  This paper presents a novel model order reduction technique tailored for
power systems with a large share of inverter-based energy resources. Such
systems exhibit an increased level of dynamic stiffness compared to traditional
power systems, posing challenges for time-domain simulations and control
design. Our approach involves rotation of the coordinate system of a linearized
system using a transformation matrix derived from the real Jordan canonical
form, leading to mode decoupling. The fast modes are then truncated in the
rotated coordinate system to obtain a lower-order model with reduced stiffness.
Applying the same transformation to the original nonlinear system results in an
approximate separation of slow and fast states, which can be truncated to
reduce the stiffness. The resulting reduced-order model demonstrates an
accurate time-domain performance, the slow eigenvalues of the linearized system
are correctly preserved, and a reduction in the model stiffness is achieved,
allowing for accurate integration with increased step size. Our methodology is
assessed in detail for a 3-bus system with generation units involving
grid-forming/following converters and synchronous machines, where it allows for
a computational speed-up of up to 100x compared to the original system. Several
standard larger test systems are also considered.
