2018 IEEE International Instrumentation and Measurement Technology Conference (I2MTC)
Rapid Voltage Changes (RVCs) are small, but frequent RMS voltage transitions between two steady-s... more Rapid Voltage Changes (RVCs) are small, but frequent RMS voltage transitions between two steady-state conditions, which can significantly affect the Power Quality (PQ) (particularly flicker) perceived by final users. Even if the IEC Standard 61000-4-30:2015 explicitly includes a proper RVC definition as well as a detection algorithm, the characterization of this kind of PQ events is still quite unexplored in the scientific literature. In this paper, the root mean square (RMS) voltage estimator adopted in the IEC detection algorithm is compared with a weighted least square (WLS) estimator originally conceived for Phasor Measurement Units (PMUs) and able to track voltage variations within each observation intervals. Multiple simulation results show that the WLS technique generally ensures faster RVC event detection and it is accurate even in the presence of harmonic distortion.
2017 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2017
In the last edition of the IEC Standard 61000-4-30 a Rapid Voltage Change (RVC) is defined as “a ... more In the last edition of the IEC Standard 61000-4-30 a Rapid Voltage Change (RVC) is defined as “a quick transition in RMS voltage between two steady-state conditions, during which the voltage does not exceed the dip/swell thresholds [1].” Because of their intrinsically sudden nature, RVC-like events are generally hard to detect and to monitor. In fact, no clear criteria to set the detection thresholds are defined at the moment. Certainly, threshold selection should take into consideration measurement uncertainty. In this respect, in this paper the uncertainty of the classic RMS estimator suggested in the IEC Standard 61000-4-30:2015 during an RVC event is evaluated both analytically and through simulations. The presented analysis paves the way to reasonable criteria (and limits) to detect RVC-like events in realistic scenarios.
2021 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2021
In this paper the Parabolic Interpolated Discrete-Time Fourier Transform (PIpDTFT) algorithm prop... more In this paper the Parabolic Interpolated Discrete-Time Fourier Transform (PIpDTFT) algorithm proposed for the frequency estimation of a complex-valued sine-wave is extended to signal weighted by a Maximum Sidelobe Decay (MSD) window and its accuracy is analyzed. A criterion is proposed that enables the determination of the maximum distance between the DTFT interpolation points that ensures a negligible estimator bias. Also, the accuracy of the PIpDTFT frequency estimator is analyzed as a function of the accuracy of the used initial frequency estimate. Moreover, the robustness of the PIpDTFT frequency estimator to the spurious tones is investigated and compared with those of different state-of-the-art frequency estimators through computer simulations.
This paper analyzes the effect of windowing and additive wideband noise on the estimates returned... more This paper analyzes the effect of windowing and additive wideband noise on the estimates returned by the real-valued Taylor-based Weighted Least Squares (TWLS) algorithm when applied to noisy sine-wave with constant amplitude and phase. The Taylor's series of the signal time-varying phasor are truncated to the second order and the two-term or three-term Minimum Sidelobe Level (MSL) and Maximum Sidelobe Decay (MSD) windows are considered. Expressions for the estimation variances are derived that hold even when the sine-wave amplitude and phase exhibit slow and limited, but significant, time variations. Then they are compared with the unbiased Cramér-Rao Lower Bounds (CRLBs) for constant parameter sine-waves in order to analyze the estimator statistical efficiency. The accuracies of the derived expressions are verified through computer simulations and validated by experimental results.
TIle paper presents an asymptotic accuracy analysis for the least square autoregressive (LS-AR) e... more TIle paper presents an asymptotic accuracy analysis for the least square autoregressive (LS-AR) estimator when it is applied to exponential signals embedded in white noise. In particular. the mean square error (MSE) of the frequency and damping factor estimaton is evaluated in the case of high signal-ta-noise ratios.
In this paper the accuracy of the complex sinusoid amplitude and phase estimators provided by the... more In this paper the accuracy of the complex sinusoid amplitude and phase estimators provided by the Interpolated Weighted Discrete-Time Fourier Transform (IpWDTFT) algorithm is analyzed. It is shown that the use of the WDTFT spectral sample corresponding to the estimated sinusoid frequency allows to minimize the estimator asymptotic Mean Square Error (MSE) due to additive wideband noise. Also, the expression of the asymptotic expected sum-squared fitting error in the reconstruction of the complex sinusoid by means of the IpWDTFT algorithm is derived. All the derived expressions are verified through computer simulations.
This paper deals with a new design criterion aimed at keeping the decisional risks associated to ... more This paper deals with a new design criterion aimed at keeping the decisional risks associated to conformance testing procedures below given target values. The proposed approach is based on two closed-form analytical expressions describing the dependence of both the consumer's risk (CR) and the producer's risk (PR) on three essential parameters for conformance testing, i.e. the process capability index (CI), the test uncertainty ratio (TUR) and the gauging to tolerance interval ratio (GTR). Such approximate expressions are not only very accurate, but also much less computationally demanding than the implicit, integration-based expressions of CR and PR. This assures faster results and less numerical problems when the values of TUR and GTR meeting the wanted CR and PR requirements are determined.
The parameters of a sine-wave are often estimated by means of the classical Interpolated Discrete... more The parameters of a sine-wave are often estimated by means of the classical Interpolated Discrete Fourier Transform (IpDFTc) method based on cosine windows since this method provides high accuracy while requiring low computational effort. When the number of acquired sine-wave cycles is small, estimation accuracy is heavily affected by the interference due to spectral leakage from both the sine-wave image component and other disturbance tones such as signal harmonics. To reduce both these detrimental effects new cosine windows are proposed in this paper. Their spectra exhibit a deep null close to the image component interfering frequency and the highest allowed sidelobe decay rate, so assuring minimization of long range spectral leakage. These windows are called Maximum Image interference Rejection windows with Rapid Sidelobe Decay rate (RSD) or simply, MIR-RSD windows. The analytical expressions of the sine-wave parameter estimators provided by the IpDFTc method based on the H-term MIR-RSD window (H ≥ 2) are also derived. To assess the effectiveness of the MIR-RSD windows in rejecting the spectral interference when analyzing noisy or harmonically distorted sine-waves, the accuracy of the proposed frequency estimator is compared with those provided by other IpDFT frequency estimators through simulation and experimental results.
2014 11th International Symposium on Electronics and Telecommunications (ISETC), 2014
In this paper two iterative interpolation algorithms proposed in the scientific literature for es... more In this paper two iterative interpolation algorithms proposed in the scientific literature for estimating the frequency of complex-valued sine-waves are generalized to a generic Maximum Sidelobe Decay (MSD) window in order to achieve highly accurate estimates even when real-valued pure or harmonically distorted sine-waves are analyzed. The analytical expressions for the frequency estimations formulas are derived. Moreover the accuracy achieved when pure, noisy, and noisy and harmonically distorted sine-waves are analyzed is compared with those provided by the classical Interpolated Discrete Fourier Transform (IpDFT) and three-point IpDFT algorithms through computer simulations. The performed comparison allows us to determine in which situations the proposed algorithms can be advantageously used.
ABSTRACT In the near future, Phasor Meaurement Units (PMUs) are expected to play a key role not o... more ABSTRACT In the near future, Phasor Meaurement Units (PMUs) are expected to play a key role not only in power transmission networks, but also to monitor power flows within distribution networks. Unfortunately, in order to face the challenges of next-generation smart grids, faster and more accurate techniques have to be developed for measuring waveform phasors, fundamental frequencies and rate of change of such frequencies (ROCOF). While the Standard IEEE C37.118.1-2011 defines clear accuracy and responsiveness boundaries for synchophasor estimation under the effect of different type of disturbances, the proposed limits have sometimes been considered as inadequate for distribution networks (either too strict or too loose). In this paper, after a brief overview of the general PMU architecture, the performance of two classes of phasor estimators (i.e. based on Discrete Fourier Transform and Least Squares optimization, respectively) are shortly, but effectively analyzed and compared both in steady-state and transient conditions.
In this paper; the authors address the prob- lem of characterizing and analyzing power systems un... more In this paper; the authors address the prob- lem of characterizing and analyzing power systems un- der non-sinusoidal conditions. A method is presented that allows the estimation of relevant parameters of the spectral components in which the signals can be decomposed, via an FFT-based procedure. The results are compared with those provided by procedures pro- posed in the literature and information is given for al- lowing a straightforward application of the algorithm.
