Artykuły w czasopismach: „Phasor Estimation Algorithms”

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Zhao, Dongfang, Fuping Wang, Shisong Li, Wei Zhao, Lei Chen, Songling Huang, Shen Wang i Haitao Li. "An Optimization of Least-Square Harmonic Phasor Estimators in Presence of Multi-Interference and Harmonic Frequency Variance". Energies 16, nr 8 (12.04.2023): 3397. http://dx.doi.org/10.3390/en16083397.

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The wide application of power electronic devices brings an increasing amount of undesired harmonic and interharmonic tones, and accurate harmonic phasor estimation under a complex signal input is an important task for smart grid applications. In this paper, an optimization of least-square dynamic harmonic phasor estimators, considering multi-interference and harmonic frequency variance, is proposed. A comprehensive error index (CEI) composed of the fundamental-leakage-led harmonic amplitude estimation error, harmonic mutual interference, out-of-band interference, and harmonic frequency deviation is employed. The largest CEI part of least-square algorithms using three different signal decomposition models is analyzed for the first time, and variables to reduce this error component are then introduced using singular value decomposition. With the CEI and defined variables, a minimum-error estimation of harmonic phasors under various interference and harmonic frequency change is discussed. Numerical tests are performed, and the test results show that after the proposed optimization is applied to least-square algorithms, the harmonic phasor estimation errors are considerably reduced, especially for low-order harmonics. We also show the possibility of choosing desired optimal phasor filter design by balancing the measurement accuracy and data latency. For example, when the window length is set to three nominal cycles, the proposed optimization can yield both good accuracy and fast measurement speed for estimating harmonic phasors under multi-interference and harmonic frequency variance.

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Chukkaluru, Sai Lakshmi, i Shaik Affijulla. "Review of Discrete Fourier Transform During Dynamic Phasor Estimation and the Design of Synchrophasor Units". ECTI Transactions on Electrical Engineering, Electronics, and Communications 21, nr 1 (28.02.2023): 248548. http://dx.doi.org/10.37936/ecti-eec.2023211.248548.

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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.

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Giotopoulos, Vasilis, i Georgios Korres. "Implementation of Phasor Measurement Unit Based on Phase-Locked Loop Techniques: A Comprehensive Review". Energies 16, nr 14 (18.07.2023): 5465. http://dx.doi.org/10.3390/en16145465.

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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.

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Tajdinian, Mohsen, Shahram Montaser Kouhsari, Kazem Mohseni i Mehdi Zareian Jahromi. "A novel method for decaying DC component removal with regard to frequency fluctuations". COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 35, nr 1 (4.01.2016): 270–88. http://dx.doi.org/10.1108/compel-01-2015-0009.

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Purpose – Decaying DC component has important effect on extracting the fundamental component phasor. It directly affects the precision of protective relaying algorithms which act based on fundamental frequency component. It can be noted that decaying DC component, harmonic components and off-nominal frequency conditions are the major issues which strongly effect phasor estimation. The paper aims to discuss these issues. Design/methodology/approach – This paper proposes a novel hybrid approach for fundamental phasor estimation in order to remove the decaying DC component using Hilbert Transform and Discrete Fourier Transform. Findings – The proposed method (PM) converges to the original value in one cycle in presence of harmonic components and off-nominal frequency condition. In addition, proposed algorithm is able to detect the frequency fluctuation. Thus, it is applicable for static and dynamic conditions. An extensive set of simulation results across static and dynamic validations demonstrated that the proposed approach has faster convergence and better precision than the present methods. In addition, during harmonic distortion and also frequency fluctuation, the PM provides a correct and reliable response. Originality/value – The PM can calculate the DC component exactly from fault current signals and can be used in digital protection algorithms for phasor estimation.

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Binek, Malgorzata, Andrzej Kanicki i Pawel Rozga. "Application of an Artificial Neural Network for Measurements of Synchrophasor Indicators in the Power System". Energies 14, nr 9 (30.04.2021): 2570. http://dx.doi.org/10.3390/en14092570.

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Dynamic phenomena in electric power systems require fast and accurate algorithms for processing signals. The processing results include synchrophasor parameters, e.g., varying amplitude, phase or frequency of sinusoidal voltage or current signals. This paper presents a novel estimation method of synchrophasor parameters that comply with the requirements of IEEE/IEC standards. The authors analyzed an algorithm for measuring the phasor magnitude by means of a selected artificial neural network (ANN), an algorithm for estimating the phasor phase and frequency that makes use of the zero-crossing method. The original components of the presented approach are: the method of the synchrophasor magnitude estimation by means of a suitably trained and applied radial basic function (RBF); the idea of using two algorithms operating simultaneously to estimate the synchrophasor magnitude, phase and frequency that apply identical calculation methods are different in that the first one filters the input signal using the FIR filter and the second one operates without any filter; and the algorithm calculating corrections of the phase shift between the input and output signal and the algorithm calculating corrections of the magnitude estimation. The error results obtained from the applied algorithms were compared with those of the quadrature filter method and the ones presented in literature, as well as with the permissible values of the errors. In all cases, these results were lower than the permissible values and at least equal to the values found in the literature.

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Olarte Dussán, Fredy Andrés, Carlos Eduardo Borda Zapata i Hernando Díaz Morales. "State Estimation-based Transmission line parameter identification". Ingeniería e Investigación 30, nr 1 (1.01.2010): 56–63. http://dx.doi.org/10.15446/ing.investig.v30n1.15208.

