Mansueto Rossi

Lightning return stroke current radiation in presence of a conducting ground: 2. Validity assessment of simplified approaches

In this paper, the developed formulation, which we shall call the “reference” one, is used to assess the validity of the most popular simplified approach for the calculation of the lightning electromagnetic field over a conducting earth, namely, the Cooray-Rubinstein (CR) approximation. This formula provides a simple method to evaluate the radial component of the electric field which is the component most affected by the finite ground conductivity and which plays an important role within the Agrawal et al. (1980) field-to-transmission line-coupling model. Several configurations are examined, with different values for the ground conductivity and different field observation points. A thorough analysis of all the simulated field components is carried out and comparisons are also made with the “ideal” field, namely, the field that would be present under the assumption of perfectly conducting ground. It is shown that for channel base current typical of subsequent strokes and for very low conductivities, the CR formula exhibits some deviations from the reference one but it still represents a conservative estimation of the radial field component, since it behaves as un upper bound for the exact curve. The developed algorithm is characterized by fast performances in terms of CPU time, lending itself to be used for several applications, including a coupling code for lightning induced overvoltages calculations.

An Algorithm for the Exact Evaluation of the Underground Lightning Electromagnetic Fields

The number of power installations lying underground has been increasing in the last few years, and such devices are very sensitive to the effect of the lightning electromagnetic fields, due to the massive presence of power electronics. As a consequence, the scientific community has devoted much effort in the direction of a more accurate modeling of underground lightning fields and their coupling to cables. The exact expressions of the underground lightning fields have been derived by Sommerfeld decades ago. However, their numerical evaluation has always been a hard task because of the presence of slowly converging improper integrals. In the past, some approximate formulas have been derived, which have been included in field-to-transmission line coupling models to estimate the effect of lightning on buried cables. In this paper, an efficient algorithm for the evaluation of the Sommerfeld expression for underground fields is presented, and its mathematical features are discussed. The numerical treatment of the Sommerfeld integrals is based on a proper subdivision of the integration domain, the application of the Romberg technique, and the definition of a suitable upper bound for the error due to the integral truncation. The remarkable efficiency in terms of CPU time of the developed algorithm makes it possible to use it directly in field-to-buried cable coupling simulation codes. Finally, the developed algorithm is used to test the validity of the Coorays simplified formula for the computation of underground horizontal electric field. It is shown that predictions of the Coorays formula are in good agreement with exact solutions for large values of ground conductivity (0.01 S/m). However, for poor conductivities (0.001 S/m or so) Coorays expression yields less satisfactory results, especially for the late time response.

Lightning electromagnetic radiation over a stratified conducting ground: 2. Validity of simplified approaches

In the first part of this paper, the rigorous theory describing the electromagnetic field radiated by a lightning return stroke over a two-layered conducting ground was presented and the exact expressions for the lightning electromagnetic fields were developed and discussed. In this part of the paper, the theory along with its time domain numerical evaluation algorithm is used for the assessment of the validity of simplified approaches proposed in the literature for the vertical electric and horizontal magnetic field components. The simplified approaches are based on the concept of ground surface impedance and its corresponding attenuation function. It is shown that the results obtained using the simplified approaches are in excellent agreement with exact results in both near (50 m) and intermediate (1000 m) distance range. However, since the vertical electric and azimuthal magnetic field components are not appreciably affected by the ground finite conductivity, they can also be evaluated assuming the ground as a perfectly conducting ground. On the other hand, the horizontal electric field above a horizontally stratified ground is very much affected by the ground electrical parameters. Its waveform is characterized by an early negative excursion due to the currents flowing into the ground followed by a late time positive excursion which is due to the elevation of the observation point from the ground level. The magnitude of the negative peak is sharper for subsequent return strokes than first return strokes and is higher for lower conducting grounds. A new formula is proposed for the evaluation of the horizontal electric field at a given height above the air-ground interface. The formula can be viewed as the generalization of the Cooray-Rubinstein formula for the case of a two-layer ground. We show that the new formula is able to reproduce in a satisfactory manner the horizontal electric field above a two-layer ground. The proposed formulation is, however, less accurate at distances as close to 10 m from the channel base and for very poor ground conductivity (0.0001 S/m).

Influence of frequency-dependent soil electrical parameters on the evaluation of lightning electromagnetic fields in air and underground

This paper is aimed at analyzing the influence of the frequency-dependent behavior of the ground electrical parameters ( conductivity and ground permittivity) on the electromagnetic field radiated by a cloud-to-ground lightning return stroke. Both radiation in air ( over the conducting ground plane) and underground are considered in the analysis. The adopted method is based on the classical Sommerfelds theory and takes advantage of an efficient ad hoc numerical procedure to face with the slow converging Sommerfelds integrals. This feature allows the electromagnetic field to be computed without any sort of mathematical approximation and, since it is carried out in the frequency domain, can be used either if the ground permittivity and conductivity are considered constant or if they vary with the working frequency with any functional law. Simulations have been performed to identify the cases in which the approximation of constant ground permittivity and conductivity leads to satisfactory results. It is shown that for soils with water contents of 2% to 10% ( ground conductivities in the order of 0.001 to 0.01 S/m), the assumption of constant electrical parameters appears to be reasonable. However, for either very poorly conducting soils (10(-4) S/m or so) or highly conducting soils (10(-1) S/m), the electromagnetic field components appear to be significantly affected by the frequency dependence of the ground electrical parameters.

