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In this article, a comprehensive method for parametric representation of wire trajectories, allowing accurate geometric description of complex and arbitrarily oriented wire bundles, is introduced. This is the starting point to develop a computationally efficient numerical transmission-line (TL) model for predicting the radiated susceptibility of arbitrarily oriented bundles of wires, illuminated by (possibly) nonuniform electromagnetic fields. The proposed method foresees solution of the field-to-wire coupling problem through suitable discretization and sampling of the bundle geometry and the incident electromagnetic field. Differently from previous models, where bundles parallel to ground were assumed, the proposed model allows for arbitrary bundle orientation by exploiting, first, exact projection of the external field onto the bundle direction, and second, evaluation of the actual wire length (instead of the longitudinal one) of each TL section. Accuracy and computational efficiency of the proposed method are assessed versus full-wave simulation for two application examples, involving parabola-shaped and trefoil knot-shaped wiring structures above ground. Although the strong nonuniformity affecting these structures forces TL theory to work very close to its limits, the achieved agreement is satisfactory and the significant reduction of computational times makes the proposed method suitable for approximate yet efficient prediction of radiated susceptibility characteristics of complex wire bundles.

Inductive instrument transformers (ITs) are still the most used voltage and current sensors in power systems. Among the numerous applications that require their use, one of the most important is surely represented by harmonics measurement. In this case, the recent literature shows that, since they suffer from both a filtering behavior due to their dynamics and from nonlinear effects produced by their iron core, they can introduce errors up to some percent. This article wants to deeply investigate, in the very same experimental conditions, about the performance of two digital signal processing techniques, recently introduced for the improvement of harmonics measurements performed through ITs, namely, SINusoidal characterization for DIstortion COMPensation (SINDICOMP) and compensation of harmonic distortion through polynomial modeling in the frequency domain (PHD). These methods have been applied to two different voltage transformers, having different specifications, by using two measurement setups based on different architectures. The impact of the voltage generator employed during the identification on the achieved accuracy is theoretically and experimentally evaluated. Modified versions of SINDICOMP and PHD compensation, which are more robust against nonidealities of the measurement setup, are presented. The performances of the techniques are evaluated by adopting voltage waveforms similar to those that can be encountered during the normal operation in a real distribution grid.

Purpose Despite its well-founded criticism and lack of proper justification under core saturation conditions, the T-equivalent transformer model (Steinmetz scheme) is obviously championing in the literature. This educational paper aims to explain in a simple manner the limitations of the T-model of a low-frequency transformer and critically analyses some attempts to improve it. Design/methodology/approach Using a simplified examination of magnetic fluxes in the core and windings and using the modeling in ATPDraw, it is shown that transient transformer models with the indivisible leakage inductance allow circumventing the drawbacks of the T-model. Findings The authors show the absence of valid grounds for subdividing the leakage inductance of a transformer between its primary and secondary windings. The connection between the use of individual leakage inductances and inaccurate prediction of inrush current peaks is outlined as an important example. Practical implications The presented models can be used either as independent tools or serve as a reference for subsequent developments. Social implications Over generations, the habitual transformer T-equivalent is widely used by engineers and Electromagnetic Transients Program experts with no attention to its inadequacy under core saturation conditions. Having studied typical winding configurations, the authors have shown that neither of them has any relation to the T-equivalent. Originality/value This educational paper will contribute to the correct understanding of the transients occurring in a transformer under abnormal conditions such as inrush current or ferroresonance events, as well as during an out-of-phase synchronization of step-up generator transformers.

With the expansion of photovoltaic cell installation in residential units, the low voltage distribution system faces a new challenge concerning the stability of the distribution network. This problem is associated with sudden flickers - that is overvoltage followed by under voltage due to the uncontrolled connection/disconnection of the photovoltaic units. This paper introduces a distribution static synchronous shunt compensator based on a modular multilevel converter as a solution to regulate the overvoltage and give the distribution network more stability.

Decaying DC (DDC) current due to impact loads causes detrimental consequences in weak grids. In this paper, the active power filter (APF) is enhanced to simultaneously compensate for the undesired harmonics, negative sequence components and the DDC component in the event of a transient. To this end, first, a novel DDC component detection method is mathematically deduced for single-phase transient current, followed by its extension to the three-phase system. With respect to existing techniques, the proposed method has a significantly reduced detection time from 1 grid cycle to approximately 0.5 grid cycle. By further exploiting the transient signal properties in dq -frame, the three-phase fundamental-frequency current in positive sequence can be separated. Finally, the enhanced APF control scheme is developed based on the proposed detection algorithm. Experiments verified the effectiveness and advancement of the proposed technique.

