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AIM:
To plot the transient of a synchronous machine for small disturbance.
THEORY:
The steady state stability refers to the ability of the power system to remain in synchronism when subjected to small disturbances. It is convenient to assume that the disturbances causing the changes disappear. The motion of the system is free, and stability is assured if the system returns to its original state. Such a behavior can be determined in a linear system by examining the characteristic equation of the system. It is assumed that the automatic controls, such as voltage
Regulator and governor , are not active.
PROBLEM:
A 60 bus synchronous generator having inertia constant H=9.94MJjMVA and a transient reactance X'd=0.3 per unit is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance are marked on the diagram on a common system base. The generator is delivered real power of 0.6 per unit, 0.8 power factor lagging to the infinite bus at a voltage of V=1 per unit.
PROGRAM:
E = 1.35, V= 1.0; H= 9.94; X=0.65; Pm=0.6; D=0.138; fO = 60;
Pmax = E*V /X, d0 = asin(Pm/Pmax) %Max. power
Ps = Pmax*cos(d0) %synchronizing power coefficient
wn = sqrt(pi*60/H*Ps) %undamped frequency of oscillation
z = Dj 2*sqrt(pi*60/ (H*Ps)) %Damping ratio
wd = wn*sqrt(l-z"2), fd = wdj(2*pi) %damped frequency oscill.
tau = Ij(z*wn) %time constant
th = acos(z) %phase angle theta
DdO = 10*pi/ 180; %initial angle in radian
t = 0:.01:3;
Dd = DdOjsqrt(l-z"2)*exp(-z*wn*t).*sin(wd*t + th);
d = (dO+Dd)*180/pi; %load angle in degree
Dw = -wn*DdOjsqrt(l-z"2)*exp(-z*wn*t).*sin(wd*t);
f = fO + Dwj (2*pi); %frequency inHz
figure(I), subplot(2, 1, 1), plot(t, d), grid
xlabel( ‘t, sec’ ), ylabel( ‘delta,degree’)
subplot(2,1,2), plot(t,f), grid
xlabel(‘t, sec’ ), ylabel(f,Hz)
%using initial function
A = [0 1; -wn"2 -2*z*wn]; %wn, z and t are defined earlier
B = [0; 0]; %column B zero-input
C = [1 0; 0 1]; %unity matrix defining o/p y as x1 and x2
D = [0; 0];
DxO = [Dd0; 0]; %zero initial cond., Dd0 is defined earlier
[y,x]= initia1(A, B, C, D, DxO, t);
Dd= x(:, 1); Dw = x(:, 2); %state variables x1 and x2
d = (dO + Dd)*180/pi; %load angle in degree
f = fO + Dw / (2*pi); %frequency in Hz
figure(2), subplot(2, 1,1), plot(t, d), grid
xlabel(‘t, sec’), ylabel(‘delta,degree’)
subplot(2, 1,2), plot(t, f), grid
xlabel(‘t, sec’ ), ylabel( ‘f,Hz’), su bplot( 111)
OUTPUT:
RESULT:
Thus the oscillation of the rotor for the small disturbance is plotted.