(based on Example 3-1)
Calculate the combined currents of a three-phase stator (adapted for 50Hz).
Import the PyLab namespace (provides set of useful commands and constants like $\pi$):
In [1]:
%pylab inline
Set up the basic conditions:
In [2]:
imax = 1 # Normalize imax to 1
freq = 50 # [Hz]
w = 2*pi*freq # [rad/s] angluar velocity
t = linspace(0, 1./50, 100) # 100 values for one period
wt = w*t # we are going to use this quite often
First, generate the three component magnetic fields
In [3]:
# amplitudes (change them to see effect of non-symmetry):
I_amp = [[1.0], [1.0], [1.0]]
# time variants
I_time = array([sin(wt),
sin(wt-2*pi/3),
sin(wt+2*pi/3)])
# vectorial shifts
I_shift = [[cos(0) + 1j*sin(0)],
[cos(2*pi/3) + 1j*sin(2*pi/3)],
[cos(-2*pi/3) + 1j*sin(-2*pi/3)]]
# all combined
I_ph = I_amp * I_time
I = I_ph * I_shift
Calculate the combined current vector:
In [4]:
Itot = I[0] + I[1] + I[2]
Calculate neutral current $I_n$:
In [5]:
# Its amplitude
In_amp = (I_ph[0] + I_ph[1] + I_ph[2])
# Its angle:
In_ang = angle(Itot)
In = In_amp * exp(1j*In_ang) # combine to a complex In
Calculate a circle representing the expected maximum value of Itot:
In [6]:
circle = 1.5 * (cos(wt) + 1j*sin(wt))
Generating the animation:
In [7]:
# First set up the figure, the axis, and the plot element we want to animate
from matplotlib import animation
fig = figure()
ax1 = fig.add_subplot(1, 2, 1)
ax2 = fig.add_subplot(1, 2, 2)
ax1.set_title('Space vectors in motion')
ax1.set_xlabel('Real')
ax1.set_ylabel('Imag')
ax1.set_xlim(-1.6, 1.6)
ax1.set_ylim(-1.6, 1.6)
ax1.set_aspect('equal')
ax2.set_title('Sinusoidal three-phase')
ax2.set_xlabel('wt [rad]')
ax2.set_xlim(0, 2*pi)
ax2.set_ylim(-1.6, 1.6)
# set up the different line colours
la, lb, lc, ltot, ctot, ln, cn = ax1.plot([], [], 'red',
[], [], 'green',
[], [], 'blue',
[], [], 'magenta',
[], [], 'magenta',
[], [], 'y',
[], [], 'y',
lw=2)
# set up the moving dots
da, db, dc, dn = ax2.plot([], [], 'ro',
[], [], 'go',
[], [], 'bo',
[], [], 'yo',
lw=2)
tight_layout() # sometimes useful when sub-plots get a bit crowded
# initialization function: plot the background of each frame
def init():
ax1.plot(real(circle), imag(circle), 'black');
ax2.plot(wt, I_ph[0,], 'red',
wt, I_ph[1,], 'green',
wt, I_ph[2,], 'blue',
wt, In_amp, 'y',
lw=1);
return
# animation function. This is called sequentially
def animate(simData):
i = simData - 1 # python index starts at 0
re = [asscalar(real(I[0,i])), asscalar(real(I[1,i])), asscalar(real(I[2,i]))]
im = [asscalar(imag(I[0,i])), asscalar(imag(I[1,i])), asscalar(imag(I[2,i]))]
ren = real(In[i])
imn = imag(In[i])
la.set_data([0, re[0]],
[0, im[0]])
lb.set_data([0, re[1]],
[0, im[1]])
lc.set_data([0, re[2]],
[0, im[2]])
ltot.set_data([0, real(Itot[i])], [0, imag(Itot[i])])
ctot.set_data(real(Itot[:i+1]),imag(Itot[:i+1]))
ln.set_data([0, real(In[i])], [0, imag(In[i])])
cn.set_data(real(In[:i]), imag(In[:i]))
da.set_data(wt[i], I_ph[0,i])
db.set_data(wt[i], I_ph[1,i])
dc.set_data(wt[i], I_ph[2,i])
dn.set_data(wt[i], In_amp[i])
return la, lb, lc, ltot, da, db, dc
# call the animator:
anim = animation.FuncAnimation(fig, animate, init_func=init,
interval=50)
If run "normally" (and not in "inline" mode like we are doing here) the command above would have opened a window with the animation running. On the server we can only run "inline" mode but there is a solution to simply generate the animation as a video and embed it right here:
In [8]:
from IPython.display import HTML
HTML(anim.to_html5_video())
Out[8]: