## 3 Definition of Main Design Parameters for Three-Phase Six-Switch Converter Example
### Pre-Design of 125 kW Grid-Connected Three-Phase Six-Switch Converter Stage  
In order to create a reference model for all further discussions, basic parameters and dedicated modules are selected, and a 125 kW AC/DC converter stage is chosen. Relevant system and converter related parameters are defined in Table 1. Mains voltage and frequency parameters are defined according to European standards for low-voltage grids (400 \(\mathrm{V_{rms}}\) and 50 Hz). The power rating of the inverter was chosen according to [15]. It should be noted that for further discussions, two additional simplifications were applied to reduce the complexity of relevant equations. First, a standard pulse width modulation (PWM) approach was selected. No space vector modulation or third harmonic injection strategies are considered. Therefore, it was opted for a total DC-link voltage (\(V_{\mathrm{DC}}\)) of 800 V to meet a modulation index \(M\) of 0.813. The additional margin of 0.187 is required to compensate dynamic events which must be compensated by current and voltage controller routines. The modulation index for such a three-phase six-switch inverter is defined by  
\[M=\frac{2\cdot\sqrt{2}\cdot V_{N,rms}}{V_{DC}}=0.813. \tag{1}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Parameter** & **Value** \\ \hline \hline Mains voltage: & \(V_{\mathrm{LL}}\) = 400 \(\mathrm{V_{rms}}\) \\ Mains frequency & \(f_{\mathrm{N}}\) = 50 Hz \\ Total DC-link voltage & \(V_{\mathrm{DC}}\) = 800 V \\ Nominal power & \(S_{\mathrm{N}}\) = \(P_{\mathrm{N}}\) = 125 kW \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System-level design specification of the three-phase converter (nominal rating). Second, it is assumed that the midpoint of the DC-link is connected to the artificial star point of the Y-connected input filter capacitors and/or neutral created by the 3-phase grid formation. This allows for simpler analytical equations compared to a floating setup. However, in such configuration, the current ripple of each phase is considerably higher due to the fixed midpoint of the DC-link and the mission common-mode voltage, which is usually introducing additional voltage levels manipulating the current ripple characteristics for the whole sinusoidal period of \(0\leq\varphi\leq 2\pi\). The selected converter stage is bidirectional. Thus, it can deliver power from the grid to load or vice versa. A phase angle of \(\varPhi=0\) denotes power delivery from the grid to load. A phase angle of \(\varPhi=\pi\) indicates power flow from load/source to grid. Furthermore, typically, grid-connected power electronics also must support the grid with additional reactive power. Adaptation of the phase angle \(\varPhi\) results in different active and reactive modes/operation of the converter. Therefore, for all further calculations, the fundamental relations apply,  
\[S_{\text{N}}=\sum_{i}V_{\text{N,rms,i}}\cdot I_{\text{N,rms,i}}=3\cdot V_{ \text{N,rms}}\cdot I_{\text{N,rms}} \tag{2}\]  
\[P_{\text{N}}=3\cdot V_{\text{N,rms}}\cdot I_{\text{N,rms}}\cdot\cos(\Phi) \tag{3}\]  
\[Q_{\text{N}}=3\cdot V_{\text{N,rms}}\cdot I_{\text{N,rms}}\cdot\sin(\Phi) \tag{4}\]  
\[I_{\text{o}}=3\cdot\frac{V_{\text{N,rms}}}{V_{\text{DC}}}\cdot I_{\text{N,rms }}\cdot\cos(\Phi) \tag{5}\]  
where \(S_{\text{N}}\), \(P_{\text{N}}\) and \(Q_{\text{N}}\) denote apparent, active and reactive power, respectively. \(I_{\text{o}}\) defines the averaged DC-current after capacitive filtering. The switching frequency of such converters in the 100 kW region is typically between 5-10 kHz, depending on whether the solution is optimized for power density or efficiency. For this evaluation, a switching frequency of 10 kHz is chosen in order to demonstrate the potential of the proposed additional WBG-based light-load circuit enhancement.