Waveforms

The figure shows one period of the output voltage $V_o$ of an inverter. $\alpha$ should be chosen such that $30^{\circ} \le \alpha \le 90^{\circ}$. Determine $\alpha$ in degrees for $V_o$ to be free from the seventh harmonic.

from IPython.display import Image
Image(filename =r'waveforms_4_fig_1.png', width=450)

import numpy as np
import matplotlib.pyplot as plt 
import gseim_calc as calc
from setsize import set_size

T = 20.0e-3
omg = 2.0*np.pi/T
deg_to_rad = np.pi/180.0

alpha = 50.0 # to be changed by user

n_div = 5000
t = np.linspace(0.0, T, (n_div+1))

alpha_rad = alpha*deg_to_rad
Vdc = 100.0
l_Vo = []

for i, t1 in enumerate(t):
    omg_t1 = omg*t1
    if omg_t1 < alpha_rad:
        v1 = Vdc
    elif omg_t1 < (np.pi-alpha_rad):
        v1 = -Vdc
    elif omg_t1 < (np.pi):
        v1 = Vdc
    elif omg_t1 < (np.pi+alpha_rad):
        v1 = -Vdc
    elif omg_t1 < (2.0*np.pi-alpha_rad):
        v1 = Vdc
    else:
        v1 = -Vdc
    l_Vo.append(v1)

Vo = np.array(l_Vo)

t_start = 0.0
t_end = T

n_fourier = 10

coeff_Vo, thd_Vo = calc.fourier_coeff_1C(t, Vo, t_start, t_end, 1.0e-8, n_fourier)

print('fourier coefficients (Vo):')
for i, c in enumerate(coeff_Vo):
    print("  %3d %11.4E"% (i, c))

xf = np.linspace(0, n_fourier, n_fourier+1)
yf = np.array(coeff_Vo)

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

set_size(6, 4, ax[0])

xf_ticks = np.arange(0.0, (float(n_fourier+1)), 1.0)

ax[0].set_xlim(left=0.0, right=T*1e3)
ax[0].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].plot(t*1e3, Vo, color='blue', linewidth=1.0, label="$V_o$")

ax[1].set_xlim(left=-1.0, right=float(n_fourier))
ax[1].set_xticks(xf_ticks)
ax[1].grid(visible=True, which='major', axis='x', color=grid_color, linestyle='-', zorder=0)

ax[0].set_xlabel('$t$ (msec)',fontsize=13)
ax[0].set_ylabel('$V_o$',fontsize=13)

ax[1].set_xlabel('$N$',fontsize=13)
ax[1].set_ylabel('$V_o^{(k)}$',fontsize=13)

bars2 = ax[1].bar(xf, yf, width=0.3, color='red', label="$V_o^{(k)}$" , zorder=3)

plt.tight_layout()
plt.show()

fourier coefficients (Vo):
    0  2.0000E-02
    1  3.6347E+01
    2  4.0000E-02
    3  1.1596E+02
    4  4.0000E-02
    5  4.2867E+01
    6  4.0000E-02
    7  1.7640E+01
    8  4.0000E-02
    9  1.4165E+01
   10  4.0000E-02

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