Time-Stepped Finite-Element Modeling of Three-Phase Transformer for Electromagnetic Transient Emulation on FPGA

Abstract

The finite-element analysis is a powerful method to obtain detailed insight into the operation of any electromagnetic equipment. However, the required computational power to solve a finite-element modeled power equipment is so heavy that most Newton-Raphson-method-based algorithms can barely achieve real-time simulation. The low latency and hardware parallelism of the fieldprogrammable gate array (FPGA) provides a path forward. In this paper, a parallel and deeply pipelined adaptive transmission-line modeling method with preconditioned conjugate gradient solver is designed in hardware and implemented on two Xilinx R XCVU37P FPGAs for the finite-element modeling of a three-phase transformer. The accuracy of the transformer solver under both currentexcited and voltage-excited conditions of the transformer was validated against the commercial FE simulation tool.Index Terms-Electromagnetic transients, finite-element method, field-programmable gate arrays (FPGAs), preconditioned conjugate gradient, parallel processing, real-time simulation, transformer, transmission-line modeling.

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

“…The structure of this low frequency transformer is simple and symmetrical; therefore, few elements of mesh can guarantee enough accuracy. This mesh has also been used in [12]. In this paper we focus on the difference between the results of the proposed POD method and the FEM.…”

“…However, in the electromagnetic finite element model, as shown in (7), the K is obtained by the nonlinear magnetic permeability calculated based on the magnetic flux density B. It is necessary to update the K r by the K in every time-step when solving the equation set (12). In particular, the Jacobian matrix is difficult to be obtained when solving the above equation set ( 12) by the Newton-Raphson method because the values in the K r lose their original relationship with the FE nodes.…”

“…The main hardware resources of the Xilinx ® XCVU37P FPGA are as follows: 4032 BRAMs, 9024 DSP48E slices, 2607360 flip-flops, and 1303680 look-up table. Compared with the case study in the reference [12] and [14], for the similar transformer model, two FPGAs are used in these papers to solve the full order model but one FPGA is enough for the low order model in this paper. The full order model is also difficult to further apply to the 3D and rotating machine geometries.…”

“…Detailed nonlinear magnetic equivalent circuit based real-time transformer models were also developed on the FPGA [11]. With further hardware development, the parallel FEM algorithms based on hardware devices such as FPGAs and GPUs were also proposed to improve computational efficiency [12]- [14]. However, when the number of FE nodes is large, the computation time is still high because the calculation often cannot be fully parallelized, limited by the computational resources of the FPGA and other hardware devices.…”