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Direct lightning poses a serious threat to the safety of power systems. In recent years, the lightning fractal model, which can reflect the fractal characteristics and randomness of lightning leaders, has been gradually applied to direct lightning protection for substations, transmission lines, etc. However, since few studies have linked simulations with experiments, the reliability of the lightning fractal model in terms of attachment probability prediction lacks experimental verification. In this paper, a series of attachment tests are carried out under a rod-rod gap. The equivalence between simulation tests and natural lightning is discussed, and the influencing factors of the attachment results are investigated. The attachment probability is simulated and compared to the test value under each test configuration. The test results show that the fractal dimension of discharge channel is consistent with the observation results of natural lightning. Under different configurations, the test value of attachment probability basically conforms to the simulation value. In general, the dispersion of the test results is slightly greater than the simulation results, but the average probability differences are all within 10%. The test results strongly indicate that the lightning fractal model is of good reliability in the prediction of strike probability. [ABSTRACT FROM AUTHOR]

In this work, an analytical electromagnetic field coupling to transmission line model is proposed to efficiently evaluate the induced voltage/current responses of loads connected at the terminals. Specifically, an equivalent circuit is developed by combining the Lorentz reciprocity theorem with the classic passive transmission line model, and it is found that active contribution by impinging field could be cast in analytic form, as a function of the far-field radiation pattern and input impedance of the transmission line system in the transmitting mode. Compared with Agrawal’s model, the proposed method reports concise and physical formulations without degrading the accuracy. Moreover, it is demonstrated that defining impinging field in spherical coordinates aligning parallelly with line is advantageous in revealing the wave propagation process. [ABSTRACT FROM AUTHOR]

Calculation of geomagnetically induced current (GIC) flowing through power system during the geomagnetic storm has attracted more attention recently. However, for high voltage power systems with transmission lines over hundreds or even thousands of kilometers, the earth model and geomagnetical field generally vary significantly. So, it is essential to take them into consideration using limited earth survey sites and geomagnetic observatories. To address this problem, a Kriging method is introduced in this paper to make earth model and geomagnetical field interpolations. It has the characteristic of spatial autocorrelation by considering not only the distances between predicted points and training points but also the distances between training points themselves. Finally, a case study of the Central China 1000 kV ultra-high voltage (UHV) grid is carried out to illustrate the applicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

To investigate the high-altitude electromagnetic pulse (HEMP) immunity of electrical equipment in operation, a 10-kV transmission line (TL) experimental platform is built in this paper. The conducted transient electromagnetic disturbance (TED) could be injected to the electrical equipment of 10-kV TL with power on or power off. The TED is produced by the pulsed current injection (PCI) generator, whose rise time is less than 20 ns and full width at half maximum is in the range of 500 ∼ 550 ns on short-circuit state with 60 Ω resistor. On the other hand, the 10-kV TL is equivalently designed in cross section to make its characteristic impedance being 330 Ω to conform to the value of practical case. The voltages and currents applied on the tested equipment can be measured at nano-second level simultaneously, which are of great use to learn the effect mechanisms and compare the results under different working conditions. Some 10-kV pin-type porcelain insulators are tested under different conditions, which shows the capacity of the proposed platform to test immunity of 10-kV electrical equipment. [ABSTRACT FROM AUTHOR]

This article proposed a modified electromagnetic field coupling to transmission line (TL) model with the objective to accounting for the impact of complex dielectric coatings. Classic TL model neglects the perturbation effects of coatings on the incident electric field; the validation of this simplification is disproved in this article for TL structure with complex dielectric coatings. Through analysis, it is corroborated that coating effect could be neglected only for longitudinal electric field component, whereas the perturbation on transverse field component needs to be taken into account by a newly introduced parameter called coating coefficient. The proposed method is verified through a case study on a differential line system, where a simulation method based on the 2-D finite element method is also proposed to evaluate the value of the coating coefficient. [ABSTRACT FROM AUTHOR]

