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Synchrophasor Estimators Accuracy: A Comparative Analysis

The real-time high-accuracy measurement of waveform phasors is one of the many open challenges that need to be addressed in future smart grids. In this paper, the accuracy of four recently proposed synchrophasor estimators is analyzed and compared with the well-known one-cycle discrete Fourier transform estimator under the effect of static frequency offsets, amplitude modulation, phase modulation, harmonic distortion, and wideband noise. Two of the considered techniques track the phasor variations through finite-difference equations that estimate the first- and second-order derivatives of the phasor itself. The other two methods are instead based on a least squares estimation of the coefficients of the phasor Taylors series expansion. The analysis reported in this paper covers the main scenarios described in the Standard IEEE C37.118.1-2011. In particular, the influence of different signal parameters on the total vector error (TVE) values is quantified and used to determine the maximum TVE increments associated with distinct parameters and the corresponding upper bounds.

Performance of Synchrophasor Estimators in Transient Conditions: A Comparative Analysis

Transient amplitude or phase changes in current or voltage waveforms may seriously affect synchrophasor estimators accuracy and responsiveness. The IEEE Standard C37.118.1-2011 specifies test conditions as well as accuracy and response delay limits for different types of disturbances. In this paper, the performances of three state-of-the-art techniques based on phasor Taylors series expansion specifically conceived to track phasors in dynamic conditions are analyzed and compared with the one-cycle discrete Fourier transform estimator under the effect of amplitude step changes, phase step changes, and linear frequency variations. Several simulation results show that the total vector error (TVE) tends to increase linearly with the step size. However, the peak TVE increments for a given step size are quite similar for all the considered techniques and are dominated by amplitude or phase errors, depending on whether the step affects the waveform amplitude or its phase, respectively. In this paper, the response times of the considered estimators for two different TVE thresholds are also analyzed and compared as a function of the step size, to assess their compliance to the requirements of the standard. Further simulation results show that in the case of linear frequency variations, responsiveness is not an issue and the TVE values of all estimators lie within the same worst case boundaries as those related to the case of static off-nominal frequency offsets.

Bayesian linear state estimation using smart meters and PMUs measurements in distribution grids

In this work we address the problem of static state estimation (SE) in distribution grids by leveraging historical meter data (pseudo-measurements) with real-time measurements from synchrophasors (PMU data). We present a Bayesian linear estimator based on a linear approximation of the power flow equations for distribution networks, which is computationally more efficient than standard nonlinear weighted least squares (WLS) estimators. We show via numerical simulations that the proposed strategy performs similarly to the standard WLS estimator on a small distribution network. A key advantage of the proposed approach is that it provides explicit off-line computation of the estimation error confidence intervals, which we use to explore the tradeoffs between number of PMUs, PMU placement and measurement uncertainty. Since the estimation error in distribution systems tends to be dominated by uncertainty in loads and scarcity of instrumented nodes, the linearized method along with the use of high-precision PMUs may be a suitable way to facilitate on-line state estimation where it was previously impractical.

Distribution network topology detection with time-series measurements

This paper proposes a novel approach to detecting the topology of distribution networks based on the analysis of time series measurements. The analysis approach draws on data from high-precision phasor measurement units (PMUs or synchrophasors) for distribution systems. A key fact is that time-series data taken from a dynamic system show specific patterns regarding state transitions such as opening or closing switches, as a kind of signature from each topology change. The algorithm proposed here is based on the comparison of the actual signature of a recent state transition against a library of signatures derived from topology simulations. The IEEE 33-bus model is used for initial algorithm validation.

Design criteria of digital filters for synchrophasor estimation

In the near future electrical waveforms in power networks are expected to exhibit strong amplitude and phase fluctuations caused by dynamic network topology changes and variable energy flows between loads and generators. Such fluctuations need to be constantly and accurately monitored both to optimize energy distribution and for safety and protection reasons. Nowadays, this task is typically accomplished by the so called Phasor Measurement Units (PMU), which measure the phasor of voltage and current waveforms on a common timescale synchronized to the Coordinated Universal Time (UTC). One of the most typical techniques for phasor estimation is based on digital down-conversion and filtering. This approach, although not explicitly recommended, is described in Annex C of Standard IEEE C37.118.1-2011, namely one of the main reference document for synchrophasor measurement in power systems. The same standard also reports two possible examples of filters for P-class and M-class phasor estimation. However, no specific filter design methods are provided. In this paper some guidelines for filter design are proposed on the basis of a model describing the behavior of a power waveform in both static and dynamic conditions. The reported design criteria are supported by some simulation results.

