Switching

The voltage $v(t)$ across and the current $i(t)$ through a power electronic switch during the turn-on process is given below, with $I_1 = 50\,$A, $I_2 = 40\,$A, $V_1 = 600\,$V, $\Delta t_1 = 2\,\mu$s, $\Delta t_2 = 1\,\mu$s, $\Delta t_3 = 4\,\mu$s. Find the energy dissipated during the turn-on transition.
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from IPython.display import Image
Image(filename =r'switching_9_fig_1.png', width=400)
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import numpy as np
import matplotlib.pyplot as plt 
import gseim_calc as calc
from setsize import set_size

I1 = 50.0
I2 = 40.0
V1 = 600.0

delt0  = 2e-6
delt1  = 2e-6
delt2  = 1e-6
delt3  = 4e-6
delt4  = 2e-6

t0 = 0.0
t1 = t0 + delt0
t2 = t1 + delt1
t3 = t2 + delt2
t4 = t3 + delt3
t5 = t4 + delt4

n_div = 2000
t = np.linspace(t0, t5, (n_div+1))

slope_V = V1/(delt2 + delt3)
slope_I_1 = I1/delt1
slope_I_2 = (I1-I2)/delt2

l_I = []
l_V = []

for i, tx in enumerate(t):
    if tx < t1:
        I0 = 0.0
        V0 = V1
    elif tx < t2:
        delt = tx - t1
        I0 = slope_I_1*delt
        V0 = V1
    elif tx < t3:
        delt = tx - t2
        I0 = I1 - slope_I_2*delt
        V0 = V1 - slope_V*delt
    elif tx < t4:
        delt = tx - t3
        I0 = I2
        V0 = V1 - slope_V*(delt2 + delt)
    else:
        I0 = I2
        V0 = 0.0
    l_I.append(I0)
    l_V.append(V0)

I = np.array(l_I)
V = np.array(l_V)
P = I*V

delE = np.trapz(P, t)

print('switching loss in turn off:', "%11.4E"%(delE), 'J')

plot_min_P, plot_max_P = calc.delta_plot_1(P, 0.2)
plot_min_V, plot_max_V = calc.delta_plot_1(V, 0.2)
plot_min_I, plot_max_I = calc.delta_plot_1(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(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, V, color=color1, linewidth=1.0, label="$v$")
ax[1].plot(t*1e6, 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:  9.2800E-02 J
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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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