This paper studies how propagation and termination losses affect full transient-based fault location techniques. Their accuracy is discussed in terms of both location uncertainty, caused by a limited spatial resolution, and systematic errors, caused by a bias in the fault-location metrics. This last case is proven to be by far likelier when propagation losses are higher than the dissipation in line termination loads. Two different location metrics are studied, namely correlation and normalized projection, as found in the literature, with correlation proven to be unbiased, since it benefits from two location mechanisms, namely frequency and time-decay matching of a line resonances, as opposed to projection, which only relies on the former mechanism. A numerical analysis of realistic lossy overhead lines confirms theoretical predictions about biased fault location and loss of spatial resolution and the role played by the frequency content of transient data. When applied to the modal analysis of a three-phase transmission line, these results help explaining why faults are located with widely variable accuracy depending on their distance and the bandwidth of the recorded transient, confirming that wide-band transient sampling does not necessarily results in the best location accuracy. [ABSTRACT FROM AUTHOR]

Based on multigap loop (MGL) antenna and low-noise norm detector, a novel nano-second (ns)-level transient magnetic-field (${H}$ -field) sensor is proposed in this article. The direct measurement result of the MGL antenna is the differential signal of the ${H}$ -field, which is capable to be digitized for storage by the norm detector. The original ${H}$ -field can be restored using the software integral method. The developed ns-level ${H}$ -field sensor exhibits two major advantages. First, it can measure the ${H}$ -field in the substation or the coupled ${H}$ -field inside the hermetically sealed cavities, such as the cockpit of vehicles or aircrafts, which is because the need for the transmission line is removed. Second, its sensitivity is significantly higher than the measurement system with the hardware passive integrator, and the integral error can also be effectively reduced by the low-noise norm detector. In this article, the realization of the ns-level transient ${H}$ -field sensor will be detailed. The simulated upper cutoff frequency of the designed MGL antenna is about 1.9 GHz. The sampling rate of the norm detector is 2 GS/s as the maximum. The dynamic range of the detector is about 42 dB and the operation bandwidth ranges from 0.3 kHz to 500 MHz by calibration. The total storage space of 128 kB can record as long as $64~\mu \text{s}$ at 2 GS/s and is extendable. Test results show that the developed sensor can measure the ns-level ${H}$ -field accurately. [ABSTRACT FROM AUTHOR]

This article presents a time-domain macromodeling algorithm for buried transmission lines subject to coupling of an incident field and terminated with linear and nonlinear loads. Different from overhead lines, the determination of the transient ground admittance is of great importance due to the complexity of the analytical expressions and the necessity of assuring a good approximation over a wide frequency range. The proposed macromodel adopts the analog behavioral modeling (ABM) library of Spice solvers to model frequency-dependent transmission line parameters directly, and calculate convolution in time domain, making it simple and convenient to treat time-domain field-to-line coupling equations without the need of time and spatial discretization and curve fitting used in other time-domain numerical algorithms. Besides, the model complexity is not limited by the line length. Hence, the proposed algorithm can significantly simplify the modeling process and improve simulation efficiency, especially for long multiconductor transmission lines. Furthermore, an effective and simplified expression for self and mutual ground impedance and admittance of underground lines is proposed in this article. With the proposed expression, the time-consuming numerical integration can be avoided, leading to a saving of 98% of the computational time. Finally, several validation examples of field coupling to buried power cables terminated with linear and nonlinear devices are investigated. The comparison of calculated waveshapes and CPU times shows the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Geo-magnetically induced currents (GICs) have attracted more attention since many Ultra-High Voltage (UHV) transmission lines have been built, or are going to be built in the world. However, when calculating GICs based on the classical model, some input parameters, such as the earth conductivity and dc resistances of the grid, are uncertain or very hard to be determined in advance. Taking this into account, the uncertainty quantification (UQ) model of the geo-electric fields and GICs is proposed in this paper. The UQ of the maximums of the geo-electric fields and GICs during storms is carried out based on the polynomial chaos (PC) method. The results of the UHV grid, 1000 kV Sanhua Grid, were presented and compared to the Monte Carlo method. The total Sobol indices are calculated by using the PC expansion coefficients. The sensitivities of geo-electric fields and GICs to the input variables are analyzed based on the total Sobol indices. Results show that the GICs and geo-electric fields can be effectively simulated by the proposed model, which may offer a better understanding of the sensitivities to input uncertain variables and further give a reasonable evaluation of the geomagnetic threat to the grid. [ABSTRACT FROM AUTHOR]

