1-phase VSI

In the half bridge inverter shown below, the switches S1 and S2 are switched alternatively at a $50\,\%$ duty cycle with a switching frequency of $1\,$kHz. The other parameters are $R=20\,\Omega$, $L=10\,$mH and $V_{dc}=200\,$V.
  1. Plot the current through the DC source and determine its average value.
  2. Determine the peak load current.
  3. Determine the RMS value of the fundamental component of the load current.
  4. What is the interval between the zero crossings of load voltage and load current?
  5. Determine the power delivered to the load.
  6. Determine the THD of the voltage across the $RL$ load.
  7. Estimate the THD of the load current.
In [1]:
from IPython.display import Image
Image(filename =r'VSI_1ph_1_fig_1.png', width=200)
Out[1]:
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In [2]:
# run this cell to view the circuit file.
%pycat VSI_1ph_1_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_1_orig.in and produces a new circuit file VSI_1ph_1.in, after replacing \$Vdc, \$L, etc. with values of our choice.

In [3]:
import gseim_calc as calc
s_Vdc = '200'
s_R = '20'
s_L = '10m'

f_hz = 1.0e3
s_f_hz = "%11.4E"%(f_hz)

T = 1/f_hz
s_Tby2 = "%11.4E"%(T/2)

l = [
  ('$Vdc', s_Vdc),
  ('$R', s_R),
  ('$L', s_L),
  ('$f_hz', s_f_hz),
  ('$Tby2', s_Tby2)
]
calc.replace_strings_1("VSI_1ph_1_orig.in", "VSI_1ph_1.in", l)
print('VSI_1ph_1.in is ready for execution')

VSI_1ph_1.in is ready for execution
Execute the following cell to run GSEIM on VSI_1ph_1.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("VSI_1ph_1.in")
os.system('run_gseim VSI_1ph_1.in')

Circuit: filename = VSI_1ph_1.in
main: calling solve_sss
solve_sss starting: sss_n_st: 1
solve_sss_ex: sss_iter_newton=0, rhs_sss_norm=4.5144e+00, sss_period_1_compute=2.0000e-03
solve_sss_ex: sss_iter_newton=1, rhs_sss_norm=3.4639e-14, sss_period_1_compute=2.0000e-03
solve_sss_ex: calling sss_solve_trns_ex for one more trns step
Transient simulation starts...
i=0
i=1000
GSEIM: Program completed.
Out[4]:
0

The circuit file (VSI_1ph_1.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on VSI_1ph_1.in) creates a data file called VSI_1ph_1.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_1.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 = t1*1e3 # convert time to msec

v_out = slv.get_array_double(i_slv,i_out,"v_out",u)
IR    = slv.get_array_double(i_slv,i_out,"IR"   ,u)
ISrc1 = slv.get_array_double(i_slv,i_out,"ISrc1",u)
ISrc2 = slv.get_array_double(i_slv,i_out,"ISrc2",u)
P_R   = slv.get_array_double(i_slv,i_out,"P_R"  ,u)
g1    = slv.get_array_double(i_slv,i_out,"g1"   ,u)
g2    = slv.get_array_double(i_slv,i_out,"g2"   ,u)

# 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_3a(t, IR   , 0.0, 2.0*T, 1.0e-4*T)
l_P_R   = calc.avg_rms_3a(t, P_R  , 0.0, 2.0*T, 1.0e-4*T)
l_ISrc1 = calc.avg_rms_3a(t, ISrc1, 0.0, 2.0*T, 1.0e-4*T)

l_IR_1 = calc.min_max_1(t, IR, 0.0, 2.0*T)

print('average source current:' , "%11.4E"%l_ISrc1[0])
print('rms source current:'     , "%11.4E"%l_ISrc1[1])
print('rms load current:'       , "%11.4E"%l_IR[1])
print('peak load current:'      , "%11.4E"%l_IR_1[1])
print('power delivered to load:', "%11.4E"%l_P_R[0])

l_cross_1_IR, l_cross_2_IR = calc.cross_over_points_1(t, IR, 0.0, 2.0*T, 0.0)
print('zero-crossing points of load current (positive slope):')
for t1 in l_cross_1_IR:
    print("  ", "%11.4E"%t1)
print('zero-crossing points of load current (negative slope):')
for t1 in l_cross_2_IR:
    print("  ", "%11.4E"%t1)

