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The paper presents analytical formulas for computation in the time domain of electromagnetic (EM) fields generated by tortuous cloud-to-cloud (CC) lightning channels over a perfectly conducting ground. For the first time, the study was not limited to a horizontal lightning path but was extended to take into account the natural, tortuous geometry of the lightning channel. After the calculation of the step response, a convolution integration was applied for the computation of the fields generated by an arbitrary current source. The produced electric and magnetic fields were then compared with the fields generated by a horizontal channel. The method can be of primary importance to evaluating the hazards for electric and electronic systems of flying aircraft, estimating the voltages induced on overhead transmission lines by CC lightning, and, in general, evaluating the induced effects on sensitive electric and electronic components. Moreover, it may represent a simple, robust, and time-saving tool for estimating important physical parameters that characterize lightning phenomena.

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.

Combined heat and power (CHP) generation is a fundamental practice to reduce primary energy consumptions and mitigate the related greenhouse gas emissions. Cogeneration plants are even more important in the Hospital sector, as they give the opportunity to operate regardless of the electric power grid, so ensuring energy availability also during grid faults while providing significant cost savings to the public healthcare system. The integration of a battery energy storage with the CHP system could further increase the expected advantages by enabling more flexible operating strategies, further energy reliability and lower operating costs. Therefore, this research paper addresses the development of a specific methodology for the energetic and economic assessment of a grid connected CHP plant assisted by a battery energy storage. More specifically, an evaluation algorithm has been developed and then coupled to a genetic evolutionary algorithm. Then, a vector optimization problem has been solved to find the optimal configurations of a modular cogeneration plant (i.e. size and number of CHP gas engines; battery size) which maximize the primary energy saving while minimizing the payback period. Results based on electricity and heat demand of a hospital facility demonstrate how the battery energy storage system allows the shifting of the Pareto frontier towards better economic results if compared with Pareto solutions found when the optimization problem does not consider a battery storage supporting the CHP plant. The proposed methodology provides an effective and flexible procedure for the optimal configuration and detailed analysis of CHP plants integrated by an electrochemical based energy storage system. In fact, the effects of a high number of interacting energetic and economic parameters are considered together with the technical constraints required to extend battery lifetime in real applications.

The problem of the shielding evaluation of an infinitesimally thin perfectly conducting circular disk against a vertical magnetic dipole is here addressed. The problem is reduced to a set of dual integral equations and solved in an exact form through the application of the Galerkin method in the Hankel transform domain. It is shown that a second-kind Fredholm infinite matrix-operator equation can be obtained by selecting a complete set of orthogonal eigenfunctions of the static part of the integral operator as expansion basis. A static solution is finally extracted in a closed form which is shown to be accurate up to remarkably high frequencies.

In this paper we consider the problem of restoring the voltage for stand-alone inverter-based Microgrids despite the effects of the time-delays arising with the information exchange among the electrical busses. To guarantee that all Distributed Generators (DGs) reach in a finite-time and maintain the voltage set-point, as imposed by a virtual DG acting as a leader, we suggest a novel robust networked-based control protocol that is also able to counteract both the time-varying communication delays and natural fluctuations caused by the primary controllers. The finite-time stability of the whole Microgrid is analytically proven by exploiting Lyapunov-Krasovskii theory and finite-time stability mathematical tools. In so doing, delay-dependent stability conditions are derived as a set of Linear Matrix Inequalities (LMIs), whose solution allows the proper tuning of the control gains such that the control objective is achieved with required transient and steady-state performances. A thorough numerical analysis is carried out on the IEEE 14-bus test system. Simulation results corroborate the analytical derivation and reveal both the effectiveness and the robustness of the suggested controller in ensuring the voltage restoration in finite-time in spite of the effects of time-varying communication delays.

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.

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).

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 outlines the potential role of Knowledge Discovery from massive Datasets in smart grid computing, presenting the most recent activities developed in this field by the Task Force on “Enabling Paradigms for High-Performance Computing in Wide Area Monitoring Protective and Control Systems” of the IEEE PSOPE Technologies and Innovation Subcommittee.

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.

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.

This paper deals with the use of distributed energy storage systems in microgrids, and proposes a planning method which accounts for the uncertainties of load and distributed generation. Objectives of the planning method are the reduction of the energy costs, while providing the supply of ancillary services as a technical support to the network. The energy costs are evaluated considering a hourly varying pricing scheme and optimizing the storage systems charging/discharging stages. The technical support is devoted to the restraint of bus voltage amplitudes, and of network components' currents/powers within admissible ranges. The input data uncertainties are managed through three decision theory criteria (i.e., the minimization of expected costs; an approach based on the weighted regret felt by the design engineer; and a stability area criterion), which allow considering the multiple design alternatives and futures (i.e., possible values of uncertain input data) in an accurate and feasible way. The design alternatives refer to the size and location of the distributed storage systems, while each future is associated with a different level of load demand and power production of distributed generation over the whole planning period. The results of numerical applications are reported and discussed with reference to a Cigré test network.

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.

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 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.

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 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.

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.

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.

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.

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 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

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.

The above-named article [ibid., vol. 28, no. 2, pp. 1213-1223, Apr. 2013] had an incorrect equation (11b). It is shown in the correct form here, using the same equation number as in the paper. All of the results in the article were obtained by using the correct equation and, therefore, are not affected.

The problem of evaluating the shielding effectiveness of a thin metallic circular disk with finite conductivity against an axially symmetric vertical magnetic dipole is addressed. First, the thin metallic disk is modeled through an appropriate boundary condition, and then, as for the perfectly conducting counterpart, the problem is reduced to a set of dual integral equations which are solved in an exact form through the application of the Galerkin method in the Hankel transform domain. A second-kind Fredholm infinite matrix-operator equation is obtained by selecting a suitable set of basis functions. A low-frequency solution is finally extracted in a closed form. Through a comparison with results obtained from a full-wave commercial software, it is shown that such a simple approximate solution is accurate up to the frequency where the surface-impedance model of the thin disk is valid.

The problem of radiation of a magnetic dipole axially symmetric with an infinitesimally thin perfectly conducting circular disk is solved in an exact closed form. This is done by transforming the original dual integral equation system describing the problem into a single second-kind Fredholm integral equation and searching for the solution as a power series. Both low-and high-frequency asymptotic limits are also discussed from which simple approximate solutions are readily derived. Numerical results are provided to validate the proposed formulation.