Cable Cross Section Research Articles

Offshore Windfarm Design Optimization Using Dynamic Rating for Transmission Components

The foreseen development of large-scale Offshore Windfarms (OWFs) further from the shore dictates that the OWF transmission system must be optimally designed based on Dynamic Thermal Rating (DTR) in order to fully utilize the intermittent nature of the wind and to keep the offshore wind cost-competitive. In this paper, a comprehensive, DTR-based, two-stage stochastic model is presented, which has been developed for investment decision support for OWF size and HVAC transmission systems. Complex DTR models for all the critical HV components are made fit for the mixed-integer linear programming problem, while accounting for the stochasticity in wind generation and component availability. The main decisions incorporate the discrete size of OWFs, HV subsea export cable cross-sections and ratings for transformers and shunt reactors. For validation, an actual testcase OWF off the east coast of U.K. has been used. Results indicate that DTR-based iterative design of OWF and its transmission components can significantly improve the business case, even though transmission efficiency and energy delivered are not maximum for the optimal design

Surrogate-based fragility analysis and probabilistic optimisation of cable-stayed bridges subject to seismic loads

The lack of computationally efficient, probabilistic performance-based design strategies for cable-stayed bridges hinders their optimal design in seismic regions. Thus, this paper proposes the implementation of parameterised fragility functions (PFFs) for the surrogate-based sensitivity analysis and performance-based optimisation of these structures. In particular, PFFs are exploited to define computationally efficient decision variables and four optimisation strategies that aim to optimise the probability of seismic damage and the direct losses related to the seismic repair cost. To illustrate this overall strategy, a 542 m three-span cable-stayed bridge is considered. The ability to predict dynamic behaviour is improved by using the measured dynamic response of the reference cable-stayed bridge to inform the numerical model’s architecture. Then, key design variables of tower and cable cross-sections are selected for optimisation. The sensitivity analysis shows conflicting demands placed upon design variables by different decision variables (e.g. damage probability and the sum of construction and repair costs, CRC) and the crucial importance of accounting for design variables interaction when making choices on design updating. Therefore, numerical optimisation emerges as the most efficient tool to deal with these issues. With respect to the reference structure, the proposed single-objective optimisation strategies reduced the system-level damage probability by 3.5 times, and yielded an 88% reduction of repair cost, and a 40% decrease of CRC. A Pareto-front of optimal design variables was also calculated to simultaneously optimise system damage probability and CRC.

Comprehensive transient analysis on control system in a photovoltaic power plant under lightning strike

Solar power plants are installed in high and open places to receive high solar radiation. However, this leaves them vulnerable to lightning strike. Lightning strike affects power plants in two ways, directly and indirectly. Direct lightning strikes can be prevented by using lightning protection systems. However, under the indirect effect of a lightning strike, the surrounding electronic devices may be damaged due to the induced voltage. In a solar power plant with a lightning protection system in Turkey, it was stated that the bypass diodes failed after a lightning strike. In this study, it is aimed to examine the effects of indirect lightning strike on the PV module. For this reason, different lightning pulse amplitudes were injected into the system and the effects of three parameters on the induced voltage were investigated with an EMT type program. These parameters were the cable lengths, cable cross-sections and the number of PV arrays. Four different panel configurations were performed in the EMT type program. Data was taken from the solar power plant in Turkey was used in fourth configuration. It was concluded that when the lightning strike fell on the air termination bar, bypass diodes in the nearest PV array were affected, and this effect decreased as the array distance increased. However, as the amplitude of the lightning strike increased, arrays in the far-distance were also affected. It has been seen that the results obtained were compatible with the malfunction information received from the solar power plant.

"Impact of Experimental Measurements Accuracy on Validation Process of Crimped Connections"

"In the process of validation of crimped connections, the determination of the connector resistance factor and of the initial scatter coefficient has a decisive role. In this paper is studied the impact of the experimental measurements accuracy on the calculation of initial scatter, cumulating data from various types of crimped connections. This coefficient provides information on the behavior of the crimped connection immediately after installation before any aging effect begins. The standards establish that 6 samples are sufficient to be tested to estimate the identification of a “family” of connectors. The measurements were performed on crimped connections of barrel of terminal lug type for three cross sections of cables and on crimped connections of bimetallic through connector type for two pairs of cross sections. The initial scatter is influenced by 6 representative measured quantities as voltage drops, currents and conductor lengths. First, it was imposed a variation by one unit of hundredths digit of initial scatter and was recorded the variation of each quantity, the others 5 quantities being kept constant. Then simultaneous variations of the 6 quantities caused by device reading errors were imposed, determining the quantities with the greatest influence on initial scatter. Useful recommendations for experimenter are made. "