Accuracy of one-cycle DFT-based synchrophasor estimators in steady-state and dynamic conditions

The real-time, high-accuracy measurement of electrical waveform phasors is one of the many open challenges that need to be tackled in future smart grids. In this paper, the accuracy of three well-known synchrophasor estimators based on the single-cycle Discrete Fourier Transform (DFT) is evaluated under the effect of static frequency offsets, amplitude modulation and phase modulation. Compared with other research works dealing with the same topic, in this paper phasor estimation accuracy is assessed exhaustively, by varying multiple model parameters at the same time in order to determine the maximum (and minimum) Total Error Vector (TVE) values. This approach leads to a fair performance comparison between the considered techniques.

On the Accuracy of Phasor Angle Measurements in Power Networks

As known, phasor measurement units (PMUs) greatly enhance smart grid monitoring capabilities with advantageous impacts on power network management. Generally, PMUs accuracy is expressed in terms of total vector error, which comprises the joint effect of both angle and magnitude errors, thus possibly concealing the algorithm ability to measure phase. Some recent research works emphasize the importance of measuring current or voltage phasor angle with high accuracy (in the order of a few milliradians) at the distribution level. Because this issue is seldom considered in the literature, in this paper the phase measurement accuracy of three algorithms, namely the basic DFT, the windowed Taylor-Fourier filter, and the interpolated dynamic DFT (IpD2 FT) estimator, is extensively analyzed by means of simulations performed in various conditions described in the Standards IEEE C37.118.1:2011 and EN 50160:2010. In addition, some meaningful considerations about the uncertainty contributions due to imperfect synchronization are reported.

On the Role of Phasor Measurement Units for Distribution System State Estimation

The Phasor Measurement Units (PMUs) are currently considered among the most useful instruments for future smart grid monitoring, due to their ability to measure with great accuracy both magnitude and phase of voltages or currents synchronized to the Coordinated Universal Time (UTC). In this paper, the role of PMUs and their impact on distribution system state estimation (DSSE) are reviewed and analyzed in a meaningful case study via numerical simulations. The reported results confirm that a limited number of PMUs can considerably improve the accuracy of state estimation based on the Weighted Least Squares (WLS) approach. However, this improvement seems to plateau when more than about 1/3 of grid nodes or branches are instrumented with PMUs, regardless of the placement sequence. When some state variables (i.e. voltage magnitudes and phases) are measured directly, the overall average estimation uncertainty is approximately a linear function of PMU accuracy, with a trend which is quite independent on the number of instruments. A more in-depth analysis of this behavior could be exploited to minimize the overall deployment expenses for a given state estimation uncertainty, once the relationship between PMU unit cost and accuracy is available.

Impact of Acquisition Wideband Noise on Synchrophasor Measurements: A Design Perspective

Next-generation phasor measurement units (PMU) are expected to be more accurate than existing ones, especially to address the stricter requirements of future active distribution grids. From this perspective, the influence of acquisition wideband noise (which includes multiple contributions both in amplitude and in phase) has to be carefully evaluated. In this context, the contribution of this paper is twofold. First, it provides a general framework to evaluate the effect of wideband noise on synchrophasor amplitude, phase, frequency, and rate of change of frequency (ROCOF) estimation. The results of this analysis show that the influence of wideband noise can become critical for compliance with the requirements reported in the IEEE standards C37.118.1-2011 and C37.118.1a-2014, especially for frequency and ROCOF estimation. In addition, this paper reports general guidelines to choose the PMU effective resolution and sampling rate for which the impact of wideband noise on both P Class and M Class PMUs is negligible.

Effect of transient conditions on DFT-based synchrophasor estimator performance

Transient amplitude or phase changes in current or voltage waveforms may seriously influence synchrophasor estimators accuracy and responsiveness. The recently released IEEE standard C37.118.1-2011 specifies test conditions as well as accuracy and response delay limits for different types of disturbances. In this paper the performances of three state-of-the-art phasor estimators are analyzed and compared in depth under the effect of magnitude step changes, phase step changes and linear frequency variations. Several simulation results show that in all cases the total vector error (TVE) tends to increase linearly with the magnitude of the step (either in amplitude or in phase). This trend is confirmed even when the waveform frequency is off-nominal, provided that the step is large enough. Moreover, the estimators including the phasor derivatives are generally characterized by longer response time than the basic DFT since the step perturbation affects two or three consecutive one-cycle observation intervals. When linear frequency increments occur, the TVE values of all the considered estimators lie within the same boundaries determined for static off-nominal frequency offsets. Therefore, the considerations on estimator accuracy are the same as in the static case.