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Numerical Method Analysis of Nonlinear Elements Behavior in Non-sinusoidal State

The analysis of the behavior of non-linear elements in electrical equipment is particularly important, especially in the non-sinusoidal regime. In this case, the non-linearity of the circuit elements generates additional current and voltage harmonics that worsen the energy quality and become dangerous for the normal operation of electrical equipment. There are specialized classical software tools for the analysis of these circuits that do not provide all the necessary information about the new harmonic content of the circuit and about the contributions of non-sinusoidal regime and non-linearity. This deficiency is solved by the method proposed by the authors. The method uses a mathematical model based on the multinomial theorem and the nonlinear characteristic i(u) of the circuit element. An original symbolic algorithm determines both the new content of the current harmonics for different operating regimes as well as the contributions of the voltage harmonics and the coefficients of the approximation polynomial i(u) to the current harmonics. The results obtained on two studied cases are compared with traditional simulation techniques and validated by their accuracy.