3-phase VSI

A three-phase inverter as shown in the figure is feeding a balanced star connected resistive load with $R=10\,\Omega$. The inverter operates in $\phi$ degree conduction mode with a switching frequency of $50\,$Hz and $V_{dc}=600\,$V. The gate signals for switches S1 and S4 of leg a are also given. The gate signals for leg b and c are phase shifted with respect to leg a by $120^{\circ}$ and $240^{\circ}$, respectively. For what values of $\phi$ can the phase voltage $v_{an}$ be expected to be free of the third harmonic?
In [1]:
from IPython.display import Image
Image(filename =r'VSI_3ph_12_fig_1.png', width=750)
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In [2]:
# run this cell to view the circuit file.
%pycat VSI_3ph_12_orig.in

We now replace the strings such as \$Vdc, \$R, with the values of our choice by running the python script given below. It takes an existing circuit file VSI_3ph_12_orig.in and produces a new circuit file VSI_3ph_12.in, after replacing \$Vdcby2, \$R, etc. with values of our choice.

In [3]:
import gseim_calc as calc
s_Vdc = "600"
s_f_clock = "50"
f_clock = float(s_f_clock)
T = 1/f_clock
s_2T = ("%11.4E"%(2.0*T)).strip()

phi = 80.0 # to be changed by user
D1 = phi/360.0
s_D1 = ("%11.4E"%(D1)).strip()

s_R = "10"

l = [
  ('$Vdc', s_Vdc),
  ('$R', s_R),
  ('$f_clock', s_f_clock),
  ('$D1', s_D1),
  ('$2T', s_2T)
]
calc.replace_strings_1("VSI_3ph_12_orig.in", "VSI_3ph_12.in", l)
print('VSI_3ph_12.in is ready for execution')
VSI_3ph_12.in is ready for execution
Execute the following cell to run GSEIM on VSI_3ph_12.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("VSI_3ph_12.in")
os.system('run_gseim VSI_3ph_12.in')
get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = VSI_3ph_12.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_12.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on VSI_3ph_12.in) creates data files called VSI_3ph_12_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_12.in")

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

col_v_an = slv.get_index(i_slv,i_out,"v_an")

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

set_size(6.5, 5, ax[0])

for i in range(2):
    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'$v_{an}$', fontsize=12)

ax[0].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_v_an], color=color7, linewidth=1.0, label="$v_{an}$")

ax[1].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_12_2.dat
filename: VSI_3ph_12_1.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

f_hz = 50.0
T = 1.0/f_hz

slv = calc.slv("VSI_3ph_12.in")

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

col_v_an = slv.get_index(i_slv,i_out,"v_an")

t_start = T 
t_end = 2.0*T

n_fourier = 20

coeff_v_an, thd_v_an = calc.fourier_coeff_1C(t1, u1[:,col_v_an], 
    t_start, t_end, 1.0e-8, n_fourier)

print("phase voltage 3rd harmonic: peak value:", "%11.4E"%(coeff_v_an[3]))

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

y_v_an = np.array(coeff_v_an)

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

set_size(5, 2.5, ax) 

plt.grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

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)

ax.set_xlim(left=-1.0, right=float(n_fourier))
ax.set_xticks(x_major_ticks)
ax.set_xticks(x_minor_ticks, minor=True)
ax.grid(visible=True, which='major', axis='x', color='#CCCCCC', linestyle='-', zorder=0)

ax.set_ylabel('$v_{an}$',fontsize=14)
ax.set_xlabel('$N$',fontsize=14)

bars1 = ax.bar(x, y_v_an, width=0.3, color='red', label="$v_{an}$", zorder=3)

plt.tight_layout()
plt.show()
filename: VSI_3ph_12_2.dat
phase voltage 3rd harmonic: peak value:  7.1916E-02
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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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