Dario Petri

The paper analyses the accuracy of the phasor estimator provided by the Taylor Weighted Least Squares (TWLS) algorithm when electrical waveforms are affected by harmonics, sub-synchronous interharmonics (sbIHs) and super-synchronous interharmonics (spIHs). At first, the accuracy of the classical TWLS algorithm is analyzed when the initial value for the fundamental frequency is provided by the two-point Interpolated Discrete Fourier Transform (IpDFT) algorithm based on the Hann window. Then, leveraging on the obtained results a revised and less computationally expensive version of the iterative TWLS (i-TWLS) algorithm recently presented in the literature, referred to as the Compensated Synchronized IHs TWLS (CSIH-TWLS) algorithm, is proposed. That algorithm estimates the phasor parameters from the residual signal obtained by removing only the sbIH, the spIH, and the harmonic closest to the fundamental component. The initial value of the fundamental frequency is estimated by applying the two-point IpDFT algorithm based on the Hann window to the residual signal. The accuracies of the classical TWLS algorithm, the CSIH-TWLS algorithm, and a state-of-the-art Taylor-Fourier Multifrequency (TFM) algorithm are analyzed through computer simulations and compared to each other in different steady-state conditions, including amplitude and phase modulations. Accuracy comparison is performed considering also real-life power signals affected by both one sbIH and one spIH.

Phasor Measurement Units (PMUs) provide high-accuracy frequency and Rate of Change of Frequency (ROCOF) measurements under quasi-stationary operating conditions. However, their measurement uncertainty can increase by up to two orders of magnitude during fast transients, thus degrading the reliability of Wide Area Monitoring, Protection, and Control Systems. To address this issue, this paper proposes event-triggered Adaptive Kalman Filters (AKFs) that, installed at PMU-equipped buses, dynamically augment local ROCOF measurements with information received from adjacent PMUs when relevant transient conditions are detected. By leveraging spatial correlation in system dynamics, the proposed strategy mitigates the reduced tracking capability of classical model-based prediction during transient events with minimal communication overhead and with no scalability problems. Simulation results on modified IEEE 5-bus and 14-bus systems show a substantial reduction in ROCOF estimation uncertainty (up to one order of magnitude in very noisy environments and if the PMU estimates are performed over data records of no more than four nominal cycles each), together with a more moderate improvement in frequency estimation accuracy. Application to real-world PMU data further confirms the stable and consistent behavior of the algorithm.

A critical challenge for the evolution of smart distribution systems is the shortage of measurement devices, along with the complexity and the high costs for deploying new fine-grained monitoring infrastructures. To address this issue, this paper investigates the feasibility of upgrading the grid synchronization algorithms running in the control unit of grid-following power converters to turn them into auxiliary embedded measurement devices supporting system observability. This goal can be achieved in two alternative ways: either by using an algorithm originally designed for a Phasor Measurement Unit (PMU) to perform grid synchronization or, conversely, by applying a grid synchronization technique for synchrophasor estimation. To compare advantages and disadvantages of either approach, both a 2-stage Tuned Lightweight version of the Taylor-Fourier Transform (2-stage TLTFT) algorithm and a Phase-Locked Loop embedding a custom Third-Order Generalized Integrator (TOGI-PLL) are analyzed both in the P Class PMU testing conditions specified in the IEEE Standard IEC/IEEE 60255-118-1:2018 and considering the requirements for grid connection reported in the IEEE Standard 1547-2023. Extensive simulation results show that the general idea of a joint solution for synchrophasor estimation and grid synchronization is viable in either way, although some improvement is needed. In particular, the 2-stage TLTFT algorithm generally returns more accurate results and shorter response times than the TOGI-PLL, but it is also more computationally demanding. Further simulations, based on a real power electronic converter model, confirm that, when either algorithm is used in the control loop for grid synchronization, the generated output voltage is stable.

