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Condition monitoring of power transformers, which are key components of electrical power systems, is essential to identify incipient faults and avoid catastrophic failures. In this paper machine learning algorithms, i.e., nonlinear autoregressive neural networks and support vector machines, are proposed to model the transformer thermal behavior for the purpose of monitoring. The thermal models are developed based on the historical measurements from nine transformers comprised of two 180-MVA units, four 240-MVA units and three 1000-MVA units. The data consist of load profile, tap position, winding indicator temperature (WTI) measurement, ambient temperature, wind speed and solar radiation. The results are validated against field measurements, and it is clearly demonstrated that the alternative algorithms surpass the IEEE Annex G thermal model. An incipient thermal fault identification algorithm is then proposed and successfully used to identify an issue using measurements taken in the field. This algorithm could be used to alert the operator and plan intervention accordingly. [ABSTRACT FROM AUTHOR]