Fundamental Frequency Phasor Research Articles

A Real-Time Setting-Free Synchronous Generator Out-of-Step Protection Scheme Based on Voltage Trajectory

This article proposes a real-time, setting-free out-of-step (OOS) protection strategy for a single synchronous generator (SG) connected to a multimachine power system. To do so, the fundamental frequency phasor of the voltage at the generator terminal is measured. It will be shown that at the point of OOS, the imaginary part of the voltage crosses the zero point and becomes negative, whereas the real part of the voltage holds a negative value. On the other hand, it will be shown that during stable power swings, the imaginary part of the voltage behaves as per an OOS event, whereas the real part of the voltage becomes positive. Therefore, this principle can be used as the criterion to detect an SG OOS. Moreover, it will be shown that the proposed principle can count the number of SG pole slip occurrences so that it can trip the generator after a certain number of pole slips. The proposed scheme is a response-based algorithm and uses only locally measured voltage at the relay location. Furthermore, the network configuration and parameters do not affect the proposed scheme. Unlike the legacy impedance-based OOS detection method, which demands rigorous offline simulation studies to determine settings, the proposed scheme does not need any setting to operate. Rigorous mathematical analyses and illustrated simulation study results are presented to substantiate the efficiency of the proposed method. The performance of the proposed scheme and the polygonal relay and concentric blinder scheme are compared through comprehensive simulation studies. The results prove that the proposed scheme can be served as an efficient method for SGs OOS protection.

An improved morphological transform filter for fundamental frequency phasor measurement of power system

The fundamental frequency phasor measurement method based on Fourier transform is affected by the decaying DC offset in fault current. To reduce this effect, a morphological transform filter (MTF) has been proposed to filter out the decaying DC offset. However, this filter is affected by fault inception angle, which makes it difficult to deal with some specific types of fault currents. Therefore, an improved morphological transform filter (IMTF) is proposed in this paper. The proposed IMTF eliminates the influence of fault inception angle by averaging the results of the morphological transform of two adjacent half-cycle. By simplifying the morphological operation of MTF, IMFT has a lower calculation burden. The real-time performance of IMTF is ensured by compensating the waveform over one cycle. Simulation studies are carried out on Matlab/Simulink and RT-Lab system, respectively, and the results show that the proposed IMTF outperforms MTF in terms of robustness. Besides, fault data recorded from the digital fault recorder is also used to test the practicability of IMTF.

Modified discrete Fourier transform algorithm for protection of shunt compensated distribution line

Introduction. The response time of the relay plays vital role when fault occurs on the line. Various algorithms are adopted to increase the sampling rate of the relay which, in turn, improves the response time. Methods. Discrete Fourier transform and modified discrete Fourier transform are the two algorithms used to calculate the fundamental frequency phasor of the signal required by the relay to initiate trip command. It is known that discrete Fourier transform takes four to five cycles to produce the fundamental frequency phasor but it fails to deal with the decaying DC component. On the other hand, modified discrete Fourier transform improves the response time by removing the decaying DC component along with the other harmonics in just one cycle and a few samples. The aim of this paper is to cover discrete Fourier transform and modified discrete Fourier transform algorithms to analyze the performance of the three overcurrent and one earth fault relaying scheme for different types of faults occurring in the distribution system. Methodology. The concept of three overcurrent and one earth fault scheme is also explained in this paper for protection of shunt-compensated distribution system. The scheme is designed for variable power factor. MATLAB/Simulink is used as the software tool to validate the results obtained for various types of faults occurring in the system. The results are represented graphically to illustrate the time of response of the protection scheme when shunt compensators are connected at the receiving end of distribution network.

