Thank you for this exposition on voltage stability. For those who are more interested in this topic, here is some additional information: The stability curve, also referred to the "nose curve" due to its shape, is coming from doing phasor analysis on the simple "generation-transmission-load" curcuit shown in the video. Say that the source, or generator voltage E leads the load voltage V by d radians, and the load current I lags the voltage V by p radians. It can be shown using phasor analysis: Real power = P = VIcos(p) = (EV/X)sin(d) --------- (1) Reactive power = Q = VIsin(p) = (EV/X)cos(p) - V^2/X -------- (2) where X is the reactance of the transmission line. Squaring (1) and (2) and adding, after some manipulation, it can be written (EV/X)^2 = P^2 + (Q + V^2/X)^2 ------------ (3) But Q = Ptan(p), eq. (3) becomes P^2 + P^2 tan^2(p) + 2P tan(p) V^2/X = (EV/X)^2 - (V^2/X)^2 ------------ (4) Also, tan(p) = sin(p) / cos (p), and sin^2(p) + cos^2(p) = 1. Then, with some manipulation, (4) can be written as P^2 + 2P sin(p)cos(p) V^2/X = (V/X)^2 (E^2 - X^2) cos^2(p) -------- (5) Complete the square on the left hand side of (5) (P + sin(p)cos(p) V^2/X)^2 - (V^2/X)^2 sin^2(p) cos^2(p) = (V/X)^2 (E^2 - X^2) cos^2(p) -------- (6) Solve (6) for P to obtain P = -(V^2/X) sin(p) cos(p) + (V/X) cos(p) sqrt(E^2 - V^2 cos^2(p)) -------- (7) The nose curve can be plotted using eq. (7). Source: Power System Dynamics: Stability and Control, by J. Machowski, J. W. Bialek, J. R. Bumby, Chapter 8
There is plenty of literature about power system topics. Since I do not know where you stand, I recommend a search on the internet and you will find what you need.
Think of the resistance of the load being very high. Then the load (i.e. the power dissipated in the load) would be very low. If you reduce the resistance, current increases and because of P = U*I the load increases, right? This is true up to the tipping point described in the lecture.
Thank you for this exposition on voltage stability. For those who are more interested in this topic, here is some additional information:
The stability curve, also referred to the "nose curve" due to its shape, is coming from doing phasor analysis on the simple "generation-transmission-load" curcuit shown in the video. Say that the source, or generator voltage E leads the load voltage V by d radians, and the load current I lags the voltage V by p radians. It can be shown using phasor analysis:
Real power = P = VIcos(p) = (EV/X)sin(d) --------- (1)
Reactive power = Q = VIsin(p) = (EV/X)cos(p) - V^2/X -------- (2)
where X is the reactance of the transmission line. Squaring (1) and (2) and adding, after some manipulation, it can be written
(EV/X)^2 = P^2 + (Q + V^2/X)^2 ------------ (3)
But Q = Ptan(p), eq. (3) becomes
P^2 + P^2 tan^2(p) + 2P tan(p) V^2/X = (EV/X)^2 - (V^2/X)^2 ------------ (4)
Also, tan(p) = sin(p) / cos (p), and sin^2(p) + cos^2(p) = 1. Then, with some manipulation, (4) can be written as
P^2 + 2P sin(p)cos(p) V^2/X = (V/X)^2 (E^2 - X^2) cos^2(p) -------- (5)
Complete the square on the left hand side of (5)
(P + sin(p)cos(p) V^2/X)^2 - (V^2/X)^2 sin^2(p) cos^2(p) = (V/X)^2 (E^2 - X^2) cos^2(p) -------- (6)
Solve (6) for P to obtain
P = -(V^2/X) sin(p) cos(p) + (V/X) cos(p) sqrt(E^2 - V^2 cos^2(p)) -------- (7)
The nose curve can be plotted using eq. (7).
Source: Power System Dynamics: Stability and Control, by J. Machowski, J. W. Bialek, J. R. Bumby, Chapter 8
This is very educational! Great series, thanks a lot
omg! thank you soo much. There's soo little information about these things!
Just thank you
You're welcome!
is there a book i can look up all of this ?
There is plenty of literature about power system topics. Since I do not know where you stand, I recommend a search on the internet and you will find what you need.
Wait so the power increases when you reduce the ohmic resistance of the load? How?
Think of the resistance of the load being very high. Then the load (i.e. the power dissipated in the load) would be very low. If you reduce the resistance, current increases and because of P = U*I the load increases, right? This is true up to the tipping point described in the lecture.
@@georgschett801 Ahh of course! thanks so much for the reply!
the sound is not good I am quite disappointed