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This article presents two state-estimation-based algorithms for identifying transmission line parameters. The identification technique used simultaneous state-parameter estimation on an artificial power system composed of several copies of the same transmission line, using measurements at different points in time. The first algorithm used active and reactive power measurements at both ends of the line. The second method used synchronised phasor voltage and current measurements at both ends. The algorithms were tested in simulated conditions on the 30-node IEEE test system. All line parameters for this system were estimated with errors below 1%.

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Frigo, Guglielmo, Paolo Attilio Pegoraro i Sergio Toscani. "Low-Latency, Three-Phase PMU Algorithms: Review and Performance Comparison". Applied Sciences 11, nr 5 (4.03.2021): 2261. http://dx.doi.org/10.3390/app11052261.

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Phasor Measurement Units are the most advanced instruments for power network monitoring, since they allow phasors, frequency and rate of change of frequency (ROCOF) to be measured in predetermined time instants with respect to an absolute time reference. The employed estimation algorithm plays a key role in overall performance under off-nominal conditions; the challenge to be faced is combining high steady-state accuracy with fast responsiveness in dynamic conditions, small reporting latency and reduced computational burden. Under regular operation, AC power networks are weakly unbalanced three-phase systems. Based on this consideration, the recent literature has proposed native three-phase estimation algorithms that effectively exploit this property to accurately identify the positive sequence synchrophasor, frequency and ROCOF. In this respect, the present paper describes three among the most promising three-phase algorithms based on the Space Vector transformation. By means of numerical simulations, it compares the achieved performance in terms of response time and estimation error both under steady-state and dynamic conditions. All the considered approaches enable a flexible design that allows balancing accuracy and responsiveness. For this analysis, the reporting latency has been limited to about one and half nominal cycles, i.e., 30 ms at 50 Hz; the P-class algorithm suggested by IEC/IEEE Std 60255-118-1 has also been included as comparison benchmark.

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Yang, Xuan, Xiao-Ping Zhang i Suyang Zhou. "Coordinated algorithms for distributed state estimation with synchronized phasor measurements". Applied Energy 96 (sierpień 2012): 253–60. http://dx.doi.org/10.1016/j.apenergy.2011.11.010.

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Silva, K. M., i F. A. O. Nascimento. "Modified DFT-Based Phasor Estimation Algorithms for Numerical Relaying Applications". IEEE Transactions on Power Delivery 33, nr 3 (czerwiec 2018): 1165–73. http://dx.doi.org/10.1109/tpwrd.2017.2738621.

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Macii, David, Daniel Belega i Dario Petri. "IpDFT-Tuned Estimation Algorithms for PMUs: Overview and Performance Comparison". Applied Sciences 11, nr 5 (5.03.2021): 2318. http://dx.doi.org/10.3390/app11052318.

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The Interpolated Discrete Fourier Transform (IpDFT) is one of the most popular algorithms for Phasor Measurement Units (PMUs), due to its quite low computational complexity and its good accuracy in various operating conditions. However, the basic IpDFT algorithm can be used also as a preliminary estimator of the amplitude, phase, frequency and rate of change of frequency of voltage or current AC waveforms at times synchronized to the Universal Coordinated Time (UTC). Indeed, another cascaded algorithm can be used to refine the waveform parameters estimation. In this context, the main novelty of this work is a fair and extensive performance comparison of three different state-of-the-art IpDFT-tuned estimation algorithms for PMUs. The three algorithms are: (i) the so-called corrected IpDFT (IpDFTc), which is conceived to compensate for the effect of both the image of the fundamental tone and second-order harmonic; (ii) a frequency-tuned version of the Taylor Weighted Least-Squares (TWLS) algorithm, and (iii) the frequency Down-Conversion and low-pass Filtering (DCF) technique described also in the IEEE/IEC Standard 60255-118-1:2018. The simulation results obtained in the P Class and M Class testing conditions specified in the same Standard show that the IpDFTc algorithm is generally preferable under the effect of steady-state disturbances. On the contrary, the tuned TWLS estimator is usually the best solution when dynamic changes of amplitude, phase or frequency occur. In transient conditions (i.e., under the effect of amplitude or phase steps), the IpDFTc and the tuned TWLS algorithms do not clearly outperform one another. The DCF approach generally returns the worst results. However, its actual performances heavily depend on the adopted low-pass filter.

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Abbaci, Mohamed, i Mohamed Ould Zmirli. "Cooley-Tukey FFT Algorithm based on GDFT for Phasor Estimation by PMU under Power Quality Disturbances". Engineering, Technology & Applied Science Research 13, nr 1 (5.02.2023): 9906–12. http://dx.doi.org/10.48084/etasr.5387.

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Due to the high penetration of renewable energy sources, such as photovoltaic panels and wind turbines, in addition to the use of different electric power supplies in the power grid, there are major disturbances in the forms of electric waves. These variations and disturbances must be monitored and controlled for the efficient management of transmission and distribution of electrical energy, safety, and electrical protection systems. Nowadays, Phasor Measurement Unit (PMU) technology is an essential tool to develop the supervision, protection, and control of the electrical power grid. PMUs measure the amplitude and angle of current and voltage waveforms on a Coordinated Universal Time (UTC) time scale and speedily measure the fundamental frequencies and their rates of change using fast and accurate estimation algorithms. This paper presents a phasor estimation using a Modified Cooley-Tukey Fast Fourier Transform algorithm based on the Generalized Discrete Fourier Transform (DFT) used in PMUs, using simulations in MATLAB. This algorithm was utilized to accelerate and simplify the computation of DFTs. To validate the performance under waveform disturbances, several tests with different waveforms and disturbances were simulated and interpreted according to the standard and compared with DFT.

