PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 283

MATLAB Solution

>> % Instantaneous power plot

>> T= 2*pi/(200*pi);

>> X= [0:.01:1];

>> t = X.*T;

>> IT = 5*cos(200*pi*t+pi/3);

>> VT = 9*cos(200*pi*t+pi/4);

>> PT = IT.*VT;

>> plot(t,PT,’o’,t,VT,’*’,t,IT,’+’); % Figure 3.64

>> legend(‘i(t)’, ‘v(t)’, ‘p(t)’)

>> grid on

>> title(‘Instantaneous Power, Current, and Voltage’)

>> xlabel(‘time in seconds’),ylabel(‘ Amplitudes of P, I, &V’)

>> VTSQ=VT.^2; % v(t)^2

>> IntVTSQ = .01*T*(trapz(VTSQ)) % integral ofv(t)^2

IntVTSQ =

0.4050

>> ITSQ = (5*cos(200*pi*t+pi/3)).^2; % i(t)^2

>> IntITSQ = .01*T*(trapz(ITSQ)) % integral of i(t)^2

IntITSQ =

0.1250

>> VRMS = sqrt((IntVTSQ)/T) % RMS value of voltage

VRMS =

6.3640

>> IRMS = sqrt((IntITSQ)/T) % RMS value of current.

IRMS =

3.5355

>> % average power using trapz

>> PowerWave = .01*T*trapz(PT)/T

PowerWave =

21.7333

>> % Power Factor numerical

>> PF = PowerWave/(VRMS*IRMS)

PF =

0.9659

>> % verify results analytically

>> VRMSANA = 9*.707

VRMSANA =

6.3630

>> IRMSANA = 5*.707

IRMSANA =

3.5350