Phasor Estimation Algorithm Research Articles

Adaptive Phasor Estimation Algorithm Based on a Least Squares Method

This paper proposes an adaptive phasor estimation algorithm based on a least square method that can suppress the adverse effect of an exponentially decreasing DC offset component in a phasor estimation process. The proposed algorithm is composed of three stages: a basic least squares model, a time constant calculation, and an adaptive least squares model. First, we use the basic least squares model to estimate the parameter of the DC offset component in the fault current signal. This model is designed to incorporate fundamental frequency, and harmonic and constant components. Second, we use the estimated parameter to calculate the time constant of the DC offset component. Third, we redesign a least squares model that incorporates fundamental frequency, harmonic components, and exponential function of the DC offset component. Since this model incorporates the exponential function of the DC offset component contained in the fault current signal, it estimates the phasor of the correct fundamental frequency component without influence of the DC offset component. We evaluated the performance of the proposed algorithm using computer generated signals and EMTP simulation signals. The evaluation results show that the proposed algorithm can effectively suppress the adverse influence of the exponentially decaying DC offset component.

Harmonic PMU Algorithm Based on Complex Filters and Instantaneous Single-Sideband Modulation

Phasor measurement units (PMUs) have become powerful monitoring tools for many applications in smart grids. In order to address the different issues related to harmonics in power systems, the fundamental phasor estimator in a PMU has been extended to the harmonic phasor estimator by several researchers around the world. Yet, the development of harmonic phasor estimators is a challenge because they have to consider time-varying frequencies since the frequency deviation in the harmonic components is proportional to the harmonic order in a dynamic way. In this work, a new algorithm for harmonic phasor estimation using an instantaneous single-sideband (SSB) modulation is presented. Unlike other SSB-based approaches, its implementation in this work is based on concepts of instantaneous phase and instantaneous frequency. In general, the proposed algorithm is divided into two stages. Firstly, the estimation of the fundamental phasor is carried out by means of a complex finite impulse response (FIR) filter which provides the analytic signal used to compute the instantaneous magnitude, phase, and frequency. Secondly, a complex FIR filter bank is proposed for the estimation of the harmonic components, where the instantaneous SSB modulation technique is applied in order to center the harmonic components into specific narrow bands for each complex filter when an off-nominal frequency occurs. The validation of the proposed algorithm is carried out by means of the current standards of phasor measurement units, i.e., Std. C37.118.1-2011 and C37.118.1a-2014, which involve steady-state, dynamic, and time performance tests.

Improved DFT-Based Phasor Estimation Algorithm Using Down-Sampling

Fast and accurate fundamental phasor-estimation is a challenging task in digital relays. This letter proposes an improved discrete Fourier transform (DFT)-based phasor estimation algorithm. The accuracy of DFT-based methods is degraded owing to presence of decaying dc component (ddc) in fault current signals. To overcome the undesired effect of ddc, this letter introduces an auxiliary signal, which is generated by down-sampling of the fault current. The fundamental phasor is precisely estimated using sample-summation of the auxiliary signal besides DFT and sample-summation of the fault-current signal. Comprehensive simulations are performed for performance evaluation. The simulation results confirm that the proposed algorithm is fast and robust against ddc, harmonics, and noise. Moreover, the algorithm reduces the computational complexity, which makes it appropriate for digital relaying.

DC Offset Removal Algorithm for Improving Location Estimates of Momentary Faults

Fault location algorithms require the input of voltage and current phasors when estimating the distance to a fault. In the case of momentary faults, phasor calculations are often complicated by the presence of an exponentially decaying dc offset. Fourier filters and cosine filters, popularly used by most phasor estimation algorithms in relays, are successful in filtering out most, but not all, of the exponentially decaying dc offset. This dc offset affects the accuracy of voltage and current phasors and may result in a significant error in location estimates. Therefore, this paper presents a dc offset removal algorithm to improve the fault location estimates of momentary faults. The algorithm uses the rms-wavelet method for fault detection and estimates voltage and current phasors using non-linear least squares methods. The proposed method uses variable window size in calculating phasors and estimates a single, but more accurate fault location than multiple locations estimated by the Fourier and cosine filters. The method is validated using simulated and actual field data. The location estimates are shown to be accurate within 5.6% in all cases.

