# Dynamic Impedance Estimation: Challenges and Considerations
## 3 Harmonic Synchrophasor Estimation  
### Review Harmonic Synchrophasor Estimation  
Estimating the harmonic phasor synchronized by satellite started in the 1990s, with a CHART (continuous harmonic analysis in real-time) [24]. However, it was only after the consolidation of the fundamental phasor estimation techniques, with the phasor measurement unit (PMU), that research for estimating the synchronized harmonic phasors had a new impulse. The harmonic synchrophasor estimation (HSpE) involves techniques and algorithms to simultaneously estimate and synchronize the harmonics' magnitude and phase. The works [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35] show some of the most recent research on this topic. Signal processing techniques can use variations of the Fourier transform [25], as well as more advanced techniques, such as Kalman filter (KF) [26], Taylor transform (TT) [27; 28; 29], wavelet transform (WT) [30], and the interpolated DFT [31; 32; 33; 34]. In the method described in [28], the authors propose using FFT with the Hanning window to estimate the harmonic phasors. In the frequency domain, a correction is applied based on the system's instantaneous frequency to improve the estimated phasors' accuracy. Performance is tested up to the 9 th order harmonic component only, in a limited test scenario without quantifying frequency deviations and without the presence of noise. In [26], a contribution is presented, using KF for the individual estimation of each frequency component. The use of the TT has also been proposed for the task of estimating harmonic phasors [27; 28; 29], named Taylor weighted least squares (TWLS). Signal contamination by noise in these studies is considered, with cases with a SNR of 60 dB. However, the algorithms have a high computational cost, making their application in low-cost devices difficult. In [30], the WT is used as an alternative to HSpE for the power system at the distribution level. The method first proposes applying an algorithm known as sample value adjustment (SVA) [31]. After this step, the FFT of the signal is applied, thus identifying the main frequency components. Next, wavelet filters are designed centered on the frequencies with significant energy. The SVA algorithm has the function of adjusting the signal samples, providing synchronous sampling in the FFT window to reduce spectral leakage. Considering a phasor estimation in scenarios with significant noise contamination, more robust techniques such as ESPRIT [32] and TWLS present better results. However, they are parametric techniques and present high computational cost, being useful onlyfor offline analysis. Besides, choosing the model order is always a challenge for parametric techniques. In [33; 34], it is proposed the use of interpolated DFT in the frequency domain (ipDFT). However, its performance lacks when it is desired to estimate low amplitude components in noise (individual harmonic content lower than 5%). In [35], ipDFT is compared with the improved SVA (MSVA). The phasor estimation results for both methods show that the interpolation in the frequency domain presents worse results concerning the time domain's interpolation strategy. Time domain's interpolation strategy, also named resampling algorithm, seems to be one of the best candidates for HspE because of the balance between the estimation performance and the computational effort. Figure 5 illustrates the basic idea behind this approach. Note that the algorithm is based on DFT and, consequently, suffers the spectrum leakage problem that can be reduced by the resampling algorithm. That is the key point for a successful harmonic phasor estimation: to choose a good resampling algorithm. Different algorithms have been reported in the literature for this purpose, among then the SVA and their variations [31; 35], Lagrange, and B-Spline algorithms [4].