PEEC-Based Simulations Using Iterative Method and Regularization Technique for Power Electronic Applications

The partial element equivalent circuit (PEEC) method has been widely used in different industrial and scientific fields for electromagnetic analysis. PEEC-based solvers have been optimized and accelerated in order to be able to solve larger and more complex problems that arise in industry. In power electronic system simulations, PEEC models are often simplified by neglecting electric field couplings and using quasi-static model. The simplified system can be further accelerated using reluctance technique and then sparsified up to high levels without degrading the accuracy of the solution. In previous work, the sparse system was solved using sparse direct solution, while in this study, an iterative approach is employed which resulted in lower time complexity of the solution. However, since matrices achieved from PEEC equations are severely ill-conditioned, regularization techniques need to be applied to avoid numerical instabilities. The regularization is done mathematically and can be interpreted as adding a frequency-dependent pseudocapacitor to each node in the PEEC model. Because the pseudocapacitors are frequency dependent, hence frequencies close to dc are not covered in this study and have left as future work. The new sparse and regularized system can then be solved using a Schur complement technique together with iterative solvers with a novel preconditioning approach.