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 $V_{dc}=300\,$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 $\phi = 120^{\circ}$,
  1. Plot pole voltage ($V_{a0}$), line-to-line voltage ($V_{ab}$), phase voltage ($V_{an}$), and neutral voltage ($V_{n0}$).
  2. Determine the RMS values of the fundamental components of phase voltage and load current.
  3. Determine the power delivered to the load.
  4. What is the average current drawn from the DC supply?
  5. Which are the dominant harmonics present in the load current?
In [1]:
from IPython.display import Image
Image(filename =r'VSI_3ph_2_fig_1.png', width=800)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat VSI_3ph_2_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_2_orig.in and produces a new circuit file VSI_3ph_2.in, after replacing \$Vdcby2, \$L, etc. with values of our choice.

In [3]:
import gseim_calc as calc
Vdc = 600.0
s_Vdcby2 = ("%11.4E"%(Vdc/2)).strip()
f_clock = 50.0
s_f_clock = ("%11.4E"%(f_clock)).strip()
T = 1/f_clock
s_2T = ("%11.4E"%(2.0*T)).strip()

phi = 120.0
D1 = phi/360.0
s_D1 = ("%11.4E"%(D1)).strip()

s_R = "10"

l = [
  ('$Vdcby2', s_Vdcby2),
  ('$R', s_R),
  ('$f_clock', s_f_clock),
  ('$D1', s_D1),
  ('$2T', s_2T)
]
calc.replace_strings_1("VSI_3ph_2_orig.in", "VSI_3ph_2.in", l)
print('VSI_3ph_2.in is ready for execution')
VSI_3ph_2.in is ready for execution
Execute the following cell to run GSEIM on VSI_3ph_2.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("VSI_3ph_2.in")
os.system('run_gseim VSI_3ph_2.in')
get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = VSI_3ph_2.in
main: i_solve = 0
main: calling solve_trns
Transient simulation starts...
i=0
GSEIM: Program completed.
Out[4]:
0

The circuit file (VSI_3ph_2.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on VSI_3ph_2.in) creates data files called VSI_3ph_2_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

slv = calc.slv("VSI_3ph_2.in")

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

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

T = t1[-1]/2

i_out = 1
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u2 = np.loadtxt(filename)
t2 = u2[:, 0]

col_v_a0 = slv.get_index(i_slv,i_out,"v_a0")
col_v_b0 = slv.get_index(i_slv,i_out,"v_b0")
col_v_c0 = slv.get_index(i_slv,i_out,"v_c0")
col_v_ab = slv.get_index(i_slv,i_out,"v_ab")
col_v_bc = slv.get_index(i_slv,i_out,"v_bc")
col_v_ca = slv.get_index(i_slv,i_out,"v_ca")
col_v_an = slv.get_index(i_slv,i_out,"v_an")
col_v_bn = slv.get_index(i_slv,i_out,"v_bn")
col_v_cn = slv.get_index(i_slv,i_out,"v_cn")
col_v_n0 = slv.get_index(i_slv,i_out,"v_n0")

i_out = 2
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u3 = np.loadtxt(filename)
t3 = u3[:, 0]

col_IRa  = slv.get_index(i_slv,i_out,"IRa")
col_IRb  = slv.get_index(i_slv,i_out,"IRb")
col_IRc  = slv.get_index(i_slv,i_out,"IRc")
col_IS1  = slv.get_index(i_slv,i_out,"IS1")
col_P_Ra = slv.get_index(i_slv,i_out,"P_Ra")
col_P_Rb = slv.get_index(i_slv,i_out,"P_Rb")
col_P_Rc = slv.get_index(i_slv,i_out,"P_Rc")

color1='green'

fig, ax = plt.subplots(6, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(5.5, 7, ax[0])

for i in range(6):
    ax[i].set_xlim(left=0, right=2.0*T*1e3)
    ax[i].set_ylim(bottom=-0.4, top=1.4)
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].plot(t1*1e3, u1[:,col_g1], color=color1, linewidth=1.0)
ax[1].plot(t1*1e3, u1[:,col_g2], color=color1, linewidth=1.0)
ax[2].plot(t1*1e3, u1[:,col_g3], color=color1, linewidth=1.0)
ax[3].plot(t1*1e3, u1[:,col_g4], color=color1, linewidth=1.0)
ax[4].plot(t1*1e3, u1[:,col_g5], color=color1, linewidth=1.0)
ax[5].plot(t1*1e3, u1[:,col_g6], color=color1, linewidth=1.0)

ax[0].set_ylabel(r'$g_1$', fontsize=12)
ax[1].set_ylabel(r'$g_2$', fontsize=12)
ax[2].set_ylabel(r'$g_3$', fontsize=12)
ax[3].set_ylabel(r'$g_4$', fontsize=12)
ax[4].set_ylabel(r'$g_5$', fontsize=12)
ax[5].set_ylabel(r'$g_6$', fontsize=12)

ax[5].set_xlabel('time (msec)', fontsize=12)

ax[0].tick_params(labelbottom=False)
ax[1].tick_params(labelbottom=False)
ax[2].tick_params(labelbottom=False)
ax[3].tick_params(labelbottom=False)
ax[4].tick_params(labelbottom=False)

