Cable Parameters Research Articles

Calculation of overhead and underground cable parameters at harmonic frequencies

This paper presents a new method for the comprehensive calculation of power cable parameters at the fundamental and harmonic frequencies and for the assessment of the power cable’s frequency responses. In spite of its growing technical importance, there seem to be very little information in the open literature about resonances in power cables, particularly, when it comes to the so-called supra-harmonic frequencies, which lie in the range 2–150 kHz. At harmonic frequencies, various phenomena, such as skin effect, ground and metallic return loops, a strong capacitive effect, long-line effects, geometric imbalances and cable cross-bonding have all a marked influence on the responses of both overhead and underground cables. The cable resistances and inductances vary in a nonlinear fashion with frequency, and the latter will cancel out with the cables’ capacitive effects at some specific frequency values giving rise to alternate resonant points along the frequency spectrum. All the relevant construction details of the cable together with its electrical and operational parameters need to be processed by suitable models and methods coded into software for the fast and accurate calculations of the frequency responses of the power cables. A computer program has been developed as part of this research, using the formula and methods outlined in the paper. The usefulness and accuracy of the new methodology are demonstrated by resorting to numerical examples.

Sensitivity of Cable Model Parameters for Traveling Wave Differential Protections in MTDC Systems

Multi-terminal HVDC systems equipped with multiple DC breakers require a protection system that selectively detects faults within a few milliseconds. In the development and application of such protection algorithms, time-domain simulation studies of various faults are essential when determining the setting and verifying the performance. However, when such protections are applied in practice, it should be expected that the models will not perfectly represent the behavior of the real system or transmission line, thereby possibly causing protections to operate unreliably. This paper presents a simulation process that evaluates the consequences for a protection algorithm when the transmission line parameters are varied. More specifically, the false differential current due to cable model parameter errors is evaluated in a traveling-wave differential protection applied in a multi-terminal HVDC system during an external fault. The purpose is to identify the most critical parameters and evaluate how inaccuracies influence the protection performance when applied in practice. It is shown that the parameters which significantly influence the propagation delay are critical for achieving the ideal performance - a strictly zero differential current during external faults.

INVESTIGATION OF THE INFLUENCE OF TWISTING METHODS MULTI-PAIR LAN CABLES ON THEIR ELECTRICAL TRANSMISSION CHARACTERISTICS

The need to study the infuence of twisting methods of cable core of multi-pair LAN cables on their main electrical transmission characteristics is justifed. Experimental studies of the electrical transmission characteristics of multi-pair LAN cables of category 5e in the frequency range up to 100 MHz have been conducted. The results of experimental studies of low-frequency and high-frequency electrical transmission characteristics of these LAN cables are presented. A detailed analysis of the results of experimental studies is carried out. It has been found that high-frequency transmission characteristics such as wave resistance and return losses are most afected by cable core twisting methods. Frequency behavior of these transmission characteristics is analyzed. It was shown that high geometric and structural uniformity of isolated cores, as well as the use of modern high-speed specialized equipment for twisting the pairs provide high transmission parameters of a four-pair LAN cable of category 5e. It was found that SZ twisting technology is unacceptable due to the introduction of geometric inhomogeneities in the manufacture of multi-pair cables. It is recommended to use unidirectional twisting bow-type stranders to minimize geometric inhomogeneities.

An accurate frequency-based method for identifying cable tension while considering environmental temperature variation

In this work, we study the influences of environmental temperature variation on the static and dynamic behaviours of cables, and we develop a very accurate method for identifying the tension of a cable while considering environmental temperature fluctuation. The dynamic equation of a cable that includes the sag effect, the inclination angle and thermal fluctuations is derived, and the numerical solution of temperature-dependent dynamic equations of the cable is obtained by using the finite difference method. The derivatives of the cable's dynamic characteristics with respect to the cable's systematic parameters and the environmental temperature are derived, which furnish an accurate parameter sensitivity method for identifying the tension of a cable subjected to a changing temperature environment. The results indicate that, when the sag-to-span ratio of a cable is between 10−3 and 10−1, the environmental temperature exerts a very important influence on the dynamic behaviours of the cable, not only because it changes the cable's tension but also because it changes the deformation of the cable's sag. In this case, the method proposed in this study is useful and practically important.

