1-phase VSI

The single-phase inverter is operated such that the voltage across the RL load is as shown below. The parameters are $V_{dc}=400\,$V, $R=5\,\Omega$, $L=1\,$mH. Find $\alpha$ in degrees for which the fundamental RMS voltage across the load is $220\,$V.
In [1]:
from IPython.display import Image
Image(filename =r'VSI_1ph_13_fig_1.png', width=700)
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In [2]:
# run this cell to view the circuit file.
%pycat VSI_1ph_13_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_13_orig.in and produces a new circuit file VSI_1ph_13.in, after replacing \$Vdc, \$L, etc. with values of our choice.

In [3]:
import gseim_calc as calc
s_Vdc = '400'
s_R = '5'
s_L = '1e-3'

alpha = 65.0 # to be changed by user

f_hz = 50.0
s_f_hz = ("%11.4E"%(f_hz)).strip()

d = 180.0 - 2.0*alpha
T = 1/f_hz
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),
  ('$L', s_L),
  ('$f_hz', s_f_hz),
  ('$t0_1', s_t0_1),
  ('$t0_2', s_t0_2)
]
calc.replace_strings_1("VSI_1ph_13_orig.in", "VSI_1ph_13.in", l)
print('VSI_1ph_13.in is ready for execution')

VSI_1ph_13.in is ready for execution
Execute the following cell to run GSEIM on VSI_1ph_13.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("VSI_1ph_13.in")
os.system('run_gseim VSI_1ph_13.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = VSI_1ph_13.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=5.5346e-06
Transient simulation starts...
i=0
i=1000
solve_ssw_ex: ssw_iter_newton=1, rhs_ssw_norm=0.0000e+00
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 (VSI_1ph_13.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on VSI_1ph_13.in) creates a data file called VSI_1ph_13.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("VSI_1ph_13.in")

i_slv = 0
i_out = 0
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u = np.loadtxt(filename)
t1 = u[:, 0]
t = 1e3*t1 # convert time to msec

col_v_out = slv.get_index(i_slv,i_out,"v_out")
col_IR    = slv.get_index(i_slv,i_out,"IR"   )
col_ISrc  = slv.get_index(i_slv,i_out,"ISrc" )
col_P_R   = slv.get_index(i_slv,i_out,"P_R"  )
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

l_IR    = calc.avg_rms_2(t, u[:,col_IR   ], 0.0, 2.0*T, 1.0e-4*T)
l_P_R   = calc.avg_rms_2(t, u[:,col_P_R  ], 0.0, 2.0*T, 1.0e-4*T)
l_ISrc  = calc.avg_rms_2(t, u[:,col_ISrc ], 0.0, 2.0*T, 1.0e-4*T)
l_v_out = calc.avg_rms_2(t, u[:,col_v_out], 0.0, 2.0*T, 1.0e-4*T)

l_IR_1 = calc.min_max_1(t, u[:,col_IR], 0.0, 2.0*T)

print('average source current:', "%11.4E"%l_ISrc[1][0])
print('rms source current:', "%11.4E"%l_ISrc[2][0])
print('rms load current:', "%11.4E"%l_IR[2][0])
print('rms load voltage:', "%11.4E"%l_v_out[2][0])
print('peak load current:', "%11.4E"%l_IR_1[1])
print('power delivered to load:', "%11.4E"%l_P_R[1][0])

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

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

set_size(5, 5, ax[0])

for k in range(2):
    ax[k].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)
    ax[k].set_xlim(left=0.0, right=2.0*T)

ax[0].plot(t, u[:,col_IR   ], color=color1, linewidth=1.0, label="$i_L$")
ax[1].plot(t, u[:,col_v_out], color=color2, linewidth=1.0, label="$V_o$")
ax[1].set_xlabel('time (msec)', fontsize=11)

ax[0].set_ylabel(r'$i_L$', fontsize=11)
ax[1].set_ylabel(r'$V_o$', fontsize=11)

plt.tight_layout()
plt.show()

filename: VSI_1ph_13.dat
average source current:  2.0508E+01
rms source current:  3.9632E+01
rms load current:  4.0472E+01
rms load voltage:  2.1081E+02
peak load current:  7.9997E+01
power delivered to load:  8.1901E+03
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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_1ph_13.in")

i_slv = 0
i_out = 0
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u = np.loadtxt(filename)
t1 = u[:, 0]
t = 1e3*t1 # convert time to msec

col_v_out = slv.get_index(i_slv,i_out,"v_out")
col_IR    = slv.get_index(i_slv,i_out,"IR"   )
col_ISrc  = slv.get_index(i_slv,i_out,"ISrc" )
col_P_R   = slv.get_index(i_slv,i_out,"P_R"  )
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

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

fig, ax = plt.subplots(5, sharex=True)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(5, 6, ax[0])

for i in range(4):
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)
    ax[i].set_xlim(left=0.0, right=2.0*T)
    ax[i].set_ylim(bottom=-0.3, top=1.3)
    ax[i].set_yticks([0.0, 1.0])

ax[0].plot(t, u[:,col_g1], color=color1, linewidth=1.0)
ax[0].set_ylabel('g1', fontsize=11)

ax[1].plot(t, u[:,col_g2], color=color2, linewidth=1.0)
ax[1].set_ylabel('g2', fontsize=11)

ax[2].plot(t, u[:,col_g3], color=color3, linewidth=1.0)
ax[2].set_ylabel('g3', fontsize=11)

ax[3].plot(t, u[:,col_g4], color=color4, linewidth=1.0)
ax[3].set_ylabel('g4', fontsize=11)

ax[4].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)
ax[4].set_xlim(left=0.0, right=2.0*T)
ax[4].plot(t, u[:,col_v_out], color=color5, linewidth=1.0)
ax[4].set_ylabel("$V_{out}$", fontsize=11)

ax[4].set_xlabel('time (msec)', fontsize=11)

plt.show()

filename: VSI_1ph_13.dat
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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_1ph_13.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_IR    = slv.get_index(i_slv,i_out,"IR"   )
col_ISrc  = slv.get_index(i_slv,i_out,"ISrc" )
col_P_R   = slv.get_index(i_slv,i_out,"P_R"  )
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"   )

