/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 15.08.2 ] */

/* [wxMaxima: title   start ]
Phase Controlled Rectifier, Half Controlled
   [wxMaxima: title   end   ] */

/* [wxMaxima: comment start ]
RMS values
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
Vrms: Vm / sqrt(2);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
current, 1st harmonic
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
assume(Iout > 0);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
Irms: Iout * sqrt((%pi - alpha) / %pi);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
I1s: 1 / %pi * (integrate(Iout * sin(x), x, alpha, %pi) + 
    integrate(- Iout * sin(x), x, %pi + alpha, 2 * %pi));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
I1c: 1 / %pi * (integrate(Iout * cos(x), x, alpha, %pi) + 
    integrate(- Iout * cos(x), x, %pi + alpha, 2 * %pi));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
I1: sqrt(I1c^2 + I1s^2);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
I1: trigsimp(I1);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
I1a: 4 / %pi * cos(alpha / 2) * Iout;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxplot2d([I1 / Iout, I1a / Iout], [alpha, 0, %pi-1e-3], [box, false], [legend, false]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
I1: I1a;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
I1rms: I1 / sqrt(2);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
DPF
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
DPF: I1s / I1;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
DPF: ratsimp(DPF);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
DPF: radcan(DPF);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
(cos(alpha / 2))^2;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
trigrat(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
DPF^2 - cos(alpha/2)^2;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
trigrat(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
DPF: cos(alpha / 2);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
P
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
P: Vrms * I1rms * DPF;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
S
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
S: Vrms * Irms;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxplot2d([P / (Vm * Iout), S / (Vm * Iout)], [alpha, 0, %pi-1e-3], [box, false], [legend, false]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
PF
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
PF: P / S;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ev(PF, alpha = 0);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ev(PF, alpha = 0, numer);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxplot2d(PF, [alpha, 0, %pi-1e-3], [box, false], [legend, false]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
verify PF-DPF relation
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
wxplot2d([PF, I1rms / Irms * DPF], [alpha, 0, %pi-1e-3], [box, false], [legend, false]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
THD
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
THD: sqrt((Irms / I1rms)^2 - 1) * 100;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxplot2d(THD, [alpha, 0, %pi-1e-3], [y, 0, 300], [box, false], [legend, false]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ev(THD, alpha = 0);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ev(THD, alpha = 0, numer);
/* [wxMaxima: input   end   ] */

/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$