The paper deals with the identification of FIR linear systems by time-domain least squares method... more The paper deals with the identification of FIR linear systems by time-domain least squares methods. Fast algorithms for solving the least squares problem are introduced. based on the notion of quasi-Toeplitz matrices. The estimation problem is solved by embedding it into a linear prediction one. and it is shown that the algorithms also allow the efficient solution of constrained least squares problems in a very common case. The iterative approach to constrained least squares identification is briefly considered. followed by the presentation of the applications considered by the authors. Finally. a few comments are made about the performances of the methods discussed.
In this paper an algorithm for frequency and damping factor estimation of a real-valued noisy dam... more In this paper an algorithm for frequency and damping factor estimation of a real-valued noisy damped sinusoid is proposed. It is an extension of the three-point Interpolated Discrete Fourier Transform (3p-IpDFT) undamped sinusoid frequency estimator based on Maximum Sidelobe Decay (MSD) windows. Analytical expressions for the frequency and the damping factor estimators are provided and the related estimation errors due to the contribution of the spectral image component are derived and compensated. The accuracies of the proposed algorithm and other stateof-the-art frequency-domain based algorithms are compared to each other through computer simulations.
2021 IEEE 11th International Workshop on Applied Measurements for Power Systems (AMPS), 2021
The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for activ... more The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for active distribution systems monitoring, requires to achieve challenging trade-offs between measurement uncertainty and responsiveness. This is particularly important for protection-oriented (i.e., P Class) PMUs. In order to improve estimation accuracy with no need to prolong the data record size and the related delays, this paper presents a Taylor Kalman Filter (TKF) enhanced with a preliminary stage able to whiten possible narrowband disturbances over short observation intervals. The use of dynamic estimators such as the TKF is motivated by the need to track possible sudden amplitude or phase changes of voltage or current AC waveforms, which are likely to occur in smart grids. However, while a basic TKF is very sensitive to disturbances different from white noise, the proposed whitening-technique is able to greatly improve the estimation accuracy of synchrophasor amplitude, phase, frequency and Rate of Change of Frequency (ROCOF) under the influence of harmonics and amplitude or phase step changes even over one-cycle observation intervals, with just a minor performance degradation in the other P Class testing conditions reported in the IEEE/IEC Standard 60255-118-1:2018.
IEEE Transactions on Instrumentation and Measurement, 2009
This paper deals with new effective guidelines for keeping the decisional risks associated with c... more This paper deals with new effective guidelines for keeping the decisional risks associated with conformance testing procedures below the given target values. The proposed approach relies on two closed-form expressions describing the dependence of both consumer's risk and producer's risk on three parameters: 1) the process capability index; 2) the test uncertainty ratio; and 3) the gauging-to-tolerance-interval ratio. Such expressions can be applied to establish the measurement uncertainty and the amount of guardbanding required to meet preset decisional risks, thus avoiding the need for numerical integration and greatly reducing the cost of conformance testing procedures.
Measurement Process of experimentally obtaining one or more quantity values that can reasonably b... more Measurement Process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity. So, a measurement process provides, as a part of the measurement result, one or more quantity values that can be attributed to a quantity intended to be measured, that is also called, always according to the VIM [1], measurand. To fully understand this definition, we have to refer to the definition of quantity. We can find it again in the VIM. Quantity Property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
This chapter analyzes one of the most common instruments in use in laboratories or fieldwork. It ... more This chapter analyzes one of the most common instruments in use in laboratories or fieldwork. It presents some history showing the characteristics of analog and digital oscilloscopes and how they have evolved through decades. The chapter also presents a brief description of the different waveforms one may find in normal engineering work. It describes different waveform characteristics and how to measure them using oscilloscopes. By describing their building blocks it is easy to understand limitations of each type of oscilloscope. The chapter gives a general idea of how to use oscilloscopes by explaining each of the most common controls found in their front panels. It shows the performance characteristics of oscilloscopes and how they can affect the measurements performed with them. The chapter outlines different types of probes available and their characteristics to be able to use the correct one for each different application.
The paper deals with the identification of FIR linear systems by time-domain least squares method... more The paper deals with the identification of FIR linear systems by time-domain least squares methods. Fast algorithms for solving the least squares problem are introduced. based on the notion of quasi-Toeplitz matrices. The estimation problem is solved by embedding it into a linear prediction one. and it is shown that the algorithms also allow the efficient solution of constrained least squares problems in a very common case. The iterative approach to constrained least squares identification is briefly considered. followed by the presentation of the applications considered by the authors. Finally. a few comments are made about the performances of the methods discussed.