Assessing the effects of DER on voltages using a smart meter-driven three-phase LV feeder model

The increasing number of residential distributed energy resources (DER) is driving the need for distribution companies to routinely assess potential voltage violations due to excessive power injections. However, this task can be quite challenging in low voltage (LV) feeders due to the limited availability of modeling data. To this end, this work proposes a practical approach to assess the effects of DER on voltages by exploiting historical time-series measurements from smart meters and head of the feeder. First, the impedances of three-phase feeders are determined assuming knowledge of feeder topology and service cable parameters. Then, the resulting smart meter-driven model is used to compute voltages due to potential DER injections. The performance of the proposed methodology is assessed using a realistic Australian three-phase LV feeder with 40 single-phase customers. Results show that, while there is some error in the calculated impedances, customer voltages are sufficiently accurate for DER management purposes.

Co-optimization of ampacity and lifetime with considering harmonic and stochastic parameters by Imperialist Competition Algorithm

This study presents a novel probabilistic algorithm for the optimal placement of underground power cables to maximize lifetime and ampacity and minimize total cost of the cable system at the same time. In this paper, the Imperialist Competition Algorithm (ICA) and Monte Carlo (MC) simulation are used to solve probabilistic optimization problem. In our previous study, we have just considered probabilistic parameters that are effective on ampacity. However, In fact, we need to consider all the other parameters such as cable’s lifetime and harmonic of demand side for co-optimizing the ampacity and lifetime to obtain the best arrangement of cable system. The cost function of optimization has been improved relative to the last one. Cable lifetime and harmonic of power system, as two important design factors, have been added to cost function in this paper. The novelty of this paper is consisted of economic co-optimization of ampacity and lifetime simultaneously. Furthermore, all statistical variations of cable system parameters, ambient temperature, dimensions of native/backfill soil and uncertainty in demand side such as load current fluctuation and harmonic are considered as design parameters at the same time. Since, all design parameters are stochastic; the change of seasons and climate can modify these parameters along the cable system. Hence, this paper indicates the necessity of consideration of uncertainty parameters at the design phase by taking into account cable lifetime based on a probabilistic approach and avoid using deterministic value. For a better explanation of this method, a numerical example is reported by using corrugated aluminum sheath cable model.

Cable tension identification via nonlinear static inverse problem

A new identification technique is proposed to evaluate the tension of a cable using a static inverse approach that couples a universal cable model with displacement sensors, strain gauges and added masses that should preserve operational affordability. An inverse problem is formulated as the minimization of a data misfit functional based on the differences in terms of vertical displacements and axial strains between two equilibrium configurations of the cable, namely, one loaded and the other free. The inverse problem formulation echoes the parametric study of a non-conventional functional suggesting a way to identify the cable parameters, namely, its length, its axial stiffness, and its mass per unit length. The computational resolution of the inverse problem is implemented as a two-step identification procedure. First, the axial stiffness and mass per unit length are kept constant and the length of the cable is approximately found via a simple line search algorithm using finite differences to estimate the functional derivatives. Second, the other physical parameters are assessed using an adjoint method for which the direct problem, the adjoint problem, and the parameter sensitivities are defined as derivatives of a Lagrangian functional with respect to dual variables, primal variables, and parameters, respectively. Due to the ill-conditioning of the problem, the proposed method does not enable an exact parameter identification but yields a good tension assessment. An experimental test campaign conducted on a multilayered 21-m long stranded cable subject to several tension levels confirms the relevance of the proposed inverse method. A field test campaign of the method on three 120-m long cables of Bonny-sur-Loire (France) suspension bridge is also presented. It proves the reliability and affordability of the overall tension identification process.

3D nonlinear dynamic analysis of cable-moored offshore structures

The nonlinear oscillations of the floating structures anchored by cables are studied in three dimensions. The floating structure is anchored by four symmetric mooring lines and the mooring lines are fixed on the seafloor at the other ends. The stiffness matrix of 3D cable element has been established and applied to analyze the dynamics of the 3D floating structures anchored by cables. The complex compatibility conditions which relate the responses of the floating body and cables have been proposed. The equations of motion for the mooring lines and floating body are individually formulated. Then they are combined as an entire system by utilizing the compatibility conditions. At last, the entire system is analyzed numerically with horizontal harmonic excitations applied on the floating body. The amplitudes for both the responses of the platform and the maximum mooring force are studied as the excitation frequency changes. The responses of the platform and the maximum mooring force are also investigated for varieties of cable parameters.

