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This paper deals with development of integrity evaluation instrument for the power line surge protective device. A reliable power supply is an essential element in the developed information and communication society by highly advances in IT technology. However, the lightning incidence also increased with the recent extreme weather events. In Korea, in order to protect the electrical system from lightning surge, SPD(Surge Protective Device) has been used for these past 30 years. However, the method of diagnosing the safety of the SPD in the industry is insufficient. In this paper, SPD integrity evaluation system was composed of a variable DC power source unit, voltage-current sensor and the embedded controller. In order to measure V-I characteristics of MOV, 3 type samples were degraded by impulse current generator. After impulse tests, the varistor voltage of all samples and nonlinearity coefficient were decreased. It confirmed the utility of the developed equipment by this experimental test and the reliability of SPD is expected for surge accident

PurposeA fast algorithm is proposed to calculate the lightning electromagnetic field over a perfectly conducting earth surface.Design/methodology/approachThe channel base current is approximated by a number of sub‐domain quadratic functions using the proposed adaptive sampling technique, and the derivative and integral of the channel base current with respect to time can be analytically expressed. With the help of these approximations, the ideal electromagnetic field of the lightning channel can be evaluated along the lightning channel with respect to the height.FindingsThe computational time can be greatly reduced using the proposed approach to evaluate the electromagnetic field of a lightning channel in the time domain.Originality/valueThe adaptive sampling technique is a general‐purposed approach, which can be potentially used in other applications to fit a function with the minimal number of intervals.

The radiated horizontal electromagnetic field of a lightning channel acts as the excitation when the lightning-induced voltages on overhead lines are under study. To accelerate the calculation of the horizontal electric field of a lightning channel, a piecewise Hermite interpolation model is proposed, which exploits the distinct feature of the transmission line whose height keeps unchanged. In the piecewise Hermite interpolation model, the key technique is fast evaluating the derivative of the horizontal electric field expressed by the generalized Sommerfeld integral. In this paper, the moment technique is utilized to calculate the derivatives efficiently. As demonstrated in the numerical examples, the piecewise Hermite interpolation model can reach a high accuracy with a very low computation cost.

The evaluation of the electromagnetic field radiated by a lightning stroke channel is a necessary step for the analysis of many electromagnetic compatibility problems. An efficient algorithm for calculating the electromagnetic field of a lightning stroke channel is presented in this paper. The electromagnetic field of a lightning stroke channel, expressed by the generalized Sommerfeld integral, is decomposed into two parts. One is a definite integral, which can be evaluated using the proposed moment technique to avoid the troublesome oscillatory integral; the other is an improper integral with an infinite upper limit, which is calculated with the newly developed asymptotic expression to reach convergence quickly. The proposed approach turns out to be very efficient. The numerical examples validate the proposed approach in both frequency and time domain.

The Cooray-Rubinstein formula has been widely utilized for evaluating the horizontal component of the electric field generated by a lightning return stroke. A fast time-domain implementation of Cooray-Rubinstein formula in time domain, by means of the piecewise quadratic convolution technique and the use of a quadrature routine of a truncated integral instead of polynomial approximations of the Bessel functions, is presented in this paper. The advantages of the proposed approach can be summarized as follows. First, the issue of the numerical overflow and the cancellation error for calculating the lightning horizontal electric field is avoided; second, the horizontal electric field of a lightning can be evaluated quickly, because the convolution has been expressed in a closed-form expression. The numerical examples demonstrate the efficiency and validity of the proposed approach.

A fast approach for evaluating the magnetic field in air generated by an underground conductor is proposed in this paper. By means of the asymptotic extraction technique, the magnetic field can be decomposed into two parts. One is the contribution from the asymptotic integrand, which can be calculated analytically; and the other can be expressed by a sum of the definite integral and the exponential integrals. Due to the fact that there is no improper integral involved, the approach proposed here is highly efficient. Meanwhile, the impact of the eddy current to the magnetic field is quantitatively analyzed. The proposed approach could be used in the electromagnetic environment assessment for underground power cable systems.

The electromagnetic fields generated by a vertical electric dipole, expressed in the form of the Sommerfeld integral, are important in the study of lightning. In this paper, an algorithm, which can analytically approximate the Sommerfeld tail integral, is proposed. Due to the fact that the tail integral is expressed by a sum of several error functions, the tail integral of a vertical electric dipole can be evaluated without the truncation of the infinite upper limit. The comparison indicates that the results calculated by the proposed algorithm are accurate, and the computational time, compared to the one using direct numerical quadrature method, is much shorter.

PurposeThe purpose of this paper is to present an original iterative nodal approach to calculate the fault current distribution on overhead lines.Design/methodology/approachBy changing the mutual couplings among different conductors into the equivalent voltage sources, node voltages are updated iteratively by using conventional nodal analysis with those additional sources until the convergence is achieved.FindingsThe proposed algorithm can handle the complicated topology of a power transmission line and has no difficulties in taking all physical couplings into account. The fault current distribution calculated by this method is in good agreement with those published in the literature. Although the proposed approach is iterative, the CPU time needed is still reasonable compared to the direct solution approach. The memory requirement is low because the coefficient matrix is highly sparse for the nodal analysis of each iteration loop.Originality/valueThe proposed approach can serve as an alternative in calculating the fault current because of its efficiency and ease of implementation.

The earth-return impedance of underground conductors, whose expression was first derived by Pollaczek, is of particular importance for the study of the electromagnetic compatibility problems among the underground conductor system. In this paper, a fast and highly accurate algorithm is presented to calculate the Pollaczek's integral. The high accuracy acquired by the proposed procedure is due to the fact that the tail of the Pollaczek's integral is approximated by a sum of several exponential integrals, which in nature means that there is no truncation to the Pollaczek integral. The extensive comparison with published data indicates that the proposed algorithm is highly accurate and the computational time is reasonable.

The evaluation of the electromagnetic field radiated by a lightning stroke is of essential importance for the study of the interaction between lightning electromagnetic fields and power lines, or other sensitive installations. A fast algorithm for calculating the fields generated by a vertical electric dipole over a lossy ground, which can be expressed by the well-known Sommerfeld integrals, is presented in this paper. The integrals are decomposed into two parts. One part can be calculated by a recursive analytical expression, and the other part can be evaluated numerically due to the fact that the extracted integrand damps rapidly with the help of the asymptotic extraction technology. A comparison with some approximate formulas is performed in detail with variable parameters, such as the soil parameters, the geometry, and the excitation frequency of dipole, which shows very good agreement as far as the lightning field is concerned. The technical merit of the proposed approach is its universality, which can be applied for arbitrary parameters, and its computing time is still competitive.

This paper describes an efficient numerical approach for the calculation of the per-unit length earth-return impedance of a conductor inside a tunnel. The influence of the tunnel on the per-unit length impedance is replaced by a set of equivalent current sources via the fictitious medium method. The main advantage of the proposed approach is that it can solve the boundary value problem within the tunnel region. The proposed method can reduce the calculation region and, thus, leads to time savings. A comparison of the numerical results with published data shows very good agreement. The proposed method is a good candidate for impedance calculation of a conductor inside a tunnel.

In this paper, a simulation model is proposed to evaluate the electromagnetic transient surge current distribution in a lightning protection system (LPS) due to a direct lightning stroke. The model is based on the coupled transmission line network in the frequency domain combined with the Fourier transform technique. The conductor of the LPS is described using the coupled transmission line model, and can be reduced to an active two-port equivalent circuit. The unknown quantities are the node voltages of the LPS at the physical junction, which leads to a fast solver at each frequency. The validation of the proposed approach is performed by comparing the results with those in the technical literature. The numerical examples show the flexibility, efficiency, and accuracy of the model in the range of practical application of LPS.

