The literature on the subject of synchrophasor estimation (SE) algorithms has discussed the use of interpolated discrete Fourier transform (IpDFT) as an approach capable to find an optimal tradeoff between SE accuracy, response time, and computational complexity. Within this category of algorithms, this paper proposes three contributions: 1) the formulation of an enhanced-IpDFT (e-IpDFT) algorithm that iteratively compensates the effects of the spectral interference produced by the negative image of the main spectrum tone; 2) the assessment of the influence of the e-IpDFT parameters on the SE accuracy; and 3) the discussion of the deployment of IpDFT- based SE algorithms into field programmable gate arrays, with particular reference to the compensation of the error introduced by the free-running clock of A/D converters with respect to the global positioning system (GPS) time reference. The paper finally presents the experimental validation of the proposed approach where the e-IpDFT performances are compared with those of a classical IpDFT approach and to the accuracy requirements of both P and M-class phasor measurement units defined in the IEEE Std. C37.118-2011. Index Terms— Discrete Fourier transform (DFT), field programmable gate array (FPGA), IEEE Std. C37.118, interpolated discrete Fourier transform (IpDFT), phasor measurement unit (PMU), synchrophasor.

Enhanced Interpolated-DFT for Synchrophasor Estimation in FPGAs: Theory, Implementation, and Validation of a PMU Prototype

Phasor measurement units (PMUs) are rapidly being deployed in electric power networks across the globe. Wide-area measurement system (WAMS), which builds upon PMUs and fast communication links, is consequently emerging as an advanced monitoring and control infrastructure. Rapid adaptation of such devices and technologies has led the researchers to investigate multitude of challenges and pursue opportunities in synchrophasor measurement technology, PMU structural design, PMU placement, miscellaneous applications of PMU from local perspectives, and various WAMS functionalities from the system perspective. Relevant research articles appeared in the IEEE and IET publications from 1983 through 2014 are rigorously surveyed in this paper to represent a panorama of research progress lines. This bibliography will aid academic researchers and practicing engineers in adopting appropriate topics and will stimulate utilities toward development and implementation of software packages.

Synchrophasor Measurement Technology in Power Systems: Panorama and State-of-the-Art

Harmonics estimation in emerging power system: Key issues and challenges

This paper investigates the accuracy of synchrophasor estimators provided by the interpolated discrete Fourier transform (IpDFT) algorithm under both steady-state and dynamic conditions when two- or three-cycle length observation intervals are considered. According to the IEEE Standard C37.118.1-2011 about synchrophasor measurements for power systems, the estimation accuracy is expressed by the total vector error (TVE). The effect on the estimation accuracy of different window functions, observation interval lengths, and processed DFT samples is analyzed through computer simulations. It is shown that most of the performance requirements specified in the Standard can be satisfied with a proper selection of the algorithm characteristics. Also, the performances of the proposed synchrophasor estimators and state-of-the-art estimators recently proposed in the scientific literature are compared and discussed. Some experimental results are presented in order to confirm the performed analysis.

Accuracy Analysis of the Multicycle Synchrophasor Estimator Provided by the Interpolated DFT Algorithm

The IEEE Standard C37.118.1 defines two performance classes, P and M, for phasor measurement units (PMUs), respectively for protection and monitoring oriented applications. The goal of this paper is to define an algorithm that allows the requirements of both classes to be met simultaneously, thus avoiding an a priori selection of either the fast response time of class P or the accuracy of the class M. The designed PMU consists of two digital channels that process in parallel the acquired samples with different algorithms: the first one allows accurate measurements of steady state signals, while the second one is better suited to follow the fast signal changes. Then, a detector identifies the possible presence of dynamic situations and selects the most appropriate output for the actual operating condition. The validation of the solution, performed by means of simulations in all the static and dynamic conditions defined in the standard, confirms that the method is able to comply with all the limits indicated for both classes for synchrophasor and frequency measurement. As for the rate of change of frequency, again the compliance to P-class is fully verified, while for the M-class the only exception is represented by the tests with out-of-band disturbances.

