PMU-Based ROCOF Measurements: Uncertainty Limits and Metrological Significance in Power System Applications

In modern power systems, the Rate-of-Change-of-Frequency (ROCOF) may be largely employed in Wide Area Monitoring, Protection and Control (WAMPAC) applications. However, a standard approach towards ROCOF measurements is still missing. In this paper, we investigate the feasibility of Phasor Measurement Units (PMUs) deployment in ROCOF-based applications, with a specific focus on Under-Frequency Load-Shedding (UFLS). For this analysis, we select three state-of-the-art window-based synchrophasor estimation algorithms and compare different signal models, ROCOF estimation techniques and window lengths in datasets inspired by real-world acquisitions. In this sense, we are able to carry out a sensitivity analysis of the behavior of a PMU-based UFLS control scheme. Based on the proposed results, PMUs prove to be accurate ROCOF meters, as long as the harmonic and inter-harmonic distortion within the measurement pass-bandwidth is scarce. In the presence of transient events, the synchrophasor model looses its appropriateness as the signal energy spreads over the entire spectrum and cannot be approximated as a sequence of narrow-band components. Finally, we validate the actual feasibility of PMU-based UFLS in a real-time simulated scenario where we compare two different ROCOF estimation techniques with a frequency-based control scheme and we show their impact on the successful grid restoration.Comment: Manuscript IM-18-20133R. Accepted for publication on IEEE Transactions on Instrumentation and Measurement (acceptance date: 9 March 2019

Compressive Sensing Applications in Measurement: Theoretical issues, algorithm characterization and implementation

At its core, signal acquisition is concerned with efficient algorithms and protocols capable to capture and encode the signal information content. For over five decades, the indisputable theoretical benchmark has been represented by the wellknown Shannon’s sampling theorem, and the corresponding notion of information has been indissolubly related to signal spectral bandwidth. The contemporary society is founded on almost instantaneous exchange of information, which is mainly conveyed in a digital format. Accordingly, modern communication devices are expected to cope with huge amounts of data, in a typical sequence of steps which comprise acquisition, processing and storage. Despite the continual technological progress, the conventional acquisition protocol has come under mounting pressure and requires a computational effort not related to the actual signal information content. In recent years, a novel sensing paradigm, also known as Compressive Sensing, briefly CS, is quickly spreading among several branches of Information Theory. It relies on two main principles: signal sparsity and incoherent sampling, and employs them to acquire the signal directly in a condensed form. The sampling rate is related to signal information rate, rather than to signal spectral bandwidth. Given a sparse signal, its information content can be recovered even fromwhat could appear to be an incomplete set of measurements, at the expense of a greater computational effort at reconstruction stage. My Ph.D. thesis builds on the field of Compressive Sensing and illustrates how sparsity and incoherence properties can be exploited to design efficient sensing strategies, or to intimately understand the sources of uncertainty that affect measurements. The research activity has dealtwith both theoretical and practical issues, inferred frommeasurement application contexts, ranging fromradio frequency communications to synchrophasor estimation and neurological activity investigation. The thesis is organised in four chapters whose key contributions include: • definition of a general mathematical model for sparse signal acquisition systems, with particular focus on sparsity and incoherence implications; • characterization of the main algorithmic families for recovering sparse signals from reduced set of measurements, with particular focus on the impact of additive noise; • implementation and experimental validation of a CS-based algorithmfor providing accurate preliminary information and suitably preprocessed data for a vector signal analyser or a cognitive radio application; • design and characterization of a CS-based super-resolution technique for spectral analysis in the discrete Fourier transform(DFT) domain; • definition of an overcomplete dictionary which explicitly account for spectral leakage effect; • insight into the so-called off-the-grid estimation approach, by properly combining CS-based super-resolution and DFT coefficients polar interpolation; • exploration and analysis of sparsity implications in quasi-stationary operative conditions, emphasizing the importance of time-varying sparse signal models; • definition of an enhanced spectral content model for spectral analysis applications in dynamic conditions by means of Taylor-Fourier transform (TFT) approaches

