Three-core Cables Research Articles

Development of an effective modeling method for the mechanical analysis of three-core submarine power cables under tension

The structural complexity of submarine power cables (SPCs) presents significant challenges in their local mechanical analysis. This paper introduces an advanced modeling method developed for analyzing the mechanical behavior of SPCs under tension, emphasizing both accuracy and efficiency. The method’s accuracy is validated through a comparison of simulation results with tension tests conducted on a three-core SPC sample. Efficiency is demonstrated by the superior calculation speed of our model relative to traditional full-scale models. This improved performance is achieved by adopting periodic boundary conditions derived from the homogenization method applied to slender beam-like structures, and by employing a specialized combination of elements to model the helical metal components within the SPCs. The resulting model provides robust capabilities for the mechanical analysis of SPCs under tension and demonstrates significant possibility in accommodating various other loadings.

A Study on the Problem of AC Corrosion of Power Umbilical Cables Caused by Electromagnetic Induction Phenomena

During the normal laying and operation of a three-core umbilical cable, AC current can easily lead to AC electrochemical corrosion on the outer surface of the steel tube. To explore the electrochemical corrosion mechanism and the factors affecting the three-core umbilical cable, this paper optimizes the internal induced potential calculation method for three-core umbilical cables. It analyzes the changes in the characteristics of the induced potential and explores the variations in the density of induced current under different conditions. The research results show that by optimizing the calculation method for the induction potential of the umbilical cable’s steel pipe, for the electromagnetic significance of the smallest repeating unit, the induction potential on the steel pipe’s surface exhibited a cyclic change. The peak part of the induction potential is most likely to experience electrochemical corrosion. Additionally, reducing the radius of the outer insulation aperture of the steel pipe and improving the conductivity of seawater will increase the density of the induced current in the insulation aperture, thereby increasing the risk of electrochemical corrosion. As the cable pitch and AC frequency increase, the current density in the steel pipe pores will also rise.

Steady-State Thermal Circuit Modeling of a 10 kV Three-core Cable Based on Distributed Structure

Abstract With the development of China’s urbanization construction, the proportion of urban power distribution cables is increasing. The existing models for the temperature calculation of urban medium and low voltage three-core cables regard the filler layer and inner sheath as isothermal body structure for research and analysis, and do not take into account the temperature inhomogeneity characteristics of the three-core cable structure itself. In the paper, the uneven distribution characteristics of the buffer layer of the three-core cable are considered, and then the temperature distribution of the inner sheath is analyzed, and the distributed modeling of the inner sheath is carried out by drawing on the idea of analogous distributed model of the electric circuit, and from the heat flow theory, the heat flux assigned to each segment of the structure such as each inner sheath is derived, and the steady-state thermal circuit model of the three-core cable is established based on the principle of equivalency, and the finite element computation method is adopted to recognize the thermal circuit parameters, and finally, after the simulation results are compared with the simulation results, the temperature of the three-core cable structure itself is considered as an isothermal structure. Finally, after comparing with the simulation results, the accuracy of the thermal circuit model reaches 95%, the change of ambient temperature has less influence on the thermal circuit model, and the model has high robustness, which provides support for the on-line detection technology of the state of three-core cables.

Prediction Model for Trends in Submarine Cable Burial Depth Variation Considering Dynamic Thermal Resistance Characteristics

Fault problems associated with submarine cables caused by variations in their burial depth are becoming increasingly prominent. To address the difficulty of detecting the burial depth of submarine cables and trends in its variation, a prediction model for submarine cable burial depth was proposed which considers the dynamic characteristics of thermal resistance. First, a parallel thermal circuit model of a three-core submarine cable was established, and a formula for calculating the submarine cable’s burial depth was derived based on a formula for calculating the submarine cable’s core temperature. Then, the calculation result was corrected by considering the dynamic characteristics of the thermal resistance of the submarine cable’s structural materials. On this basis, feature vectors associated with the seabed cable burial depth calculation data and time nodes were mined by a convolutional neural network and used as the input parameters of a long short-term memory network for optimization and training, and a prediction model for trends in seabed cable burial depth variation was obtained. Finally, an example analysis was carried out based on the actual electrical parameter data of submarine cables buried by an offshore oil and gas platform. The results showed that the prediction model for trends in variations in the burial depth of submarine cables based on the CNN-LSTM neural network can achieve high prediction accuracy and prediction efficiency.