A Fast and Accurate PMU Algorithm for P+M Class Measurement of Synchrophasor and Frequency

Estimates of the dynamic phasor and its derivatives are obtained through the weighted least squares solution of a Taylor approximation using classical windows as weighting factors. This solution leads to differentiators with ideal frequency response around the fundamental frequency and to very low sidelobe level over the stopband, which implies low noise sensitivity. The differentiators are maximally flat in the interval centered at the fundamental frequency and have a linear phase response. Therefore, their estimates are free of amplitude and phase distortion and are obtained at once. No further patch is needed to improve their accuracy. Examples of dynamic phasor estimates are illustrated under transient conditions. Special emphasis is put on frequency measurements.

Dynamic Phasor and Frequency Estimates Through Maximally Flat Differentiators

A new dynamic harmonic estimator is presented as an extension of the fast Fourier transform (FFT), which assumes a fluctuating complex envelope at each harmonic. This estimator is able to estimate harmonics that are time varying inside the observation window. The extension receives the name “Taylor-Fourier transform (TFT)” since it is based on the McLaurin series expansion of each complex envelope. Better estimates of the dynamic harmonics are obtained due to the fact that the Fourier subspace is contained in the subspace generated by the Taylor-Fourier basis. The coefficients of the TFT have a physical meaning: they represent instantaneous samples of the first derivatives of the complex envelope, with all of them calculated at once through a linear transform. The Taylor-Fourier estimator can be seen as a bank of maximally flat finite-impulse-response filters, with the frequency response of ideal differentiators about each harmonic frequency. In addition to cleaner harmonic phasor estimates under dynamic conditions, among the new estimates are the instantaneous frequency and first derivatives of each harmonic. Two examples are presented to evaluate the performance of the proposed estimator.

Dynamic Harmonic Analysis Through Taylor–Fourier Transform

Broken rotor bar (BRB) fault is common in cage rotor induction motors. Motor current signature analysis (MCSA) has been a popular method to detect BRB faults. In the MCSA, the fault signature frequencies for BRB are close to the fundamental frequency. This spectral nearness leads to the requirement of larger observation windows, which inherently increases BRB fault detection time. This paper presents an alternative algorithm to detect BRB faults in induction motors from MCSA using two Taylor–Kalman (TK) filters in cascade with a subsampling scheme. The proposed BRB fault detection approach allows to use the TK filter to estimate lower frequencies with less computational burden in comparison to conventional TK analysis. Experimental analysis shows that nearly accurate estimates and competitive detection time can be achieved by the proposed BRB detection method. The performance of the proposed algorithm has been compared with classical spectral techniques using numerical simulations and records acquired from induction motors under real operating conditions.

A Multiresolution Taylor–Kalman Approach for Broken Rotor Bar Detection in Cage Induction Motors

Recently, the Taylor-Fourier transform (TFT) was proposed to analyze the spectrum of signals with oscillating harmonics. The coefficients of this linear transformation were obtained through the calculation of the pseudoinverse matrix, which provides the classical solution to the normal equations of the least-squares (LS) approximation. This paper presents a filtering design technique that obtains the coefficients of the filters at each harmonic by imposing the maximally flat conditions to the polynomials defining their frequency responses. This condition can be used to solve the LS problem at each particular harmonic frequency, without the need of obtaining the whole set, as in the classical pseudoinverse solution. In addition, the filter passband central frequency can follow the fluctuations of the fundamental frequency. Besides, the method offers a reduction of the computational burden of the pseudoinverse solution. An implementation of the proposed estimator as an adaptive algorithm using its own instantaneous frequency estimate to relocate its bands is shown, and several tests are used to compare its performance with that of the ordinary TFT.

Miguel Angel Platas-Garza

Papers

Dynamic Phasor and Frequency Estimates Through Maximally Flat Differentiators

Dynamic Harmonic Analysis Through Taylor–Fourier Transform

A Multiresolution Taylor–Kalman Approach for Broken Rotor Bar Detection in Cage Induction Motors

Polynomial Implementation of the Taylor–Fourier Transform for Harmonic Analysis

Maximally flat differentiators through WLS Taylor decomposition