Phasor Estimation Research Articles

Internal clock errors in synchrophasor ambient data: Effects, detection, and a posteriori estimation-based correction

Synchrophasor data from real world power systems are exposed to numerous adverse cyber-and-physical operating conditions that can negatively impact their fitness for use in PMU applications. Although the most significant impairments such as GPS loss, instrument transformer failure, data drop-off, etc., have been studied in the literature, there exist other more complex nuisances that impact PMU data quality. This is the case of differences in how clock synchronization, time disciplining, and phasor estimation is performed by different PMU vendors, which have important implications on the PMUs’ data fitness for use in PMU applications. In particular, ambient data applications, which have increasingly become a focus for tracking grid performance indicators, are extremely sensitive to periodic clock errors. Using synchrophasor and waveform data from Dominion Energy’s power system, this article provides an in-depth analysis of the effect of seemingly minor device clock errors on the measurement signals’ content. Finally, a method to distinguish clock errors from normal system dynamics and to correct them is proposed.

A new least squares error based method for accurate phasor estimation of fault currents in series-compensated transmission lines

Phasor estimation of the fundamental component of the fault current is of great importance for the fault location unit in distance relays. In series-compensated transmission lines, the transient component of the fault current may appear in the complicated wave shape of an exponential-sinusoidal function. Thus, phasor estimation is a major challenge owing to the fact that more unknown parameters should be found, especially during off-nominal frequency conditions. Therefore, in this paper, a new method is put forward, on the strength of the least squares error (LSE), in order to accurately estimate the fundamental component phasor of the fault current in a series-compensated transmission line for off-nominal frequency conditions. The performance of the established method is also investigated through extensive simulation studies, taking care of different fundamental components, harmonic contents, and transient components. Moreover, the performance of the proposed method is evaluated for off-nominal frequencies. The results obtained in this study demonstrate that the mean absolute error of the estimated amplitude and phase for the fundamental component is less than 1% and 1°, respectively. Furthermore, the accuracy of the proposed method is not affected by the noise up to a signal-to-noise ratio of 30 dB. Thus, the established method is capable to effectively be employed for the phasor estimation in fault location applications.

Enhanced Estimation of Frequency and Symmetrical Component Phasors of Three-Phase Voltage Signals

Enhanced Estimation of Frequency and Symmetrical Component Phasors of Three-Phase Voltage Signals

Performance enhancement of band-pass FIR filter-based M-class phasor estimation

Abstract The paper presents the performance enhancement of band-pass filter-based M-class phasor estimation. The performance of the M-class phasor estimation using a band-pass FIR filter is enhanced with a magnitude correction factor for the off-nominal frequency range. The band-pass filter is implemented for the phasor estimation with various window functions Tukey, Rife Vincent class-I order-2 (RV2), Hamming, Hanning, Blackman, and Flat-top (FT) and its performance are evaluated under the steady and dynamic state tests prescribed by the standard. A rigorous performance analysis of enhanced phasor estimation using band-pass FIR filter with various window functions is presented with the accuracy indices of total vector error (TVE), frequency error (FE), and rate of change of frequency error (RFE). The result analysis reveals that the performance enhanced phasor estimation using band-pass FIR filter offers significantly less error than reported work at the low sampling rate. The design and performance analysis of the phasor estimation using the band-pass FIR filter is performed in the MATLAB platform.

Synchronized measurement method for urban distribution networks based on proportional-integral control

In the context of the rising prevalence of renewable energy, the need for precise and synchronized measurements in urban distribution networks has become increasingly critical. Conventional synchronization techniques, which predominantly depend on Global Navigation Satellite System (GNSS) timing signals, are often plagued by significant sampling time errors. Addressing this challenge, this study introduces an innovative automatic synchronization measurement method employing proportional-integral (PI) control. This method is composed of three integral components: the monitoring of local clock phases via pulses per second (PPS) signals, modulation of the clock phase through a PI controller, and the estimation of grid phasors from the synchronized sampled data. The test results of this method on a hardware platform demonstrate its capability to significantly reduce the sampling error from 2 × 10−3 V to an impressive 1 × 10−5 V, while also meeting the requirements of the synchronized phasor measurement standards outlined in C37.118.1. These advancements underscore the significant potential of PI-controlled simultaneous sampling in enhancing the operational efficiency and reliability of urban distribution networks, particularly in environments with a high integration of renewable energy sources.

A Novel Method for Removal of Dual Decaying DC Offsets to Enhance Discrete Fourier Transform-Based Phasor Estimation

This paper presents a novel method for the removal of dual decaying DC offsets (DDCOs) to enhance discrete Fourier transform-based phasor estimation. The method proposed in this paper uses the sum of even samples and the sum of odd samples from the input signal to remove the AC components, thereby precisely estimating the primary and secondary DDCOs. The fluctuations induced by DCCOs present in the output of traditional DFT methods are eliminated by using the estimated DCCOs. The performance of the method was evaluated in terms of both mathematical-generated signals and fault current signals from a 154 kV Korean overhead transmission system. PSCAD/EMTDC was used to generate fault current signals at various fault distances and angles. The results show that the proposed method can estimate the phasor of the fundamental frequency component accurately regardless of the primary and secondary DCCOs. The paper concludes by describing the hardware implementation in a prototype unit that considers the real-world requirements of power system protection.

Graphic tools for analysing the influence of noise and aperiodic components in the performance of digital filters: a case study

An accurate phasor estimation is an important task for a correct operation of control and protection devices. The presence of aperiodic components in electrical signals is a major problem for the correct performance of digital filters. In addition, their stability is heavily conditioned by the distortion resulting from the noise inherent to signal processing. Consequently, a complete study of the behaviour of any filtering algorithm (in the presence of noise and aperiodic components) must be carried out before its implementation. Usually, numerical performance indices are used to measure the accuracy of a proposed method. In order to ease the analysis and comparison of different digital filters, a new set of graphic tools is presented in this paper. To illustrate the application of these graphic tools, a case study is presented with three different filtering algorithms developed for protection relaying.

Single-cycle P Class phasor estimation based on harmonics whitening and off-nominal frequency offset adjustment

Phasor Measurement Units (PMUs) are essential for real-time power system monitoring and control. In this paper, a novel algorithm for protection (i.e., P Class) PMUs is presented. The proposed algorithm consists of four steps: preliminary narrowband disturbance whitening; estimation of the off-nominal fundamental frequency offset through the Interpolated Discrete Time Fourier Transform (IpDFT); data record length adjustment to refine narrowband disturbance whitening over an integer number of fundamental periods; time-domain estimation of the Taylor's series coefficients of the synchrophasor function through a weighted least-squares estimator (after correction of possible static off-nominal deviations). The key novel contribution of the proposed approach is its superior ability to smooth harmonic disturbances over shorter observation intervals than many existing algorithms (which typically require at least two-cycle-long data records to meet P Class accuracy requirements), while ensuring a good tracking capability of transient events with a reasonable execution time. Several simulation and experimental results confirm that, in the case of multi-harmonic distortion, the proposed approach returns more accurate results than both the basic Taylor-series-based Weighted Least-Squares (TWLS) estimator and other whitening-based techniques, while ensuring compliance with P Class specifications even over one-cycle-long data records.

Measurement accuracy verification of phasor measurement unit with dynamic phasor estimation

Measurement accuracy verification of phasor measurement unit with dynamic phasor estimation

Addendum to “Fast Iterative-Interpolated DFT Phasor Estimator Considering Out-of-Band Interference”

Addendum to “Fast Iterative-Interpolated DFT Phasor Estimator Considering Out-of-Band Interference”

Real-Time Frequency Adaptive Tracking Control of the WPT System Based on Apparent Power Detection

In wireless power transfer (WPT) systems, inverters are used to achieve high-frequency conversion of DC/AC, and their conversion efficiency and working frequency are key factors affecting the system’s power transfer efficiency. In practical applications, many hardware issues, such as power transistor shutdown and loss, are the main reasons that affect the inverter conversion efficiency. On the other hand, the working frequency of WPT systems ranges from hundreds of kHz to a few MHz, and traditional voltage and current phasor estimation requires a very high sampling rate which is difficult to achieve. To overcome these limitations, this paper introduces a phase-shifting full bridge inverter using a zero-voltage switching (ZVS) soft switching technology to optimize the conversion efficiency of the inverter. Meanwhile, apparent power is introduced to detect the operating frequency and phase angle. Combined with an FPGA soft switching control strategy, this approach allows for the quick adjustment of the driving pulse of MOS transistors, as well as the voltage and current at the transmitting end, to a completely symmetrical state in real-time, effectively suppressing frequency offset and achieving efficient frequency tracking control and maximum efficiency tracking (MET) control of the WPT system. Through simulation and experiments, the ZVS soft switching technology has been achieved with the inverter control strategy, leading to improved conversion efficiency. The frequency offset that can be corrected can reach 0.1 Hz using the apparent power detection method, and the maximum transfer efficiency of the WPT system can reach 91%.

An extended impedance‐based fault location algorithm in power distribution system with distributed generation using synchrophasors

AbstractAccurately locating power distribution faults reduces the total outage duration and provides better system reliability. Fault location using the traditional impedance‐based method may be very challenging in an active distribution system. However, taking into consideration the ease of implementation and cost effectiveness, a novel impedance‐based method is proposed to locate the fault by using the highly accurate time‐synchronized voltage and current phasors obtained from distribution phasor measurement units. The synchrophasor measurements obtained from the substation and various feeder segments are used in a two‐step algorithm based on the apparent impedance calculation to locate the exact source of the event. The algorithm uses phasor estimates to first identify the faulted feeder sub‐region and later uses measurements from a remote end device to eliminate pseudo‐faulted points to obtain the actual fault location. The effectiveness of the proposed method is realized using IEEE 34 bus system. Based on different fault types simulated at various parts of the system, the algorithm accurately estimates fault location in the range of ±1% of the line length. The proposed method is effective in locating faults for any type of network and topologies, with as many or as few (minimum 2) phasor measurement units in the system.

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.

Estimation of Wideband Multi-Component Phasors Considering Signal Damping.

