*6.4. DC Link Converter*

The generated seven phase AC output is fed as an input to the seven phase rectifier which converts AC to DC. The rectified DC output voltage feeds the boost converter. The boost converter output voltage and current of 845 V and 279 A is achieved, as shown in Figure 12a,b.

**Figure 12.** (**a**) Boost Voltage; (**b**) Boost Current.

#### *6.5. Grid Integration*

The grid tied inverter is the power electronic converter that converts the DC signal into AC, but with the appropriate synchronizing techniques. It is basically used in the integration of renewable energy to the utility line. The magnitude and phase of the inverter voltage should be the same as that of the grid and its output frequency should be equal to the grid frequency for proper grid synchronization. The output phase voltage of the inverter is 365 V (peak) and a current of about 508 V (peak) is achieved at a 0.85 modulation index with a DC input of 845 V as shown in Figures 13 and 14. The line voltage of the inverter is given by Figure 15.

**Figure 13.** Vdc and Modulation Index.

**Figure 14.** Inverter Output Voltage and Inverter Current.

**Figure 15.** Inverter Line Voltage.

The *d*- and *q*-axis voltage of the *d-q* PLL and frequency tracking is shown in Figure 16. The voltage and current drawn by the load connected at the point of common coupling is shown in Figure 17. The grid voltage and current are shown in Figure 18. The power injected into the grid is about 196 kW, which is shown in Figure 19.

**Figure 16.** Graph of *Vd*, *Vq*, and Frequency.

**Figure 17.** Load Voltage and Load Current.

**Figure 18.** Grid Voltage (Vgrid) and Grid Current (Igrid).

**Figure 19.** Power injected into the Grid.

The grid is subjected to different fault conditions to investigate the performance of the SRF PLL. Figure 20a shows the frequency and phase detection variation during a line to line fault. It is clear from the figure that phases B and C are in phase with each other and their magnitude is less than phase A, whereas the magnitude of phase of B and C are zero during a line to line ground fault as shown in Figure 21a. The voltages of the *d-q*-axis also vary, as it contains second harmonic ripples as given by Equation (35), which is illustrated by Figures 20b and 21b.

**Figure 20.** (**a**) Frequency and Phase Angle Variation during a Line to Line Fault; (**b**) *q-*axis and *d-*axis Voltage Magnitude during a Line to Line Fault.

During unbalanced grid voltage condition, the sinusoidal nature of the *q*-axis voltage component affects the output of the PI controller. Therefore, the PI controller generates a sinusoidal error signal, angular frequency is shown in Figure 22a,b, which is similar to that of the line to line fault.

**Figure 21.** *Cont*.

**Figure 21.** (**a**) Frequency and Phase Angle Variation during a Line-Line ground LLG Fault; (**b**) *q-*axis and *d-*axis Voltage Magnitude during a LLG Fault.

**Figure 22.** (**a**) Frequency and Phase Detection Variation during Unbalanced Grid Voltages; (**b**) *q-*axis and *d-*axis Voltage Magnitude during Unbalanced Grid Voltages.

The SRF PLL performance during voltage sag is shown in Figure 23a,b. Voltage sag occurs in the grid such that the magnitude of all phase voltages are equal and their magnitudes are 50% of the nominal voltage. It is noticed that it does not cause any oscillations in the frequency and the *d-q* voltages. Balanced voltage sag does not affect PLL tracking. However, a sudden change in the magnitude causes a dip in the estimated frequency of *d-q* PLL, and later it tracks the phase angle of the grid voltages.

**Figure 23.** (**a**) Frequency and Phase Detection Variation during Voltage Sag; (**b**) *q-*axis and *d-*axis Voltage Magnitude during Voltage Sag.

#### **7. Conclusions**

In this article, a comprehensive model of a wind driven 7PIG in grid connected mode was developed using the two axis *d-q* equivalent circuit. A seven phase wind electric generator is integrated using the individual system components and the performance of the seven phase wind electric generator is analysed for varying wind speed [46]. A synchronous reference frame PLL incorporated for the grid interface is simulated and analysed. The enhanced performance of 7PIG is evaluated through the fault tolerant capability and high output power with reduced current per phase when compared with the three phase model. The performance of SRF-PLL incorporated in the grid connected seven phase wind electric generator was analysed for various operating grid conditions. The use of multiphase machines along with the PLL synchronization of the grid increases the reliability of the WEG. Notably by the possibility of achieving post-fault disturbance free operation provided by the seven phase machine, as well as the constant voltage and frequency operation enabled by the *d-q* PLL.

#### **Acknowledgments:** No funding resources.

**Author Contributions:** Kalaivani Chandramohan, Sanjeevikumar Padmanaban, and Rajambal Kalyanasundaram, has developed the concept of the research proposed and developed the numerical background; Mahajan Sagar Bhaskar involved in the implementation of numerical simulation along with other authors for its depiction in quality of the work with predicted output results. Lucian Mihet-Popa has contributed his experience in AC drives and Wind Energy Conversion for further development and verification of theoretical concepts. All authors involved in articulating the paper work in its current form in each part their contribution to research investigation.

**Conflicts of Interest:** The authors declare no conflict of interest.
