Load Angle or Power Angle and It’s Significance
Load Angle in synchronous machine is defined as the angle between the filed mmf or flux and the resultant air gap mmf or flux. Load angle and power angle are same thing which are used synonymously.
There are basically three different types of flux in a rotating electrical machine: Stator flux, Rotor flux and Resultant air gap flux. Resultant air gap flux is the net flux in the air gap of machine due to combined action of stator as well as rotor flux. In Synchronous machine, we are well aware of the term Armature Reaction which affects the field (field winding is wound on the rotor for synchronous machine) generated flux.
Load angle is also defined as the angle between the no load excitation voltage E_{f} and terminal voltage V_{t}. Note that this definition is having no difference with the previous definition. How? This is because; under no load condition the emf will be induced in the armature or stator winding just because of the field flux or rotor flux Ø_{f}. This emf will be lagging by 90 degree with the field flux.
Always remember that the generated emf always lags by 90 degree the flux that generates it. Here emf is induced by the field flux; hence it lags the field flux by 90 degree. |
Terminal voltage is the voltage across the armature terminal which is induced due to the resultant air gap flux. Thus terminal voltage V_{t} will lag behind the resultant air gap flux Ø_{r} by 90 degree. Thus the angle between E_{f} and V_{t} will be equal to the angle between field flux and resultant air gap flux. A simple phasor diagram showing the relation between the E_{f}, V_{t}, Ø_{f} and Ø_{r}.
Power angle can also be defined in terms of armature or stator mmf and resultant air gap mmf. In a synchronous generator, the stator mmf lags behind the resultant air gap mmf. This angle of lag is called load or power angle.
Significance of Load Angle
In synchronous machine, load angle is a very important parameter. Let us first understand the physical significance of this parameter before going into some sort of mathematical formula or expression. As discussed earlier in this post, load angle is the angle between the field flux and the resultant air gap flux. This means, as the mechanical power input to the synchronous generator is increased through prime mover, the field poles will be dragged ahead of the stator pole or flux. This in turn will increase the load angle. An increased load angle will cause electromagnetic torque to increase. Since the electromagnetic torque opposes the prime mover torque in synchronous machine, as soon as this torque balances the prime mover torque, the mechanical input will be converted to electrical output. Thus increasing the load angle increases the power output.
The power output of a synchronous generator is given as
P = (E_{f}V_{t}Sinδ) / X_{s}
From the above expression, it is clear that increase in angle δ increases the power output provided field excitation and generator terminal voltage is kept constant. This is the reason, load angle is also known as power angle. Now you might think, can we keep on increasing the load angle to increase the generator output?
No, we cannot. Why? This is because if we increase the angle δ beyond 90 degree, the generator output will fall below its maximum output of (E_{f}V_{t})/ X_{s}. Since the electrical output of generator has decreased while the mechanical input is still more, the generator will lose synchronism. Thus the steady state stability is affected by the load angle.
could you explain the part where you said ” An increased load angle will cause electromagnetic torque to increase. Since the electromagnetic torque opposes the prime mover torque in synchronous machine, as soon as this torque balances the prime mover torque, the mechanical input will be converted to electrical output”…
I’m trying hard to understand this but missing out something. Would really help if you elaborate it a bit.
Thank You
See, in turbo generator the mechanical input is converted into electrical power. But how this mechanical energy is converted into electrical power? The idea is there must be some electrical happening inside the generator. This is elecrical torque. The torque developed by the turbine is counterbalanced by the electragnetic torque.
When there is an increase in load angle, this means the steam input to the turbine has increased. Therefore the electromagnetic torque must also increase to counter balance it and hence maintain the synchronous speed.
In view of the above, the electrical power(totquexspeed) will increase.
when steam input to turbine is increased, the torque of the turbine increases because of which the load angle increases. At this point the electromagnetic torque is created in damper windings right? And this torque that is developed in damper windings, will oppose the prime mover torque right?
Please correct me if i’m wrong
Thank you
Electromagnetic torque is developeed in main winding. You can read Torque equation for better understanding.
Please check the statement just after phasor diagram stating that “Power angle can also be defined in terms of armature or stator mmf and resultant air gap mmf. In a synchronous generator, the stator mmf lags behind the resultant air gap mmf. This angle of lag is called load or power angle”.
This sounds wrong. Load angle is between rotor mmf(main field mmf) and air gap(resultant) mmf. Stator mmf and rotor mmf are not same in magnitude to give resultant exactly at mid of angle between them. Kindly check and verify.
Thank you for asking. The definition has been checked and is correct. However, load angle is also defined as the angle between the resultant air gap mmf and rotor mmf.For both the definition, the equation for torque will change accordingly.