Rectifier_12PulseTransformerCurrent.ipynb

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        "<a href=\"https://colab.research.google.com/github/bingsen-wang/PowerElectronics/blob/main/Rectifier_12PulseTransformerCurrent.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "<center><h1><b>Currents Flowing through the 12-Pulse Transformer</h1></b>\n",
        "\n",
        "Dr. Bingsen Wang\n",
        "\n",
        "3/31/2024\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Delta Winding Currents"
      ],
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      "source": [
        "For the delta winding currents, the following equations hold\n",
        "$$\\begin{align}\n",
        "i_{ba2} - i_{ac2} &= i_{a2}\\tag{1}\\\\\n",
        "i_{cb2} - i_{ba2} &= i_{b2}\\tag{2}\n",
        "\\end{align}\n",
        "$$\n",
        "\n",
        "Since there is no circulation current inside the delta winding, then we have\n",
        "$$i_{ba2} + i_{cb2} + i_{ac2} =0\\tag{3}$$\n",
        "\n",
        "Adding equations (1) and (3) yields\n",
        "$$2i_{ba2} +  i_{cb2} = i_{a2}\\tag{4}$$\n",
        "\n",
        "Substituting (4) into (2) yields\n",
        "$$i_{ba2} = \\frac{i_{a2} - i_{b2}}{3}\\tag{5}$$\n",
        "Then it follows that\n",
        "$$i_{cb2} = \\frac{i_{b2} - i_{c2}}{3}\\\\\n",
        "i_{ac2} = \\frac{i_{c2} - i_{a2}}{3}\\tag{6}$$"
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      "source": [
        "#Python Code\n",
        "The Python code illustrates waveforms of the 12-pulse transformer."
      ]
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            "<ipython-input-48-f5f89b8b3a1c>:265: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n",
            "  fig.tight_layout()\n"
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              "<Figure size 1600x900 with 6 Axes>"
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          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib\n",
        "from os import linesep\n",
        "import numpy as np\n",
        "from numpy import linspace,cos,sin,pi,heaviside,array,sqrt,angle,exp,sign\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.colors import to_rgba, to_hex, to_rgb\n",
        "from matplotlib.path import Path\n",
        "import matplotlib.patches as mp\n",
        "from matplotlib.collections import PatchCollection\n",
        "from matplotlib import animation,rc,transforms\n",
        "rc('animation', html='jshtml')\n",
        "plt.rcParams.update({\"font.family\" : \"serif\",\"mathtext.fontset\" : \"cm\"})\n",
        "\n",
        "#modulation functions\n",
        "def mf(t,f,phi):\n",
        "  mt = []\n",
        "  for k in range(3):\n",
        "    mt.append(cos(2*pi*f*t+phi - k*2*pi/3))\n",
        "  return mt\n",
        "\n",
        "#switching functions for the high-side diodes\n",
        "def hh(t,f,phi):\n",
        "  ht = []\n",
        "  for k in range(3):\n",
        "    ht.append(heaviside(mf(t,f,phi)[k]-mf(t,f,phi)[(k+1)%3],0)*heaviside(mf(t,f,phi)[k]-mf(t,f,phi)[(k+2)%3],0))\n",
        "  return ht\n",
        "\n",