Development of Dictionary-Based Phasor Estimator Suitable for P-Class Phasor Measurement Unit

The paper proposes a simple phasor estimator by utilizing the dictionary-based sparse representation of signals for control and protection applications in power system. It is also observed that the proposed method is found to be suitable for extracting the fundamental component of the signal required for protective relays with few number of samples. The simulations have been carried out to test the performance of proposed phasor estimator as per the requirements provided in IEEE C37.118.1a-2014 standard and also on a modified two-area power system. To further validate the effectiveness of proposed algorithm, it has also been tested on an analog radial power system simulator with fault in the laboratory experimental setup. The measured voltage and current signals are fed to the developed prototype of phasor measurement unit (PMU) with the proposed algorithm running for phasor estimation of signals in the power system. The real-time hardware and IEEE standard test results reveal that the proposed phasor estimation algorithm is able to estimate the phasor accurately in the presence of harmonics, decaying dc components, amplitude, and phase modulation, which are typically involved during disturbances. Furthermore, the proposed algorithm is able to estimate the phasor of a signal accurately with few measured samples, thus an analog-to-digital converter with lower sampling rate is suitable for developing a prototype of low cost P-class PMU for several applications in smart grids.

Modified DFT-Based Phasor Estimation Algorithms for Numerical Relaying Applications

In this paper, new modifications of the conventional full-cycle and half-cycle discrete Fourier transform (DFT)-based phasor estimation algorithms are proposed. The key idea is to combine two consecutive outputs of their real and imaginary part filters to eliminate the harmful effect of the decaying dc components on phasor estimation, thereby a new strategy to estimate the exponential term is also reported. The proposed algorithms are compared with other DFT-based algorithms by using both computer-simulated and alternative transients program-generated signals. The obtained results reveal that proposed algorithms present excellent results, even taking into account multiple decaying dc components.

Conditional Maximum Likelihood of Three-Phase Phasor Estimation for μPMU in Active Distribution Networks

Micro phasor measurement units (μPMU) installed in active distribution networks are very useful for improving observability by acquiring system real-time data. However, three-phase imbalance and harmonic power flows adversely impact the accuracy of synchronous measurements, which implies the importance of phasor estimation errors. This paper proposes a new phasor estimation algorithm for μPMU in active distribution networks that uses a conditional maximum likelihood (CML) estimation method. Firstly, the signal model of three-phase, three-wire and four-wire imbalance systems is established. Then, the probability distributions of the magnitude and phase angles are derived from the geometric characteristics of the CML method by solving the geometric equation. Simulation results show that the proposed CML based method is effective for estimating phasor and impedance models of active distribution networks by using μPMU measurement data.

Development of Phasor Estimation Algorithm for P-Class PMU Suitable in Protection Applications

This paper proposes a phasor estimation algorithm for P-class phasor measurement unit suitable in protection applications using Hilbert transform and convolution of a signal. As the protective relay requires extracted fundamental component of the phasor for its operation, the author's introduced an algorithm to estimate a robust phasor corresponding to the fundamental component which is close to the actual signal in L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm. Though IEEE C37.118.1a-2014 standard does not specify the accuracy requirements of phasor under transient condition, the performance of phasor estimator is tested under different dynamic conditions as per IEEE C37.118.1a-2014 standard. The effectiveness of proposed algorithm has also been verified on modified two area power system during fault along with the data generated by the experimental setup in laboratory. The results revealed that the proposed algorithm estimates the phasor accurately irrespective of distortion present in the sinusoidal signals. Furthermore, the proposed estimator inherently filters harmonics, immune to decaying dc components, detects sharp changes in a signal during faults, and effectively works under complex modulated conditions. The above scenario appears frequently in a power system with distributed energy sources. The simplicity, robustness, and generality of the proposed algorithm suits for wide area measurement systems to measure the voltage and current phasors during disturbance in the smart power system networks.

A Phasor Estimation Algorithm based on Hilbert Transform for P-class PMUs

Phasor measurement units (PMUs) play an important role in many applications of power systems. In order to ensure a reliable performance, the phasor estimation algorithm has to satisfy ...