#plt.tight_layout()
plt.show()
filename: VSI_3ph_2_1.dat
filename: VSI_3ph_2_2.dat
filename: VSI_3ph_2_3.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("VSI_3ph_2.in")

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

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

T = t1[-1]/2

i_out = 1
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u2 = np.loadtxt(filename)
t2 = u2[:, 0]

col_v_a0 = slv.get_index(i_slv,i_out,"v_a0")
col_v_b0 = slv.get_index(i_slv,i_out,"v_b0")
col_v_c0 = slv.get_index(i_slv,i_out,"v_c0")
col_v_ab = slv.get_index(i_slv,i_out,"v_ab")
col_v_bc = slv.get_index(i_slv,i_out,"v_bc")
col_v_ca = slv.get_index(i_slv,i_out,"v_ca")
col_v_an = slv.get_index(i_slv,i_out,"v_an")
col_v_bn = slv.get_index(i_slv,i_out,"v_bn")
col_v_cn = slv.get_index(i_slv,i_out,"v_cn")
col_v_n0 = slv.get_index(i_slv,i_out,"v_n0")

i_out = 2
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u3 = np.loadtxt(filename)
t3 = u3[:, 0]

col_IRa  = slv.get_index(i_slv,i_out,"IRa")
col_IRb  = slv.get_index(i_slv,i_out,"IRb")
col_IRc  = slv.get_index(i_slv,i_out,"IRc")
col_IS1  = slv.get_index(i_slv,i_out,"IS1")
col_P_Ra = slv.get_index(i_slv,i_out,"P_Ra")
col_P_Rb = slv.get_index(i_slv,i_out,"P_Rb")
col_P_Rc = slv.get_index(i_slv,i_out,"P_Rc")

l_IS1   = calc.avg_rms_2(t3, u3[:,col_IS1 ], T, 2.0*T, 1.0e-4*T)
l_P_Ra  = calc.avg_rms_2(t3, u3[:,col_P_Ra], T, 2.0*T, 1.0e-4*T)

print('average power delivered to load:', "%11.4E"%(3.0*l_P_Ra[1][0]))
print('average DC supply current:', "%11.4E"%l_IS1[1][0])

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

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

set_size(5.5, 7, ax[0])

for i in range(4):
    ax[i].set_xlim(left=0, right=2.0*T*1e3)
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].plot(t2*1e3, u2[:,col_v_a0], color=color1, linewidth=1.0, label="$V_{a0}$")
ax[1].plot(t2*1e3, u2[:,col_v_ab], color=color2, linewidth=1.0, label="$V_{ab}$")
ax[2].plot(t2*1e3, u2[:,col_v_an], color=color3, linewidth=1.0, label="$V_{an}$")
ax[3].plot(t2*1e3, u2[:,col_v_n0], color=color4, linewidth=1.0, label="$V_{n0}$")

ax[3].set_ylim(bottom=-1, top=1)
ax[3].set_xlabel('time (msec)', fontsize=12)

for i in range(4):
    ax[i].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_2_1.dat
filename: VSI_3ph_2_2.dat
filename: VSI_3ph_2_3.dat
average power delivered to load:  1.8003E+04
average DC supply current:  3.0000E+01
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In [7]:
import numpy as np
import matplotlib.pyplot as plt 
import gseim_calc as calc
from setsize import set_size

slv = calc.slv("VSI_3ph_2.in")

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

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

T = t1[-1]/2

i_out = 1
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u2 = np.loadtxt(filename)
t2 = u2[:, 0]

col_v_a0 = slv.get_index(i_slv,i_out,"v_a0")
col_v_b0 = slv.get_index(i_slv,i_out,"v_b0")
col_v_c0 = slv.get_index(i_slv,i_out,"v_c0")
col_v_ab = slv.get_index(i_slv,i_out,"v_ab")
col_v_bc = slv.get_index(i_slv,i_out,"v_bc")
col_v_ca = slv.get_index(i_slv,i_out,"v_ca")
col_v_an = slv.get_index(i_slv,i_out,"v_an")
col_v_bn = slv.get_index(i_slv,i_out,"v_bn")
col_v_cn = slv.get_index(i_slv,i_out,"v_cn")
col_v_n0 = slv.get_index(i_slv,i_out,"v_n0")

i_out = 2
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u3 = np.loadtxt(filename)
t3 = u3[:, 0]

col_IRa  = slv.get_index(i_slv,i_out,"IRa")
col_IRb  = slv.get_index(i_slv,i_out,"IRb")
col_IRc  = slv.get_index(i_slv,i_out,"IRc")
col_IS1  = slv.get_index(i_slv,i_out,"IS1")
col_P_Ra = slv.get_index(i_slv,i_out,"P_Ra")
col_P_Rb = slv.get_index(i_slv,i_out,"P_Rb")
col_P_Rc = slv.get_index(i_slv,i_out,"P_Rc")