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Lee, Kyung-Yong, Jung-Sung Park i Yun-Su Kim. "Optimal Placement of PMU to Enhance Supervised Learning-Based Pseudo-Measurement Modelling Accuracy in Distribution Network". Energies 14, nr 22 (19.11.2021): 7767. http://dx.doi.org/10.3390/en14227767.

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This paper introduces a framework for optimal placement (OP) of phasor measurement units (PMUs) using metaheuristic algorithms in a distribution network. The voltage magnitude and phase angle obtained from PMUs were selected as the input variables for supervised learning-based pseudo-measurement modeling that outputs the voltage magnitude and phase angle of the unmeasured buses. For three, four, and five PMU installations, the metaheuristic algorithms explored 2000 combinations, corresponding to 40.32%, 5.56%, and 0.99% of all placement combinations in the 33-bus system and 3.99%, 0.25%, and 0.02% in the 69-bus system, respectively. Two metaheuristic algorithms, a genetic algorithm and particle swarm optimization, were applied; the results of the techniques were compared to random search and brute-force algorithms. Subsequently, the effects of pseudo-measurements based on optimal PMU placement were verified by state estimation. The state estimation results were compared among the pseudo-measurements generated by the optimal PMU placement, worst PMU placement, and load profile (LP). State estimation results based on OP were superior to those of LP-based pseudo-measurements. However, when pseudo-measurements based on the worst placement were used as state variables, the results were inferior to those obtained using the LP.

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Silva, R. P. M., A. C. B. Delbem i D. V. Coury. "Genetic algorithms applied to phasor estimation and frequency tracking in PMU development". International Journal of Electrical Power & Energy Systems 44, nr 1 (styczeń 2013): 921–29. http://dx.doi.org/10.1016/j.ijepes.2012.07.070.

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Hua, Feng, Wengen Gao, Yunfei Li, Pengfei Hu i Lina Qiao. "Joint Detection and State Estimate with GSAs in PMU-Based Smart Grids". Energies 16, nr 15 (31.07.2023): 5731. http://dx.doi.org/10.3390/en16155731.

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The Phasor Measurement Unit (PMU) with a GPS signal receiver is a synchronized sensor widely used for power system state estimation. While the GPS receiver ensures time accuracy, it is vulnerable to network attacks. GPS spoofing attacks can alter the phase angle of PMU measurement signals and manipulate system states. This paper derives a power system state model based on PMUs under GPS spoofing attacks, according to the characteristics of changes in bus voltages and branch currents after GSA. Based on the characteristics of this model, a detection and correction algorithm for attacked data is proposed to detect GSA and correct attacked measurements. The corrected measurements can be used for power system state estimation. Simulation results on the IEEE 14-bus system show that the proposed algorithm improves the accuracy of state estimation under one or multiple GSAs, especially when multiple GSAs are present, compared to classical Weighted Least Squares Estimation (WLSE) and Alternating Minimization (AM) algorithms. Further research indicates that this algorithm is also applicable to large-scale networks.

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Guillen, Daniel, Christian Salas, Luis Fernando Sanchez-Gomez i Luis M. Castro. "Enhancement of dynamic phasor estimation-based fault location algorithms for AC transmission lines". IET Generation, Transmission & Distribution 14, nr 6 (27.03.2020): 1091–103. http://dx.doi.org/10.1049/iet-gtd.2019.0051.

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Thilakarathne, Chathura, Lasantha Meegahapola i Nuwantha Fernando. "Real-time voltage stability assessment using phasor measurement units: Influence of synchrophasor estimation algorithms". International Journal of Electrical Power & Energy Systems 119 (lipiec 2020): 105933. http://dx.doi.org/10.1016/j.ijepes.2020.105933.

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Kunac, Antonijo, Marin Despalatović i Dario Šantić. "Synchrophasors Determination Based on Interpolated FFT Algorithm". Journal of Energy - Energija 69, nr 1 (18.02.2020): 7–12. http://dx.doi.org/10.37798/202069133.

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Within the standard IEEE C37.118 applications and proposed hardware structure of a phasor measurement unit (PMU) are described. This paper presents the concept of the system for measuring and transferring synchrophasors from a theoretical aspect. Synchrophasor algorithms are developed in MATLAB/Simulink for the purpose of easier verification and hardware deployment on today’s market available and affordable real time development kits. Analysis of the synchrophasor measurement process is performed gradually. Firstly, by defining the synchrophasor based on three-phase to αβ-transformation and then introducing a discrete Fourier transform (DFT) based on synchrophasor estimation algorithm. Later, accompanying adverse effects resulting from its application are analyzed by means of simulation. To increase accuracy and improve estimation algorithm interpolated discrete Fourier transform (IpDFT) with and without windowing technique is used. To further optimize algorithm performance convolution sum in recursive form has been implemented instead of classical DFT approach. This study was carried out in order to validate described measurement system for the monitoring of transients during island operation of a local power electric system. Finally, simulation and experimental results including error analysis are also presented.

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Baba, Maveeya, Nursyarizal B. M. Nor, Taib B. Ibrahim i M. Aman Sheikh. "A comprehensive review for optimal placement of phasor measurement unit for network observability". Indonesian Journal of Electrical Engineering and Computer Science 19, nr 1 (1.07.2020): 301. http://dx.doi.org/10.11591/ijeecs.v19.i1.pp301-308.