Half‐cycle method for exponentially DC components elimination applicable in phasor estimation

Decaying DC component has considerable effect on both accuracy and speed of convergence in numerical and digital relays for estimating fundamental phasor. Basically, this component causes unwanted and undesired oscillations in the time response of the fundamental phasor. As a result, it extremely affects decision making of the protective relay, which operates according to fundamental phasor component. In this study, a novel hybrid algorithm based on integration and half-cycle discrete Fourier transform (HDFT) is presented. Proposed method of this study is able to efficiently estimate fundamental frequency component by taking different parameters, including DC offset in the fault current, DC offset in a current transformer secondary side and off-nominal frequency condition into account. Moreover, in this study, modified DFT-based method for phasor estimation that is called combined integration and HDFT (CIHDFT) is put forward, which accurately estimates the original value of fundamental frequency phasor in half-cycle by considering the presence of harmonics in the waveforms. The proposed method is successfully applied to different test cases, followed by discussion on the results. Analysing the simulation results, it can be concluded that CIHDFT algorithm has remarkable performance in comparison with previous phasor estimation algorithms.

An Adaptive Phasor Estimation Algorithm for Numerical Protective Relays Based on the Generalized Delayed Signal Cancelation Method

In this paper the generalized delayed signal cancelation (GDSC) method is used for estimating the fundamental-frequency positive-sequence, negative-sequence and zero-sequence vector components of the voltages and currents to be processed by a distance relay. The GDSC filtering characteristics allow fast frequency-adaptive extraction of the sequence components of distorted three-phase signals, avoiding the use of the Fortescue transform. The proposed algorithm is incorporated into a symmetrical component distance relay, and the code is implemented in a low-cost digital signal processor. Real fault data obtained from digital fault recorders are used for evaluating the performance of the proposed relay algorithm.

Positive sequence voltage memory filter for numerical digital relaying applications

A positive sequence voltage memory filter for numerical digital relaying applications is proposed. It is designed based on converting an analogue first-order lowpass filter into an infinite impulse response digital filter using the backward difference method. Its combination with both recursive and non-recursive phasor estimation algorithms is discussed. The obtained results reveal the decaying time constant of the proposed filter transient response is easily set, providing a simple and stable mean to adaptively adjust the positive sequence voltage memory polarisation of numerical relays.

Fast algorithm for estimating power frequency phasors under power system transients

Power frequency phasors are widely used in the measurement, analysis, control and protection of power systems. When disturbances occur in such systems, power frequency phasors must be estimated quickly to ensure an accurate restoration to normal operation. Hence, a fast and accurate estimation algorithm would be a significantly useful tool. In consideration of the composition of transient signals in power systems, a novel algorithm for power frequency phasor estimation is proposed. Based on the double matrix pencil method, a unitary reference matrix of complex-valued exponential signals is formed. The power frequency phasor estimation is then transformed to a brief multiplication of matrices. Thus, the QR decomposition, generalised eigenvalue calculation, and secondary estimation can be avoided and no complex multiplication is introduced. Therefore, the computational efficiency of the proposed method is improved compared with previous estimation techniques. Analytical and experimental investigations show that the proposed algorithm can extract power frequency phasors accurately, stably and quickly under power system transients.

Real-time electrical variables estimation based on recursive wavelet transform

Abstract In frequency and phasor estimation algorithms, the undesired components are required to be filtered out from the original signals. In power systems, the undesired components are the decaying dc offset and harmonics. These components could cause delay in algorithm convergence time and deviation from the desired results to a great extent. This paper proposes a new recursive algorithm for accurate and fast estimation of the instantaneous electrical variables such as frequency, amplitude and phase angle. The new algorithm provides an improvement over the existing recursive wavelet transform and, therefore, it is called IRWT. The IRWT performance is compared with the commonly used full-cycle discrete Fourier transform (DFT) and the recursive wavelet transform (RWT) methods. Since it uses a special mother wavelet function, it reduces computational complexity compared to the conventional DFT based method. Compared to the recursive wavelet transform (RWT) method, it has a faster response time. It is shown that IRWT possesses an improvement over a wide range of decaying dc component, harmonic distortions, frequency deviation and sampling frequency compared to the previously proposed methods. This characteristic of IRWT makes it a good candidate for the real-time applications in any power systems.

Accurate Dynamic Phasor Estimation Based on the Signal Model Under Off-Nominal Frequency and Oscillations

Accurate and fast estimation of power system phasors is the key to reliable operation of power system and its control/protective equipment. There have been many studies on phasor estimation techniques under dynamic and transient conditions. Although the performance under dynamic conditions of estimators based on the static phasor model has improved, significant errors still exist during large dynamic deviations. Two fast and precise dynamic phasor estimation algorithms under power system oscillations and off-nominal frequency conditions are described in this paper. The methods use the signal model under these dynamic conditions, linearize them by using Taylor’s series expansion, and estimate the phasor using least squares technique. Frequency and its rate of change are also calculated using adjacent phasors with minimum complexity. Results obtained show that the performance errors of the proposed methods are way below the minimum requirement of the standard and better than other similar dynamic phasor algorithms.

