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 (also known as implicit state space, generalized state space, singular 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 inductor or capacitor systems, and modified IEEE 14-bus, 68-bus, and 118-bus generator-inverter-composite systems.