Traveling Wave Method Research Articles

Chirped envelope optical solitons for Kaup–Newell equation

We investigate the Kaup-Newell equation that represents one of the forms of derivative nonlinear Schrödinger equation. The model applies to the description of sub-pico-second pulse propagation through an optical fiber. A special complex envelope traveling-wave method is applied to find a nonlinear equation with a fifth-degree nonlinear term describing the dynamics of field amplitude in the nonlinear media. It is shown that the phase associated to the obtained pulses has a nontrivial form and possesses two intensity dependent chirping terms in addition to the simplest linear contribution. A class of soliton solutions of the bright, dark and singular type are derived for the first time. The requirements concerning the optical material parameters for the existence of these chirped structures are also discussed.

Propagation of chirped gray optical dips in nonlinear metamaterials

Abstract We investigate the existence and stability properties of nonlinearly chirped solitary waves on a continuous-wave background in nonlinear metamaterials with higher-order effects such as pseudo-quintic nonlinearity and self-steepening effect. Novel classes of chirped gray solitary pulses (dark pulses with nonzero minimum intensity) are derived by employing the traveling-wave method. The conditions for the formation of these localized pulses as well as the nonlinear chirp associated to them are presented. The stability of the obtained structures is also demonstrated numerically under finite initial perturbations. The results show that the envelope pulses obtained here represent new types of extremely robust nonlinear chirped structures in highly nonlinear metamaterials.

Type D travelling wave fault location on branched underground low‐voltage networks

Low voltage cable faults are frequently associated with arcing at the fault which creates 2 high frequency transients which propagate away from the fault towards opposite ends of the cable and whose difference in arrival times can be used to determine the fault's location using the Type D method. A variant of the Type D method, known as the Transient Recording System (TRS) using asynchronous data acquisition units (ADAU) has been used successfully in situations where multiple branches on a cable have precluded the use of other travelling wave methods. The range, and precision of location, of the TRS method is extended by the use of a Marker Unit (MU) which allows the distance and direction to a fault to be determined relative to the point of connection of the MU. The asynchronous data acquisition units operate in ‘listening’ mode and are triggered by the arrival of the transients created by the fault arc. Prior to triggering, the ADAUs continuously (over)write all received data into their cyclic buffers, including the low amplitude MU pulses. Shortly after triggering the (over)writing of the cyclic buffer stops and earlier (pre-trigger) data retained – including the received MU pulses.

Computation of ion exchange buried microring resonator waveguide for THz communication applications

Abstract The ion exchange creates the optical buried waveguides, whereas it is the method that the glass doping occurs with the condition of existence of the mobile metal ions. The most common ion used is silver (Ag+) due to its broad variation in the refractive index. The proposed application presented in this work is to use the microring resonator (MRR) system based on the buried waveguides simulated by the ion exchange method. The passive MRRs are realized as the multi-wavelength transceiver, applicable in optical technologies such as the optical sensing, Terahertz (THz) communication and optical switching. The cross-sectional view of the simulated buried optical waveguide for the Ag+ concentrations of 0.8 mol/m3 is presented. The fundamental mode propagation is simulated using the time-domain traveling wave method, where the simulation of the optical power flow density and the electric field distributions of the buried waveguides were performed. The two coupled MRRs are used to generate tunable dual-wavelength with spacing in the range of Terahertz (THz). As results, the dual wavelengths in the range between 0.25 and 0.96 THz were generated at the throughput and drop port of the MRRs system.

Location of Faulty Section and Faults in Hybrid Multi-Terminal Lines Based on Traveling Wave Methods

Traveling-wave-based fault location methods are widely used for modern power systems owing to their high accuracy on two-terminal lines. However, they perform poorly on hybrid multi-terminal lines. Many traveling-wave-based methods have been developed recently to solve this problem, but they have high computational burdens and complex fault location procedures. To tackle this challenge, a new fault location method is presented in this paper. First, to ensure that the implementation of the proposed method is not affected by different line parameters, a normalization algorithm is used for hybrid multi-terminal lines, which consist of overhead lines and cables. To reduce the complexity, a novel fault section identification method that depends only on the first three arrival times is applied to separate a three-terminal fault section from the multi-terminal lines. Consequently, the fault can be located using a corresponding two-terminal fault location method in this fault section. To verify its effectiveness, fault case studies and performance evaluations are performed in the PSCAD and MATLAB/Simulink environment. The simulation results reveal that the proposed method can correctly identify the fault section and accurately locate the faults, which is simple and suitable for hybrid multi-terminal lines.

