Assessment of nonlinear interaction between nonlinearly coupled modes using higher order spectra

Higher order spectral analysis techniques are used to identify nonlinear interaction involving the electromechanical modes of oscillation in complex power systems. First, the presence and extent of nonlinear interactions between frequency components in oscillatory processes following large perturbations are identified using bispectrum and bicoherence analysis methods. Then, the strength and distribution of nonlinear couplings between frequency components is investigated using the phase relationships between spectral components. A case study with a 377-generator model of the Mexican interconnected system is used to illustrate nonlinear aspects arising from the nonlinear interaction of the different low-frequency inter-area modes. The results of the numerical simulations show that low-frequency modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. Such an identification can be used as a benchmark for validation of nonlinear analysis methods, and to reduce the burden associated with these methods.