# Flexible Simulation Platform for Generating Realistic Waveforms with Voltage Notches
## 2 Background on Voltage Notches  
Voltage notches, also referred to as commutation notches [3; 13] or notching [2; 5], are caused by the normal operation of line-commutated power converters [1; 2; 3]. The notch occurs in the converter when the current is transferred from one conducting arm to another. In this finite time interval, both arms conduct simultaneously, leading also to a short duration overcurrent [13]. As depicted in Figure 1a, the main characteristics of a voltage notch include the following [5]:  
* Depth: The average depth, \(\Delta U_{com}\), of the voltage notch from an ideal voltage sine wave. Common practice is the use of relative depth, \(d_{com}\), with respect to the peak value of the fundamental component \(\hat{U}_{1}\), i.e., \(d_{com}=\Delta U_{com}/\hat{U}_{1}\)[14].
* Width: The duration of the notch, \(\Delta t_{com}\), usually expressed in \(\upmu\)s.
* Area: The product of the notch depth, \(\Delta U_{com}\), multiplied by the notch width, \(\Delta t_{com}\).  
Commutation oscillations, caused by capacitive elements, are another key characteristic of voltage notches. Oscillations in the kHz range, as depicted in Figure 1b, are linked to capacitor banks, filters, and capacitive loads in the LV network. Higher-frequency oscillations, as shown in Figure 1c, result from snubber capacitors in the power converter.  
Table 1 presents the notch limits according to the standard IEEE 519. Emission is restricted solely to notch depth and area. However, various studies, including [4; 8], emphasize the need for a comprehensive analysis of commutation oscillations and the potential excitation of natural frequencies in the network impedance.  
Commutation Phenomenon and Voltage Notch GenerationVoltage notches in a six-pulse controlled rectifier occur during the commutation process when current transfers between phases in the AC input.  
* Ideal conditions: No commutation inductance leads to no voltage notches, with instantaneous commutation and an ideal six-pulse output DC voltage (\(U_{D}\)). This is shown in Figure 2a for a firing angle \(\alpha=30^{\circ}\).
* Non-ideal conditions: The presence of commutation inductance causes an overlap period where two SCRs conduct simultaneously, creating a transient AC short circuit and resulting in notches on phase-to-neutral and phase-to-phase voltages, also affecting \(U_{D}\). This is shown in Figure 2b for \(\alpha=30^{\circ}\).  
The firing angle \(\alpha\) ranges from \(0^{\circ}\) to \(180^{\circ}\), but the analysis in this paper focuses on the rectifier mode with \(\alpha<90^{\circ}\). Practical constraints, such as the need for sufficient gate triggering voltage, limit \(\alpha\) to a range of \(10^{\circ}\) to \(90^{\circ}\) to ensure proper firing of SCRs [15].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Characteristic** & **Special Applications** & **General System** & **Dedicated System** \\ \hline \(d_{com}\) & 0.1 & 0.2 & 0.5 \\ \(A_{com}\) (V\(\cdot\upmu\)s) * & 16,400 & 22,800 & 36,500 \\ \hline \hline \end{tabular}
* The values indicated for \(A_{com}\) are applicable to systems with a phase-to-phase voltage of 480 V. A conversion is then required for application at other voltage levels.  
\end{table}
Table 1: Recommended limits on voltage notches according to IEEE standard 519 (data from ref. [5]).  
Figure 1: Characteristics of voltage notches. (**a**) Depth, width, and area of a classical notch (adapted from ref. [5]). (**b**) Notch with commutation oscillations due to a capacitor bank with no detuning. (**c**) Notch with commutation oscillations due to snubber capacitance.