% PWM Examples of three-phase Inverter--AC Output
% This file demonstrates the AC output of a PWM inverter for different
% modulation indeces. The modulation index is incremented every time clicking the left
% mouse button on the figure. Click the right mouse button to stop.

% The file contains two independent cells. The first cell dipicts the
% control signals of the inverter and the phase voltages.

% The second cell gives the output harmonics as the user changes the 
% modulation index.

%% Control signals and Phase Voltage v. Modulation index
%Enter the frequency modulation index below.
close all;clear all;clc
%Data
mf=9;%frequency modulation index: Odd multiple of 3.

%Calculations
fr=1;%reference frequency
fc=mf*fr;%carrier frequency
t=0:(1/80/fc):1/fr;%normalized time
tp=360*t;%Degrees
ph=0*pi/180;%phase shift for visual effect
tha=2*pi*fr*t+ph;thb=2*pi*fr*t-2*pi/3+ph;thc=2*pi*fr*t+2*pi/3+ph;%argument of phase a, b, and c reference sine

trc=2*asin(sin(2*pi*fc*t+mf*ph))/pi;%carrier
%
% Plot Carrier and the three reference signals
%
figure
b=1;
m=0;
while b==1
    vra=m*sin(tha);vrb=m*sin(thb);vrc=m*sin(thc);%Reference waveforms
    ga=(vra>=trc);%Gate signal for phase a
    gb=(vrb>=trc);%Gate signal for phase b
    gc=(vrc>=trc);%Gate signal for phase c
    
    vab=ga-gb;vbc=gb-gc;vca=gc-ga;%line-to-line voltage

    subplot(4,2,1)
    plot(tp,trc,'k',tp,vra,'r',tp,vrb,'b',tp,vrc,'g')
    set(gca,'PlotBoxAspectRatio',[5,1,1])
    axis([0 360 -1.5 1.5])
    line([0 360],[0 0],'Color','k','LineStyle','--')
    title(['Freq. Mod. Indx, m_f=',num2str(mf),'; Ampl. Mod. Indx, m=',num2str(m)])
    %legend('Carrier','phase a','phase b','phase c','Location','SouthOutside','Orientation','Horizontal')

    subplot(4,2,3)
    plot(tp,ga,'r')
    line([0 360],[0 0],'LineStyle','--','Color','k')
    axis([0 360 0 1.2])
    title('Phase a Gate Signal')
    xlabel('Degs')
    
    subplot(4,2,5)
    plot(tp,gb,'b')
    line([0 360],[0 0],'LineStyle','--','Color','k')
    axis([0 360 0 1.2])
    title('Phase b Gate Signal')
    xlabel('Degs')
   
    subplot(4,2,7)
    plot(tp,gc,'g')
    line([0 360],[0 0],'LineStyle','--','Color','k')
    axis([0 360 0 1.2])
    title('Phase c gate Signal')
    xlabel('Degs')
    
    
    subplot(4,2,4)
    plot(tp,vab,'r')
    line([0 360],[0 0],'LineStyle','--','Color','k')
    axis([0 360 -1.2 1.2])
    title('Vab')
    xlabel('Degs')
    
    subplot(4,2,6)
    plot(tp,vbc,'b')
    line([0 360],[0 0],'LineStyle','--','Color','k')
    axis([0 360 -1.2 1.2])
    title('Vbc')
    xlabel('Degs')
    
    subplot(4,2,8)
    plot(tp,vca,'g')
    line([0 360],[0 0],'LineStyle','--','Color','k')
    axis([0 360 -1.2 1.2])
    title('Vca')
    xlabel('Degs')
                
    
    if m<1.5; m=m+0.1;else;m=m+0.5;end
    [x,y,b]=ginput(1);
    if m>30; b=0; end
end

%% Harmonic Output 
% 
    
clear all;close all;clc
mf=21;%Frequency modulation index: Odd multiple of 3.

%Calculations
fr=1;%reference frequency
fc=mf*fr;%carrier frequency
harmn=0:3*mf+5;%Harmonic numbers to be plotted
t=0:(1/60/fc):1/fr;%normalized time
tp=360*t;%Degrees
ph=-120*pi/180;%phase shift for visual effect
tha=2*pi*fr*t+ph;thb=2*pi*fr*t-2*pi/3+ph;thc=2*pi*fr*t+2*pi/3+ph;%argument of phase a, b, and c reference sine

trc=2*asin(sin(2*pi*fc*t+mf*ph))/pi;%carrier

figure
b=1;
m=0;
while b==1
    vra=m*sin(tha);vrb=m*sin(thb);vrc=m*sin(thc);%Reference waveforms
    ga=(vra>=trc);%Gate signal for phase a
    gb=(vrb>=trc);%Gate signal for phase b
    gc=(vrc>=trc);%Gate signal for phase c
    
    vab=ga-gb;vbc=gb-gc;vca=gc-ga;%line-to-line voltage
    
    Vab=fft(vab)/length(t);Vab(2:end)=2*Vab(2:end);%Fourier Series

    vab1=abs(Vab(2))*cos(2*pi*fr*t+angle(Vab(2)));%Fundamental of the line voltage

    THD=100*sqrt(sum(abs(Vab(3:end/2-1)).^2))/abs(Vab(2));
    
    subplot(3,1,1)
    plot(tp,trc,'k',tp,vra,'r',tp,vrb,'b',tp,vrc,'g')
    axis([0 360 -1.5 1.5])
    line([0 360],[0 0],'Color','k','LineStyle','--')
    title(['Freq. Mod. Indx, m_f=',num2str(mf),'; Ampl. Mod. Indx, m=',num2str(m)])

    subplot(3,1,2)    
    plot(tp,vab,'r',tp,vab1,'k')
    line([0 360],[0 0],'LineStyle','--','Color','k')
    axis([0 360 -1.2 1.2])
    title(['Voltage v_a_b and its Fundamental, v_a_b_1=',num2str(abs(Vab(2)))])
    xlabel('Degs')
   
    subplot(3,1,3)
    bar(harmn,abs(Vab(harmn+1)))
    axis([0 harmn(end) 0 1.15])
    title(['Harmonics of v_a_b, ','%THD=',num2str(THD)])
    xlabel('Harmonic Order')
     
    if m<1.5; m=m+0.1;else;m=m+0.5;end
    [x,y,b]=ginput(1);
    if m>30; b=0; end
end