Temporal and spatial variability of corrosion of high-strength steel wires within a bridge stay cable

The temporal and spatial corrosion variability of high-strength steel wires has a significant influence on the service performance deterioration behaviors of bridge stay cable. To proposed quantitative descriptions of the temporal and spatial variability, three different kinds of specimens are manufactured by Galvanized steel wires, and the accelerated corrosion experiments are conducted. For the single-wire specimens, the uniform corrosion process, the variation of surface microtopography and the time-dependent pitting corrosion model are investigated. In addition, the spatial corrosion variability of wires within a cable cross section is investigated by considering different damage conditions of sheath. It is found that the uniform corrosion process of the single-wire specimen can be divided into two stages, which correspond to the corrosion of Galvanized coating and substrate, respectively. The variability of uniform corrosion depth decreases firstly and then tends to be steady. The microtopography of corroded wire surface tends from compact spherical structure to be porous, hollow and loose. In the second corrosion stage, the corrosion products seem to be small clumps fluffy or flowery floccule, and then tend to be lamellar cross form and sand granular. The block maximum pitting factor of a single wire can be described by Gumbel distribution, and in the developed time-dependent model, both the location parameter and scale parameter decrease exponentially in the first corrosion stage and linearly in the second corrosion stage. The corrosion process difference factor of wires in adjacent layers of stay cable can be described by Normal distribution when the sheath is globally aging, and the mean value and coefficient of variation are 0.6758 and 0.2543, respectively. The spatial corrosion variability of cable wires is significantly affected by the broken shape of sheath. The difference of global corrosion degree of wires in different layers decreases with the extension of the exposure period. The sheath with rectangular broken shape and quadrate broken shape will lead to stronger spatial corrosion variability in cable wires than that with semi-annular broken shape.

A FRACTAL PRESSURE DROP MODEL FOR CABLE-IN-CONDUIT CONDUCTORS BASED ON POROUS MEDIA ANALOGY

Assessment of the pressure drop that occurs in cable-in-conduit conductors (CICCs) requires a reliable predictive model. In this paper, a fractal model to predict the pressure drop of helium flows in CICCs is proposed based on the porous media analogy and fractal theory. A fractal friction factor correlation is also derived using the proposed pressure drop model. The good agreement between the predictions and the experimental data for conductors with [Formula: see text] verifies the validity of both the fractal pressure drop model and the friction factor correlation for such configuration conductors. The fractal correlation indicates that the friction factor of the cable bundle in a CICC is related not only to the void fraction but also to the average hydraulic diameter, the tortuosity of the fluid flow paths, the maximum pore size and the fractal dimension of the cable cross-section. This theoretical correlation does not contain any fitting constants and each parameter has a clear physical meaning.

Seismic behavior of dual buckling-restrained steel braced frame with eccentric configuration and post-tensioned frame system

The buckling-restrained steel braced frames with eccentric configurations (BRBFEs) have high energy dissipation capacities and an architectural advantage to create openings. However, recent investigations have shown that after the earthquake at the MCE hazard level, the residual drift in buildings with buckling-restrained steel braced frames (BRBF) is remarkable. In the present study, to reduce the residual drift in a BRBFE system, it has been suggested to add a post-tensioned frame (PTF) in parallel and create a BRBFE-PTF combined system. Moreover, a method has been proposed to design this combined system. In this method, the values of the two parameters of the self-centering ratio and cable cross-section area are selected arbitrarily. Then, after verifying the modeling, the pushover, cyclic, and time-history analyses of the prepared numerical models were performed. The results showed that if appropriate values were selected for the self-centering ratio and cable cross-section area, the proposed system had the desirable seismic performance in maximum drift demand and residual drift.

Numerical solution through finite elements for dielectric materials in space

The study of physical models is generally modeled by means of partial differential equations which is still an open field in current research, such is the case of Laplace’s differential equation which is surely one of the most important representations of the telecommunications industry. In the following article we will use techniques based on finite elements, through this technique we will find the behavior of the electrostatic potential in each part of the conductor: dielectric conductive material and armored material. The configuration of the coaxial cable allows to find the distribution of the dielectric displacement in the entire composition of the same in such a way that it guarantees the maximum data transfer as the signal transmission frequency increases and the attenuation of the external interference signals increases. In the first section we propose to obtain the linear terms that will calculate the weights of the values of a linear combination that numerically approximates the variable of interest through Galerkin’s residual theory applying the finite element method, which for the two-dimensional case with elements Triangular linear lines that discretize the cross section of the coaxial cable, in such a way that it is easier to find these constants including the initial conditions and contour, thus allowing to guarantee the existence of a numerical solution.

