中文摘要：

利用WZ模型将绝缘介质离散化，使用分形理论讨论了绝缘介质中电树发展的随机性和确定性。在原有WZ模型的基础上引入了分布耐电强度的概念，建立了新的模型。通过此二维模型仿真了在绝缘介质中嵌入了耐电强度高于原介质的屏障后的电树生长情况。在针板电极结构下用模型仿真了在绝缘介质中所嵌入屏障耐电强度的不同对电树发展造成的不同影响，并比较了不同情况下的平均击穿距离。通过比较得出，当嵌入耐电强度远大于原介质的屏障后，电树发展过程中需要绕过屏障进行生长，从而等效于增加了原有介质的厚度，使得整个介质的绝缘性能有一定程度的提高。

英文摘要：

Dielectric material is dispersed using WZ model, and the distribution of the potential in dielectric meets the Laplace＇s equation. The randomicity and certainty of the development of electrical trees in dielectric are discussed using fractal technology. Based on WZ model, a newly parameter breakdown strength is introduced to characterize the differences of insulation performance between different dielectric materials. The development of electrical trees in dielectric with barriers whose breakdown strength are higher than that of the surrounding dielectric is investigated by means of two-dimensional numerical simulations. In contrast to conventional approaches the introduced newly model is based on a deterministic model together with a spatial distribution of the electrical breakdown strength. The simulation is done in needle-plane electrode geometry. The effect of barriers with different breakdown strength upon the development of electrical trees is simulated. Moreover the mean breakdown distances are compared for different setups. For each set-up, the values of breakdown strength of embedded barriers are different, but they are all higher than the breakdown strength of surrounding dielectric. Fractal dimensions of simulating figures are calculated and compared, and from this comparison it is concluded that the embedded barriers whose breakdown strength is much higher than that of the surrounding dielectric increases the insulation performance in a certain extent. That is because barriers are embedded in dielectric, when electrical trees grow next to the barriers, they are forced to grow steering clear of the barriers, and the increase of the breakdown distances is equal to the extension of the thickness of the dielectric, so the insulation performance of the dielectric is improved.