Toshiaki Kikuma

A Robust and Efficient Iterative Scheme for the EMT Simulations of Nonlinear Circuits

This paper presents a robust and efficient iterative scheme for solving nonlinear circuits as a solution method for electromagnetic transient (EMT) simulations. In most EMT simulations, the characteristics of nonlinear components can be represented by piece-wise linear curves. With this assumption, the Newton-Raphson (NR) method shows high efficiency, but it is prone to get into an infinite loop, resulting in nonconvergence. First, the NR method is extended to utilize the information of both axes of the nonlinear characteristics, and this modified method is called a biaxial NR method. The biaxial NR method shows a significantly improved convergence performance with additional computation. Next, an iterative scheme, which combines the standard NR, the biaxial NR, and the Katzenelson method is proposed. It first tries the standard NR that is the most efficient but the least convergent. If it fails to converge, the biaxial NR, which is more convergent but less efficient, is employed. Just in case when the biaxial NR does not converge, finally, the Katzenelson method, whose convergence is mathematically guaranteed but least efficient, is used. In this way, the proposed scheme always converges with a relatively small number of iterations. Illustrative and practical examples are shown to validate the proposed scheme.

A robust and efficient iterative scheme for the EMT simulations of nonlinear circuits

Summary form only given. This paper presents a robust and efficient iterative scheme for solving nonlinear circuits as a solution method for electromagnetic transient (EMT) simulations. In most EMT simulations, the characteristics of nonlinear components can be represented by piece-wise linear curves. With this assumption, the Newton-Raphson (NR) method shows high efficiency, but it is prone to get into an infinite loop resulting in non-convergence. First, the NR method is extended to utilize the information of both axes of the nonlinear characteristics, and this modified method is called a biaxial NR method. The biaxial NR method shows significantly improved convergence performance with additional computation. Next, an iterative scheme which combines the standard NR, the biaxial NR, and the Katzenelson method is proposed. It first tries the standard NR that is the most efficient but the least convergent. If it fails to converge, the biaxial NR which is more convergent but less efficient is employed. Just in case when the biaxial NR does not converge, finally the Katzenelson method whose convergence is mathematically guaranteed but least efficient is used. In this way, the proposed scheme always converges with a relatively small number of iterations. Illustrative and practical examples are shown to validate the proposed scheme.