Carlo Alberto Nucci

Influence of a lossy ground on lightning-induced voltages on overhead lines

A comprehensive study on the effect of a lossy ground on the induced voltages on overhead power lines by a nearby lightning strike is presented. The ground conductivity plays a role in both the evaluation of the lightning radiated fields and of the line parameters. To be calculated by means of a rigorous theory, both fields and line constants need important computation time, which, for the problem of interest, is still prohibitive. The aim of this paper is to discuss and analyze the various simplified approaches and techniques that have been proposed for the calculation of the fields and the line constants when the ground cannot be assumed as a perfectly conducting plane. Regarding the radiated electromagnetic field, it is shown that the horizontal electric field, the component which is most affected by the ground finite conductivity, can be calculated in an accurate way using the Cooray-Rubinstein simplified formula. The presence of an imperfectly conducting ground is included in the coupling equations by means of two additional terms: the longitudinal ground impedance and the transverse ground admittance, which are both frequency-dependent. The latter can generally be neglected for typical overhead lines, due to its small contribution to the overall transverse admittance of the line. Regarding the ground impedance, a comparison between several simplified expressions used in the literature is presented and the validity limits of these expressions are established. It is also shown that for typical overhead lines the wire impedance can be neglected as regard to the ground impedance.

Lightning-induced voltages on overhead lines

A modeling procedure that permits calculation of lightning-induced voltages on overhead lines starting from the channel-base current is discussed. The procedure makes use of a coupling model already presented in the literature, based on transmission line theory, for field-to-overhead line coupling calculations. Both models are discussed and compared with experimental results. The hypothesis of perfect conducting ground, used to analyze the voltages induced on an overhead line by a nearby lightning return stroke with a striking point equidistant from the line terminations, and the limits of its validity are determined. A comparison shows that peak value and maximum front steepness of the induced voltages calculated using other lightning return-stroke models differ. It is also shown that another coupling model used in the power-lightning literature by several other authors may result in a less accurate estimation of the induced voltages. >

Current and electromagnetic field associated with lightning-return strokes to tall towers

An analysis of electric and magnetic fields radiated by lightning first and subsequent return strokes to tall towers is presented. The contributions of the various components of the fields, namely, static, induction, and radiation for the electric field, and induction and radiation for the magnetic field are illustrated and discussed. It is shown in particular that the presence of a tower tends, in general, to increase substantially the electric and magnetic field peaks and their derivatives. This increase is mainly caused by the presence of two oppositely propagating current wavefronts originating from the tower top and by the very high propagation velocity of current pulses within the tower, and depends essentially on the wavefront steepness of the channel-base current. Because of the last factor, the increase of the field magnitudes is found to be significantly higher for subsequent return strokes, which are characterized by much faster risetimes compared to first return strokes. The presented results are consistent with experimental observations of current in lightning strokes to the Toronto CN Tower and of the associated electric and magnetic fields measured 2 km away. These findings partially explain the fact that subsequent return strokes characterized by lower current peaks but higher front steepnesses and return stroke speeds may result in higher field peaks. The results obtained have important implications in electromagnetic (EM) compatibility. It is found that lightning strokes to tall metallic objects lead to increased EM field disturbances. Also, subsequent return strokes are to be considered an even more important source of EM interference than first return strokes. Indeed, EM fields from subsequent strokes are characterized by faster fronts and additionally, they may reach greater peaks than first strokes. Lastly, findings of this study emphasize the difficulty of extracting reliable lightning return stroke current information from remote EM field measurements using oversimplified formulae.

Short-Term Scheduling and Control of Active Distribution Systems With High Penetration of Renewable Resources

Among the innovative contributions to electric distribution systems, one of the most promising and qualified is the possibility to manage and control distributed generation. Therefore, the latest distribution management systems tend to incorporate optimization functions for the short-term scheduling of the various energy and control resources available in the network (e.g., embedded generators, reactive power compensators and transformers equipped with on-load tap changers). The short-term scheduling procedure adopted in the paper is composed by two stages: a day-ahead scheduler for the optimization of distributed resources production during the following day, an intra-day scheduler that every 15 min adjusts the scheduling in order to take into account the operation requirements and constraints of the distribution network. The intra-day scheduler solves a non-linear multi-objective optimization problem by iteratively applying a mixed-integer linear programming (MILP) algorithm. The linearization of the optimization function and the constraints is achieved by the use of sensitivity coefficients obtained from the results of a three-phase power flow calculation. The paper shows the application of the proposed approach to a medium-voltage 120 buses network with five wind plants, one photovoltaic field, ten dispatchable generators, and two transformers equipped with on-load tap changers.

