Scaling of normal form analysis coefficients under coordinate change

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.