In the DFIG Tem>0 and S<0 than the mode of operation and speed of the machine is Generator, ωm> ωs Motor, ωm> ωs Generator, ωm< ωs Generator, ωm> ωs

The question seems to be about the operation mode and speed of a Doubly Fed Induction Generator (DFIG).

In a DFIG, the rotor is connected to the grid via a converter which allows for control of the rotor's speed and power factor. The speed of the machine (ωm) and the synchronous speed (ωs) determine the mode of operation.

1. If the torque (Tem) is greater than 0 and the slip (S) is less than 0, the DFIG operates as a generator. This means that it is converting mechanical power into electrical power.

2. If ωm is greater than ωs, the machine is operating above synchronous speed. This is typically the case when the DFIG is operating as a generator.

3. If ωm is less than ωs, the machine is operating below synchronous speed. This is typically the case when the DFIG is operating as a motor, converting electrical power into mechanical power.

So, based on the given conditions (Tem>0 and S<0), the mode of operation would be a generator and the speed of the machine would be ωm> ωs.