Phasor Estimation Algorithm Research Articles

A Phasor Estimation Algorithm Based on Iterative Filtering to Remove the Decaying Direct Current Component

A Phasor Estimation Algorithm Based on Iterative Filtering to Remove the Decaying Direct Current Component

Fast Dynamic Phasor Estimation Algorithm Considering DC Offset for PMU Applications

Because of the volatility and intermittence of the renewable energy units in the novel power system, the electrical variables usually exhibit dynamic characteristics. Under fault conditions, the electrical variables usually contain a decaying DC (DDC) component. Currently, when considering the DDC component and the dynamic characteristics of electrical variables, it is difficult to obtain highly precise estimation results in most references. In this paper, a fast dynamic phasor estimation algorithm considering the DC offset is proposed to obviate errors caused by dynamic characteristics and the DDC component. The algorithm consists of two parts. The first part establishes the mathematical model of DDC using exponential functions and obtains the exact DDC component by iteration. The second part establishes the compressive sensing Taylor Fourier Multi-Frequency (CSTFM) model of the dynamic phasor. The improved sparsity adaptive matching pursuit (ISAMP) algorithm is used to quickly and accurately estimate the dynamic phasor, frequency and rate of change of frequency (ROCOF). Simulation and field data test results show that the proposed algorithm can accurately estimate the fault current phasor, frequency, and ROCOF compared with existing phasor estimation algorithms.

A Survey on the Application of Phasor Measurement Units to the Protection of Transmission and Smart Distribution Systems

Renewable energy resources have increasingly been integrated into electric power grids. Moreover, new challenges constantly arise, showing the need for modernization in monitoring, control, and protection. Transmission and distribution systems have explored the use of phasor measurement units (PMUs) in an attempt to meet these requirements. The decreasing cost of hardware components of PMUs, similar to what occurred with digital relays, is an important factor in terms of their worldwide use in different applications. Low-cost variations of PMUs focused on distribution systems, such as micro- and D-PMUs, are growing in number. Thus, this survey article presents significant and recent research conducted in the field of power systems using PMUs. Firstly, it briefly describes the characteristics of PMUs concerning hardware and phasor estimation algorithms. Afterward, recent studies related to transmission and distribution system protection based on PMUs are presented, such as fault detection and location, stability, and wide-area protection. Finally, the article also provided important guidelines, which certainly can be useful for future research in the years to come.

Implementation of Phasor Measurement Unit Based on Phase-Locked Loop Techniques: A Comprehensive Review

The dynamic monitoring, control, and protection of modern power systems in real time require time-stamped electrical measurements to accurately estimate the bus voltage phasors using the state estimation function under normal and abnormal conditions. These measurements can be acquired by time-synchronized devices, known as phasor measurement units (PMUs). PMUs can measure bus voltage and branch current phasors of a three-phase network, as well as the frequency and the rate of change of frequency (ROCOF), with high speed, accuracy and time stamping provided by global positioning system (GPS) at the coordinated universal time (UTC). Various phasor estimation algorithms have been proposed in the literature, while most of them are concentrated in the discrete Fourier transform (DFT) algorithm, where an integer number of samples multiple of the nominal frequency is required for the computations. In cases where the frequency of the power grid deviates from its nominal value, the raw application of the DFT approach can lead to large errors during phasor estimation. Another approach of the phasor estimation is based on the phase-locked loop (PLL) techniques, widely used in grid tie inverters. PLL techniques can track dynamically (continuous time) the estimated frequency to the time-variant frequency of the power grid. A brief introduction to the basic concepts of the synchrophasor definition is provided, while the main DFT methods for synchrophasor estimation according to recent literature are mentioned. PLL-based PMU techniques are reviewed for both steady-state and dynamic conditions according to IEEE standards. In conclusion, the performance of PLL-based PMU algorithms presented in this literature review is discussed.

A Modified DFT-Based Phasor Estimation Algorithm Using an FIR Notch Filter

Accurate and fast extraction of the fundamental parameters of fault signals is a critical issue in the overall performance of protective relays. The decaying DC terms (DDTs) in the fault current challenge the discrete Fourier transform (DFT), the reference algorithm for phasor estimation. To meet this challenge, a new modification for half and full-cycle DFT algorithms is proposed in this paper. In the first step, a finite impulse response (FIR) notch filter designed for fundamental frequency is applied to the output of the DFT algorithm. After that, the outcome of the FIR notch filter and its complex conjugate make it possible to extract error terms. Finally, the estimated phasors are emptied from DDTs error. The ability of the proposed method for estimating phasor and tolerating disturbances was assessed using practical simulated signals. The results perform that the proposed method is much more robust, accurate, and faster than previous methods and enhances the efficiency of the DFT algorithm faced by multiple DDTs.

