solar system

The potential for solar system is enormous, foe instance, it is estimated that about 1% of the area of sahara Desert covered with solar thermal power plant would theoretically be sufficient to meet the entire global demand of electrical energy , therefor the solar thermal power system will  play an important rule in the global future electricity supply, the largest cost involve in solar thermal power plant is the initial capital cost to build the plant rather than operating costs.solar thermal  plant have the added advantages over photovoltaic electric generation in that it is possible to generate electricity during unfavorable weather and its at night using heat exchange system the vast amount of heat transfer fluid circulating in the solar field already represent a considerable storage capacity which can bridge short term cloudy case.

however ,due to poor part load behavior of solar thermal power , such power plant should been installed in region with a minimum of around 2000 full load hours . this is the case in region with direct normal irradiance of more than 2000kwh/meter square ,these irradiance values can be found in the earth sunbelt, thermal storage can increase thes number of full load hours significantly.

code for the generation of signals in matlab

Dear friends generation of signals in matlab is very simple method once you understand the code you can easily plot any kind of signal for your engineering works etc , here is some code and prepare plot signals along with diagram, read it carefully and try to understand each and every point of it,

PLOTTING A CONTINUOUS TIME COMPLEX EXPONENTIAL SIGNAL

 

c=10;

f=5;

ph=pi/2;

T=1/f;

t=0:T/40:10*T; %10 cycles

x=c*cos(2*pi*f*t+ph);

a=input('enter 1,0 or -1;a='); %enter either positive, negative, zero

y=exp(a*t);

z=y.*x;

plot(t,z),

xlabel('t'),

ylabel('z'),

title('PLOTTING A CONTINUOUS TIME COMPLEX EXPONENTIAL SIGNAL'),

grid on

 

   

TASK-3:

TO PLOT A PIECE-WISE SIGNAL

%for first segment

t0=-2:0.01:0;

x0=t0;

%for second segment

t1=0:0.01:3;

x1=4*ones(size(t1));

%for third segment

t2=3:0.01:4;

x2=-3*t2+4;

x=[x0 x1 x2 ];

t=[t0 t1 t2 ];

plot(t,x,'red','linewidth',3);

xlabel('time');

ylabel('x(t)');

title('PLOTTING PIECEWISE CONTINUOUS TIME SIGNAL');

axis([-3 4 -10 5]);

grid on;

 

TASK-4:

TIME TRANSFORMATION OFF A PIECE WISE SIGNAL

%for first segment

t0=-2:0.01:0;

x0=t0;

%for second segment

t1=0:0.01:3;

x1=4*ones(size(t1));

%for third segment

t2=3:0.01:4;

x2=-3*t2+4;

x=[x0 x1 x2 ];

t=[t0 t1 t2 ];

subplot(2,1,1),

plot(t,x,'red','linewidth',5), 

xlabel('time'),

ylabel('x(t)'),

title('TIME TRANSFORMATION OF CT SIGNAL(ORIGINAL SIGNAL)'),

grid on,

axis([-4 8 -10 5]);

%TIME TRANSFORMATION (Shifting, Scaling, Reversal)

t4=-2*t+4;

subplot(2,1,2),

plot(t4,x,'black','linewidth',5),

xlabel('time'),

ylabel('x(t)'),

title('TIME TRANSFORMATION OF CT SIGNAL(TRANSFORMED SIGNAL)'),

grid on,

axis([-4 8 -10 5]);

 

TASK-5:

3D PLOT OF  CONTINUOUS TIME EXPONENTIAL SIGNAL

t=0:0.0001:10;

x=20*exp(i*5*t);

subplot(2,2,1),

plot(t,real(x)),

xlabel('time'),

ylabel('real part'),

title('PLOTTING REAL PART');

subplot(2,2,2),

plot(t,imag(x)),

xlabel('time'),

ylabel('imag part'),

title('PLOTTING IMAGINARY PART');

subplot(2,2,3),

plot(t,x),

xlabel('time'),

ylabel('x'),

title('PLOTTING(X)');

subplot(2,2,4),

plot3(real(x),imag(x),t),

xlabel('real part'),

ylabel('imag part'),

zlabel('time'),

title('3D PLOT OF A CONTINUOUS TIME SIGNAL');

