1-phase rectifier

In the circuit given below, $R=10\,\Omega$ and $L=10\,$mH. Under steady state, determine
  1. the duration for which diode D1 conducts in one cycle
  2. the average current through R
In [1]:
from IPython.display import Image
Image(filename =r'rectifier_1ph_2_fig_1.png', width=400)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat rectifier_1ph_2_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_2_orig.in and produces a new circuit file rectifier_1ph_2.in, after replacing \$R (etc) with values of our choice.

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

s_R = "10"
s_L = "10e-3"

l = [
  ('$R', s_R),
  ('$L', s_L),
]
calc.replace_strings_1("rectifier_1ph_2_orig.in", "rectifier_1ph_2.in", l)
print('rectifier_1ph_2.in is ready for execution')

rectifier_1ph_2.in is ready for execution
Execute the following cell to run GSEIM on rectifier_1ph_2.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("rectifier_1ph_2.in")
os.system('run_gseim rectifier_1ph_2.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = rectifier_1ph_2.in
Circuit: n_xbeu_vr = 0
Circuit: n_ebeu_nd = 4
main: i_solve = 0
ssw_allocate_1 (2): n_statevar=1
main: calling solve_trns
mat_ssw_1_e: n_statevar: 1
mat_ssw_1_e0: cct.n_ebeu: 5
Transient simulation starts...
i=0
i=1000
solve_ssw_e: ssw_iter_newton=0, rhs_ssw_norm=9.7919e+00
Transient simulation starts...
i=0
i=1000
solve_ssw_e: ssw_iter_newton=1, rhs_ssw_norm=1.1323e-01
Transient simulation starts...
i=0
i=1000
solve_ssw_e: ssw_iter_newton=2, rhs_ssw_norm=7.2552e-03
Transient simulation starts...
i=0
i=1000
solve_ssw_e: ssw_iter_newton=3, rhs_ssw_norm=1.5403e-04
Transient simulation starts...
i=0
i=1000
solve_ssw_e: ssw_iter_newton=4, rhs_ssw_norm=1.2434e-14
solve_ssw_e: calling solve_ssw_1_e for one more trns step
Transient simulation starts...
i=0
i=1000
solve_ssw_1_e over (after trns step for output)
solve_ssw_e ends, slv.ssw_iter_newton=4
GSEIM: Program completed.
Out[4]:
0

The circuit file (rectifier_1ph_2.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on rectifier_1ph_2.in) creates a data file called rectifier_1ph_2.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_2.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_vs  = slv.get_index(i_slv,i_out,"vs")

l_ID1 = calc.avg_rms_2(t, u[:,col_ID1], 0.0, 2.0*T, 1.0e-5*T)
l_ID2 = calc.avg_rms_2(t, u[:,col_ID2], 0.0, 2.0*T, 1.0e-5*T)
t_ID1 = np.array(l_ID1[0])
t_ID2 = np.array(l_ID2[0])

# IR and ID1 are the same:
print('average value of IR:', "%11.4E"%l_ID1[1][0])

l_cross_1_ID1, l_cross_2_ID1 = calc.cross_over_points_1(t, u[:,col_ID1], 0.0, 2.0*T, 1.0e-10)
print('zero-crossing points of ID1 (positive slope):')
for t1 in l_cross_1_ID1:
    print("  ", "%11.4E"%t1)
print('zero-crossing points of ID1 (negative slope):')
for t1 in l_cross_2_ID1:
    print("  ", "%11.4E"%t1)
t_conduction_D1 = l_cross_2_ID1[1]-l_cross_1_ID1[0]
print("conduction duration for D1:", t_conduction_D1)

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

fig, ax = plt.subplots(3, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(5.5, 6, ax[0])

for i in range(3):
    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'$v_s$',    fontsize=12)
ax[1].set_ylabel(r'$I_{D1}$', fontsize=12)
ax[2].set_ylabel(r'$I_{D2}$', fontsize=12)

ax[0].tick_params(labelbottom=False)
ax[1].tick_params(labelbottom=False)

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

ax[1].plot(t_ID1*1e3, l_ID1[1], color=color2, linewidth=1.0, label="$I_{D1}^{avg}$", linestyle='--', dashes=(5,3))
ax[2].plot(t_ID2*1e3, l_ID2[1], color=color3, linewidth=1.0, label="$I_{D2}^{avg}$", linestyle='--', dashes=(5,3))

ax[2].set_xlabel('time (msec)', fontsize=11)

for k in range(1, 3):
    ax[k].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_2.dat
average value of IR:  3.1822E+00
zero-crossing points of ID1 (positive slope):
    1.4980E-02
    3.4980E-02
zero-crossing points of ID1 (negative slope):
    5.0200E-03
    2.5020E-02
conduction duration for D1: 0.010039975176272718
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.