Review of Discrete Fourier Transform During Dynamic Phasor Estimation and the Design of Synchrophasor Units

In a large and complex interconnected power system, the measurement of synchronized bus voltage and line current plays a vital role in the monitoring and precise control of various sophisticated electrical equipment for secure and reliable operation. Phasor measurement units (PMUs) are incorporated into a wide area of the power system to extract the different signals of synchronized phasors. In this paper, the capacity of the PMU phasor estimation algorithm is explored based on discrete Fourier transform (DFT) under different sampling frequency rates during various dynamic scenarios in accordance with the IEEE C37.118.1a-2014 standard. Furthermore, the performance of the DFT algorithm varies according to the phase angle and dynamic parameters such as frequency, frequency ramp rates, modulation frequency, harmonic levels, step change, decaying dc, and noise levels. The simulation results reveal that accuracy of the phasor estimation algorithm based on DFT can be achieved at high sampling frequency rates. Furthermore, the results of DFT-based phasor estimation are compared with Shank’s estimation method (SEM) and the least-squares estimation method (LEM). The presented method is best suited to PMU algorithms development based on DFT for better visualization of the smart electric grid.

Design and Implementation of Low-Cost PMU for Off-Nominal Frequency and DDC in Compliance with IEEE C37.118 Standard

The transition of the conventional power grid into the smart grid requires continuous monitoring of integrated grids speared over wide-area through Phasor Measurement Units (PMU). These PMUs additionally perform protection and state estimation functions in the smart grid. This paper discusses implementation of a new phasor estimation method to eliminate the effects of Decaying DC (DDC) component and off-nominal frequencies during the extraction of the phasors from a relaying signal. The practical implementation of the proposed method in a low-cost microcontroller (ESP32-WROOM-32 development board) in compliance with the requirements of IEEE C37.118.1a-2011 standard is also demonstrated. The analysis of various existing algorithms estimating the phasors is carried out. The microcontroller is programmed with the best among the analysed algorithm and its feasibility to function as a proper Phasor Measurement Unit is tested. The newly designed PMU is rigorously tested with different estimation methods compliant with IEEE C37.118a-2011 standard. The comparison of the proposed method with different phasor estimation algorithms is also discussed.

Comparative Study of Phasor and Frequency Estimation Algorithms for Distribution Networks

Abstract: Next-generation phasor measurement units (PMUs) are critical for proper distribution network monitoring in future smart grids. In the highly dynamic environments of future distribution systems, more advanced algorithms for detecting amplitude, phase, and frequency changes in power waveforms will be required. In this context, the goal of this study is to discuss the advantages and disadvantages of commonly used PMU algorithms. Many commonly used approaches for power system phasors and frequency estimation algorithms for distribution networks are reviewed and evaluated in this work from the perspective of phasor and frequency identification. According to various performance criteria, e-IpDFT (Enhanced Interpolated Discrete Fourier Transform) and DDPE (Dictionary-based Dynamic Phasor Estimator) provided the best performance among the algorithms. This study provides some insights into the shortcomings of current phasor estimation algorithms and will be useful in the development of future estimation techniques.

Two modified DFT‐based algorithms for fundamental phasor estimation

The discrete Fourier transform (DFT) is a powerful phasor estimation algorithm conventionally used in digital relaying applications. The DFT-based phasor estimation is usually accompanied by oscillatory error due to the presence of the decaying DC (DDC) components in fault current signals. Accordingly, two modified DFT-based phasor estimation algorithms are proposed in this paper. The proposed algorithms accurately estimate the exact fundamental phasor by extracting the DDC components using successive outputs of the conventional DFT algorithm. The performance of the proposed algorithms is validated by the mathematically generated and PSCAD-simulated signals and is compared with previous algorithms. The results demonstrate that the proposed algorithms in this paper are more robust than other ones. Moreover, they are applicable in the DFT algorithm with different data windows.

Impact of DFT-Based phasor estimation errors due to commutation failures of LCC-HVDC links on the protection of AC lines in the near vicinity

Commutation failure (CF) is an inherent issue for Line-Commutated Converter (LCC) HVDC technology. Whenever it happens, voltage and current waveforms throughout the AC system in the near vicinity of LCC-HVDC links become quite distorted. In this paper, it is assessed the impact of such kind of distortion on transient response of phasor estimation algorithms and, in turn, on the performance of AC transmission lines protection. Different discrete Fourier transform (DFT) based algorithms are implemented, and distance, differential and directional protection functions are evaluated. The obtained results reveal that phasor estimation errors arise whenever CFs take place, which may lead protection functions to misoperate, such that false trip command may be issued for external faults.