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Real time synchronized phasor measurement in power network is obtained by the improvement in monitoring, control and, protection of the power system. In recent time, the installation ratio of Phasor Measurement Units (PMUs) is constantly increasing for the real time measurement throughout worldwide. The increment in the number of PMU installation is to only focus on the improvement of system state estimation (SE) performance. However, the expensive nature of the metering device requires huge amount of installation cost with the other communication facilities, therefore an optimal placement of PMU is necessary. Different techniques have been designed and used to overcome this matter. The paper presents numerous optimization algorithms such as, Mathematical programming, Heuristic, and Meta-Heuristic techniques which are specially used for the optimization of PMU placement with complete network observability. Furthermore, each PMU technique is explained, and performances are compared for the most appropriate and optimal placement of PMU methods, which can be recommended for a future work to get complete network observability.

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Senyuk, Mihail, Murodbek Safaraliev, Aminjon Gulakhmadov i Javod Ahyoev. "Application of the Conditional Optimization Method for the Synthesis of the Law of Emergency Control of a Synchronous Generator Steam Turbine Operating in a Complex-Closed Configuration Power System". Mathematics 10, nr 21 (26.10.2022): 3979. http://dx.doi.org/10.3390/math10213979.

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Stochastic renewable sources of energy have been causing changes in the structure and operation of power systems. High penetration of this type of generation results in decreased inertia of a power system, increased active power fluctuations, and a higher probability of false tripping of emergency control devices. Traditional algorithms of emergency control are not adaptable and flexible enough for systems with high penetration of renewables and flexible alternating current transmission systems. Integration and development of phasor measurement units make it possible to create adaptable emergency control systems, which would require minimal pre-defined data. The purpose of this study is to develop an adaptable algorithm of turbine fast valving control synthesis and transient stability estimation for a generator. The suggested algorithm is based on the equal area criterion in the domain synchronous generator Torque—Load angle. The measurements of the generator operation under consideration are used as the input data for the steam turbine fast valving control synthesis. Thus, the algorithm becomes adaptable because no pre-defined parameters of a power system model are required.

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Chen, Liang, Songlin Gu, Ying Wang, Yang Yang i Yang Li. "Stacked Autoencoder Framework of False Data Injection Attack Detection in Smart Grid". Mathematical Problems in Engineering 2021 (3.07.2021): 1–8. http://dx.doi.org/10.1155/2021/2014345.

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The advanced communication technology provides new monitoring and control strategies for smart grids. However, the application of information technology also increases the risk of malicious attacks. False data injection (FDI) is one kind of cyber attacks, which cannot be detected by bad data detection in state estimation. In this paper, a data-driven FDI attack detection framework of the smart grid with phasor measurement units (PMUs) is proposed. To enhance the detecting accuracy and efficiency, the multiple layer autoencoder algorithm is applied to abstract the hidden features of PMU measurements layer by layer in an unsupervised manner. Then, the features of the measurements and corresponding labels are taken as inputs to learn a softmax layer. Last, the autoencoder and softmax layer are stacked to form a FDI detection framework. The proposed method is applied on the IEEE 39-bus system, and the simulation results show that the FDI attacks can be detected with higher accuracy and computational efficiency compared with other artificial intelligence algorithms.

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Guo, Yufu, Hang Xu i Aobing Chi. "Broadband Dynamic Phasor Measurement Method for Harmonic Detection". Electronics 11, nr 11 (24.05.2022): 1667. http://dx.doi.org/10.3390/electronics11111667.

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A large number of nonlinear loads and distributed energy sources are connected to the power system, leading to the generation of broadband dynamic signals including inter-harmonics and decaying DC (DDC) components. This causes deterioration of power quality and errors during power measurement. Therefore, effective phasor estimation methods are needed for accurate monitoring and effective analysis of harmonics and interharmonic phasors. For this purpose, an algorithm is proposed in this paper that is implemented in two parts. The first part is based on the least square method in order to obtain accurate DDC component. In the second part, a Taylor–Fourier model of broadband dynamic harmonic phasor is established. The regularization optimization problem of the sparse acquisition model is solved by harmonic vector estimation method. Finally, the piecewise Split-Bregman Iterative (SBI) framework is used to obtain the estimated value of the harmonic phasor measurement and to realize the reconstruction of the original signal. Through simulation and performance test, the proposed algorithm significantly improves the accuracy of the phasor measurement and estimation, and can provide a reliable theoretical basis for the PMU measurement.

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Mejia-Barron, Arturo, David Granados-Lieberman, Jose Razo-Hernandez, Juan Amezquita-Sanchez i Martin Valtierra-Rodriguez. "Harmonic PMU Algorithm Based on Complex Filters and Instantaneous Single-Sideband Modulation". Electronics 8, nr 2 (29.01.2019): 135. http://dx.doi.org/10.3390/electronics8020135.

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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.

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Bonavolontà, Francesco, Luigi Pio Di Noia, Davide Lauria, Annalisa Liccardo i Salvatore Tessitore. "An Optimized HT-Based Method for the Analysis of Inter-Area Oscillations on Electrical Systems". Energies 12, nr 15 (31.07.2019): 2935. http://dx.doi.org/10.3390/en12152935.

