EE 255 - Chapter 3a

EE 255 - Chapter 3a - 63 Chapter 3 : Introduction to Power...

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Unformatted text preview: 63 Chapter 3 : Introduction to Power Electronics 3-1. Calculate the ripple factor of a three-phase half-wave rectifier circuit, both analytically and using MATLAB. S OLUTION A three-phase half-wave rectifier and its output voltage are shown below /6 5 /6 2 /3 ( ) sin A M v t V t = ( ) ( ) sin 2 / 3 B M v t V t =- ( ) ( ) sin 2 / 3 C M v t V t = + S OLUTION If we find the average and rms values over the interval from /6 to 5 /6 (one period), these values will be the same as the average and rms values of the entire waveform, and they can be used to calculate the ripple factor. The average voltage is ( ) 5 / 6 / 6 1 3 ( ) sin 2 DC M V v t dt V t d t T = = 5 6 6 3 3 3 3 3 3 cos 0.8270 2 2 2 2 2 M M DC M M V V V t V V = - = --- = = The rms voltage is ( ) 5 / 6 2 2 2 rms / 6 1 3 ( ) sin 2 M V v t dt V t d t T = = 5 / 6 2 rms / 6 3 1 1 sin2 2 2 4 M V V t t =- 64 2 rms 3 1 5 1 5 sin sin 2 2 6 6 4 3 3 M V V =--- 2 2 rms 3 1 5 3 1 3 3 sin sin 2 3 4 3 3 2 3 4 2 2 M M V V V =-- =--- 2 2 rms 3 1 3 3 3 3 0.8407 2 3 4 2 2 2 3 4 M M M V V V V =--- = + = The resulting ripple factor is 2 2 rms DC 0.8407 1 100% 1 100% 18.3% 0.8270 M M V V r V V =- =- = The ripple can be calculated with MATLAB using the ripple function developed in the text. We must right a new function halfwave3 to simulate the output of a three-phase half-wave rectifier. This output is just the largest voltage of ( ) t v A , ( ) t v B , and ( ) t v C at any particular time. The function is shown below: function volts = halfwave3(wt) % Function to simulate the output of a three-phase % half-wave rectifier. % wt = Phase in radians (=omega x time) % Convert input to the range 0 <= wt < 2*pi while wt >= 2*pi wt = wt - 2*pi; end while wt < 0 wt = wt + 2*pi; end % Simulate the output of the rectifier. a = sin(wt); b = sin(wt - 2*pi/3); c = sin(wt + 2*pi/3); volts = max( [ a b c ] ); The function ripple is reproduced below. It is identical to the one in the textbook. function r = ripple(waveform) % Function to calculate the ripple on an input waveform. % Calculate the average value of the waveform nvals = size(waveform,2); temp = 0; for ii = 1:nvals temp = temp + waveform(ii); end average = temp/nvals; % Calculate rms value of waveform 65 temp = 0; for ii = 1:nvals temp = temp + waveform(ii)^2; end rms = sqrt(temp/nvals); % Calculate ripple factor r = sqrt((rms / average)^2 - 1) * 100; Finally, the test driver program is shown below. % M-file: test_halfwave3.m % M-file to calculate the ripple on the output of a % three phase half-wave rectifier. % First, generate the output of a three-phase half-wave % rectifier waveform = zeros(1,128); for ii = 1:128 waveform(ii) = halfwave3(ii*pi/64) ; end % Now calculate the ripple factor r = ripple(waveform); % Print out the result string = ['The ripple is ' num2str(r) '%.']; disp(string); When this program is executed, the results are...
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EE 255 - Chapter 3a - 63 Chapter 3 : Introduction to Power...

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