Model Order Reduction for Real-Time FPGA-Based Finite Element Transient Simulation of Three-Phase Transformer

The finite element method (FEM) is commonly used in modeling the electromagnetic field of transformers with high accuracy; however, the computation time of the FEM is prohibitively high for real-time simulation due to high model order. Reducing the model order is helpful to improve the computational efficiency of the FEM. The proper orthogonal decomposition (POD) is an efficient method to reduce the linear model order but encounters difficulties with nonlinear models. In this paper, a model order reduction (MOR) method based on the combination of POD and the transmission-line modeling (TLM) is proposed to reduce the nonlinear finite element model order and computation time. The TLM method is used to separate the nonlinear components from the model, and then the POD is used to reduce the linear domain order of the model. The nonlinear components obtained by TLM can be solved in parallel on the field programmable gate array (FPGA) to improve computational efficiency further. This paper has studied the transient states of a three-phase transformer with the current excitation and field-circuit coupling. The real-time hardware emulation results are validated by results from offline simulation using Comsol®.