## 3 Modelling and Simulation
### Mode #2 Harmonic Supply and Nonlinear Load  
Let's consider systems supplied from a harmonic network and equipped with 3-, 5-, and 2-phase diode rectifiers with a capacitive filter and linear resistive R load, Figure 12(a)-c.  
Figure 12: Waveforms of distortion power components \(D_{av}(k)\) during transient states calculated by different methods (MAF-, DFIR, and DIIR filters) **(a)**, and the corresponding deformation component of the current using the MAF method **(b)**. Figure 13: _Cont._  
Figure 14: Network voltages (**a**) and currents (**b**) in \(a,b,c\)- coordinate systems. Figure 15: Voltage (**a**) and current (**b**) on the DC side of a rectifier, under step change of resistive load. Figure 16: Load parameters for steady states before and after load change. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Load** & \(R\) **[\(\Omega\)]** & \(C\) **[mF]** \\ \hline before & 55.90 & 1.88 \\ after & 27.95 & 1.88 \\ \hline \(U_{rms}=230\) V, \(f=50\) Hz, 5-phase supply system. & \\ \hline \hline \end{tabular}
\end{table} 
Table 19: Load parameters for steady states before and after load change. Figure 16: Phase voltages (**a**), currents (**b**) in \(a,b,c,d,e\)- coordinate system during transient. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Time** & \(\mathbf{U_{a,rms}\) [V]} & \(\mathbf{U_{b,rms}\) [V]} & \(\mathbf{I_{a,rms}\) [A]} & \(\mathbf{I_{b,rms}\) [A]} & \(\mathbf{A_{1}\) [A]} & \(\mathbf{\varphi_{1}}\) [\({}^{\circ}\)**el.]** & **cos \(\mathbf{\varphi_{1}}\) [\({}^{-}\)**]** \\ \hline \(\mathrm{t}=0.1\,\mathrm{s}\) & \(229.8\) & \(229.8\) & \(12.17\) & \(12.17\) & \(8.352\) & \(-5.988\) & \(0.9945\) \\ \(\mathrm{t}=0.2\,\mathrm{s}\) & \(229.8\) & \(229.8\) & \(20.42\) & \(20.42\) & \(16.60\) & \(-7.137\) & \(0.9923\) \\ \hline \hline \end{tabular}
\end{table} 
Table 20: Simulation results before and after the change (at steady states). Figure 17: Voltage (**a**) and current (**b**) in the DC side under step change of resistive load. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Time** & \(\mathbf{S_{av}\) [VA]} & \(\mathbf{P_{av}\) [W]} & \(\mathbf{Q_{av}\) [VAr]} & \(\mathbf{D_{av}\) [VAd]} & \(\mathbf{PF}\) [\({}^{-}\)] & \(\mathbf{THD_{1}\) [\%]} & \(\mathbf{P_{lap}\) [W]} & \(\mathbf{P_{max}\) [W]} \\ \hline \(\mathrm{t}=0.1\,\mathrm{s}\) & \(13,247.7\) & \(6359.6\) & \(-621.7\) & \(11,667.4\) & \(0.4797\) & \(88.07\) & \(6348.4\) & \(0\) \\ \(\mathrm{t}=0.2\,\mathrm{s}\) & \(24,278.7\) & \(13,887.3\) & \(-1798.8\) & \(9833.4\) & \(0.5719\) & \(40.50\) & \(13,383.1\) & \(0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 21: Simulation results before and after the change (at steady states). 3.2.3. Comparison of Power Components in 2-,3- and 5-Phase Supply Systems under Rectifier Load  
Apparent, active, blind, and distortion powers during transient states are shown in Figure 20a-d. The simulation was performed under the same load phase parameters (\(R\), \(C\)); therefore, the magnitudes are proportionately different. Figure 19: Voltage (**a**) and current (**b**) on the DC side under resistive load. Figure 20: Apparent—(**a**), active—(**b**), blind—(**c**), and distortion (**d**) power components during transient states for 3-, 5-, and 2-phase systems under mains supplied rectifier load. The waveforms of all power components per unit are very similar to those in the previous case, Mode#1. In the case of the reactive power component (Figure 20c), nearly the same blind reactive powers of 3- and 5-phase systems are generated at steady-state \(t\in\langle 0.1;0.2\rangle\) despite DC powers being different. This is mainly due to the fact that the line-to-line voltages of a 5-phase system are not equal to \(\sqrt{3}\times U_{\text{a,b,c}}\) as in a 3-phase one, but they are lower. Moreover, the distortion power of a 3-phase system is slightly higher than in a 5-phase one (Figure 20d, \(t\in\langle 0.04;0.1\rangle\)). Distortion components of all connections are rather high due to impulse current taken from the network.