# IpDFT-Tuned Estimation Algorithms for PMUs: Overview and Performance Comparison
## 3 Estimation Results and Performance Analysis
### \(P\)_Class_ and \(M\)_Class_ Steady-State and Dynamic Testing Conditions
The tuned TWLS approach over 2-cycle intervals returns accurate results in most cases, but it is strongly affected by the presence of harmonics. On the other hand, if 4-cycle observation intervals are used, the IpDFTc, the tuned TWLS, and the DCF approach with the LSF filter exhibit comparable performances. Table 5a,b shows the maximum values of TVE, \(|\)FE\(|\) and \(|\)RFE\(|\) (computed over 1000 records) obtained over 6-cycle (a) or 8-cycle (b) observation intervals in the _M Class_ testing conditions listed at the beginning of this Section. In this case, longer observation intervals are considered as they are needed to ensure a higher measurement accuracy. The _M Class_ limits mentioned in the Standard (when defined) are also shown. The values exceeding such limits are highlighted in bold, whereas the cells containing the best results obtained in each test are shaded. Again, both the IpDFTc and the tuned TWLS algorithm rely on a Hann window. The LSF FIR filters used with the DCF approach is again based on least-squares frequency response error minimization assuming 6-cycle-long and 8-cycle-long impulse responses, respectively. On the contrary, the _M Class_ STD filter suggested in Annex D of the Standard does no longer exhibit a triangular impulse response. In fact, it results from the classic window design method: the non-causal sinc-shaped impulse response of the ideal low-pass filter is indeed modulated by a Hamming window. The results in Table 5a,b can be summarized as follows. * As far as synchrophasor estimation is concerned, the maximum TVE values basically confirm the conclusions drawn in the _P Class_ case. The IpDFTc algorithm is generally preferable in steady-state testing conditions and in the presence of wideband noise, whereas the tuned TWLS estimator is superior when dynamic disturbances (i.e., modulations and frequency ramps) are considered. However, in the _M Class_ case, such differences are exacerbated. The tuned TWLS approach is not able to meet the Standard limits in the presence of out-of-band inter-harmonics over 6-cycle intervals, but it meets the Standard requirements over 8-cycle intervals. Quite interestingly, the accuracy of the tuned TWLS algorithm over longer intervals under dynamic conditions slightly degrades due to the larger Taylor's series approximation errors of the phasor model at the edges of the observation intervals [29]. The IpDFTc estimator is not able to meet the Standard limits over 8-cycle intervals when amplitude or phase oscillations perturb the fundamental component. Only the DCF approach is able to meet the Standard limits with both interval lengths, although in some testing conditions it exhibits a slightly worse accuracy than the other algorithms. * The \(|\)FE\(|\) values exhibit a trend similar to the TVE ones. The main difference is in the case of the DCF approach whose behavior is more heterogeneous. In this case, ensuring compliance with the Standard requirements is much more challenging. Indeed, no estimator is able to meet the Standard limits in the case of inter-harmonic interference over 6-cycle intervals. Over 8-cycle intervals instead, the IpDFTc estimator returns generally the best results except in the case of amplitude and phase modulations, which are more effectively mitigated by the DCF approach with the LSF filter. * Finally, in the case of ROCOF estimation, almost all algorithms except the DCF approach with the STD filter exhibit good results. They are indeed compliant with the limits reported in the Standard (when defined). Globally, the IpDFTc estimator is preferable over 6-cycle intervals, whereas the tuned TWLS algorithm is better over 8-cycle intervals in accordance with the TVE trend.