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The analytical modeling of a three-core cable system is challenging because of the non-concentric configuration of the components involved. Given these limitations, a 2D finite element modeling of the cable is developed in order to obtain the values of the self, mutual and sequence impedances and admittances. To calculate the series impedance, a ma...

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... is applied at one metallic element and measured the voltage in this and others. The self impedance is found by dividing the induced voltage by the current at the element that the current is applied. The mutual impedances are found by dividing the induced voltage at the elements that have no current by the current that produced this induction. Fig. 2 presents a three-core cable impedance diagram where: (i) the letters a, b, and c represent each core; (ii) the numbers 1, 2, and 3 represent each sheath; (iii) and g represents the ...

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... Where Z aa , Z bb , and Z cc represent the self-series impedance, and Z ab , Z bc , and Z ac are the mutual impedances. Additionally, it was considered that the cable was constructed using the trefoil method, which results in the series impedance being symmetric [19]. Thus, the sequence parameters are obtained as: ...

This paper proposes a nonlinear analysis of the parameter estimation problem in overhead and submarine power cable applications. The proposed methodology is able to estimate both positive and zero sequence parameters. Also, the measurement model incorporates random uncertainty in a rigorous manner, addressing the issue of noise propagation after applying symmetrical components. Three nonlinear estimation methods were studied to address the nonlinear least squares problems. Several noise levels and sample sizes were considered to demonstrate the robustness of the proposed approach. Finally, the methods were validated using both a simplified 2‐bus system and the IEEE 14‐bus system. The results obtained demonstrated significantly better performance compared to similar results found in the technical literature.

... Often, no distinction is made in this respect between cables with round ( Fig. 3, a) and sector-shaped conductors (Fig. 3, b), nor between stranded and solid cores. In spite of this, another aspect which requires attention is the presence or absence of a concentric neutral (Fig. 3, c), the latter is studied to a higher extent in [28][29][30]. This is due to the implications that a shield (and/or concentric neutral conductor) has on the magnetic flux and thus on the self-and mutual impedance. ...

The volatility of distributed production and the uncoordinated charging of electric vehicles cause major challenges in terms of supply reliability and local congestion problems in the distribution networks. In order to tackle these two aspects preventively, digital twin models are introduced to analyse the impacts of these stochastic distributed grid exchanges. Herein, line impedances are a key feature which determines the accuracy of the model. The chosen software environment to set up these digital twins, is based on Carson’s equations which are typically used for overhead high voltage lines. Hence, in this contribution an adapted model of Carson’s equations on low-voltage underground cables at 50 Hz is presented, with the aim to develop a digital twin for analysing the integration of nowadays loads and distributed sources on low voltage distribution systems. Finally, the model will be validated based on realistic grid and smart meter data provided by a distribution system operator.

... Other studies have developed models for computing electric field, emitted by subsea lines of HV and MV of monopolar, bipolar and three-phase cables systems, to detect structural isolation default of material by partial discharge (using analytical or numerical calculations) [13][14][15]. Other research has shown the magnetic effect by varying many parameters like the cable type: the distance between conductors, the resistivity of sol, harmonics and balanced load between the three phases in the power transmission line [16][17][18][19][20]. On the other hand, there were a few studies on the magnetic effect with electric fault variation of extra-high voltage cable (EHV) depending on time variation [21,22]. ...

Several researches have been conducted on the electromagnetic effect in submarine power cables due to the magnetic interaction of the power lines on materials and environment. Our work aims to study the two-dimensional numerical simulation by using the finite element method of a three-core submarine power cable. The simulation findings illustrate the magnetic field in normal and abnormal conditions: under overload and different waveforms of current faults as functions of time and distance, in three phases. The results expose the magnetic field emission of high voltage submarine electric cable, distribution, waveform and intensities around and near the subsea cable.

