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There are many electrical equipment inside ultra-high voltage converter valve hall, including converter transformer, converter transformer bushing, wall bushing and other typical electrical equipment. Among them, there are many insulation media inside the converter valve hall, including gas insulation, liquid insulation and solid insulation media. For layered medium, there are two problems in the ultra-high voltage converter valve hall: 1) The layered medium in the valve hall includes the interface between different insulating mediums such as the epoxy impregnated paper and oil impregnated paper. The layered interface belongs to the macro category, which can be fully described by applying the classical electromagnetic theory. Its transient process can be characterized by the classical lumped parameter differential equation model, and its time constant scale is around 5000s. Its spatial scale is near cm scale. 2) The layered interface of semiconductor devices inside the valve hall converter belongs to the micro category, with spatial scale in the nm scale and the time scale distributed near the ns dimension. Internal charge and potential distribution can be described by partial differential equations, and the parameters of the differential equations are variables with clear physical quantities. In this paper, firstly, the substrate free of impurities of multi gate MOS capacitors is analyzed from the microscopic carrier level, and the minority carrier term and acceptor impurity concentration Na at any point x near the surface are given. Based on the full mathematical derivation and analysis of the micro particle's sink and sink analytic expressions, the space charge distribution inside the layered insulating medium is obtained, especially at the interface of layered medium. Furthermore, for the electrical equipment inside the converter valve hall, which is subject to the combined action of high voltage and large current, the closed analytical solution of the electro-thermal coupling is derived from the perspective of analytical model through Bessel function, and the quantitative characterization relationship between the leakage current and voltage is obtained. This paper derives full theoretical analytical relationship between the space potential and charge distribution of the layered medium in the UHV converter valve hall from theoretical point of view, which has the good theoretical guidance and the practical application value for operation and maintenance of electrical equipment in the UHV converter valve hall.
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