# A Two-Grid Interline Dynamic Voltage Restorer Based on Two Three-Phase Input Matrix Converters
## 7 Simulation Results and Discussion
### Case 1: Voltage Sag with Harmonic Distortion  
A sag is defined as the decrease in the rms (Root Mean Square) value of the supply voltage, between 0.1 and 0.9 pu, at the feeding frequency and with a duration from 0.5  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Quantity/Parameter** & **Values and Units** \\ \hline Capacitors of the input filters & 10 \(\mu\)F \\ Resistance of the input filters & 50 \(\Omega\) \\ Inductors of the input filters & 2.2 mH \\ Output filter capacitor & 4.7 \(\mu\)F \\ Output filter resistance & 100 \(\Omega\) \\ Output filter inductor & 25 mH \\ Load resistance & 120 \(\Omega\) \\ Load inductor & 8 mH \\ Feeder 1 and 2 & 100 Vp, 60 Hz \\ Load reference voltages 1 and 2 & 100 Vp, 60 Hz \\ CSI switching frequency & 3.6 KHz \\ TTI-MC switching frequency & 7.2 KHz \\ Gains of the PI controllers & \(Kp=30\), \(Ki=0.001\) \\ \hline \end{tabular} \(Kp\) and \(Ki\) correspond to the proportional and integral gains of the PI controller.  
\end{table}
Table 1: TI-IDVR simulation parameters.  
Figure 10: Model of the CSI 1 control algorithm.  
Figure 9: Models for the generation of the reference voltages of feeder 1.  
cycle to 1 min. Voltage distortion in power supplies is one of the most common problems of PQ and has a negative impact on electrical networks and on loads sensitive to voltage variations.  
In this section, the performance of the proposed TI-IDVR in the compensation of voltage sags with harmonic distortion in the feeders is verified. To simulate this event, the peak voltage of the feeders is reduced from 100 Vp to 65 Vp and the fifth harmonic with an amplitude of 20% with respect to the fundamental is added.  
When the disturbance occurs, the TI-IDVR behaves like an IDVR and draws power from the two feeders to compensate for the disturbance, as well as keeping the voltage on the sensitive load stable. The event occurs on feeder 1 in the 50 ms to 100 ms time interval, and on feeder 2 from 150 ms to 200 ms. The waveforms of the voltages and currents obtained in the simulation are shown in Figures 11 and 12.  
Feeder 1 voltages, compensation 1 voltages, load 1 voltages, and the voltage on the virtual dc-link are shown in Figure 11. The figure shows how the voltages of load 1 remain practically at their nominal values despite the disturbance in feeder 1. It can also be seen how effectively the TTI-MC integrates the power from the two feeders to construct the virtual dc-link voltage and thus provides the necessary power to CSI 1 so that it can synthesize the appropriate compensation voltages. In Figure 11, the voltages in feeder 2 and sensitive load 2 remain unchanged in the presence of the disturbance in feeder 1. In the same way, when the voltage sag occurs in feeder 2, the TTI-MC integrates the power of the two feeders, CSI 2 generates the desired injection voltage, and the voltage in load 2 remains unchanged despite the disturbance in feeder 2 as shown in Figure 11.  
Figure 11: System waveforms in the compensation of voltage sags and harmonic distortion. (**a–c**) feeder 1 waveforms; (**d–f**) feeder 2 waveforms; (**g**) virtual dc-link voltage waveform.  
Figure 12 shows the phase \(a\) waveforms of the system. The figure shows that when the disturbance occurs, the voltages and currents in the loads remain practically unchanged despite the disturbance in the feeder. In addition, the voltages and currents of both feeders are in phase. However, in the presence of the disturbance, the TI-IDVR demands a higher current from the feeders; this does not represent a disadvantage since the higher current consumption is an inherent characteristic of the configuration of DVRs without energy storage systems when connected on the source side.  
Finally, the behavior of the system without the TI-IDVR is shown in Figure 12. Comparing Figures 11 and 12, the effectiveness of the proposed TI-IDVR in compensating for voltage sags and harmonic distortion that occur in the feeders can be seen.