        "#switching functions for the low-side diodes\n",
        "def hl(t,f,phi):\n",
        "  ht = []\n",
        "  for k in range(3):\n",
        "    ht.append(heaviside(-mf(t,f,phi)[k]+mf(t,f,phi)[(k+1)%3],0)*heaviside(-mf(t,f,phi)[k]+mf(t,f,phi)[(k+2)%3],0))\n",
        "  return ht\n",
        "\n",
        "#ac current\n",
        "def iac(t,f,phi):\n",
        "  i = [] #high side current\n",
        "  for k in range(3):\n",
        "    i.append(hh(t,f,phi)[k] - hl(t,f,phi)[k])\n",
        "  return i\n",
        "\n",
        "\n",
        "#draw inductor symbol\n",
        "def drawInductor(ax,x0,y0,n,h,w,theta,lw,color):\n",
        "  \"\"\"n: number of coils;  h: height or width; lw: line weight\n",
        "  theta: orientation 0 for horizontal 90 for vertical \"\"\"\n",
        "  w= w/(0.7*n+0.3)#width of larger coil\n",
        "  plg, psm = ([],[]) #the half coil with larger curvature\n",
        "  codes=[Path.MOVETO,Path.CURVE4,Path.CURVE4,Path.CURVE4]\n",
        "  verts=[(x0,y0),(x0,y0+0.4*h),(x0+w,y0+0.4*h),(x0+w,y0)]\n",
        "  for k in range(n):\n",
        "    if k==0:\n",
        "      plg.append(mp.PathPatch(Path(verts,codes)))\n",
        "    else:\n",
        "      p = Path([(x0 + 0.7*k*w,y0),(x0 + 0.7*k*w,y0+0.4*h),\n",
        "                (x0+(0.7*k+1)*w,y0+0.4*h),(x0+(0.7*k+1)*w,y0)], codes)\n",
        "      plg.append(mp.PathPatch(p))\n",
        "      p = Path([(x0 + 0.7*k*w,y0),(x0 + 0.7*k*w,y0-0.2*h),\n",
        "                (x0+(0.7*k+0.3)*w,y0-0.2*h),(x0+(0.7*k+0.3)*w,y0)], codes)\n",
        "      psm.append(mp.PathPatch(p))\n",
        "  rot=transforms.Affine2D().rotate_deg_around(x0,y0,theta)+ax.transData\n",
        "  pc=PatchCollection(np.concatenate((plg,psm)),ec=color,fc='none',lw=lw,transform=rot,capstyle='round')\n",
        "  ax.add_collection(pc)\n",
        "  return\n",
        "\n",
        "#draw transformer winding\n",
        "def drawTransformerWinding(ax,x0,y0,n,h,w,theta,lw,color,dotpos='start'):\n",
        "  codes = [Path.MOVETO,Path.LINETO,Path.MOVETO,Path.LINETO]\n",
        "  drawInductor(ax,x0+w/6*cos(theta*pi/180),y0+w/6*sin(theta*pi/180),n,h,w*2/3,theta,lw,color)\n",
        "  p = Path([(x0,y0), (x0+w/6,y0), (x0+5/6*w,y0), (x0+w,y0)], codes)\n",
        "  rdot = h/12 #dot radius\n",
        "  if dotpos == 'start':\n",
        "    dot = mp.Circle((x0+w/6,y0-2*rdot),rdot)\n",
        "  else:\n",
        "    dot = mp.Circle((x0+w*5/6,y0-2*rdot),rdot)\n",
        "  rot=transforms.Affine2D().rotate_deg_around(x0,y0,theta)+ax.transData\n",
        "  pc = PatchCollection([mp.PathPatch(p),dot],ec=color,fc=color,lw=lw,transform=rot)\n",
        "  ax.add_collection(pc)\n",
        "\n",
        "  return\n",
        "\n",
        "#draw ac voltage source symbol\n",
        "def drawVoltSourceAc(ax,x0,y0,h,theta,lw,color):\n",
        "  \"\"\" x0,y0: top or left end of the voltage source lead\n",
        "  h: height or width; lw: line weight\n",
        "  theta: orientation 0 for horizontal 90 for vertical\"\"\"\n",
        "  ps=[] # container of the zig-zags\n",
