# Improved PR Control Strategy for an LCL Three-Phase Grid-Connected Inverter Based on Active Damping
## 4 Case Analysis
### Frequency Fluctuation Analysis Based on the Improved QPIR Controller  
Figure 17 is a chart of the power grid frequency fluctuation. A sawtooth wave is used to simulate the power grid frequency fluctuation, and the frequency fluctuation range is 49.5-50.5 Hz. Figure 18 shows power waveforms of the system using the QPIR controller and PR controller under the condition of grid frequency fluctuation according to Figure 17. Figure 19 shows power waveforms of the system using the QPIR controller and QPR controller under the condition of grid frequency fluctuation according to Figure 17.  
Figure 16: Step tracking waveforms of active and reactive power.  
Figure 15: Step waveforms of active and reactive power.  
Figure 19: Power waveforms controlled by the QPIR and QPR controllers when the grid frequency fluctuates.  
Figure 17: Power grid frequency fluctuation diagram.  
Figure 18: Power waveforms controlled by the QPIR and PR controllers when the grid frequency fluctuates.  
As can be seen from the power waveform in Figure 18, when the power grid frequency fluctuates, both the QPIR controller and PR controller systems can maintain stable operation. When the power grid frequency fluctuates, the active power changes with the change in frequency, but the active power fluctuation of the QPIR controller is obviously smaller than that of the PR controller, and the reactive power is almost not affected by the frequency change. For the PR controller, the maximum deviation of active power is 300 W (at 1.2 s) and the deviation of reactive power is 45 var. For the improved QPIR controller, the maximum deviation of active power is only 75 W (at 1.2 s), and the reactive power approaches to 0. This shows that the control accuracy of the QPIR controller is significantly higher than that of the PR controller when the power grid frequency fluctuates.  
As can be seen from the power waveform in Figure 19, when the power grid frequency fluctuates, the active power fluctuation of the QPIR controller is obviously smaller than that of the QPR controller, and the reactive power is almost not affected by the frequency change. For the QPR controller, the maximum deviation of active power is 200 W (at 1.2 s) and the deviation of reactive power is 50 var. For the improved QPIR controller, the maximum deviation of active power is only 75 W (at 1.2 s), and the reactive power approaches 0. This shows that the control accuracy of the QPIR controller is significantly higher than that of the QPR controller when the power grid frequency fluctuates, which verifies that the QPIR controller can adapt to the fluctuation of power grid frequency within the normal range.  
The simulation results show that the steady-state control accuracy of the QPIR controller is higher than that of the PR and QPR controllers under the condition of stable power grid frequency of 49.5 Hz and 50.5 Hz. Under the condition of power grid frequency fluctuation and load variation, the steady-state control accuracy of the QPIR controller is also higher than that of the PR and QPR controllers, which has stronger adaptability to power grid frequency fluctuation and verifies the correctness and effectiveness of the theoretical analysis.