Low frequency AC transmission systems for offshore wind power plants: Design, optimization and comparison to high voltage AC and high voltage DC

Low frequency AC technology has been presented as a configuration that can potentially reduce the total cost of existing transmission systems. Such cost reduction could be achieved by increasing the power transfer capacity of High Voltage AC cables operating at low frequency and removing the offshore converter when compared to High Voltage DC systems. The purpose of this paper is to suggest an optimal design of Low Frequency AC transmission systems. This results in obtaining the optimal Low Frequency AC voltage level, location, number of reactors and the Back-to-Back converter size for an Offshore Wind Power Plants with a defined rated power and distance to shore. Additionally, the Low Frequency AC, High Voltage AC and High Voltage DC equivalent configurations are compared in terms of total cost and the final transmission system is selected. The analysis of a practical case study is presented in detail, followed by an expansion of the methodology application on various configurations. Also, cost sensitivity analyses for two opposed cases are provided to identify the variation of the break-even distance of Low Frequency AC with High Voltage AC and High Voltage DC. Lastly, different non-standard transmission frequencies are analyzed and an optimal frequency is defined for a range of Offshore Wind Power Plants rated powers and distances. The paper presents a methodology that can be applied considering different relevant parameters, e.g. transmission voltages, cable cross sections and cost data. Based on parameters available in the literature, the study results show that Low Frequency AC is not currently viable.

Electro–Thermal–Mechanical Coupled Analysis on Two High-Current Composite Umbilical Cable Cross Sections

Abstract A new type of umbilical cable named “high-current composite umbilical cable” is composed of electronic cables, optical cables, steel tubes, and structural strengthening components. It can be regarded as a key piece of industrial equipment in subsea production systems that provide control functions, high electric current, and hydraulic remote transmission. When it is oriented at a power supply with a relatively high rated current, power transmission will produce a lot of heat. Then, the cross-sectional temperature increases, which affects the performances of its material and mechanical responses. Therefore, electro–thermal–mechanical coupled analysis is critical for the cross-sectional design of the high-current composite umbilical cable. Accordingly, a multi-physics coupled analysis was performed based on two typical umbilical cable cross sections. Finite element models were established and subjected to electro–thermal analysis to obtain a temperature distribution of the two sections at different current capacities. Based on results of temperature field analysis, the section models were subjected to thermo–mechanical analysis. The results of the two types of analyses are compared and differences are discussed, which illustrate the multi-physics coupled effect cannot be neglected. The armored layers will relatively reduce the heat dissipation performance, but compared with the umbilical cable model without the armored layers, the model with double-armored layers is less affected by temperature, so its capacity of resistance external pressure is relatively better. The proposed coupled analysis methodology provides a new guidance for the design of the high-current composite umbilical cables.

A Novel Shape Finding Method for the Main Cable of Suspension Bridge Using Nonlinear Finite Element Approach

The determination of the final cable shape under the self-weight of the suspension bridge enables its safe construction and operation. Most existing studies solve the cable shape segment-by-segment in the Lagrangian coordinate system. This paper develops a novel shape finding method for the main cable of suspension bridge using nonlinear finite element approach with Eulerian description. The governing differential equations for a three-dimensional spatial main cable is developed before a one-dimensional linear shape function is introduced to solve the cable shape utilizing the Newton iteration method. The proposed method can be readily reduced to solve the two-dimensional parallel cable shape. Two iteration layers are required for the proposed method. The shape finding process has no need for the information of the cable material or cross section using the present technique. The commonly used segmental catenary method is compared with the present method using three cases study, i.e., a 1666-m-main-span earth-anchored suspension bridge with 2D parallel and 3D spatial main cables as well as a 300-m-main-span self-anchored suspension bridge with 3D spatial main cables. Numerical studies and iteration results show that the proposed shape finding technique is sufficiently accurate and operationally convenient to achieve the target configuration of the main cable.

