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In this paper, a recently-developed algorithmic method of deriving the state equations of power systems containing power electronic components is described. Therein the system is described by the pertinent branch parameters and the circuit topology; however, unlike circuit-based algorithms, the difference equations are not implemented at the branch level. Instead, the composite system state equations are established. A demonstration of the computer implementation of this algorithm to model a variable-speed, constant-frequency aircraft generation system is described. Because of the large number of states and complexity of the system, particular attention is placed on the development of a model structure which provides optimal simulation efficiency.