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A systematic approach based on linear graph theory is suggested for linear and non-linear state model formulation of a system comprising of a dual-excited synchronous generator, connected to an infinite bus through a transmission line, and controlled by voltage regulator, angle regulator and a speed governor. Viewing the system as an interconnection of five simple subsystems, each being represented in isolation by a directed terminal graph and a set of terminal equations, leads to the generation of a system graph. A minimal state characterization is easily obtained through selecting a maximal forest, getting constraint equations therefrom, and substituting them in suitably arranged terminal equations. The method is applicable in general for any complex system. Besides presenting some of the computed results from the model thus formulated, for comparison with the experimental data available in the literature, investigations in this paper are further directed towards studies aimed at improving the stability regions to their maximum limit and cutting down the rotor copper losses to a minimum level. The effect of system operation in these modes on the relative choice of the three controller parameters is discussed with the help of various parameter-plane stability-limit loci plots.