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The paper deals with a novel method to measure inter-area oscillations, i.e., electromechanical oscillations involving groups of generators geographically distant from one another and ranging within the frequency interval from 0.1 Hz up to 1 Hz. The estimation of the parameters characterizing inter-area oscillations is a crucial objective in order to take the necessary actions to avoid the instability of the transmission electrical system. The proposed approach is a signal-based method, which uses samples of electrical signals acquired by the phasor measurement unit (PMU) and processes them to extract the individual oscillations and, for each of them, determine their characteristic parameters such as frequency and damping. The method is based on Hilbert transformations, but it is optimized through further algorithms aiming at (i) improving the ability to separate different oscillatory components, even at frequencies very close to each other, (ii) enhancing the accuracy associated with the damping estimates of each oscillation, and (iii) increasing the robustness to the noise affecting the acquired signal. Results obtained in the presence of signals involving the composition of two oscillations, whose damping and frequency have been varied, are presented. Tests were conducted with signals either synthesized in simulated experiment or generated and acquired with actual laboratory instrumentation.

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Priyadarshi, Alok, Vishal Rathore i Krishna Bihari Yadav. "Observability Enhancement of Smart Grid Based on Optimal Placement of PMUs". ECTI Transactions on Electrical Engineering, Electronics, and Communications 20, nr 3 (12.10.2022): 383–91. http://dx.doi.org/10.37936/ecti-eec.2022203.247514.

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This paper presents an efficient observation concerning the enhancement of smart grid (SG) based on the optimal placement of phasor measurement units (OPP) using nonlinear programming (NLP). The proposed algorithm tries to achieve two objectives: (i) to ascertain the minimum number of phasor measurement units (PMUs) and (ii) to increase the redundancy of the SG at all the buses. Synchronized current and voltage phasors are obtained to enhance the accuracy of the state estimation results—a minimum number of PMUs results in a lack of communication facilities at the substation. PMU losses will lead to unobservable buses at the SG. Therefore, PMU losses and communication constraints should be considered during the design process. Limited channel capacity, conventional measurement, and zero-injection bus measurements are also included in the proposed PMU formulation. The proposed algorithm is examined on IEEE~14-, 30-, 57-, 118-, and 300-bus test systems in MATLAB to verify its effectiveness. Furthermore, the results are compared with the simplex linear programming and mixed linear programming methods to prove the efficacy of the presented algorithm. The output thus obtained reveals that the NLP algorithm obtains approximately the same PMUs as other methods.

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Hussein, Husham. "State Estimation via Phasor Measurement Units for Iraqi National Super Grid Power System Network". Iraqi Journal for Electrical and Electronic Engineering 12, nr 1 (1.06.2016): 12–22. http://dx.doi.org/10.37917/ijeee.12.1.2.

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In this paper describes the operation of power system networks to be nearest to stability rated values limits. State estimation for monitoring and protection power system is very important because it provides a real-time (RT) Phase angle of different nodes of accuracy and then analysis and decided to choose control way (methods). In order to detect the exact situation (instant state) for power system networks parameters. In this paper proposes a new monitoring and analysis system state estimation method integrating with MATLAB environment ability, by using phasor measurement units (PMU's) technology, by this system the estimation problem, iterations numbers, and processing time will reduce. The measurements of phasors value of voltage signal and current estimated and analyzed. Mat lab/PSAT package use as a tool to design and simulate four electrical power systems networks such as INSG 24 buses, IEEE14 bus, Diyala city 10buses (IRAQ), and IEEE6 bus and then installed and applied PMU’s devices to each system. Simulation results show that the PMU's performances effectiveness appear clearly. All results show the validation of PMU’s devices as an estimator to power system networks states and a significant improvement in the accuracy of the calculation of network status. All results achieved and discussed through this paper setting up mathematical models with Graph Theoretic Procedure algorithm.

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Chi, Aobing, Chengbi Zeng, Yufu Guo i Hong Miao. "A Bregman-Split-Based Compressive Sensing Method for Dynamic Harmonic Estimation". Entropy 24, nr 7 (17.07.2022): 988. http://dx.doi.org/10.3390/e24070988.

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In order to overcome the spectral interference of the conventional Fourier transform in the International Electrotechnical Commission framework, this paper introduces a Bregman-split-based compressive sensing (BSCS) method to estimate the Taylor–Fourier coefficients in a multi-frequency dynamic phasor model. Considering the DDC component estimation, this paper transforms the phasor problem into a compressive sensing model based on the regularity and sparsity of the dynamic harmonic signal distribution. It then derives an optimized hybrid regularization algorithm with the Bregman split method to reconstruct the dynamic phasor estimation. The accuracy of the model was verified by using the cross entropy to measure the distribution differences of values. Composite tests derived from the dynamic phasor test conditions were then used to verify the potentialities of the BSCS method. Simulation results show that the algorithm can alleviate the impact of dynamic signals on phasor estimation and significantly improve the estimation accuracy, which provides a theoretical basis for P-class phasor measurement units (PMUs).

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Gholami, Mohammad, Ali Abbaspour Tehrani-Fard, Matti Lehtonen, Moein Moeini-Aghtaie i Mahmud Fotuhi-Firuzabad. "A Novel Multi-Area Distribution State Estimation Approach for Active Networks". Energies 14, nr 6 (23.03.2021): 1772. http://dx.doi.org/10.3390/en14061772.

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This paper presents a hierarchically distributed algorithm for the execution of distribution state estimation function in active networks equipped with some phasor measurement units. The proposed algorithm employs voltage-based state estimation in rectangular form and is well-designed for large-scale active distribution networks. For this purpose, as the first step, the distribution network is supposed to be divided into some overlapped zones and local state estimations are executed in parallel for extracting operating states of these zones. Then, using coordinators in the feeders and the substation, the estimated local voltage profiles of all zones are coordinated with the local state estimation results of their neighboring zones. In this regard, each coordinator runs a state estimation process for the border buses (overlapped buses and buses with tie-lines) of its zones and based on the results for voltage phasor of border buses, the local voltage profiles in non-border buses of its zones are modified. The performance of the proposed algorithm is tested with an active distribution network, considering different combinations of operating conditions, network topologies, network decompositions, and measurement scenarios, and the results are presented and discussed.