In this article, a systematic procedure to derive equivalent circuit networks accurately reproducing the frequency response of the input impedance of magnetic cores in a broad frequency range is presented. The proposed procedure foresees to represent the effective complex permeability spectra of a magnetic core (i.e., the permeability resulting from the superposition of intrinsic material properties and effects due to structural features of the core) by a high-order Debye series expansion, which is subsequently synthesized into suitable Foster and Cauer networks. Such networks can be implemented in any circuit simulator, and are particularly favorable for time-domain transient simulation since they can be easily combined with hysteresis models. Two nanocrystalline tape-wound cores and a commercial bulk current injection probe are used as test cases to prove the effectiveness of the proposed method both in terms of accuracy and ease of implementation.

Lithium ion batteries are being used in an increasing number of applications. However, one of their major weaknesses is their sensitivity to temperature. Indeed, their safety and aging strongly depend on their temperature. In order to control cell temperatures, each cell in a battery pack is usually equipped with a thermal sensor. This paper proposes an integrated electro-thermal model that is capable of predicting the thermal behavior of a battery cell based only on its current and ambient conditions. The proposed model was tuned and validated by means of experimental results. The obtained precision is sufficient to predict the temperature of a battery with an acceptable accuracy considering the low complexity of the proposed model.

Inverter-based standalone power systems (ISPSs), with limited inertia/damping, are prone to significant changes in frequency indicators encompassing frequency deviation and rate of change of frequency (RoCoF), which can easily exceed the pertinent relay thresholds and cause power outages. Limited by estimating the disturbance and system inertia/damping deficiency, existing controls cannot ensure system frequency stability. To overcome this issue, a frequency trajectory planning (FTP) based strategy is developed in this article to improve frequency stability of droop-controlled ISPS. This frequency-indicator-oriented control relates system frequency with several pre-defined planning parameters, decoupling from system’s disturbances and inertia/damping deficiency that are difficult to evaluate. During normal operation or when the disturbance level is insignificant, the inverter operates in standard droop mode since the system intrinsic inertia/damping features suffice to regulate the frequency. In the event of a large disturbance, an FTP block is triggered by detected frequency indicators, and a marginally safe frequency trajectory is planned according to the requirement of the grid code. In this case, by tracking the planned frequency trajectory, the inverter provides suitable inertia/damping support needed by the system, thereby guaranteeing frequency stability of the ISPS. Finally, simulation and experimental results proved the effectiveness and advancement of the FTP based strategy.

The widespread diffusion of nonlinear power electronics-based devices in distribution grids has raised the interest toward power quality monitoring. In this respect, the estimation of synchronized harmonic phasors would enable the employment of algorithms that allow identifying the sources of harmonic disturbances, which, until now, have only been tested through numerical simulations or implemented on small-scale. However, the impact of the uncertainty due to the employed voltage transformers (VTs) and to the other devices that compose the measurement chain has to be analyzed. In this framework, the present article proposes a class of harmonic synchrophasor estimation algorithms that allows compensating the frequency response function of the instrument transformer. The technique has been tested and validated under realistic conditions considering an inductive VT. Experimental results highlight its effectiveness, especially when taking into account its ease of implementation. The black-box approach allows abstracting from the operating principle of the VT.

Change in density will cause errors in measurement for indirect-based level sensing approaches, such as capacitive sensors. In addition, there is growing attention in measuring density accurately not only in laboratory conditions but also in a real-time dynamic environment. To address the above-mentioned issues, an independent instrument based on differential pressure sensors is proposed in this article. Synchronous detection is used to detect the desired signal by calculating the coefficients of the digital Fourier transform. The characterization of the sensor is experimentally determined under a steady-state condition, where a linear response is observed. The thermal behavior of the proposed sensor is studied and compensated using the polynomial fitting technique. Evaluating the uncertainty due to reference values, linearity, and repeatability, the obtained results show a combined uncertainty lower than 7.5 (mg/cm3), mainly limited by observed asymmetric hysteresis at higher temperatures.