A Non-Iterative Fault Location Algorithm for Transposed/Untransposed Transmission Line Immune to Unsynchronized Measurements

This paper presents an impedance-based non-iterative fault location algorithm for a two-terminal line considering unsynchronized measurements to account for the loss of Global Positioning System (GPS) signal. Based on the availability of pre-fault signals two algorithms are proposed, one using pre-fault data and the other without using pre-fault data. The algorithms are formulated by using fundamental frequency phasor based decoupled modal components of the measured signals at both ends of the line while considering distributed line model. Application of decoupled modal components with distributed model enhances the accuracy of the presented algorithms in both transposed and untransposed configuration of the line. The proposed algorithms have been tested and analyzed with different fault conditions simulated in EMTP-RV platform. Comparative analysis with existing methods is also presented to establish prominent features of the proposed methods. The algorithms have also been tested with practical data of Power Grid Corporation of India Limited (PGCIL) and the test result validates the accuracy of the developed fault location algorithms.

A robust and accurate discrete Fourier transform‐based phasor estimation method for frequency domain fault location of power transmission lines

Frequency domain methods had been commonly used in power transmission line fault location. To improve the accuracy of frequency domain fault location methods, this paper studies a robust and accurate discrete Fourier transform (DFT)-based phasor estimation method. First, this paper analyses the deviation characteristics of DFT output phasors caused by decaying DC components with data window sliding. Based on these characteristics, this paper employs rotation factor computation to construct linear equations for the purpose of estimating the accurate fundamental frequency phasor during fault transient process. In this way, the accurate fundamental frequency phasor can be calculated by a two-step linear operation. Furthermore, to eliminate the effect of off-nominal frequency, the proposed method adjusts frequency deviation by using interpolation method. To further enhance the robustness for frequency domain fault location, the PauTa criterion is used to exclude the anomalous equations in the phasor estimation process. Finally, electro-magnetic fault simulation is used to evaluate the proposed method. The test results demonstrate that the proposed method improve the accuracy of fault location during the fault transient process.

Shifted frequency analysis-EMTP multirate simulation of power systems

This paper presents a novel hybrid multirate protocol to interface a Shifted Frequency Analysis (SFA) simulator and an Electromagnetic Transients (EMT) simulator. The proposed protocol is based on the Multi-Area Thévenin Equivalent conceptual framework and uses a second parallel simulation of the EMT simulator to track the imaginary part of the complex-valued solution from the SFA simulator. Having a Real-Part EMT simulation and an Imaginary-Part EMT simulation, running in parallel, maintains the analyticity and synchronicity of the SFA/EMT hybrid simulator and enables the use of large time steps in the SFA solution. This also allows the extraction of the fundamental frequency phasor of the EMT solution directly through the SFA transformation. The interfacing algorithm is demonstrated on the IEEE 39-bus system. The proposed protocol shows very good accuracy for capturing the electromechanical transients with the SFA simulator and an EMT-comparable accuracy with the EMT simulator. The results show the capability of the hybrid simulator to use significantly different solution steps in the SFA and EMT simulators, which results in considerable savings compared with an all-EMT solution. The proposed simulator would be very useful in conducting transient stability-type of studies when there is a need to model some devices with EMT accuracy.

Integrating Signals With High Sampling Rates for Transmission Line Protection in Digital Substations

Travelling wave based protection functions require significantly higher sampling rates than protection functions based on time-domain superimposed quantities or fundamental frequency phasors. Integrating these high sampling rates in digital substations leads to a significant increase of the communication load of process-level networks and causes high computational cost for centralized protection systems. This paper builds on a distributed signal processing approach, which allocates the filtering operations among standalone merging units (SAMU). In particular, the paper presents a decimation filter design to integrate signals with high sampling rates at the process-level. Thereby, signal sequences with high, medium and low sampling rates are provided according to the requirements of the respective protection function. The decimation filter structure is optimized with respect to time delay by the Remez exchange algorithm and with respect to computational cost by a multistage approach and a sparse filter design algorithm. In addition, the filter response is verified against the accuracy constraints defined in IEC 61869-6 and IEC 61869-13. The paper shows that it is feasible to distribute the filtering operations among SAMUs, while keeping the time delay below the maximum allowable processing delay of 2 ms.

