Simplified Modeling and Identification of Nonlinear Systems Under Quasi-Sinusoidal Conditions

This paper proposes a simplified Volterra model able to represent the steady-state behavior of nonlinear systems in quasi-sinusoidal conditions. A wide class of nonlinear systems can be modeled using the conventional Volterra approach, but as the order of nonlinearity or the memory length increases, the number of coefficients grows exponentially, thus making the identification of the Volterra model troublesome. By considering a system whose input is a periodic signal containing a main frequency component which is much higher than the others, it is possible to drastically reduce the number of coefficients of its frequency-domain Volterra model without affecting the model accuracy. The proposed technique is particularly suitable to represent the behavior of the electrical devices connected to the ac mains, since they typically operate in quasi-sinusoidal conditions. In particular, its application to voltage and current transducers takes on great importance in the field of instrumentation and measurement, since it allows overcoming their usual characterization. Thanks to the proposed model, dynamics and nonlinearities can be considered simultaneously, while avoiding the complexity usually associated with the conventional Volterra approach. For example, the proposed technique is applied to model a Hammerstein system, which is often employed to represent the behavior of electrical devices, and the results are deeply discussed.