Comparative Study on the Ampacity of 500 kV Single-Core and Three-Core Submarine Cable

Submarine cable is an important equipment for data communication and power transmission in power systems, which has a complex laying environment. According to its structure, submarine cables can be divided into two types, single-core cables and three-core cables. In practical engineering, cable selection is crucial to ensure the safe and stable operation of the cable and reduce the cost. The present work compares the ampacity of 500 kV single-core cable and three-core cable with the same conductor cross-section area under certain laying conditions. And the temperature rise situation of the three-core cable and the single-core cable is compared under the application of the same current. The results reveals that the ampacity of the three-core cable is less than one-core cable under certain laying situations. And the maximum ampacity reduction of the three-core cable is 28.96%. Furthermore, the highest temperature rise point of the three-core cable is the air section of the J-tube, and the maximum temperature reaches 130.07°C.

Research on Temperature Sensing Method for Three-Core Cable Intermediate Joint Considering Three-Phase Load Imbalance

Temperature is a key factor affecting the insulation performance and operation safety of cable joints. Accurate acquisition of hot spot temperatures of cable joints is a difficult issue in cable operation and maintenance. Three-core cables may have unbalanced three-phase loads in actual operation. This paper takes a 10 kV three-core cable joint as the research object; based on the temperature field numerical simulation method, it analyzes the diffusion path of the main heat flow inside the joint and establishes an inversion model that fits the hot spot temperature of the joint through the surface temperature of the cable body. At the same time, considering the special situation of the unbalanced three-phase load of a three-core cable, the joint hot spot temperature inversion model of a three-core cable under an unbalanced three-phase load is further established. This paper further uses the cable joint multi-step unbalanced load temperature rise test to verify the accuracy of the cable joint hot spot temperature inversion model. The maximum error of the transient hot spot temperature inversion does not exceed 4.5 °C, and the steady-state error is within 3 °C. A higher inversion accuracy was achieved. The research results of this article can provide a reference for real-time monitoring of the hot spot temperature of cable joints.

Exploration of Temperature Inversion in Intermediate Joints of 10 kV Three-Core Cable

In order to precisely ascertain the temperature at the hot spot within the intermediate joint of a three-core cable, this study focused on a 10 kV three-core cable joint as its primary subject. A three-dimensional finite element model of the cable joint was constructed, enabling the calculation of both the steady-state hot spot temperature field distribution and the transient temperature rise curve of the joint. Employing a one-dimensional transient thermal path model for the cable body, a radial inversion model for the cable core temperature was established. Through simulating the transient temperature field of the cable joint under varying currents, a fitting relationship was determined for the axial temperature points of the cable core. Subsequently, an inversion perception model was devised to calculate the hot spot temperature of the cable joint based on temperature measurements at specific points on the outer surface of the cable. Under both continuous and periodic loads, the inversion results revealed a consistent trend in the temperature at the joint crimping point with the finite element calculation outcomes, demonstrating a maximum error of within 3 degrees Celsius. This verification underscores the precision of the temperature combination inversion method when applied to three-core cable joints.

Simulation of Electrical Trees Grow in Three-Core Submarine Cable

Simulation of Electrical Trees Grow in Three-Core Submarine Cable

Numerical modeling and fatigue analysis of the dynamic response of main pump cable in nuclear power plant

Abstract The structural temperature rise and thermal stress caused by operation current and ambient temperature are some of the main factors affecting cable fatigue life. Combined with the operating and environmental conditions of the main cooling pump of the nuclear power plant, the thermal-structural coupling field numerical modeling and fatigue analysis of the 6kV single-core and three-core cable of the main pump is carried out. Based on obtaining the steady-state operating current, the motor start-up transient current, and the circulating ambient temperature, the thermal-structural coupling field numerical model of the main pump cable is established using the load transfer method to obtain the thermal and stress field distribution of the internal structural layer. The load history of one cycle is extracted for the fatigue numerical simulation of the main pump cable. The stress time history of the cable structure layer was constructed by the stress calculation results and the load time history of a single period, and the fatigue life of the main pump cable was obtained based on the S-N curve of the main insulation material and the Miner’s linear cumulative damage theory. The simulation results show that the force acting on the main pump cable by the operating current and ambient temperature is an approximately symmetric cyclic load of constant amplitude. The life cycle of the cable can reach 2.235*e4 times, and the overall life of the cable is about 63.97 years. This study can provide theoretical guidance for the safety and reliability design and state operation and maintenance of the main pump cable of the nuclear power plant.