A Phasor Estimation Algorithm Robust to Decaying DC Component

Phasor measurement is widely used in fault detection and localization of power systems. To improve the phasor measurement accuracy when the fault signal contains the decaying dc component (DDC), this article proposes a half-cycle DFT (HCDFT)-based phasor estimation algorithm. The error caused by DDC is estimated and removed from the phasor estimate by combining multiple HCDFT results that are computed using both the conventional basis vector and its corresponding complex conjugate. Both the numerical tests and the IEEE 39-bus system simulation tests are implemented to evaluate the performance of the proposed algorithm in comparison with four related phasor estimation algorithms. Test results show that the proposed algorithm can achieve accurate phasor estimation in the presence of DDC of a wide range of time constants under the interference of harmonics and noise. Moreover, the proposed algorithm is computationally efficient and its performance is independent of sampling rate. These merits make the proposed algorithm suitable to be applied in measurement and protection devices in real power systems.

A New Method for Analysis and Estimation of Microgrid Signals Under Fault Conditions

Accurate phasor estimation under various faulty conditions is one of the most critical issues in the monitoring, protecting, and controlling of a microgrid (MG). This paper presents a new phasor estimation algorithm (PEA) under fault conditions for MG applications. The main features of this method are to accurately phasor estimation of the signal combination of a decaying dc offset, a decaying fundamental frequency component, and harmonics. In this strategy, a Taylor series is replaced by the exponential functions of the fundament frequency and decaying dc offset component. Then, the time constants and the magnitudes of decaying components are estimated by the least square method. The proposed method is explained theoretically, and its performance is demonstrated by simulating various numerical signals in MATLAB and measured signals during fault conditions. The simulation results indicate that the proposed method estimates the dynamic phasor during fault conditions, accurately. Furthermore, a comprehensive comparison with the conventional methods is carried out to show the effectiveness of the proposed algorithm.

A Fast and Adaptive Dynamic Phasor Estimation Algorithm Implemented on Field Programmable Gate Array (FPGA)

A fast and precise dynamic phasor estimation algorithm using an adaptive improved second order Levenberg–Marquadt algorithm under stressed and off-nominal frequency circumstances is proposed in this paper. The proposed algorithm ventures a faster quasi-second-order method and in addition, the learning rate is also made adaptive to speed up the convergence. Moreover, the projected estimator essentially filters harmonics, estimates transients in a signal during faults and effectually performs in complex modulated setting which is found commonly in a power system with distributed energy resources. Outcomes reveal that the estimation errors and the convergence time of the proposed approach is way below the minimum requirement of the IEEE C37.118.1 standard. Besides, due to its reduced complexity, the estimator has been successfully implemented on the field programmable gate array (FPGA) platform and has been verified on a practical microgrid scenario including photo voltaic systems. The performance during testing indicates that the proposed technique has potential ability to perform under stressed conditions conforming the accuracy and speed of response.

Three-Point Synchrophasor Estimator With Better Off-Nominal Frequency Leakage Reduction

Synchronous phasor measurements have long been an important tool in power flow modelling and network state estimation as well as in many other tasks that support power grid observability. Classic phasor estimation algorithms are often preferred over complex alternatives. They are based on a variant of the Discrete Fourier Transform (DFT) while relying on a sampling frequency locked to the system nominal frequency. The spectral leakage caused by the small off-nominal frequency excursions in such settings introduces errors that are handled by the estimation algorithms to a different extent. Well-known three-point averaging filter (3P) is a low-cost spectral leakage reduction technique in one of the simplest estimators based on a single-bin DFT. However, it only partially removes the oscillating components. When an independent standard-based frequency tracking is available, the errors can be further compensated with minimal cost. We propose a frequency-corrected three-point estimator (F3P) to eliminate the induced spurious spectrum progressively with the increasing sampling rate while building on the analytical expression of the remaining error. We show performance benefits of the F3P under finite sampling rates when compared to the baseline 3P and to the classical Interpolated DFT (IPDFT) in static conditions. The F3P removes most of the leakage without the need of data resampling. In less ideal conditions with additive 50-dB noise, up to a 10-fold reduction of the 3P error is achieved. The error ratio of the reference IPDFT over the F3P is approximately 1.4 under the same conditions and largely independent of the frequency excursion. The presented simulation results prove the algorithm's superior performance in most of the steady-state tests defined by the relevant Standard, whereas the dynamic performance can be brought to an acceptable level by the use of a single-cycle observation window, with the response times comparable to those of the IPDFT.

