The load angle primarily used for synchronous generator and torque angle is the same thing for synchronous motor. Power angle is also same in context of synchronous machines but it is more generic – also used in power transmission line.
Let me explain what they are:
Load angle (or Torque angle): For a synchronous generator, the magnetic field rotates at synchronous speed and the rotating magnetic field is created in the stator. These two fields are not fully aligned. The stator field lags the rotating field. This lagging expressed in angle is called load angle. The power developed by the generator is directly proportional to sine of this angle. This angle plays an important role for the stability of the generator. If the angle goes beyond 90º, the generator becomes unstable. This may happen when sudden change of large load occurs or fault sustains longer time. The generator instability is one of reason for massive blackout in case of major fault occurs in transmission line.
For the case of synchronous motor, the angle is called torque angle and the rotating field lags the stator field in this case.
Power angle: For a generator, the power angle is the difference between the generator induced voltage and the generator terminal voltage. The value of the power angle is same as the load angle. So, in context of generator, power angle and load angle mean same thing.
For the case of transmission line the power angle is the angle between the angles of the voltages at two different points (bus). The transfer of power between the two points of power system is proportional to the sine of this angle.
Though there is a distinct difference between these three terms, they are used anonymously in many cases in power system.
Power Angle Equation of a Generator is as follows.
P = (V*E/Xd )Sin D
P – Power generated
V – Terminal voltage
E – Generated Emf
Xd – Generator reactance
D – Delta, Power angle (The direct angle between rotor load axis and No load axis
The characteristic between Power vs D is Power angle characteristic of a generator.