The proliferation of distributed energy resources and plug-in electric vehicles is expected to ch... more The proliferation of distributed energy resources and plug-in electric vehicles is expected to change present distribution systems, thus stressing the role of measurement instrumentation enabling safe and flexible smart grid operation. In this context, Phasor Measurement Units (PMUs) are required to measure amplitude, phase, frequency and rate of change of frequency (ROCOF) of AC waveforms not only in steady state, but also, and above all, under dynamic conditions, while still ensuring extremely low measurement uncertainty and high reporting rates. In this paper a lightweight signal processing algorithm based on the so-called Teager's energy operator is adopted to measure amplitude, phase, frequency and ROCOF of AC waveforms in some of the testing conditions prescribed by the IEEE Standard C37.118.1-2011 and the IEEE Amendment C37.118.1a-2014. The reported analysis shows that the Teager's algorithm can provide high-rate and reasonably accurate measurement results under dynamic conditions. However, due to its sensitivity to wideband and narrowband disturbances, a preliminary band-pass filter is needed. In addition, instantaneous frequency and, above all, ROCOF estimates should be averaged to remove the residual effect of disturbances and to meet the limits reported in the IEEE Standards.
Wiener-Hammerstein models are flexible, well known and often studied. The main challenge in ident... more Wiener-Hammerstein models are flexible, well known and often studied. The main challenge in identifying a Wiener-Hammerstein model is to distinguish the linear time invariant (LTI) blocks at the front and the back. This paper presents a nonparametric approach to separate the front and back dynamics starting from the best linear approximation (BLA). Next, the nonparametric estimates of the LTI blocks in the model can be parametrized, taking into account a phase shift degeneration. Once the dynamics are known, the estimation of the static nonlinearity boils down to a simple linear least squares problem. The consistency of the proposed approach is discussed and the method is validated on the Wiener-Hammerstein benchmark that was presented at the IFAC SYSID conference in 2009.
In the considered scenario, a wireless sensor network (WSN) operates in a difficult to reach (or ... more In the considered scenario, a wireless sensor network (WSN) operates in a difficult to reach (or even hostile) environment, and is therefore required to autonomously configure itself and tune its parameters. We investigate techniques that guarantee a good compromise between conflicting requirements: 1) a good coverage of the area, 2) a long lifetime, 3) a good temporal accuracy in classifying the events. Our solution is based on the combination of two complementary techniques. The first one, the wakeup scattering algorithm, iteratively identifies a periodic schedule that keeps the node awake for a limited time, so saving power. In this paper, we consider the global convergence of this algorithm. The second technique is a small overhead distributed algorithm for the synchronization of the nodes, which takes into account the communication delays.
The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for activ... more The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for active distribution systems monitoring, requires to achieve challenging trade-offs between measurement uncertainty and responsiveness. This is particularly important for protection-oriented (i.e., P Class) PMUs. In order to improve estimation accuracy with no need to prolong the data record size and the related delays, this paper presents a Taylor Kalman Filter (TKF) enhanced with a preliminary stage able to whiten possible narrowband disturbances over short observation intervals. The use of dynamic estimators such as the TKF is motivated by the need to track possible sudden amplitude or phase changes of voltage or current AC waveforms, which are likely to occur in smart grids. However, while a basic TKF is very sensitive to disturbances different from white noise, the proposed whitening-technique is able to greatly improve the estimation accuracy of synchrophasor amplitude, phase, frequency and Rate of Change of Frequency (ROCOF) under the influence of harmonics and amplitude or phase step changes even over one-cycle observation intervals, with just a minor performance degradation in the other P Class testing conditions reported in the IEEE/IEC Standard 60255-118-1:2018.