A General Design Method for Phasor Estimation in Different Applications

Driven by the increasing development and complexity of bulk power systems, the requirements of phasor estimation methods differ for different scenarios and applications. In this study, a general design method for phasor estimation algorithms in different applications is proposed based on a complex finite impulse response (FIR) bandpass filter. A design framework based on mathematical error models is proposed to facilitate the design of a complex bandpass filter for different requirements and to reduce the trial and error process. The general error models between the filter gain and the error limitations of all variables measured by the phasor measurement units (PMUs) are established separately, according to the absolute value inequality. The filter design criteria obtained from the error models can determine the passband and stopband gain range of the complex bandpass filters. Three phasor algorithms for different classes of PMUs are designed, and their performances are validated and compared using experimental tests. The results demonstrate that the proposed method can design phasor algorithms to provide accurate measurements under different scenarios.

Study on the DFT-based phasor estimation algorithm for removal of the decaying DC offset

Protection relays respond to the fault condition of power system using real-time voltage and current signals. Estimation of the voltage and current phasors is necessary. However, the decaying DC component contained in the signal causes overshoot and oscillations in the magnitude and angle of the phasor estimated by the traditional DFT algorithm. Two types of estimation algorithms removing effect of the decaying DC component are studied and compared in this paper. The two improved algorithms include an error estimation (EE) algorithm featured with estimating the decaying DC component characteristics and a differential DFT (DD) algorithm featured with prefiltering of the current signal prior to phasor estimation. Performance of the two algorithms is evaluated using simulated signals from Matlab and PSCAD software. Accuracy of the phasor estimation is improved and the DD algorithm has more excellent performance than the EE algorithm.

Micro‐PMU based on Savitzky–Golay filter

This study describes a synchrophasor estimation method and its hardware implementation applicable at the distribution level of the power system, under steady-state or dynamic conditions. The method proposed is based on the discrete Fourier transform and uses the Savitzky–Golay filter in the frequency estimation process. The main goal of this study is to present the signal processing algorithm for phasor estimation and some important issues regarding its implementation in real-time systems. The performance of the micro-phasor measurement unit ( μ -PMU) is validated using a waveform generator and real-time power system simulator.

Algorithm for phasor estimation during current transformer saturation and/or DC component presence: definition and application in arc detection on overhead lines

During the current transformer (CT) saturation, the secondary current waveform of a CT is notably different from the primary current's waveform. When the discrete Fourier transform (DFT) is applied to such a distorted secondary current of a CT, the obtained root mean square (RMS) value is significantly lower than it actually is, which can lead to the malfunctioning of the relay protection devices. The operation of some relay protection algorithms (such as certain algorithms for electric arc detection on overhead lines) is conditioned by higher fault current harmonics. Obviously, due to the secondary current's distortion, the higher current harmonics cannot be accurately estimated. On the other hand, even when there is no CT saturation, the RMS value can be incorrectly estimated under DFT due to the fault current's direct component. This study presents a new algorithm which enables an accurate RMS value estimation regardless of the CT saturation and/or presence of the direct fault current component. What is more, the algorithm also enables the estimation of higher fault current harmonics under CT saturation. Various tests have indicated a high precision and robustness of the proposed algorithm and the possibility of combining this algorithm with the algorithm for electric arc detection on overhead lines.

A High-Accuracy Phasor Estimation Algorithm for PMU Calibration and Its Hardware Implementation

Phasor measurement units (PMUs) are one of the most effective devices for measuring power system dynamics, and it is critically important that they have good performance. This paper proposes a high-accuracy synchrophasor estimation algorithm and builds a PMU calibrator to offer reference values for PMU test and calibration in the laboratory. Based on a general signal-fitting model, a nonlinear-fitting-based phasor and frequency estimation algorithm using an iterative solution are proposed. A rate-of-change-of-frequency (ROCOF) estimation method using the filter spectrum characteristic of a least-squares method is proposed to improve ROCOF measurement accuracy under dynamic conditions. For PMU laboratory tests, an interference suppression method and a post-processing method for step tests are presented. Then, the selected hardware for the PMU calibrator is tested, and its influence on phasor measurement is analyzed. Simulations and experiments verify that the accuracy of the calibrator is at least 30 times better than the requirements in PMU compliance standards of both IEEE and China, indicating that it can be used for PMU testing and calibration. In addition, the calibrator is also verified that it can offer references with high accuracy under combined tests, since the proposed algorithm is based on one general signal-fitting model.

An efficient phasor and frequency estimation algorithm for wide frequency range

Synchrophasor estimation accuracy can be improved by expanding the dynamic phasor in a Taylor series near the real value of the fundamental frequency. However, this approach requires solving a weighted least square (WLS) problem in each reporting frame. In this paper, a method with reduced complexity is proposed to improve the phasor and frequency estimation under off-nominal conditions such as frequency deviation and power oscillation. It has been shown that, for adequately chosen window function, the estimation accuracy can be noticeably improved simply by shifting the nominal WLS frequency response towards the estimated frequency. In this way, the computational complexity is significantly reduced. Simulation results show that the proposed algorithm outperforms the considered algorithms in a variety of scenarios.