An accurate and efficient time-domain macromodeling algorithm based on the analog behavioral modeling (ABM) and generalized method of characteristics is proposed to calculate current and voltage responses of multiconductor transmission lines (MTLs) to incident field coupling. The proposed macromodel adopts the frequency response table of Laplace-domain elements in ABM library of Spice solvers to model the characteristic impedance (or admittance) and propagation operator of transmission lines and calculate the convolution in the time domain. Time-domain convolution is implemented by the solver, without the need of delay extraction and rational approximation for the MTLs solution. Compared with the existing algorithms for calculating the responses of incident field coupling to MTLs, the proposed algorithm largely simplifies the modeling and simulation process while ensuring stable responses, especially for long MTLs. Besides, it is also applicable and efficient to solve the case of nonlinear terminal elements, directly in the time domain. Several numerical examples of single conductor, two conductors, and three-phase 35 kV power transmission lines loaded with nonlinear metal oxide arresters are studied. The calculation results and CPU times are compared with those of other existing algorithms to validate the accuracy and efficiency of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

The traveling-wave Marx generator was first proposed by Carl Baum to analyze the switch-closure propagation process in fast pulsed-power systems. To improve the performance of the transistorized sub-nanosecond pulse generator, the traveling-wave Marx circuit with inter-stage transmission lines is studied. Simulations indicate that the delay time and the impedance of inter-stage transmission lines [microstrip lines on printed circuit board (PCB)] are main factors affecting the pulse waveform. Based on it, the series connection of modularized Marx circuits is proposed, which has the advantages of adjustable amplitude and bendable circuit layout. A compact high-amplitude pulse generator is developed with the amplitude of 8.2 kV, the rise time of 150 ps, and the PCB length of 35 cm. For higher pulse repetition rate, the heat dissipation design of PCB is necessary; however, due to the variations in the microstrip line structure, the commonly used metallic heat sink may cause a significant decrease in pulse amplitude. Thus, a novel heat dissipation design is proposed by optimizing the layout of metallic sinks and introducing heat-conducting ceramic sinks. A high-repetition-rate pulse generator is developed with the maximum pulse repetition rate of 600 kHz, the amplitude of 1.1 kV, and the rise time of 160 ps. [ABSTRACT FROM AUTHOR]

Lightning electromagnetic fields can couple to overhead power transmission and distribution lines, causing serious effects to the power system. Lightning electromagnetic fields that couple to overhead lines have a nonuniform distribution along the line conductors. Therefore, to ensure the accuracy of the numerical calculation results, a large number of discretization points are needed along the line, which might dramatically increase the computation time since the evaluation of lightning electromagnetic fields in the presence of a lossy soil involves, in general,Sommerfeldintegrals, or, even in the case of a perfectly conducting ground, numerical integration along the channel. This paper proposes a new approach to address this problem. The proposed approach is based on the Agrawalet al. coupling model, in which the horizontal lightning electric field along the line is represented by the complex exponential functions in the frequency domain using the matrix pencil method. The method is highly efficient in terms of computation time since the lightning-induced response of the line can be solved semi-analytically. The proposed approach is validated by two different validation examples. [ABSTRACT FROM AUTHOR]

This paper develops a one-dimensional norm detector for nanosecond-level transient electric field (E-field) measurement based on the digital measurement technology. It has two main advantages over the traditional measurement method. First, the measured signals can be stored and no transmission line is needed. Hence, it can detect the E-field coupled in hermetically sealed cavities, such as the cockpit of an aircraft or a vehicle under electromagnetic compatibility test. Second, commonly used norms of the measured waveform can be acquired by the signal processing software quickly and conveniently. Therefore, the efficiency of the measurement experiment can be improved. This paper describes the detailed realization of the norm detector and the design of its signal processing software. The maximum sampling rate of the norms detector is 2 GSPS and the memory depth is 8 kB. Via adjusting the height of the antenna, the measuring range can be 0.1–55 kV/m and the estimated operation bandwidth is 1 kHz–460 MHz. The norm detector is tested and compared with the traditional E-field sensor with the fiber-optic link by measuring the square waveform and the actual electromagnetic pulse waveform. Furthermore, the norm detector can measure magnetic field, coupled current or high-voltage pulse by a simple structural modification. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed analytical representation and Gauss–Seidel iterative technique (Seidel-DARIT-field), which has a faster convergence rate than the Jacobi-DARIT-field method in the simulation of electromagnetic pulse (EMP) radiated field coupling to multiconductor transmission lines (MTLs) and is more valid and accurate. The process of the first iteration in this method is similar to that in the Jacobi-DARIT-field method. At the second iteration and after, every line will be updated based on the present iteration state of other lines. [ABSTRACT FROM AUTHOR]

