Bi-directional converter

A single-phase bi-directional voltage source conveter is connected to an AC voltage source through an impedance $Z = R + j\,\omega\,L$ with $R=0.1\,\Omega$ and $L=10\,$mH. The output voltage of the converter $V_{BD}$ is a quasi-square wave with fundamental frequency $50\,$Hz. The DC source voltage is $400\,$V. If $\alpha = 30^{\circ}$ and $v_s(t) = 250\,\sin(100\,\pi\,t - 30^{\circ})\,$V, what is the RMS value of the fundamental component of the current through the AC source?
In [1]:
from IPython.display import Image
Image(filename =r'VSC_bi_6_fig_1.png', width=700)
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In [2]:
# run this cell to view the circuit file.
%pycat VSC_bi_6_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 VSC_bi_6_orig.in and produces a new circuit file VSC_bi_6.in, after replacing \$Vdc, \$L, etc. with values of our choice.

In [3]:
import gseim_calc as calc
s_Vdc = '400'
s_R = '0.1'
s_L = '10e-3'
s_A_sin = '250'

s_f_hz = '50'
f_hz = float(s_f_hz)

alpha = 30.0
s_phi = ("%11.4E"%(-alpha)).strip()
T = 1/f_hz
d = 180.0 - 2.0*alpha
t0_1 = (alpha/360)*T
t0_2 = t0_1 + (d/360)*T

s_t0_1 = ("%11.4E"%(t0_1)).strip()
s_t0_2 = ("%11.4E"%(t0_2)).strip()

l = [
  ('$Vdc', s_Vdc),
  ('$R', s_R),
  ('$L', s_L),
  ('$phi', s_phi),
  ('$A_sin', s_A_sin),
  ('$f_hz', s_f_hz),
  ('$t0_1', s_t0_1),
  ('$t0_2', s_t0_2)
]
calc.replace_strings_1("VSC_bi_6_orig.in", "VSC_bi_6.in", l)
print('VSC_bi_6.in is ready for execution')

VSC_bi_6.in is ready for execution
Execute the following cell to run GSEIM on VSC_bi_6.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("VSC_bi_6.in")
os.system('run_gseim VSC_bi_6.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = VSC_bi_6.in
main: i_solve = 0
main: calling solve_trns
mat_ssw_1_ex: n_statevar: 1
Transient simulation starts...
i=0
i=1000
solve_ssw_ex: ssw_iter_newton=0, rhs_ssw_norm=2.0752e+01
Transient simulation starts...
i=0
i=1000
solve_ssw_ex: ssw_iter_newton=1, rhs_ssw_norm=2.0108e-12
solve_ssw_ex: calling solve_ssw_1_ex for one more trns step
Transient simulation starts...
i=0
i=1000
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 (VSC_bi_6.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on VSC_bi_6.in) creates a data file called VSC_bi_6.datin 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("VSC_bi_6.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_BD = slv.get_index(i_slv,i_out,"v_BD")
col_v_ac = slv.get_index(i_slv,i_out,"v_ac")
col_IL   = slv.get_index(i_slv,i_out,"IL")
col_g1   = slv.get_index(i_slv,i_out,"g1")
col_g2   = slv.get_index(i_slv,i_out,"g2")
col_g3   = slv.get_index(i_slv,i_out,"g3")
col_g4   = slv.get_index(i_slv,i_out,"g4")

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

T = t[-1]/2

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

set_size(6.5, 7, 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'$g_x$'   , fontsize=12)
ax[1].set_ylabel(r'$v_{BD}$', fontsize=12)
ax[2].set_ylabel(r'$i_L$'   , fontsize=12)

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

color1 = "tomato"
color2 = "dodgerblue"
color3 = "olive"
color4 = "blue"
color5 = "crimson"
color6 = "green"

ax[0].plot(t*1e3, (u[:,col_g1]      ), color=color1, linewidth=1.0, label="$g_1$")
ax[0].plot(t*1e3, (u[:,col_g2] - 1.5), color=color2, linewidth=1.0, label="$g_2$")
ax[0].plot(t*1e3, (u[:,col_g3] - 3.0), color=color3, linewidth=1.0, label="$g_3$")
ax[0].plot(t*1e3, (u[:,col_g4] - 4.5), color=color4, linewidth=1.0, label="$g_4$")

ax[0].tick_params(left = False)
ax[0].set_yticks([])

ax[1].plot(t*1e3, u[:,col_v_BD], color=color5, linewidth=1.0, label="$v_{BD}$")
ax[1].plot(t*1e3, u[:,col_v_ac], color=color3, linewidth=1.0, label="$v_{ac}$")
ax[2].plot(t*1e3, u[:,col_IL  ], color=color6, linewidth=1.0, label="$i_L$")

ax[2].set_xlabel('time (msec)', fontsize=12)

for k in range(2):
    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: VSC_bi_6.dat
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In [6]:
import numpy as np
import matplotlib.pyplot as plt
import gseim_calc as calc
from setsize import set_size

slv = calc.slv("VSC_bi_6.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_BD = slv.get_index(i_slv,i_out,"v_BD")
col_IL   = slv.get_index(i_slv,i_out,"IL")

T = t[-1]/2

t_start = 0.0
t_end = T

n_fourier = 20
coeff_IL, thd_IL = calc.fourier_coeff_1C(t, u[:,col_IL], 
    t_start, t_end, 1.0e-4*T, n_fourier)
print("IL fundamental: RMS value: ", "%11.4E"%(coeff_IL[1]/np.sqrt(2.0)))

coeff_v_BD, thd_v_BD = calc.fourier_coeff_1C(t, u[:,col_v_BD],
    t_start, t_end, 1.0e-4*T, n_fourier)

x_IL   = np.linspace(0, n_fourier, n_fourier+1)
x_v_BD = np.linspace(0, n_fourier, n_fourier+1)

y_IL   = np.array(coeff_IL)
y_v_BD = np.array(coeff_v_BD)

fig, ax = plt.subplots(2, sharex=False)

bars1 = ax[0].bar(x_IL  , y_IL  , width=0.3, color='red' , label="$i_L$")
bars2 = ax[1].bar(x_v_BD, y_v_BD, width=0.3, color='blue', label="$V_{BD}$")

ax[0].set_ylabel('$i_L$'   , fontsize=11)
ax[1].set_ylabel('$v_{BD}$', fontsize=11)

for k in range(2):
    ax[k].set_xlabel('N', fontsize=11)
    ax[k].set_xlim(left=0, right=n_fourier)
    ax[k].xaxis.set_ticks(np.arange(0, n_fourier, 2))
    ax[k].legend(loc = 'upper 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: VSC_bi_6.dat
IL fundamental: RMS value:   5.7581E+01
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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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