        "  codes=[Path.MOVETO,Path.LINETO,Path.MOVETO,Path.LINETO]\n",
        "  p = Path([(x0,y0),(x0+.2*h,y0),(x0+.8*h,y0),(x0+h,y0)],codes)\n",
        "  ps.append(mp.PathPatch(p))\n",
        "  ps.append(mp.Circle((x0+.5*h,y0),.3*h))\n",
        "  ps.append(mp.Arc((x0+.4*h,y0),.2*h,.2*h,theta2=180))\n",
        "  ps.append(mp.Arc((x0+.6*h,y0),.2*h,.2*h,theta1=180))\n",
        "  rot=transforms.Affine2D().rotate_deg_around(x0,y0,theta)+ax.transData\n",
        "  pc=PatchCollection(ps,ec=color,fc='none',lw=lw,transform=rot,capstyle='round')\n",
        "  ax.add_collection(pc)\n",
        "  return\n",
        "\n",
        "#draw the +/- voltage polarity with variable distance/color\n",
        "def drawVoltSign(ax,x0,y0,h,theta,lw,color):\n",
        "  \"\"\"\n",
        "  x0,y0: center between \"+\" and \"-\"\n",
        "  h: height or width\n",
        "  theta: orientation 0 for horizontal 90 for vertical\n",
        "  lw: line weight\n",
        "  \"\"\"\n",
        "  p = Path([(x0-0.5*h,y0-0.1*h),(x0-0.5*h,y0+0.1*h),(x0-0.6*h,y0),(x0-0.4*h,y0),\n",
        "            (x0+0.5*h, y0-0.08*h),(x0+0.5*h, y0+0.08*h)],\n",
        "           [Path.MOVETO,Path.LINETO,Path.MOVETO,Path.LINETO,\n",
        "            Path.MOVETO,Path.LINETO])\n",
        "  rot=transforms.Affine2D().rotate_deg_around(x0,y0,theta)+ax.transData\n",
        "  ax.add_patch(mp.PathPatch(p,ec=color,fc='none',lw=lw,transform=rot,capstyle='round'))\n",
        "  return\n",
        "\n",
        "\n",
        "\n",
        "#moving dots for current flow, only works for any lines\n",
        "def drawMovingDots(ax,path,space,n_steps,nth_step,rdot,color):\n",
        "  for k in range(len(path)-1):\n",
        "    pk = path[k][0] +1j*path[k][1] #complex number of point k\n",
        "    pk1 = path[k+1][0] +1j*path[k+1][1] #complex number of point k+1\n",
        "    dp = pk1-pk\n",
        "    theta = angle(dp)\n",
        "    if k==0:\n",
        "      lst = space*nth_step/n_steps# distance of starting point\n",
        "    for kk in range(int((abs(dp)-lst)/space)+1):\n",
        "      ax.add_patch(mp.Circle([(pk+(lst+kk*space)*exp(1j*theta)).real,\n",
        "       (pk+(lst+kk*space)*exp(1j*theta)).imag],radius=rdot,fc=color))\n",
        "    lst = space - (abs(dp)-lst)%space #update the distance of starting point\n",
        "  return\n",
        "\n",
        "#draw non-animated parts of the circuitry\n",
        "def drawRectifierNa(ax,lw,clst,txlst):\n",
        "  args = dict({'lw':lw,'capstyle':'round', 'fc':'None'})\n",
        "  args1=  dict({'size':24,'va':'center'})\n",
        "  codes=[Path.MOVETO,Path.LINETO,Path.MOVETO,Path.LINETO]\n",
        "  x=2\n",
        "  y=4.5\n",
        "  x0 = x+1 #center for primary 3-ph winding\n",
        "  y0 = y #center for primary 3-ph winding\n",
        "  x1 = x+3 #center for secondary 3-ph wye winding\n",
        "  y1 = 6.5 #center for secondary 3-ph wye winding\n",
        "  x2 = x1 #center for secondary 3-ph delta winding\n",
        "  y2 = 2.5 #center for secondary 3-ph delta winding\n",
        "  for k in range(3):\n",
