Switching

The current through and the voltage across a power switching device during the turn-off transient is given below. The device switches off a current $I_1$ to block a voltage $V_1$. The current linearly falls from $I_1$ to $0\,$A in the interval $\Delta t$. The voltage rises with a square law given by, $v(t) = k\,(t-t_0)^2$ for $t_0 < t < t_1$. The switching frequency is $100\,$kHz. The average turn-off power loss in Watts in the power switching device is $125\,W$. If $\Delta t = 0.5\,\mu$s, $I_1 = 50\,$A, find $V_1$.

from IPython.display import Image
Image(filename =r'switching_5_fig_1.png', width=370)

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

I1 = 50.0
V1 = 450.0 # to be changed by user

delt0  = 1e-6
delt1  = 0.5e-6
delt2  = 1e-6

f0 = 100.0e3
T0 = 1/f0

# take starting time as 0

t0 = delt0
t1 = t0 + delt1
t2 = t1 + delt2

n_div = 2000
t = np.linspace(0.0, t2, (n_div+1))

k_V = V1/(delt1*delt1)
slope_I = I1/delt1

l_I = []
l_V = []

for i, tx in enumerate(t):
    if tx < t0:
        I = I1
        V = 0.0
    elif tx < t1:
        delt = tx - t0
        I = I1 - slope_I*delt
        V = k_V*delt*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

delE = np.trapz(P, t)
print('switching loss in turn off:', "%11.4E"%(delE), 'J')
Pavg = delE/T0
print('average power lost in turn off:', "%11.4E"%(Pavg), 'W')

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=t2*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()

switching loss in turn off:  9.3749E-04 J
average power lost in turn off:  9.3749E+01 W

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