1-phase controlled rectifier

In the single phase voltage controller circuit shown in the figure, the source voltage is $v_s(t)=325\,\sin(100\,\pi\,t)$. Determine the maximum triggering angle ($\alpha$) for which the power transferred to the $R$-$L$ load is maximum.

from IPython.display import Image
Image(filename =r'controlled_rectifier_1ph_2_fig_1.png', width=300)

# run this cell to view the circuit file.
%pycat controlled_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 controlled_rectifier_1ph_2_orig.in and produces a new circuit file controlled_rectifier_1ph_2.in, after replacing \$R (etc) with values of our choice.

import gseim_calc as calc
import numpy as np

s_R = "10"
s_L = "20e-3"
s_alpha = "45" # to be changed by user

l = [
  ('$R', s_R),
  ('$L', s_L),
  ('$alpha', s_alpha),
]
calc.replace_strings_1("controlled_rectifier_1ph_2_orig.in", "controlled_rectifier_1ph_2.in", l)
print('controlled_rectifier_1ph_2.in is ready for execution')

controlled_rectifier_1ph_2.in is ready for execution

Execute the following cell to run GSEIM on controlled_rectifier_1ph_2.in.

import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("controlled_rectifier_1ph_2.in")
os.system('run_gseim controlled_rectifier_1ph_2.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = controlled_rectifier_1ph_2.in
Circuit: n_xbeu_vr = 2
Circuit: n_ebeu_nd = 4
main: i_solve = 0
ssw_allocate_1 (2): n_statevar=1
main: calling solve_trns
mat_ssw_1_ex: n_statevar: 1
mat_ssw_1_e0: cct.n_ebeu: 5
Transient simulation starts...
i=0
i=1000
i=2000
solve_ssw_ex: ssw_iter_newton=0, rhs_ssw_norm=1.4450e+01
Transient simulation starts...
i=0
i=1000
i=2000
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
i=1000
i=2000
solve_ssw_1_ex over (after trns step for output)
solve_ssw_ex ends, slv.ssw_iter_newton=1
GSEIM: Program completed.

0

The circuit file (controlled_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 controlled_rectifier_1ph_2.in) creates a data file called controlled_rectifier_1ph_2.dat in the same directory. We can now use the python code below to compute/plot the various quantities of interest.

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("controlled_rectifier_1ph_2_orig.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_v_s = slv.get_index(i_slv,i_out,"v_s")
col_v_o = slv.get_index(i_slv,i_out,"v_o")
col_g1  = slv.get_index(i_slv,i_out,"g1")
col_g2  = slv.get_index(i_slv,i_out,"g2")
col_I_T1 = slv.get_index(i_slv,i_out,"I_T1")
col_I_T2 = slv.get_index(i_slv,i_out,"I_T2")
col_I_R  = slv.get_index(i_slv,i_out,"I_R")
col_P_R  = slv.get_index(i_slv,i_out,"P_R")

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

print('average power delivered to R:', "%11.4E"%l_P_R[1][0])

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

fig, ax = plt.subplots(7, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(5.5, 11, ax[0])

for i in range(7):
    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'$g_1$'   , fontsize=12)
ax[2].set_ylabel(r'$g_2$'   , fontsize=12)
ax[3].set_ylabel(r'$v_o$'   , fontsize=12)
ax[4].set_ylabel(r'$I_{T1}$', fontsize=12)
ax[5].set_ylabel(r'$I_{T2}$', fontsize=12)
ax[6].set_ylabel(r'$I_R$'   , fontsize=12)

ax[1].set_yticks([0.0, 1.0])
ax[2].set_yticks([0.0, 1.0])

for k in range(6):
    ax[k].tick_params(labelbottom=False)

ax[0].plot(t*1e3, u[:,col_v_s ], color=color1, linewidth=1.0, label="$v_s$")
ax[1].plot(t*1e3, u[:,col_g1  ], color=color2, linewidth=1.0, label="$g_1$")
ax[2].plot(t*1e3, u[:,col_g2  ], color=color2, linewidth=1.0, label="$g_2$")
ax[3].plot(t*1e3, u[:,col_v_o ], color=color3, linewidth=1.0, label="$v_o$")
ax[4].plot(t*1e3, u[:,col_I_T1], color=color4, linewidth=1.0, label="$I_{T1}$")
ax[5].plot(t*1e3, u[:,col_I_T2], color=color4, linewidth=1.0, label="$I_{T2}$")
ax[6].plot(t*1e3, u[:,col_I_R ], color=color4, linewidth=1.0, label="$I_R$")

ax[6].set_xlabel('time (msec)', fontsize=12)

#plt.tight_layout()
plt.show()

filename: controlled_rectifier_1ph_2.dat
average power delivered to R:  3.3945E+03

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