        "    p1 = Path([(x-1.75,y0+(1-k)*sqrt(3)/2*1.5),(x-1.5,y0+(1-k)*sqrt(3)/2*1.5)], codes[0:2])\n",
        "    ax.add_patch(mp.PathPatch(p1,**args))\n",
        "    drawVoltSourceAc(ax,x-1.5,y+(1-k)*sqrt(3)/2*1.5,.5,0,lw,clst[k])\n",
        "    ax.text(x0-1.75,y0+.2+1.5*sqrt(3)/2*(1-k),txlst[0][0][k],color=clst[k],ha='center',**args1) #iabc\n",
        "    ax.text(x1+2.25,y1+.2+1.5*sqrt(3)/2*(k-1),txlst[1][0][k],color=clst[k],ha='center',**args1) #iabc1\n",
        "    ax.text(x2+2.25,y2+.2+1.5*sqrt(3)/2*(k-2/3),txlst[2][0][k],color=clst[k],ha='center',**args1) #iabc2\n",
        "  p2 = Path([(x-1.75,y+1.5*sqrt(3)/2), (x-1.75,y-1.5*sqrt(3)/2)], codes[0:2]) #source neutral vertical\n",
        "  p3 = Path([((x0+x1)*.5-.02,y1+1.5*sqrt(3)/2), ((x0+x1)*.5-.02,y2-sqrt(3)/2),\n",
        "             ((x0+x1)*.5+.02,y1+1.5*sqrt(3)/2), ((x0+x1)*.5+.02,y2-sqrt(3)/2)], codes) #core\n",
        "  ax.add_patch(mp.PathPatch(p2,**args))\n",
        "  ax.add_patch(mp.PathPatch(p3,**args))\n",
        "  # drawInductor(ax,x+9,2.5,5,.75,1,0,lw,'k') #dc inductor\n",
        "  # ax.text(x+8,0,txlst[0][0],color=clst[0],ha='center',**args1) #vdc\n",
        "  return\n",
        "\n",
        "#draw animated parts of the circuitry\n",
        "def drawRectifierAnim(ax,i_ani,ip,isy,isd,isdph,lw,clst):\n",
        "  x=2\n",
        "  y=4.5\n",
        "  x0 = x+1 #center for primary 3-ph winding\n",
        "  y0 = y #center for primary 3-ph winding\n",
        "  x1 = x+3 #center for secondary 3-ph wye winding\n",
        "  y1 = 6.5 #center for secondary 3-ph wye winding\n",
        "  x2 = x1 #center for secondary 3-ph delta winding\n",
        "  y2 = 2.5 #center for secondary 3-ph delta winding\n",
        "  args = dict({'lw':lw,'capstyle':'round', 'fc':'None'})\n",
        "  codes=[Path.MOVETO,Path.LINETO,Path.MOVETO,Path.LINETO]\n",
        "  for k in range(3):\n",
        "    drawTransformerWinding(ax,x0,y0,10,0.3,1.5,60+k*120,lw,\n",
        "                           to_rgba(clst[k],max(abs(ip[k])/2.16,0.1)),dotpos='end') #primary\n",
        "    drawTransformerWinding(ax,x1,y1,10,0.3,1.5,240+k*120,lw,to_rgba(clst[k],max(abs(isy[k]),0.1)),dotpos='end') #2nd y\n",
        "    drawTransformerWinding(ax,x2+sqrt(3)/2*cos(-pi/2+k*2*pi/3),\n",
        "                           y2+sqrt(3)/2*sin(-pi/2+k*2*pi/3),\n",
        "                           17,0.3,1.5,60+k*120,lw,to_rgba(clst[k],max(abs(isdph[k]),0.1)),dotpos='start') #2nd delta\n",
        "    points_prim = [(x-1,y0+(1-k)*sqrt(3)/2*1.5),\n",
        "     (x0+1.5*cos(pi/3+k*2*pi/3),y0+(1-k)*sqrt(3)/2*1.5)]\n",
        "    p1 = Path(points_prim, codes[0:2]) #primary\n",
        "    points_sy = [(x1+2.5,y1+1.5*sin(4*pi/3 + k*2*pi/3)),\n",
        "     (x1+1.5*cos(4*pi/3 + k*2*pi/3),y1+1.5*sin(4*pi/3 + k*2*pi/3))]\n",
        "    p2 = Path(points_sy,codes[0:2]) #2nd wye\n",
        "    if k==2:\n",
        "      points_sd = [(x2+sqrt(3)/2*cos(-pi/2 + k*2*pi/3),y2+sqrt(3)/2*sin(-pi/2 + k*2*pi/3)),\n",
        "                 (x2+sqrt(3)/2*cos(-pi/2 + k*2*pi/3),y2+sqrt(3)/2*sin(-pi/2 + k*2*pi/3)+1.5*sqrt(3)/2),\n",