A Modified Empirical Mode Decomposition Filtering-Based Adaptive Phasor Estimation Algorithm for Removal of Exponentially Decaying DC Offset

This paper proposes a modified empirical-mode decomposition (EMD) filtering-based adaptive dynamic phasor estimation algorithm for the removal of exponentially decaying dc offset. Discrete Fourier transform does not have the ability to attain the accurate phasor of the fundamental frequency component in digital protective relays under dynamic system fault conditions because the characteristic of exponentially decaying dc offset is not consistent. EMD is a fully data-driven, not model-based, adaptive filtering procedure for extracting signal components. But the original EMD technique has high computational complexity and requires a large data series. In this paper, a short data series-based EMD filtering procedure is proposed and an optimum hermite polynomial fitting (OHPF) method is used in this modified procedure. The proposed filtering technique has high accuracy and convergent speed, and is greatly appropriate for relay applications. This paper illustrates the characteristics of the proposed technique and evaluates its performance by computer-simulated signals, PSCAD/EMTDC-generated signals, and real power system fault signals.

Programmable logic design of a compact Genetic Algorithm for phasor estimation in real-time

The main objective of this work is to present an efficient method for phasor estimation based on a compact Genetic Algorithm (cGA) implemented in Field Programmable Gate Array (FPGA). To validate the proposed method, an Electrical Power System (EPS) simulated by the Alternative Transients Program (ATP) provides data to be used by the cGA. This data is as close as possible to the actual data provided by the EPS. Real life situations such as islanding, sudden load increase and permanent faults were considered. The implementation aims to take advantage of the inherent parallelism in Genetic Algorithms in a compact and optimized way, making them an attractive option for practical applications in real-time estimations concerning Phasor Measurement Units (PMUs).

A Simple Synchrophasor Estimation Algorithm Considering IEEE Standard C37.118.1-2011 and Protection Requirements

In this paper, a simple synchrophasor estimation algorithm has been proposed considering power system steady state, dynamic conditions, and protection requirements. The new IEEE Standard C37.118.1-2011 for synchrophasor measurements includes the dynamic performance requirements for the phasor measurement units. It is shown that the proposed method satisfies all the steady state and dynamic requirements of the new IEEE Standard. Presently, synchrophasors are mainly used for wide area monitoring. Increasingly, synchrophasors are being considered for protection applications in smart grids. Protection applications require shorter response times and lower overshoot/undershoot values for estimated phasors during large disturbances. It is shown that the proposed method performs satisfactorily during system faults, which is an important requirement for protection applications. A detailed performance comparison with the existing phasor estimation algorithms has also been presented.

A dynamic phasor estimation algorithm based on angle-shifted energy operator

Under dynamic conditions, the signals of power system have time-varying magnitude and frequency, which might lead to considerable errors for synchrophasor measurement. The traditional discrete Fourier transform (DFT) based algorithms used in Phasor Measurement Unit (PMU) are hard to meet the requirements of measurement accuracy because of the existence of spectral leakage. A dynamic phasor measurement algorithm is proposed in this paper in which the input sampled data are considered as non-stationary signals with amplitude modulation-frequency modulation (AM-FM) form, and the measurement is achieved by AM-FM demodulation. An angle-shifted energy operator (ASEO) is used to extract the instantaneous amplitude and low pass differential filter is introduced for frequency estimation. Simulation results indicate that the proposed algorithm can effectively improve the phasor measurement accuracy and has very short response time for PMU under dynamic conditions.

DFT based phasor estimation algorithm for numerical digital relaying

A novel phasor estimation algorithm is proposed, by means of an innovative modification of the traditional full cycle discrete Fourier transformer (FCDFT) algorithm. The main idea is to combine the FCDFT outputs for even and odd sample-setsobtained for one cycle data window decimated by two and by four. Its performance was compared with the ones of other full cycle algorithms reported in the late literature on the subject. The obtained results reveal the proposed algorithm leads to the best performance, even considering both the decaying DC component of the fault current and the one caused by the current transformer secondary circuit.