In this paper, a systematic approach for electromagnetic compatibility (EMC) modelling of hand-assembled, complex cable bundles is presented. The first part of the article focuses on bundles laid out above a ground plane, with layout approximately parallel to the reference ground. In order to generate smooth and physics-based trajectories, polynomial curves are used to represent the conductors in the bundle. A suitable process for the generation of bundle samples is developed, which allows for controlling the degree of randomness and avoiding conductors overlapping. Parametric representation of more general bundle structures with arbitrary orientation is then addressed, and the modeling approach is extended to more complex bundle structures, such as bundles involving twisted-wire pairs. To assess the ability of Transmission Line (TL) theory to deal with complex and locally highly non-uniform bundle shapes, a fictitious bundle trajectory shaped as a trefoil knot is introduced. All the generated bundle geometries are used in combination with TL-based EMC models in order to predict the disturbances induced in the bundle terminal units due to crosstalk or coupling with external electromagnetic fields. Prediction accuracy is assessed by comparison versus full-wave electromagnetic simulation of the same bundle structures. Suitable examples are presented to show the high numerical efficiency and good accuracy of the proposed modeling approach, as well as the need for accurate and physics-based representation of the bundle geometry in order to achieve solid EMC prediction in a wide frequency range.

Modeling the effects of uncertainty is of crucial importance in the signal integrity and Electromagnetic Compatibility assessment of electronic products. In this article, a novel machine-learning-based approach for uncertainty quantification problems involving both random and epistemic variables is presented. The proposed methodology leverages evidence theory to represent probabilistic and epistemic uncertainties in a common framework. Then, Bayesian optimization is used to efficiently propagate this hybrid uncertainty on the performance of the system under study. Two suitable application examples validate the accuracy and efficiency of the proposed method.

In this article, a novel procedure for the frequency-domain solution of nonuniform transmission lines (NUTLs) is presented. The procedure is based on a recently proposed perturbative technique, which is proven to be computationally more efficient than standard solution approaches, which are based on line subdivision into uniform cascaded sections. With respect to the original perturbation technique, the procedure proposed here offers more flexibility, as it provides a representation of the NUTL under analysis in terms of $S$ and/or $T$ parameters at its ports. Moreover, it retains the same prediction accuracy at the price of a slight increase in computational burden, which can be mitigated anyway through parallel computing. Furthermore, even without ad hoc (parallel) implementations, the proposed procedure outperforms other approaches to solve differential lines with partially or fully repetitive geometries. Namely, it assures accurate prediction of output quantities with reduced simulation time. This is proven by three application examples, namely, two differential trapezoidal tabbed lines (one with interdigital tabs and one with facing tabs), and a differential microstrip line with a varying common-mode (CM) impedance (as such reducing CM noise). Comparison with full-wave simulations allows assessing the prediction accuracy of the proposed procedure. Comparison with the aforementioned transmission-line-based solutions allows appreciating the enhanced computational efficiency.

Synchronized phasor and frequency measurements are key tools for the monitoring and management of modern power systems. Under dynamic conditions, it is vital 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 the Kalman filter approach. This article proposes a three-phase synchrophasor estimator based on the extended Kalman filter; state variables are obtained from Taylor expansions of amplitudes and phase angles. The underlying dynamic model considers the inherent relationship among the phases and includes harmonics in an effective way. The process noise covariance matrix that allows representing the uncertainty introduced by the dynamic model has been written by considering that practical ac power systems are nearly three-phase symmetric during typical operation. This a priori information allows improving noise rejection and increasing accuracy in the presence of amplitude modulation, as highlighted by the reported simulation results.

The measurement of modal impedances of switching-mode power supplies (SMPSs) is of paramount importance in electromagnetic compatibility applications, especially when designing electromagnetic interference filters to suppress the conducted and radiated electromagnetic emissions is the target. A novel measurement technique that makes use of an impedance analyzer and a coupling transformer and allows extracting the complex value of common- and differential-mode noise source impedance of an SMPS is proposed. The measurement procedure is first studied from the theoretical point of view, then experimentally validated with passive components, and eventually implemented in a CISPR-25 conducted emission test setup to measure the magnitude and phase of modal impedances of an automotive SMPS under different operation conditions.

To achieve a reliable and accurate liquid-level detection, a differential pressure-based instrument is proposed in this article. The phase-sensitive demodulation of the signal is performed by the discrete Fourier transform (DFT) through a microcontroller. A good linearity in both ac and dc measurements has been observed. AC-based-level sensing demonstrated reliable and robust-level detection compared with dc, in both steady state conditions and while experiencing turbulence on the surface. In addition, thermal behavior of the proposed instrument is characterized and compensated, in order to evaluate its uncertainty as a liquid-level sensor. The obtained results show a combined uncertainty lower than 1 mm, which is mainly limited by sloshing conditions.

Fast synchronized measurements of the phasor, frequency, and rate of change of frequency are expected to be very important for the automated control actions in the smart grid context. In this regard, measurement latency must be kept as short as possible for an effective control implementation when networks characterized by extremely fast dynamics are concerned. Kalman filter (KF)-based estimation algorithms appear to be attractive in this context; however, the conventional implementations suffer from significant limitations in their ability to deal with different types of dynamic conditions due to approximations in the model and in the associated uncertainty. This article proposes an innovative solution, based on an extended KF algorithm using a Taylor model, which is shown to provide improved tracking ability in a vast range of dynamic conditions. A novel element in the proposed technique is the representation of model uncertainty, which takes into account the intrinsic correlation among errors that appear in the state–space description under dynamic conditions. A compatibility check between the forecast and measurement result is also introduced as an effective and metrologically sound approach to detect large unexpected changes in the tracked parameters in order to achieve a fast response of the algorithm also under those conditions. The performance of the algorithm is thoroughly investigated by means of simulation to demonstrate the significant improvement compared to other KF solutions in some conditions of practical relevance.

We measure the noise of the converted frequency-modulated (cFM) signal in a self-mixing interferometer (SMI) and confirm the theoretical prediction of a dependence of rms noise from ( $1+ C)^{-1}$ , where $C$ is the Acket feedback factor, up to a high value (i.e., $C=30$ ) in region III of Tkach and Chraplyvy feedback diagram. We also verify the minor dependence of noise from the phase factor 2 ks + atan $\alpha $ . Finally, we show that the cFM SMI easily attains an unprecedented limit of small-signal detection, with amplitudes down to 0.25 pm/ $\surd $ Hz.

In this paper, a hybridization of the classical stochastic Galerkin method (SGM) with two perturbative solution techniques is proposed to speed up the statistical analysis of nonuniform multiconductor transmission line (MTL) structures with parameters affected by uncertainty. The first method leverages a recently developed deterministic perturbation technique (PT) to deal with nonuniformity affecting the SGM-augmented MTL equations. This approach is proven to be computationally more efficient than the traditional solution based on line subdivision into uniform cascaded sections, yet its performance is still affected by the so-called "curse of dimensionality." To further mitigate this issue, a second method is proposed, which resorts to the solution of uncoupled MTLs having the same size as the original structure, and where the effects of both nonuniformity and stochasticity are iteratively included by means of distributed sources. The accuracy and computational efficiency of the proposed approaches are assessed based on the statistical prediction of the mixed-mode S-parameters of microstrip-line structures with different numbers of random parameters. The test cases demonstrate that the hybrid SGM-PT approach is applicable to problems with a few tens of random variables, which is an unprecedented result for state-of-the-art SGM implementations.

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.

In this paper, transmission-line (TL) theory is applied to formulate a worst-case analysis for the assessment of wideband intentional electromagnetic interference radiated onto a cable harness (with terminal units) above ground. Given the bandwidth and the energy density of the high-power electromagnetic pulse impinging on the cable, the pulse spectrum maximizing the peak value of the common-mode voltage waveform induced at a cable end is obtained. Unlike in a full-wave solution to the problem, the proposed TL model allows for, first, deriving closed-form expressions in the special case of a cable terminated in a matched load at the opposite end; second, computationally efficient evaluation of the spectrum for any other loading conditions. The obtained results clearly unveil the impact of the system parameters (cable length, height, terminal loads, and pulse bandwidth) on the statistics of the worst-case voltage peak for the random direction of incidence and polarization.