The Power Losses in Cable Lines Supplying Nonlinear Loads

This paper presents the skin effect impact on the active power losses in the sheathless single-core cables/wires supplying nonlinear loads. There are significant conductor losses when the current has a distorted waveform (e.g., the current supplying diode rectifiers). The authors present a new method for active power loss calculation. The obtained results have been compared to the IEC-60287-1-1:2006 + A1:2014 standard method and the method based on the Bessel function. For all methods, the active power loss results were convergent for small-cable cross-section areas. The proposed method gives smaller power loss values for these cable sizes than the IEC and Bessel function methods. For cable cross-section areas greater than 185 mm2, the obtained results were better than those for the other methods. There were also analyses of extra power losses for distorted currents compared to an ideal 50 Hz sine wave for all methods. The new method is based on the current penetration depth factor calculated for every considered current harmonics, which allows us to calculate the precise equivalent resistance for any cable size. This research is part of our work on a cable thermal analysis method that has been developed.

An analysis of models for the estimation of the impact of skin effect on the value of active resistance of solid and multi-conductor cores of power cables

The article analyzes some relations that are used in order to determine the influence of skin effect on the value of the active resistance of solid and stranded conductors of power cables. It is shown that the applying of the considered relations leads to the conclusion that the complication of the structure of the core of the power cable due to its manufacture from twisted together wires leads to the decreasing of the influence of skin effect on the resistance of power cable core in comparison with a solid core of a similar nominal cross-section. It was shown that this reduction takes place due to the calculation of the electrical resistance of power cable core based on the relation which is based on the applying of the nominal cross-section of the power cable core. In the range of core cable cross-section values from 240 mm2 to 500 mm2, despite some increase in core resistance, the influence of skin effect is not significant enough to transfer the value of the complex resistance to the region almost independent of the generalized parameter x phase angle. In the same range of values of the cross sections of the core such a transition of its complex resistance in the region of almost constant value of the phase angle can be achieved by increasing the frequency of current flowing through the core, however, this transition occurs in the frequency range much higher than the value of the industrial frequency.

A radial-grouping-based planning method for electrical collector systems in tidal current generation farms

This paper proposes a radial-grouping-based planning method for the electrical collector systems (ECSs) to design the topology and select the cross-sections of ECS submarine cables in tidal current generation farms (TCGFs) while minimizing investment and operation costs. First, an angle-based radial-grouping method is proposed to group the tidal current turbines (TCTs) in a TCGF, considering their capacity limitations while avoiding the trans-region crossing of submarine cables. Second, an optimal planning model is presented to determine the connection scheme for the TCTs within the same group in a TCGF. The investment and trenching costs of submarine cables and ECS power losses are modeled to minimize the comprehensive annual equivalent cost of ECS, while satisfying the submarine cables’ voltage drop and capacity limitation constraints. Third, an efficient solution method is developed by modifying a genetic algorithm with the Prufer number, which retains the ECS radial topology and connectivity with high computational efficiency. Finally, two TCGFs with distinct characteristics in the North Orkney Islands, Scotland, and their measured tidal current data are used to demonstrate the effectiveness, correctness and adaptability of the proposed method.

Analytical model for the bending of parallel wire cables considering interactions among wires

Bending behaviors can be critical in simulating cables, such as the local effects close to cable end regions or dynamic properties of short cables. Wires form up the cable and tend to slip relative to each other under bending load. Complex interactions among wires make the modeling of cables challenging. In this work, we propose an analytical model for bending parallel wire cables in which the cable cross section with layered wires is idealized as a composite section of the laminated beam. The slips and interactive forces among wires are modeled by the interfacial slips and the resulting interactive forces at the interfaces of the composite section. In this way, the bending cable can transform into an in-plane stress state laminated beam. The state space method is then applied to solve the problem, and the numerical results agree well with the experimental results and analytical formulations in the literature. Bending stiffness of the cable differs from lower bound to upper bound according to the anti-slip ability among wires, from full-slip state to no-slip state. The overall deflection, as well as the local deformations and stresses of the bending cable, can be simultaneously obtained. These results show that the present model is efficient and accurate in simulating bending cables, which is capable of extending to more cable studies.