 TASK-6:

A)PLOTTING  CONTINUOUS TIME SQUARE WAVE USING FOURIER SERIES

B)PLOTTING CONTINUOUS TIME TRIANGULAR WAVE USING FOURIER SERIES

% Square Wave

t=-10:0.001:10;

dc=1/2;

sum=0;

for k=1:2:200;

    sum=sum+(3/(k*pi))*sin(k*t);

end

x=sum+dc;

subplot(2,1,1),

plot(t,x),

xlabel('time'),

ylabel('magnitude'),

title('square wave'),

 

%Triangular Wave

t=0:0.01:5;

sum=0;

for k=1:2:200;

    sum=sum+(-16/(k^2*pi^2))*cos(6*pi*k*t);

end

subplot(2,1,2),

plot(t,sum),

xlabel('time'),

ylabel('magnitude'),

title('triangular wave')

 

 

 

TASK-7:

SOLVING DERIVATIVES, INTEGRALS & DIFFERENTIAL EQUATIONS

% DERIVATIVE

syms x a b c f 

f=3*x^3-4*x^2+6*x-3;

a=diff(f,x)

b=diff(a,x)

c=diff(b,x)

RESULT:

%a = 9*x^2 - 8*x + 6

%b = 18*x - 8

%c = 18

% PARTIAL DERIVATIVE

f=x^2*y+x*y^3-x^3+y^2;

a=diff(f,x)

b=diff(f,y)

RESULT:

%a = - 3*x^2 + 2*x*y + y^3

%b =  x^2 + 3*x*y^2 + 2*y

%INTEGRALS

PART-A:

f=3*x^3-4*x^2+5*x-3;

a=int(f,x)

b=int(f,x,0,5)

RESULT:

% a = (3*x^4)/4 - (4*x^3)/3 + (5*x^2)/2 - 3*x

% b = 4195/12

PART-B:

f=cos(x)*sin(y);

a=int(f,x,pi/2,pi)

b=int(a,y,0,2*pi)

RESULT:

 % a = -sin(y)

 % b = 0

%DIFFERENTIAL EQUATION

PART-A:

d=dsolve('D2y+3*Dy+2=sin(t)','t')

RESULT:

% d =C18 - (2*t)/3 - (3*cos(t))/10 - sin(t)/10 + C19/exp(3*t) + 2/9

PART-B:

f=dsolve('3*D2y+4*Dy=sin(t)','t')

RESULT:

%f =C25 - (4*cos(t))/25 - (3*sin(t))/25 + C26/exp((4*t)/3)

PART-C:

g=dsolve('D2y+2*Dy+3=sin(x)','y(0)=0','x')

RESULT:

%g =C30/exp(2*x) - (3*x)/2 - (2*cos(x))/5 - sin(x)/5 - C30 + 2/5

TASK-8:

EVALUATING LAPLACE TRANSFORM AND Z-TRANSFORMS

% LAPLACE TRANSFORM

>> syms f a t F  C b

f=exp(-a*t)*heaviside(t); 

// heaviside(t), 0 for t<0, 1 for t>0 and 0.5 for t==0

F=laplace(f)

RESULT:

% F = 1/(a + s)

>> syms x h t X H Y y

x=sin(t);

h=10*exp(10*t);

X=laplace(x)

H=laplace(h)

Y=H*X;

y=ilaplace(Y) // inverse laplace 

RESULT:

% X = 1/(s^2 + 1)

%H  = 10/(s - 10)

%y  =(10*exp(10*t))/101 - (10*cos(t))/101 - (100*sin(t))/101

% z-transform

>>syms x h X H Y y a n

x=a^n;

h=b^(-n);

X=ztrans(x)

RESULT:

% X = -z/(a - z)

TASK-9:

DISCRETE TIME SIGNAL 

PLOTTING

 % DISCRETE TIME SEQUENCE

n=-4:4;

x=[9 1 -2 4 -5 6 -1 7 -8];

stem(n,x);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT Sequence');

axis([-5 5 -10 10]);

 

% DISCRETE TIME EXPONENTIAL SIGNAL (n>=0)

% case 01(a>1)

c=2;

a=5;

n=0:15;

x=c*a.^n;

subplot(3,2,1);

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when a>1');

grid on;

