Switching

Waveforms for the voltage $v(t)$ across and the current $i(t)$ through a switch during the turn-on and turn-off transitions are given below. The forward voltage drop across the switch when it is ON is $V_{on}$. The total energy dissipation in the switch during the switching transitions in one cycle (i.e., the energy dissipation in intervals $\Delta t_1$ and $\Delta t_2$ together) is $720\,\mu\,$J. If $I_1 = 20\,$A, $V_{on}= 2\,$V, $\Delta t_1 = \Delta t_2 = 20\,\mu$sec, find $V_1$.

from IPython.display import Image
Image(filename =r'switching_2_fig_1.png', width=450)

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

I1 = 20.0
V1 = 30.0 # to be changed by user
Von = 2.0

delt0  = 2e-6
delt1  = 2e-6
delt1a = 8e-6
delt2  = 2e-6
delt3  = 2e-6

t0 = 0.0
t1 = t0 + delt0
t2 = t1 + delt1
t3 = t2 + delt1a
t4 = t3 + delt2
t5 = t4 + delt3

n_div = 2000
t = np.linspace(t0, t5, (n_div+1))
deltx = (t5-t0)/float(n_div)

slope_V = (V1-Von)/delt1
slope_I = I1/delt1

l_I = []
l_V = []

for i, tx in enumerate(t):
    if tx < t1:
        I = 0.0
        V = V1
    elif tx < t2:
        delt = tx - t1
        I = slope_I*delt
        V = V1 - slope_V*delt
    elif tx < t3:
        I = I1
        V = Von
    elif tx < t4:
        delt = tx - t3
        I = I1 - slope_I*delt
        V = Von + slope_V*delt
    else:
        I = 0.0
        V = V1
    l_I.append(I)
    l_V.append(V)

np_I = np.array(l_I)
np_V = np.array(l_V)
P = np_I*np_V

P1 = InterpolatedUnivariateSpline(t, P, k=1)  # k=1 gives linear interpolation
delE1 = P1.integral(t1, t2)
delE2 = P1.integral(t3, t4)

print('delE1:', "%7.2f"%(delE1*1e6), 'micro-Joules')
print('delE2:', "%7.2f"%(delE2*1e6), 'micro-Joules')

delEttl = delE1 + delE2
print('switching loss in transitions:', "%7.2f"%(delEttl*1e6), 'micro-Joules')

plot_min_P, plot_max_P = calc.delta_plot_1(P   , 0.2)
plot_min_V, plot_max_V = calc.delta_plot_1(np_V, 0.2)
plot_min_I, plot_max_I = calc.delta_plot_1(np_I, 0.2)

color1='blue'
color2='red'
color3='green'

fig, ax = plt.subplots(3, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(6.5, 5, ax[0])

for i in range(3):
    ax[i].set_xlim(left=0.0, right=t5*1e6)
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

ax[0].set_ylim(bottom=plot_min_V, top=plot_max_V)
ax[1].set_ylim(bottom=plot_min_I, top=plot_max_I)
ax[2].set_ylim(bottom=plot_min_P, top=plot_max_P)

ax[0].set_ylabel(r'$v$', fontsize=12)
ax[1].set_ylabel(r'$i$', fontsize=12)
ax[2].set_ylabel(r'$p$', fontsize=12)

ax[0].tick_params(labelbottom=False)
ax[1].tick_params(labelbottom=False)

ax[0].plot(t*1e6, np_V, color=color1, linewidth=1.0, label="$v$")
ax[1].plot(t*1e6, np_I, color=color2, linewidth=1.0, label="$i$")
ax[2].plot(t*1e6, P   , color=color3, linewidth=1.0, label="$p$")

ax[2].set_xlabel(r'time ($\mu$sec)', fontsize=12)

#plt.tight_layout()
plt.show()

delE1:  226.66 micro-Joules
delE2:  226.66 micro-Joules
switching loss in transitions:  453.33 micro-Joules

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