Definition of Simplified Frequency-Domain Volterra Models With Quasi-Sinusoidal Input

The Volterra approach to the modeling of nonlinear systems has been employed for a long time thanks to its conceptual simplicity and flexibility. Its main drawback lies in the number of coefficients, which rapidly grows with memory length and nonlinearity order. In some important cases, such as power system applications, the input signal is periodic and contains a fundamental component that is much larger with respect to the others. This peculiarity can be exploited in order to dramatically reduce the number of coefficients defining the frequency-domain Volterra model with slight drawbacks in terms of accuracy. A systematic procedure for the definition of simplified, frequency-domain models of arbitrary order is proposed. Thanks to the simplification, very high orders of nonlinearity can be managed. The proposed approach has been employed to model the behavior of two electrical devices with different amount of nonlinearity, and that of a power grid containing linear and nonlinear loads. Accuracy is discussed and compared with that obtained with a conventional Volterra model defined by a similar number of coefficients. Results show the effectiveness of the approach, which is particularly suitable to model and test voltage and current transducers as well as other ac power system devices.