The theoretical model for the analysis of grounding system encased in the foundation region in a horizontal multilayer soil is presented. By means of fictitious conductivity concept, the effects of foundation are replaced by a set of equivalent current sources. The analysis of grounding system can be carried out by combining the moment method with additional equivalent current sources. The main advantage of the proposed approach is that it can be linked with the existing codes easily. The results are compared with those found in the literature and obtained by other popular software

A fast and efficient adaptive sampling algorithm to obtain the response surface of multivariable objective function is presented. The algorithm is divided into two stages. First, starting with a low-rank interpolation model, the technique systematically increases the rank by optimally choosing new support points in the areas of the highest error until the required accuracy is achieved. Second, the verification between the fitted result and the exact one is carried out. The optimization of grounding grids is performed to show the effectiveness of the proposed algorithm

A Fredholm integral equation of the first kind has been developed for analyzing the performance of the toroidal high-voltage direct current (HVDC) grounding system buried in the horizontal multilayer soil. The method of moment is used to solve the equations. The formulation of potential in the earth due to a circular current is proposed in closed form by means of conception of the complex resistivity and depth, which leads to the saving of the computational time greatly. The numerical results show the good agreements with those in other papers and the measured data

The design of grounding system often relies on the performance simulations. The evaluation of the current distribution of grounding system for many frequencies by using the method of moments (MoM) may take a long time since the impedance matrix must be recomputed at each new frequency. A multiobject adaptive spatial sampling approach is presented to construct the fitted model of the electric field intensity generated by a horizontal electric dipole. The [Z] matrix spatial interpolation technology with MoM is described to reduce the computational time needed for the transient characteristics analysis of a horizontal grounding system. The accuracy and computational time of the [Z] matrix interpolation method are compared with those of the direct MoM. The numerical examples show that the [Z] matrix spatial interpolation method can reduce the computation requirement effectively

Soil ionization has a great effect on the performance of grounding electrodes fed by currents of high magnitude. In this paper, a numerical method is proposed to analyze the transient performance of grounding system, which takes account of the dynamic and nonlinear effects of soil ionization. The method couples moment method with circuit theory and Fourier transform. The transient performance of grounding system considering the soil ionization effect is compared with that not considering soil ionization effect.

How to precisely measure the grounding impedance of large-scale substations is a fundamental guarantee for the safe operation of power systems. If the ground wires were connected to the grounding grid, these ground wires would shunt a part of the injected measuring current and allow the measured grounding impedance to be smaller than the actual impedance of the grounding system. Based on an actual 500-kV grounding system, this paper discusses how to analyze the influence of the overhead ground wire on the measured grounding impedance and how to obtain the real grounding impedance of the grounding system. A numerical analysis model considering the grounding system, the transmission lines, towers, and their grounding devices, based on the multilayer soil model analyzed from field test data of apparent soil resistivity, was constructed to analyze the influence of ground wires and tower grounding resistances on grounding impedance, and the general effects of different parameters, such as tower impedance, grounding impedance, and circuits of transmission lines, were analyzed. The real grounding impedance of the substation with connected overhead ground wires was validated, and some useful results have been obtained, based on the field-measured values and numerical analysis.

The shielding failure is the occurrence of a lightning stroke that bypasses the overhead ground wires and terminates on the phase conductors. The correct design to improve the shielding effect of transmission line to lightning is one of the key problems of transmission line design. A numerical analysis model for shielding failure of transmission line based on electromagnetic field theory is proposed in this paper. The electrical field of the system including lightning leader, transmission line and ground is solved, the range of lightning current striking the phase conductor is obtained, and the shielding failure probability of transmission line is calculated. The lightning leader model and the critical breakdown electrical field intensity of long gap are discussed. The analyzed results by numerical analysis model are compared with those by the electrogeometric model.

