DC motor drive

A single-phase half-controlled AC-DC converter feeds a separately excited DC motor. The parameters of the DC motor are $R_a=0.4\,\Omega$, $L_a=0.5\,$H, $K_T=0.5\,$N-m/A, $J=0.001\,$kg-m$^2$, $B=0.001\,$N-m-s/rad. The rated voltage of the motor is $200\,$V DC, and the rated torque is $1\,$N-m. The grid voltage is $130\,$V, $50\,$Hz. Determine the following if the rated voltage and torque are applied to the motor.
  1. Firing angle of the converter,
  2. Average motor current,
  3. Speed of motor,
  4. RMS source current,
  5. Source power factor,
  6. THD in the source current,
  7. Harmonic content in the electromagnetic torque.
In [1]:
from IPython.display import Image
Image(filename =r'dcmc_2_fig_1.png', width=250)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat dcmc_2_orig.in

We now replace the strings such as \$La with the values of our choice by running the python script given below. It takes an existing circuit file dcmc_2_orig.in and produces a new circuit file dcmc_2.in, after replacing \$La (etc) with values of our choice.

In [3]:
import gseim_calc as calc
import numpy as np

Vm_ac = 230.0*np.sqrt(2.0)
s_Vm_ac = ("%11.4E"%Vm_ac).strip()
s_Ra = "0.4"
s_La = "0.5"
s_k_e = "0.5"
s_J = "0.001"
s_b_damp = "0.001"
s_TL = "1"
s_alpha = "35.0" # to be changed by user

l = [
  ('$Vm_ac', s_Vm_ac),
  ('$Ra', s_Ra),
  ('$La', s_La),
  ('$k_e', s_k_e),
  ('$J', s_J),
  ('$b_damp', s_b_damp),
  ('$TL', s_TL),
  ('$alpha', s_alpha),
]
calc.replace_strings_1("dcmc_2_orig.in", "dcmc_2.in", l)
print('dcmc_2.in is ready for execution')

dcmc_2.in is ready for execution
Execute the following cell to run GSEIM on dcmc_2.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("dcmc_2.in")
os.system('run_gseim dcmc_2.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = dcmc_2.in
Circuit: n_xbeu_vr = 4
Circuit: n_ebeu_nd = 4
main: i_solve = 0
ssw_allocate_1 (2): n_statevar=2
main: calling solve_trns
mat_ssw_1_ex: n_statevar: 2
mat_ssw_1_e0: cct.n_ebeu: 6
Transient simulation starts...
i=0
i=1000
i=2000
solve_ssw_ex: ssw_iter_newton=0, rhs_ssw_norm=7.2179e+01
Transient simulation starts...
i=0
i=1000
i=2000
solve_ssw_ex: ssw_iter_newton=1, rhs_ssw_norm=5.0955e+01
Transient simulation starts...
i=0
i=1000
i=2000
solve_ssw_ex: ssw_iter_newton=2, rhs_ssw_norm=8.8442e-13
solve_ssw_ex: calling solve_ssw_1_ex for one more trns step
Transient simulation starts...
i=0
i=1000
i=2000
solve_ssw_1_ex over (after trns step for output)
solve_ssw_ex ends, slv.ssw_iter_newton=2
GSEIM: Program completed.
Out[4]:
0

The circuit file (dcmc_2.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on dcmc_2.in) creates a data file called dcmc_2.dat 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("dcmc_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_v_s    = slv.get_index(i_slv,i_out,"v_s")
col_i_s    = slv.get_index(i_slv,i_out,"i_s")
col_tem    = slv.get_index(i_slv,i_out,"tem")
col_wrm    = slv.get_index(i_slv,i_out,"wrm")
col_v_dcmc = slv.get_index(i_slv,i_out,"v_dcmc")
col_i_dcmc = slv.get_index(i_slv,i_out,"i_dcmc")

i_out = 1
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_IT1 = slv.get_index(i_slv,i_out,"IT1")
col_IT2 = slv.get_index(i_slv,i_out,"IT2")
col_ID1 = slv.get_index(i_slv,i_out,"ID1")
col_ID2 = slv.get_index(i_slv,i_out,"ID2")

p_s = u1[:,col_i_s]*u1[:,col_v_s]

l_i_s    = calc.avg_rms_2(t1, u1[:,col_i_s   ], 0, 2.0*T, 1.0e-5*T)
l_v_s    = calc.avg_rms_2(t1, u1[:,col_v_s   ], 0, 2.0*T, 1.0e-5*T)
l_p_s    = calc.avg_rms_2(t1, p_s             , 0, 2.0*T, 1.0e-5*T)
l_i_dcmc = calc.avg_rms_2(t1, u1[:,col_i_dcmc], 0, 2.0*T, 1.0e-5*T)
l_v_dcmc = calc.avg_rms_2(t1, u1[:,col_v_dcmc], 0, 2.0*T, 1.0e-5*T)
l_tem    = calc.avg_rms_2(t1, u1[:,col_tem   ], 0, 2.0*T, 1.0e-5*T)
l_wrm    = calc.avg_rms_2(t1, u1[:,col_wrm   ], 0, 2.0*T, 1.0e-5*T)

t_i_s    = np.array(l_i_s[0])
t_i_dcmc = np.array(l_i_dcmc[0])
t_v_dcmc = np.array(l_v_dcmc[0])
t_tem    = np.array(l_tem[0])
t_wrm    = np.array(l_wrm[0])

Pavg = l_p_s[1][0]
Irms = l_i_s[2][0]
Vrms = l_v_s[2][0]
pf_s  = Pavg/(Vrms*Irms)

print('rms value of i_s:'       , "%11.4E"%l_i_s   [2][0])
print('average value of i_dcmc:', "%11.4E"%l_i_dcmc[1][0])
print('average value of v_dcmc:', "%11.4E"%l_v_dcmc[1][0])
print('average value of tem:'   , "%11.4E"%l_tem   [1][0])
print('average value of wrm:'   , "%11.4E"%l_wrm   [1][0])
print('source power factor:'    , "%11.4E"%pf_s)

fig, ax = plt.subplots(7, sharex=False,  gridspec_kw={'height_ratios': [1, 1.5, 1, 1, 1, 1, 1]})
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(6.5, 9, ax[0])

for i in range(7):
    ax[i].set_xlim(left=0.0, right=2.0*T*1e3)
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

for i in range(6):
    ax[i].tick_params(labelbottom=False)

ax[0].set_ylabel(r'$V_{ac}$'   , fontsize=12)
ax[1].set_ylabel(r'$g_x$'      , fontsize=12)
ax[2].set_ylabel(r'$\omega$'   , fontsize=12)
ax[3].set_ylabel(r'$\tau_{em}$', fontsize=12)
ax[4].set_ylabel(r'$i_s$'      , fontsize=12)
ax[5].set_ylabel(r'$v_o$'      , fontsize=12)
ax[6].set_ylabel(r'$i_o$'      , fontsize=12)

color1 = "red"
color2 = "green"
color3 = "violet"
color4 = "tomato"
color5 = "dodgerblue"
color6 = "olive"
color7 = "blue"
color8 = "lightseagreen"

ax[0].plot(t1*1e3, u1[:,col_v_s], color=color1, linewidth=1.0, label="$V_{ac}$")

ax[1].plot(t2*1e3, (u2[:,col_g1]      ), color=color2, linewidth=1.0, label="$g_1$")
ax[1].plot(t2*1e3, (u2[:,col_g2] - 1.2), color=color3, linewidth=1.0, label="$g_2$")

ax[2].plot(t1*1e3, u1[:,col_wrm   ], color=color4, linewidth=1.0, label=r"$\omega$")
ax[3].plot(t1*1e3, u1[:,col_tem   ], color=color5, linewidth=1.0, label=r"$\tau_{em}$")
ax[4].plot(t1*1e3, u1[:,col_i_s   ], color=color6, linewidth=1.0, label=r"$i_s$")
ax[5].plot(t1*1e3, u1[:,col_v_dcmc], color=color7, linewidth=1.0, label=r"$v_o$")
ax[6].plot(t1*1e3, u1[:,col_i_dcmc], color=color8, linewidth=1.0, label=r"$i_o$")

ax[2].plot(t_wrm   *1e3, l_wrm[1]   , color=color4, linewidth=1.0, label=r"$\omega^{avg}$"   , linestyle='--', dashes=(5,3))
ax[3].plot(t_tem   *1e3, l_tem[1]   , color=color5, linewidth=1.0, label=r"$\tau_{em}^{avg}$", linestyle='--', dashes=(5,3))
ax[4].plot(t_i_s   *1e3, l_i_s[2]   , color=color6, linewidth=1.0, label=r"$i_s^{rms}$"      , linestyle='--', dashes=(5,3))
ax[5].plot(t_v_dcmc*1e3, l_v_dcmc[1], color=color7, linewidth=1.0, label=r"$v_{dcmc}^{avg}$" , linestyle='--', dashes=(5,3))
ax[6].plot(t_i_dcmc*1e3, l_i_dcmc[1], color=color8, linewidth=1.0, label=r"$i_{dcmc}^{avg}$" , linestyle='--', dashes=(5,3))

ax[1].tick_params(left = False)
ax[1].set_yticks([])

ax[6].set_xlabel('time (msec)', fontsize=12)

for i in [1, 3, 4, 5, 6]:
    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: dcmc_2_1.dat
filename: dcmc_2_2.dat
rms value of i_s:  2.5388E+00
average value of i_dcmc:  2.7483E+00
average value of v_dcmc:  1.8834E+02
average value of tem:  1.3741E+00
average value of wrm:  3.7413E+02
source power factor:  8.8691E-01
No description has been provided for this image
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("dcmc_2.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_i_s = slv.get_index(i_slv,i_out,"i_s")
col_tem = slv.get_index(i_slv,i_out,"tem")

# compute Fourier coeffs:

t_start = 0.0
t_end = T

n_fourier = 20
coeff_i_s, thd_i_s = calc.fourier_coeff_1C(t, u[:,col_i_s], 
    t_start, t_end, 1.0e-4*T, n_fourier)
print("THD (source current): ", "%5.2f"%(thd_i_s*100.0), "%")

coeff_tem, thd_tem = calc.fourier_coeff_1C(t, u[:,col_tem],
    t_start, t_end, 1.0e-4*T, n_fourier)

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

y_i_s = np.array(coeff_i_s)
y_tem = np.array(coeff_tem)

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

bars1 = ax[0].bar(x, y_i_s, width=0.3, color='red' , label=r"$i_s$")
bars2 = ax[1].bar(x, y_tem, width=0.3, color='blue', label=r"$\tau_{em}}$")

for k in range(2):
    ax[k].set_xlabel('N', fontsize=11)
    ax[k].set_xlim(left=-1, right=n_fourier)
    ax[k].xaxis.set_ticks(np.arange(0, n_fourier, 2))


ax[0].set_ylabel(r'$i_s$'      , fontsize=11)
ax[1].set_ylabel(r'$\tau_{em}$', fontsize=11)

plt.tight_layout()
plt.show()

filename: dcmc_2_1.dat
THD (source current):  26.87 %
No description has been provided for this image

This notebook was contributed by Prof. Nakul Narayanan K, Govt. Engineering College, Thrissur. He may be contacted at nakul@gectcr.ac.in.

In [ ]: