Waveforms
The waveform of the current $i$ drawn by a load from a sinusoidal AC voltage source is shown in the figure. The current waveform is a quasi-square wave and is free from the third harmonic component. The amplitude of voltage and current are $325\,$V and $10\,$A, respectively. Determine the following.- the angle $\alpha$
- the RMS values of voltage and current
- the fundamental RMS of current
- the average power delivered to the load
- the load power factor
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from IPython.display import Image
Image(filename =r'waveforms_7_fig_1.png', width=500)
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import numpy as np
import matplotlib.pyplot as plt
import gseim_calc as calc
from setsize import set_size
T = 20.0e-3
Vm = 325.0
Im = 10.0
omg = 2.0*np.pi/T
alpha = 45.0 # to be changed by user
alpha_rad = alpha*np.pi/180.0
n_div = 5000
t = np.linspace(0.0, 2*T, (n_div+1))
v = Vm*np.sin(omg*t)
T1 = np.pi - alpha_rad
T2 = np.pi
T3 = 2.0*np.pi - alpha_rad
l_i = []
for k, t1a in enumerate(t):
t1 = t1a % T
omg_t1 = omg*t1
if omg_t1 < T1:
i1 = Im
elif omg_t1 < T2:
i1 = 0.0
elif omg_t1 < T3:
i1 = -Im
else:
i1 = 0.0
l_i.append(i1)
i = np.array(l_i)
p = v*i
l_v_1 = calc.avg_rms_2(t, v, 0.0, 2.0*T, 1.0e-5*T)
l_i_1 = calc.avg_rms_2(t, i, 0.0, 2.0*T, 1.0e-5*T)
l_p_1 = calc.avg_rms_2(t, p, 0.0, 2.0*T, 1.0e-5*T)
print('v: rms value:', "%11.4E"%l_v_1[2][0])
print('i: rms value:', "%11.4E"%l_i_1[2][0])
print('p: average value:', "%11.4E"%l_p_1[1][0])
v2 = np.array(l_v_1)
i2 = np.array(l_i_1)
p2 = np.array(l_p_1)
n_fourier_i = 10
coeff_i, thd_i = calc.fourier_coeff_1C(t, i,
T, 2.0*T, 1.0e-4*T, n_fourier_i)
print('fourier coefficients (load current):')
for k, c in enumerate(coeff_i):
print(" %3d %11.4E"% (k, c))
print("load current fundamental: RMS value: ", "%11.4E"%(coeff_i[1]/np.sqrt(2.0)))
Irms = l_i_1[2][0]
Vrms = l_v_1[2][0]
pf = l_p_1[1][0]/(Vrms*Irms)
print('load power factor:', "%6.3f"%pf)
x_i = np.linspace(0, n_fourier_i, n_fourier_i+1)
y_i = np.array(coeff_i)
fig, ax = plt.subplots(3, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)
grid_color='#CCCCCC'
set_size(6, 6, ax[0])
color1 ='blue'
color2 ='olive'
color3 ='crimson'
for k in range(3):
ax[k].set_xlim(left=0.0, right=2.0*T*1e3)
ax[k].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)
ax[1].set_ylim(top=15.0, bottom=-15.0)
ax[0].set_ylabel('$v$',fontsize=13)
ax[1].set_ylabel('$i$',fontsize=13)
ax[2].set_ylabel('$p$',fontsize=13)
ax[0].tick_params(labelbottom=False)
ax[1].tick_params(labelbottom=False)
ax[2].set_xlabel('$t$ (msec)',fontsize=13)
ax[0].plot(t*1e3, v, color=color1, linewidth=1.0, label="$v$")
ax[1].plot(t*1e3, i, color=color2, linewidth=1.0, label="$i$")
ax[2].plot(t*1e3, p, color=color3, linewidth=1.0, label="$p$")
ax[0].plot(v2[0]*1e3, v2[2], color=color1, linewidth=1.0, label="$v_{rms}$", linestyle='-.')
ax[1].plot(i2[0]*1e3, i2[2], color=color2, linewidth=1.0, label="$i_{rms}$", linestyle='-.')
ax[2].plot(p2[0]*1e3, p2[1], color=color3, linewidth=1.0, label="$p_{avg}$", linestyle='-.')
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].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[2].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()
v: rms value: 2.2981E+02 i: rms value: 8.6614E+00 p: average value: 1.7660E+03 fourier coefficients (load current): 0 4.0000E-03 1 1.1763E+01 2 8.0000E-03 3 1.6242E+00 4 8.0000E-03 5 9.7449E-01 6 8.0000E-03 7 1.6804E+00 8 8.0000E-03 9 1.3070E+00 10 8.0000E-03 load current fundamental: RMS value: 8.3178E+00 load power factor: 0.887
In [3]:
import numpy as np
import matplotlib.pyplot as plt
import gseim_calc as calc
from setsize import set_size
# Note: we are using variables assigned in the previous cell;
# we need to execute the previous cell before this one.
fig, ax = plt.subplots()
grid_color='#CCCCCC'
set_size(6, 2, ax)
bars1 = ax.bar(x_i, y_i, width=0.3, color='red', label="$i_{load}$")
ax.set_xlabel('N', fontsize=11)
ax.set_ylabel('$i_{load}$', fontsize=11)
ax.set_xlim(left=0, right=n_fourier_i)
ax.xaxis.set_ticks(np.arange(0, n_fourier_i+1, 1))
plt.tight_layout()
plt.show()
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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