... Habib and Kordi implemented modal analysis [9] for evaluating per unit parameter of an arbitrary cross-sectioned cable. Besides, the finite element analysis method (FEM) has been introduced in ref. [10] for impedance matrix formation of a three-core cable. Further improvisation has been made by Shafieipour et al. with the implementation of a novel method-of-moment [11] for parameter calculation of several structured cables. ...

... As per the number of samples per sec the sampling frequency has been chosen. Hence, Table 1 represents the associated frequency with each wavelet signal, which has been carried out by using equations (10) and (11). The decomposition of the transient current signatures and their subsequent reconstruction for six levels are shown in Figure 8. Notable changes can be observed from D4 onwards in the case of switching current. ...

Low voltage cable is primarily connected from the transmission system to several household applications. It is quite common that switching transient in the power system during the energization of the high voltage and low voltage cables have a very crippling effect on the cable as well as the power system components. Hence, an experiment has been performed in the laboratory with a low voltage cable-connected motor system. The experimental results have been validated in the simulation platform, and they are capable of predicting the transient behavior during power cable energization. The effect of transients on power cables during the energization of devices has been investigated in this study in the form of voltage, current, and frequency. Discrete wavelet transform is implemented for the decomposition of the transient current. The generated approximation signal is used to quantify the severity during switching transient condition.

... It was initially employed to evaluate the power losses in TCACs, as in [4][5][6], where the use of additional constraints in 2D-FEM models were proposed to take into account the relative twisting between the armor wires and the phase conductors. This feature has led to quite a few studies aiming at understanding and characterizing phenomena like induced losses [7][8][9], thermal behavior [10][11][12][13][14], and electrical parameters [15][16][17][18][19], as well as paving the way for the development of new analytical approaches to improve the IEC standard [20][21][22]. ...

Due to recent advances, the numerical analysis of submarine three-core armored cables can nowadays be developed through the finite element method (FEM) in a small slice of the cable. This strongly reduces the computational burden and simulation time. However, the performance of this ultra-shortened 3D-FEM model is still to be fully assessed with experimental measurements. This paper focuses on this validation for an extensive variety of situations through the experimental measurements available in the specialized literature for up to 10 actual cables. In particular, it deals not only with relevant calculations at power frequency, like the series resistance and inductive reactance or the induced sheath current, but also with other aspects never analyzed before through 3D-FEM simulations, such as the zero sequence impedance, the magnetic field distribution around the power cable, as well as side effects due to the nonlinear properties of the armor wires. All this considering different armoring and sheath bonding configurations. Results show a very good agreement between measured and computed values, presenting the ultra-shortened 3D-FEM model as a suitable tool for the analysis and design of three-core armored cables, and opening the possibility to reduce the need of extensive experimental tests in the design stage of new cables.

... Numerical determination of circular shape conductor cable parameters is well documented in the literature [13] [14]. Here, attempts are made to introduce a dedicated approach in conjunction with the work of [10] to approximate a sector-shaped cable into a circular shape conductor enclosed in pipetype cable, as shown in Fig. 2, with reasonable trade-off between the core and insulator dimensions. ...

... Fig. 1. Section-shaped cable Fig. 2. Pipe type cable Traditionally, circular shaped three core pipe-type cable, in three-phase distribution networks are modelled by the impedance and admittance with corrected resistivity and permittivity under balanced network condition [14]. For sector-shaped four core, pipe-type cable shown in Fig. 3, the cable parameters in TABLE I. are normally provided by the manufacture [15] and calculated using equations presented in British Standard BS7870, which consider conductor material, insulation material, and conductor size. ...

... The self earth return path impedance of underground cable has been derived by Wedepohl's and Wilcos approximation [7] [8]. (14) The impedance between the i-th conductor and pipe or earth wire [11]: ...

... The cable section in the grid was a 3-core cable whose cores are arranged in a trefoil arrangement. A cross-section with representational construction details of the cable is presented in Fig. 2. As the PMUs are measuring current and voltage at the conductors, only core-core sub-matrices of the complete cable impedance and admittance model are used to select the significant parameters [16]. ...