Investment Cost Analysis with Structural Design of Concrete Duct Bank Power Cables

Capital investment in underground duct bank cables is very expensive. Therefore, the design and planning for underground power cables is important. It is often done with analysis of the power demands minimizing costs over the lifetime of the cables. This work presents an evaluation of underground power cable ampacity and the total costs during the anticipated operational life of the equipment. It was evaluated with variation of concrete duct bank dimensions. Analysis of ampacity depends on temperature. The thermal model of the current study uses a finite element method. The total costs evaluated by the economic model in terms of net present value analysis consist of the initial investment costs and the value of losses over the life of the cable. These were based on installation costs, load factors, annual load growth, the price of energy, the price of demand charges and the forecast discount rate. The results show that cable spacing parameters are a significant factor that influences ampacity. Ampacity can be improved while reducing the losses in power cables. This is because appropriate cable spacing can reduce the effect of Joule heating from neighboring cables. However, this leads to increased construction costs. The total costs of power cables over their lifetime can be reduced by decreasing the horizontal distance between the center of a casing pipe and the side edge of the concrete layer. This is because the contribution of reduced construction costs is more than that of the effect of increased losses. Therefore, the dimensions of the concrete duct bank significantly influence ampacity, the construction costs and the losses of power cables in an analysis of total costs over the lifetime of power cables.

Loss Simulation Analysis and Optimization of U-Groove Leaky Coaxial Cable

Leakage coaxial cable is a kind of coaxial cable with various slot structures on the outer conductor of the cable. It can transmit signal and transmit or receive signal and has dual functions of signal transmission line and antenna. Leakage cable has the advantages of strong environmental adaptability, uniform signal coverage, and less attenuation. It is not only widely used in closed or semiclosed space with high signal reception quality, such as tunnels, subway, underground parking lot, and elevators but also can realize security and theft-proof monitoring and protection in some areas, such as oil wells, mining fields and natural resource protection areas, military fortresses, museums, airports, banks, and schools. This paper introduces the classification and electrical parameters of leaky coaxial cables. On the basis of U-groove leaky coaxial cables, the relationship between the parameters of groove holes in U-groove and the loss of leaky coaxial cables is simulated and analyzed by HFSS software. The improved method of U-groove structure is obtained, and the curved hook-groove leaky coaxial cables are designed according to this method. The simulation results show that the coupling loss of the cable is lower than that of the U-groove leakage cable, and the transmission loss is still within the national standard. It lays a theoretical foundation for the design and development of leaky coaxial cable with low coupling loss.

On the Application of Modal Transient Analysis for Online Fault Localization in HVDC Cable Bundles

This paper presents the modal analysis of different HVDC cable bundles. Using modal theory, specific transformation matrices are presented, and the modal equivalent circuits are illustrated. The behavior of the resulting modes is studied in a wide frequency range, the impact of different cable parameters and burial configurations on the modal characteristics are analyzed. A concept for online fault localization in HVDC cable transmission based on the difference between the modal velocities and consequently the arrival times of the modal traveling wave initial peaks is presented. In this method, modal voltages and currents are used instead of direct measurements and the proposed concept uses one-sided measurement without needing to detect the second TW reflections. Multiple faults are applied to CIGRE HVDC models in PSCAD/EMTDC and the modal analysis is obtained in MATLAB. The impact of different sampling frequencies, fault resistance, fault location and different grounding schemes on the proposed modal fault location principle is analyzed. The theoretical results show the accuracy of the proposed modal fault localization concept for different HVDC cable bundles.

다양한 케이블 변수에 따른 동축 케이블의 HEMP 결합 신호 해석

In this study, we analyze the coupled signal for various cable parameters when a high-altitude electromagnetic pulse(HEMP) is incident on a cable connected to an EMP protection shelter. The structural conditions or operating environments vary depending on the purpose of use, such as to supply power or transmit communication signals to the internal devices of the shelter. Using the cable equivalent model and simulations, we interpret the coupled signal that is induced in the cable according to the presence or absence of a shielding layer, number and thickness of inner core wires, braiding conditions of the shielding layer, cable length, height from the ground plane, and whether the input terminal is grounded. We compare and analyze the induced current according to the cable parameters based on an RG58 coaxial cable.