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Jafarpisheh, Babak, i Anamitra Pal. "A Robust Algorithm for Real-Time Phasor and Frequency Estimation under Diverse System Conditions". Energies 14, nr 21 (1.11.2021): 7112. http://dx.doi.org/10.3390/en14217112.

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This paper presents a comprehensive approach for performing phasor and frequency estimation from voltage and/or current signals of the modern power system. Undesirable components, such as decaying DC, if present in the input signal, are first attenuated using a complex-gain filter. The initial estimates of phasor and frequency are obtained next using the discrete Fourier transform and an improved estimation of signal parameters via rotational invariance technique, respectively. Finally, the accuracy of phasor and frequency estimates are increased based on the identified system condition. Simulations performed to evaluate the proposed approach confirm that it can do fast and accurate estimation of phasor and frequency under diverse operating conditions, making it ideal for wide-area monitoring, protection, and control applications in power systems.

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29

Zhou, Zhiguo, Ruliang Lin, Lifeng Wang, Yi Wang i Hansen Li. "Research on Discrete Fourier Transform-Based Phasor Measurement Algorithm for Distribution Network under High Frequency Sampling". Energies 11, nr 9 (23.08.2018): 2203. http://dx.doi.org/10.3390/en11092203.

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This paper proposes a phasor measurement algorithm that is suitable for a distribution network. Under the condition of fixed interval and high frequency sampling, the algorithm uses a dynamic calibration factor to correct the traditional Discrete Fourier Transform (DFT) algorithm, which solves the shortcomings of the rapid decline in traditional algorithm measurement accuracy under the condition of power system frequency deviation or dynamic measurement. Under the high sampling rate of the international distribution network waveform data, the conventional phasor is used to represent the theoretical phasor, and the value of the conventional phasor is compensated to make the result closer to the theoretical value. Finally, the phasor measurement software simulation platform is built in Matlab/Simulink, based on the principle of the algorithm, providing a simulation environment for researchers to verify the phasor measurement algorithm of the distribution network and the fault location, state estimation, or other advanced applications.

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30

Sidhu, T. S., X. Zhang i V. Balamourougan. "A New Half-Cycle Phasor Estimation Algorithm". IEEE Transactions on Power Delivery 20, nr 2 (kwiecień 2005): 1299–305. http://dx.doi.org/10.1109/tpwrd.2004.834677.

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Zhao, Dongfang, Shisong Li, Fuping Wang, Wei Zhao i Songling Huang. "Estimation of Wideband Multi-Component Phasors Considering Signal Damping". Sensors 23, nr 16 (10.08.2023): 7071. http://dx.doi.org/10.3390/s23167071.

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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.

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32

Kim, Nam i Kang. "Adaptive Phasor Estimation Algorithm Based on a Least Squares Method". Energies 12, nr 7 (10.04.2019): 1387. http://dx.doi.org/10.3390/en12071387.

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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.

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Khandelwal, Arpit, Ankush Tandon i Akash Saxena. "Power System State Estimation by Novel Approach of Kalman Filter". Indonesian Journal of Electrical Engineering and Computer Science 6, nr 2 (1.05.2017): 241. http://dx.doi.org/10.11591/ijeecs.v6.i2.pp241-253.

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<p>The electrical network measurements by measuring device Phasor Measurement Device (PMU) are usually sent to the control centers using data acquisition system and other communication protocols available. However, these measurements contain uncertainties due to the measurements and communication noise (errors), incomplete metering or unavailability of some of measurements. The overall aim of state estimation is to calculate the state variables of the power system by minimizing errors available at the control center. Due to generate desired quantities by optimal estimate which is given the set of measurements, Kalman filters are widely used. This paper discusses the application of an Extended Kalman Filter (EKF) algorithm, the Unscented Kalman Filter (UKF) algorithm, and New EKF+M and UKF+M estimator algorithm, those are modification of EKF and UKF for enhance accuracy and elapse time is less. The effectiveness and performance of EKF+M and UKF+M Estimator over another Filtration algorithm is shown. These state estimation techniques applied on IEEE-30 bus, 14 bus and 9 bus test system.</p>

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Rozgić, Dimitrije, i Predrag B. Petrović. "New Procedure for Estimation of Power Fundamental Phasor Parameters in Presence of Decaying DC Components". WSEAS TRANSACTIONS ON POWER SYSTEMS 17 (6.10.2022): 280–96. http://dx.doi.org/10.37394/232016.2022.17.29.

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The paper proposes new algorithm for estimation of the fundamental phasor in a power system, based on removal of exponentially decaying DC components (DDCs). These components, as well as high-order harmonics and noise components, have a considerable effect on accuracy and speed of convergence in numerical and digital relays – speed of the protection relay operation. A Discrete Fourier Transform (DFT) based approach with modified Prony method was used to calculate and remove the unwanted effect of DDCs in a time interval slightly longer than the period of the fundamental harmonics. The proposed procedure offers the possibility to estimate the parameters of unwanted DDCs in a simpler and analytically more precise way, thus facilitating its program implementation. The algorithm offers the ability to easily adjust the response speed - detection time. This flexibility of the algorithm provides a compromise in terms of response speed as well as expected reliability and security of fault detection. The developed procedure enables the monitoring of the very demanding dynamics of the current signal in short-circuit conditions, and thus the estimation of the phasor parameters of the energy signal so that the relay protection is able to respond to this emergency situation in the most adequate (adaptive) way - it becomes more precise and faster in its response. The algorithm has low numerical and computational complexity, while maintaining its high performances even in conditions of a very strong noise signal. The simulation results for different test signals demonstrate high precision in the estimation of fundamental phasor of the proposed algorithm.

