3 PHASE SINUSOIDAL PULSE- WIDTH MODULATION IN MATLAB

 

3 PHASE SINUSOIDAL PULSE- WIDTH MODULATION

To generate output pulses by varying modulating index (ma) and to find the THD and FFT analysis.

Software Used: MATLAB R2018a

Theory:

The term SPWM stands for “Sinusoidal pulse width modulation” is a technique of pulse width modulation used in inverters. An inverter generates an output of AC voltage from an input of DC with the help of switching circuits to reproduce a sine wave by generating one or more square pulses of voltage per half cycle

Three-phase SPWM inverters are controlled in the same way as a single-phase SPWM inverter. Three sinusoidal modulating signals at the frequency of the desired output but displaced from each other by 120° are compared with a triangular carrier waveform of suitably high frequency. The resulting switching signals from each comparator are used to drive the inverter switches of the corresponding leg. The switching signals for each inverter leg are complementary, and the switching signals for each switch have 180° of conduction.

In this, we can get different types of modulation

1.      Linear Modulation Range, m < 1

The RMS value of the fundamental of this voltage varies linearly with the depth of modulation m.

2.      Over-modulation, m > 1

If the peak amplitude of the control voltage is greater than the peak of the carrier waveform, the fundamental output voltage will increase,

 

3 PHASE SINUSOIDAL PULSE- WIDTH MODULATION

MATLAB Code:

clc; %clear the command window

clear all; %clear the workspace

close all; %close all previous figure window

f=50; %Frequency

w=2*pi*f;

t=0:0.00001 :1/f; %range of time period

s1=sin(w*t); %sine pulse

s2=sin(w*t+(2*pi/3)); %sine pulse with 120 degree phase shift

s3=sin(w*t-(2*pi/3)); %sine pulse with 240 degree phase shift

car2=-asin(sin(20*w*t))*(1.333); %carrier pulse

% subplot(4,1,1)

% plot(t,s1);

% hold on

% plot(t,s2);

% hold on

% plot(t,s3);

% hold on

% plot(t,car2);

 

% o1=(s1>=car2)

% o2=(s3>=car2);

% o3=o1-o2;

 ma=0.01:0.01:1

 for(i=1:max(size(ma)))

   sq2=ma(i)*s1; %Modulation Index in product with reference sine 1

   sq3=ma(i)*s3; %Modulation Index in product with reference sine 2

   subplot(2,1,1)

   plot(t,sq2)

   hold on

  

   subplot(2,1,2)

   plot(t,sq3)

   hold on

  

   o1(i,:)=(sq2>=car2)

   o2(i,:)=(sq3>=car2);

   o3(i,:)=o1(i,:)-o2(i,:); % Output Pulse

  

    N=max(size(o3(i,:)));

    y(i,:)=(2/N)*abs(fft(o3(i,:),N));    %FFT analysis formula

    C1(i,:)=sum(y(i,:).^2);             %Sum of the hormonic componets in output signal

    C2(i,:)=sqrt(C1(i,:)-y(i,2).^2);    %Square root of (sum of hormonic components-First hormonic component)

    C3(i,:)=C2(i,:)/y(i,2);             % Finding Total harmonic distortion(THD)

end

 

figure()

plot(t,o3(80,:))                        %  Plot of Output signal with modulation index=0.8

figure()                                %To plot seperate figure

bar(ma,C3(:,1))

axis([0 .1 -1 11])

figure()

plot(ma,y(:,2:2:8));                    % Plot of Modulation index vrs THD

set(gca,'Xdir','reverse');

   

 

 

Waveforms:

Fig6.1: Comparison of 3 Phase Reference Wave with Carrier wave

Fig6.2: Reference Pulse of different ma

Fig6.3: Harmonics Profile of 3 Phase SPWM

Fig6.4: Modulation Index Vs THD

Fig6.5: Output Pulse for 3 Phase SPWM for ma=0.80

Fig.6.6  FFT Analysis of 3 Phase PWM

Observation:

1.     As the ma increases, THD of the output pulse decreases as seen from FFT analysis of signal.

2.     By varying the ma value, we can vary the width of the output pulse.

3.     If we multiply some constant value with the THD and take a plot of ma vs THD, at low value of ma THD become high which is undesirable.

4.     AS seen from ma Vs THD plot fig 6.4, up to 1 it is Linear modulation more than 1 it is overmodulation but as the curve becomes constant THD is a square wave.

Result: By In the above experiment we can say that if ma is varied from 0 to 1, output pulse generation will be as shown in fig 6.5 for ma = 0.80. THD and FFT analysis is also done for the same ma i.e. 0.80. Also a separate plot is plotted by increasing the value of ma to 5.