expressions are considered and derived:  
* Rectifier apparent power: The rated apparent power (\(S_{r}\)) and line current (\(I_{s}\)) are related by (4)-(6). \[S_{r}=\sqrt{3}\cdot U_{s}\cdot I_{s},\] (4) \[I_{s}=\sqrt{\frac{2}{3}}\cdot I_{D}.\] (5) \[S_{r}=\sqrt{2}\cdot U_{s}\cdot I_{D}.\] (6)
* DC load: The DC load model includes an inductor (\(L_{D}\)) with typical values for DC motors provided in Table 4.  
* Commutation reactance: The commutation reactance (\(X_{com}\)) is inversely related to \(d_{com}\), and directly related to \(\Delta t_{com}\), as expressed in (7) to (10) [14]. \[X_{com}=u_{com}.\frac{U_{s}^{2}}{S_{r}},\] (7)