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The purpose of this paper is to analyse the dynamics of a thermal field generated in a tubular bus with rated current by using two models of electrical resistivity of copper.

The boundary-initial problem of the modified heat equation was formulated for the tubular bus. Analytical solutions were obtained by means of Green’s functions as the kernels of the integral operator inverse to the corresponding differential operator. The results were presented graphically and verified using the finite element method. The calculations were made by considering the example of the Storm Power Components tubular bus (USA).

Analytical field models were used to determine time- and space-variable heating curves, time constants and steady-state current ratings.

This paper is related to the structure of a hollow cylinder. Other bus sections can be taken into account by using the coordinate systems of different curvilinear orthogonal symmetry.

Using the analytical method, the influence of the variable (temperature dependent) electrical resistivity on some important parameters and characteristics of the tubular bus was investigated. The system was considered as an element with distributed parameters.

The purpose of this paper is to present a method of solving a thermal conduction equation in three‐zone axially‐symmetrical systems.

In the method developed, the field functions are determined in the analytical way by the superposition of states and separation of variables method. The coefficients of the field functions and eigenvalues of the boundary‐initial problem are computed by the numerical method. The coefficients are the solution to the corresponding sets of equations. These sets are the result of scalar products of non‐orthogonal functions at the respective zones of the cable. The eigenvalues are determined by an algorithm, which uses the field properties and elements of the golden cut method.

The method made it possible to develop a mathematical model of the dynamics of the thermal field in a polymer DC cable. This model has good physical interpretation. The paper also presents the field distributions determined in an analytical form. Some arguments of the expressions derived are however computed numerically. The results obtained by the paper's method and by the finite elements methods were compared. The relative differences are less than 6 per cent.

The method concerns axially‐symmetrical three‐zone systems under nominal conditions.

By means of the method important parameters of DC lines can be determined (e.g. spatial‐temporal heat‐up curves, admissible sustained currents, time constants).

An analytical‐numerical method of analysis of the thermal field in a three‐zone axially‐symmetrical system was developed. Its original element is the algorithm of determination of eigenvalues of the boundary‐initial problem and coefficients of non‐orthogonal field functions.

The purpose of this paper is to prepare procedures for determination of characteristics and parameters of DC cables on the basis of transient and steady thermal field distribution in their cross-sections.

Steady-state current rating was computed iteratively, with the use of steady thermal field distribution in the cable. The iterative process was regulated with respect to this field by changes of the mean surface temperature of the sheath of the cable. It was also controlled with respect to the unknown current rating by deviations of the temperature of the core from the maximum sustained temperature of the insulation (material zone) adjacent to the core. Heating curves were determined (in arbitrarily selected points of the cross-section of the cable) by a parallel algorithm described thoroughly in the first part of the paper. The algorithm was used for computing of transient thermal field distribution throughout the whole cross-section. Thermal time constant distributions were determined by the trapezium rule, where the upper integration limit of respective thermal field distributions was being changed.

Using the methods prepared the following characteristics/parameters of the cable were determined: steady-state current rating, spatial-time heating curves, mean thermal time constant distribution. The results were verified and turned to be in conformance with those of the IEC 287 Standard and a commercial software – Nisa v. 16. Speedup and efficiency of the parallel computations were calculated. It was concluded that the parallel computations took less time than the sequential ones.

The specialized algorithms and software are dedicated to cylindrical DC cables.

The knowledge of the determined characteristics and parameters contributes to optimal exploitation of a DC cable during its use.

The algorithms of determination of the steady-state current rating and thermal time constant are original. The software described in the appendix has also been made by the authors.

The paper aims to propose a parallel algorithm in order to increase speed and efficiency of an analysis of transient thermal field in layered DC cables.

Initial-boundary problem of thermal field was discretized by means of implicit finite difference method in cylindrical coordinates. A two-stage time decomposition method was applied to introduce parallel computations. An assumed duration of the transient state was decomposed. The system of algebraic equations was being solved with the use of a conjugate gradient method (with diagonal preconditioning) in all time intervals simultaneously.

A method for solving (with the use of parallel computing system) the transient heat conduction equation in a DC cable consisting of arbitrary number of material layers was given. The dependence of the convective heat transfer coefficient on the location on the perimeter of the cable and on its surface temperature (which introduced non-linearity in the boundary condition) was taken into account. The influence of the determined field on the efficiency of the heat source was also taken into consideration in the model.

The main limitation is induced by cylindrical and coaxial structure of the consecutive layers of the system. Thermal field is generated by direct current flow only. The length of the fragment of the cable under consideration should be much greater than its diameter.

The time-spatial distribution of thermal field in the cross-section of the cable can be used for analysis of its reliability and for determination of important characteristics and parameters of the system.

A parallel algorithm of solving initial-boundary parabolic problem was proposed as a result of synthesis of three methods (finite difference, time decomposition and conjugate gradient). An algorithm of minimization of disturbances of the solution introduced at the division points was given. Equations approximating real distribution of heat transfer coefficient from the surface of the cable were proposed.