# Adaptive PI + VPI Harmonic Current Compensation Strategy under Weak Grid Conditions
## 5 Simulation Analysis and Experiment  
### Phase-Locked Performance Verification under Various Grid Voltage Conditions  
To verify the correctness and effectiveness of the proposed PLL algorithm, a simulation system based on Simulink is established. The three-phase grid voltage is unbalanced and distorted. To verify the tracking characteristics of the frequency deviation, the step frequency deviation is simulated at 0.2 s, from 50 Hz to 54 Hz. The grid-side voltage unbalance and distortion-related parameters are shown in Table 3, and the proposed synchronous phase-locked loop parameters are selected according to Table 2.  
The simulation results are shown in Figure 15.  
Figure 15a presents the three-phase grid voltage, the red, blue and yellow lines represent the \(abc\) three-phase of the three-phase voltage, respectively; the total harmonic distortion rate is 5.86%; and the waveform is obviously unbalanced. Figure 15b-d is the waveforms of the phase and frequency estimation and tracking error when using the three-phase conventional synchronous phase-locked loop (SRF-PLL), notch filter-based synchronous phase-locked loop (NF-PLL) and adaptive notch filter-based synchronous phase-locked loop (ANF-PLL), respectively. The following conclusions can be drawn from Figure 15b: In the case of unsatisfactory grid voltage, SRF-PLL cannot track the phase angle and frequency of the grid well regardless of whether the frequency is at the rated frequency. The phase tracking error contains obvious 2 nd and 6 th harmonic fluctuation components, and the maximum deviation reaches 0.06 rad. The frequency tracking error is more obvious. Before and after the frequency mutation, the maximum deviation value of the tracking error reaches approximately 7 Hz.  
Through Figure 15c, it can be concluded that the NF-PLL method can better estimate the phase and frequency of the power grid even if the three-phase power supply has unbalance and distortion, and the tracking error of the two is very small. However, when the power grid changes suddenly, the tracking accuracy is reduced; the tracking error of  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline \(V_{1}\) & 311 V & \(V_{5}=0.05V_{1}\) & 15.55 V \\ \(\gamma\) & 0.05 & \(V_{7}=0.02V_{1}\) & 6.22 V \\ \(\mu\) & \(-0.05\) & \(V_{11}=0.008V_{1}\) & 2.49 V \\ THD & 5.86\% & \(V_{13}=0.002V_{1}\) & 0.62 V \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of unbalance and distortion of the grid voltage.  
the frequency reaches \(\pm\)4 Hz; and the tracking error of the phase angle reaches \(\pm\)0.012 rad. Nevertheless, the phase and frequency errors are much smaller than those of SRF-PLL.  
Figure 15d shows that under the condition of an unbalanced and distorted three-phase power supply, the ANF-PLL method can better estimate the phase angle and frequency at the rated frequency. When the frequency changes abruptly, after nearly one fundamental  
Figure 15: Comparative study of three PLL phase frequency tracking. **(a)** Three-phase unbalanced and distorted grid voltage **(b)** wave forms for SRF-PLL, **(c)** wave forms for NF-PLL, **(d)** wave forms for ANF-PLL.  
cycle adjustment, the frequency can be estimated again with higher accuracy. The phase and frequency estimation errors can be maintained below 0.0005 rad and 0.2 Hz. The ANF-PLL method has the highest adaptability among the three phase-locked loops and maintains high phase and frequency tracking performance under typical weak grid conditions. High-precision phase and frequency estimation will be beneficial to support the harmonic current given link and current tracking control link, especially the VPI controller to achieve higher performance.