# Improved PR Control Strategy for an LCL Three-Phase Grid-Connected Inverter Based on Active Damping
## 4 Case Analysis
### Analysis of Voltage and Current Based on the Improved QPIR Controller  
The voltage and current waveforms, active power waveforms, and reactive power waveforms of the PR controller, QPR controller, and QPIR controller at a grid frequency of 49.5 Hz are shown in Figures 9-11, respectively.  
Figure 8: Bode diagram of \(T\)(s) with PR, QPR, and QPIR controllers.  
Figure 9: Steady-state waveforms of grid-connected current and voltage using PR, QPR, and QPIR controllers (at 49.5 Hz).  
In Figure 9, when the PR controller is used, the phase error between grid-connected current and voltage is 0.09\({}^{\circ}\), and the effective value of the grid-connected current is 60.26 A, which is less than the current loop reference value (60.606 A). In Figures 10 and 11, \(P\) represents active power and \(Q\) represents reactive power. When the PR controller is used, the active power is 39,740 W, which is less than the given value 40 kW, and the reactive power reaches 60 var. This shows that the PR controller has errors in controlling amplitude and phase.  
When the QPR controller is used, the phase error between the grid-connected current and voltage is 0.06\({}^{\circ}\), and the effective value of the grid-connected current is 60.44 A, which is slightly less than the reference value. In Figures 10 and 11, when the QPR controller is used, the active power is 39,870 W and the reactive power is 40 var. It is verified that the gain of the QPR controller at 49.5 Hz is not large enough to realize static error-free adjustment.  
When the QPR controller is used, the grid-connected current basically has no phase error. The effective value of the grid-connected current is 60.60 A, and the error between the grid-connected current and the reference value is basically 0. As shown in  
Figure 11: Reactive power waveforms controlled by PR, QPR, and QPIR controllers (at 49.5 Hz).  
Figure 10: Active power waveforms controlled by PR, QPR, and QPIR controllers (at 49.5 Hz).  
In Figure 12, when the PR controller is used, the phase error between the grid-connected current and voltage is 0.11\({}^{\circ}\), and the effective value of the grid-connected current is 60.91 A, which is greater than the current loop reference value (60.606 A). In Figures 13 and 14, \(P\) represents active power and \(Q\) represents reactive power. When the PR controller is used, the active power is 40,180 W, which is greater than the given value 40 kW, and the reactive power reaches 80 var. This shows that the PR controller has errors in controlling amplitude and phase.  
When the QPR controller is used, the phase error between grid-connected current and voltage is 0.07\({}^{\circ}\), and the effective value of grid-connected current is 60.8 A, which is slightly higher than the reference value. In Figures 13 and 14, when the QPR controller is used, the active power is 40,110 W and the reactive power is 50 var. It is verified that the gain of the QPR controller at 50.5 Hz is not large enough to realize static error-free adjustment.  
When the QPR controller is used, the grid-connected current basically has no phase error. The effective value of the grid-connected current is 60.61 A, and the error between the grid-connected current and the reference value is basically 0. As shown in Figures 13 and 14, when the QPR controller is used, the active power approaches 40 kW and the reactive power approaches 0 var. It is verified that the QPR controller can eliminate the static error of the system and achieve the operating condition of unit power factor.