It is widely accepted that in many industrial and commercial applications, as well as in the areas of health, safety, environmental protection, and forensics, decisions are mostly based on measurement results that are compared with one or more threshold values to state whether the measured quantity conforms to tolerance limits, or maximum admissible limits set by Standards or Laws. It is also known that the risk of making the wrong decision always exists, and is closely related to the credibility of the data entered in the decision-making process. When the input data are measurement results, their credibility is evaluated in terms of measurement uncertainty. Different decision rules have been proposed in literature and in the Standards, the ISO Std. 14253-1 and ISO Guide 98-4 above all, which consider measurement uncertainty, evaluated according to the recommendations of the Guide to the expression of Uncertainty in Measurement (GUM), in conformity assessment. However, given the tolerance limit, they do not fully explore the relationship between the measured value, measurement uncertainty, and the risk of wrong decision, and how any of them can be set, given the two other ones. This paper aims to discuss how to establish suitable decision rules, fully explain the underlying assumptions about measurement uncertainty and risk, and show how the proper definition of the decision rule may increase efficiency by reducing costs and may, consequently, represent a step forward in the direction of sustainability.

Modern power systems exhibit fast dynamics and require increasing resilience and swift responses to possible faults and transients. As known, the Rate of Change of Frequency (ROCOF) in power systems should be around zero. Thus, sudden variations generally highlight significant changes in operating conditions. Transmission System Operators (TSOs) increasingly rely on ROCOF data from Phasor Measurement Units (PMUs) deployed across the grid. In this paper, a novel Consistent ROCOF Data Fusion (CRDF) algorithm is proposed to improve the quality of the information that can be extracted from multiple distributed PMU ROCOF values. The CRDF algorithm consists of three main stages. In the first one, the key parameters of the algorithm are properly computed and initialized. In the second stage, possible outliers and the data affected by largest uncertainty are progressively excluded, to retain the most consistent data only. Finally, in the third stage, such data are aggregated through a weighted average that accounts for measurement uncertainty. The algorithm performance is first analyzed in two scenarios consisting of just 5 buses, but with rather different features. Then, further results obtained considering a 36-bus power system confirm that the CRDF algorithm is scalable and it is able to identify and to aggregate the consistent ROCOF data that dominate across two different zones of the grid.

Leveraging on Interpolated Discrete Time Fourier Transform (IpDTFT) algorithms recently proposed in the literature, this paper proposes three frequency and damping factor estimators of real-valued damped sinusoids. The proposed algorithms minimize the effect of wideband noise and compensate the contribution of the fundamental image component on the estimated parameters by exploiting three interpolation points and weighting the analyzed signal with a Maximum Sidelobe Decay (MSD) window. The accuracies of all the proposed algorithms and other state-of-the-art frequency-domain and time-domain algorithms are compared with each other through simulations considering noisy and noisy and harmonically distorted damped sinusoids. The comparison is performed using both simulations based on a real-life model and experimental results.

In this paper, an analytical expression for the overall bias of the complex-valued noisy sine wave frequency estimator returned by the interpolated discrete Fourier transform algorithm is derived. That bias is due to the effect of both the algorithm intrinsic approximation when rectangular windowing is adopted and wideband noise. The effect of the number of analyzed samples and the signal-to-noise ratio on the ratio between the overall estimation bias and the estimator standard deviation is also investigated. In addition, leveraging on the derived expression, a frequency estimator that compensates for the contribution due to the algorithm intrinsic approximation is proposed and its accuracy is compared with that of the classical frequency estimator.

This paper proposes new real-valued damped sinusoid frequency and damping factor estimators. They exploit a three-point Interpolated discrete Fourier transform (IpDFT) algorithm based on the Rife-Vincent class I (RVCI) windows and complex-valued DFT samples. The accuracies of the proposed estimators are compared with those provided by other state-of-the-art interpolated Fourier algorithms using computer simulations when pure, noisy, and noisy and harmonically distorted damped sinusoids are analyzed.

This paper proposes an Interpolated Discrete-Time Fourier Transform (LIpDTFT) estimator for complex-valued noisy sinewave frequency based on the Linearization of the DTFT module behavior around the spectrum peak. It belongs to a class of LIpDTFT estimators that compensate the poor Discrete Fourier Transform (DFT) frequency resolution by interpolating two DTFT samples located very close to an initial frequency estimate. As compared with other DTFT-based frequency estimators recently proposed in the literature, the proposed LIpDTFT estimator ensures a smaller interpolation error and a lower processing effort. Moreover, if the rectangular window is adopted, it almost attains the unbiased Cramér-Rao Lower Bound (CRLB) even if a very small number of samples is analyzed. The accuracies ensured in different operating conditions by the proposed frequency estimator and other state-of-the-art DTFT-based algorithms are compared to each other through computer simulations.