Thermal Distortion of Signal Propagation Modes Due to Dynamic Loading in Medium-Voltage Cables

Temperature variation from dynamic cable loading affects the propagation characteristics of transient signals. The distortion of modal signal components as a function of temperature in a three-phase medium-voltage cable is investigated. The temperature influence arises mainly through the complex insulation permittivity, which has a non-linear relationship with temperature. Near the maximum operating temperature of the cross-linked polyethylene insulation, the propagation velocity increases by 0.56% per degree centigrade but is an order of magnitude less sensitive at ambient temperature. The paper presents modeling results based on cable impedance and admittance matrices obtained from electromagnetic field simulation, taking into account the time-varying temperature distribution in the cable cross-section. The results are verified by applying Rayleigh–Schrödinger perturbation analysis. In the time domain, signal patterns shift when the modal propagation velocities change upon cable loading. Moreover, separation of degenerate modes is observed when the cable phase conductors carry an unbalanced current. The perspectives for exploiting the temperature dependency of signal propagation for pinpointing cable defects and for dynamic rating of underground power cables are discussed.

Development of standard cable cross-sections of rural electrical networks

For the optimal development of electric networks, not only the optimal choice of the network element parameter from the existing standard scale (parametric series) of sizes is important, but also the optimization of standard scales of equipment sizes or checking their optimality. The method of economic intervals explores the existing parametric series of standard cross-sections of 10 kV cable cores and establishes that the existing series does not satisfy the conditions for optimizing the use of cable lines in rural areas. Since cable lines have not yet found wide distribution in rural areas, there are conditions not only to verify the optimality of the existing scale of cable conductor cross-sections but also to establish an optimal scale of 10 kV cable conductor cross-sections, intended for the construction of cable power transmission lines in rural areas (if the existing scale does not meet optimality conditions). For rural distribution electric networks, the initial and final sections in a parametric series (25 and 120 mm2) are determined and the optimal for rural areas parametric series of cable cross-sections of 10 kV (25; 50; 120 mm2) is recommended.

Economic load intervals for selecting 10 kV cable cross-sections for agricultural consumers

District electric networks for agricultural purposes are characterized by a constant increase in loads. In these conditions, it is important to choose the correct parameters of power lines and, first of all, the cross-sections of overhead lines (overhead lines) and cable lines. There are technical possibilities to increase the capacity of overhead power lines, which can be carried out in the following ways: voltage regulation; reactive power compensation; replacement of existing wires with wires of a larger cross-section; load unbundling; transfer of the network to an increased voltage. Increasing the capacity of cable transmission lines by all of these methods is not possible due to their design features. Thus, due to the difficulties of increasing the capacity of cable lines and dynamically developing networks, the problem of choosing the optimal cable cross-section for lines with an ever-increasing load is becoming more acute. Currently, agricultural distribution electric networks have a constant increase in load. In these conditions, the correct choice of the parameters of cable lines and the residential cable line is of great importance. Due to the complexity of increasing the throughput of cable lines and dynamic networks, problems arise with the choice of optimal paths for wires and residential cables for agricultural lines.

On the Periodic Solution of an Oscillator Single Degree of Freedom with a Damping Coefficient that Changes Periodically

In this paper will be studied a simple one degree of freedom system related to the dynamics of cable-stayed bridges. As a result of wind and rain that hits the bridge cable, it will cause vibrations from the cable to become unstable conditions. The presence of water flowing in the cable changes the cable cross-section as experienced by the wind plane. So, this is what causes the instability of cable vibrations. The idea to model this problem is to consider a horizontal cylinder supported by springs in such a way that only one degree of freedom, i.e. vertical vibration is possible. It will be studied a ridge on the surface of the cylinder parallel to the axis of the cylinder. Additionally, let the cylinder with ridge be able to oscillate, with small amplitude, around the axis such that the oscillations are excited by an external force. In this paper it will be studied the possibilities of the damping of the oscillator that changes periodically by using a perturbation method.

Experimental research of electrical loads in residential and public buildings

The Association “Roselectromontazh” conducted a study of electrical loads for residential and public buildings in the Republic of Tatarstan showed that actual electrical loads are 1.5 - 2.5 times lower than in regulatory documents. Recently constructed cable networks and transformer substations of 0.4 / 10 kV in fact turn out to be underloaded. Moreover, this underload is such that most of the transformers rarely operate at 30% of their capacity during hours of maximum power consumption. The calculation of electric load is the basis for designing the power supply system of any capital construction facility. According to the open joint-stock company “Network Company” and with the support of the President of the Republic of Tatarstan, the Association “Roselectromontazh” carried out an experimental study on updating the requirements for calculating electricity consumption in public and public buildings of the Republic of Tatarstan. The actualization of electrical loads will lead to a significant economic effect by reducing the declared capacity and accordingly the power and number of power transformers reducing the cross-sections of power cables and consequently, capital costs during construction and operation.