# A Low-Cost Evaluation Tool for Synchronization Methods in Three-Phase Power Systems
## 2 Evaluation Tool and Methodology of Use
### The Methodology of Use
#### 2.2.5 Methods and Evaluation of Synchronization Algorithms  
The evaluation tool considers the evaluation of the synchronization algorithms using indicators such as the (i) mean error (ME) and (ii) root-mean-square error (RMSE) between the reference and estimated steady-state (SS) signals, as well as the (iii) settling time (\(t_{s}\)), (iv) overshoot (OS) at step change, and (v) execution time (\(t_{ex}\)).  
The evaluation process considers the following steps after connecting the digital controller to the emulator, selecting the algorithm and the case study to be implemented:  
1. To evaluate the emulated and estimated signals from the three-phase grid: * Display the next signals in the oscilloscope: \(v_{sal,ref}(t)\), \(v_{sal,o}(t)\), and \(v_{sa,in}(t)\); * Obtain the instantaneous error \(\Delta v_{sal}(t)\) between \(v_{sal,o}(t)\) and \(v_{sal,ref}(t)\), and compute the steady-state ME and RMSE; \(\Delta v_{sal}(t)\) can be computed using the mathematical function of the scope (\(\Delta v_{sal}(t)=v_{sal,o}(t)-v_{sal,ref}(t)\)), while the ME and RMSE can be computed using the average value and the rms value of the channel of the mathematical function.
2. To evaluate the reference and estimated amplitude and frequency: * Display the next signals in the oscilloscope: \(A_{1,ref}(t)\), \(A_{1,o}(t)\), \(f_{1,ref}(t)\), and \(f_{1,o}(t)\); * Compute \(t_{s}\) and OS in a transient state (TS); it is possible to obtain the instantaneous error of the frequency \(\Delta f_{1}(t)\) and/or amplitude \(\Delta A_{1}(t)\), and to calculate the steady-state EM; \(\Delta f_{1}(t)\) and \(\Delta A_{1}(t)\) can be computed using the mathematical function of the scope (\(\Delta f_{1}(t)=f_{1,o}(t)-f_{1,ref}(t)\), \(\Delta A_{1}(t)=A_{1,o}(t)-A_{1,ref}(t)\)), while the ME can be computed using the average value of the channel of the mathematical function.
3. To evaluate the reference and the estimated phase: * Display the next signals in the oscilloscope: \(\theta_{1,ref}(t)\), \(\theta_{1,o}(t)\); * Calculate the phase angle between signals; the signals \(\theta_{1,ref}(t)\) and \(\theta_{1,o}(t)\) vary as a sawtooth signal within the range \([0,360]\)\({}^{\circ}\); the phase angle can be computed using the phase measurement of the oscilloscope.
4. Evaluate the \(t_{ex}\) of the synchronization algorithms: * Display the signal in the oscilloscope: \(DT(t)\); * Use the calculation method proposed in [33], which uses a digital output to determine \(t_{ex}\), keeping the output in a high state during the algorithm execution; measures the time of the high state (\(t_{high}\)); and subtracts the execution time from the previously determined high-low state change (\(t_{down}\)) (Equation (2) and Figure 9); \(t_{high}\) can be computed using the positive pulse-width measurement of the oscilloscope.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Value** & **Description** \\ \hline \hline \multirow{3}{*}{\(sw_{lec,a}(t)\)\(sw_{lec,b}(t)\)} & 0 0 & SRF-PLL \\  & 0 1 & MAF-PLL * \\ \cline{1-1}  & 1 0 & CDSC-PLL * \\ \cline{1-1}  & 1 1 & DSOGI-PLL with LPF \\ \hline \hline \end{tabular}  
* Not tested in Section 3.2.  
\end{table}
Table 8: Synchronization technique selection.  
The oscilloscope must be configured considering the voltage range of the output signals, the methods of analysis selected, and the position of the emulated, reference, and estimated signals to be displayed. Table 9 proposes three configurations for a four-channel oscilloscope with digital inputs:  
* Configuration I: Evaluation of the emulated and estimated signals of the three-phase grid, \(v_{sal,ref}(t)\), \(v_{sal,o}(t)\), and \(v_{sa}(t)\);
* Configuration II: Evaluation of the reference and estimated amplitude, phase, and frequency;
* Configuration III: Evaluation of the execution time of the synchronization algorithms.