        "               (x2+2.5,y2+sqrt(3)/2*sin(-pi/2 + k*2*pi/3)+1.5*sqrt(3)/2)]\n",
        "      p3 = Path(points_sd,codes[0:2]+[codes[-1]])\n",
        "    else:\n",
        "      points_sd = [(x2+sqrt(3)/2*cos(-pi/2 + k*2*pi/3),y2+sqrt(3)/2*sin(-pi/2 + k*2*pi/3)),\n",
        "                 (x2+2.5,y2+sqrt(3)/2*sin(-pi/2 + k*2*pi/3))]\n",
        "      p3 = Path(points_sd,codes[0:2]) #2nd delta\n",
        "    ax.add_patch(mp.PathPatch(p1,color=to_rgba('k',max(abs(ip[k])/2.16,0.1)),**args))\n",
        "    ax.add_patch(mp.PathPatch(p2,color=to_rgba('k',max(abs(isy[k]),0.1)),**args))\n",
        "    ax.add_patch(mp.PathPatch(p3,color=to_rgba('k',max(abs(isd[k]),0.1)),**args))\n",
        "    points_prim.append((x0,y0)) #primary moving dots path\n",
        "    drawMovingDots(ax,points_prim[::int(sign(ip[k]))],0.3,16,i_ani%16,.045*sqrt(abs(ip[k])),clst[k])\n",
        "    points_sy.append((x1,y1)) #secondary wye, moving dots path\n",
        "    if sign(isy[k])!=0:\n",
        "      drawMovingDots(ax,points_sy[::int(-sign(isy[k]))],0.25,16,i_ani%16,.045*sqrt(abs(isy[k])),clst[k])\n",
        "    if sign(isd[k])!=0:\n",
        "      drawMovingDots(ax,points_sd[::int(sign(isd[k]))],0.25,16,i_ani%16,.045*sqrt(abs(isd[k])),clst[k])\n",
        "    points_sdph = [(x2+sqrt(3)/2*cos(-pi/2 + (k+1)*2*pi/3),y2+sqrt(3)/2*sin(-pi/2 + (k+1)*2*pi/3)),\n",
        "                   (x2+sqrt(3)/2*cos(-pi/2 + k*2*pi/3),y2+sqrt(3)/2*sin(-pi/2 + k*2*pi/3))]\n",
        "    drawMovingDots(ax,points_sdph[::int(sign(isdph[k]))],0.25,16,i_ani%16,.045*sqrt(abs(isdph[k])),clst[k])\n",
        "\n",
        "  return\n",
        "\n",
        "#parameters\n",
        "f=1\n",
        "Nf = 500\n",
        "t=linspace(0,1,Nf)\n",
        "tmax = max(t)\n",
        "phi = 30*pi/180\n",
        "mt = mf(t,f,phi) #time domain modulation functions\n",
        "iabc1 = iac(t,f,phi) #currents of 2nd wye winding\n",
        "iabc2 = iac(t,f,phi-pi/6) #currents line 2nd delta winding line currents\n",
        "ibacbac2 = [(iabc2[0]-iabc2[1])/3, (iabc2[1]- iabc2[2])/3, (iabc2[2] - iabc2[0])/3]\n",
        "iabc = [iabc1[0]+ibacbac2[0]*sqrt(3),\n",
        "        iabc1[1]+ibacbac2[1]*sqrt(3),iabc1[2]+ibacbac2[2]*sqrt(3)] #primary\n",
        "#set up figures\n",
        "fig = plt.figure(figsize=(16,9)) #overall plot area\n",
        "km = 1.1 # margin\n",
        "ax_frame = [[(0, 0, .5, 1),[0,8],[0,9]], #circuit diagram\n",
        "            [(0, 0, .5, 1),[0,8],[0,9]], #animated circuit\n",
        "            [(.5, .75, .5, .25), [-.05*km,1*km],[-2.5*km,2.5*km]], #iabc\n",
        "            [(.5,  .5, .5, .25), [-.05*km,1*km],[-1.2*km,1.2*km]], #iabc1\n",
        "            [(.5, .25, .5, .25), [-.05*km,1*km],[-1.2*km,1.2*km]], #iabc2\n",
        "            [(.5,  0,  .5, .25), [-.05*km,1*km],[-.8*km,.8*km]], #iab,bc,ca2\n",
        "            ]# [pos-boundary, xlim, ylim] for subplots\n",
        "ax_lst=[] #axis list or the list of subplots\n",
        "ax_lbl=[\n",
        "        [['$i_{a}$', '$i_{b}$', '$i_{c}$'],  '$t$'],\n",
        "        [['$i_{a1}$','$i_{b1}$','$i_{c1}$'], '$t$'],\n",
