SELECTIVE HARMONICS ELIMINATION

 

SELECTIVE HARMONICS ELIMINATION

To Eliminate the 3^rd, 5^th and 7^th Harmonic Component from the Signal.

Software Used: MATLAB R2018a

Theory:

Using selective harmonic elimination (SHE) as a modulation technique allows the switching of the inverter to selectively eliminate intrinsic harmonics. The fundamental component of the AC output voltage can also be adjusted within a desirable range. Since the AC output voltage obtained from this modulation technique has an odd half and odd quarter-wave symmetry, even harmonics do not exist. Any undesirable odd (N-1) intrinsic harmonics from the output waveform can be eliminated.

Actually, in Selective Harmonic Elimination (SHE), harmonics are not removed but just are replaced. It means that when you calculate the angles using, SHE equations and some numerical method techniques, the solutions are approximated values.

MATLAB Code:

clc;

clear all;

m1=0:0.01:1;

for ii=1:101

alpha1=40*pi/180;

alpha2=51*pi/180;

alpha3=80*pi/180;

for i=1:100

T=[m1(ii)*pi/4 0 0 ]';

F=[cos(alpha1)-cos(alpha2)+cos(alpha3);cos(3*alpha1)-cos(3*alpha2)+cos(3*alpha3);cos(5*alpha1)-cos(5*alpha2)+cos(5*alpha3)];

dF=2*[-sin(alpha1) +sin(alpha2) -sin(alpha3) ;-3*sin(3*alpha1) +3*sin(3*alpha2) -3*sin(3*alpha3) ;-5*sin(5*alpha1) +5*sin(5*alpha2) -5*sin(5*alpha3) ];

dalpha=(inv(dF))*(T-F);

alpha=[alpha1;alpha2;alpha3]*180/pi

dalpha*180/pi

alpha1=alpha1+dalpha(1);

alpha2=alpha2+dalpha(2);

alpha3=alpha3+dalpha(3);

if dalpha>-1e-15 & dalpha<1e-15

    break;

end

end

alpha11(ii)=alpha1*180/pi;

alpha22(ii)=alpha2*180/pi;

alpha33(ii)=alpha3*180/pi;

end

plot(m1,alpha11);

hold on;

plot(m1,alpha22);

hold on;

plot(m1,alpha33);

ylim([0 90]);

grid on;

xlabel('Modulation Index(M)');

ylabel('Swiching Angles(deg)');

title('Switching Angle Vs Modulation Index');

 

Waveforms:

Observations:

If we consider alpha as far means alpha 1 as 60, alpha 2 as 70 and alpha 3 as 72, iteration does not converge so while doing this kind of technique, we have to consider close to values like 3 harmonics we want to remove so take 30,60,90 still try with some more values close ad accurate to get the curve smooth, so I took 40,51,80 with which I got the smooth curve.

Conclusion:

Hence the Switching angles and modulation index curve is plotted and the selective harmonic elimination is studied.