Dynamic Analysis of Uncertain Structures Using an Interval-Wave Approach

Due to the uncertainties of material, geometrical and load parameters, dynamic responses of actual engineering structures are uncertain. The paper investigates dynamic responses of uncertain frameworks by combining the interval method with the traveling wave method. The uncertainties of material, physical dimension and loads are firstly characterized by interval parameters. The waveguide and transmission equations of uncertain framework structures with interval parameters are then proposed based on the traveling wave method. The uncertain junction scattering equation is extracted from the force equilibrium conditions and displacement compatibility conditions and the interval form of dynamic responses are developed using interval arithmetic rules. Finally, the numerical examples including a single beam and a planar frame structure have been presented to verify the feasibility and validity of the proposed method.

Families of exact solutions of a new extended $$\varvec{(2+1)}$$(2+1)-dimensional Boussinesq equation

A new variant of the $$(2+1)$$ -dimensional [ $$(2+1)d$$ ] Boussinesq equation was recently introduced by Zhu [Line soliton and rational solutions to (2+1)-dimensional Boussinesq equation by Dbar problem, 2017. arXiv:1704.02779v2 ; see eq. (3)]. First, we derive in this paper the one-soliton solutions of both bright and dark types for the extended $$(2+1)d$$ Boussinesq equation by using the traveling wave method. Second, N-soliton, breather, and rational solutions are obtained by using the Hirota bilinear method and the long-wave limit. Nonsingular rational solutions of two types were obtained analytically, namely (i) rogue wave solutions having the form of W-shaped lines waves and (ii) lump-type solutions. Two generic types of semi-rational solutions were also put forward. The obtained semi-rational solutions are as follows: (iii) a hybrid of a first-order lump and a bright one-soliton solution and (iv) a hybrid of a first-order lump and a first-order breather.

An Adaptive Fault-Location Method for a Power-Transmission Line Using Pulse Registration on a High-Frequency Wave Path

An adaptive traveling-wave method to improve the accuracy of fault location has been developed. The suggested method can compensate for an error of the two-sided method caused by the dispersive nature of a phase wire along which a high-frequency electromagnetic pulse propagates from the point of the fault. The error in fault location has been determined depending on the means of registration of a high-frequency signal. Some recommendations on connection of facilities to register electromagnetic pulses used in the devices of traveling-wave fault location have been provided. The suggested method allows one to substantially reduce errors of estimation of distance to the point of a fault and is less affected by external factors. The developed method can be applied in both in existing and future devices for fault location.

Chirped singular solitons for Chen-Lee-Liu equation in optical fibers and PCF

This paper obtains chirped singular optical soliton solutions that is modeled by Chen-Lee-Liu equation in the context of optical fibers and PCF. A special complex envelope traveling-wave method is applied to find a nonlinear equation with a fifth-degree nonlinear term describing the dynamics of field amplitude in the nonlinear media. It is shown that the chirp associated to the obtained solutions is directly proportional to the intensity of the wave and its amplitude is controlled by self steepening term. Parametric conditions for the existence of the chirped singular structures are also presented.

Response of exact solutions of the nonlinear Schrödinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry

We discuss the effect of small perturbation on nodeless solutions of the nonlinear Schrödinger equation in 1 + 1 dimensions in an external complex potential derivable from a parity-time symmetric superpotential that was considered earlier (Kevrekidis et al 2015 Phys. Rev. E 92 042901). In particular, we consider the nonlinear partial differential equation , where represents the complex potential. Here, we study the perturbations as a function of b and m using a variational approximation based on a dissipation functional formalism. We compare the result of this variational approach with direct numerical simulation of the equations. We find that the variational approximation works quite well at small and moderate values of the parameter product bm which controls the strength of the imaginary part of the potential. We also show that the dissipation functional formalism is equivalent to the generalized traveling wave method for this type of dissipation.