Asymmetrical working conditions of the utility grid introduce the large-amplitude negative-sequence component to the output current of the voltage source converter (VSC), causing power semiconductor devices to suffer from thermal fatigue and thermal damage. Though the conventional phase-locked loop (PLL) based voltage oriented control (VOC) solution can suppress the steady-state negative-sequence current effectively, it has a weak suppression ability of transient overload current, and even aggravates the transient current asymmetry and causes more severe transient impact to the VSC. This paper first analyzes the transient performance of the conventional VOC strategy, especially its dynamic response time and the main factors for performance limitation. On this basis, the PLL-free VOC strategy for VSCs tied to unbalanced grids is proposed, and its critical parts, namely, the reference current calculation and the fast detection of the grid voltage sequence components, are implemented. Besides, to improve the frequency adaptability, a high-performance grid frequency detection strategy is developed based on the difference-frequency phase caused by the frequency variation. Finally, experiments are performed to verify the effectiveness and advancement of the proposed method. Specifically, the results proved the rapidity, accuracy, and frequency adaptability of the proposed method in suppressing the VSC negative-sequence current, both in transient and steady-state conditions.

Amplitude-phase information of the voltage/current phasor, which is the prerequisite for grid-tied converter control and protection, can change almost instantaneously in low-voltage distribution systems with small X/R ratios. However, the equivalent impedances of high-voltage power systems are usually inductive (with large X/R ratios), and the power flow of pertinent grids generates decaying dc (DDC) components with large amplitude and long duration during large disturbances. Therefore, the X/R ratios and DDC components must be fully considered in amplitude-phase detection to achieve effective converter control and protection. To this end, the main components present in the transient voltage/current of a high-voltage power system after unbalanced disturbance are first analyzed, and the general transient model is obtained by synthesizing multimode DDC components. Then, by resorting to waveform characteristics of different components, an amplitude-phase detection algorithm is proposed based on the multicomponent parallel-detection structure. Compared to existing techniques, the detection time is reduced to half grid cycle. Finally, an iterative variable-interval integral algorithm is developed, improving the antinoise ability of detection algorithm and overcoming the computational burden issue. This enables the direct integration of algorithm into the converter's embedded processor. Experiment results verified the effectiveness and superiority of the proposed technique.

Power Line Communication (PLC) technologies are being used in many applications and offer the advantage of utilizing existing power cables for both power and data transmission, thus minimizing cost and complexity. Nevertheless, PLC technology requires further investigation to solve possible co-existence issues. Indeed, recent studies confirmed that alternative modulation schemes such as Random Pulse Width Modulation (RPWM), applied to switching-mode power converters to minimize conducted emissions, detrimentally interfere with the PLC system. This paper presents an experimental test campaign aimed at investigating the effects of RPWM on the G3-PLC system, with the final goal of understanding the conditions under which RPWM schemes can be considered as an effective alternative to conventional Pulse Width Modulation (PWM) in applications involving PLC systems. In details, the effects of different RPWM parameters such as switching frequency, modulation index, and Random Number Update Rate (RNUR) on the G3-PLC is investigated. In addition, different RPWM schemes such as Random Frequency Modulation (RFM) and Random Pulse Position Modulation (RPPM) are compared in terms of performance so as to highlight which RPWM is best suited to assure coexistence with PLC systems. The impact of RPWM on the communication channel is evaluated in terms of Frame Error Rate (FER), Channel Capacity, and Channel Capacity Loss metrics. Experimental results confirmed that randomly modulated converters with switching frequencies near the G3-PLC bandwidth cause more significant disturbance and possible coexistence issues than the switching frequencies out of this range. Results also show that the modulation index and the RNUR of RPWM have a direct effect on the communication channel. Moreover, a trade-off between Electromagnetic Interference (EMI) reduction and coexistence issues is observed: RFM, which is very effective for EMI reduction, is found to be very disruptive for G3-PLC, compared to alternative random modulation techniques such as RPPM.

In this work, a two-step procedure to predict maximum (worst-case scenario) and minimum (best-case scenario) noise levels induced by bulk current injection (BCI) at the terminal sections of a wiring harness is presented. To this end, common mode (CM) and differential mode (DM) quantities are introduced by a suitable modal transformation, and equivalent modal circuits are derived, where CM (dominant mode) into DM (secondary mode) conversion is modelled by induced sources included into the DM circuit. The procedure initially foresees the solution of the CM circuit to provide input data for subsequent solution of the DM circuit. Such a two-step approach is then used to develop a probabilistic-possibilistic framework for computationally-efficient estimation of lower and upper boundaries to the variability of the noise voltages induced at the bundle terminations. To this end, random uncertainty affecting certain setup parameters is addressed through probability theory, whereas epistemic uncertainty is represented via possibility theory. Accuracy and computational efficiency of the proposed two-step method are assessed by examples involving seven and nineteen wire harnesses.