%case 02(0<a<1)

c=2;

a=0.5;

n=0:15;

x=c*a.^n;

subplot(3,2,3);

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when 0<a<1');

grid on;

%case 03(a=1)

c=2;

a=1;

n=0:15;

x=c*a.^n;

subplot(3,2,5)

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when a=1');

grid on;

%case 04(a<-1)

c=4;

a=-2;

n=0:60;

x=c*a.^n;

subplot(3,2,2);

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when a<-1');

grid on;

%case 05(-1<a<0)

c=2;

a=-0.5;

n=0:30;

x=c*a.^n;

subplot(3,2,4);

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when -1<a<0');

grid on;

%case 06(a=-1)

c=2;

a=-1;

n=0:15;

x=c*a.^n;

subplot(3,2,6)

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when a=-1');

grid on;

 

% DISCRETE TIME EXPONENTIAL SIGNAL (n<=0)

% case 01(a>1)

c=2;

a=5;

n=-15:0;

x=c*a.^-n;

subplot(3,2,1);

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when a>1');

grid on;

%case 02(0<a<1)

c=2;

a=0.5;

n=-15:0;

x=c*a.^-n;

subplot(3,2,3);

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when 0<a<1');

grid on;

%case 03(a=1)

c=2;

a=1;

n=-15:0;

x=c*a.^-n;

subplot(3,2,5)

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when a=1');

grid on;

%case 04(a<-1)

c=4;

a=-2;

n=-60:0;

x=c*a.^-n;

subplot(3,2,2);

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when a<-1');

grid on;

%case 05(-1<a<0)

c=2;

a=-0.5;

n=-30:0;

x=c*a.^-n;

subplot(3,2,4);

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when -1<a<0');

grid on;

%case 06(a=-1)

c=2;

a=-1;

n=-15:0;

x=c*a.^-n;

subplot(3,2,6)

stem(n,x,'linewidth',2);

xlabel('time(sampled)');

ylabel('magnitude');

title('DT exponential signal when a=-1');

grid on;

 

TASK-10:

DISCRETE TIME CONVOLUTION  

n0=0:20;

x=5*(-0.5).^n0;

n1=-10:5;

h=(2/3).^n;

n2=-20:10;

y1=conv(x,h);

y=y1(1:length(n2));

subplot(3,1,1);

stem(n0,x);

xlabel('time(sampled)');

ylabel('magnitude x(n)');

title('input signal');

grid on;

subplot(3,1,2);

stem(n1,h);

xlabel('time(sampled)');

ylabel('magnitude h(n)');

title('transfer function h(n)');

grid on;

subplot(3,1,3);

stem(n2,y);

xlabel('time(sampled)');

ylabel('magnitude y(n)');

title('output signal');

grid on;

 

TASK-11:

CONTINUOUS TIME CONVOLUTION  

t=0:0.01:10;

x=ones(1,length(t));

h=2*exp(-1*t);

y1=conv(x,h)*0.01; //multiplying with step size

y=y1(1:length(t));

figure(1);

subplot(3,1,1);

plot(t,x);

xlabel('time');

ylabel('x(t)');

title('convolution of continuous time signal');

subplot(3,1,2);

plot(t,h);

xlabel('time');

ylabel('h(t)');

subplot(3,1,3);

plot(t,y);

xlabel('time');

ylabel('y(t)');

title('convolved signal')

grid on;

 

PLOTTING A CONTINUOUS TIME SINUSIOD

To plot a continuous time sinusiodal copy this code and paste it in installed matlab sofware, run the program you will get wave given below in the diagram.

%PART-A

a=10;

f=1000;

ph=pi/2;

T=1/f;

t=0:T/40:10*T; %10 cycles

x=a*sin(2*pi*f*t+ph);

plot(t,x),

xlabel('t'),

ylabel('x'),

title('PLOTTING A CONTINUOUS TIME SINUSIOD'),

grid on

%PART-B

a=10;

f=1000;

ph=pi/2;

T=1/f;

t=0:T/40:10*T; %10 cycles

x=a*cos(2*pi*f*t+ph);

plot(t,x),

xlabel('t'),

ylabel('x'),

title('PLOTTING A CONTINUOUS TIME SINUSIOD'),

grid on