中文摘要：

针对目前缺少介电功能梯度材料（d-FGM）内部介电特性分布的优化方法这一问题,提出了一种适用于交变电压下的叠层式介电常数FGM（ε-FGM）绝缘子内部介电特性的优化算法。该算法以降低绝缘子沿面最大电场强度为目标,使用迭代方法,根据当前电场强度、目标电场强度及介电常数上下限等设计参数,自适应地调整每层材料的介电常数,获得优化的介电常数分布;通过改变迭代系数和缩减系数,控制算法收敛过程,降低计算时间和资源消耗。仿真结果表明：相对于匀质绝缘子,ε-FGM绝缘子内部及沿面附近电场的不均匀程度得到明显改善,沿面最大场强的降幅超过60%;绝缘子的单层厚度应当在工艺条件满足的基础上尽可能地减小;沿面最大场强会随着介电常数上限的增加而非线性降低,存在饱和现象,饱和阈值与优化前的沿面最大场强呈正相关。研究结果验证了该算法的有效性,且表明以ε-FGM为代表的d-FGM具有优异的电场分布优化效果,有望在各类高压设备的固体绝缘系统中获得广泛的应用。

英文摘要：

At the present there lacks proper optimization method for internal dielectric properties of dielectric functionally-graded-material （d-FGM）. An optimization algorithm of internal permittivity distribution for multi-layer permittivity FGM （ε-FGM） insulator under AC voltage is proposed, which aims at weakening the maximum electric field （e-field） strength along the insulator surface. According to design parameters, such as current e-field strength, objective e-field value and permittivity range, the permittivity value of each layer is self-adaptively updated with iterations to obtain the optimized permittivity distribution. The iterative coefficient and shrinking coefficient are adjusted to control the convergence process and shorten calculation period. Compared with uniform insulator, e-field distribution inside and along the surface of ε-FGM insulator is more uniform and the maximum e-field strength along surface is weakened more than 60%, and the layer thickness of the multi-layer ε-FGM insulator ought to be set as small as possible under the allowed fabrication conditions. The maximum surface e-field strength decreases nonlinearly with the increasing permittivity upper limit and saturates as the upper limit reaches certain threshold value, which has positive correlation with the maximum e-field strength before optimization.