  State space is widely used for modeling power systems and analyzing their
dynamics but it is limited to representing causal and proper systems in which
the number of zeros does not exceed the number of poles. In other words, the
system input, output, and state can not be freely selected. This limits how
flexibly models are constructed, and in some circumstances, can introduce
errors because of the addition of virtual elements in order to connect the
mismatched ports of subsystem models. An extension known as descriptor state
space can model both proper and improper systems and is a promising candidate
for solving the noted problems. It facilitates a modular construction of power
system models with flexible choice of ports of subsystems. Algorithms for
mathematical manipulation of descriptor state space models are derived such as
preforming inverse, connection, and transform. Corresponding physical
interpretations are also given. Importantly, the proposed algorithms preserve
the subsystem states in the whole system model, which therefore enables the
analysis of root causes of instability and mode participation. Theoretical
advances are validated by example power systems of varied scales including a
single-inductor or -capacitor system, two-inductor or -capacitor system, and a
modified IEEE 14-bus generator-inverter-composite system.