        "        [['$i_{a2}$','$i_{b2}$','$i_{c2}$'], '$t$'],\n",
        "        [['$i_{ba2}$','$i_{cb2}$','$i_{ac2}$'], '$t$'],\n",
        "        ] #variables for yx axes of each subplot\n",
        "clst=['tab:red','tab:blue','tab:brown','tab:purple'] #list of colors used for plots\n",
        "text_tls = [] #place holder for titles of each plot updated during animation\n",
        "\n",
        "#draw axes and label them for each subplot and setup the plot lines\n",
        "lines = [] #array containing all the line segments\n",
        "for k in range(len(ax_frame)):\n",
        "  ax=fig.add_axes(ax_frame[k][0],xlim=ax_frame[k][1], ylim=ax_frame[k][2],\n",
        "                  fc='none') #remove frame face color\n",
        "  if k<2:\n",
        "    ax.axis('off') #turn the first 2 axes for circuit digram completely off\n",
        "  else: #the rest axes\n",
        "    ax.spines[:].set_visible(False) #set all spines off\n",
        "    ax.spines['left'].set_position(('data', 0)) #set spines to cross zero\n",
        "    ax.set_xticks([]) #set x-axis ticks off\n",
        "    xmin,xmax,ymin,ymax=np.concatenate((ax_frame[k][1],ax_frame[k][2]))\n",
        "    ax.annotate(\"\", xy=(xmax, 0), xytext=(xmin, 0),\n",
        "          arrowprops=dict(arrowstyle=\"->\")) #draw x-axis with arrow\n",
        "    ax.annotate(\"\", xy=(0,ymax), xytext=(0,ymin),\n",
        "          arrowprops=dict(arrowstyle=\"->\")) #draw y-axis with arrow\n",
        "    ax.text(xmax-0.025,0,ax_lbl[k-2][-1],\n",
        "            size=24,va='top',ha='right',color='k') #label x axis of subplot\n",
        "    for kk in range(len(ax_lbl[k-2][0])):\n",
        "      ax.text(kk*0.08,ymax,ax_lbl[k-2][0][kk],size=24,va='center',color=clst[kk])\n",
        "      lines.append(ax.plot([],[],color=clst[kk],lw=2)[0])\n",
        "  ax_lst.append(ax)\n",
        "fig.tight_layout()\n",
        "\n",
        "\n",
        "# animation function. This is called sequentially\n",
        "def animate(i):\n",
        "  print(i) #for monitoring\n",
        "  # i = 34\n",
        "  for k in range(3):\n",
        "    lines[k].set_data(t[0:i]/tmax,iabc[k][0:i])\n",
        "    lines[3+k].set_data(t[0:i]/tmax,iabc1[k][0:i])\n",
        "    lines[6+k].set_data(t[0:i]/tmax,iabc2[k][0:i])\n",
        "    lines[9+k].set_data(t[0:i]/tmax,ibacbac2[k][0:i])\n",
        "\n",
        "  ax_lst[1].clear()\n",
        "  ax_lst[1].set_xlim(ax_frame[1][1])\n",
        "  ax_lst[1].set_ylim(ax_frame[1][2])\n",
        "  ax_lst[1].axis('off')\n",
        "  drawRectifierAnim(ax_lst[1],i,array(iabc)[:,i],array(iabc1)[:,i],\n",
        "                    array(iabc2)[:,i],array(ibacbac2)[:,i],1,clst)\n",
        "  return\n",
        "\n",
        "drawRectifierNa(ax_lst[0],1.5,clst,ax_lbl)\n",
        "anim = animation.FuncAnimation(fig, animate, frames=Nf, interval=50)\n",
        "writervideo = animation.FFMpegWriter(fps=20)\n",
        "anim.save('rectifier_12PulseTransformer.mp4', writer=writervideo,dpi = 240)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}