IEEE Transactions on Instrumentation and Measurement, 2000
In this paper, the authors address the problem of estimating the average power of electrical syst... more In this paper, the authors address the problem of estimating the average power of electrical systems under nonsinusoidal conditions. At first, a time-domain-based algorithm is proposed, which smoothes sampled data using suitable coefficients, prior to their numerical integration. Then, the algorithm accuracy is quantified with respect to wide-band noise. Last, simulation and experimental results are presented showing its effectiveness in estimating average power when starting from multifrequency voltage and current samples.
IEEE Transactions on Instrumentation and Measurement, 2006
Spectral leakage is a well-known phenomenon induced by the windowing process and usually revealed... more Spectral leakage is a well-known phenomenon induced by the windowing process and usually revealed in the frequency domain. Scientific literature has deeply investigated the spectral leakage of narrow-band components. However, the problem of windowing a wide-band colored noise has not yet been fully characterized. In this paper, the effect of the windowing process on the estimate of the in-band ∆Σ-shaped quantizationnoise power spectral density is investigated. The reported analysis holds for any modulator order and for any kind of real and symmetric window and proves the necessity of the windowing process in order to reduce the in-band noise power estimation bias. Moreover, an a priori criterion for designing the optimal window that reduces the shaped-noise spectral leakage and for choosing the minimum number of acquired samples to be employed is derived.
The system of measurement units is a subject with a highly conventional content, susceptible to c... more The system of measurement units is a subject with a highly conventional content, susceptible to changes with the technological evolution, and with legislative implications, which compel to express relations and definitions in words. This chapter considers the structure and general features of a coherent unit system, such as Systeme International d'unites (SI) from a general theoretical point of view. It then analyzes the SI in detail and also considers the basic units in their formal and most substantial aspects, looking for the underlying mathematical relations beyond the wording of definitions. The chapter outlines the perspective of short-term evolution of the system. It addresses the role of the standards and the problem of realizing a measurement unit and describes that its solution is applied to the basic and other important units to obtain the primary standards and the unit dissemination.
2018 IEEE International Instrumentation and Measurement Technology Conference (I2MTC)
Rapid Voltage Changes (RVCs) are small, but frequent RMS voltage transitions between two steady-s... more Rapid Voltage Changes (RVCs) are small, but frequent RMS voltage transitions between two steady-state conditions, which can significantly affect the Power Quality (PQ) (particularly flicker) perceived by final users. Even if the IEC Standard 61000-4-30:2015 explicitly includes a proper RVC definition as well as a detection algorithm, the characterization of this kind of PQ events is still quite unexplored in the scientific literature. In this paper, the root mean square (RMS) voltage estimator adopted in the IEC detection algorithm is compared with a weighted least square (WLS) estimator originally conceived for Phasor Measurement Units (PMUs) and able to track voltage variations within each observation intervals. Multiple simulation results show that the WLS technique generally ensures faster RVC event detection and it is accurate even in the presence of harmonic distortion.
2017 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2017
In the last edition of the IEC Standard 61000-4-30 a Rapid Voltage Change (RVC) is defined as “a ... more In the last edition of the IEC Standard 61000-4-30 a Rapid Voltage Change (RVC) is defined as “a quick transition in RMS voltage between two steady-state conditions, during which the voltage does not exceed the dip/swell thresholds [1].” Because of their intrinsically sudden nature, RVC-like events are generally hard to detect and to monitor. In fact, no clear criteria to set the detection thresholds are defined at the moment. Certainly, threshold selection should take into consideration measurement uncertainty. In this respect, in this paper the uncertainty of the classic RMS estimator suggested in the IEC Standard 61000-4-30:2015 during an RVC event is evaluated both analytically and through simulations. The presented analysis paves the way to reasonable criteria (and limits) to detect RVC-like events in realistic scenarios.
