# Improved PR Control Without Load Current Sensors and Phase-Locked Loops for APFs
## 4 Simulation Verification
### Traditional PR Control Simulation Analysis  
For comparative verification, this paper reproduces the traditional PR control strategy based on PLL and coordinate transformation described in [27]. The proposed method transforms the harmonic command current into the \(dq\) coordinate system, converting adjacent odd harmonics into even harmonics, thereby reducing the number of PR controllers. For example, the third and fifth harmonics are uniformly converted into the fourth harmonic. Four groups of PR controllers are used in the simulation, corresponding to the 6 th, 10 th, 14 th, and 18 th harmonics, respectively, which indirectly suppress the main odd harmonics (5 th to 19 th).  
Figure 6 shows the simulation waveform of the traditional PR control strategy under steady-state conditions. When the APF was put into operation at t = 0.1 s, the total harmonic distortion (THD) of the grid current dropped rapidly from the initial 28% to 4.5%, indicating that the control strategy has good harmonic suppression capability under steady-state conditions. Figure 6e further provides a spectrum analysis of the grid current, showing that the main low-order harmonics have been effectively suppressed.  
To further verify the dynamic performance of the control strategy, Figure 7 shows the load being suddenly reduced from 120 \(\Omega\) to 60 \(\Omega\) at t = 0.2 s to simulate a load mutation. In Figure 7, at the moment of load mutation, the grid current waveform does not show obvious overshoot, and the system recovers to a new steady state within about 20 ms, reflecting good dynamic response characteristics. The THD of the grid current before and after the mutation is 4.5% and 2.6%, respectively. The spectrum analysis corresponding to the current after the mutation is shown in Figure 7e, which further verifies the effectiveness of the control strategy under dynamic conditions.  
Figure 6: Steady-state situation of traditional PR control: (**a**) grid voltage, (**b**) grid current, (**c**) DC voltage, (**d**) grid connection point voltage, and (**e**) FFT of traditional PR control grid current before mutation.  
Figure 7: Traditional PR control load mutation situation: (**a**) grid voltage, (**b**) grid current, (**c**) DC voltage, (**d**) grid connection point voltage, and (**e**) FFT of grid current after mutation.  
However, the traditional PR control strategy needs to design multiple PR controllers during implementation to compensate for different harmonics. For example, to suppress harmonics from the 5 th to the 19 th order, individual PR controllers must be configured for the 6 th, 10 th, 14 th, and 18 th harmonics. This significantly increases system complexity and computational burden. In addition, the strategy also requires the installation of a current sensor on the load side to detect the current and the use of a PLL to extract the phase information of the current. However, the PLL has the characteristic of slow response speed, especially when the frequency changes suddenly or the system is disturbed; its dynamic response performance is poor, affecting the overall performance of the system.