Partial Element Equivalent Circuit Method for Electromagnetic Transient Simulation of Power System Apparatus

Abstract

Electromagnetic (EM) equipment are ubiquitous in electrical power generation, transmission, and distribution systems, and they should be studied for reliable and continuous operation under switching operations, faults, and other transient conditions. Conventional lumped models lack the capability to consider EM field interactions, while distributed methods, such as the finite element method (FEM), are widely employed to address these interactions. The partial element equivalent circuit (PEEC) method effectively solves Maxwell's equations in integral form and the method has gained interest in EM modeling due to its equivalent circuit behavior and its potential for optimization using circuit solver techniques. Electromagnetic models can be classified into two categories based on geometry: 2D geometry-based models and 3D geometry-based models. This thesis presents two main contributions toward the efficient simulation of EM systems. It proposed a transmission line modeling (TLM) based PEEC approach for the parallel simulation of 2D power system apparatus. The method was later extended to perform 3D power system simulations, including electrodynamic and electrostatic scenarios. Additionally, model order reduction techniques were introduced to achieve higher performance. First, a novel TLM-based parallel PEEC time-domain solver is developed to solve nonlinear 2D EM problems. The method substitutes both linear and nonlinear components in the standard PEEC equivalent circuit with corresponding TLM models, leading to an electrical current based linear network and a magnetic current based nonlinear network. The proposed hybrid TLM-PEEC method effectively decouples the nonlinear elements from the linear network, enabling individual solutions for the nonlinearities and making it highly suitable for parallel processing. Each nonlinear element is solved using parallel Newton-Raphson (N-R) iterations, and the analytical calculation of the Jacobian is presented along with the solution process. The parallelization of the proposed hybrid TLM-PEEC method is explored and implemented on a many-core graphics processing unit (GPU) and a multi-core central processing unit (CPU) to provide detailed field-oriented information on electromagnetic transients (EMTs) in a single-phase 2D shell-type transformer. The proposed architecture was easily coupled with an external network, and the accuracy and computational efficiency of the TLM-PEEC method was verified through similar simulation results obtained from Comsol Multiphysics. Secondly, the hybrid TLM-PEEC technique is proposed for 3D EM transient simulations, providing comprehensive details on the matrix solver, time-domain algorithms, and the N-R solver for nonlinear magnetics. The 3D hybrid TLM-PEEC approach defines separate linear and nonlinear equivalent circuits, introducing parallel TLM iterations for the linear system, and individual solutions for the nonlinear network using the N-R method, thereby enabling parallel computing. The proper orthogonal decomposition (POD) method, a model order reduction (MOR) technique, was integrated into the hybrid TLM-PEEC method to improve performance by removing unnecessary features in the system. The parallelization of the methods has been fully explored and implemented on both many-core GPU and multi-core CPU, enabling field-oriented transient simulation for a 3-phase 3D core-type transformer coupled with external circuits, as well as quasi-static 3D simulation for a high-voltage insulator. The accuracy and computational efficiency of the proposed architectures were verified through simulation results obtained from similar case studies implemented in Comsol Multiphysics