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, 6, ax[0])

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

ax[0].plot(t, IR, color=color1, linewidth=1.0, label="$i_L$")
ax[0].set_xlim(left=0.0, right=2.0*T)
ax[0].axhline(y=l_IR[1], color=color1, linewidth=1.0, label="$i_L^{rms}$", linestyle='--', dashes=(5,3))
ax[0].plot(t, ISrc1, color=color2, linewidth=1.0, label="$i_1$")
ax[0].axhline(y=l_ISrc1[0], color=color2, linewidth=1.0, label="$i_1^{avg}$", linestyle='--', dashes=(5,3))
ax[0].set_xlabel('time (msec)', fontsize=11)
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[1].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)
ax[1].set_xlim(left=0.0, right=2.0*T)
ax[1].plot(t, v_out, color=color1, linewidth=1.0, label="$V_o$")
ax[1].set_xlabel('time (msec)', fontsize=11)
ax[1].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_1ph_1.dat
average source current:  3.8148E-01
rms source current:  1.9436E+00
rms load current:  2.7476E+00
peak load current:  4.6133E+00
power delivered to load:  1.5099E+02
zero-crossing points of load current (positive slope):
    1.8957E-01
    1.1896E+00
zero-crossing points of load current (negative slope):
    6.8957E-01
    1.6896E+00
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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_1.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]

v_out = slv.get_array_double(i_slv,i_out,"v_out",u)
IR    = slv.get_array_double(i_slv,i_out,"IR"   ,u)
ISrc1 = slv.get_array_double(i_slv,i_out,"ISrc1",u)
ISrc2 = slv.get_array_double(i_slv,i_out,"ISrc2",u)
P_R   = slv.get_array_double(i_slv,i_out,"P_R"  ,u)
g1    = slv.get_array_double(i_slv,i_out,"g1"   ,u)
g2    = slv.get_array_double(i_slv,i_out,"g2"   ,u)

# 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 = 0.0
t_end = T

n_fourier_IR = 20
coeff_IR, thd_IR = calc.fourier_coeff_1C(t, 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)))

n_fourier_v_out = 20
coeff_v_out, thd_v_out = calc.fourier_coeff_1C(t, 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), "%")

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_1.dat
fourier coefficients (load current):
    0  6.3207E-06
    1  3.8550E+00
    2  1.8360E-06
    3  4.4698E-01
    4  8.5322E-07
    5  1.6153E-01
    6  8.3377E-07
    7  8.2534E-02
    8  1.3224E-06
    9  4.9989E-02
   10  2.1110E-06
   11  3.3514E-02
   12  3.0401E-06
   13  2.4046E-02
   14  4.2005E-06
   15  1.8114E-02
   16  5.4861E-06
   17  1.4159E-02
   18  6.9502E-06
   19  1.1397E-02
   20  8.5378E-06
THD (load current):  12.65 %
load current fundamental: RMS value:   2.7259E+00
fourier coefficients (load voltage):
    0  5.1020E-02
    1  2.5465E+02
    2  1.0205E-01
    3  8.4874E+01
    4  1.0207E-01
    5  5.0916E+01
    6  1.0211E-01
    7  3.6359E+01
    8  1.0216E-01
    9  2.8270E+01
   10  1.0222E-01
   11  2.3120E+01
   12  1.0230E-01
   13  1.9553E+01
   14  1.0239E-01
   15  1.6936E+01
   16  1.0250E-01
   17  1.4933E+01
   18  1.0262E-01
   19  1.3351E+01
   20  1.0276E-01
THD (load voltage):  48.31 %
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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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