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35

Li, Zengqin, Weifeng Zhang, Zhiyuan Zhuang i Tao Jin. "A Novel Synchrophasor Estimation Based on Enhanced All-Phase DFT with Iterative Compensation and Its Implementation". Energies 15, nr 19 (23.09.2022): 6964. http://dx.doi.org/10.3390/en15196964.

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Synchrophasor estimation was mostly used in transmission systems in the past, and it is difficult to directly apply an existing synchrophasor algorithm to a distribution system with a more complex structure and environment. A synchrophasor estimation algorithm with a high accuracy and fast response speed is required to complete the calculation of the phasor in the face of the complex and changeable power signal of a distribution network. Therefore, an enhanced all-phase discrete Fourier transform (e-apDFT) algorithm is proposed for a distribution system in this paper, and the algorithm is deployed in a phasor measurement unit (PMU) prototype based on digital signal processing (DSP). Aiming to solve the problem of the accuracy of the traditional apDFT being reduced when the response speed is fast due to the influence of a dense spectrum, the existing algorithm is improved through iteratively compensating the spectral interferences to the main bin produced by adjacent bins. The experimental results show that the e-apDFT algorithm still has a fast response speed and that its estimation accuracy is much better than that of the traditional apDFTs in the presence of adjacent harmonic components. The proposed algorithm also complies with the IEEE standards for P-class PMUs.

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36

Jafarpisheh, Babak, Seyed M. Madani i Siamak Jafarpisheh. "Improved DFT-Based Phasor Estimation Algorithm Using Down-Sampling". IEEE Transactions on Power Delivery 33, nr 6 (grudzień 2018): 3242–45. http://dx.doi.org/10.1109/tpwrd.2018.2831005.

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37

Silva, K. M., i B. F. Küsel. "DFT based phasor estimation algorithm for numerical digital relaying". Electronics Letters 49, nr 6 (marzec 2013): 412–14. http://dx.doi.org/10.1049/el.2012.3920.

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38

Mahari, Arash, Majid Sanaye-Pasand i Sayyed Mohammad Hashemi. "Adaptive phasor estimation algorithm to enhance numerical distance protection". IET Generation, Transmission & Distribution 11, nr 5 (30.03.2017): 1170–78. http://dx.doi.org/10.1049/iet-gtd.2016.0911.

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39

de Apráiz, Matilde, Ramón Diego i Julio Barros. "An Extended Kalman Filter Approach for Accurate Instantaneous Dynamic Phasor Estimation". Energies 11, nr 11 (26.10.2018): 2918. http://dx.doi.org/10.3390/en11112918.

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This paper proposes the application of a non-linear Extended Kalman Filter (EKF) for accurate instantaneous dynamic phasor estimation. An EKF-based algorithm is proposed to better adapt to the dynamic measurement requirements and to provide real-time tracking of the fundamental harmonic components and power system frequencies. This method is evaluated using dynamic compliance tests defined in the IEEE C37.118.1-2011 synchrophasor measurement standard, providing promising results in phasor and frequency estimation, compliant with the accuracy required in the case of off-nominal frequency, amplitude and phase angle modulations, frequency ramps, and step changes in magnitude and phase angle. An important additional feature of the method is its capability for real-time detection of transient disturbances in voltage or current waveforms using the residual of the filter, which enables flagging of the estimation for suitable processing.

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40

Kong, Wang, Yuan i Yu. "Multi Objective for PMU Placement in Compressed Distribution Network Considering Cost and Accuracy of State Estimation". Applied Sciences 9, nr 7 (11.04.2019): 1515. http://dx.doi.org/10.3390/app9071515.

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A phasor measurement unit (PMU) can provide phasor measurements to the distribution network to improve observability. Based on pre-configuration and existing measurements, a network compression method is proposed to reduce PMU candidate locations. Taking the minimum number of PMUs and the lowest state estimation error as the objective functions and taking full observability of distribution network as the constraint, a multi objective model of optimal PMU placement (OPP) is proposed. A hybrid state estimator based on supervisory control and data acquisition (SCADA) and PMU measurements is proposed. To reduce the number of PMUs required for full observability, SCADA measurement data are also considered into the constraint by update and equivalent. In addition, a non-dominated sorting genetic algorithm-II (NSGA-II) is applied to solve the model to get the Pareto set. Finally, the optimal solution is selected from the Pareto set by the technique for order preference by similarity to ideal solution (TOPSIS). The effectiveness of the proposed method is verified by IEEE standard bus systems.

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41

Messina, Francisco, Pablo Marchi, Leonardo Rey Vega i Cecilia G. Galarza. "A Self-Adaptive Contractive Algorithm for Enhanced Dynamic Phasor Estimation". IEEE Transactions on Smart Grid 11, nr 3 (maj 2020): 2367–80. http://dx.doi.org/10.1109/tsg.2019.2953583.