Continuous-Wavelet Transform for Fault Location in Distribution Power Networks: Definition of Mother Wavelets Inferred From Fault Originated Transients

The paper presents a fault location procedure for distribution networks based on the wavelet analysis of the fault-generated traveling waves. In particular, the proposed procedure implements the continuous wavelet analysis applied to the voltage waveforms recorded during the fault in correspondence of a network bus. In order to improve the wavelet analysis, an algorithm is proposed to build specific mother wavelets inferred from the fault-originated transient waveforms. The performance of the proposed algorithm are analyzed for the case of the IEEE 34-bus test distribution network and compared with those achieved by using the more traditional Morlet mother wavelet.

Transient analysis of multiconductor lines above a lossy ground

In this paper, we first extend the Sunde logarithmic approximation for the single-wire line ground impedance to the case of a multiconductor line. The new approximate forms are compared to the general expressions which involve integrals over an infinitely long interval and an excellent agreement is found. The inverse Fourier transform of the ground impedance presents singularities which complicate the numerical solution of the transmission line equations. The order of the singularity is reduced by 1, and a careful numerical treatment is then employed to derive an equivalent and numerically more appropriate form of coupling equations in which there is no longer a singular term. Finally, finite-difference time-domain (FDTD) solutions of the coupling equations are presented and the theory is applied to calculate lightning-induced voltages on a multiconductor line. The lightning-induced voltages are calculated for the case of lossless/lossy, single-conductor/multiconductor lines and the effect of ground losses and the presence of other conductors on the magnitude and shape of induced voltages are illustrated.

Mitigation of lightning-induced overvoltages in medium Voltage distribution lines by means of periodical grounding of shielding wires and of surge arresters: modeling and experimental validation

In this paper, we investigate the effect of periodically-grounded shielding wires and surge arresters on the attenuation of lightning-induced voltages. We discuss the adequacy of the commonly made simplification of assuming the shielding wire at ground potential, instead of being treated as one of the conductors of the multiconductor system. We also compare then the mitigation effect of shielding wires with that achievable by the insertion of surge arresters along the line. The computation results are first validated by means of calculations obtained by other authors referring to a simple line configuration, and then by means of experimental results obtained using a reduced-scale line model illuminated by a nuclear electromagnetic pulse (NEMP) simulator. One of the main conclusions is that the effectiveness of shielding wires and surge arresters depends mostly on the spacing between two adjacent grounding points or surge arresters.

An Improved Procedure for the Assessment of Overhead Line Indirect Lightning Performance and Its Comparison with the IEEE Std. 1410 Method

This paper deals with the assessment of the lightning performance of distribution lines, namely the estimation of the annual number of lightning-induced flashovers versus the critical flashover voltage of the line insulators. The procedure proposed by the authors is compared with the one described in IEEE Std. 1410-2004 Guide for improving the lightning performance of electric power overhead distribution lines. The two methods differ: 1) for the models adopted to evaluate the induced voltages and 2) for the adopted statistical approach. The reasons for differences in the results predicted by the two methods are discussed and the parameters playing the major role in the achievement of the results are identified. The proposed method represents an improvement compared to IEEE Std. 1410 because it takes into account more realistic line configurations and the effect of the finite ground conductivity

Lagrangian heuristics based on disaggregated Bundle methods for hydrothermal unit commitment

The paper presents a simple and effective Lagrangian relaxation approach for the solution of the optimal short-term unit commitment problem in hydrothermal power generation systems. The proposed approach, based on a disaggregated Bundle method for the solution of the dual problem, with a new warm-starting procedure, achieves accurate solutions in few iterations. The adoption of a disaggregated Bundle method not only improves the convergence of the proposed approach but also provides information that are suitably exploited for generating a feasible solution of the primal problem and for obtaining an optimal hydro scheduling. A comparison between the proposed Lagrangian approach and other ones, based on subgradient and Bundle methods, is presented for a simple yet reasonable formulation of the hydrothermal unit commitment problem.

On dynamic load models for voltage stability studies

Appropriate modelling of dynamic loads is of primary importance in voltage stability studies. The paper deals with the modelling of a load consisting of a static load plus an aggregate of induction motors. The behavior of three simplified models for such a load configuration is compared. The three models are (A) a generic nonlinear dynamic model of the first order as proposed by Karlsson and Hill, (B) a static exponential load plus a dynamic first-order model for the induction motors, and (C) a static exponential load plus a dynamic third-order model for the induction motors. A power system with a longitudinal structure is chosen as the case-study. It is shown that for the same perturbation (tripping of one of two high-voltage parallel lines) the simulation results are quite different from each other and, in certain cases, only the third-order dynamic model correctly predicts the voltage collapse phenomena at the load bus. An interpretation of the different behavior of the various models is given.