Powr Angle

[Hameedulla-Ekhlas]

Greeting all,

I have attached one photo which shows the power angle graph. I know when power angle is less than 90 degree, the system is stable. When it is more thant 90 degree it is not stable

the power flow formula is as below

P = Vs x Vr x Sin0 / X


Suppose, if we have a sytem with power angle of 30 degree we call it stable and if the power angle is at 150 degree we say it is not stable. Why?

But according to formula both sin(30) and sin(150) are same.

Hope to make it a little bit clear for me

 

[rcwilson]

I asked the same question in my EE lab years ago and my prof ran me through a series of questions and thought exercises for the answer. I’ll see if I can briefly explain.

At 30 degrees power angle, if a system disturbance occurs and causes the generator's power angle to oscillate a little, it will settle out back at 30 degrees. As it goes to 31 degrees (sin 31 = 0.515, 3% increase) power flow to the external system increases. The added load on the generator increases torque on the turbine which brings the angle back toward 30 degrees, where it settles out.

Look at the same occurrence at 150 degree power angle. A bump occurs and the angle goes to 151. But power output drops about 3% so the turbine's torque can increase the power angle to 152 degrees then 153, 160 .... until it accelerates on past 180 and hopefully pulls back into synch at 30 degrees. Meanwhile, the currents have grown very large because the two voltages went 180 out of phase.

What we are looking for in a system is a stable operating point where the natural tendency in response to a disturbance is a return to the original operating point. It's like balancing a broom on end or hanging from a hook. Both hold the weight directly in line with the support point, but when the broom is bumped and starts to swing, gravity helps the hanging broom settle out and accelerates the balanced broom to the floor.

 

[skeshesh]

Bob explained it very well indeed. It is basically that the system's response is in some form of damped oscillation where the system returns to the base point at a finite time. There's other ways to look at the stability criteria using zeros and poles when you start looking at the system as a transfer function. Looking at it in terms of more abstract math is good fun, but I did enjoy Bob's explanation a lot :grin:

 

[Hameedulla-Ekhlas]

Yes, it is really what I was looking for. Great explaination Bob!