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Until now, different assumptions have been made during the determination of model parameters of synchronous machines from the characteristic quantities obtained from measurements (or calculations). This can lead to considerable errors in the results of simulation for certain machines. The paper shows how one can analytically compute these model parameters rigorously from characteristic quantities, without making any simplifying assumptions or iteration. The pertinent additional measurements are given. Comparisons in four examples demonstrate the extent to which the common assumptions can affect modelling a synchronous machine.