This article investigates the problem of fault detection for continuous time systems with network communication links. A network communication channel is assumed to be existing between the plant and the fault detection filter, and three types of incomplete measurements which typically appear in a network environment are simultaneously addressed, including measurement quantisation effect, signal transmission delay and data packet dropout. A mathematical model is presented to account for those issues in a unified form. Based on that, a full-order fault detection filter is designed such that the residual system is asymptotically stable and preserves a guaranteed performance. A sufficient condition of the existence of the fault detection filter is obtained and all the results are formulated in the form of linear matrix inequalities, which can be readily solved via standard numerical software. Finally, a simulation example is provided to illustrate the usefulness of the developed theoretical results. [ABSTRACT FROM AUTHOR]

This paper provides a novel iterative solution in an analytical (as opposed to numerical) fashion in the frequency domain for crosstalk on multiconductor transmission lines. The proposed method employs the distributed analytical representation of equivalent coupling sources and an iterative technique originated in transverse waveform relaxation. The effects of adjacent lines at each iteration are considered as equivalent distributed sources along the lines rather than lumped sources at the end of the lines or segments. By means of combined voltage waves, these equivalent distributed sources are further implemented analytically in the form of exponential function combinations, leading to a more efficient updating process since the time-consuming numerical integration over the line is avoided. The voltages and currents at the terminals are solved by the Baum–Liu–Tesche equation considering the symmetry of the coupled transmission lines. One major advantage is that the solution at each iteration is obtained analytically and exactly in terms of the per-unit-length parameters, loads, and some predetermined coefficients, which is highly suitable for illustrating the factors that influence the crosstalk. The validation results in a wide range cases show that the proposed method can efficiently handle transmission lines with a large number of conductors and lossy as well as frequency-dependent parameters. [ABSTRACT FROM PUBLISHER]

We present an improved structure of the tapered magnetically insulated transmission line oscillator (MILO). Simulation results show that this structure can obtain more microwave power with higher efficiency. Studies indicate that the distance between the load support legs and the last vane can affect the operation characteristics of this device. In the experiments, we obtain microwave with peak power of 2 GW, frequency of 2.63 GHz, and mode TM01. The beam to microwave power efficiency is 11%. [ABSTRACT FROM AUTHOR]

• Upper bound of field-induced overvoltage peak in power line network could be assessed both numerically and analytically. • Complex power line system could be equally represented by its coupling-dominate branch for assessing the overvoltage peak. • Specific segment lengths do not influence the predicted upper bound. • Relative orientation between adjacent line segments has strong impact on the upper bounds. This paper deals with the assessment of the maximal peak of the overvoltage induced in a power-line network due to the field-to-wire coupling from an external electromagnetic disturbance. A worst-case analysis is here combined with the transmission line model to find the terminal overvoltage, induce by radiated electromagnetic disturbances of constrained energy density and bandlimits. The approach was applied to canonic power line network topologies, from statistic viewpoint, it is demonstrated that dominant coupling can be ascribed to the branch containing the most twisted segments. Accordingly, efforts have been devoted to find analytical solution to overvoltage peak upper bound for the coupling-dominant zigzag branch. In this connection, both versatile implicit solution and approximated explicit expressions of the upper bound are formulated, which reveals the relations between the upper bound of zigzag branch and its segments, quantitively interpreting the effect of segment orientations and length. Finally, numerical simulations corroborate the model validity and suggest that the estimations of upper bound are sufficiently accurate for analyzing practical power line network. This proposed approach will be instructive for power system insulation coordination and protection design. [ABSTRACT FROM AUTHOR]