Nonhomogeneous Transmission Lines Research Articles

Two-terminal traveling-wave-based non-homogeneous transmission-line protection

This paper presents a two-terminal traveling-wave-based protection algorithm applied to non-homogeneous transmission lines comprising any number of sections with different topologies and considering the effect of the sampling rate. Existing two-terminal traveling wave protection functions cannot protect the line under close-in faults and present limitations in non-homogeneous transmission lines. However, the effects of the sampling rate, considered in the proposed method, result in well-defined protection and unprotected zones, essential for protection security and coordination to deal with the issue of close-in faults in non-homogeneous transmission lines. Furthermore, the algorithm can accurately detect the faulted section, allowing its use in advanced protection functions such as adaptive automatic auto-reclosing and high-speed protection schemes. A protection device was modeled considering a sampling frequency equal to 1 MHz, including functions to detect traveling waves via wavelet transform, and the proposed protection algorithm to discriminate line internal from external faults, and to select the faulted section. The algorithm was evaluated using a large number of ATP fault simulations. The results show that the algorithm is robust and reliable for protection devices installed in non-homogeneous lines.

Conservation Laws -- a Source for Distortionless Propagation and Time Delays

Since the very first paper of J. Bernoulli in 1728, a connection exists between initial boundary value problems for hyperbolic Partial Differential Equations (PDE) in the plane (with a single space coordinate accounting for wave propagation) and some associated Functional Equations (FE). From the point of view of dynamics and control (to be specific, of dynamics for control) both type of equations generate dynamical and controlled dynamical systems. The functional equations may be difference equations (in continuous time), delay-differential (mostly of neutral type) or even integral/integro-differential. It is possible to discuss dynamics and control either for PDE or FE since both may be viewed as self contained mathematical objects. A more recent topic is control of systems displaying conservation laws. Conservation laws are described by nonlinear hyperbolic PDE belonging to the class ``lossless'' (conservative); their dynamics and control theory is well served by the associated energy integral. It is however not without interest to discuss association of some FE. Lossless implies usually distortionless propagation hence one would expect here also lumped time delays. The paper contains some illustrating applications from various fields: nuclear reactors with circulating fuel, canal flows control, overhead crane, drilling devices, without forgetting the standard classical example of the nonhomogeneous transmission lines for distortionless and lossless propagation. Specific features of the control models are discussed in connection with the control approach wherever it applies.

Phasor-based fault location algorithm for three-end multi-section nonhomogeneous parallel transmission lines

In order to estimate the fault location on three-terminal multi-section mixed nonhomogeneous transmission lines, all the previously published algorithms utilize the synchronized voltage and current measurements at all ends. In this article, a fault location algorithm for three-terminal multi-section mixed double-circuit untransposed transmission lines is presented utilizing only unsynchronized current measurements. Considering issues related to the shunt capacitance, un-transposition of the line, and mutual couplings between all phases, a threshold free identification algorithm is developed to differentiate the faulted line branch. In addition, analytical fault location equation is deduced independent of fault resistance and fault type. The three-terminal power system is modeled using MATLAB environment, and several fault cases are conducted, including all fault types, different fault resistances and locations, as well as different fault inception angles. The introduced work shows high accuracy under the effect of measurement and synchronization errors as well as line parameters errors.

Fault Location Algorithm for Non-Homogeneous Transmission Lines Considering Line Asymmetry

This article presents a novel phasor domain approach to determine the location of faults in non-homogeneous transmission lines. Best implementation requires synchronized voltage and current phasor measurements at all terminals of the transmission line. The overall non-homogeneous transmission line model with fault is established by systematically combining the generalized compact models of all homogeneous line sections. The location of the fault is introduced as an additional state of the overall model. The derivation procedure of the model is without further assumptions, resulting in full consideration of three phase line asymmetry as well as distributed parameters of non-homogeneous transmission lines. Afterwards, the location of the fault is identified using the state estimation algorithm. Extensive numerical experiments in a two-terminal and a multi-terminal non-homogeneous transmission line demonstrate that the method has higher accuracy than existing fault location methods, independent of fault types, locations and impedances.

On Exact Controllability of Infinite-Dimensional Linear Port-Hamiltonian Systems

Infinite-dimensional linear port-Hamiltonian systems on a 1-D spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of nonhomogeneous transmission lines. The main result shows that well-posed port-Hamiltonian systems, with state space L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ((0,1); C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ) and input space C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , are exactly controllable.

