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Synchronous machines, that is, practically all generators together with synchronous motors and synchronous compensators, are the most important power system components in the analysis of electromechanical and electromagnetic dynamics in power systems. Power system modelling (PSM) in general is an area of ongoing interest in the transmission management and control systems community. Continual development is driven by the traditional task of model maintenance and management to achieve increased accuracy with the expenditure of fewer resources . Derived higher order models are simplified because they are very difficult to use for simulations, analysis and control. Simplification is therefore necessary and must be done methodically; this makes an understanding of the underlying assumptions imperative. Traditional methods of simplification include linearization for small signal stability analyses and reduced order procedures used in transient stability analyses [4-5]. This paper presents three of the existing synchronous machine mathematical models and the assumptions made in the process of their simplification, and introduces methods which are used to solve these models numerically for stability studies assessment.