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Is there a way or formula which can let us to calculate the counter torque at a generator? If the generator rotor is rotating at a constant speed, does that mean the counter torque is equal to the applied torque?

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For your second question - generally - yes. Constant speed means no acceleration. Acceleration is proportional to the torque. Acceleration zero means torque (sum of total torques) zero. As for the first one, you can use an energy equilibrium equation: $$E_{electrical}=E_{mechanical}$$ $$E_{electrical}=V\cdot I$$ $$E_{mechanical}=\tau\cdot\omega$$ Plus applicable loses. Here V and I are voltage and the current, tau and omega are the torque and angular velocity.
(Well, strictly speaking these are not energies, but power, but since we are interested in a momentary values, the equality still valid).

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