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A direct finite element method for the simulation of the steady state load operating point of a synchronous generator is introduced. The terminal constraints of the generator under load are conveniently expressed in terms of the system state vector. This makes it possible to solve the finite element equations along with the terminal constraints in a single run, hence avoiding unnecessary iterations. The method presented is applicable to both turbo- and waterwheel generators in so far as saliency is concerned. However, since a two dimensional analysis has been adopted, it is expected that the prominent end region effect will be more noticeable in short stack hydro units.