Direct steady-state solutions for circuit models of nonlinear electromagnetic devices

What is it about?

This paper presents a method for the steady-state analysis of electromagnetic devices described by circuit models, based on a discrete integral operator of periodic functions. Such an operator allows for the formulation of finite-integral relations with low computational complexity, which is particularly important for electromagnetic devices described by high-dimensional non-linear differential equations. That integral operator is based on the discrete differential operator of periodic functions, which is carefully analysed and allows us to find an analytical form of the discrete integrating operator. An iterative algorithm determining the steady-state solution is proposed, which eliminates the necessity of solving high-order finite-difference equations, commonly used, and reduces the problem to a multiplication of matrices only. The application of this algorithm to steady-state analysis is verified through two examples; elementary circuit with nonlinear coil and a three-phase transformer with nonlinear core. The results are compared with those of other algorithms and simulations.

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