Fault location and classification of combined transmission system: Economical and accurate statistic programming framework

An effective statistical feature extraction approach of data sampling of fault in the combined transmission system is presented in this paper. The proposed algorithm leads to high accuracy at minimum cost to predict fault location and fault type classification. This algorithm requires impedance measurement data from one end of the transmission line. Modal decomposition is used to extract positive sequence impedance. Then, the fault signal is decomposed by using discrete wavelet transform. Statistical sampling is used to extract appropriate fault features as benchmark of decomposed signal to train classifier. Support Vector Machine (SVM) is used to illustrate the performance of statistical sampling performance. The overall time of sampling is not exceeding 1¼ cycles, taking into account the interval time. The proposed method takes two steps of sampling. The first step takes ¾ cycle of during-fault and the second step takes ¼ cycle of post fault impedance. The interval time between the two steps is assumed to be ¼ cycle. Extensive studies using MATLAB software show accurate fault location estimation and fault type classification of the proposed method. The classifier result is presented and compared with well-established travelling wave methods and the performance of the algorithms are analyzed and discussed.

Discontinuous deformation analysis of super section tunnel surrounding rock stability based on joint distribution simulation

Based on binocular stereo photography measurement technology, the actual distribution information of joints and fractures in the tunnel face were obtained via image processing and feature extraction, and the preliminary evaluation of surrounding rock stability of Laohushan tunnel was conducted according to surrounding rock classification method. Since all available surrounding rock classification approaches didn’t consider the influences of the size effect of tunnel excavation span and unfavorable geologic bodies such as weak-fracture zones, an improved discontinuous deformation analysis (DDARF) method was adopted to conduct a numerical simulation of the deformation and fracture processes of the surrounding rock. Using the traveling wave method, triangle DDA blocks were automatically generated in the calculation zone, and the block boundaries were divided into real joints and virtual joints. Based on the real joint information obtained via aforementioned photographic measurement, the real joints in the tunnel face were dynamically modified, in order to achieve the simulation of joint distribution. The results revealed that the fracture evolution regularity, deformation failure mechanism, and block dropping phenomenon that the DDARF joint simulation model calculated are in good agreement with actual conditions, while those obtained based on conventional models present differences from field situation. Additionally, focusing on the localised rockfall phenomenon of Laohushan tunnel, the crack extension rate was introduced to conduct a quantitative comparison of the rock crack evolution process with or without anchor supporting. The research results offer practical guidance for field construction and anchorage support scheme optimization.

Simulation of mode lock lasers using microring resonators integrated with InGaAsP saturable absorbers

Add-drop microring resonators (MRRs) are used in a wide variety of practical applications. To add or drop special wavelength division multiplexing, an optical wavelength selective ring resonator can be used. This paper presents a system of multiple mode lock lasers consisting of an add-drop MRR integrated into a smaller ring with a saturable absorber (SA). In the case of mode-locking, a semiconductor is presented as the SA. This study uses an InGaAsP/InP semiconductor with an InP substrate and a direct bandgap as the MRR. The time-domain traveling wave method is utilized to model the presented photonic circuits. The generated multi-wavelength mode lock lasers have a bandwidth and free spectral range (FSR) of 1.1 and 30.24 nm, corresponding to 0.137 and 3.77 THz, respectively. The drop port output signals have a bandwidth and FSR of 1.5 and 30.24 nm, corresponding to 0.187 and 3.77 THz in the frequency domain. A finesse of 20.16 is obtained, and the Q-factor is ~1 × 103. The side bands of the mode lock lasers have an FSR of 0.86 nm.

Damage Analysis of One-Dimensional Euler–Bernoulli Cracked Beam with Traveling Wave Method

Based on the elastic fracture mechanics, we establish a continuous model of one-dimensional Euler–Bernoulli cracked beam using the traveling wave method, and analyze the damage characteristics of cracked beam through the changes of deflection and power flow response. First, the control equation of bending vibration of healthy beam is deduced by traveling wave method. Then, the reflection and transmission matrices of waves at force point, constraint point, crack point are derived. The analytic solutions of deflection and power flow are expressed explicitly as the function of crack location and size. The effects of crack width and depth on deflection and power flow response of cracked beam are revealed. Finally, the numerical example illustrates the effectiveness of the proposed method.

Of the Fault Location Methods for Phase-to-Ground Short Circuits in Unearthed Sub-Transmission Networks

This paper provides a coherent classification of the existing methods for phase-to-ground fault location in power sub-transmission networks operated with unearthed neutral. The theoretical background of each approach is briefly presented, specifying whether a method is suitable for on-line or off-line applications. The analysis is mainly focused on comparing the limitations of the algorithms, especially concerning the general properties of the lines of a sub-transmission power system. The aim of authors is to present an overview of the existing approaches in literature by identifying five method categories, i.e. signal injection method, impedance-based method, travelling wave method, fault transient analysis method and composite location method. The main pros and cons of each method are described in order to give the reader a useful guide to identify the better fault location procedure, on the basis of the user own needs.