Development of Severity and Location Indices Based Condition Monitoring Scheme for Underground Cables by Impedance Spectroscopy

This work presents the development of a condition monitoring scheme for detection, severity assessment and localization of small cavities in cable insulation by impedance measurement in frequency domain. A high frequency model of cable incorporating the frequency dependence of cable parameters is developed to analyze the impedance changes during the occurrence of cavities in the insulation. The simulation and analysis of impedance with cavities in a 11 kV, 95 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> cable reveals the parameters such as Severity Index (SI) and Location Index (LI) which shows gradual changes with change in size and location of void and have potential scope to be used for severity assessment and localization of cable deformations. Thus based on the dataset of SI and LI, the condition of cables while in service can be predicted. It is experimentally validated for deformation such as cavities at the outer surface of insulation in 11 kV XLPE cables having conductor areas of 95 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and 150 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The reliability of the proposed method for detection and localization of cavities inside the insulation near cable joints is validated by measurement and analysis on 11 kV, 95 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> XLPE cables with artificially created voids at the insulation region near cable joints.

Vibration analysis of shallow cable with horizontal spring and dashpot at one end

In this study, a general closed-form equation is derived for the steady-state response of a cable with both ends at the same horizontal level, and a horizontal protective device composed of a horizontal spring and dashpot at one end. The cable is subject to vertical constant-amplitude harmonic loading. Nondimensional parameters describing the response are identified. A comparison is performed with the steady-state response from numerical methods, obtained after the transient solution has become negligible. The effects of the nondimensional parameters on the modal damping ratio, modal frequency, maximum displacement, and axial force are quantified. Using the response information obtained, as well as practical considerations, ranges of parameters useful for cable design/construction are proposed. Finally, a step-by-step methodology to obtain the peak deformation and axial force is developed, and this is illustrated with an example. It was shown that the multiple-scale method solved the equations of motion, thus allowing the force and vertical displacement at any point on the cable to be obtained. Three nondimensional parameters representing spring stiffness γk, dashpot damping ν, and cable characteristic αb2, and a load parameter were also obtained from the general solution. Not all quantities were obtained explicitly, but some needed to be solved numerically. The solution was consistent with the published solution when the spring was infinitely rigid. Numerical-method solutions matched the peak closed-form solutions with a maximum error of less than 10%. The modal damping ratio increased with decreasing spring stiffness and increasing cable parameter. The modal frequency tended to increase with increasing spring stiffness and dashpot damping. The values of the peak displacement and peak axial force associated with resonance were reduced by an increased cable parameter and decreased spring stiffness. When considering the likely cost, shallow cable definition, total and spring amplitude, and predictivity of behaviour, the recommended ranges of shallow cable design values were given for the nondimensional dashpot damping, spring stiffness, and cable parameter. A design example following design steps indicated that for a 20 m cable with γk = 0.38, ν = 12.22, αb2 = 0.26, and amplitude of external harmonic load 0.5 kN/m, the peak displacement and axial force were 2.74 m and 1.08 × 103 kN, respectively.

Electrodynamic Parameters of a Coaxial Cable at Bipolar Pulses Propagation

All-in-interworking technology, based on IEEE 802.3 standard, was mainly developed for the separable media cabling and data transmission speed increase. Although the high-speed networking is already provided by a fiber optic cable, coaxial guides are in demand for similar applications. Time-domain analysis is undertaken to estimate electrodynamic states of inner and outer guiding conductors at periodic bipolar pulses propagation on a coaxial cable. An electric current density distribution on the cross-section of the inner conductor is obtained from a solution of Maxwell equations under periodic boundary conditions that are prescribed by a product of two functions. The first one is introduced implicitly for a profile of surface current density in the axial direction, while the other determines this profile transient states. As for shielding braid, which is the cable outer conductor, its current density distribution is derived from an analysis of field harmonics that penetrate into conductive subsurface layers under similar boundary conditions. It is also shown that prescribed implicative boundary conditions for both conductors allow to obtain, at least under auxiliary assumption, some completed formulae useful to the estimation of the pulses duration admissible decrease at their transmission on the coaxial cable. The paper contains some comparative and numerical results as well

Approach to assessing the effective integration of solid-state transformers in LV networks

Solid-state transformers (SSTs) have been recognised as a promising technology that can realise more flexible power and voltage control in distribution networks compared to conventional low-frequency transformers. The flexibility and controllability offered by this technology can be an enabler of DSO functions. Harnessing these additional functionalities of SSTs requires the identification of tailored approaches to understanding the impact of SST integration on LV networks. Therefore, this study presents a methodology that can assist DNOs to assess the potential impact of SSTs and determine whether it is an appropriate alternative to conventional reinforcement. This approach has been demonstrated with an SST model built within PowerFactory applied to a detailed LV network model based on an example real UK LV network and load. The analysis has demonstrated that SSTs in simple schemes can effectively control network voltage and alleviate loading constraints on existing secondary distribution transformers. However, the level of contribution that an SST can offer is clearly dependent on seasonal loading conditions, network location and cable parameters. This work is a component of the LV Engine project being led by SP Energy Network and funded through the UK&apos;s Network Innovation Competition.

