Low-Frequency Stability in Electroquasistatic Simulations

In the industrial design process of high-voltage equipment, the simulation of electroquasistatic problems is frequently applied. One example of such a case are insulators (see Figure). The simulation and optimization of the electric field, i.e. to avoid overvoltages, within these insulators are important for ensuring the safety and reliability of the device. For slowly varying fields, the numerical solution of the underlying field problem including conductors and inductors poses a challenge as the formulation suffers from an inherent instability, the so-called low-frequency breakdown.

The problem is caused by the badly conditioned system matrix due to the substantial differences in the capacitive and resistive material properties of conductors and inductors. This inherent poor conditioning of the system is further amplified when dealing with low frequencies or large time steps in the frequency and time domains, respectively. When transitioning to the static case, the equations in the insulator even vanish.

In a collaboration with Siemens, a simple but effective way to stabilize the problem was recently proposed in 10.1109/TDEI.2023.3277414. The stabilization is achieved through a suitable scaling of the system by orders of magnitude of frequency/time step and material constants. This scaling stabilizes the simulation for low frequencies and also extends its robustness down to zero-frequency scenarios, i.e., static problems. Therefore, this approach eliminates the need for different solvers for the electrostatic, electroquasistatic, and stationary current flow approximations of Maxwell’s equations.