1-phase VSI (PWM)

The figure below shows a full-bridge bi-polar PWM voltage source inverter connected to an ac voltage source $V_{S1} $ through inductor $L=10\,$mH. The ac voltage is sinusoidal, with amplitude $325\,$V and frequency $50\,$Hz. The inverter is pumping $5\,$kW of power to the ac voltage source at unity power factor. The DC link voltage $V_{dc}$ of the inverter is $400\,$V, and the switching frequency is $2\,$kHz. Determine
  1. Modulation wave of the inverter (amplitude and phase with respect to $V_{S1}$)
  2. RMS value of the fundamental component of $V_{BD}$
  3. RMS value of the fundamental component of $i_L$
  4. lowest-order harmonics in $i_{dc}$
In [1]:
from IPython.display import Image
Image(filename =r'VSI_1ph_9_fig_1.png', width=550)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat VSI_1ph_9_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 VSI_1ph_9_orig.in and produces a new circuit file VSI_1ph_9.in, after replacing \$Vdc, \$L, etc. with values of our choice.

In [3]:
import gseim_calc as calc
s_Vdc = "400"
s_L = "10e-3"
s_S1 = "325"
s_f_carrier = "2e3"
s_sin = "0.6" # to be changed by user
s_phi_sin = "25" # to be changed by user
s_dt_min = "0.1e-6"
s_dt_nrml = "10e-6"

f_S1 = 50.0
s_f_S1 = ("%11.4E"%(f_S1)).strip()

T = 1/f_S1
s_2T = ("%11.4E"%(2.0*T)).strip()

l = [
  ('$Vdc', s_Vdc),
  ('$L', s_L),
  ('$f_S1', s_f_S1),
  ('$A_S1', s_S1),
  ('$f_carrier', s_f_carrier),
  ('$A_sin', s_sin),
  ('$phi_sin', s_phi_sin),
  ('$2T', s_2T),
  ('$dt_min', s_dt_min),
  ('$dt_nrml', s_dt_nrml)
]
calc.replace_strings_1("VSI_1ph_9_orig.in", "VSI_1ph_9.in", l)
print('VSI_1ph_9.in is ready for execution')

VSI_1ph_9.in is ready for execution
Execute the following cell to run GSEIM on VSI_1ph_9.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("VSI_1ph_9.in")
os.system('run_gseim VSI_1ph_9.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = VSI_1ph_9.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=1000
i=2000
i=3000
i=4000
GSEIM: Program completed.
Out[4]:
0

The circuit file (VSI_1ph_9.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on VSI_1ph_9.in) creates two data files called VSI_1ph_9.dat and VSI_1ph_9_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("VSI_1ph_9.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_Idc   = slv.get_index(i_slv,i_out,"Idc"  )
col_P_dc  = slv.get_index(i_slv,i_out,"P_dc" )
col_P_S1  = slv.get_index(i_slv,i_out,"P_S1" )

i_out = 1
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u1 = np.loadtxt(filename)
t1 = u1[:, 0]

col_s  = slv.get_index(i_slv,i_out,"s" )
col_t  = slv.get_index(i_slv,i_out,"t" )
col_g1 = slv.get_index(i_slv,i_out,"g1")
col_g2 = slv.get_index(i_slv,i_out,"g2")

# 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_IL    = calc.avg_rms_2(t, u[:,col_IL   ], T, 2.0*T, 1.0e-4*T)
l_v_out = calc.avg_rms_2(t, u[:,col_v_out], T, 2.0*T, 1.0e-4*T)
l_Idc   = calc.avg_rms_2(t, u[:,col_Idc  ], T, 2.0*T, 1.0e-4*T)
l_P_dc  = calc.avg_rms_2(t, u[:,col_P_dc ], T, 2.0*T, 1.0e-4*T)
l_P_S1  = calc.avg_rms_2(t, u[:,col_P_S1 ], T, 2.0*T, 1.0e-4*T)

print('rms load voltage:', "%11.4E"%l_v_out[2][0])
print('average power delivered by dc source:', "%11.4E"%l_P_dc[1][0])
print('average power delivered by VS1:', "%11.4E"%l_P_S1[1][0])

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

fig, ax = plt.subplots(4, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(7, 7, ax[0])

for i in range(4):
    ax[i].set_xlim(left=0, right=T*1e3)

ax[0].set_ylim(bottom=-1.4, top=1.4)
ax[1].set_ylim(bottom=-500, top=500)

ax[0].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)
ax[1].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)
ax[2].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)
ax[3].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].plot((t1-T)*1e3, u1[:,col_t], color=color5, linewidth=1.0, label="$t$")
ax[0].plot((t1-T)*1e3, u1[:,col_s], color=color4, linewidth=1.0, label="$s$")

ax[1].plot((t-T)*1e3, u[:,col_v_out], color=color1, linewidth=1.0, label="$V_{out}$")
ax[2].plot((t-T)*1e3, u[:,col_Idc  ], color=color3, linewidth=1.0, label="$i_{dc}$")
ax[3].plot((t-T)*1e3, u[:,col_IL   ], color=color2, linewidth=1.0, label="$i_L$")

ax[1].set_ylabel(r'$V_{out}$', fontsize=14)
ax[2].set_ylabel(r'$i_{dc}$',  fontsize=14)
ax[3].set_ylabel(r'$i_L$',     fontsize=14)

ax[3].set_xlabel('time (msec)', fontsize=14)

ax[0].legend(loc = 'lower right',frameon = True, fontsize = 10, title = None,
   markerfirst = True, markerscale = 1.0, labelspacing = 0.5, columnspacing = 2.0,
   prop = {'size' : 12},)

ax[0].tick_params(labelbottom=False)
ax[1].tick_params(labelbottom=False)
ax[2].tick_params(labelbottom=False)

#plt.tight_layout()
plt.show()

filename: VSI_1ph_9.dat
filename: VSI_1ph_9_1.dat
rms load voltage:  4.0000E+02
average power delivered by dc source:  5.2301E+03
average power delivered by VS1: -5.2197E+03
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In [6]:
import numpy as np
import matplotlib.pyplot as plt 
from matplotlib.ticker import (MultipleLocator, AutoMinorLocator)
import gseim_calc as calc
from setsize import set_size

slv = calc.slv("VSI_1ph_9.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_Idc   = slv.get_index(i_slv,i_out,"Idc"  )
col_P_dc  = slv.get_index(i_slv,i_out,"P_dc" )
col_P_S1  = slv.get_index(i_slv,i_out,"P_S1" )

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

T = t[-1]/2

# compute Fourier coeffs:

t_start = T 
t_end = 2.0*T

n_fourier = 50

coeff_IL, thd_IL = calc.fourier_coeff_1C(t, u[:,col_IL], 
    t_start, t_end, 1.0e-8, n_fourier)

coeff_v_out, thd_v_out = calc.fourier_coeff_1C(t, u[:,col_v_out], 
    t_start, t_end, 1.0e-8, n_fourier)

coeff_Idc, thd_Idc = calc.fourier_coeff_1C(t, u[:,col_Idc], 
    t_start, t_end, 1.0e-8, n_fourier)

print("THD (IS1): ", "%5.2f"%(thd_IL*100.0), "%")
print("I_S1 fundamental: RMS value: ", "%11.4E"%(coeff_IL[1]/np.sqrt(2.0)))
print("THD (Vout): ", "%5.2f"%(thd_v_out*100.0), "%")
print("Vout fundamental: RMS value: ", "%11.4E"%(coeff_v_out[1]/np.sqrt(2.0)))
print("Idc fundamental: RMS value: ", "%11.4E"%(coeff_Idc[1]/np.sqrt(2.0)))

x = np.linspace(0, n_fourier, n_fourier+1)

y_IL    = np.array(coeff_IL)
y_v_out = np.array(coeff_v_out)
y_Idc   = np.array(coeff_Idc)

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

set_size(7, 6, ax[0])

delta = 10.0
x_major_ticks = np.arange(0.0, (float(n_fourier+1)), delta)
x_minor_ticks = np.arange(0.0, (float(n_fourier+1)), 1.0)

for i in range(3):
    ax[i].set_xlim(left=-1.0, right=float(n_fourier))
    ax[i].set_xticks(x_major_ticks)
    ax[i].set_xticks(x_minor_ticks, minor=True)
    ax[i].grid(visible=True, which='major', axis='x', color=grid_color, linestyle='-', zorder=0)

ax[0].set_ylabel('$i_L$',fontsize=14)
ax[1].set_ylabel('$v_{out}$', fontsize=14)
ax[2].set_ylabel('$i_{dc}$',  fontsize=14)

ax[2].set_xlabel('N', fontsize=14)

bars1 = ax[0].bar(x, y_IL,    width=0.3, color='red',   label="$i_L$",     zorder=3)
bars2 = ax[1].bar(x, y_v_out, width=0.3, color='blue',  label="$V_{out}$", zorder=3)
bars3 = ax[2].bar(x, y_Idc,   width=0.3, color='green', label="$i_{dc}$",  zorder=3)

plt.tight_layout()
plt.show()

filename: VSI_1ph_9.dat
THD (IS1):   7.23 %
I_S1 fundamental: RMS value:   3.3186E+01
THD (Vout):  213.44 %
Vout fundamental: RMS value:   1.6970E+02
Idc fundamental: RMS value:   1.4493E+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.

In [ ]: