3-phase VSI
A three-phase voltage source inverter is supplied from a $600\,$V DC source as shown in the figure below. The inverter operates in $180^{\circ}$ conduction mode with a switching frequency of $50\,$Hz. The inverter is connected to a balanced star-connected series $RL$ load with $R=10\,\Omega$, $L=0.01\,$H.- Plot pole voltage ($V_{a0}$), line-to-line voltage ($V_{ab}$), phase voltage ($V_{an}$), and neutral voltage ($V_{n0}$).
- Determine the RMS values of the fundamental components of phase voltage and load current.
- Determine the values of the load current at the corner points.
- Determine the power delivered to the load.
- What is the average current drawn from the DC supply?
- Which are the dominant harmonics present in the DC source current?
- Which are the dominant harmonics present in the load current?
In [1]:
from IPython.display import Image
Image(filename =r'VSI_3ph_1_fig_1.png', width=750)
Out[1]:
In [2]:
# run this cell to view the circuit file.
%pycat VSI_3ph_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_3ph_1_orig.in and produces a new circuit file VSI_3ph_1.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()
s_R = "10"
s_L = "0.01"
s_f_clock = "50"
l = [
('$Vdcby2', s_Vdcby2),
('$R', s_R),
('$L', s_L),
('$f_clock', s_f_clock),
]
calc.replace_strings_1("VSI_3ph_1_orig.in", "VSI_3ph_1.in", l)
print('VSI_3ph_1.in is ready for execution')
VSI_3ph_1.in is ready for execution
Execute the following cell to run GSEIM on VSI_3ph_1.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("VSI_3ph_1.in")
os.system('run_gseim VSI_3ph_1.in')
get_lib_elements: filename gseim_aux/xbe.aux get_lib_elements: filename gseim_aux/ebe.aux Circuit: filename = VSI_3ph_1.in main: i_solve = 0 main: calling solve_trns mat_ssw_1_ex: n_statevar: 3 Transient simulation starts... i=0 solve_ssw_ex: ssw_iter_newton=0, rhs_ssw_norm=2.7710e+01 Transient simulation starts... i=0 solve_ssw_ex: ssw_iter_newton=1, rhs_ssw_norm=7.1054e-15 solve_ssw_ex: calling solve_ssw_1_ex for one more trns step Transient simulation starts... i=0 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_3ph_1.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on VSI_3ph_1.in) creates data files called VSI_3ph_1_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_1.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_1_1.dat filename: VSI_3ph_1_2.dat filename: VSI_3ph_1_3.dat
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_1.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_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_1_1.dat filename: VSI_3ph_1_2.dat filename: VSI_3ph_1_3.dat average power delivered to load: 2.0176E+04 average DC supply current: 3.3625E+01
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_1.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")
# time points where i_Ra(t) has corners:
l_t1 = [0, 1, 2, 3, 4, 5, 6]
delt1 = T/6
print("salient points in IRa(t):")
for k in l_t1:
t_given = float(k)*delt1
IRa = calc.get_value_1(t3, u3[:,col_IRa], t_given)
print('t:', str(k) + "*(T/6)", ' IRa:', "%11.4E"%IRa)
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_1_1.dat filename: VSI_3ph_1_2.dat filename: VSI_3ph_1_3.dat salient points in IRa(t): t: 0*(T/6) IRa: -2.0741E+01 t: 1*(T/6) IRa: 1.8425E+01 t: 2*(T/6) IRa: 3.9166E+01 t: 3*(T/6) IRa: 2.0721E+01 t: 4*(T/6) IRa: -1.8436E+01 t: 5*(T/6) IRa: -3.9166E+01 t: 6*(T/6) IRa: -2.0721E+01
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_1.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_IS1, thd_v_IS1 = calc.fourier_coeff_1C(t3, u3[:,col_IS1],
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_IS1 = np.array(coeff_IS1)
y_IRa = np.array(coeff_IRa)
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 = 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)
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('$i_{S1}$',fontsize=14)
ax[1].set_ylabel('$i_{Ra}$', fontsize=14)
ax[1].set_xlabel('N', fontsize=14)
bars1 = ax[0].bar(x, y_IS1, width=0.3, color='red', label="$i_{S1}$", zorder=3)
bars2 = ax[1].bar(x, y_IRa, width=0.3, color='blue', label="$i_{Ra}$", zorder=3)
plt.tight_layout()
plt.show()
filename: VSI_3ph_1_1.dat filename: VSI_3ph_1_2.dat filename: VSI_3ph_1_3.dat THD (IRa): 13.18 % I_Ra fundamental: RMS value: 2.5711E+01 V_an fundamental: RMS value: 2.7009E+02
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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