Dual active bridge DC-DC converter

The dual active bridge DC-DC converter shown in the figure is operated in phase shift modulation with a switching frequency of $50\,$kHz. The other parameters of the converter are $V_s = 50\,$V, $N_1:N_2 = 1:10$, $L_{LK} = 20\,\mu$H, $C_{out} = 22\,\mu$F, $R = 100\,\Omega$.
  1. Plot the output voltage $V_o$ versus $\phi$ for $0 < \phi < 0.5$.
  2. Determine $\phi$ for which the output power is maximum.
In [1]:
from IPython.display import Image
Image(filename =r'bridge_dcdc_4_fig_1.png', width=900)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat bridge_dcdc_4_orig.in
In [3]:
import numpy as np
import gseim_calc as calc
import os
import dos_unix
import matplotlib.pyplot as plt 
from setsize import set_size

s_Vdc = "50"
s_LLK = "20e-6"
s_R = "100"
s_C = "22e-6"
s_N1 = "1"
s_N2 = "10"

f_hz = 50.0e3
T = 1/f_hz
s_Tend = "120e-3"
Tend = float(s_Tend)
T1 = Tend - 2.0*T
s_T1 = ("%12.5E"%(T1)).strip()

l_phi = [
  0.025,
  0.050,
  0.075,
  0.100,
  0.125,
  0.150,
  0.175,
  0.200,
  0.225,
  0.250,
  0.275,
  0.300,
  0.325,
  0.350,
  0.375,
  0.400,
  0.425,
  0.450,
  0.475,
]

l_v_out_all = []
l_P_R_all = []

for phi in l_phi:
    s_phi = "%11.4E"%phi
    t0 = phi*T
    s_t0 = ("%11.4E"%(t0)).strip()

    l = [
      ('$Vdc', s_Vdc),
      ('$LLK', s_LLK),
      ('$R', s_R),
      ('$C', s_C),
      ('$N1', s_N1),
      ('$N2', s_N2),
      ('$Tend', s_Tend),
      ('$T1', s_T1),
      ('$t0', s_t0),
    ]
    print('phi:', phi)
    calc.replace_strings_1("bridge_dcdc_4_orig.in", "bridge_dcdc_4.in", l)

    # uncomment for windows:
    #dos_unix.d2u("bridge_dcdc_4.in")
    os.system('run_gseim bridge_dcdc_4.in')

    slv = calc.slv("bridge_dcdc_4.in")

    i_slv = 0
    i_out = 0
    filename = slv.l_filename_all[i_slv][i_out]
    u = np.loadtxt(filename)
    t = u[:, 0]
    t0 = t[0]
    t = t - t0

    col_v_out = slv.get_index(i_slv,i_out,"v_out")
    col_P_R   = slv.get_index(i_slv,i_out,"P_R")

    l_v_out = calc.avg_rms_2(t, u[:,col_v_out], 0.0, 2.0*T, 1.0e-4*T)
    l_P_R   = calc.avg_rms_2(t, u[:,col_P_R  ], 0.0, 2.0*T, 1.0e-4*T)

    v_out_avg = l_v_out[1][0]
    P_R_avg = l_P_R[1][0]

    l_v_out_all.append(v_out_avg)
    l_P_R_all.append(P_R_avg)

    print('v_out_avg:', "%5.1F"%v_out_avg, 'V')
    print('P_R_avg:', "%5.1F"%P_R_avg, 'W')

color1='red'
color2='blue'

fig, ax = plt.subplots(2, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(5.5, 4, ax[0])

for i in range(2):
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].set_ylabel(r'$V_{out}$', fontsize=12)
ax[1].set_ylabel(r'$P_R$'    , fontsize=12)

ax[0].tick_params(labelbottom=False)

ax[0].plot(l_phi, l_v_out_all, color=color1, linewidth=1.0, label="$V_{out}$")
ax[1].plot(l_phi, l_P_R_all  , color=color2, linewidth=1.0, label="$P_R$")

ax[1].set_xlabel(r'$\phi$', fontsize=12)

#plt.tight_layout()
plt.show()

phi: 0.025
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  11.9 V
P_R_avg:   1.4 W
phi: 0.05
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  22.5 V
P_R_avg:   5.1 W
phi: 0.075
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  31.8 V
P_R_avg:  10.1 W
phi: 0.1
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  39.9 V
P_R_avg:  16.0 W
phi: 0.125
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  46.8 V
P_R_avg:  21.9 W
phi: 0.15
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  52.4 V
P_R_avg:  27.5 W
phi: 0.175
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  56.7 V
P_R_avg:  32.3 W
phi: 0.2
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  59.8 V
P_R_avg:  35.9 W
phi: 0.225
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  61.7 V
P_R_avg:  38.2 W
phi: 0.25
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  62.3 V
P_R_avg:  38.9 W
phi: 0.275
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  61.7 V
P_R_avg:  38.2 W
phi: 0.3
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  59.8 V
P_R_avg:  35.9 W
phi: 0.325
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  56.7 V
P_R_avg:  32.2 W
phi: 0.35
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  52.3 V
P_R_avg:  27.5 W
phi: 0.375
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  46.7 V
P_R_avg:  21.9 W
phi: 0.4
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  39.9 V
P_R_avg:  15.9 W
phi: 0.425
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  31.8 V
P_R_avg:  10.1 W
phi: 0.45
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  22.4 V
P_R_avg:   5.0 W
phi: 0.475
Circuit: filename = bridge_dcdc_4.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=100000
GSEIM: Program completed.
v_out_avg:  11.8 V
P_R_avg:   1.4 W
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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.