Phasor Measurement Units Algorithms Research Articles

A Low-Cost Test Platform for Performance Analysis of Phasor Measurement Units

In this paper, a customizable low-cost voltage waveform generator based on a real-time desktop PC and embedded data acquisition card synchronized with Coordinated Universal Time (UTC) is presented. A software approach to phase-locked loop synchronization with an external Global Positioning System (GPS) pulse signal is utilized to achieve a time uncertainty of ±1μs. This avoids expensive hardware modules for synchronization and timing purposes, which are commonly presented in literature. Besides the application for controlling the test platform, our own phasor data concentrator (PDC) application is running concurrently on the host PC. The latter is used for collecting and comparing the syncrophasor data from the test platform against the syncrophasor data measured by phasor measurement units (PMUs) under the test. The paper describes all procedures for generating reference test signals. Numerous case studies were performed, and experimental results for steady-state compliance as well as frequency ramp and phase modulation tests for dynamic compliance are presented in detail. All tests confirm that customizable test platform meets the requirements of IEEE/IEC standards. Compared to other calibrators, the cost as well as the specifications and point-by-point concept of data processing makes the described test platform suitable for performance analysis of PMU algorithms implemented on various development boards.

Tracking power system events with accuracy-based PMU adaptive reporting rate

Fast dynamics and transient events are becoming more and more frequent in power systems, due to the high penetration of renewable energy sources and the consequent lack of inertia. In this scenario, Phasor Measurement Units (PMUs) are expected to track the monitored quantities. Such functionality is related not only to the PMU accuracy (as per the IEC/IEEE 60255-118-1 standard) but also to the PMU reporting rate (RR). High RRs allow tracking fast dynamics, but produce many redundant measurement data in normal conditions. In view of an effective tradeoff, the present paper proposes an adaptive RR mechanism based on a real-time selection of the measurements, with the target of preserving the information content while reducing the data rate. The proposed method has been tested considering real-world datasets and applied to four different PMU algorithms. The results prove the method effectiveness in reducing the average data throughput as well as its scalability at PMU concentrator or storage level.

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

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

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

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

Comparative Study of Phasor and Frequency Estimation Algorithms for Distribution Networks

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

An integrated PMU architecture for power system applications

Abstract Time synchronized phasors obtained using Phasor Measurement Units (PMU) spread across wide areas have revolutionized power system monitoring and control. These synchronized measurements must be accurate and fast in order to comply with the latest IEEE standards for synchrophasor measurements. The speed at which a PMU provides an output depends on the group delay associated with that PMU and the permissible group delay in-turn decides the utility of a PMU for either control or measurement application. Based on the group delay compensation techniques, in the literature, two individual types of PMUs, such as causal and non-causal PMUs have been introduced. This paper presents an approach where both causal and non-causal PMUs are combined in an integrated PMU architecture. This method not only illustrates the group delay performance of two PMUs in a single module, but also can be used for multiple functions. In this environment several PMU algorithms have been compared with respect to their group delays and their effect on the response time. Application of the integrated PMU architecture to a four-machine 10-bus power system has been demonstrated using a six-input PMU with three-phase voltage and current signals as inputs. Different causal compensation schemes are introduced due to the availability of voltage and current-based frequency and ROCOF signals. Impact of these compensation schemes on PMU accuracy is evaluated through the Total Vector Error (TVE) index. The influence of these compensation schemes on measurements like power and impedance is also investigated. Finally, outputs from the integrated PMU architecture are fed into a Power System Stabilizer (PSS) to control the small-signal stability performance of a power system during dynamic conditions.

An Optimized Subspace-Based Approach to Synchrophasor Estimation

We present two improvements to the subspace-based phasor measurement unit (PMU) algorithms based on ESPRIT frequency estimation. The first is a dynamic, real-time thresholding method to determine the size of the signal subspace. This allows for accurate ESPRIT-based frequency estimates of the nominal system frequency and the frequencies of any out-of-band interference or harmonic frequencies. Since other frequencies are included in the least squares (LS) estimate, the interference from frequencies other than nominal can be excluded. This results in a near flat estimation error over changes in: 1) nominal system frequency; 2) harmonic distortion; and 3) out-of-band interference. We also reduce the computational burden of ESPRIT and demonstrate the proposed algorithm running in real time on resource-constrained platforms. The accuracy of this algorithm is evaluated using the IEEE standard for synchrophasor estimation, IEC/IEEE 60255-118-1, and compared with another state-of-the-art PMU algorithm.

