1-phase rectifier

For the circuit given below (assuming ideal diode), the input current is $i_s(t)=10\pi \cos (\omega t)$. Determine
  1. the average voltage across the parallel $RC$ load
  2. the average power dissipated in the $10\,\Omega$ resistor
In [1]:
from IPython.display import Image
Image(filename =r'rectifier_1ph_10_fig_1.png', width=300)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat rectifier_1ph_10_orig.in

We now replace the strings such as \$R with the values of our choice by running the python script given below. It takes an existing circuit file rectifier_1ph_10_orig.in and produces a new circuit file rectifier_1ph_10.in, after replacing \$R (etc) with values of our choice.

In [3]:
import gseim_calc as calc
import numpy as np
import sys

s_R = "10"
s_C = "10e-6"

l = [
  ('$R', s_R),
  ('$C', s_C),
]
calc.replace_strings_1("rectifier_1ph_10_orig.in", "rectifier_1ph_10.in", l)
print('rectifier_1ph_10.in is ready for execution')

rectifier_1ph_10.in is ready for execution
Execute the following cell to run GSEIM on rectifier_1ph_10.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("rectifier_1ph_10.in")
os.system('run_gseim rectifier_1ph_10.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = rectifier_1ph_10.in
Circuit: n_xbeu_vr = 1
Circuit: n_ebeu_nd = 3
main: i_solve = 0
ssw_allocate_1 (2): n_statevar=2
main: calling solve_trns
mat_ssw_1_ex: n_statevar: 2
mat_ssw_1_e0: cct.n_ebeu: 5
Transient simulation starts...
i=0
solve_ssw_ex: ssw_iter_newton=0, rhs_ssw_norm=3.1377e-03
Transient simulation starts...
i=0
solve_ssw_ex: ssw_iter_newton=1, rhs_ssw_norm=0.0000e+00
solve_ssw_ex: calling solve_ssw_1_ex for one more trns step
Transient simulation starts...
i=0
solve_ssw_1_ex over (after trns step for output)
solve_ssw_ex ends, slv.ssw_iter_newton=1
GSEIM: Program completed.
Out[4]:
0

The circuit file (rectifier_1ph_10.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on rectifier_1ph_10.in) creates a data file called rectifier_1ph_10.dat in the same directory. We can now use the python code below to compute/plot the various quantities of interest.

In [5]:
import numpy as np
import matplotlib.pyplot as plt 
import gseim_calc as calc
from setsize import set_size

f_hz = 50.0
T = 1.0/f_hz

slv = calc.slv("rectifier_1ph_10.in")

i_slv = 0
i_out = 0
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u = np.loadtxt(filename)
t = u[:, 0]

col_ID1   = slv.get_index(i_slv,i_out,"ID1")
col_ID2   = slv.get_index(i_slv,i_out,"ID2")
col_I_S   = slv.get_index(i_slv,i_out,"I_S")
col_V_R   = slv.get_index(i_slv,i_out,"V_R")
col_P_R   = slv.get_index(i_slv,i_out,"P_R")

l_V_R = calc.avg_rms_2(t, u[:,col_V_R], 0.0, 2.0*T, 1.0e-5*T)
l_P_R = calc.avg_rms_2(t, u[:,col_P_R], 0.0, 2.0*T, 1.0e-5*T)

t_V_R =  np.array(l_V_R[0])

print('average voltage across RC load:', "%11.4E"%(l_V_R[1][0]))
print('average power dissipated in R:' , "%11.4E"%(l_P_R[1][0]))

color1 = 'blue'
color2 = 'green'
color3 = 'red'
color4 = 'dodgerblue'

fig, ax = plt.subplots(4, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(5.5, 8, ax[0])

for i in range(4):
    ax[i].set_xlim(left=0.0, right=2.0*T*1e3)
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].set_ylabel(r'$I_s$'   , fontsize=12)
ax[1].set_ylabel(r'$V_R$'   , fontsize=12)
ax[2].set_ylabel(r'$I_{D1}$', fontsize=12)
ax[3].set_ylabel(r'$I_{D2}$', fontsize=12)

for i in range(3):
    ax[i].tick_params(labelbottom=False)

ax[0].plot(t*1e3,  u[:,col_I_S], color=color1, linewidth=1.0, label="$I_s$")
ax[1].plot(t*1e3,  u[:,col_V_R], color=color2, linewidth=1.0, label="$V_R$")
ax[2].plot(t*1e3,  u[:,col_ID1], color=color3, linewidth=1.0, label="$I_{D1}$")
ax[3].plot(t*1e3,  u[:,col_ID2], color=color4, linewidth=1.0, label="$I_{D2}$")

ax[1].plot(t_V_R*1e3, l_V_R[1], color=color2, linewidth=1.0, label="$V_R^{avg}$", linestyle='--', dashes=(5,3))

ax[3].set_xlabel('time (msec)', fontsize=11)

ax[1].legend(loc = 'lower right',frameon = True, fontsize = 10, title = None,
  markerfirst = True, markerscale = 1.0, labelspacing = 0.5, columnspacing = 2.0,
  prop = {'size' : 12},)

#plt.tight_layout()
plt.show()

filename: rectifier_1ph_10.dat
average voltage across RC load:  9.9997E+01
average power dissipated in R:  2.4638E+03
No description has been provided for this image

This notebook was contributed by Prof. Nakul Narayanan K, Govt. Engineering College, Thrissur. He may be contacted at nakul@gectcr.ac.in.