Auxiliary Prony‐based algorithm for performance improvement of DFT phasor estimator against transient of CCVT

The measured fault voltage signal through coupling capacitor voltage transformer (CCVT) contains transient components which highly affect the estimated fundamental frequency phasor. This paper presents a new hybrid method which aims to calculate and remove the unwanted effect of CCVT transient on the fundamental phasor estimation. The main novelty of the proposed method is that proposed method is independent from the CCVT parameters involved in the transient response. In other words, unlike previously published papers, this method calculates the CCVT characteristics involved in the transient response. To such aim, by utilizing frequency modulation, fault voltage signal is shifted. Utilizing simple but comprehensive formulations based on integration and Prony-complex theory, the CCVT characteristics are calculated in the first cycle after fault inception. After that, by utilizing modified discrete Fourier transform (MDFT), the fundamental phasor component is calculated in one cycle. Several simulated test signals are applied to the proposed method. The simulation results illustrate that the proposed method removes the unwanted effects of CCVT. Also, it is fast and has a good precision in estimating the fundamental phasor component of fault voltage signal under different simulation scenarios.

Fault Detection During Power Swings Using the Properties of Fundamental Frequency Phasors

Among short-circuit faults, those occurring during power swings are more harmful to power system stability and thus, they should be detected quickly and reliably. However, discrimination of power swing and such kinds of faults is not always easy, especially in case of three-phase faults which are symmetrical similar to power swings. This paper shows that fundamental frequency phasors of voltage and current have some proper characteristics which can be used for the mentioned discrimination. In doing so, two new fault detection methods are proposed and tested on simulated systems considering single-mode and multi-mode swings. Field data are also utilized to substantiate the presented analyses. The obtained results demonstrate the correctness of presented analyses and the efficiency of proposed methods in fault detection during power swings.

Hybrid approach for immunisation of DFT‐based phasor estimation method against decaying DC components

In addition to high-order harmonic and noise components, the fault current may contain decaying DC components which highly affect the estimated fundamental frequency phasor. This study presents a new hybrid method which aims to calculate and remove the unwanted effect of decaying DC components on fundamental phasor estimation. The main novelty of the proposed method is that the proposed method is independent of the dynamic behaviour of the current transformer (CT). In other words, unlike previously published papers, this method analytically calculates the CT time constant. To such aim, utilising frequency modulation, fault current signal is shifted. Utilising simple but comprehensive formulations based on integration and Prony-complex theory, the magnitude and time constant of decaying DC components are calculated in one cycle. After that, utilising a modified discrete Fourier transform the fundamental phasor component is calculated. Several test signals and also practical fault signals are applied to the proposed method. The simulation results illustrate the proposed method simply but comprehensively remove the unwanted effects of the decaying DC components. Also, it has quick speed as well as a high-precision response in the estimation of fundamental phasor under different simulation scenarios.

Wavelet-fuzzy based protection scheme of EHV-AC transmission system and efficacy of discrete Fourier transform

Extra high voltage (EHV) transmission system is the vital links between the generating units and the transmission substations. Transmission of power to the utilities located over long distances through extra high voltage (EHV) transmission is efficient and cost effective. It has the advantage of allowing the bulk amount of energy transmission from generating units to the widely distributed load centers economically. However, detection of faults on EHV transmission system is critical and a challenging task for a large variation in fault operating condition such as high fault resistance involved, inception of fault at the voltage zero crossing situation and the variation in load angles and the system loading levels. Moreover, fault characteristics on EHV transmission lines differ to those on medium and high voltage (MV/HV) due to the presence of larger shunt capacitance, higher voltage level, longer transmission radius and weakly damped decaying dc current caused by the high system reactance to resistance ratio. A number of deterministic and intelligent models based protection schemes of transmission systems are endorsed by several authors where attempts have been made to detect, classify and to locate the fault and the faulted section of the line but they have their own limitations and complexities and the results are not satisfactory. Keeping in view of the aforesaid difficulties, this paper proposes a new approach for the protection of EHV-AC transmission system based on novel application of discrete wavelet transform (DWT) in combination with fuzzy logic using discrete Fourier transform (DFT) at the fundamental frequency phasor. The proposed method retains both fundamental and the high frequency components of the fault current signals to achieve high reliability and selectivity of the protection. The obtained results have been validated with the well established mathematical model of the given EHV-AC transmission system. It is found that the proposed method is accurate, computationally simpler, faster and valid for a wide range of fault operating conditions.