Optimal design of liquid cooling structures for superfast charging cable cores under a high current load

Superchargers have become a focus of much research into new-energy vehicles, for which the cooling of high-current cable cores is a key problem that needs to be solved. To estimate influences of different core structures of liquid-cooled cables on the fluid flow and heat transfer characteristics in circular pipes, nine helical cable core structures with insertion of smooth pipes were designed taking dimethyl silicone oil as the coolant. The fluid flow and heat transfer in the pipes were studied through computational fluid dynamics (CFD) numerical simulation at different inlet velocities (0.2–2.0 m/s), and the models were verified by building an experimental platform. Numerical calculation results show that under conditions of the same Re and pitch of cable cores, the average surface temperature of three-core cables is lower than those of single-core and double-core cables. Moreover, the mean flow velocity v in pipes, heat transfer performance Nu, resistance factor f, evaluation factor for comprehensive heat transfer performance (PEC), and field synergy number Fc all increase with the decrease in the pitch of cable cores. This finding indicates that the heat transfer effect is gradually enhanced. The research implies that when the pitch p is 22.4 mm (cable C6), the velocity field is the most synergetic with the temperature field and the comprehensive heat transfer performance is optimal. This research provides an excellent cooling scheme for cable cores in superchargers under a high current load.

High-efficiency magnetic field energy harvesting from a three-core cable

Alternating magnetic fields generated by ac power lines are renewable energy sources that can be scavenged by magnetic energy harvesting cores for wireless sensor networks (WSNs). However, traditional magnetic cores are suffering from low efficiency when applied to three-core cables. This paper systematically analyzed the characteristics of the magnetic induction intensity of a three-core cable by finite element methods (FEM), figured out the optimal energy harvesting position, innovatively designed and fabricated a novel notched ring core (NNRC) to better match the magnetic field characteristics of three-core cables. Compared with the previously reported core, the NNRC has 2.3 times the output voltage per turn and more space allowance for winding coil. According to experimental results, the open-circuit output voltage amplitude of NNRC was 16.6 V with 9000 turns of wire and 100 AAMP ac current in each phase of the cable. Finally, a non-controlled AC/DC circuit was applied and 28.4 mW maximum dc power was obtained.

A 2D FEM Model for Impedance and Loss Calculation of Armored Three-Core Cables With Inclusion of 3D Pitching Effects

A method is introduced for impedance and loss calculation of three-core power cables with steel armoring, based on 2D finite element method (FEM) computations. The pitching effect of the cores and armor wires is taken into account by 1) enforcing identical net current on the wires, and by 2) introducing a fictitious non-conductive material between the wires having a complex-valued permeability. The permeability is obtained by considering the effect of the pitching on the total energy in a volume slab around each wire, which involves the solving of a small 2D FEM problem in an optimization loop. The method permits to calculate the positive-sequence and zero-sequence impedance on cables, induced sheath currents, and losses in cores, sheaths, and armor. The method is validated against published results using a full 3D FEM model. The calculations are fast, requiring only a few seconds of computation time. The procedure is simplified by use of pre-calculated look-up tables for the fictitious material permeability value.

Underwater Cable Localization Method Based on Beetle Swarm Optimization Algorithm

Dear Editor, This letter concerns the localization of three-core underwater cables which are widely deployed for offshore energy transmission. It is a non-trivial problem, since the external magnetic field of three-core underwater cables is variable which reduces the accuracy of localization. To solve this problem, in this letter, an approximate equation is firstly derived to formulate the external magnetic field of a three-core armored underwater cable by considering the seafloor environments and the structure of three-core cables. Then, a new underwater cable localization method is proposed based on dual three-axis magnetic sensor array and the beetle swarm optimization (BSO) algorithm. The method constructs a fitness function based on the magnetic flux density amplitude and replaces the existing analytical geometry method with an optimization algorithm to achieve underwater cable localization with higher accuracy.