Low cost, flexible, and distribution level universal grid analyser platform: designs and implementations

This study presents the designs and implementations of a distribution level open-universal grid analyser (Open-UGA) platform. The proposed Open-UGA platform consists of distribution-level phasor measurement units (PMUs), a standard signal generator, a router, and a server. Firstly, an overall introduction for the software, hardware, and server architectures of the Open-UGA platform is given. To give a detailed design, the software, hardware, server block diagrams, flowcharts, and printed circuit board photo of the Open-UGA platform are presented in detail. Then, four different types of distribution level PMU algorithms are introduced and implemented in the Open-UGA platform to verify the flexibility and reconfigurability. The flowcharts and functionalities of these four UGAs with different PMU algorithms are given as example implementations. Finally, a performance comparison is conducted with both quantitative and illustrative results.

A Phasor Measurement Unit Algorithm Using IIR Filters for FPGA Implementation

Phasor measurement units (PMU) are increasingly used in electrical power transmission networks, to maintain stability and protect the network. PMUs accurately measure voltage, phase, frequency, and rate of change of frequency (ROCOF). For reliability, it is desirable to implement a PMU using an FPGA. This paper describes a novel algorithm, suited to implementation in an FPGA and based on a simple PMU block diagram. A description of its realization using low hardware complexity infinite impulse response (IIR) filters is given. The IEC/IEEE standard 60255-118-1:2018 Part 118-1: Synchrophasor measurements for power systems, describes “reference” Finite Impulse Response (FIR) filters for implementing PMU hardware. At the 10 kHz sampling frequency used for our implementation, each “reference” FIR filter requires 100 multipliers, while an 8th order IIR filter only requires 12 multipliers. This paper compares the performance of different order IIR filter-based PMUs with the performance of the same PMU algorithm using the IEC/IEEE FIR reference filter. The IIR-based PMU easily satisfies all the requirements of IEC/IEEE standard and has a much better out of band signal rejection performance than a FIR-based PMU. Steady state errors for a rated voltage ± 10% and a rated frequency ± 5 Hz are < 0.000001% for total vector error (TVE) and < 1 µHz for frequency, with a latency of two mains cycles.

An adaptive filters based PMU algorithm for both steady-state and dynamic conditions in distribution networks

Although synchronized phasor measurement unit (PMU) technology is widely applied in transmission networks, conventional PMU algorithms suffer from new challenges (e.g. large frequency deviation, multiple interferences and dynamic behaviors, etc.) if directly applied to distribution networks. On the basis of predecessors' research, this paper presents a comprehensive PMU algorithm, using adaptive filters to simultaneously satisfy the high-precision and dynamic-response requirements of phasor estimation in distribution networks. In this algorithm, out-of-band (OOB) interferences that are difficult to be filtered out, are specifically considered in both steady-state and dynamic signal modelling processes. Based on the models, a finite impulse response (FIR) filter and a Taylor–Fourier transform (TFT) filter that both contains notches at the OOB interferences are elaborately designed and implemented in two parallel channels. With the support of a super-resolution frequency analysis method for signal components, the filters’ central frequency and notches’ position can be online adaptively adjusted. Finally, the outputs are switched between the two-channel estimations according to a designed transient recognition strategy. Test results in IEEE standard scenarios and some other realistic but severe scenarios demonstrate the effectiveness and reliability of this proposed algorithm.

PMU Multilevel End-to-End Testing to Assess Synchrophasor Measurements During Faults

This paper introduces a framework for comprehensive testing and evaluation of the phasor measurement units (PMUs) and synchrophasor systems under normal power system operating conditions, as well as during disturbances such as faults. The evaluation is suggested to be accomplished using three different testing approaches, namely, type testing, application testing, and end-to-end testing, for each of which, systematic characterization of the hardware and software modules is presented in detail. Through the proposed approach of PMU testing in a controlled environment and detailed analysis of different estimation techniques used in PMU algorithms, one can gain insights on which estimation technique is most accurate for a certain end-use application. This hypothesis has been validated through series of realistic test scenarios on a 23-bus system running on an Opal Real Time simulator using the hardware-in-the-loop interface. In addition, the impact of synchrophasor estimation errors and their propagation from the PMU toward the end-use applications has been quantified for a fault location algorithm that uses only PMU measurements.

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.

