Discharging capacitors

In [1]:

    

# Definitions of parameters of the circuit

# Capacitance of generator [F]
C = 1e-6 

# Parallel resistance (discharging the capacitor in the generator forming the tail of the impulse) [Ohm]
R1 = 4

# Series resistance (forming the head) [Ohm]
R2 = 150

# Inductance of the loop [H]
L = 1e-3

# Capacitance of the test object [F]
Co = 1e-6


    

In [2]:

    

# defining the time of the analysis
import numpy as np

t = np.linspace(0,6e-4, 1000)


    

In [3]:

    

# Case 1 two capacitors and the resistor

def dx1(y,t):
    uco = y[0]
    
    duco = 1/(R2*Co)*(Uo - uco - Co/C*uco)
    
    return [duco]


    

In [4]:

    

# initial conditions
Uo = 200
y0 = [0.0]


    

In [5]:

    

# time constant
Cz = C*Co/(C+Co)
R2*Cz


    

    
Out[5]:





7.5e-05

In [6]:

    

from scipy.integrate import odeint, ode, romb, cumtrapz

X1 = odeint(dx1, y0, t)


    

In [7]:

    

uco = X1[:,0]


    

In [8]:

    

# the current and the other capacitor voltage

i = 1/(R2)*(Uo - uco - Co/C*uco)

uc = Uo - Co/C*uco

# current starting value
Uo/R2

# discharge voltage

ud = C*Uo/(C+Co)

Uo/R2, ud


    

    
Out[8]:





(1.3333333333333333, 100.0)

In [9]:

    

from bokeh.plotting import figure, output_notebook, show
from bokeh.layouts import column
from bokeh.palettes import RdYlGn4


    

In [10]:

    

output_notebook()


    

    






    

        
        Loading BokehJS ...
    






    

In [11]:

    

p = figure(plot_width=800, plot_height=400)

p.line(t, uco, color="firebrick", legend = "cap charging")
p.line(t, uc, legend = "cap discharging")

p.xaxis.axis_label = "time [s]"
p.xaxis.axis_label_text_font_size = "10pt"
p.yaxis.axis_label = "voltage [V]"
p.yaxis.axis_label_text_font_size = "10pt"

p2 = figure(plot_width=800, plot_height=400)

p2.line(t, i, color='#1a9641')

p2.xaxis.axis_label = "time [s]"
p2.xaxis.axis_label_text_font_size = "10pt"
p2.yaxis.axis_label = "current [A]"
p2.yaxis.axis_label_text_font_size = "10pt"

show(column(p, p2))


    

In [12]:

    

# Adjustment of parameters for case 2

L = 1e-2 # interesting values for L: 1e-3 (very little influence); 5e-3 (small oscillation); 1e-2 bigger oscillation
t2 = np.linspace(0,10e-4,1000)


    

In [13]:

    

# Case 2: two capacitors, resistor and inductor

def dx2(y,t):
    i, uco = y[0], y[1]
    
    di = 1/L*(Uo - Co/C*uco - i*R2 - uco)
    duco = 1/Co*i
    
    return [di, duco]


    

In [14]:

    

# initial conditions
Uo = 200

y02 = [0.0, 0.0]


    

In [15]:

    

X2 = odeint(dx2, y02, t2)


    

In [16]:

    

i2 = X2[:,0]
uco2 = X2[:,1]

uc2 = Uo - Co/C*uco2


    

In [17]:

    

p3 = figure(plot_width=800, plot_height=400)

p3.line(t2, uco2, color="firebrick", legend = "cap charging")
p3.line(t2, uc2, legend = "cap discharging")

p3.xaxis.axis_label = "time [s]"
p3.xaxis.axis_label_text_font_size = "10pt"
p3.yaxis.axis_label = "voltage [V]"
p3.yaxis.axis_label_text_font_size = "10pt"

p4 = figure(plot_width=800, plot_height=400)

p4.line(t2, i2, color='#1a9641')

p4.xaxis.axis_label = "time [s]"
p4.xaxis.axis_label_text_font_size = "10pt"
p4.yaxis.axis_label = "current [A]"
p4.yaxis.axis_label_text_font_size = "10pt"

show(column(p3, p4))


    

In [18]:

    

# Adjustment of parameters for case 3

L = 1e-3 # interesting values for L: 1e-3 (very little influence); 5e-3 (small oscillation); 1e-2 bigger oscillation
t3 = np.linspace(0,10e-4,1000)


    

In [19]:

    

# Case 3: circuit for the impulse withstand tester

def dx(y,t):
    #state vector variables
    i2, uco, uc = y[0], y[1], y[2]
    
   
    di2 = 1/L*(uc-i2*R2-uco)
    duco = 1/Co*i2
    duc = -1/C*(uc/R1+i2)
        
    return [di2, duco, duc]


    

In [20]:

    

# initial conditions

# capacitor voltage [V]
Uo = 200

# vector of the initial conditions

y0 = [0.0, 0.0, Uo]


    

In [21]:

    

#from scipy.integrate import odeint, ode, romb, cumtrapz

X = odeint(dx, y0, t3)


    

In [22]:

    

i2 = X[:,0]
uco = X[:,1]
uc = X[:,2]


    

In [23]:

    

#output_notebook()

p5 = figure(plot_width=800, plot_height=400)

p5.line(t3, uco, color="firebrick", legend ="Object")

p5.xaxis.axis_label = "time [s]"
p5.xaxis.axis_label_text_font_size = "10pt"
p5.yaxis.axis_label = "voltage [V]"
p5.yaxis.axis_label_text_font_size = "10pt"

p7 = figure(plot_width=800, plot_height=400)

p7.line(t3, uc, legend = "Main capacitor")

p7.xaxis.axis_label = "time [s]"
p7.xaxis.axis_label_text_font_size = "10pt"
p7.yaxis.axis_label = "voltage [V]"
p7.yaxis.axis_label_text_font_size = "10pt"

p6 = figure(plot_width=800, plot_height=400)

p6.line(t3, i2, color='#1a9641')

p6.xaxis.axis_label = "time [s]"
p6.xaxis.axis_label_text_font_size = "10pt"
p6.yaxis.axis_label = "current [A]"
p6.yaxis.axis_label_text_font_size = "10pt"

show(column(p5, p7, p6))


    

In [24]:

    

# Capacitor discharging to a resistor

def dk(y,t):
    u = y[0]
    
    du = -1/(R1*C)*u
    
    return [du]


    

In [25]:

    

y03 = [200.0]


    

In [26]:

    

X5 = odeint(dk, y03, t3)


    

In [27]:

    

u = X5[:,0]


    

In [28]:

    

p7 = figure(plot_width=800, plot_height=400, x_range = (0,4e-5))

p7.line(t3, u, color="firebrick")

p7.xaxis.axis_label = "time [s]"
p7.xaxis.axis_label_text_font_size = "10pt"
p7.yaxis.axis_label = "voltage [V]"
p7.yaxis.axis_label_text_font_size = "10pt"

show(p7)


    

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