# A Low-Cost Evaluation Tool for Synchronization Methods in Three-Phase Power Systems
## 3 Results
### Experimental Implementation of the Evaluation Tool  
The evaluation tool presented in Section 2.1 (Figure 4) is implemented using the steps of the proposed methodology (Figure 5). Figure 10 shows the connection between the emulator and the digital controller, while Figure 11 shows the experimental setup used. The digital controller is implemented on an Arduino Due board, which is an accessible platform and can be used as a digital control platform for three-phase power converters [32]. In particular, Figure 10 shows the emulated voltages \(v_{sa}(t)\), \(v_{sb}(t)\), and \(v_{sc}(t)\) generated by the emulator, along with the output signals of the synchronization algorithms implemented in the digital controller. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Configuration** & **Signal** & **Description** & **Oscilloscope Channel** & **V/div, Position * \\ \hline always & \(sync(t)\) & Synchronization (trigger) & Digital input & 5, div +3 \\ \hline \multirow{3}{*}{I} & \(v_{sal,ref}(t)\) & \(v_{sal}(t)\) reference, \(out_{0}(t)\) & CH1 & \\  & \(v_{sal,o}(t)\) & \(v_{sa}(t)\) synchronized, \(out_{1}(t)\) & CH2 & 500 m, div \(-2\) \\  & \(v_{sa}(t)\) & Emulated and acquired voltage signal & CH3 & \\ \hline \multirow{3}{*}{II} & \(out_{0}(t)\) & \(v_{sal,ref}(t)\), \(A_{1,o}(t)\), \(\theta_{1,o}(t)\) & CH1 & 500 m, div \(-2\) \\  & \(out_{1}(t)\) & \(v_{sal,o}(t)\), \(f_{1,o}(t)\) & CH2 & 500 m, div \(-4\) \\  & \(out_{A}(t)\) & \(A_{1,ref}(t)\), \(\theta_{1,ref}(t)\) & CH3 & 500 m, div \(-2\) \\  & \(out_{B}(t)\) & \(f_{1,ref}(t)\) & CH4 & 500 m, div \(-4\) \\ \hline \multirow{3}{*}{III} & \(DT(t)\) & Execution time of synchronization technique & CH4 & 1.00, div \(-2\) \\ \cline{2-6}  & & & & \\ \hline \end{tabular}  
* The positions of each channel refer to the central horizontal axis.  
\end{table} 
Table 9: Proposed configurations for oscilloscope channels. Figure 9: Execution time measurement method. In order to illustrate the performance of the proposal, Figures 12 and 13 show the emulated grid signals and the reference signals generated by the emulator for different case studies. In particular, Figure 12a,b shows the emulated grid voltage \(v_{sa}(t)\) and the fundamental reference voltage \(v_{sa1,ref}(t)\) with amplitude 1 p.u. and a frequency of 50 Hz, without harmonic and with the presence of harmonics, respectively. Figure 12c,d shows the amplitude and frequency references for case studies 1 and 2, respectively. In case study 1, the references are programmed to change at \(t_{0}\) in the falling edge of the signal \(sync(t)\) and at \(t_{5}\) in the rising edge. References from case study 2 are synchronized with the falling edge of \(sync(t)\) at change \(t_{0}\). Figure 12e shows the variations in the emulated voltage and reference voltage of case study 1 generated by the emulator. Figure 13 shows the signals \(v_{sa}(t)\), \(v_{sa1,ref}(t)\), and \(\theta_{1,ref}(t)\) generated in the emulator for the change \(t_{5}\) in case study 1 and for the change \(t_{o}\) in case study 2 (Tables 5 and 6). The signals of case study 1 in Figure 13a show the voltage variation from a reference amplitude of 1 p.u. to 0.5 p.u. and a phase jump from \(0^{\circ}\) to \(20^{\circ}\). On the other hand, the voltage signals in case study 2 vary in frequency from 50 Hz to 55 Hz, maintaining their amplitude at 1 p.u. and phase zero (Figure 13b). The phase reference \(\theta_{1,ref}(t)\) for case studies 1 and 2 is shown in Figure 13c,d, respectively. Phase \(\theta_{1,ref}(t)\) varies as a sawtooth signal between \(0^{\circ}\) to \(360^{\circ}\), considering frequency changes and not phase jump. The period of the signal \(\theta_{1,ref}(t)\) varies with the change in the reference frequency from 50 Hz to 55 Hz at a time \(t_{0}\) in case study 2. Figure 11: Implementation of the proposed evaluation tool. Figure 10: Connection between LAUNCHXL-F28379D and Arduino Due digital platform.