Nonlinear time-periodic phenomena in electrical engineering

Nonlinear problems abound in electrical engineering. The most prominent cause for nonlinearity is the saturation of ferromagnetic materials exposed to a high field intensity. Besides this, the relationship between electric field intensity and current density in some ceramics is also nonlinear (varistor effect) and, in ferroelectric crystals, the electric flux density saturates at high electric field intensities. Frequently, the time dependence of the excitations is sinusoidal but, due to nonlinearity, the steady state responses are non-sinusoidal although time-periodic. It is often desired to obtain this steady state periodic solution at the lowest possible cost. This means avoiding the computation of possibly long transient phenomena preceding the steady state response by appropriate numerical measures. The project research is aimed at developing efficient numerical techniques to solve this problem in conjunction with finite element models of nonlinear electromagnetic devices. The proposed method is based on the observation that, in linear problems, the equations written for the time steps within one period can be made decoupled. Using a special iterative technique, it is possible to extend this decomposition to nonlinear problems. The same idea can be employed in the frequency domain, too. The result is an ideal solution for the problem of determining the steady state time-periodic answer in dynamic electromagnetic systems. The final outcome is an efficient possibility to predict the behaviour of electromagnetic devices under steady state sinusoidal excitation with nonlinear material properties taken into account.

Nonlinear problems abound in electrical engineering. The most prominent cause for nonlinearity is the saturation of ferromagnetic materials exposed to a high field intensity. Besides this, the relationship between electric field intensity and current density in some ceramics is also nonlinear (varistor effect) and, in ferroelectric crystals, the electric flux density saturates at high electric field intensities. Frequently, the time dependence of the excitations is sinusoidal but, due to nonlinearity, the steady state responses are non-sinusoidal although time-periodic. It is often desired to obtain this steady state periodic solution at the lowest possible cost. This means avoiding the computation of possibly long transient phenomena preceding the steady state response by appropriate numerical measures. The project research is aimed at developing efficient numerical techniques to solve this problem in conjunction with finite element models of nonlinear electromagnetic devices. The proposed method is based on the observation that, in linear problems, the equations written for the time steps within one period can be made decoupled. Using a special iterative technique, it is possible to extend this decomposition to nonlinear problems. The same idea can be employed in the frequency domain, too. The result is an ideal solution for the problem of determining the steady state time-periodic answer in dynamic electromagnetic systems. The final outcome is an efficient possibility to predict the behaviour of electromagnetic devices under steady state sinusoidal excitation with nonlinear material properties taken into account.