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This paper deals with the determination of large synchronous machine characteristic quantities using an extended 2D-finite element method and based on the knowledge of the geometry and of the physical properties of the electrical and magnetic circuits of the machine. In this respect sudden no-load three phase short-circuits and short-circuits in the quadrature axis under load conditions at cosphi = 0 are simulated in rotation using a numerical, virtual test platform. The saturation effect, the eddy currents in the damper circuit and in the rotor solid iron parts are taken into account. The results of these two tests lead to all characteristic quantities in both axis of the machine. Other tests can be performed on this numerical test platform (standstill frequency response, DC decay, low speed, symmetrical and asymmetrical load tests), which can also be used as a design optimization tool. Comparisons between calculations and measurements for three large existing units (turbo-generators and hydro-generators) are presented