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.

Speed and security improvements of distance protection based on Discrete Wavelet and Hilbert transform

In order to maintain power system stability, modern transmission networks demand a high fault detection speed. At the same time, a high level of protection security is required, since each protection maloperation might lead to a system blackout and high economic loss. The protection speed and security represent conflicting requirements fundamentally limited by the Heisenberg’s Uncertainty Principle. Traditional line protection approach relies on fundamental frequency phasor estimation based on Discrete Fourier Transform. There are also various Discrete Wavelet Transform algorithms, typically based on Daubechies wavelet families, which may be used to estimate phasors. In this paper wavelet families other than Daubechies are evaluated as methods for estimating phasors. Two new algorithms based on Reverse Biorthogonal mother wavelets are presented and compared to the previous solutions. The protection speed and security are evaluated via a very demanding test formed on the basis of several thousands of fault simulations, as well as on 60 fault records from 400kV and 220kV transmission networks.

An Improved Algorithm to Remove DC Offsets From Fault Current Signals

Fault current signals that are processed by digital relays consist of dc, fundamental, and harmonic components. Filtering algorithms are necessary to eliminate the dc and harmonic components from these signals. Several algorithms have been proposed for this task which vary in their accuracy, response time, and computational burden. The conventional discrete Fourier transform (DFT) can eliminate harmonics and is commonly used to estimate the fundamental frequency phasor, but its accuracy is lower as it does not filter the dc offset. Other algorithms including variants of DFT attempt to improve the accuracy and response time. This paper proposes a technique that takes into account the exponential variation of the dc offset and more accurately determines the fundamental component. The effectiveness of this method is evaluated by simulation on a two-machine system and also compared against existing phasor measurement methods. Simulations confirm that the proposed method can more accurately estimate the fundamental component compared to the existing methods.

Prony method implementation in distance relays to mitigate the effect of series-compensated transmission lines

This paper characterizes the error in distance relay operation due to the existence of asynchronous frequency components when a fault in a line with series compensation occurs. The distance relay model and the impact of non-filtered frequency components using the conventional digital filters is presented, an error will appear in voltage and current fundamental frequency phasors estimation and, by consequence an error, in apparent impedance estimation. Then, the proposed distance relay algorithm using the Prony method as a filter and its application considerations are described. Next, the line series compensation effects in distance relay estimation are presented, showing the importance of the estimation of the fundamental frequency phasor. Afterward, the effect of series compensation in distance relay performance is characterized by evaluating a simulated fault event. Finally, the proposed algorithm is evaluated in reach and operation time of the simulated and real fault events using a 3D operation characteristic of the relay.

Prony filter vs conventional filters for distance protection relays: An evaluation

This article presents a performance evaluation of Prony method vs conventional digital filters in distance relay protection algorithms, and characterizes the error when asynchronous frequency components (subharmonics or interharmonics) are embedded in voltage and current signals during fault period when conventional digital filters of distance relay algorithms (cosine or Fourier filter) are used to estimate the fundamental frequency phasors. First, the signal processing overview of conventional distance relays is presented. Then, the effects of line series compensation in distance relay estimation during the fault period are presented by analyzing two events of recorded data signals in a laboratory test system of a series compensated line and using a mho operation characteristic. Next, Prony method and its considerations for the implementation in distance relay algorithms are described. Then, the performance of Prony method using simulated signals is evaluated. Lastly, an assessment of Prony as a digital filter in distance relay algorithm is performed by analyzing two fault events in a laboratory test system using a quadrilateral operation characteristic, and the results of Prony vs conventional digital filters in distance relay algorithms are presented.