Harmonic and interharmonic content in power system signals is increasing with the development of renewable energy generation and power electronic devices. These multiple signal components can seriously degrade power quality, trip thermal generators, cause oscillations, and threaten system stability, especially the interharmonic tones with positive damping factors. The first step to mitigate these adverse effects is to accurately and quickly monitor signal features, including frequency, damping factor, amplitude, and phase. This paper proposes a concise and robust index to identify the number of modes present in the signal using the singular values of the Hankel matrix and discusses the scope of its application by testing the influence of various factors. Next, the simplified matrix pencil theory is employed to estimate the signal component frequency and damping factor. Then their estimates are considered in the modified least-squares algorithm to extract the wideband multi-component phasors accurately. Finally, this paper designs a series of scenarios considering varying signal frequency, damping factor, amplitude, and phase to test the proposed algorithm thoroughly. The results verify that the proposed method can achieve a maximum total vector error of less than 1.5%, which is more accurate than existing phasor estimators in various signal environments. The high accuracy of the proposed method is because it considers both the estimation of the frequency number and the effect of signal damping.

O Splines-Based Fixed-Frequency Integral Sliding-Mode Controller for PFC Rectifier

This paper proposes a fast-response sliding mode controller (SMC) for a semi-bridgeless boost converter under large and quick load fluctuations to ensure tight output voltage regulation and unity power factor correction (PFC) at the line side. In this sense, a novel approach for estimating the reference current profile is presented focusing on the real-time phasor estimation via the O-splines of the discrete-time Taylor-Fourier transform (DTTFT). This method allows for improving the computational efficiency and dynamic performance of the estimations of amplitude, frequency and phase of the network voltage used for the generation of the reference current profile. Several aspects of the controller design are discussed, including the choice of the sliding surface, the existence and stability conditions, and the implementation of an adaptive hysteresis band to fix the switching frequency and reduce zero-crossing distortion. Experimental results of a GaN-based prototype validate the theoretical predictions, exhibiting a PF close to 1 and a total harmonic distortion lower than 3.2% in presence of load changes of up to 50% and changes in the output voltage set point. Several comprehensive experimental comparisons between the proposed framework and the most widely used methods recently reported in the literature are accomplished in terms of transitory and steady-state responses. The robustness of the proposed control approach is experimentally demonstrated under sag conditions and a wide operating range of the input voltage.

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.

Evaluation of single-ended impedance-based transmission fault location using fixed and variable window phasor estimation approaches

In this paper, the performances of fixed and variable window size phasor-based techniques reported in the literature are evaluated on a classical one-terminal impedance-based fault locator, pointing out the challenges and alternatives for applications in transmission systems equipped with high-speed protection functions. To do so, several Alternative Transients Program (ATP) fault simulations were carried out in a 230 kV/60 Hz power network, varying their parameters such as type, location, inception angle and resistance. The obtained results attest that phasors estimated from variable window size strategies may improve the fault locator performance, even in the first cycles after the disturbance occurrence, appearing themselves as potential alternatives to be applied in combination with high-speed phasor-based protection routines.

Data window selection for removal of decaying DC component in current phasor estimation for distance protection

In distance protection, the fault current signal is usually distorted by the decaying direct current (DC) and harmonics preventing accurate and fast estimation of the fault current phasor. This paper presents a method based on the carefully selected data windows and least square (LSQ) method to improve the performance of the current phasor estimation. The method comprises a short and variable data window for fast operation of distance relay for close faults and a fixed data window for the accurate operation of the relay for faults close to the boundary of Zone 1. The short and variable data window can achieve high speed in the phasor estimation in a quarter of cycle, whereas the second algorithm uses a fixed data window with an excellent frequency response to increase the accuracy of the phasor estimation. The proposed method is first tested using mathematical formulation under different conditions such as different characteristics of the DC component, noise, harmonics and frequency deviation. Then the method is tested by more realistic samples taken from a simulated transmission system under different fault conditions for flexibility, speed and accuracy. All the test results validate the aforementioned features of the proposed algorithms.

A SVD-Based Dynamic Harmonic Phasor Estimator With Improved Suppression of Out-of-Band Interference

The diffusion of nonlinear loads and power electronic devices in power systems deteriorates the signal environment, and increases the difficulty of measuring harmonic phasors. Considering accurate harmonic phasor information is necessary to deal with harmonic related issues, this paper focuses on realizing accurate dynamic harmonic phasor estimation when the signal is contaminated by certain interharmonic tones, i.e. the out-of-band interference (OBI). Specifically, this work introduces the singular value decomposition into the Taylor-Fourier transform algorithm, deriving a general decomposition form for harmonic phasor filters, and yielding a set of adjustable parameters. Then these parameters are configured to minimize the negative influence of OBI on the dynamic harmonic phasor filters. Based on the recommended parameter values, the optimized harmonic estimator is obtained, and then tested under signals distorted by OBI, harmonic, noise, and in worse cases, frequency deviation, and some dynamic conditions. Test results show the proposal achieves good harmonic phasor estimation even under multiple interferences and dynamic scenarios, and has a much weaker dependence on OBI tones compared to conventional approaches.