# IpDFT-Tuned Estimation Algorithms for PMUs: Overview and Performance Comparison
###### Abstract  
The Interpolated Discrete Fourier Transform (IpDFT) is one of the most popular algorithms for Phasor Measurement Units (PMUs), due to its quite low computational complexity and its good accuracy in various operating conditions. However, the basic IpDFT algorithm can be used also as a preliminary estimator of the amplitude, phase, frequency and rate of change of frequency of voltage or current AC waveforms at times synchronized to the Universal Coordinated Time (UTC). Indeed, another cascaded algorithm can be used to refine the waveform parameters estimation. In this context, the main novelty of this work is a fair and extensive performance comparison of three different state-of-the-art IpDFT-tuned estimation algorithms for PMUs. The three algorithms are: (i) the so-called corrected IpDFT (IpDFTc), which is conceived to compensate for the effect of both the image of the fundamental tone and second-order harmonic; (ii) a frequency-tuned version of the Taylor Weighted Least-Squares (TWLS) algorithm, and (iii) the frequency Down-Conversion and low-pass Filtering (DCF) technique described also in the IEEE/IEC Standard 60255-118-1:2018. The simulation results obtained in the _P Class_ and _M Class_ testing conditions specified in the same Standard show that the IpDFTc algorithm is generally preferable under the effect of steady-state disturbances. On the contrary, the tuned TWLS estimator is usually the best solution when dynamic changes of amplitude, phase or frequency occur. In transient conditions (i.e., under the effect of amplitude or phase steps), the IpDFTc and the tuned TWLS algorithms do not clearly outperform one another. The DCF approach generally returns the worst results. However, its actual performances heavily depend on the adopted low-pass filter. P 2021  
the capability to measure all quantities at times synchronized with the Universal Coordinated Time (UTC);
* the capability to stream real-time data to the so-called Phasor Data Concentrators (PDCs) with reporting rates ranging between about 10 frame/s and 100 frame/s;
* high measurement accuracy, as specified in the IEEE/IEC Standard 6025-118-1:2018, in the following simply referred to as the \"Standard\" for the sake of brevity [10];
* fast responsiveness (in the order of a few power line cycles) in order to trigger adequate protection schemes when severe phasor magnitude or phase changes occur due to faults or grid topology changes [11]. In this respect, the IEEE/IEC Standard classifies PMUs as protection-oriented (_P Class_) or measurement-oriented (_M Class_) devices. The former ones can indeed be less accurate than the latter, but of course they must be considerably faster. Quite importantly, in the case of active distribution systems, the maximum Total Vector Error (TVE) of PMU measurements has to be even smaller than the Standard limits, i.e., in the order of 0.1% [12], and with phase uncertainty contributions not greater than a few mrad [13]. The need to meet the specifications shortly summarized above required remarkable research efforts in the area of signal processing and metrology. In particular, both flexible testbeds for PMU algorithm characterization [14], and new PMU calibrators were developed [15; 16]. Among the many estimation algorithms for PMUs proposed over the last few years, the Interpolated Discrete Fourier Transform (IpDFT) is definitely one of the most popular, due to its low computational complexity and its good capability to compensate for the effect of off-nominal frequency deviations [17]. Such deviations might otherwise heavily affect the waveform parameter estimation based on the classic Discrete Fourier Transform (DFT) [18]. Even if the use of the IpDFT in signal processing is well established (e.g., for multi-tone parameter estimation [19]), its use in power systems monitoring applications was proposed only a few years ago. Since then, a number of IpDFT variants and multi-step algorithms based on the IpDFT stage have been developed to overcome the inherent limitation of the basic algorithm.