Torsional Optical Fiber Stress Analysis and Vortex-Induced Vibration Study of Three-Core Submarine Cable

Due to current scouring, submarine cables are prone to be exposed, suspended, and even vortex-induced vibration, which is not conducive to the safe operation of the power grid. In this contribution, the finite element simulation model of a 35 kV three-core optical fiber composite submarine cable with a suspended span length of 9.5 m is established. The natural frequency of the model is obtained through modal analysis. Then the vortex-induced vibration is simulated by the fluid–structure coupling method, and the stress distribution and change law of the torsional optical fiber is extracted. The results show that in the submarine cable, there appears to be a beating vibration and locking phenomena respectively, under two flow velocities. The transverse vibration amplitude of the latter increases significantly due to a resonance state. When the flow direction is perpendicular to the submarine cable, the stress distribution of the torsional optical fiber at the initial moment and at the 1/2 T moment of a vibration cycle approximately represents a mirror image relationship. In addition, the frequency of the stress change is the same as the frequency of the vortex-induced vibration, which can judge whether the vortex-induced vibration occurs. Moreover, the vortex-induced vibration range can be determined by the maximum stress change location.

Unbalanced Current Identification of Three-Core Power Cables Based on Phase Detection of Magnetic Fields

Identifying unbalanced phase currents is crucial for control and fault alarm rates in power grids, especially in urban distribution networks. The zero-sequence current transformer, specifically designed for measuring unbalanced phase currents, offers advantages in measurement range, identity, and size, compared to using three separate current transformers. However, it cannot provide detailed information on the unbalance status beyond the total zero-sequence current. We present a novel method for identifying unbalanced phase currents based on phase difference detection using magnetic sensors. Our approach relies on analyzing phase difference data from two orthogonal magnetic field components generated by three-phase currents, as opposed to the amplitude data used in previous methods. This enables the differentiation of unbalance types (amplitude unbalance and phase unbalance) through specific criteria and allows for the simultaneous selection of an unbalanced phase current in the three-phase currents. In this method, the amplitude measurement range of magnetic sensors is no longer a critical factor, allowing for an easily attainable wide identification range for current line loads. This approach offers a new avenue for unbalanced phase current identification in power systems.

Fault Location Method for Three-Core Cable Using Amplitude Ratio of Shield-Grounding Wire Currents

With significant technological advancements in power grids, three-core cables are widely employed for their safety and other benefits. In general, three-core cables in medium-voltage distribution systems are laid underground during operation. As a result, the harsh working environment and complex fault conditions can bring massive challenges to fault location issues. To address the problem, the distinctive cable features are extensively considered in this article, including relatively larger capacitance, cable shield effects, and shield bonding methods. Initially, an equivalent cable model is developed to analyze the relationship between shield-grounding wire currents and the fault point. A single-phase grounding fault location method is then formulated based on the ratio of shield-grounding wire currents at both terminals. In PSCAD/EMTDC, a range of fault scenarios are simulated to verify the proposed method. In comparison to conventional similar approaches, the proposed method exhibits higher accuracy and robustness to fault resistance and diverse fault conditions. Finally, the effectiveness of the proposed method is validated on a real 10 kV distribution network experimental platform under several fault scenarios.

Technical-economic study of PVC-based formulations intended to industrial 3-wire electric cables, using a full factorial design methodology

In the present study, full factorial designs were used to model and optimize the mechanical properties of PVC-based formulations constituting three-core power cables: sheathing, insulation and stuffing, while respecting the standards in force, and aiming for a minimum cost. The effects of 4 parameters: plasticizer content (X1), filler content (X2), stabilizing agent content (X3) and the kind of plasticizer were investigated on the following properties: Density (D), Hardness (H), Elongation at break (EB) and Fracture resistance (FR), as well as the price (DA/kg of formulation). The desirability-based optimization gave the following values: EB = 214.72%, FR = 19.94 MPa and Price = 116.71 DA/kg for the sheathing; EB = 198.11%, FR = 4.38 MPa and Price = 61.73 DA/kg for the stuffing; EB = 207.84%, FR = 19.35 MPa and Price = 102.73 DA/kg for the insulation. The study revealed also that the order of significance of the effects on the mechanical properties was: X1>X2>X3 and that the use of cheapest plasticizer did not affect greatly the mechanical properties.

