## 3 Regulation Range of Compensation Voltage Amplitude
### Pulse Duty Factors Calculation
Their value determines the value of the compensation voltages. For the case shown in Figure 14, a symmetrical change in the voltage values in each phase of the grid is observed; therefore, the coefficients \(D_{1}\) and \(D_{2}\) are equal. If the voltage change occurs only in one of the phases, the values of these coefficients differ. Such a situation is shown in Figure 15, where the voltage sag occurs only in the first phase \(V_{m\ sag1}=0.7\)\(V_{m}\), where \(V_{m\ sag1}\) is the voltage value during the sag for phase 1 of the grid voltage. As already mentioned, the proposed topology allows for the compensation of voltage loss in one phase of the network voltage. Then, in the phase in which the voltage loss occurred, a compensating voltage is generated from the voltages of the other two phases. An example of such compensation is illustrated by the time waveforms presented in Figure 16.  
As can be seen, using the proposed system, it is possible to compensate for voltage sags and swells (both single-phase and three-phase), slowly changing voltage fluctuations, as well as voltage decay in one of the phases. It is also possible to compensate for two-phase faults with a change in the phase shift of the input voltages, but this requires more detailed research and analysis, which will be the subject of future research. The proposed voltage regulation or voltage compensation system can operate continuously by regulating the voltage in such a way that it is at a constant level or within a certain range of changes. That is, they can regulate the voltage in the distribution network, the increase of which was caused by the excessive generation of energy through distributed generation systems, e.g., prosumer PV systems or wind systems. The results of the tests in Figure 14, showing the compensation of slow-changing voltage fluctuations, model changes occurring in a real distribution network with distributed generation systems, where the voltage level changes rather often as a result of changes in weather conditions. It should be emphasized that the simulation tests were performed in an open control loop. The lack of feedback causes the voltages on the load to differ from the reference values. These differences result from voltage drops on system elements--chokes of input and output filters, power electronic switches, input and coupling transformers. The inaccuracy of shaping the output voltages is also affected by the phase shift between the input and output voltages introduced by the passive elements (\(L\) and \(C\)) of the input and output low-pass filters. Sample results of simulation tests showing the described differences between the reference and measured values of output voltages, for symmetrical 0.7 voltage sag, are shown in Figure 17. Both the difference in voltage amplitude and a slight phase shift are visible. Figure 12: Symmetrical voltage sag. Figure 13: Symmetrical overvoltage. Figure 14: Low-frequency voltage fluctuation. Figure 15: Voltage change in one phase. The determination of the duty cycle factors of the control pulses \(D_{1}\) and \(D_{2}\) is the initial phase for controlling the system in a closed feedback loop. The analysis and selection of the control structure with feedback and the settings of the regulator parameters will be a stage of future research. An important issue in the operation of the proposed AC voltage compensator is the value of the current drawn from the power grid. This issue is important in the context of compensation, especially of voltage sags, which are caused by short-circuits in the depth of  
Figure 9:0 Voltage loss in one phase. Figure 9:1 Differences between the reference values and the measured values of the output voltages at a symmetrical three-phase voltage sag. the power grid. The operation of such a compensator will constitute an additional load for the power grid. Figure 18 shows exemplary values of currents drawn from the network during compensation of a voltage dip equal to 0.7 \(V_{m}\).