In a high soil resistivity area, counterpoise wires are applied to decrease the grounding resistance of tower grounding devices. If the conductor of counterpoise wire is very long, although the power frequency grounding resistance of the tower grounding device is decreased, the lightning protection performance of the transmission line is still not good. The influences of the length of grounding electrodes on the lightning transient characteristic were analyzed. The dynamic and nonlinear effect of soil ionization around the grounding electrode was considered in the analysis model of transient characteristics for the grounding electrodes under lightning impulse. The counterpoise wire has an effective length when lightning passes through it. When the length of a grounding electrode exceeds the effective length, the grounding conductor will not be utilized effectively. The simulating experiments were performed to analyze influences of the length of the counterpoise wire on the impulse characteristics. The formulae to calculate the impulse effective lengths of counterpoise wires were proposed. The model proposed in the paper has been validated by comparing the numerical results with experimental tests.

A two-stage algorithm is presented to determine an analytical model-based rational function by adaptively selecting sampling points. At the first stage, the rational interpolation function is created by using Stoer-Bulirsch algorithm and comparing the fitted model with the different ranks. At the second stage, the fitted model is validated by comparing with the first-principle model at a set of checking points. Some checking points will be added to the sampling series determined in the first stage to improve the fitted model. The new proposed algorithm is more accurate and effective than that using Stoer-Bulirsch interpolation only due to the fact that it appends the validation approach. When a highly oscillating curve is approximated, the validation ensures the fitting precision. With the two-stage MBPE algorithm, some time-consuming electromagnetic computations can be replaced by the interpolation from the fitting functions, which can increase the computational efficiency greatly. This method i...

A fast electric field integral in time domain using the uneven discretization and the implicit scheme is proposed to calculate the switching electromagnetic transient at a substation. The switching transient currents and the resultant radiated electromagnetic field are calculated. The propose d approach has the strength to model the bus system at a substation with a more complicated and realistic configuration that is difficult to simulate using the circuit-based method, because all the electromagnetic couplings within the bus system are included globally. The proposed method might be one of good candidates to predicate the EMI level at a substation.

Based on the multiconductor transmission line model, this paper analyzed the electromagnetic conductive interference in the driving system of fuel cell bus by calculation. Firstly, the propagation characteristics of the conductive interference in the cable were analyzed. Then, the common mode current and its coupling effect were investigated. Finally, the coupling between the driving system and the low voltage system was researched. The results will be useful for restrict the electromagnetic conductive interference in the fuel cell bus.

This paper analyzed the distribution and the characteristic of the disturbances in the driving system of a fuel cell bus by measuring both the conductive and radiative emission. Statistical method was used to investigate the parameters of the typical voltage waveforms, which were compared with the standard ones in IS07637-2. The results are useful for the farther investigation of the EMC problems in the fuel cell bus.

A fast cortical-imaging approach is proposed to reconstruct the equivalent source distribution in a four-layer head model. The key idea is to calculate the coefficient matrix K used in LORETA analytically by extracting the cortex potential contribution from dipoles inside brain. Numerical examples have shown the computational time is reduced greatly

GFCI (ground fault circuit interrupter) is widely used to prevent from fire hazards, electronic shock and injury to persons by a persistent earth leakage current. On account of a application of GFCI, however the occurrence of false tripping due to lightning and switching surge has been growing. This unwanted tripping caused by the transient ground potential rise due to nearby lightning strokes could bring about a fatal loss like a power outage or a deterioration of power quality. In order to analyze the cause of malfunction, various samples of GFCI were investigated experimentally. When lightning impulse and EFT (electrical fast transient) were injected to GFCIs with the different leakage current detecting circuits and the wiring configurations, various false tripping characteristics were showed. Most of them showed malfunctions under surge current less than 3 kA. Also, it was found that a false tripping is dependent on a wiring of GFCI circuit and position of protective component Countermeasures using MOV (metal oxide varistor) and zener diode were suggested to prevent from a false tripping in this study.