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42

Petrović, Predrag, i Nada Damljanović. "Dynamic Phasors Estimation Based on Taylor-Fourier Expansion and Gram Matrix Representation". Mathematical Problems in Engineering 2018 (26.11.2018): 1–17. http://dx.doi.org/10.1155/2018/7613814.

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The paper presents a new approach to estimation of the dynamic power phasors parameters. The observed system is modelled in algebra of matrices related to its Taylor-Fourier-trigonometric series representation. The proposed algorithm for determination of the unknown phasors parameters is based on the analytical expressions for elements of the Gram’s matrix associated with this system. The numerical complexity and algorithm time are determined and it is shown that new strategy for calculation of Gram’s matrix increases the accuracy of estimation, as well as the speed of the algorithm with respect to the classical way of introducing the Gram’s matrix. Several simulation examples of power system signals with a time-varying amplitude and phase parameters are given by which the robustness and accuracy of the new algorithm are confirmed.

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43

Matsukawa, Watanabe, Wahab i Othman. "Voltage Stability Index Calculation by Hybrid State Estimation based on Multi Objective Optimal Phasor Measurement Unit Placement". Energies 12, nr 14 (12.07.2019): 2688. http://dx.doi.org/10.3390/en12142688.

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Operation of a power system close to the voltage stability limit due to increasing of load demand and limited power sources may result in disastrous economic loss with voltage collapse of the entire power system. A system operator has to understand how far the system is from the critical boundary of the voltage collapse. This paper investigated the influence of State Estimation (SE) in the calculation of the Critical Boundary Index (CBI) as a voltage stability index. For SE, Hybrid State Estimation (HSE), including the measurement set of both Remote Terminal Unit (RTU) in Supervisory Control and Data Acquisition (SCADA) and Phasor Measurement Unit (PMU), is employed. Concurrently, the CBI is estimated using voltage phasor estimated by HSE based on optimal PMU location, which is selected from a Pareto optimal front obtained by the Non-dominated Sorting Genetic Algorithm II (NSGA-II). As a result of CBI estimation, HSE using PMU is relatively accurate in voltage stability index estimation compared to SCADA SE, which uses the RTU alone. However, when a mixed measurement condition in some lines affects the CBI estimation, it is suggested that it may be necessary to discard PMU measurements in some cases.

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Rajendra, K., S. Subramanian, N. Karthik, K. Naveenkumar i S. Ganesan. "State Estimation for Electric Power System with Load Uncertainty and False Data Using Cuckoo Search Algorithm". International Journal on Recent and Innovation Trends in Computing and Communication 11, nr 4s (5.05.2023): 209–14. http://dx.doi.org/10.17762/ijritcc.v11i4s.6530.

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State estimate serves a crucial purpose in the control centre of a modern power system. Voltage phasor of buses in such configurations is referred to as state variables that should be determined during operation. A precise estimation is needed to define the optimal operation of all components. So many mathematical and heuristic techniques can be used to achieve the aforementioned objective. An enhanced power system state estimator built on the cuckoo search algorithm is described in this work. Several scenarios, including the influence of load uncertainty and the likelihood of false data injection as significant challenges in electrical energy networks, are proposed to analyses the operation of estimators. The ability to identify and correct false data is also assessed in this regard. Additionally, the performance of the presented estimator is compared to that of the weighted least squares and Cuckoo Search algorithm. The findings demonstrate that the Cuckoo search algorithm overcomes the primary shortcomings of the conventional approaches, including accuracy and complexity, and is also better able to identify and rectify incorrect data. On IEEE 14-bus and 30-bus test systems, simulations are run to show how well the method works.

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Tang, Mingsheng, Huiming Zou, Hongbo Xu, Shuangquan Shao i Changqing Tian. "Stroke and natural frequency estimation for linear compressor using phasor algorithm". International Journal of Applied Electromagnetics and Mechanics 46, nr 4 (1.10.2014): 763–74. http://dx.doi.org/10.3233/jae-141972.

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Bi, Tianshu, Hao Liu, Qian Feng, Cheng Qian i Yilu Liu. "Dynamic Phasor Model-Based Synchrophasor Estimation Algorithm for M-Class PMU". IEEE Transactions on Power Delivery 30, nr 3 (czerwiec 2015): 1162–71. http://dx.doi.org/10.1109/tpwrd.2014.2353816.

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47

Terzija, V. V., M. B. Djuric i B. D. Kovacevic. "Voltage phasor and local system frequency estimation using Newton type algorithm". IEEE Transactions on Power Delivery 9, nr 3 (lipiec 1994): 1368–74. http://dx.doi.org/10.1109/61.311162.

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48

Jin, XiaNing, FuPing Wang i ZanJi Wang. "A dynamic phasor estimation algorithm based on angle-shifted energy operator". Science China Technological Sciences 56, nr 6 (4.05.2013): 1322–29. http://dx.doi.org/10.1007/s11431-013-5227-0.

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Chauhan, Kapil, Motakatla Venkateswara Reddy i Ranjana Sodhi. "A Novel Distribution-Level Phasor Estimation Algorithm Using Empirical Wavelet Transform". IEEE Transactions on Industrial Electronics 65, nr 10 (październik 2018): 7984–95. http://dx.doi.org/10.1109/tie.2018.2801837.

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Tosato, Pietro, David Macii, Mario Luiso, Davide Brunelli, Daniele Gallo i Carmine Landi. "A Tuned Lightweight Estimation Algorithm for Low-Cost Phasor Measurement Units". IEEE Transactions on Instrumentation and Measurement 67, nr 5 (maj 2018): 1047–57. http://dx.doi.org/10.1109/tim.2017.2775458.

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