Abstract A Renewable Energy Community (REC) is a legal entity aggregating different users sharing... more Abstract A Renewable Energy Community (REC) is a legal entity aggregating different users sharing their own resources to reduce both electricity bills and CO 2 emissions. This paper presents and analyses the impact of a bi-objective strategy to optimise the capacity of the Battery Energy Storage Systems (BESSs) of REC prosumers equipped with photovoltaic (PV) generators. The optimisation problem is solved through a custom implementation of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and has two contrasting objectives: maximising the self-sufficiency of the REC from the main grid, while minimising the BESS capacity of all REC members. A key novelty of this study is the prosumer-driven perspective, which allows to exclude the REC members who do not want to install a BESS through a linear optimisation constraint. Moreover, the proposed approach ensures that probabilities of over- or under-voltages are compliant with the limits specified by Distribution System Operators (DSOs). Such probabilities, as well as the line and BESS losses, are estimated within the optimisation loop through grid-level simulations performed in OpenDSS. Both a standard peer-to-grid (P2G) and a more REC-oriented peer-to-peer (P2P) energy sharing policy are analysed and their performance is assessed in different seasons and considering both the current energy demand and a possible future scenario, in which electrical heat pumps are widely used. The results of a case study based on a modified version of the IEEE 906-bus European Low Voltage distribution grid show that a if the total BESS capacity assigned to all REC prosumers exceeds a given threshold value, the benefits for the REC become minor. Assuming to choose the optimal BESS capacity solutions corresponding to the threshold value in the summer season (i.e., when PV and BESSs are most exploited), the overall energy losses are reduced roughly by 20%–40% for both P2G and P2P battery controls. The CO 2 emissions instead, are reduced by 10% to 50% with the P2P policy having a slight edge over the P2G one. The P2P energy sharing policy spreads the economic benefits of energy savings more evenly among REC members, and the return on investment is generally higher if the electricity demand increases.
IEEE Transactions on Instrumentation and Measurement, Oct 1, 2014
ABSTRACT Next-generation phasor measurement units (PMUs) are expected to play a key role for moni... more ABSTRACT Next-generation phasor measurement units (PMUs) are expected to play a key role for monitoring the behavior of future smart grids. While most of the PMUs used nowadays in transmission networks rely on static phasor models, more sophisticated representations and stricter accuracy requirements are needed to track amplitude, phase, and frequency changes of power waveforms in strongly dynamic scenarios as those expected in future distribution systems. In this paper, a discrete Fourier transform (DFT)-based algorithm based on a dynamic phasor model (referred to as interpolated dynamic DFT-based synchrophasor estimator) is used to estimate not only amplitude and phase of the collected waveforms, but also their frequency and rate of change of frequency. The performances of the proposed method are evaluated through multiple simulations in different steady-state and transient conditions described in the Standard IEEE C37.118.1-2011.
The paper deals with the identification of FIR linear systems by time-domain least squares method... more The paper deals with the identification of FIR linear systems by time-domain least squares methods. Fast algorithms for solving the least squares problem are introduced. based on the notion of quasi-Toeplitz matrices. The estimation problem is solved by embedding it into a linear prediction one. and it is shown that the algorithms also allow the efficient solution of constrained least squares problems in a very common case. The iterative approach to constrained least squares identification is briefly considered. followed by the presentation of the applications considered by the authors. Finally. a few comments are made about the performances of the methods discussed.
In this paper an algorithm for frequency and damping factor estimation of a real-valued noisy dam... more In this paper an algorithm for frequency and damping factor estimation of a real-valued noisy damped sinusoid is proposed. It is an extension of the three-point Interpolated Discrete Fourier Transform (3p-IpDFT) undamped sinusoid frequency estimator based on Maximum Sidelobe Decay (MSD) windows. Analytical expressions for the frequency and the damping factor estimators are provided and the related estimation errors due to the contribution of the spectral image component are derived and compensated. The accuracies of the proposed algorithm and other stateof-the-art frequency-domain based algorithms are compared to each other through computer simulations.
2021 IEEE 11th International Workshop on Applied Measurements for Power Systems (AMPS), 2021
The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for activ... more The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for active distribution systems monitoring, requires to achieve challenging trade-offs between measurement uncertainty and responsiveness. This is particularly important for protection-oriented (i.e., P Class) PMUs. In order to improve estimation accuracy with no need to prolong the data record size and the related delays, this paper presents a Taylor Kalman Filter (TKF) enhanced with a preliminary stage able to whiten possible narrowband disturbances over short observation intervals. The use of dynamic estimators such as the TKF is motivated by the need to track possible sudden amplitude or phase changes of voltage or current AC waveforms, which are likely to occur in smart grids. However, while a basic TKF is very sensitive to disturbances different from white noise, the proposed whitening-technique is able to greatly improve the estimation accuracy of synchrophasor amplitude, phase, frequency and Rate of Change of Frequency (ROCOF) under the influence of harmonics and amplitude or phase step changes even over one-cycle observation intervals, with just a minor performance degradation in the other P Class testing conditions reported in the IEEE/IEC Standard 60255-118-1:2018.
IEEE Transactions on Instrumentation and Measurement, 2009
This paper deals with new effective guidelines for keeping the decisional risks associated with c... more This paper deals with new effective guidelines for keeping the decisional risks associated with conformance testing procedures below the given target values. The proposed approach relies on two closed-form expressions describing the dependence of both consumer's risk and producer's risk on three parameters: 1) the process capability index; 2) the test uncertainty ratio; and 3) the gauging-to-tolerance-interval ratio. Such expressions can be applied to establish the measurement uncertainty and the amount of guardbanding required to meet preset decisional risks, thus avoiding the need for numerical integration and greatly reducing the cost of conformance testing procedures.
Measurement Process of experimentally obtaining one or more quantity values that can reasonably b... more Measurement Process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity. So, a measurement process provides, as a part of the measurement result, one or more quantity values that can be attributed to a quantity intended to be measured, that is also called, always according to the VIM [1], measurand. To fully understand this definition, we have to refer to the definition of quantity. We can find it again in the VIM. Quantity Property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.
This chapter analyzes one of the most common instruments in use in laboratories or fieldwork. It ... more This chapter analyzes one of the most common instruments in use in laboratories or fieldwork. It presents some history showing the characteristics of analog and digital oscilloscopes and how they have evolved through decades. The chapter also presents a brief description of the different waveforms one may find in normal engineering work. It describes different waveform characteristics and how to measure them using oscilloscopes. By describing their building blocks it is easy to understand limitations of each type of oscilloscope. The chapter gives a general idea of how to use oscilloscopes by explaining each of the most common controls found in their front panels. It shows the performance characteristics of oscilloscopes and how they can affect the measurements performed with them. The chapter outlines different types of probes available and their characteristics to be able to use the correct one for each different application.
The paper deals with the identification of FIR linear systems by time-domain least squares method... more The paper deals with the identification of FIR linear systems by time-domain least squares methods. Fast algorithms for solving the least squares problem are introduced. based on the notion of quasi-Toeplitz matrices. The estimation problem is solved by embedding it into a linear prediction one. and it is shown that the algorithms also allow the efficient solution of constrained least squares problems in a very common case. The iterative approach to constrained least squares identification is briefly considered. followed by the presentation of the applications considered by the authors. Finally. a few comments are made about the performances of the methods discussed.
The proliferation of distributed energy resources and plug-in electric vehicles is expected to ch... more The proliferation of distributed energy resources and plug-in electric vehicles is expected to change present distribution systems, thus stressing the role of measurement instrumentation enabling safe and flexible smart grid operation. In this context, Phasor Measurement Units (PMUs) are required to measure amplitude, phase, frequency and rate of change of frequency (ROCOF) of AC waveforms not only in steady state, but also, and above all, under dynamic conditions, while still ensuring extremely low measurement uncertainty and high reporting rates. In this paper a lightweight signal processing algorithm based on the so-called Teager's energy operator is adopted to measure amplitude, phase, frequency and ROCOF of AC waveforms in some of the testing conditions prescribed by the IEEE Standard C37.118.1-2011 and the IEEE Amendment C37.118.1a-2014. The reported analysis shows that the Teager's algorithm can provide high-rate and reasonably accurate measurement results under dynamic conditions. However, due to its sensitivity to wideband and narrowband disturbances, a preliminary band-pass filter is needed. In addition, instantaneous frequency and, above all, ROCOF estimates should be averaged to remove the residual effect of disturbances and to meet the limits reported in the IEEE Standards.
Wiener-Hammerstein models are flexible, well known and often studied. The main challenge in ident... more Wiener-Hammerstein models are flexible, well known and often studied. The main challenge in identifying a Wiener-Hammerstein model is to distinguish the linear time invariant (LTI) blocks at the front and the back. This paper presents a nonparametric approach to separate the front and back dynamics starting from the best linear approximation (BLA). Next, the nonparametric estimates of the LTI blocks in the model can be parametrized, taking into account a phase shift degeneration. Once the dynamics are known, the estimation of the static nonlinearity boils down to a simple linear least squares problem. The consistency of the proposed approach is discussed and the method is validated on the Wiener-Hammerstein benchmark that was presented at the IFAC SYSID conference in 2009.