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

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

set_size(5.5, 6, ax[0])

for i in range(4):
    ax[i].set_xlim(left=0, right=2.0*T*1e3)
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].plot(t3*1e3, u3[:,col_IRa], color=color1, linewidth=1.0, label="$I_{Ra}$")
ax[1].plot(t3*1e3, u3[:,col_IRb], color=color2, linewidth=1.0, label="$I_{Rb}$")
ax[2].plot(t3*1e3, u3[:,col_IRc], color=color3, linewidth=1.0, label="$I_{Rc}$")
ax[3].plot(t3*1e3, u3[:,col_IS1], color=color4, linewidth=1.0, label="$I_{S1}$")

ax[3].set_xlabel('time (msec)', fontsize=12)

ax[0].set_ylabel(r'$I_{Ra}$', fontsize=12)
ax[1].set_ylabel(r'$I_{Rb}$', fontsize=12)
ax[2].set_ylabel(r'$I_{Rc}$', fontsize=12)
ax[3].set_ylabel(r'$I_{S1}$', fontsize=12)

plt.tight_layout()
plt.show()
filename: VSI_3ph_2_1.dat
filename: VSI_3ph_2_2.dat
filename: VSI_3ph_2_3.dat
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In [8]:
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_3ph_2.in")

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

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

T = t1[-1]/2

i_out = 1
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u2 = np.loadtxt(filename)
t2 = u2[:, 0]

col_v_a0 = slv.get_index(i_slv,i_out,"v_a0")
col_v_b0 = slv.get_index(i_slv,i_out,"v_b0")
col_v_c0 = slv.get_index(i_slv,i_out,"v_c0")
col_v_ab = slv.get_index(i_slv,i_out,"v_ab")
col_v_bc = slv.get_index(i_slv,i_out,"v_bc")
col_v_ca = slv.get_index(i_slv,i_out,"v_ca")
col_v_an = slv.get_index(i_slv,i_out,"v_an")
col_v_bn = slv.get_index(i_slv,i_out,"v_bn")
col_v_cn = slv.get_index(i_slv,i_out,"v_cn")
col_v_n0 = slv.get_index(i_slv,i_out,"v_n0")

i_out = 2
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u3 = np.loadtxt(filename)
t3 = u3[:, 0]

col_IRa  = slv.get_index(i_slv,i_out,"IRa")
col_IRb  = slv.get_index(i_slv,i_out,"IRb")
col_IRc  = slv.get_index(i_slv,i_out,"IRc")
col_IS1  = slv.get_index(i_slv,i_out,"IS1")
col_P_Ra = slv.get_index(i_slv,i_out,"P_Ra")
col_P_Rb = slv.get_index(i_slv,i_out,"P_Rb")
col_P_Rc = slv.get_index(i_slv,i_out,"P_Rc")

# compute Fourier coeffs:

t_start = T 
t_end = 2.0*T

n_fourier = 20

coeff_v_an, thd_v_an = calc.fourier_coeff_1C(t2, u2[:,col_v_an], 
    t_start, t_end, 1.0e-8, n_fourier)

coeff_IRa, thd_IRa = calc.fourier_coeff_1C(t3, u3[:,col_IRa], 
    t_start, t_end, 1.0e-8, n_fourier)

print("THD (IRa): ", "%5.2f"%(thd_IRa*100.0), "%")
print("I_Ra fundamental: RMS value: ", "%11.4E"%(coeff_IRa[1]/np.sqrt(2.0)))
print("V_an fundamental: RMS value: ", "%11.4E"%(coeff_v_an[1]/np.sqrt(2.0)))

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

y_IRa = np.array(coeff_IRa)

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

set_size(6, 2, ax)

delta = 2.0
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=grid_color, linestyle='-', zorder=0)

ax.set_ylabel('$i_{Ra}$', fontsize=14)
ax.set_xlabel('N', fontsize=14)

bars2 = ax.bar(x, y_IRa, width=0.3, color='blue', label="$i_{Ra}$", zorder=3)

plt.tight_layout()
plt.show()
filename: VSI_3ph_2_1.dat
filename: VSI_3ph_2_2.dat
filename: VSI_3ph_2_3.dat
THD (IRa):  31.06 %
I_Ra fundamental: RMS value:   2.3393E+01
V_an fundamental: RMS value:   2.3393E+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.

In [ ]: