  In this paper, nonlinear model reduction for power systems is performed by
the balancing of empirical controllability and observability covariances that
are calculated around the operating region. Unlike existing model reduction
methods, the external system does not need to be linearized but is directly
dealt with as a nonlinear system. A transformation is found to balance the
controllability and observability covariances in order to determine which
states have the greatest contribution to the input-output behavior. The
original system model is then reduced by Galerkin projection based on this
transformation. The proposed method is tested and validated on a system
comprised of a 16-machine 68-bus system and an IEEE 50-machine 145-bus system.
The results show that by using the proposed model reduction the calculation
efficiency can be greatly improved; at the same time, the obtained state
trajectories are close to those for directly simulating the whole system or
partitioning the system while not performing reduction. Compared with the
balanced truncation method based on a linearized model, the proposed nonlinear
model reduction method can guarantee higher accuracy and similar calculation
efficiency. It is shown that the proposed method is not sensitive to the choice
of the matrices for calculating the empirical covariances.