Multi-Terminal Nonhomogeneous Transmission Line Fault Location Utilizing Synchronized Data

This paper presents an innovative fault location method for multi-terminal nonhomogeneous transmission lines by using synchronized voltage and current phasors acquired from phasor measurement units or intelligent electronic devices. We extend the previously published two-terminal and three-terminal nonhomogeneous transmission line fault location techniques developed in our lab to multi-terminal nonhomogeneous transmission lines. Specifically, a graph theory based indices and an optimal calculation data window is applied to identify the faulty line branch and to mitigate the undesirable influence caused by dc decay and the arc phenomenon of circuit breaker. The high performance of the proposed fault location method is validated by simulation results and real world utility fault data.

Backscattering in Twisted-Pair Nonhomogeneous Transmission Lines

The development of the communication networks tends gradually toward exploiting higher frequencies, sometimes even reaching the lowest microwave band (P-band). As the signal bandwidth used for transmission over twisted-pairs increases, as recommended by G.fast and other broadband systems, new phenomenon was observed, namely, backscattering. Motivated by the measurements of copper cables in frequency band up to 400 MHz, we propose a novel backscattering model. It may be productively applied to the problem of loop diagnostics. The methods to accurately and reliable determine the relevant transmission-line parameters are sine qua non condition to appropriately exploit the potential of short-to-medium range access lines. In this paper, a recursive formulation of the frequency-domain response of the backscattering is used for a space–time characterization. To confirm the practical use of the finding, we evaluate the properties of a loop using wideband, high-frequency $S_{11}$ measurements of the real cables. These laboratory results confirm the effectiveness and accuracy of the proposed method.

Novel Fault Location in MTDC Grids With Non-Homogeneous Transmission Lines Utilizing Distributed Current Sensing Technology

This paper presents a new method for locating faults in multi-terminal direct current (MTDC) networks incorporating hybrid transmission media, including segments of underground cables and overhead lines. The proposed traveling wave type method uses continuous wavelet transform applied to a series of line current measurements obtained from a network of distributed optical sensors. The technical feasibility of optically-based dc current measurement is evaluated through laboratory experiments using Fiber–Bragg Grating sensors and other commercially available equipment. Simulation-based analysis has been used to assess the proposed technique under a variety of fault types and locations within an MTDC network. The proposed fault location scheme has been found to successfully identify the faulted segment of the transmission media as well as accurately estimating the fault position within the faulted segment. Systematic evaluation of the method is presented considering a wide range of fault resistances, mother wavelets, scaling factors, and noisy inputs. Additionally, the principle of the proposed fault location scheme has been practically validated by applying a series of laboratory test sets.

Synchrophasor measurement‐based fault location technique for multi‐terminal multi‐section non‐homogeneous transmission lines

This study presents a fault-location technique for multi-terminal multi-section non-homogeneous transmission lines which combine overhead lines with underground power cables, by using voltage and current synchrophasors obtained from phasor measurement units. First, a faulty line branch is selected to narrow down the suspected faulty area. Then, the faulty section and the exact fault location can be identified by calculating the normalised fault distance for each section on the selected faulty branch. Computational burden of the proposed analytical scheme is very low because it avoids iterative computations. Promising simulation results show that the proposed fault location technique can accurately locate the fault regardless of the fault type, fault resistance, fault location, pre-fault loading and line parameters inaccuracies.

C 0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain

Hyperbolic partial differential equations on a one-dimensional spatial domain are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of nonhomogeneous transmission lines. The main result of this paper is a simple test for $C_{0}$-semigroup generation in terms of the boundary conditions. The result is illustrated with several examples.

An Algorithm for Locating Faults in Three-Terminal Multisection Nonhomogeneous Transmission Lines Using Synchrophasor Measurements

This paper presents a fault location algorithm for three-terminal multisection nonhomogeneous transmission lines using synchronized phasor measurements (synchrophasors) obtained from GPS based PMUs or digital relays with embedded PMUs or off-line data synchronization algorithms. The algorithm is extended from a two-terminal fault location technique to an algorithm for three-terminal multisection nonhomogeneous lines which combine overhead lines with underground power cables. An exclusively three-terminal faulty branch indicator/fault locator for nonhomogeneous lines is proposed, which can not only distinguish an external/internal fault but is able to locate a fault on an overhead line or an underground cable as well. The algorithm provides an exact solution for fault location estimation and excludes computational costs since neither fault type selections nor iterative operations are required. An extensive series of simulations and field evaluations have been conducted to show the effectiveness of the method. The proposed algorithm has already been implemented in Taiwan 161 kV transmission system. So far the technique yields excellent accuracy and robustness compared to existing fault location functions of digital relays in Taiwan.