Detection Sensitivity of Input Impedance to Local Defects in Long Cables

Broadband impedance spectroscopy (BIS) has become a new method for detecting cable insulation defects, but the sensitivity of this method to local defects in cables has not been fully studied. Taking long submarine cable as an example, firstly, the intrinsic correlations between the impedance spectroscopy characteristics and the cable parameters are studied, and the influence of local defects on the peak of impedance spectrum is studied by establishing a simplified model of long cables with insulation defects. Secondly, the formula for calculating the sensitivity of input impedance to the insulation defects is proposed and the characteristics of sensitivity are studied. Finally, the sensitivity of the input impedance to different positions and degrees of defects at the first resonant frequency is analyzed, which can be verified by simulation and experimental. The Results show that, for long cable with length l, under the condition of open-circuit, the sensitivity trends to zero when the defects occur at 25% or 75% of the cable length l, and under the condition of short-circuit, the sensitivity trends to zero when the defects occur to the end of the cable. Therefore, in the application of BIS, the above positions should be paid attention to, and the cable length can be changed and measured again to confirm its insulation status.

Parameters Calculation of Underground Cables Using MATLAB

With the development of technology, more and more options are available for insulated cables in power systems. Different cable construction types have different impedance, voltage drop and power losses. In order to efficiently design these cable systems and adequately model them for system analysis, engineers should be able to calculate the parameters of different types of cables. Although the methods of parameters calculation are very mature, few types of software are used to calculate all these parameters for different cables. The objective of this paper is to build a user-friendly software to calculate these parameters with greater flexibility even if the users are not familiar with the methods of estimating the parameters of different types of cables. A program that is used to calculate the parameters of different cross-sections of cables is built by combining the method of estimating these parameters with the graphical user interface (GUI). Using this program, users can input or choose any type of cables, and calculate the parameters they need. In the future, more functions can be added to the program and the code could be switched to python or C# and develop a better GUI (Graphical User Interface).

Incipient Fault Location Method of Cable Based on Both-End Electric Quantities

The early fault of a cable is usually a incipient fault, which is difficult to find and can easily develop into an insulation breakdown fault. Thus, it is of great significance to quickly and accurately find an incipient cable fault. This paper presents an fault location method for cable insulation based on the electric quantities of both ends. Based on the equivalent circuit model of three-phase single-core cable distribution parameters, the calculation method of the voltage along the cable is derived. The equivalent model of cable insulation in resistive and capacitive parallel is proposed and applied to the early fault modeling of cable. On the basis of the calculation formula of the voltage along the cable and the electric quantity at both ends of the cable, the analytical expression of the cable fault location is obtained by solving the fault equation directly. Extensive simulations show that the algorithm, this method can locate the incipient fault accurately, and is not affected by the fault point, fault resistance and fault inception angle.

Parameter Identification for Digital Fabrication: A Gaussian Process Learning Approach

Tensioned cable nets can be used as supporting structures for the efficient construction of lightweight building elements, such as thin concrete shell structures. To guarantee important mechanical properties of the latter, the tolerances on deviations of the tensioned cable net geometry from the desired target form are very tight. Therefore, the form needs to be readjusted on the construction site. In order to employ model-based optimization techniques, the precise identification of important uncertain model parameters of the cable net system is required. This paper proposes the use of Gaussian process regression to learn the function that maps the cable net geometry to the uncertain parameters. In contrast to previously proposed methods, this approach requires only a single form measurement for the identification of the cable net model parameters. This is beneficial since measurements of the cable net form on the construction site are very expensive. For the training of the Gaussian processes, simulated data is efficiently computed via convex programming. The effectiveness of the proposed method and the impact of the precise identification of the parameters on the form of the cable net are demonstrated in numerical experiments on a quarter-scale prototype of a roof structure.