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Experience and applications of currently available methods for online monitoring and diagnostics of high-voltage power apparatus are briefly reviewed. Based on dielectric physics, a new definition of dielectric loss factor with harmonics emphasis is proposed to evaluate the operational conditions of power apparatus on a more reasonable basis, along with corresponding digitised algorithms. Two approaches, namely the decoupling algorithm and the approximating algorithm, are presented to implement the methodologies with the new definition of dielectric loss factor. The impact of background noise and power-frequency fluctuation on estimation accuracy are analysed by computer simulations, showing better application qualities of the approximating algorithm than the decoupling algorithm. A comprehensive strategy of simultaneous monitoring of sum current, dielectric loss factor, resistive current and capacitive current is recommended to give an effective assessment and diagnosis.