Forward converter

The forward converter shown in the figure has an input voltage of $30\,$V and is connected to a load resistance of $5\,\Omega$. The duty ratio of the converter is 0.4, and the switching frequency is $50\,$kHz. The turns ratio of the transformer is 6:2:3. The output capacitance is $20\,\mu$F, and the filter inductance is $500\,\mu$H. The magnetizing inductance of the transformer as seen from the source side is $1\,$mH. If the diodes have a forward drop of $0.7\,V$ and the switches have a drop of $1\,$V, determine the following.
  1. the output voltage
  2. the duration for which diode $D_1$ conducts.
  3. the efficiency of the converter.
In [1]:
from IPython.display import Image
Image(filename =r'forward_2_fig_1.png', width=450)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat forward_2_orig.in

We now replace the strings such as \$Vdc, \$L, with the values of our choice by running the python script given below. It takes an existing circuit file forward_2_orig.in and produces a new circuit file forward_2.in, after replacing \$Vdc, \$L, etc. with values of our choice.

In [3]:
import gseim_calc as calc
s_D = "0.4"
s_Vdc = "30"
s_Lm = "1e-3"
s_L = "500e-6"
s_R = "5"
s_C = "20e-6"
s_N1 = "6"
s_N2 = "2"
s_N3 = "3"
s_f_hz = "50e3"

l = [
  ('$D', s_D),
  ('$Vdc', s_Vdc),
  ('$Lm', s_Lm),
  ('$L', s_L),
  ('$R', s_R),
  ('$C', s_C),
  ('$N1', s_N1),
  ('$N2', s_N2),
  ('$N3', s_N3),
  ('$f_hz', s_f_hz),
]
calc.replace_strings_1("forward_2_orig.in", "forward_2.in", l)
print('forward_2.in is ready for execution')

forward_2.in is ready for execution
Execute the following cell to run GSEIM on forward_2.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("forward_2.in")
os.system('run_gseim forward_2.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = forward_2.in
main: i_solve = 0
main: calling solve_trns
mat_ssw_1_ex: n_statevar: 4
Transient simulation starts...
i=0
solve_ssw_ex: ssw_iter_newton=0, rhs_ssw_norm=1.9648e-01
Transient simulation starts...
i=0
solve_ssw_ex: ssw_iter_newton=1, rhs_ssw_norm=1.5543e-15
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 (forward_2.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on forward_2.in) creates two data files called forward_2.dat and forward_2_1.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

slv = calc.slv("forward_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_v_out = slv.get_index(i_slv,i_out,"v_out")
col_IL    = slv.get_index(i_slv,i_out,"IL"   )
col_ILm   = slv.get_index(i_slv,i_out,"ILm"  )
col_IS    = slv.get_index(i_slv,i_out,"IS"   )
col_ID1   = slv.get_index(i_slv,i_out,"ID1"  )
col_IVs   = slv.get_index(i_slv,i_out,"IVs"  )
col_P_R   = slv.get_index(i_slv,i_out,"P_R"  )
col_P_Vs  = slv.get_index(i_slv,i_out,"P_Vs" )

# since we have stored two cycles, we need to divide the last time point
# by 2 to get the period:

T = t[-1]/2

l_v_out = calc.avg_rms_2(t, u[:,col_v_out], T, 2.0*T, 1.0e-4*T)

print('average Vo:', "%11.4E"%l_v_out[1][0], "Volts")

l_v_out_1 = calc.min_max_1(t, u[:,col_v_out], 0.0, 2.0*T)
v_out_ptop = l_v_out_1[1] - l_v_out_1[0]
print('peak-to-peak ripple in Vo:', "%11.4E"%v_out_ptop, " Volts")

ndiv = 5000
n_ID1 = 0

delt_ID1, ID1p = calc.interp_linear_1(t, u[:,col_ID1], ndiv)

for k in range(ndiv):
    if (ID1p[k] > 0): n_ID1 += 1

print('duration of conduction for D1 in one cycle:',
  "%11.4E"%(1.0e6*float(n_ID1)*delt_ID1/(2.0)), 'micro seconds.')

l_P_Vs = calc.avg_rms_2(t, u[:,col_P_Vs], 0.0, 2.0*T, 1.0e-3*T)
l_P_R = calc.avg_rms_2(t, u[:,col_P_R], 0.0, 2.0*T, 1.0e-3*T)

print('average power (VS):', "%11.4E"%l_P_Vs[1][0], "W")
print('average power (load):', "%11.4E"%l_P_R[1][0], "W")

print('efficiency:', "%5.2f"%(100.0*l_P_R[1][0]/l_P_Vs[1][0]), "per cent")

color1='green'
color2='crimson'
color3='goldenrod'
color4='blue'
color5='cornflowerblue'
color6='red'

fig, ax = plt.subplots(6, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(7, 7, ax[0])

for i in range(6):
    ax[i].set_xlim(left=0, right=2.0*T*1e6)
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].plot(t*1e6, u[:,col_IL   ], color=color1, linewidth=1.0, label="$i_L$")
ax[1].plot(t*1e6, u[:,col_IVs  ], color=color2, linewidth=1.0, label="$i_{Vs}$")
ax[2].plot(t*1e6, u[:,col_IS   ], color=color3, linewidth=1.0, label="$i_S$")
ax[3].plot(t*1e6, u[:,col_ID1  ], color=color4, linewidth=1.0, label="$i_{D1}$")
ax[4].plot(t*1e6, u[:,col_v_out], color=color5, linewidth=1.0, label="$V_o$")
ax[5].plot(t*1e6, u[:,col_ILm  ], color=color5, linewidth=1.0, label="$i_{Lm}$")

ax[0].set_ylabel(r'$i_L$'   , fontsize=14)
ax[1].set_ylabel(r'$i_{Vs}$', fontsize=14)
ax[2].set_ylabel(r'$i_S$'   , fontsize=14)
ax[3].set_ylabel(r'$i_{D1}$', fontsize=14)
ax[4].set_ylabel(r'$V_o$'   , fontsize=14)
ax[5].set_ylabel(r'$i_{Lm}$', fontsize=14)

ax[5].set_xlabel('time (' + r'$\mu$' + 'sec)', fontsize=14)

for i in range(5):
    ax[i].tick_params(labelbottom=False)

#plt.tight_layout()
plt.show()

filename: forward_2.dat
average Vo:  5.0970E+00 Volts
peak-to-peak ripple in Vo:  1.7419E-02  Volts
duration of conduction for D1 in one cycle:  2.6160E+00 micro seconds.
average power (VS):  6.2002E+00 W
average power (load):  5.1960E+00 W
efficiency: 83.80 per cent
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This notebook was contributed by Prof. Nakul Narayanan K, Govt. Engineering College, Thrissur. He may be contacted at nakul@gectcr.ac.in.

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