An Improved Traveling-Wave Protection Scheme for LCC-HVDC Transmission Lines

Line-commutated converter-based-high-voltage direct-current (LCC-HVDC) transmission technology has been developing very rapidly. However, the sensitivity and reliability of HVDC line protection require further improvement. An analysis of different line fault types is conducted to show that the normalized voltage change rate without the influence of wave propagation can more effectively distinguish between internal and external faults with high fault resistances. Owing to the difficulty of obtaining an accurate solution for a traveling wave, a novel traveling-wave propagation calculation method is developed by making use of the step response of a transmission line with consideration for its frequency-dependent characteristics. A novel traveling-wave protection (TWP) scheme for two-terminal LCC-HVDC transmission lines is then proposed based on the developed traveling-wave propagation calculation method and fault analysis results. The proposed protection scheme is tested based on fault simulation data using an EMTDC/PSCAD simulation platform and the fault-recorded data from an actual undesired tripping event of conventional TWP. The results demonstrate that the proposed TWP scheme, compared with conventional TWP, can more reliably and correctly detect faults with high transition resistances under different operation modes.

Optimal Time Delay Extraction for Transmission Line Modeling

The frequency-dependent transmission line modeling by the traveling wave method requires approximating the propagation function with a delayed rational function. Some approaches are based on modal decomposition where scalar functions are fitted with a rational model plus a single time delay. The delay is calculated from the modal velocity and the minimum-phase-shift angle that can be reconstructed from the magnitude function. This paper shows that the accuracy in the phase reconstruction as calculated by Bode's magnitude-phase integral relation can be greatly improved by removal of a singularity in the integrand and by prediction of out-of-band samples for the magnitude derivative. It is further shown that the time delay giving the smallest rms-error in the final rational approximation is often substantially larger than the mps induced delay. An improved estimation is calculated via an auxiliary magnitude function and used for determining a bracketing interval for the true optimum that is identified by searching.

The Comprehensive Evaluation Algorithm with Fault Location in HVDC Transmission Line

China has a vast territory with a great demand for electricity. However, the resources are in reverse distribution in the country. Therefore, high voltage direct current transmission has great practical significance and been widely used. However, traditional fault location methods have a lot of problems in engineering application for the length of transmission line and the complexity of the terrain. This paper proposes a comprehensive evaluation algorithm based on the travelling wave method and time domain method. It also proposes a concept of fault point reliability. This algorithm analyzes the fault point reliability in the whole transmission line to determine the specific location of the fault point. This paper proves that the algorithm has high reliability by PSCAD simulation software.

An Improved Traveling-Wave-Based Fault Location Method with Compensating the Dispersion Effect of Traveling Wave in Wavelet Domain

The fault generated transient traveling waves are wide band signals which cover the whole frequency range. When the frequency characteristic of line parameters is considered, different frequency components of traveling wave will have different attenuation values and wave velocities, which is defined as the dispersion effect of traveling wave. Because of the dispersion effect, the rise or fall time of the wavefront becomes longer, which decreases the singularity of traveling wave and makes it difficult to determine the arrival time and velocity of traveling wave. Furthermore, the dispersion effect seriously affects the accuracy and reliability of fault location. In this paper, a novel double-ended fault location method has been proposed with compensating the dispersion effect of traveling wave in wavelet domain. From the propagation theory of traveling wave, a correction function is established within a certain limit band to compensate the dispersion effect of traveling wave. Based on the determined arrival time and velocity of traveling wave, the fault distance can be calculated precisely by utilizing the proposed method. The simulation experiments have been carried out in ATP/EMTP software, and simulation results demonstrate that, compared with the traditional traveling-wave fault location methods, the proposed method can significantly improve the accuracy of fault location. Moreover, the proposed method is insensitive to different fault conditions, and it is adaptive to both transposed and untransposed transmission lines well.

Band gap properties of periodic tapered beam structure using traveling wave method

The wave motion equations of a tapered beam with respect to axial, torsional and flexural deformations are deduced including the transmission and waveguide equations. Combining the force equilibrium and displacement coordination conditions at the junction, we obtain the relation between the wavenumber and frequency, and the band gap properties of periodic tapered beam structures by the Bloch theorem. The modeling accuracy and efficiency of the traveling wave method are verified by the finite element method. The band gap properties of periodic tampered and uniform beam structures are analyzed and compared for the same materials and lengths as well as the same volumes.