A Novel Method for Screening the PMU Phase Angle Difference Data Based on Hyperplane Clustering

Compared with the traditional supervisory control and data acquisition (SCADA) data, phasor measurement unit (PMU) data is characterized by phase angle measurement and high reporting speed (perhaps 100 Hz). The high reporting speed provides dynamic characteristics of the power system frequency, voltage, and current measurement. PMUs have become one of the important data sources for smart grid monitoring. PMU/WAMS (wide area measurement system) based advanced applications have been widely used in the dispatch centers. Some of the applications, such as line parameter identification and state estimation, depend not only on phase angle data but also on phase angle difference between different locations. Field data can suffer from errors, such as time synchronization error, transducer error, PMU algorithm error, hardware error or malicious attacks, etc. A time synchronization error can directly cause an error in the phase angle difference calculated between the two ends of a transmission line that could degrade a PMU based application. In this paper, a novel method to cluster the phase angle difference data, assess the data quality and screen out the bad PMU phase angle difference data is proposed. First, we develop the hyperplane cluster method to cluster the phase angle difference data. Second, in order to screen out the right data type, this paper compares the virtual reactance parameters of each data type obtained by voltage mean to the line reactance parameter given by the system model. Finally, the performance of the proposed methods has been verified by a simulation. The efficiency of the proposed method has been analyzed. The application of the proposed method using field measured PMU data shows the engineering practicability of the proposed method. In addition, the comparison of the proposed method with other clustering methods is discussed.

Experimental Quantification of Hardware Requirements for FPGA-Based Reconfigurable PMUs

Phasor Measurement Units (PMUs) are becoming intrinsic components of modern power systems. The synchrophasor estimation algorithms in PMUs pose stringent computational demands, which makes the application of Field Programmable Gate Arrays (FPGA) highly attractive. Previous works reported the implementation of PMU algorithms on specific FPGA-targets using a particular PMU design. This paper explores the implementation of different PMU designs on multiple FPGA targets using Xilinx and NI software and hardware infrastructures and toolsets. In this process, a metric has been formulated to predict FPGA-target hardware requirements. The metric allows predicting if an FPGA-target meets the needs to deploy a given PMU design resulting in significant engineering design time savings. Since the compilation/synthesis on FPGAs is a time-consuming job, this metric can reduce the implementation time for FPGA-based PMUs drastically and can help in determining if additional functionalities can be added.

Effect of Unbalance on Positive-Sequence Synchrophasor, Frequency, and ROCOF Estimations

Phasor measurement units (PMUs) are the measurement devices fostering the transformation of electric power networks towards the smart grid paradigm. They should accurately measure synchrophasors, frequency, and rate of change of frequency (ROCOF), so that the management and control applications relying on PMU-based distributed monitoring systems can operate effectively. Commercial PMUs performance is typically guaranteed by the compliance with the IEEE standard C37.118.1, which is focused on PMUs for power transmission systems and defines testing conditions and error limits. However, actual operating conditions are much more variable than those covered by the standard, especially when PMUs are used in distribution networks. In particular, the standard does not consider unbalance, which may be negligible neither in transmission nor in distribution grids. For the first time, this paper analyzes the impact of unbalance on the accuracy of four of the most significant classes of signal processing algorithms for PMU measurements. Synchrophasor, frequency, and ROCOF estimation performances under different unbalance conditions are investigated in the test cases suggested by the IEEE C37.242-2013 guide. Novel analytic expressions to predict the errors are derived and validated, and they are proved to be useful for an effective implementation of PMU algorithms intended for both distribution and transmission systems.

Impact of Causality on Performance of Phasor Measurement Unit Algorithms

Most existing phasor measurement units (PMUs) are noncausal PMUs and they compensate for the group delay in PMU applications by shifting time stamps, which may result in high latency that will impair performance of PMU applications. This paper presents causal PMUs to reduce the group delay caused latency without shifting time stamps, and studies the impact of causality on performance of PMU algorithms. The paper first analyzes how causal and noncausal PMUs compensate for the group delay caused by digital filters and it is found that causal PMUs normally reduce latency by the group delay, whereas noncausal PMU will not. Then, the impact of causality on performance of PMU algorithms is investigated and analyzed by using the Hydro Quebec Research Institute (IREQ) PMU model and the IEEE PMU model. Finally, the simulation results carried out on two test systems highlight the difference between the causal method and the noncausal method under fault conditions in realistic multimachine setups.