Feasibility Study on Online Diagnosis of Aging and Deterioration of Medium Voltage (MV) Three-Core Cable Based on Impedance Spectroscopy

In order to explore the feasibility of impedance spectroscopy in the application of online diagnosis of aging and deterioration of medium voltage (MV) three-core cables, based on the theory of transmission line equation, an aging and deterioration model of the MV three-core cable has been established. The impedance spectroscopy of the cable head-end under healthy and different aging and degradation states has been simulated and analyzed. Further, the effects the extent of aging, local deterioration size and position, line length, load rate and other factors on the impedance spectroscopy have been studied. Based on the influence of the various factors on the impedance spectroscopy, a set of aging and deterioration diagnosis procedures and methods are proposed. The simulation results indicate that the impedance spectroscopies of healthy state and different aging and/or deterioration states have certain characteristics. These characteristics can be determined by specific criterion indicators such as the monotonous decrease of the value of the resonance peaks and the phase amplitudes, the value of the resonance peaks, and the eigen propagation frequency, etc. Therefore, impedance spectroscopy has broad application prospects for online diagnosis of aging and deterioration of MV three-core cable.

Evaluation of the power frequency magnetic field generated by three-core armored cables through 3D finite element simulations

The great expansion in offshore power plants is raising the concern regarding the cumulative effect of the electromagnetic field emissions caused by submarine power cables. In this sense, owners are required to predict these emissions during the permitting and consenting process of new power plants. This is a challenging task, especially in the case of HVAC three-core armored cables due to their complex geometry. Customarily, 2D approaches based on the finite element method (FEM) have been employed for evaluating the magnetic field emissions caused by these cables. However, inaccurate results are obtained since the phase conductors and armor twisting is omitted. This work develops, for the first time in the literature, an in-depth analysis of the magnetic field caused by this type of cable through an ultra-shortened 3D-FEM model, which is also faced to experimental measurements taken on an actual 132 kV, 800 mm 2 three-core armored cable. Relevant conclusions are derived regarding the impact of the cable design on the magnetic field emissions, including material properties, as well as single and double-layer armors, presenting the proposed model not only as a valuable tool for predicting purposes, but also for optimizing cable design in terms of magnetic field emissions. • 2D approaches overestimate the magnetic field emitted by three-core armored cables. • Ultra-shortened 3D-FEM models include the effect of conductor and armor twisting. • Good accuracy in predicting the magnetic field emitted by the three-core cable. • In-depth analysis of the impact of cable design on magnetic field emissions. • Application for evaluating the environmental impact of power cables in the seabed.

A Coreless Current Probe for Multicore Cables

To measure the current on each conductor in a three-phase three-core cable or a three-phase four-core cable without an armor or the armor that is made of nonmagnetic material, one has to remove its sheath/armor and applies a traditional device, such as a current transformer (CT) to each conductor, which is invasive and inconvenient. In this article, a Coreless current probe, composed of a tunnel-magnetoresistance (TMR)-based magnetic sensor array, is presented to nondestructively achieve current measurement for multicore cables. The conductor positions, incline angles, and current phasors of a multicore cable are simultaneously identified by solving a nonlinear least square (NLLS) problem. The current waveforms are reconstructed in real time through a real-valued matrix multiplication using the measured time-domain TMR sensor voltage signals. Both simulation and experiment are performed to validate the feasibility of the proposed method. The simulation study is first conducted and demonstrates that a maximum relative current amplitude error of less than 5% and a maximum phase error of lower than 4° can be achieved, and three-phase current waveforms with many harmonics are also successfully reconstructed by simulation. A prototype Coreless current probe is designed and fabricated. The experimental study involving fundamental current phasor measurement and current waveform reconstruction is subsequently performed on a three-phase three-core cable. The experimental results indicate that the maximum relative current amplitude error and phase error, respectively, have average values of 5.44% and 2.58°. Meanwhile, three-phase current waveforms with many harmonics generated by three types of appliances are also successfully reconstructed.