3-phase VSI

A three-phase voltage source inverter is connected to a balanced three-phase delta connected resistive load. The inverter is operated with 180 degree conduction mode. Comment on the presence/absence of the third harmonic component in the line current and the phase current.
In [1]:
from IPython.display import Image
Image(filename =r'VSI_3ph_10_fig_1.png', width=350)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat VSI_3ph_10_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_3ph_10_orig.in and produces a new circuit file VSI_3ph_10.in, after replacing \$Vdcby2, \$L, etc. with values of our choice.

In [3]:
import gseim_calc as calc
s_Vdc = "600"
s_R = "10"
s_f_clock = "50"

l = [
  ('$Vdc', s_Vdc),
  ('$R', s_R),
  ('$f_clock', s_f_clock),
]
calc.replace_strings_1("VSI_3ph_10_orig.in", "VSI_3ph_10.in", l)
print('VSI_3ph_10.in is ready for execution')
VSI_3ph_10.in is ready for execution
Execute the following cell to run GSEIM on VSI_3ph_10.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("VSI_3ph_10.in")
os.system('run_gseim VSI_3ph_10.in')
get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = VSI_3ph_10.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
i=1000
i=2000
GSEIM: Program completed.
Out[4]:
0

The circuit file (VSI_3ph_10.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on VSI_3ph_10.in) creates data files called VSI_3ph_10_1.dat, etc. 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

f_hz = 50.0
T = 1.0/f_hz

slv = calc.slv("VSI_3ph_10.in")

i_slv = 0
i_out = 2
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u1 = np.loadtxt(filename)
t1 = u1[:, 0]

col_IRab = slv.get_index(i_slv,i_out,"IRab")
col_i_a  = slv.get_index(i_slv,i_out,"i_a")

i_out = 0
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u2 = np.loadtxt(filename)
t2 = u2[:, 0]

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")
col_g5 = slv.get_index(i_slv,i_out,"g5")
col_g6 = slv.get_index(i_slv,i_out,"g6")

fig, ax = plt.subplots(3, sharex=False, gridspec_kw={'height_ratios': [2, 1, 1]})
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(6.5, 6, 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'$i_a$'   , fontsize=12)
ax[2].set_ylabel(r'$i_{ab}$', fontsize=12)

for i in range(2):
    ax[i].tick_params(labelbottom=False)

color1 = "tomato"
color2 = "dodgerblue"
color3 = "olive"
color4 = "blue"
color5 = "grey"
color6 = "green"
color7 = "crimson"

dy = 1.5

ax[0].plot(t2*1e3, (u2[:,col_g1]       ), color=color1, linewidth=1.0, label="$g_1$")
ax[0].plot(t2*1e3, (u2[:,col_g2] -   dy), color=color2, linewidth=1.0, label="$g_2$")
ax[0].plot(t2*1e3, (u2[:,col_g3] - 2*dy), color=color3, linewidth=1.0, label="$g_3$")
ax[0].plot(t2*1e3, (u2[:,col_g4] - 3*dy), color=color4, linewidth=1.0, label="$g_4$")
ax[0].plot(t2*1e3, (u2[:,col_g5] - 4*dy), color=color5, linewidth=1.0, label="$g_5$")
ax[0].plot(t2*1e3, (u2[:,col_g6] - 5*dy), color=color6, linewidth=1.0, label="$g_6$")

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

ax[1].plot(t1*1e3, u1[:,col_i_a] , color=color7, linewidth=1.0, label="$i_a$")
ax[2].plot(t1*1e3, u1[:,col_IRab], color=color4, linewidth=1.0, label="$i_{ab}$")

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

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})

#plt.tight_layout()
plt.show()
filename: VSI_3ph_10_3.dat
filename: VSI_3ph_10_1.dat
No description has been provided for this image
In [6]:
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("VSI_3ph_10.in")

i_slv = 0
i_out = 2
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u1 = np.loadtxt(filename)
t1 = u1[:, 0]

col_IRab = slv.get_index(i_slv,i_out,"IRab")
col_i_a  = slv.get_index(i_slv,i_out,"i_a")

t_start = T 
t_end = 2.0*T

n_fourier = 20

coeff_IRab, thd_IRab = calc.fourier_coeff_1C(t1, u1[:,col_IRab], 
    t_start, t_end, 1.0e-8, n_fourier)
coeff_i_a, thd_i_a = calc.fourier_coeff_1C(t1, u1[:,col_i_a], 
    t_start, t_end, 1.0e-8, n_fourier)

print("line current 3rd harmonic: peak value:", "%11.4E"%(coeff_IRab[3]))
print("phase current 3rd harmonic: peak value:", "%11.4E"%(coeff_i_a[3]))

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

y_IRab = np.array(coeff_IRab)
y_i_a  = np.array(coeff_i_a)

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

set_size(6, 4, ax[0])

delta = 5.0
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(2):
    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('$i_{ab}$',fontsize=14)
ax[1].set_ylabel('$i_a$'   ,fontsize=14)

bars1 = ax[0].bar(x, y_IRab, width=0.3, color='red',   label="$i_{ab}$", zorder=3)
bars2 = ax[1].bar(x, y_i_a , width=0.3, color='green', label="$i_a$"   , zorder=3)

plt.tight_layout()
plt.show()
filename: VSI_3ph_10_3.dat
line current 3rd harmonic: peak value:  7.8998E-04
phase current 3rd harmonic: peak value:  9.0000E-04
No description has been provided for this image

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

In [ ]: