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In this study, the implementation of different corona discharge models in a transient program for overhead multiconductor lines based on the implicit Crank‐Nicolson Finite Difference Time Domain method is presented. Among different corona models available in the literature, two empirical models (Gary's and Suliciu's models) and a physics‐based model (Malik's model) are discussed, which are broadly used in EMT programs, and their predictions under fast‐front lightning surges and slow‐front switching impulses are assessed. The authors critically review the dynamic capacitance approach in terms of numerical accuracy, when dealing with slowly varying voltages, and applicability, regarding dispersive models assuming a non‐instantaneous charge‐voltage relation. The alternative voltage‐controlled generator approach is proposed, which is successfully included in the implicit Crank‐Nicolson scheme. One of the objectives of this study is to show how different corona models may predict overvoltages with huge discrepancies, depending on the transient waveform and the propagation distance, despite the similarity of the q‐v hysteresis curves. More evident discrepancies between models under fast‐front voltage waves are reported, rather than for switching impulses. The consistency of these results in terms of the models' features and q‐v curves is analysed, highlighting the necessity for new engineering tools for corona simulation of general predictive capability.

The improvement of the lightning performance of overhead distribution lines, hit by direct strokes, is investigated considering the use of additional shield wires beneath the phase conductors. The frequency-domain theory of multiconductor transmission lines with periodical grounding is adopted permitting a rigorous evaluation of the phase and shield wire currents and of the overvoltages across insulators. These can be minimized by careful positioning of the underbuilt shield wires. A sensitivity analysis on the overvoltages is conducted by varying either the position of the underbuilt shield wires and the grounding impedance.

This work investigates voltages on overhead distribution lines produced by direct strokes, protected by shield wires, placed both above and below phase conductors. An improved formulation based on transfer matrix method and theory of multiconductor transmission lines with periodic grounding allows to eliminate the need of two characteristic wave impedance matrices. Based on the theoretical formulation developed in the first part of this work, as well as on the models there presented for the pole and grounding systems, we report here a wealth of simulation results concerning the line overvoltages subsequent to a pole being hit by lightning. Results are discussed considering a variety of factors, namely, position of the victim pole, type of load at both ends of the line, presence or absence of underbuilt shield wires, waveform of the lightning current, soil parameters and parameters of the frequency-dependent impedance of the pole grounding system. The good performance of the developed method is assessed by comparing our results with some EMTPRV simulations. The transfer matrix method is then used to show the effect of shield wires in conjunction with periodic grounding: we assess the effects of terminations, frequency dependent models of the pole footing and grounding systems and frequency dependent models of lossy ground.

This work is devoted to the analysis of voltages produced on overhead distribution lines hit by direct lightning. We will consider arbitrary terminations at both line ends and, also, arbitrary positioning of the pole being struck. We will deal with lines protected by shield wires, placed either above or below the phase conductors. The analytical tools chosen to deal with such complex system are the transfer matrix method and the theory of multiconductor transmission lines with periodic grounding. The innovation of an articial symmetrical unit cell has been introduced to eliminate the need of two characteristic wave impedance matrices and to ease computation ow.

Typically, in partial discharges (PD) diagnostics tests carried out in a laboratory, harmonic content in a voltage waveform is ignored. However, during the operation of variable-frequency drives (VFD)-fed electric motors, the distorted voltage waveform is produced due to the addition of harmonics components in the sinusoidal voltage waveform. The distortion level increases when the VFD is operated at a lower speed ratio. The additional spectral components in the applied voltage waveform can have a significant impact on the PD behavior in the insulation of the electric motor. Therefore, during online PD monitoring, overlooking the harmonic regime in the applied voltage may lead to a false interpretation of PD data. This article investigates the influence of voltage harmonics distortion produced during the variable-speed operation of VFD on PD characteristics. For this purpose, online PD measurements have been carried out by performing a series of experiments on eight VFD-fed motors under variable operating conditions. The PD severity at different harmonic compositions is experimentally investigated by determining various PD characteristic parameters including PD inception voltage, accumulated apparent charge, average discharge current, discharge power, and quadratic rate. Also, two terms Gaussian models have been mathematically developed using 288 data samples to quantify the variations in PD characteristic parameters against distortion parameters. The article proposes a framework for properly evaluating harmonics impact in PD for electric motors and correctly estimating stator insulation degradation.

In this paper, that is an extended version of a work [1] presented at the 2019 International Symposium on Lightning Protection (XV SIPDA), a survey of analytical solutions available in the literature for the evaluation of the lightning-induced voltages in case of both step and linearly rising channel-base currents is presented. Two tools, CiLIV and LIV, based on some of the above mentioned analytical solutions are also presented. Finally, a validation of both analytical solutions and tools is presented.

Here, we propose a new deep learning scheme to solve the energy time series prediction problem. The model implementation is based on the use of Long Short-Term Memory networks and Convolutional Neural Networks. These techniques are combined in such a fashion that inter-dependencies among several different time series can be exploited and used for forecasting purposes by filtering and joining their samples. The resulting learning scheme can be summarized as a superposition of network layers, resulting in a stacked deep neural architecture. We proved the accuracy and robustness of the proposed approach by testing it on real-world energy problems.

The Multiple Microgrids (MMGs) concept has been identified as a promising solution for the management of large-scale power grids in order to maximize the use of widespread renewable energies sources. However, its deployment in realistic operation scenarios is still an open issue due to the presence of non-ideal and unreliable communication systems that allow each component within the power network to share information about its state. Indeed, due to technological constraints, multiple time-varying communication delays consistently appear during data acquisition and the transmission process and their effects must be considered in the control design phase. To this aim, this paper addresses the voltage regulation control problem for MMGs systems in the presence of time-varying communication delays. To solve this problem, we propose a novel hierarchical two-layer distributed control architecture that accounts for the presence of communication latencies in the information exchange. More specifically, the upper control layer aims at guaranteeing a proper and economical reactive power dispatch among MMGs, while the lower control layer aims at ensuring voltage regulation of all electrical buses within each MG to the desired voltage set-point. By leveraging a proper Driver Generator Nodes Selection Algorithm, we first provide the best choice of generator nodes which, considering the upper layer control goal, speeds up the voltage synchronization process of all the buses within each MG to the voltage set-point computed by the upper-control layer. Then, the lower control layer, on the basis of this desired voltage value, drives the reactive power capability of each smart device within each MG and compensates for possible voltage deviations. Simulation analysis is carried out on the realistic case study of an MMGs system consisting of two identical IEEE 14-bus test systems and the numerical results disclose the effectiveness of the proposed control strategy, as well as its robustness with respect to load fluctuations.

Surge arresters may represent an efficient choice for limiting lightning surge effects, significantly reducing the outage rate of power lines. The present work firstly presents an efficient numerical approach suitable for insulation coordination studies based on an implicit Crank–Nicolson finite difference time domain method; then, the IEEE recommended surge arrester model is reviewed and implemented by means of a local implicit scheme, based on a set of non-linear equations, that are recast in a suitable form for efficient solution. The model is proven to ensure robustness and second-order accuracy. The implementation of the arrester model in the implicit Crank–Nicolson scheme represents the added value brought by the present study. Indeed, its preserved stability for larger time steps allows reducing running time by more than 60 % compared to the well-known finite difference time domain method based on the explicit leap-frog scheme. The reduced computation time allows faster repeated solutions, which need to be looked for on assessing the lightning performance (randomly changing, parameters such as peak current, rise time, tail time, location of the vertical leader channel, phase conductor voltages, footing resistance, insulator strength, etc. would need to be changed thousands of times).

In this paper, we thoroughly review all analytical solutions (both exact and approximate) presented to date in the literature for evaluation of voltages induced on a lossless horizontal conductor, placed over an infinite-conductivity ground, and excited by an external field produced by either a step function or a linearly rising current, moving unattenuated and undistorted along a vertical lightning channel. We also obtain the exact analytical solution for the step-function current case in the time domain via development in the s -domain. To date, there had been three attempts to obtain such solution, all of which yielding incorrect results.

In this paper, we present a new solution for the evaluation of the horizontal electric field in the presence of finitely conducting ground in the time domain. The solution is general, numerically robust, and overcomes the problems related to previously proposed approaches.

In the present work we assess the lightning performance against direct strokes of overhead distribution lines, making use of the theory of multiconductor transmission lines with periodical grounding, recently developed by the authors. We assume that the lightning protection is provided by shield wires that are placed both above and below (underbuilt construction) the phase conductors. We adopt the transmission line model to include the propagation effects on the poles. We investigate the effects of geometrical parameters, and, by the analyses of different arrangements, we evaluate the impact on the lightning performance. The core of the work is the demonstration that addition of underbuilt ground wires can be a viable solution for improving the lightning protection of distribution lines.

The probability of flashovers due to indirect lightning on overhead lines is us ually calculated assuming a statistical distribution for the induced voltages, and a deterministic and specified value for the insulation level of the line. However, more accurate practices of insulation coordination suggest a statistical treatment for the insulation level too, in order to relate the probabilistic nature of both electrical stress (induced voltage) and the electrical strength (insulation level). In this paper, a statistical insulation coordination method is applied for the assessment of induced-voltage flashovers and, more in general, for the indirect lightning performance of the line. Such a statistical approach, which is inherently more accurate than the traditional approach, allows also to discriminate among probability of occurrence of flashovers on one, two, or on all phases.

Modern power distribution systems require reliable, self-organizing and highly scalable voltage control systems, which should be able to promptly compensate the voltage fluctuations induced by intermittent and non-programmable generators. However, their deployment in realistic operation scenarios is still an open issue due, for example, to the presence of non-ideal and unreliable communication systems that allow each component within the power network to share information about its state. Indeed, due to technological constraints, time-delays in data acquisition and transmission are unavoidable and their effects have to be taken into account in the control design phase. To this aim, in this paper, we propose a fully distributed cooperative control protocol allowing the voltage control to be achieved despite the presence of heterogeneous time-varying latencies. The idea is to exploit the distributed intelligence along the network, so that it is possible to bring out an optimal global behavior via cooperative distributed control action that leverages both local and the outdated information shared among the devices within the power network. Detailed simulation results obtained on the realistic case study of the IEEE 30-bus test system are presented and discussed in order to prove the effectiveness of the proposed approach in the task of solving complex voltage control problems. Finally, a robustness analysis with respect to both loads variations and hard communication delays was also carried to disclose the efficiency of the approach.

The large-scale integration of renewable power generators in power grids may cause complex technical issues, which could hinder their hosting capacity. In this context, the mitigation of the grid voltage fluctuations represents one of the main issues to address. Although different control paradigms, based on both local and global computing, could be deployed for online voltage regulation in active power networks, the identification of the most effective approach, which is influenced by the available computing resources, and the required control performance, is still an open problem. To face this issue, in this paper, the mathematical backbone, the expected performance, and the architectural requirements of a novel decentralized control paradigm based on dynamic agents are analyzed. Detailed simulation results obtained in a realistic case study are presented and discussed to prove the effectiveness and the robustness of the proposed method.

In this paper the results of the estimated electric field associated with tortuous lightning paths at close distance (50 m to 500 m) are shown. Such results are compared with experimental data available in the literature and are illustrated along with a quantitative analysis of the field waveforms and their frequency spectra. The limits of the usual straight-vertical channel assumption and the influence of tortuosity at different azimuth and distances from the lightning channel base are also highlighted.

The large-scale deployment of pervasive sensors and decentralized computing in modern smart grids is expected to exponentially increase the volume of data exchanged by power system applications. In this context, the research for scalable and flexible methodologies aimed at supporting rapid decisions in a data rich, but information limited environment represents a relevant issue to address. To this aim, this paper investigates the role of Knowledge Discovery from massive Datasets in smart grid computing, exploring its various application fields by considering the power system stakeholder available data and knowledge extraction needs. In particular, the aim of this paper is dual. In the first part, the authors summarize the most recent activities developed in this field by the Task Force on &ldquo, Enabling Paradigms for High-Performance Computing in Wide Area Monitoring Protective and Control Systems&rdquo, of the IEEE PSOPE Technologies and Innovation Subcommittee. Differently, in the second part, the authors propose the development of a data-driven forecasting methodology, which is modeled by considering the fundamental principles of Knowledge Discovery Process data workflow. Furthermore, the described methodology is applied to solve the load forecasting problem for a complex user case, in order to emphasize the potential role of knowledge discovery in supporting post processing analysis in data-rich environments, as feedback for the improvement of the forecasting performances.

In the modern scenario of smart-grids, the concept of virtual power plant (VPP) is undoubtedly a cornerstone for the smooth integration of renewable energy sources into existing energy systems with a high penetration level. A VPP is the aggregation of decentralized medium-scale power sources, including photovoltaic and wind power plants, combined heat and power units, as well as demand-responsive loads and storage systems, with a twofold objective. On one hand, VPP relieves the stability and dispatchability problems on the external smart grid since it can be operated on an individual basis, appearing as a single system on the whole. On the other hand, VPP improves flexibility coming from all the networked units and enable traders to enhance forecasting and trading programs of renewable energies. This paper proposes a novel distributed decentralized prediction method for the management of VPPs. The novelty of the proposed technique is to effectively combine the concepts of neural networks and machine learning with a distributed architecture that is suitable for the aggregation purposes of the VPP.

We propose a new channel-base current model, which is particularly well suited for lightning-induced voltage calculations. We will show that this new proposal meets a significant number of characteristics required to these applications, and favorably compares to existing solutions.

In this paper the effects of different parameters affecting lightning-induced voltages are analyzed. Both a parametric and a statistical analysis is carried out by means of the Andreotti et al. solutions, both for a step-function and a Iinearly-rising channel base currents. Use of exact analytical solutions represents the main contribution of this paper.

In this paper, we propose a new channel-base current function for lightning studies. Main features of the new function are presented, also by comparison with existing expressions; relevant advantages are highlighted. For this new function, closed-form solutions of the time integral (representing the transferred charge), of the Fourier transform, and of the specific energy are given.

A rigorous formula representing the counterpart of the Cooray–Rubinstein expression in the time domain has recently been derived by the authors. In this paper, the formula is particularized for the cases of a unit step and a linearly rising channel-base current, waveforms frequently used in lightning performance studies. Furthermore, an approximate kernel of the formula is also presented, allowing a very compact and straightforward solution for the case of linearly rising currents.

We present a study on lightning-induced voltages on overhead lines produced by tortuous lightning channels, by using a recently developed tool called CiLIV (Andreotti et al . 2015). CiLIV, initially developed for straight and vertical channels, is here extended to account for tortuosity. High-resolution stereoscopic images of six triggered lightning channels have been 3-D digitized and used as input data for CiLIV. The result is that tortuosity, usually ignored in lightning-induced voltage assessment, can instead play a significant role: an attempt is made in characterizing and quantifying these effects. It is shown that, in contrast to other lightning parameters, like channel-base peak current, which are log-normally distributed and generate log-normally distributed induced voltages too, tortuosity generates normally distributed induced voltages. It is also shown that these voltages can deviate up to 23% (relative standard deviation) from the mean value.

In this paper, a new formulation in the time domain of the Cooray-Rubinstein expression is presented. This new formulation overcomes the problems related to the previous formulation: The Dirac pulse contained in the kernel of the previous formulation is extracted, making the numerical treatment easier and more accurate.

Recently, Andreotti et al. (2015) have presented a new tool for lightning induced voltage calculations on power networks. This tool, named Circuit for Lightning Induced Voltage (CiLIV), has been initially developed for straight and vertical lightning channels; afterwards, the tool has been extended to evaluate induced voltages produced by tortuous lightning channels. However, in the aforementioned studies, only simple power network configurations have been examined. Therefore, aim of this paper is twofold: 1) to apply CiLIV to more complex network configurations, that is, complex networks equipped with transformers, surge arresters, groundings, and so on; 2) to investigate the effects of channel tortuosity on the voltages induced in these complex networks.

in this paper, we present a new tool for lightning-induced voltage calculations. The tool, a circuit model which can be integrated into power systems simulators, is based on the theory developed by Andreotti et al. (2001, 2009, 2013). In Part II, the accuracy, stability, and efficiency of the new tool are demonstrated via comparison with other solutions/codes found in the literature and with experimental data

in the companion paper (Part I), a new tool for lightning-induced voltage calculations, called CiLIV, has been presented. In this paper (Part II), predictions made with the new tool are compared to experimental data and to outputs of analytical procedures/numerical codes found in the literature.

In this paper, which is an extended version of the paper presented by the authors at the 34th International Conference on Lightning Protection (ICLP 2018), a parametric and a statistical analysis of lightning-induced voltages on overhead lines has been carried out by means of exact analytical solutions, for both step-function and linearly rising channel-base currents. The role played by the various parameters affecting the induced voltages has been analyzed. Further, the statistical investigations has allowed us to identify the parametric statistical distributions which best fit the data obtained by simulations. Based on this statistical investigation, an analysis of the lightning performance of an overhead line has been carried out too.

Effects of lightning channel tortuosity and tilt on lightning electric fields and voltages induced on overhead conductors are examined. Overall inclination of the bottom few hundred meters of the lightning channel can appreciably change both the ground-level vertical electric field at distances less than 1 km or so and induced voltage peak relative to the vertical-channel assumption. Smaller-scale tortuosity is responsible for the fine structure of field and induced voltage waveforms. This fine structure can be pronounced at some hundreds of meters and beyond, but is insignificant at shorter ranges

We present the evaluation of the induced voltages in a lossless single transmission line, located at a given height over an infinite conductivity ground plane, and exited by an external field due to a step current moving along a vertical channel. This is a classic topic of the theory of lightning-induced voltages on power lines. The technical literature related to this topic has performed a significant effort; however, only approximated formulas have been obtained so far. In this paper, we derive the exact closed-form solution. We also will discuss, evaluate, and compare the approximated formulas with reference to the proposed exact one, thus contributing to clarifying a matter that still is debated and sometimes misleading, as we will show in the paper. We furthermore recall that the examined lightning-induced voltages model is fundamental for the IEEE standard 1410, a guide for improving the lightning performance of power distribution line.

We propose an improved procedure to identify the lightning return stroke current characteristics. This procedure follows the inverse approaches, presenting a new expansion basis able to widen the class of function which can be reconstructed.

In this paper, it is shown that the problem of the electromagnetic field coupling to a line of finite length can be put into "a standard form" of dual integral equations. A general method for solving such dual integral equations is presented and discussed. It basically consists of a transformation of the first kind Fredholm equation into a linear system of algebraic equations by means of a suitable Neumann expansion of the unknown function. This procedure, carried out in the frequency domain, has allowed evaluating the current induced on the line, which has also been computed with the classical method of moment in order to have a validation of the procedure itself.

An identification procedure for lightning return strokes is proposed. It makes it possible to reconstruct the return stroke height‐dependent attenuation function making use only of the measured vertical component of the electric field radiated by the lightning channel and it can be performed without any information about the channel base current, the measurement of which is generally very difficult and noisy. It is also shown that the method, with suitable modifications, can also be employed for the mathematical evaluation of the lightning channel height, which is a physical quantity a priori unknown. The approach has been validated by means of the numerical simulation of classical TL, MTLL and MTLE engineering models for a wide class of return strokes, with height ranging in the interval 15‐30km.

In this paper an inverse procedure for the identification and the reconstruction of the waveform of the lightning return stroke current is presented. It is based on the acquisition of the vertical component of the electric field radiated by the discharge channel at different locations on the ground and it does not require any information about the channel base current. The approach has been validated by means of the numerical simulation of the classical Transmission Line, Modified Transmission Line Linear and Modified Transmission Line Exponential engineering models, showing good accuracy in all cases.

We propose a procedure to identify the lightning return stroke current characteristics, in the context of return stroke engineering models. The main effort of the up-to-date literature is to find approximate current shapes, which best fit the experimental data. The method hereafter proposed does not follow these approaches, but proposes an inverse algorithm, which allows us to accurately identify the return stroke current for simulated data.