T = t[-1]/2

# compute Fourier coeffs:

t_start = 0.0
t_end = T

n_fourier_IR = 20
coeff_IR, thd_IR = calc.fourier_coeff_1C(t, u[:,col_IR], 
    t_start, t_end, 1.0e-4*T, n_fourier_IR)
print('fourier coefficients (load current):')
for i, c in enumerate(coeff_IR):
    print("  %3d %11.4E"% (i, c))
print("THD (load current): ", "%5.2f"%(thd_IR*100.0), "%")
print("load current fundamental: RMS value: ", "%11.4E"%(coeff_IR[1]/np.sqrt(2.0)))
print("load current 3rd harmonic: RMS value: ", "%11.4E"%(coeff_IR[3]/np.sqrt(2.0)))
print("load current 5th harmonic: RMS value: ", "%11.4E"%(coeff_IR[5]/np.sqrt(2.0)))

n_fourier_v_out = 20
coeff_v_out, thd_v_out = calc.fourier_coeff_1C(t, u[:,col_v_out],
    t_start, t_end, 1.0e-4*T, n_fourier_v_out)
print('fourier coefficients (load voltage):')
for i, c in enumerate(coeff_v_out):
    print("  %3d %11.4E"% (i, c))
print("THD (load voltage): ", "%5.2f"%(thd_v_out*100.0), "%")
print("load voltage fundamental: RMS value: ", "%11.4E"%(coeff_v_out[1]/np.sqrt(2.0)))
print("load voltage 3rd harmonic: RMS value: ", "%11.4E"%(coeff_v_out[3]/np.sqrt(2.0)))
print("load voltage 5th harmonic: RMS value: ", "%11.4E"%(coeff_v_out[5]/np.sqrt(2.0)))

x_IR = np.linspace(0, n_fourier_IR, n_fourier_IR+1)
x_v_out = np.linspace(0, n_fourier_v_out, n_fourier_v_out+1)

y_IR = np.array(coeff_IR)
y_v_out = np.array(coeff_v_out)

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

bars1 = ax[0].bar(x_IR, y_IR, width=0.3, color='red', label="$i_{load}$")
bars2 = ax[1].bar(x_v_out, y_v_out, width=0.3, color='blue', label="$V_{out}$")

ax[0].set_xlabel('N', fontsize=11)
ax[0].set_ylabel('$i_{load}$', fontsize=11)
ax[0].set_xlim(left=0, right=n_fourier_IR)
ax[0].xaxis.set_ticks(np.arange(0, n_fourier_IR, 2))
ax[0].legend(loc = 'upper right',frameon = True, fontsize = 10, title = None,
   markerfirst = True, markerscale = 1.0, labelspacing = 0.5, columnspacing = 2.0,
   prop = {'size' : 12},)

ax[1].set_xlabel('N', fontsize=11)
ax[1].set_ylabel('$v_{out}$', fontsize=11)
ax[1].set_xlim(left=0, right=n_fourier_v_out)
ax[1].xaxis.set_ticks(np.arange(0, n_fourier_v_out, 2))
ax[1].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: VSI_1ph_13.dat
fourier coefficients (load current):
    0  1.5054E-04
    1  4.2945E+01
    2  2.9779E-04
    3  3.2119E+01
    4  2.8843E-04
    5  1.5781E+01
    6  2.7428E-04
    7  1.1427E+00
    8  2.5699E-04
    9  6.8072E+00
   10  2.3806E-04
   11  7.3613E+00
   12  2.1868E-04
   13  3.3535E+00
   14  1.9963E-04
   15  1.2259E+00
   16  1.8135E-04
   17  3.5381E+00
   18  1.6409E-04
   19  2.9618E+00
   20  1.4791E-04
THD (load current):  88.11 %
load current fundamental: RMS value:   3.0366E+01
load current 3rd harmonic: RMS value:   2.2712E+01
load current 5th harmonic: RMS value:   1.1159E+01
fourier coefficients (load voltage):
    0  3.0122E-08
    1  2.1523E+02
    2  5.9587E-08
    3  1.6396E+02
    4  5.7713E-08
    5  8.3409E+01
    6  5.4882E-08
    7  6.3346E+00
    8  5.1422E-08
    9  3.9977E+01
   10  4.7635E-08
   11  4.6055E+01
   12  4.3757E-08
   13  2.2421E+01
   14  3.9944E-08
   15  8.7695E+00
   16  3.6289E-08
   17  2.7061E+01
   18  3.2836E-08
   19  2.4185E+01
   20  2.9601E-08
THD (load voltage):  95.85 %
load voltage fundamental: RMS value:   1.5219E+02
load voltage 3rd harmonic: RMS value:   1.1594E+02
load voltage 5th harmonic: RMS value:   5.8979E+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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