In the considered scenario, a wireless sensor network (WSN) operates in a difficult to reach (or ... more In the considered scenario, a wireless sensor network (WSN) operates in a difficult to reach (or even hostile) environment, and is therefore required to autonomously configure itself and tune its parameters. We investigate techniques that guarantee a good compromise between conflicting requirements: 1) a good coverage of the area, 2) a long lifetime, 3) a good temporal accuracy in classifying the events. Our solution is based on the combination of two complementary techniques. The first one, the wakeup scattering algorithm, iteratively identifies a periodic schedule that keeps the node awake for a limited time, so saving power. In this paper, we consider the global convergence of this algorithm. The second technique is a small overhead distributed algorithm for the synchronization of the nodes, which takes into account the communication delays.
The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for activ... more The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for active distribution systems monitoring, requires to achieve challenging trade-offs between measurement uncertainty and responsiveness. This is particularly important for protection-oriented (i.e., P Class) PMUs. In order to improve estimation accuracy with no need to prolong the data record size and the related delays, this paper presents a Taylor Kalman Filter (TKF) enhanced with a preliminary stage able to whiten possible narrowband disturbances over short observation intervals. The use of dynamic estimators such as the TKF is motivated by the need to track possible sudden amplitude or phase changes of voltage or current AC waveforms, which are likely to occur in smart grids. However, while a basic TKF is very sensitive to disturbances different from white noise, the proposed whitening-technique is able to greatly improve the estimation accuracy of synchrophasor amplitude, phase, frequency and Rate of Change of Frequency (ROCOF) under the influence of harmonics and amplitude or phase step changes even over one-cycle observation intervals, with just a minor performance degradation in the other P Class testing conditions reported in the IEEE/IEC Standard 60255-118-1:2018.
Abstract A Renewable Energy Community (REC) is a legal entity aggregating different users sharing... more Abstract A Renewable Energy Community (REC) is a legal entity aggregating different users sharing their own resources to reduce both electricity bills and CO 2 emissions. This paper presents and analyses the impact of a bi-objective strategy to optimise the capacity of the Battery Energy Storage Systems (BESSs) of REC prosumers equipped with photovoltaic (PV) generators. The optimisation problem is solved through a custom implementation of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and has two contrasting objectives: maximising the self-sufficiency of the REC from the main grid, while minimising the BESS capacity of all REC members. A key novelty of this study is the prosumer-driven perspective, which allows to exclude the REC members who do not want to install a BESS through a linear optimisation constraint. Moreover, the proposed approach ensures that probabilities of over- or under-voltages are compliant with the limits specified by Distribution System Operators (DSOs). Such probabilities, as well as the line and BESS losses, are estimated within the optimisation loop through grid-level simulations performed in OpenDSS. Both a standard peer-to-grid (P2G) and a more REC-oriented peer-to-peer (P2P) energy sharing policy are analysed and their performance is assessed in different seasons and considering both the current energy demand and a possible future scenario, in which electrical heat pumps are widely used. The results of a case study based on a modified version of the IEEE 906-bus European Low Voltage distribution grid show that a if the total BESS capacity assigned to all REC prosumers exceeds a given threshold value, the benefits for the REC become minor. Assuming to choose the optimal BESS capacity solutions corresponding to the threshold value in the summer season (i.e., when PV and BESSs are most exploited), the overall energy losses are reduced roughly by 20%–40% for both P2G and P2P battery controls. The CO 2 emissions instead, are reduced by 10% to 50% with the P2P policy having a slight edge over the P2G one. The P2P energy sharing policy spreads the economic benefits of energy savings more evenly among REC members, and the return on investment is generally higher if the electricity demand increases.
IEEE Transactions on Instrumentation and Measurement, Oct 1, 2014
ABSTRACT Next-generation phasor measurement units (PMUs) are expected to play a key role for moni... more ABSTRACT Next-generation phasor measurement units (PMUs) are expected to play a key role for monitoring the behavior of future smart grids. While most of the PMUs used nowadays in transmission networks rely on static phasor models, more sophisticated representations and stricter accuracy requirements are needed to track amplitude, phase, and frequency changes of power waveforms in strongly dynamic scenarios as those expected in future distribution systems. In this paper, a discrete Fourier transform (DFT)-based algorithm based on a dynamic phasor model (referred to as interpolated dynamic DFT-based synchrophasor estimator) is used to estimate not only amplitude and phase of the collected waveforms, but also their frequency and rate of change of frequency. The performances of the proposed method are evaluated through multiple simulations in different steady-state and transient conditions described in the Standard IEEE C37.118.1-2011.
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Papers by Dario Petri