A phase-locked loop (PLL) is a nonlinear negative-feedback control system that synchronizes its output in frequency as well as in phase with its input PLLs are now widely used for the synchronization of power-electronics-based converters and also for monitoring and control purposes in different engineering fields In recent years, there have been many attempts to design more advanced PLLs for three-phase applications The aim of this paper is to provide overviews of these attempts, which can be very useful for engineers and academic researchers

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Three-Phase PLLs: A Review of Recent Advances

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

Digital control system analysis and design

Harmonics estimation in emerging power system: Key issues and challenges

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

Prony's method can be used as a dynamic phasor estimator. It can be regarded as the adaptive approximation of its complex exponential signal model to the dynamic phasor of an oscillation over a finite time interval. Equipped with a closed signal model, it is possible to implement it in one cycle. In its first adaptive stage, it estimates the best damping and frequency for its signal model; and, in the second one, the best phasor over the considered time window. This paper compares the performance of Prony's method with that of the very wellknown one-cycle Fourier filter. With a higher flexibility, due to its adaptive nature, Prony estimates improve the Fourier ones under oscillation conditions. The Fourier filter can be considered as a static subclass of the Prony filters. With its static signal model, it is unable to accurately follow oscillations when the frequency fluctuates. Additionally, the Prony filter, together with its phasor estimates, provides instantaneous estimates of damping and frequency, corresponding to the first derivative of amplitude and phase, which are very useful to assess the power system stability. Finally, by being implemented in one-cycle windows, and its good rejection of the dc or exponentially attenuated components, it can also be used in protection applications.

Synchrophasor Estimation Using Prony's Method

Synchrophasor estimation research has recently shifted emphasis from the phasor to the frequency and rate of change of frequency estimation problem. The main concern now is to achieve finer dynamic spectral analysis from the power system signals. This paper proposes the use of the Taylor–Fourier filters to reduce the error of the whole set of estimated parameters. This reduction is attained by exploiting their capability to match the phase pattern of the signal from one estimation to the next. By being endowed with their own phase follower, they are able to point their basis vectors toward the given signal, providing the best possible estimates from the nearest available subspace. The adaptive filters, provided with their own polynomial phase-locked loop, follow the instantaneous frequency of the given signal. Since most of the signals stipulated in the synchrophasor standard are defined by Taylor polynomials, the performance of this family of filters is remarkable, for durations from two cycles. They obtain estimates with zero error in the full set of parameters, when the test signal is in the focused Taylor–Fourier subspace. Very small estimation errors can be obtained for signal to noise ratios greater than 50 dB. Harmonic interference can also be constrained, but with higher computational cost.

Synchrophasor Measurement With Polynomial Phase-Locked-Loop Taylor–Fourier Filters

The digital Taylor-Fourier transform (DTFT) is used to identify low-frequency electromechanical modes in power systems. The identification process is based on the time-frequency analysis of nonlinear signals that arise after a large disturbance. The DTFT creates a signal decomposition, from which mono-component signals are extracted by spectral analysis using a filter bank. This analysis is accomplished through sliding-window data, which is updated each sample, yielding estimates of the reconstructed signal and providing information of its instantaneous damping and frequency. Results demonstrate the applicability of the proposition.

Jose Antonio de la O Serna

Papers

Dynamic Phasor and Frequency Estimates Through Maximally Flat Differentiators

Dynamic Harmonic Analysis Through Taylor–Fourier Transform

Synchrophasor Estimation Using Prony's Method

Synchrophasor Measurement With Polynomial Phase-Locked-Loop Taylor–Fourier Filters

Identification of Electromechanical Modes Based on the Digital Taylor-Fourier Transform