Real-Time FEM Computation of Nonlinear Magnetodynamics of Moving Structures on FPGA for HIL Emulation

Finite-element method (FEM) based hardware-in-the-loop emulation provides the most accurate and fast prototype platform for real-time design and testing of electric machines in a nondestructive environment. The application of transmission line modeling (TLM) can expeditiously reduce the FEM execution time by decoupling the nonlinear elements of the FEM equivalent network using transmission lines to keep the stiffness matrix unchanged through the simulation for static cases. However, in electric machines the TLM method suffers from the change of stiffness matrix in the time-stepped procedure due to movement. Furthermore, time consumption for the solution of numerous decoupled nonlinear equations for a fairly large number of TLM iterations in comparison with the conventional Newton-Raphson method remains a challenge. This paper proposes a novel real-time TLM method based on finite precalculated lower and upper triangular decompositions and field programmable gate array hardware implementation to exploit TLM parallelism for real-time simulation of magnetodynamics in electric machines. A two-dimensional FEM simulation of a single-sided linear induction machine is emulated in hardware and the results are validated experimentally and with Jmag-Designer software to show the effectiveness of the proposed method.