Electric torque analysis (ETA) is a widely-used technique to study the damping torque of the oscillation stability in power systems. Energy dissipation method (EDM) as an alternative method could estimate the damping of the oscillation stability based on the dissipation coefficient of energy flowing in the respective branches computed by the data from the wide area measurement system (WAMS). In this paper, the consistency of the energy flow dissipation coefficient estimated by EDM and damping torque obtained theoretically from ETA is rigorously proven, in both the single machine infinite bus (SMIB) power system and the multi-machine power system, regardless of the model complexity of the generator. Finally, the theoretical consistency is validated by time domain simulations in two typical study cases. Clear physical explanations of the derived tracking functions can be identified for the monitoring and analysis of various oscillations associated with power electronic converter- connected systems in further research.