2021 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2021
In this paper the Parabolic Interpolated Discrete-Time Fourier Transform (PIpDTFT) algorithm prop... more In this paper the Parabolic Interpolated Discrete-Time Fourier Transform (PIpDTFT) algorithm proposed for the frequency estimation of a complex-valued sine-wave is extended to signal weighted by a Maximum Sidelobe Decay (MSD) window and its accuracy is analyzed. A criterion is proposed that enables the determination of the maximum distance between the DTFT interpolation points that ensures a negligible estimator bias. Also, the accuracy of the PIpDTFT frequency estimator is analyzed as a function of the accuracy of the used initial frequency estimate. Moreover, the robustness of the PIpDTFT frequency estimator to the spurious tones is investigated and compared with those of different state-of-the-art frequency estimators through computer simulations.
This paper analyzes the effect of windowing and additive wideband noise on the estimates returned... more This paper analyzes the effect of windowing and additive wideband noise on the estimates returned by the real-valued Taylor-based Weighted Least Squares (TWLS) algorithm when applied to noisy sine-wave with constant amplitude and phase. The Taylor's series of the signal time-varying phasor are truncated to the second order and the two-term or three-term Minimum Sidelobe Level (MSL) and Maximum Sidelobe Decay (MSD) windows are considered. Expressions for the estimation variances are derived that hold even when the sine-wave amplitude and phase exhibit slow and limited, but significant, time variations. Then they are compared with the unbiased Cramér-Rao Lower Bounds (CRLBs) for constant parameter sine-waves in order to analyze the estimator statistical efficiency. The accuracies of the derived expressions are verified through computer simulations and validated by experimental results.
TIle paper presents an asymptotic accuracy analysis for the least square autoregressive (LS-AR) e... more TIle paper presents an asymptotic accuracy analysis for the least square autoregressive (LS-AR) estimator when it is applied to exponential signals embedded in white noise. In particular. the mean square error (MSE) of the frequency and damping factor estimaton is evaluated in the case of high signal-ta-noise ratios.
In this paper the accuracy of the complex sinusoid amplitude and phase estimators provided by the... more In this paper the accuracy of the complex sinusoid amplitude and phase estimators provided by the Interpolated Weighted Discrete-Time Fourier Transform (IpWDTFT) algorithm is analyzed. It is shown that the use of the WDTFT spectral sample corresponding to the estimated sinusoid frequency allows to minimize the estimator asymptotic Mean Square Error (MSE) due to additive wideband noise. Also, the expression of the asymptotic expected sum-squared fitting error in the reconstruction of the complex sinusoid by means of the IpWDTFT algorithm is derived. All the derived expressions are verified through computer simulations.
This paper deals with a new design criterion aimed at keeping the decisional risks associated to ... more This paper deals with a new design criterion aimed at keeping the decisional risks associated to conformance testing procedures below given target values. The proposed approach is based on two closed-form analytical expressions describing the dependence of both the consumer's risk (CR) and the producer's risk (PR) on three essential parameters for conformance testing, i.e. the process capability index (CI), the test uncertainty ratio (TUR) and the gauging to tolerance interval ratio (GTR). Such approximate expressions are not only very accurate, but also much less computationally demanding than the implicit, integration-based expressions of CR and PR. This assures faster results and less numerical problems when the values of TUR and GTR meeting the wanted CR and PR requirements are determined.
The parameters of a sine-wave are often estimated by means of the classical Interpolated Discrete... more The parameters of a sine-wave are often estimated by means of the classical Interpolated Discrete Fourier Transform (IpDFTc) method based on cosine windows since this method provides high accuracy while requiring low computational effort. When the number of acquired sine-wave cycles is small, estimation accuracy is heavily affected by the interference due to spectral leakage from both the sine-wave image component and other disturbance tones such as signal harmonics. To reduce both these detrimental effects new cosine windows are proposed in this paper. Their spectra exhibit a deep null close to the image component interfering frequency and the highest allowed sidelobe decay rate, so assuring minimization of long range spectral leakage. These windows are called Maximum Image interference Rejection windows with Rapid Sidelobe Decay rate (RSD) or simply, MIR-RSD windows. The analytical expressions of the sine-wave parameter estimators provided by the IpDFTc method based on the H-term MIR-RSD window (H ≥ 2) are also derived. To assess the effectiveness of the MIR-RSD windows in rejecting the spectral interference when analyzing noisy or harmonically distorted sine-waves, the accuracy of the proposed frequency estimator is compared with those provided by other IpDFT frequency estimators through simulation and experimental results.
