Finite element analysis of transient non-linear coupled field problems

With recent advances in computer software and hardware technology, numerical simulation of transient nonlinear coupled field problems is becoming less costly and less time consuming than analytical and experimental study. Thus many problems of economic importance can be addressed with transient nonlinear finite element analysis which cannot be addressed experimentally, for example because the scale on which they occur is too small for experimental study. To address such problems, a 2-D finite element program has been developed for the numerical study of transient nonlinear coupled (electrical, magnetic, thermal and mechanical) field problems. The program uses the Crank-Nicolson time stepping scheme for the time domain discretization with adaptive time-stepping, accommodates position, field, and temperature-dependent material properties, time-dependent boundary conditions (e.g., time-dependent applied voltage), and allows coupling of at least two fields, e.g., electric and thermal. The program has been tested against experimental data in several contexts, with good agreement. The program has been applied successfully to the analysis of defect-induced high electric field phenomena in cross linked polyethylene (XLPE), conversion of water trees to electrical trees in distribution cable, and electro-thermal phenomena in ZnO surge arrester disks, magnetic losses in pipe-type cable, etc. During studies of high field phenomena in XLPE electric and mechanical fields were computed in the vicinity of a conducting defect for a wide range of conditions, including AC and impulse waveforms. The study shows that substantial mechanical stresses are generated by the thermally-induced expansion of the XLPE during an impulse, and the space charge-induced local temperature rise also causes-the yield stress of XLPE to drop precipitously as the XLPE crystallites melt. Yielding of the XLPE is likely to create a cavity surrounding the defect which is capable of supporting partial discharge. Field experience indicated that lightning impulses can convert water trees to electrical trees which then grow to failure. The numerical study suggests that during a lightning impulse, polarization current in the water within a water tree channel can cause the water temperature to rise to the point that the water pressure causes the XLPE to yield, generating a cavity large enough to support partial discharge, which would lead to conversion of the water tree to a fault-inducing electrical tree. Pipe type transmission power cables are based on a dielectric fluid-filled steel pipe which contains the three cable phases. Magnetic losses in the pipe are a significant factor in thermal design of such systems. However, the permeability of the pipe is strongly field-dependent, which, combined with the three phase current within the pipe, makes computation of pipe losses difficult. Pipe loss computations with the transient nonlinear field program have produced good agreement with available data, and we have been able to extend computations to the case of unbalanced phase currents which could not be computed previously. The nonlinear I-V characteristic of ZnO is used to protect everything from consumer products to high voltage transmission systems from transient over-voltages. The large magnitude and short duration of lightning current impulses causes nonuniform heating of ZnO elements. Numerical studies show that mechanical stress caused by localized thermal expansion can cause damage or failure of the ZnO disk. Nonlinear aspects of this computation include the field-dependent conductivity, temperature-dependent heat capacity, and temperature-dependent thermal conductivity of the ZnO. Computations of the thermal fields and resulting mechanical stresses have provided useful data for ZnO disk design. As a result of this work, the energy absorption capability of commercial ZnO disks has been increased by 50%.