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In this work, we present a nonlinear model reduction approach for reducingtwo commonly used nonlinear dynamical models of power grids: the effectivenetwork (EN) model and the synchronous motor (SM) model. Such models areessential in real-time security assessments of power grids. However, as powergrids are often large-scale, it is necessary to reduce the models in order toutilize them in real-time. We reformulate the nonlinear power grid models asquadratic systems and reduce them using balanced truncation based onapproximations of the reachability and observability Gramians. Finally, wepresent examples involving numerical simulation of reduced EN and SM models ofthe IEEE 57 bus and IEEE 118 bus systems.

Nonlinear model reduction of dynamical power grid models using quadratization and balanced truncation