Federico Delfino

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.

Optimal Control and Operation of Grid-Connected Photovoltaic Production Units for Voltage Support in Medium-Voltage Networks

The strong increase in the number of installed photovoltaic (PV) production plants has slowly changed the assets and the operating conditions of the electricity power system. In this context, the supply and control of the reactive power from the renewable generation plants are becoming an important issue to be exploited that can facilitate the integration of PV and wind power in electricity grids. The aim of this paper is to propose an optimized control strategy to manage the reactive power resource generated by PV plants in order to improve the quality of the low/medium voltage distribution network and meet the latest technical requirements listed by distribution system operators in their grid codes. A methodology to define the optimal reactive power references for each PV unit connected to a generic distribution network is presented for a specified goal (e.g., the achievement of suitable voltage levels at the grid nodes). Such reference signals are then provided to the PV plants regulation systems, which are designed in order to guarantee the decoupling between the active and reactive power channels, due to the use of the Feedback Linearization control technique. The problem is formulated in a generalized way, so that it can be extended to any possible grid configuration.

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.

Cooray–Rubinstein Formula for the Evaluation of Lightning Radial Electric Fields: Derivation and Implementation in the Time Domain

Ground conductivity plays an important role both in the evaluation of the electromagnetic (EM) fields due to a lightning event and in the calculation of the line parameters, which are, in turn, fundamental in the analysis of the lightning-induced voltages on overhead lines. The exact formulation of the EM fields over a lossy ground involves the numerical evaluation of the Sommerfeld integrals, which are slowly converging and can only be computed in the frequency domain. For this reason, a great effort has been devoted in the derivation of approximate formulas that can provide accurate results with low computational costs. The most popular one is the Cooray-Rubinstein formula, which has been proposed in the frequency domain. Here, its time-domain counterpart is mathematically derived, and an efficient algorithm for its implementation is presented together with some comparisons with the exact approach.

An integrated active and reactive power control scheme for grid-connected photovoltaic production systems

The paper presents an advanced control scheme for a photovoltaic unit (PV) to suitably drive the injection of both active and reactive power into a MV radial distribution grid. Such algorithm allows a decoupled control of active and reactive power by properly adjusting the modulating signals of the PWM interface converter with the grid. A closed loop regulation scheme has been derived and guidelines for the design of the regulators are provided. The control algorithm has been applied to a real MV grid-connected PV power plant and several simulations have been performed in order to analyze the behavior of the system and to verify the effectiveness of the adopted regulation. The positive effect of reactive power support has been highlighted showing benefits on grid current and voltage profiles with respect to the typical case of the sole active power production.

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).

Equivalent sources methods for the numerical evaluation of magnetic force with extension to nonlinear materials

In this paper the equivalent sources methods, written in terms both of the actual and of the external field, are used for the computation of the total force in two-dimensional axisymmetric problems. A Finite Element modeling of the magnetizing currents as field sources is presented in order to improve the formulations using the external field. The numerical accuracy of all the proposed formulae is thoroughly checked on linear and nonlinear test examples.

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 Multilevel Approach for the Optimal Control of Distributed Energy Resources and Storage

An approach is proposed to deal with distributed energy resources, renewables and storage devices connected to microgrids. Specifically, a multilevel architecture is introduced and evaluated for the following main purposes: to reduce the computational complexity, to deal with different decentralized microgrids, different decision makers, and multiple objectives. A two-level decision architecture based on a Model Predictive Control (MPC) scheme is presented, in which the upper decision level has the function of fixing the values of a certain set of parameters (reference values), by assuming a certain structure of the control strategies to be applied at the lower decision level. On the basis of such parameters, each decision maker at the lower level solves its own optimization problem by tracking the reference values provided by the upper level. The effectiveness of the proposed approach is demonstrated. The application of the proposed control architecture to a specific case study (Savona, Italy) is presented and discussed.

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.