Search

It is not uncommon for oscillatory electric power system modes to move close to a resonance in which eigenvalues coincide. In a weak resonance, the modes are decoupled and the eigenvalues do not interact. We analyze general perturbations of a weak resonance and find two distinct behaviors, including interactions near strong resonances in which the eigenvalues quickly change direction. The possible perturbations are illustrated with interactions between electromechanical modes in a 4-generator power system. Some of the interactions are similar to subsynchronous resonance and can lead to oscillatory instability. Index Terms--Eigenvalues and eigenfunctions, Hopf bifurcation, oscillations, power system dynamic stability, resonance, root loci, snbsynchronous resonance.

Power system normal form analysis has developed coefficients and indices in modal coordinates to quantify nonlinear modal interactions. We study the changes in the coefficients and indices when the power system equations are expressed in different coordinates or units and show that they can be normalized to be invariant to coordinate changes and thus intrinsic to the power system. The results are illustrated on a 4-generator system. An example shows that the coefficients and indices not only detect nonlinear interactions but also can become very large near a strong resonance in the system linearization. Index Terms--Nonlinear modal behavior, normal form method, power system dynamics, strong resonance.