A correspondence has been published to comment on the recently published paper “A new channel–base current function for lightning studies” by the authors. The correspondence contains a number of criticisms to the solutions presented in that paper. In this paper, we provide our replies to the raised criticisms.

We present CiLIV (Circuit for Lightning Induced Voltage), a new tool for lightning induced voltage calculations. The tool can be integrated into power systems simulators, and is based on the theory proposed by Andreotti et al. (2001, 2009, 2013). The accuracy, stability and efficiency of the new tool has been demonstrated by comparison with other solutions/codes found in the literature and with experimental data.

An exact closed form solution for the calculation of lightning-induced voltages on overhead lines has been recently proposed by A. Andreotti et al. (2012). Predictions of this exact formulation are compared here to those based on approximate analytical solutions proposed in the literature. DOI: http://dx.doi.org/10.5755/j01.eee.20.5.2967

An inverse remote-sensing procedure is presented for reconstructing the spatial waveform of the lightning return stroke current throughout a numerical-field synthesis procedure, based on working regularization methods. The approach uses as input data the acquisition of time-domain recordings of the electric and/or magnetic field generated by the lightning current, at various locations on the ground and converts these signals into harmonics by Fourier decomposition. This combination between the proposed solving procedures and harmonic filtering yields numerical results that are in good agreement with the testing functions.

Andreotti (2009, 2013) have presented analytical solutions for the evaluation of voltages induced on lossless, single-, and multi-conductor lines for the case of infinite-conductivity ground and both step and linearly rising currents moving without attenuation and at a constant speed along a vertical lightning channel. These solutions were derived in an exact way (i.e., no approximations were introduced in their derivation). In this paper (Part I), the previous work is extended to the case of lossy ground. In the companion paper (Part II), the results obtained using this new formulation are compared with those given by other formulas/solutions found in the literature.

In the companion paper (Part I), an analytical approach for calculating lightning-induced voltages for the case of lossy ground has been developed. In this paper (Part II), predictions of the new formulation are compared to those based on other approaches found in the literature.

Recently, Andreotti (2009) have presented an analytical solution for the evaluation of voltages induced on an infinitely long, lossless, single-conductor located at a given height above an infinite-conductivity ground plane, and excited by an external field due to a step current wave moving without attenuation and at a constant speed along a vertical lightning channel. The solution presented, in contrast to previously published solutions, was derived in an exact way, i.e., no approximations were introduced in its derivation. In this paper, this exact approach is extended to more practical line configurations. Specifically, still for the case of an external field due to a step current and perfectly conducting ground, the cases of terminated single-conductor line and multiconductor line (including grounded conductors) will be studied. Further, single- and multiconductor lines (including grounded conductors) excited by an external field due to a linearly rising current will be examined.

In this paper the authors are to be commended for the significant contribution in the area of wind power prediction. The methodology presented allows the power production calculation through a two-step procedure: in the first step, the wind direction and velocity are predicted some minutes ahead, and then, in the second step, the power output is calculated using power curves direction-dependent. The authors comments on a method for short-term wind power prediction with multiple observation points are appreciated.

The paper deals with energy storage systems applications in Smart Grids. Several services can be performed thanks to the energy storage systems use, with objectives aimed at meeting needs internal or external to the Smart Grid. Optimal nonlinear constrained problems can be formulated and properly solved in order to perform the services in the best economical and technical way. In this paper, optimal control strategies are proposed in order to allow the Smart Grid to minimize internal losses and to sell energy and ancillary services during high power prices periods. The procedure involves the formulation of optimal power flow problems; proper objective functions and constraints are imposed to satisfying the services that have to be carried out. A numerical application on a 30-bus low voltage Smart Grid shows the effectiveness of the proposed procedure.

The problem of accurate prediction of lightning-induced overvoltages on power lines still attracts considerable attention. A variety of approaches of different levels of sophistication have been proposed. In particular, transmission-line (TL) approximation is widely used for describing electromagnetic coupling of lightning with power lines. In this paper, validity of this approach for lossless lines is demonstrated by analytically demonstrating that, under the assumptions that are typically justified for practical power distribution lines, the TL approximation and the more rigorous full-wave analysis lead to identical results.