Jerzy Golebiowski and Robert Piotr Bycul
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Research limitations/implications
The specialized algorithms and software are dedicated to cylindrical DC cables.
Practical implications
The knowledge of the determined characteristics and parameters contributes to optimal exploitation of a DC cable during its use.
Originality/value
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.
Details
Keywords
Jerzy Golebiowski and Robert Piotr Bycul
– 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.
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Research limitations/implications
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.
Practical implications
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.
Originality/value
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.