  In recent years, the sub-synchronous oscillation (SSO) accidents caused by
wind power have received extensive attention. A method is needed to distinguish
if nonlinear behavior exists in the recorded equal-amplitude accident
waveforms, so that different methods can be adopted to analyze the mechanism of
the oscillation. The theory of higher-order statistics (HOS) has become a
powerful tool for detection of nonlinear behavior (DNB) in production quality
control since 1960s. However, HOS analysis has been applied in mechanical
condition monitoring and fault diagnosis, even after being introduced into the
power system and wind farms. This paper focuses on the voltage source converter
(VSC) control systems in wind farms and tries to detect the nonlinear behavior
caused by the bilateral or unilateral saturation hard limits based on HOS
analysis. First, the traditional describing function is extended to obtain more
frequency domain information, and hereby the harmonic characteristics of
bilateral and the unilateral saturation hard limit are studied. Then the
bispectrum and trispectrum are introduced as HOS, which are extended into
bicoherence and tricoherence spectrums to eliminate the effects from linear
parts in the VSC control system. The effectiveness of DNB and classification
based on HOS is strictly proved and its detailed calculation and estimation
process is illustrated. Finally, the proposed method is demonstrated and
further discussed through simulation results.
