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Arrhenius equations with Weibull distribution have been broadly deployed to quantify the loss of life and probability of failure of power transformers. This model is highly nonlinear, and this non-linearity makes it challenging to use this model for grid management and optimization. In this study, equations are linearized using Taylor series expansion to provide a linear formulation for transformer loss of life and probability of failure as a function of ambient temperature and transformer loading. The proposed formulation allows transformer constraints to be incorporated in grid management applications within conventional optimization approaches, such as linear programming, and decreases the calculation burden caused by nonlinearity.

Linear Arrhenius-Weibull Model for Power Transformer Thermal Stress Assessment