# A Low-Cost Evaluation Tool for Synchronization Methods in Three-Phase Power Systems
## 3 Results
### Evaluation of Synchronization Algorithms
#### 3.2.1 Case Study 1: Amplitude Changes  
Figures 15 and 16 show the results of implementing the SRF-PLL and DSOGI-PLL with LPF synchronization algorithms under a power grid with amplitude changes (Table 5). Figure 15 shows the performance of the algorithms in a grid without harmonic content, allowing us (i) to evaluate the dynamic response of the estimated amplitude \(A_{1,\sigma}(t)\) and estimated frequency \(f_{1,\sigma}(t)\) when the amplitude reference \(A_{1,ref}(t)\) changes in step forms (Figure 15a), (ii) to observe the instantaneous error of the estimated voltage \(\Delta v_{val}(t)\) when the reference amplitude \(v_{val,ref}(t)\) decreases from 1.0 p.u. to 0.5 p.u. with a phase jump of \(20^{\circ}\) a \(t_{5}\) (Figure 15b), (iii) to compute the ME and RMSE between the reference voltage \(v_{val,ref}(t)\) and estimated voltage \(v_{val,\sigma}(t)\) at SS (Figure 15c), and (iv) to determine the OS and \(t_{s}\) from the dynamic response of the amplitude \(A_{1,\sigma}(t)\) to a step change (Figure 15d). Figure 14: Diagrams of the synchronization algorithms: (a) synchronous reference frame PLL (SRF-PLL); (b) dual second-order generalized integrator PLL (DSOGI-PLL) with a low-pass filter (LPF). Figure 13: Emulated and signals generated by the Emulator with reference changes: (a) \(v_{sa}(t)\) and \(v_{val,ref}(t)\) for change \(t_{5}\) in case study 1; (b) \(v_{sa}(t)\) and \(v_{val,ref}(t)\) for change \(t_{o}\) in case study 2; (c) \(\theta_{1,ref}(t)\) for change \(t_{S}\) in case study 1; (d) \(\theta_{1,ref}(t)\) for change \(t_{o}\) in case study 2. Figure 15: The performance of the SRF-PLL (left column) and DSOGI-PLL with LPF (right column) algorithms with the proposed evaluation tool. Case study 1, amplitude change without harmonic content: (**a**) references and estimated signals in digital controller outputs; (**b**) reference, estimation, and error of voltage in change \(t_{5}\); (**c**) reference, estimation, and error of voltage in a steady state of \(t_{5}\), measuring ME and RMSE of \(\Delta\sigma_{\text{ssl}}(t)\); (**d**) amplitude signals in the transient state for change \(t_{5}\), measuring \(t_{s}\) and OS in \(A_{1,o}(t)\). Figure 16 shows the performance of the algorithms in a grid with harmonic content, allowing us (i) to observe the dynamics of the amplitude and frequency (Figure 16a). In particular, for the frequency variation at \(t_{5}(t)\), Figure 16b shows the transient response  
Figure 16: The performance of the SRF-PLL (left column) and DSOGI-PLL with LPF (right column) algorithms with the proposed evaluation tool. Case study 1, amplitude change with harmonic content: (**a**) references and estimated signals in digital controller outputs; (**b**) reference, estimation, and error of voltage in change \(t_{5}\), measuring \(t_{s}\) and OS in \(A_{1\rho}(t)\); (**c**) Phase signals in a steady state of \(t_{5}\), measuring phase angle; (**d**) \(DT(t)\) signal in a steady state after variation in \(t_{5}\) for the calculation of the execution time. of the frequency where the OS and \(t_{s}\) are obtained, (ii) the estimated phase \(\theta_{1,o}(t)\), and fundamental reference \(\theta_{1,ref}(t)\) (Figure 16c), and (iii) the signal \(DT(t)\) for calculating the execution time \(t_{ex}\) of the algorithms implemented in the digital controller. The execution time considers the time \(t_{down}\) equal to 2.1 \(\upmu\)s [34]. The implementation of the evaluation methods shown in Figures 15 and 16 and Table 10 allows us (i) to verify the operation of the synchronization algorithms implemented in the digital controller and (ii) to know the response of the algorithms to variations in amplitude and harmonic content of 5 th, 7 th and 11 th order.