Fast Iterative-Interpolated DFT Phasor Estimator Considering Out-of-band Interference

For interpolated discrete Fourier transform (IpDFT)-based phasor estimators, the out-of-band interference (OOBI) test is among the most challenging ones. The typical iterative-interpolated DFT (i-IpDFT) phasor estimator utilizes a two-step iterative framework to eliminate the effects of the negative frequency and OOBI. However, the speed of estimation is limited by the adopted frequency estimator and the redundant iterations. To this end, this article proposes a fast i-IpDFT (FiIpDFT) method for the phasor estimation of an OOBI contaminated signal, which utilizes the three-point IpDFT (I3pDFT) technique. The proposed method first applies a noniterative frequency, amplitude, and phase estimator to eliminate the negative frequency interference. Then, a straightforward formula and two-stop criterion are introduced to reduce the computational burden of the OOBI elimination process. The accuracy and effectiveness of the proposed FiIpDFT method are validated by simulations. These are designed, under steady and dynamic conditions, according to the requirements of the Standard IEC/IEEE 60255-118-1

Impact of Estimation Uncertainty in PMU-Based Resynchronization of Continental Europe Synchronous Areas

Power system stability is a task that every system operator (SO) is required to achieve daily to ensure an uninterruptible power supply. Especially at the transmission level, for each SO it is of utmost importance to ensure proper exchange of information with other SOs, mainly in case of contingencies. However, in the last years, two major events led to the splitting of Continental Europe into two synchronous areas. These events were caused by anomalous conditions which involved in one case the fault of a transmission line and in the other a fire outage in proximity to high-voltage lines. This work analyzes these two events from the measurement point of view. In particular, we discuss the possible impact of estimation uncertainty on control decisions based on measurements of instantaneous frequency. For this purpose, we simulate five different configurations of phasor measurement units (PMUs), as characterized by different signal models, processing routines, and estimation accuracy in the presence of off-nominal or dynamic conditions. The objective is to establish the accuracy of the frequency estimates in transient conditions, more specifically during the resynchronization of the Continental Europe area. Based on this knowledge, it is possible to set more suitable conditions for resynchronization operations: the idea is to consider not only the frequency deviation between the two areas but also to take into account the respective measurement uncertainty. As confirmed by the analysis of the two real-world scenarios, such an approach would allow for minimizing the probability of adverse or even dangerous conditions such as dampened oscillations and inter-modulations

Filter design masks for C37.118.1a-compliant frequency-tracking and fixed-filter M-class Phasor Measurement Units (PMUs)

The new amendment to the Phasor Measurement Unit (PMU) standard C37.118.1a makes several significant changes, compared to 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 trade-off 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 2.5dB, 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 to the mask required for fixed-filter devices. The M-class PMU with reporting rate 25Hz 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

Three-Phase Synchrophasor Estimation Through Taylor Extended Kalman Filter

Synchronized phasor and frequency measurements are key tools for the monitoring and management of modern power systems. In a dynamic scenario, it is fundamental to define algorithms that allow accurately measuring time-varying signals, with short latencies and high reporting rates. A dynamic phasor model can help the design of these algorithms and, in particular, of those based on Kalman filtering approach. In this paper, an Extended Kalman filter formulation that considers the Taylor expansions of amplitudes and phase angles in three-phase signals is introduced. The proposed dynamic model takes into account the inherent relationship among the phases and includes harmonics in a effective way. The performance of the method permitting both synchrophasor and frequency measurements are assessed by simulations, considering also the combined effect of dynamics and disturbances. The algorithm shows tracking capabilities and the flexibility which is mandatory to deal with different conditions

Proposals and Analysis of Space Vector-Based Phase-Locked-Loop Techniques for Synchrophasor, Frequency, and ROCOF Measurements

