## 4 Simulations and Experiments  
### Simulation Results  
Figure 14 shows the DVR simulation circuit diagram of the proposed scheme. The simulation circuit consisted of a visual C, a dll unit for the interface, a single-phase full-bridge inverter unit, a grid voltage, and a power filter. To implement the actual grid voltage used in the industrial field, the effective value of the grid voltage fundamental wave was set to 200 V. In addition, the peak values of the three-harmonic, five-harmonic, and seven-harmonic voltages were set to 7 V, 5 V, and 7 V, respectively.  
Figure 15 shows the simulation results for a multi-pointer filter with a circular structure. The first waveform shows the output of the all-pass filter output and the phase angle with a 90-degree phase to estimate the phase angle of the grid voltage. It is evident that the estimation characteristics of the phase angle (theta) of the grid voltage in the first waveform in Figure 15 are good. The second waveform shows the characteristics of the multi-pointer filter and reaches a steady state within the fifth cycle of the grid voltage; however, there is a  
Figure 12: Multi-pointer memory filter with circular structure.  
Figure 13: Operating principle of the multi-pointer memory filter with circular structure.  
slight phase difference between the two voltages. The third waveform was a waveform with a circular memory filter. In the first 1 cycle of the power supply, the output appears to be zero as it does not reach one cycle of the circular filter. From the 2 nd cycle, an output with a low-pass characteristic is formed and a phase shift is performed, leading to a steady state. The figure also shows that the grid voltage and the output of the multi-pointer filter with circular structure are perfectly consistent. Therefore, the filter algorithm proposed in this paper can measure periodic waveforms without phase delay. It is anticipated to exhibit exceptional attributes when used as a feed-forward controller in an AC power supply.  
Figure 14: Circuit diagram for the configuration of the DVR system.  
Figure 15: Simulation results of the multi-pointer memory filter with circular structure.  
Figure 16 shows the simulation results for analyzing the filter characteristics near the voltage zero point. The cutoff frequency of the grid voltage and the analog filter were set to 900 Hz, and at this point, with a grid voltage of 60 Hz, the gain was 0.998 and the phase delay was approximately 3.8\({}^{\circ}\). With a phase lag of 3.8\({}^{\circ}\), the input-output difference was approximately 30 V at 220 V. It can also be seen that the phase-shifted waveform compensates for the phase difference between the sampled filter voltage output (Vg_f), and the actual grid voltage matches the grid voltage.  
Figure 17 shows the simulation results for the DVR voltage compensation. The voltage compensator was controlled after 0.1 s, considering the time constant of the multi-pointer filter with a circular structure. As a result, the output voltage was estimated from 200 V to the command voltage of 220 V within 4 ms.  
Figure 16: Simulation results of the filter characteristic analysis near the voltage zero point.  
Figure 17: Simulation result of DVR voltage compensation.  
Figure 18 shows the waveform of the simulation results of the voltage compensation of the steady DVR. Looking at the first waveform, the grid voltage and the output voltage of the multi-pointer filter with a circular structure are identical, and the inverter output voltage of the second waveform forms a waveform for fundamental wave voltage compensation and the elimination of the high-frequency voltage. It is evident that the output voltage, which is the sum of the grid voltage and the inverter voltage, is a 220 V sine wave.