  This paper proposes to analyze the motion stability of synchro-nous generator
power systems using a Lagrangian model derived in the configuration space of
generalized position and speed. In the first place, a Lagrangian model of
synchronous generators is derived based on Lagrangian mechanics. The
generalized potential energy of inductors and generalized kinetic energy of
capacitors are defined. The mechanical and electrical dynamics can be modelled
in a unified manner through constructing a Lagrangian function. Taking the
first benchmark model of subsynchronous oscillation as an example, a Lagragian
model is construct-ed and numerical solution of the model is obtained to
validate the accuracy and effectiveness of the model. Compared with the
traditional EMTP model in PSCAD, the obtained Lagrangian model is able to
accurately describe the electromagnetic transient process of the system.
Moreover, the Lagrangian model is analytical, which enables to analyze the
motion stability of the system using Lyapunov motion stability theory. The
Lagrangian model can not only be used to discuss the power angle stability, but
also used for analyzing the stability of node voltages and frequency. It
provides the feasibility for studying the unified stability of power systems.