Shifting Window Average Method for Phasor Measurement at Offnominal Frequencies

A shifting window average method (SWAM) is proposed for phasor measurement at offnominal frequencies. The proposed SWAM is not only applicable for fundamental frequency phasor measurement, but also for harmonic phasor measurement as well. SWAM is based on a mathematical analysis of the errors induced in the commonly used DFT method at offnominal frequency inputs. First, a comprehensive derivation of magnitude and phase-angle measurement errors of discrete Fourier transform (DFT) is proposed. It is indicated that the errors are caused by modulations between different exponential components in the signal, and can be modeled by quasisinusoids with frequencies equal to the frequency differences between modulated components. SWAM is then introduced to eliminate the errors by examining the analytic form of the errors. Simulation tests have been performed on several benchmark signals. Simulation cases have validated that SWAM achieves higher accuracy compared with the DFT-based method and the three-sample average filter method. Experimental tests were also performed to validate the accuracy of the proposed method. Due to its high accuracy and reasonably low processing effort, SWAM is a valuable candidate for online phasor measurement in power systems.

A new method for arcing fault location using discrete wavelet transform and wavelet networks

SUMMARYThis paper presents a new method for arcing (transient) fault location by combining discrete wavelet transform (DWT) and wavelet networks (WNs). The single‐end relaying point voltage and current waveforms (captured with a sampling rate of 2.5 kHz) are de‐noised by DWT to obtain a higher signal‐to‐noise ratio. The feature vectors contain the magnitudes of the three phase post‐fault voltage and current fundamental frequency phasors obtained by DWT. The feature vectors for different arcing fault conditions are applied to WN for training and testing purposes. Although the prime aim of the proposed method is arcing fault location, it can also be applied for permanent faults. The accuracy of the proposed method has been tested and verified under various fault conditions on a 400 kV overhead line using the Electro‐Magnetic Transient Program (EMTP) software package. Performance of the new method has also been compared with several existing methods under similar fault conditions, and the test results show better accuracy of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

Accurate Noniterative Fault-Location Algorithm Utilizing Two-End Unsynchronized Measurements

This paper presents a new two-terminal impedance-based fault-location algorithm, which takes into account the distributed parameter line model. The algorithm utilizes unsynchronized measurements of voltages and currents from two ends of a line and is formulated in terms of the fundamental frequency phasors of symmetrical components of the measured signals. First, an analytical synchronization of the unsynchronized measurements is performed with use of the determined synchronization operator. Then, the distance to fault is calculated as for the synchronized measurements. Simultaneous usage of two kinds of symmetrical components for determining the synchronization operator makes that the calculations are simple, noniterative, and at the same time highly accurate. The developed fault-location algorithm has been thoroughly tested using signals of Alternate Transients Program-Electromagnetic Transients Program versatile simulations of faults on a transmission line. The presented evaluation shows the validity of the developed fault-location algorithm and its high accuracy.

A Novel Algorithm for Locating Faults on Transposed/Untransposed Transmission Lines Without Utilizing Line Parameters

This paper puts forward a novel algorithm for locating faults on power transmission lines without requiring line parameters. The algorithm utilizes unsynchronized measurements of voltages and currents from both ends of a transmission line and is formulated in terms of the fundamental frequency phasors of the measured signals. Both prefault and postfault phasors are processed for determining the sought distance to fault and the synchronization angle. The calculations are performed initially for a lumped parameter line model with neglecting shunt capacitance. Then, these results are used as starting values for an iterative process, where the impacts of the shunt capacitance of the line are considered. The proposed two-stage fault-location algorithm is applicable for transposed and untransposed transmission lines and is independent of the fault resistance and source impedances. Evaluation studies using reliable Alternate Transients Program-Electromagentic Transients Program simulation data verify that the proposed algorithm can yield quite accurate results.