Can a synchronous machine have a negative torque angle, and what does this imply?

A synchronous machine can indeed have a negative torque angle. When the torque angle is negative, it indicates that the rotor of the machine is lagging behind the stator's magnetic field rather than leading it, which occurs when the machine operates in certain conditions, particularly while supplying active power to the grid or a load.

In this scenario, the machine is actively delivering power to the system. When the torque angle is negative, the machine is still functioning as a generator but is operating under a specific condition where the rotor's magnetic field is not in phase with that of the stator. This implies that the synchronous machine is absorbing active power from the system rather than supplying it.

Understanding the relationship between torque angle, power factor, and reactive power absorption is crucial. Typically, a positive torque angle results in the machine supplying reactive power to the grid, while a negative angle suggests it's absorbing active power while potentially supplying reactive power depending on the depth of the negative angle and the load characteristics.