Why Does Increasing Steam Input to an Alternator Increase the Load Angle?

[kuchun]

After going through the chapter of Alternator (i.e Synchronous Generator) I have come to know that if the steam input to the turbine which is coupled to the rotor shaft of the alternator is increased the load angle will increase.. but what is the reason behind this ? I want to know both mathematical and physical explanation. What is the significance of load angle and why is it also called the torque angle ? Please help me to understand these things.
Thank you

 

[gerbi]

After going through the chapter of Alternator (i.e Synchronous Generator) I have come to know that if the steam input to the turbine which is coupled to the rotor shaft of the alternator is increased the load angle will increase.. but what is the reason behind this ? I want to know both mathematical and physical explanation. What is the significance of load angle and why is it also called the torque angle ? Please help me to understand these things.
Thank you

Considering a synchronous generator connected to a power grid - we have fixed frequency and voltage of our machine. Also the excitation voltage is assumed const.

Now, if You change the amount of steam send to turbine You will change the torque driving the generator. Torque of a generator can be described as:

(1) T=c*((Vs*Vr)/Xd)*sin(theta)

T-torque; c-some constant; Vs-stator voltage; Vr-rotor (excitation) voltage; theta-load angle
Assuming as said above, change of driving torque will affect the load angle (theta).

So much for a math. Now, load angle is a angle between the stator and rotor fields. In general the theta can change from -90 to + 90 deg. In practice it's much smaller (20-40 deg at rated load).
The load angle is very important - it's closely connected with real and imaginary power generated by a generator. It must be kept in allowed range of each individual type of generator (to stay in synchronism and not allow excessive stator core end-region losses). There is much more about this to say..

Physical explanation (in some BIG simplification):
Everyone knows how to calculate force on a wire in a magnetic field:

(2) F=c*I*B*sin(alfa)
F-force; c-some constant; I-current caried by a conductor; B-induction of a field; alfa-angle between field vector and wire with a current

We can treat synch. generator like a rotating wire excited with a current and rotating magnetic field (both rotating same direction and speed - in synchronism).

This equation (2) can be transferred to a rotating system - then we'll have torque instead of a force. Maximum torque can be observed at +/- 90 deg (just like maximum torque of a generator). In this rotating system (much simplified!) we provide driving torque to the wire. The angle between wire and magnetic field will change (load-torque angle) so bigger torque (2) will counteract driving torque. It's all fine when alfa is in +/-90 deg range (synch. mode). I hope that is clear.

Last thing, power and torque are connected:

(3) P=T*omega

P-power; T-torque; omega-rotating speed of machine (fixed by grid frequency)

I hope now it's clear why load angle is called torque angle (it depends on the load thus torque).