Electrical Engineering: Transient Analysis and Stability Homework

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Electrical Engg.
Transient analysis stability and surge protection
Student Name –
Student ID -
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Solution 1 a) Synchronous Generator:
Equation describing motion of rotor angle and the generator frequency :
2 H dw/dt = J d2θ / dt2
. w = generator frequency
. θ = Rotor angle
H = inertia constant
J =Total moment of inertia
b) Critical Angle = 0 degree
Critical clearing time = 0.4 seconds
Solution 1) c)
a)
Matlab Code :
E = 1.5;
V = 1;
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X = 10;
Pm = 0.6 ;
H = 9.94;
D = 0.16;
f0 = 50;
Pmax = E*V/X;
d0 = asin (Pm/Pmax);
Ps = Pmax * cos (d0);
wn = sqrt (pi*60/H*Ps);
z = D/2*sqrt(pi*60/(H*Ps));
wd = wn * sqrt (1-z^2);
fd = wd / (2*pi);
tau = wd/(2*pi);
th = acos (z);
Dd0 = 10*pi/180;
t = 0:0.01:3;
Dd = Dd0 / sqrt (1-z^2)* exp (-z * wn * t).* sin(wd*t);
d = (d0 + Dd) * 180/pi;
Dw = -wn*Dd0/sqrt(1-z^2)*exp(-z*wn*t).*sin(wd*t);
f = f0+Dw/(2*pi);
subplot (2,1,1);
plot(t,abs(d));
xlabel ('t(sec)');
ylabel('Dela(deg)');
subplot (2,1,2);
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plot(t,abs(f));
xlabel ('t(sec)');
ylabel('Frequency(Hz)');
%% axis([0 3 59.85 60.1]);
Figure 1
Solution 1) c)
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b)
MATLAB Code:
clear all;
clc;
E = 1.5;
V = 1;
X1 = 1;
X2 = 0.2;
X3 = 0.3;
Pm = 0.6 ;
H = 9.94;
Pe1max = E*V/X1;
Pe2max = E*V/X2;
Pe3max = E*V/X3;
delta = 0:0.01:pi;
Pe1 = Pe1max * sin (delta);
Pe2 = Pe2max * sin (delta);
Pe3 = Pe3max * sin (delta);
d0 = asin(Pm/Pe1max);
dmax = pi - asin(Pm/Pe3max);
cosdc = (Pm*(dmax-d0)+Pe3max*cos(dmax)-Pe2max*cos(d0))/(Pe3max-Pe2max);
dc = acos(cosdc);
Pmx = [0 pi-d0]*180/pi;
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Pmy = [Pm Pm];
x0 = [d0 d0]*180/pi;
y0 = [0 Pm];
xc = [dc dc]*180/pi;
yc = [0 Pe3max*sin(dc)];
xm =[dmax dmax]*180/pi;
ym =[ 0 Pe3max*sin(dmax)];
d0 = d0*180/pi;
dmax = dmax * 180/ pi;
dc = dc*180/pi;
x = (abs(d0):0.1:abs(dc));
y = Pe2max*sin(x*pi/180);
y1 = Pe2max*sin(d0*pi/180);
y2 = Pe2max*sin(dc*pi/180);
x = [d0 x dc];
y = [Pm y Pm];
xx = abs(dc) :0.1:abs(dmax);
h = Pe3max*sin(xx*pi/180);
xx = [dc xx dmax];
hh = [ Pm h Pm];
delta = delta*180/pi;
if H ~=0
d0r = d0*pi/180;
dcr=dc*pi/180;
tc = sqrt(2*H*(dcr-d0r)/(pi*50*Pm));
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else
end
fprintf('\n Initial power angle = %7.3f\n',d0);
fprintf('Maximum angle swing = %7.3f\n',dmax);
fprintf('\n Critical clearing angle = %7.3f\n\n',dc);
fprintf('Critical clearing time = %7.3f sec. \n\n',tc);
h = figure;
figure(h);
fill(abs(x),abs(y),'m');
hold;
fill(abs(xx),abs(hh),'c');
plot (abs(delta),abs(Pe1),'k-',abs(delta),abs(Pe2),'r-',abs(delta),abs(Pe3),'g-',abs(Pmx),
abs(Pmy),'r-',abs(x0),abs(y0),abs(xc),abs(yc),abs(xm),abs(ym));
grid;
plot (abs(Pmx),abs(Pmy),'r--',abs(x0),abs(y0),abs(xc),abs(yc),abs(xm),abs(ym));
grid;
xlabel('Power angle (degree)');
ylabel('Electrical power output (pu)');
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Figure 2
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Figure 3
Initial power angle = 23.578
Maximum angle swing = 173.108
Critical clearing angle = 0.000
Critical clearing time = 0.426 sec.
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Solution 2 )
Impediments for adopting renewable energy resources in the existing grid in terms of
transient stability – It does not make the system stable.
Reason : The reason for this is the low amount of stability offered by such systems.
Ways to overcome such impediments to incorporate more renewable energy sources in the
grid :
They can be incorporated if the overall system can be stabilized by use of systems.
Solution 3 )
(1)
s = tf ('s');
G1 = 1/(2*3*s+1);
G2 = 1/(2*5*s+1);
G3 = 1/(2*6*s+1);
F = 1/(0.0625*(1+0.25*s)*(1+0.55*s));
T1 = feedback(G1,F);
T2 = feedback(G2,F);
T3 = feedback(G3,F);
step(T1,'b',T2,'r',T3,'g');
legend('Hs=3','Hs=5','Hs=6');
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Figure 4
Solution 3)
2)
s = tf ('s');
G1 = 1/(2*5*s+0.8);
G2 = 1/(2*5*s+0.9);
G3 = 1/(2*5*s+1.2);
F = 1/(0.0625*(1+0.25*s)*(1+0.55*s));
T1 = feedback(G1,F);
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T2 = feedback(G2,F);
T3 = feedback(G3,F);
step(T1,'b',T2,'r',T3,'g');
legend('D=0.8','D=0.9','D=1.2');
Figure 5
Solution 3) (3) Impact of H and D ( Rotating mass and load ) on frequency :
As the value of H increases, peak value decreases. Change in value of D does not have much
effect on response.
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Reason of reduced Generator inertia constant , H in the grid :
Reduced H gives more peak value and faster response.
References
[1] Nabi, Ghulam, Muhammad Kashif, and Muhammad Tariq. "Hydraulic transient analysis
of surge tanks: Case study of Satpara and Golen Gol Hydropower projects in
Pakistan." Pakistan Journal of Engineering and Applied Sciences (2016).
[2] Shameem, Sk, Sk Nazma, and Ch Rami Reddy. "Improving Transient Stability of a
Distribution Network by using Resonant Fault Current Limiter." International journal of
innovative technologies 6.01 (2018): 0376-0383.
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