Dynamic Phasor Estimation Through DSTKF Under Transient Conditions

This paper presents a double suboptimal-scaling-factor adaptive strong tracking Kalman filter (DSTKF)-based phasor measurement unit algorithm which can meet the accuracy requirement of the IEEE standard C37.118.1 under the dynamic condition. This method uses a $k$ th Taylor polynomial to linearize the complex exponential of the signal model, and estimates the dynamic phasor using DSTKF. The antialias filter unit for DSTKF algorithm is included to suppress high-order harmonics which will augment computing burden. By applying double suboptimal-scaling factors, DSTKF adjusts the process noise covariance matrix and the prediction covariance matrix in real time. Thereafter, amplitude and frequency measurement performances under various dynamic conditions are assessed in detail. Theoretical analysis and comprehensive experimental results validate the effectiveness of the proposed method.

Design and Performance Prediction of Space Vector-Based PMU Algorithms

Phasor measurement units (PMUs) are expected to be the basis of modern power networks monitoring systems. They are conceived to allow measuring the phasor, frequency, and rate of change of frequency (ROCOF) of electrical signals in a synchronized way and with unprecedented accuracy. PMUs are intended to apply to three-phase systems and to track signal parameters evolution during network dynamics. For these reasons, the design of the algorithms and, in particular, of the filters that allow rejecting the disturbances while preserving the passband signal content is a paramount concern. In this paper, a novel space vector approach is proposed. It exploits the three-phase nature of the monitored signals together with proper lowpass and differentiation filters. Analytical formulas for performance prediction under almost all the test conditions prescribed by the synchrophasor standard C37.118.1 for PMUs, are introduced. The given expressions are extremely accurate, thus allowing to derive the filter design criteria for phasor, frequency, and ROCOF computation, so that the requirements in terms of estimation errors can be easily translated into filter specifications. The implications of the proposed approach in practical PMU design are illustrated by means of two simple design examples matching P and M compliance classes, respectively, for all the test cases of the standard. The reported performance proves the validity of the proposal.

Compressive Sensing of a Taylor-Fourier Multifrequency Model for Synchrophasor Estimation

Synchrophasor measurements, performed by phasor measurement units (PMUs), are becoming increasingly important for power system network monitoring. Synchrophasor standards define test signals for verification of PMU compliance, and set acceptance limits in each test condition for two performance classes ( $P$ and $M$ ). Several PMU algorithms have been proposed to deal with steady-state and dynamic operating conditions identified by the standard. Research and discussion arising from design, implementation, testing and characterization of PMUs evidenced that some disturbances, such as interharmonic interfering signals, can seriously degrade synchrophasor measurement accuracy. In this paper, a new compressive sensing (CS) approach is introduced and applied to synchrophasor measurements using a CS Taylor–Fourier (TF) multifrequency (CSTFM) model. The aim is to exploit, in a joint method, the properties of CS and the TF transform to identify the most relevant components of the signal, even under dynamic conditions, and to model them in the estimation procedure, thus limiting the impact of harmonic and interhamonic interferences. The CSTFM approach is verified using composite tests derived from the test conditions of the synchrophasor standard and simulation results are presented to show its potentialities.

Filter Design Masks for C37.118.1a-Compliant Frequency-Tracking and Fixed-Filter M-Class Phasor Measurement Units

The new amendment to the phasor measurement unit (PMU) standard C37.118.1a makes several significant changes compared with the standard C37.118.1 (2011). This paper highlights some of the most important changes, with a particular emphasis applied to how those changes relate to the way that an M-class PMU filter needs to be designed. In particular, there is a delicate tradeoff between passband flatness (the bandwidth test) and stopband rejection in the out-of-band (OOB) test. For a PMU algorithm using frequency-tracking and adaptive filters, it is shown that passband flatness can be relaxed to about 2.5 dB, but that the stopband needs to begin up to 14.8% closer to 0 Hz than for a fixed-filter PMU. This is partly due to the exact procedures of the C37.118.1a OOB testing and partly due to the adaptive nature of a frequency-tracking PMU filter section. Both the above lead to modified filter masks being required for frequency-tracking devices compared with the mask required for fixed-filter devices. The M-class PMU with a reporting rate of 25 Hz is the most difficult to design, for reasons given in this paper. The validity of the masks is shown using filter Bode plots and simulated C37.118.1a test results of a fixed-filter and frequency-tracking device, which have been designed to meet the masks defined in this paper.