A Feedback Linearization Control Scheme for the Integration of Wind Energy Conversion Systems Into Distribution Grids

This paper focuses on the development of a control strategy for integration of wind energy conversion systems (WECS) into the electrical distribution networks with particular attention to the combined provision of energy and ancillary services. Typically, a WECS is composed by a variable speed wind turbine coupled with a direct driven permanent magnet (DDPM) synchronous generator. This configuration offers a considerable flexibility in design and operation of the power unit, as its output is delivered to the grid through a fully controlled frequency converter. Here, a new control scheme to regulate electrical and mechanical quantities of such generation unit is proposed, aimed both at reaching optimal performances in terms of power delivered to the grid and at providing the voltage support ancillary service at the point of common coupling. The control scheme is derived resorting to the feedback linearization (FBL) technique, which allows both decoupling and linearization of a non linear multiple input multiple output system. Several numerical simulations are then performed in order to show how the flexibility of the DDPM wind generator can be fully exploited, thanks to the use of the FBL approach, which assures independent control of each variable and significant simplifications in controller synthesis and system operation, thus making it easier to integrate WECS into modern day smart grids.

Time-Domain Implementation of Cooray–Rubinstein Formula via Convolution Integral and Rational Approximation

One of the most popular techniques to take into account the finite ground conductivity in the evaluation of the radial component of the electric field generated by a lightning return stroke is the Cooray-Rubinstein (CR) formula. As this formula is derived in the frequency domain, its application in time-domain simulation codes for the analysis of lightning-induced overvoltages on overhead lines might be challenging. In this paper, two methods allowing a simple time-domain implementation of the formula are discussed. The first one is an enhanced version of an algorithm recently proposed by two of the authors, while the second consists of a new technique, based on a suitable rational approximation of the impedance term appearing in the CR formula. This second approach is characterized by an intrinsic easiness in time-domain implementation and a considerable computational efficiency compared with conventional methods.

A system of systems model for the control of the university of Genoa Smart Polygeneration Microgrid

Experimental tests and demonstration projects are very useful to derive new methods and tools for the optimal control of smart grids. In this work, the University of Genoa Smart Polygeneration Microgrid (SPM) is firstly presented, in connection with the different sub-systems that compose the overall system. Then, a simplified mathematical dynamic model, that can be used for optimal control purposes, is described. Finally, a dynamic optimization problem is formalized and solved.

Lightning electromagnetic radiation over a stratified conducting ground: Formulation and numerical evaluation of the electromagnetic fields

The formulation describing the electromagnetic field radiated by a lightning return stroke over a two-layered conducting ground is presented in this paper. The derivation of the Greens functions required to solve the problem is first discussed in detail, and the expressions for the lightning electromagnetic fields are determined. Afterward, an efficient method for the numerical evaluation of the electromagnetic field is proposed. The proposed method is based on a suitable modification of a previously developed model for the evaluation of the fields in the presence of a lossy but homogeneous soil. Particular attention is devoted to the soil reflection coefficient properties, both from a physical and from a mathematical point of view. In part 2 of the paper, the developed approach and numerical algorithms will be used to evaluate the effect of the soil stratification on the radiated fields and to perform the validity assessment of simplified approaches proposed in the literature.

Planning and management of sustainable microgrids: The test-bed facilities at the University of Genoa

The aim of this paper is to describe the system composed by the SPM (Smart Polygeneration Microgrid) feeding the SEB (Sustainable Energy Building) at the University of Genoa (Savona Campus), and to assess the Campus operating costs, CO2 emissions, and primary energy annual savings determined by the combined SPM-SEB system. This work highlights the main difference between two scenarios (AS-IS and TO-BE) with specific reference to operation and management of various power units. As demonstrated by the work, besides research and testing of new devices, the SPM-SEB can be used also for demonstration and teaching activities, and contributes to increase the overall energy efficiency of the Campus, lowering its primary energy consumption.

Prony Series Representation for the Lightning Channel Base Current

In this paper, a new representation for the lightning channel base current is proposed in terms of the so-called Prony series, obtained by means of a modified time-domain variant of the well-known vector fitting technique. This method allows both to reproduce in an equivalent way previous analytical representations such as Heidlers function and, more interestingly, to obtain a smooth analytical interpolation of measured raw data, in an automatic though tunable way, without the need of filtering, and taking into account the desired behavior of the current for t = 0. Furthermore, a Prony series, i.e., a representation in terms of a sum of exponentials and/or dumped sinusoids, permits us to carry out the computation of the integrals expressing the lightning electromagnetic fields by means of a recursive convolution algorithm, thus reducing the required CPU time. This makes the proposed approach extremely useful for studies of lightning performance of distribution lines, which require the simulation of an appreciable number of cases.