Space vector (SV)-based estimation algorithms represent attractive methods for synchronized phasor, frequency, and rate of change of frequency measurements in three-phase ac power systems. Recently, a phase-locked-loop (PLL) solution for improving the demodulation of the SV signal has been proposed. In this article, the potentialities of the SV-PLL approach are investigated in order to optimize accuracy and computational load. First, the impact of the PLL update rate on achieved performance is analyzed. Then, a novel two-step SV-PLL algorithm is presented so that the accuracy of a fast PLL execution frequency can be matched with a considerably lower computational cost. The behavior in the case of fast phase angle variations has been also significantly improved. The proposed synchrophasor estimation technique has been validated through simulations; exemplary dynamic performance suggests that it is particularly suitable for grid control applications. Experimental tests carried out on a real-time implementation confirm simulation results

Definition and assessment of reference values for PMU calibration in static and transient conditions

The calibration of Phasor Measurement Units (PMUs) consists of comparing Coordinated Universal Time (UTC) time-stamped phasors (synchrophasors) estimated by the PMU under test, against reference synchrophasors generated through a PMU calibrator. The IEEE Standard C37.118-2011 and its amendment (IEEE Std) describe compliance tests for static and dynamic conditions, and indicate the relative limits in terms of accuracy. In this context, the paper focuses on the definition and accuracy assessment of the reference synchrophasors in the test conditions dictated by the above IEEE Std. In the first part of the paper, we describe the characterization of a nonlinear least-squares (NL-LSQ) fitting algorithm used to determine the parameters of the reference synchrophasors. We analyse the uniqueness and robustness of the solution provided by the algorithm. We assess its accuracy within the whole range of static tests required by the IEEE Std. In the second part, we discuss the appropriateness of synchrophasor model to evaluate the PMU performance in step test conditions. We compare the proposed algorithm against two synchrophasor estimation algorithms. Finally, we propose a time domain process for the better evaluation of PMU performances in transient conditions

DFT-based Synchrophasor Estimation Algorithms and their Integration in Advanced Phasor Measurement Units for the Real-time Monitoring of Active Distribution Networks

The increasing penetration of Distributed Energy Resources (DERs) at the low and medium-voltage levels is determining major changes in the operational procedures of distribution networks (DNs) that are evolving from passive to active power grids. Such evolution is causing non-negligible problems to DN operators (DNOs) and calls for advanced monitoring infrastructures composed by distributed sensing devices capable of monitoring voltage and current variations in real-time. In this respect, Phasor Measurement Units (PMUs) definitely represent one of the most promising technologies. Their higher accuracy and reporting rates compared to standard monitoring devices, together with the possibility of reporting time-tagged measurements of voltage and current phasors, enable the possibility to obtain frequent and accurate snapshots of the status of the monitored grid. Nevertheless, the applicability of such technology to DNs has not been demonstrated yet since PMUs where originally conceived for transmission network applications. Within this context, this thesis first discusses and derives the requirements for PMUs expected to operate at power distribution level. This study is carried out by analyzing typical operating conditions of Active Distribution Networks (ADNs). Then, based on these considerations, an advanced synchrophasor estimation algorithm capable of matching the accuracy requirements of ADNs is formulated. The algorithm, called iterative-interpolated DFT (i-IpDFT) improves the performances of the Interpolated-DFT (IpDFT) method by iteratively compensating the effects of the spectral interference produced by the negative image of the spectrum and at the same time allows to reduce the window length up to two periods of a signal at the nominal frequency of the power system. In order to demonstrate the low computational complexity of such an approach, the developed algorithm has been subsequently optimized to be deployed into a dedicated FPGA-based PMU prototype. The influence of the PMU hardware components and particularly the effects of the stability and reliability of the adopted UTC-time synchronization technology have been verified. The PMU prototype has been metrologically characterized with respect to the previously defined operating conditions of ADNs using a dedicated PMU calibrator developed in collaboration with the Swiss Federal Institute of Metrology (METAS). The experimental validation has verified the PMU compliance with the class-P requirements defined in the IEEE Std. C37.118 and with most of the accuracy requirements defined for class-M PMUs with the exception of out of band interference tests