# IpDFT-Tuned Estimation Algorithms for PMUs: Overview and Performance Comparison
###### Abstract
In particular, the classic IpDFT algorithm can be used to obtain a preliminary estimate of some quantities of interest (most notably the fundamental frequency of the analyzed signal) prior to applying a further algorithm to return more accurate estimates of synchrophasor amplitude, phase, frequency, and ROCOF. For instance, in [20], a three-point IpDFT algorithm is proposed to compensate for the infiltration of the spectral image of the fundamental component on the estimated parameters. However, this algorithm returns only a frequency estimate. This is indeed the most common case [21; 22; 23], although a dynamic ROCOF estimator based on IpDFT and Kalman filtering has been recently presented in [24]. The same idea also underlies the so-called enhanced IpDFT [25], which mitigates the detrimental effect of the image component on the estimated synchrophasor parameters by applying the IpDFT iteratively. In [26] this approach is further extended to compensate for the effect of harmonics and inter-harmonic components. The so-called corrected IpDFT (IpDFTc) consists of a two-step IpDFT designed to remove the spectral leakage due to both the image of the fundamental tone and the second-order harmonic [27]. In fact, these steady-state components are often the most critical ones for synchrophasor estimation, especially over short observation intervals. Quite importantly, the IpDFTc algorithm is not iterative. Therefore, it requires a lower computational burden than the estimator proposed in [26]. In [28] and [29] the fundamental frequency estimated through a classic IpDFT is used to tune the matrix coefficients of real-valued weighted least-squares estimators obtained from the [PERSON]'s series expansion of the dynamic synchrophasor model. In the original version of such estimators, the matrix coefficients are computed at the nominal frequency. As a consequence, the estimates are significantly affected by off-nominal frequency deviations. The IpDFT-based frequency tuning instead significantly improves the estimation accuracy of both the so-called Taylor-Fourier filter (which does not include the harmonics in the signal model) [30], and the Taylor-Fourier Transform (that instead includes a number of harmonics in the signal model) [31]. The preliminary fundamental frequency estimation based on the IpDFT can be also used to perform a better direct down-conversion of the voltage or current waveforms, before extracting synchrophasor amplitude and phase through low-pass filtering [32]. To the best of the Authors' knowledge, the three IpDFT-tuned algorithms described above are among those that exhibit excellent performance in terms of both accuracy and computational complexity. Unfortunately, the results reported in the scientific literature do not allow a fair and easy comparison of their actual performances because different observation interval lengths or testing conditions are considered. Thus, this paper aims at presenting a thorough performance comparison of the IpDFTc estimator [27], the tuned Taylor Weighted Least Squares (TWLS) algorithm [28], and a tuned implementation of the frequency down-conversion and low-pass filtering (DCF) technique [32]. The rest of the paper is structured as follows. In Section 2, the theoretical background of the algorithms considered is briefly presented. In Section 3, the simulation results achieved in the steady-state, dynamic and transient testing conditions described in the IEEE/IEC Standard 60255-118-1:2018 are shown and commented on. Section 4 presents some final comments on the considered IpDFT-tuned algorithm compliance, advantages and disadvantages. Section 5 presents some further experimental results in borderline operating conditions compliant with the Standard EN 50160:2010 [33]. Finally, Section 6 concludes the paper.