... The flux linkage of phase a conductor with radius r is given by the sum of internal and external flux [16]: ...

... where i is the effective electric permittivity insulation between the core and jacket [16]. The conductivity of the insulation is very small and is considered zero [19]. ...

... One of the most employed type of cable is the three-core armored, where the armor is composed of steel wires twisted around the three cores. Mainly due to the presence of this armor, the global and disaggregated cable losses estimation is challenging, and several approaches have been proposed previously [2][3][4][5][6][7][8][9][10], highlighting the fact that the IEC 60287 standard [11] introduces important errors in the computation of the armor losses since it does not take into account the relative twisting between phases and armor wires. This is of importance because, apart from using it for economic analysis, the losses knowledge is a requirement for the temperature estimation inside the cable, and hence the thermal capacity. ...

... Nonetheless, for a design and planning analysis, simulations based on the finite element method (FEM) models have been extensively employed for the computation of the electrical parameters and the power losses in three-core armored cables. For this task, 2D and 3D approaches are usually considered, although 2D models are preferred [7][8][9][10]. In this case, the electromagnetic and thermal problems can be easily coupled and iteratively solved for a cross section of the power cable with low computational requirements (Fig. 1). ...

This paper presents the main features of a 3D FEM-based modelling framework of submarine three-core power cables with the final aim of estimating the ampacity of this type of cables when operating at certain conditions (buried in the seabed in steady-state). This assessment provides valuable information for the cable manufacturer during the design stage and for the owner of the evacuation line mostly in the planning stage, apart from being used as a reference for the development of other less computationally intensive analytic models. Moreover, the paper analyzes the impact that some design parameters have on the temperature of the cable, providing same concluding remarks.

... However, in different works, different values are found for the magnetic permeability of the armor. In [17], the transversal magnetic permeability used for the armor is considered µ 0 , because it is composed of wires that are not in direct contact. On the other hand, in [5], the relative magnetic permeability of the armor in a metallic pipe is 500. ...

... The mathematical description of the line is based on known telegraph equations. Solving such equations of state in partial derivatives by the finite element method for a particular time moment provides the highest accuracy of the analysis [4]. However, these equations can hardly be solved using numerical methods over a given time interval. ...

The mathematical model of the frequency converter cable branch as a part of the mine section power network with a single phase-to-ground fault is clarified. The model takes into account a discrete nature of the output voltage and power switches commutation inertia of a voltage inverter as a part of the converter. A technique is proposed for the formation of a mathematical model of a cable line with distributed parameters as a set of differential equations of state and algebraic coupling equations in matrix form. In this case, the cable is divided into three-phase elementary sections, for a set of typical equivalent circuits of which a graph is built, the matrix of the main sections and the matrix coefficients of the equations are calculated. The latter are solved by numerical methods. This allows to take into account the wave processes in the cable for a high-frequency pulse-width modulated output voltage of the frequency converter. Also the asymmetry of the insulation ground resistance, accompanying a ground fault, is taken into account. The matrix-topological approach allows to avoid operations with partial derivatives with respect to geometric coordinates of the cable. The relevance of the research resulted from the neglect of significant factors in known models, which reduces the accuracy of the analysis. In particular, the influence of the discrete nature of the output voltage of the frequency converter, the distributed nature of the cable line insulation parameters and the transverse asymmetry in emergency mode on the instantaneous values of the ground fault current are not taken into account. As a result of numerical simulation for the network of specific configuration, it was found that the occurrence of ground fault through a human body in the cable branch of the frequency converter is characterized by an unacceptably high probability of fatal electrocution. The monitoring method of the insulation resistance of the power network branch, equipped with the semiconductor frequency converter, is proved. The implementation of the method will improve the electrical safety of underground electrical networks due to the timely detection of insulation damage of the frequency converter cable branch and the transmission of a signal to turn off the supply voltage.