  This paper deals with the joint reduction of dynamic states (internal states
of generator, solar, and loads, etc) and algebraic variables (states of the
network e.g., voltage and phase angles) of a nonlinear differential-algebraic
equation (NDAE) model of power networks. Traditionally, in the current
literature of power systemmodel order reduction (MOR), the algebraic
constraints are usually neglected and the power network is commonly modeled via
a set of ordinary differential equations (ODEs) instead of NDAEs. Thus,
reduction is usually carried out for the dynamic states only and the algebraic
variables are kept intact. This leaves a significant part of the system's size
and complexity unreduced. This paper addresses this aforementioned limitation,
by jointly reducing both dynamic and algebraic variables. As compared to the
literature the proposedMOR techniques herein are endowed with the following
features: (i) no system linearization is required, (ii) requires no
transformation to an equivalent or approximate ODE representation, (iii)
guarantee that the reduced order model to be NDAE and thus preserves the
differential-algebraic structure of original power system model, and (iv) can
seamlessly reduce both dynamic and algebraic variables while maintaining high
accuracy. Case studies performed on a 2000-bus power system reveal that the
proposedMOR techniques are able to reduce system order while maintaining
accuracy
