# Low-Latency, Three-Phase PMU Algorithms: Review and Performance Comparison
## 3 Simulation Results
### Tests under Steady-State Conditions
#### 3.2.2 Harmonic Disturbances
Under the same conditions, the SV-F method provides very good synchrophasor and frequency estimates, with maximum TVE and \(\mid\)FE\(\mid\) below \(2\cdot 10^{-3}\%\) and \(0.2\,\)mHz; \(\mid\)RFE\(\mid\) is significant, reaching a maximum value of \(0.39\,\)Hz/s, which is still compliant with the P-class limit of the IEC/IEEE standard. The SV-TF method results in the highest errors, with maximum TVE of \(3.6\cdot 10^{-2}\%\) (thus well below the 1% limit prescribed by the IEC/IEEE standard) in the presence of the 2 nd order harmonic, and then decaying for the higher-order components thanks to the response of the TF filter. Conversely, \(\mid\)FE\(\mid\), exceeds \(13\,\)mHz at the 4 th order harmonic, namely significantly higher with respect to the \(5\,\)mHz limit; \(\mid\)RFE\(\mid\) almost reaches \(0.6\,\)Hz/s, also in this case higher than the corresponding limit. However, harmonic rejection capability of the SV-TF approach can be dramatically improved by applying weighting coefficients to the samples, such as those of a Hann window. Harmonic rejection capability has been tested also under off-nominal frequency (not requested by the IEC/IEEE standard), namely considering \(f=49\,\)Hz; results are reported in the following Figures 6-8. Figure 6: Maximum TVE in the presence of 1% harmonic disturbances, \(f=49\,\)Hz. Figure 7: Maximum \(|\)FE\(|\) in the presence of 1% harmonic disturbances, \(f=49\,\)Hz. The first consideration is that from the previous graphs the envelope of the errors reflects the response of the filters employed by the different algorithms. The somewhat jagged trend occurs since, according to their harmonic order, superimposed disturbances in the SV signal have alternatively positive angular speed, negative angular speed, or zero magnitude. Under these conditions, it is clear that IEC-P and SV-IpDFT are no longer able to fully reject harmonic disturbance. When looking at the TVE values (Figure 6), the SV-IpDFT algorithm still results in excellent accuracy: maximum is about \(3\cdot 10^{-4}\)% at the 4 th order harmonic; the IEC-P method reaches a larger maximum TVE slightly above \(2\cdot 10^{-3}\)%, which is still pretty low. As for the SV-F algorithm, performance is very close to that achieved at nominal frequency. The same applies to the SV-TF algorithm, with the highest error now occurring at the 4 th order harmonic. From Figure 7, maximum frequency errors for SV-F and SV-TF algorithms are similar to those with \(f=f_{0}\), while the SV-IpDFT approach guarantees the best results; this means that the adopted Hann window is very effective in preventing spectral interference. Frequency estimates provided by the IEC-P method are affected by significant errors, but they remain below 2.5 mHz. Finally, when analyzing the results in terms of RFE, values obtained with the SV-F algorithm are also in this case very similar to those measured with nominal frequency; maximum | RFE| of the SV-TF technique slightly increases to almost 0.8 Hz/s at the 4 th order harmonic. SV-IpDFT ensures the best performance also in terms of ROCOF estimate, while the | RFE| values corresponding to the IEC-P algorithm are extremely large. The impact of harmonic disturbances affecting the positive sequence synchrophasor estimates, which are no more suppressed by the triangular window, is highly magnified by the second order differentiator that allows computing the ROCOF.