2014 11th International Symposium on Electronics and Telecommunications (ISETC), 2014
In this paper two iterative interpolation algorithms proposed in the scientific literature for es... more In this paper two iterative interpolation algorithms proposed in the scientific literature for estimating the frequency of complex-valued sine-waves are generalized to a generic Maximum Sidelobe Decay (MSD) window in order to achieve highly accurate estimates even when real-valued pure or harmonically distorted sine-waves are analyzed. The analytical expressions for the frequency estimations formulas are derived. Moreover the accuracy achieved when pure, noisy, and noisy and harmonically distorted sine-waves are analyzed is compared with those provided by the classical Interpolated Discrete Fourier Transform (IpDFT) and three-point IpDFT algorithms through computer simulations. The performed comparison allows us to determine in which situations the proposed algorithms can be advantageously used.
ABSTRACT In the near future, Phasor Meaurement Units (PMUs) are expected to play a key role not o... more ABSTRACT In the near future, Phasor Meaurement Units (PMUs) are expected to play a key role not only in power transmission networks, but also to monitor power flows within distribution networks. Unfortunately, in order to face the challenges of next-generation smart grids, faster and more accurate techniques have to be developed for measuring waveform phasors, fundamental frequencies and rate of change of such frequencies (ROCOF). While the Standard IEEE C37.118.1-2011 defines clear accuracy and responsiveness boundaries for synchophasor estimation under the effect of different type of disturbances, the proposed limits have sometimes been considered as inadequate for distribution networks (either too strict or too loose). In this paper, after a brief overview of the general PMU architecture, the performance of two classes of phasor estimators (i.e. based on Discrete Fourier Transform and Least Squares optimization, respectively) are shortly, but effectively analyzed and compared both in steady-state and transient conditions.
In this paper; the authors address the prob- lem of characterizing and analyzing power systems un... more In this paper; the authors address the prob- lem of characterizing and analyzing power systems un- der non-sinusoidal conditions. A method is presented that allows the estimation of relevant parameters of the spectral components in which the signals can be decomposed, via an FFT-based procedure. The results are compared with those provided by procedures pro- posed in the literature and information is given for al- lowing a straightforward application of the algorithm.
IEEE Transactions on Instrumentation and Measurement, 2000
In this paper, the authors address the problem of estimating the average power of electrical syst... more In this paper, the authors address the problem of estimating the average power of electrical systems under nonsinusoidal conditions. At first, a time-domain-based algorithm is proposed, which smoothes sampled data using suitable coefficients, prior to their numerical integration. Then, the algorithm accuracy is quantified with respect to wide-band noise. Last, simulation and experimental results are presented showing its effectiveness in estimating average power when starting from multifrequency voltage and current samples.
IEEE Transactions on Instrumentation and Measurement, 2006
Spectral leakage is a well-known phenomenon induced by the windowing process and usually revealed... more Spectral leakage is a well-known phenomenon induced by the windowing process and usually revealed in the frequency domain. Scientific literature has deeply investigated the spectral leakage of narrow-band components. However, the problem of windowing a wide-band colored noise has not yet been fully characterized. In this paper, the effect of the windowing process on the estimate of the in-band ∆Σ-shaped quantizationnoise power spectral density is investigated. The reported analysis holds for any modulator order and for any kind of real and symmetric window and proves the necessity of the windowing process in order to reduce the in-band noise power estimation bias. Moreover, an a priori criterion for designing the optimal window that reduces the shaped-noise spectral leakage and for choosing the minimum number of acquired samples to be employed is derived.
The system of measurement units is a subject with a highly conventional content, susceptible to c... more The system of measurement units is a subject with a highly conventional content, susceptible to changes with the technological evolution, and with legislative implications, which compel to express relations and definitions in words. This chapter considers the structure and general features of a coherent unit system, such as Systeme International d'unites (SI) from a general theoretical point of view. It then analyzes the SI in detail and also considers the basic units in their formal and most substantial aspects, looking for the underlying mathematical relations beyond the wording of definitions. The chapter outlines the perspective of short-term evolution of the system. It addresses the role of the standards and the problem of realizing a measurement unit and describes that its solution is applied to the basic and other important units to obtain the primary standards and the unit dissemination.
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Papers by Dario Petri