Dimension Reduction for the Design Optimization of Large Scale High Voltage Devices Using Co-Kriging Surrogate Modeling

In high voltage (HV) technology, the electrical field distribution can be improved using different field grading methods. These can be categorized into two groups: 1) capacitive or geometrical field grading and 2) resistive field grading. To obtain the optimized field grading effects, some geometrical or material parameters of the HV devices should be optimized. However, these devices are often nonrotationally symmetric and simulation is computationally very time consuming. In this paper, a multilevel surrogate method using co-Kriging methodology is proposed to optimize such large-scale 3-D HV devices. To compute the electrical field distribution of these HV devices, a finite-element method simulator can be run at different levels of complexity, i.e., by reducing the 3-D model into a 2-D model under certain additional assumptions. The co-Kriging method combines expensive runs of highly complex 3-D simulations with relatively inexpensive dimension reduced 2-D simulations. This approach is shown to allow for a faster optimization of a large-scale nonrotationally symmetric problem, while preserving a sufficiently high level of accuracy.