SpaceVector_SinusoidalPulseWidthModulation.ipynb

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      "name": "python3",
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  "cells": [
    {
      "cell_type": "markdown",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/bingsen-wang/PowerElectronics/blob/main/SpaceVector_SinusoidalPulseWidthModulation.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>Space Vector of Three-Phase Sinusoidal Pulse Width Modulated Waveforms</h1></b>\n",
        "\n",
        "Dr. Bingsen Wang\n",
        "\n",
        "7/13/2024\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Space Vector"
      ],
      "metadata": {
        "id": "mlJ4vEv60KCg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The space vector is complex variable defined as\n",
        "$$\\underline f = {2\\over3}\\left(f_a + f_be^{j\\frac{2\\pi}{3}} + f_ce^{j\\frac{4\\pi}{3}}\\right)\\tag{1}$$\n",
        "where $f_a,f_b,f_c$ are the three-phase variables. In electrical systems, the variable $f$ can be voltage $v$, current $i$, or flux linkage $\\lambda$. In power electronics systems, the variable $f$ can be the modulation function or switching function."
      ],
      "metadata": {
        "id": "C7_kB2GF0OKT"
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      "cell_type": "markdown",
      "metadata": {
        "id": "Hv0YxDrWU4h8"
      },
      "source": [
        "#Python Code\n",
        "The Python code illustrates the space vector of three-phase SPWM waveforms."
      ]
    },
    {
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      "execution_count": 2,
      "metadata": {
        "id": "XeGsHYTt8IXU",
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          "height": 1000
        },
        "outputId": "3c09710b-6409-46fd-d605-c1182c5b5124"
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      "outputs": [
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          "name": "stdout",
          "text": [
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          "data": {
            "text/plain": [
              "<Figure size 900x1600 with 3 Axes>"
            ],
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib\n",
        "from os import linesep\n",
        "import numpy as np\n",
        "from numpy import linspace,cos,arccos,pi,exp\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.patches as mp\n",
        "from matplotlib import animation,rc\n",
        "rc('animation', html='jshtml')\n",
        "plt.rcParams.update({\"font.family\" : \"serif\",\"mathtext.fontset\" : \"cm\"})\n",
        "\n",
        "#parameters\n",
        "Nf = 900\n",
        "f = 1 #frequency in Hz\n",
        "fs = 6*f #switching frequency\n",
        "T = 1/f #period\n",
        "Tsw = 1/fs #switching period\n",
        "\n",
        "t=linspace(0,T,int(Nf))\n",
        "wt = 2*pi*f*t\n",
        "V = 2.4 #voltage in V\n",
        "theta=0\n",
        "MI=0.9 #modulation index\n",
        "v0 = -MI/6*cos(3*(wt+theta))*0 #third harmonic\n",
        "va1=MI*cos(wt+theta)+v0 #modulation function with 3rd harmonic\n",
        "vb1=MI*cos(wt+theta-2*pi/3)+v0\n",
        "vc1=MI*cos(wt+theta-4*pi/3)+v0\n",
        "\n",
        "carr= 2/pi*arccos(cos(2*pi*fs*t))-1 #carrier ranges [-1,1]\n",
        "va2 = V*(np.heaviside(va1-carr,0)*2-1) #PWM waveform\n",
        "vb2 = V*(np.heaviside(vb1-carr,0)*2-1)\n",
        "vc2 = V*(np.heaviside(vc1-carr,0)*2-1)\n",
        "vabc_modulation=[va1,vb1,vc1]\n",
        "vabc_pwm = [va2,vb2,vc2]\n",
        "v_sv = 2/3*(va2+vb2*exp(1j*2*pi/3)+vc2*exp(1j*4*pi/3))\n",
        "\n",
        "xymax = 4.5\n",
        "clst=['tab:red', 'tab:blue', 'tab:brown']\n",
        "fig = plt.figure(figsize=(9,16))\n",
        "fig.tight_layout()\n",
        "ax=fig.add_axes((0.05,7/16,.9,.9*9/16),xlim=[-xymax,xymax], ylim=[-xymax,xymax],fc='none') #no fc\n",
        "ax0=fig.add_axes((0.05,7/16,.9,.9*9/16),xlim=[-xymax,xymax], ylim=[-xymax,xymax],fc='none') #no fc for animated parts\n",
        "ax1=fig.add_axes((0.05,0,.9,7/16),xlim=[-.1,2*xymax-.1], ylim=[-xymax*7/9,xymax*7/9],fc='none') #no fc\n",
        "ax.axis('off') #turn off axis frames\n",
        "ax1.axis('off') #turn off axis frames\n",
        "ax.annotate(\"\", (xymax, 0), (-xymax, 0),arrowprops={'arrowstyle':\"->\"}) #x-axis for space vector\n",
        "ax.annotate(\"\", (0,xymax), (0,-xymax),arrowprops={'arrowstyle':\"->\"}) #y-axis for space vector\n",
        "ax1.annotate(\"\", (2*xymax-.2, 0), (-.1, 0),arrowprops={'arrowstyle':\"->\"}) #x-axis for voltages\n",
        "ax1.annotate(\"\", (0,xymax*7/9), (0,-xymax*7/9),arrowprops={'arrowstyle':\"->\"}) #y-axis for voltages\n",
        "ax.text(xymax,-.03,'Re',size=24,va='top',ha='right') #x-axis label\n",
        "ax.text(0.01,xymax,'Im',size=24,va='top') #y label\n",
        "ax.text(xymax*.5,xymax*.87,'Space Vector',size=28,ha='center')\n",
        "ax.text(xymax*.5,xymax*.72,r'$v\\underbar = \\frac{2}{3}\\left(v_a + v_b e^{j\\frac{2\\pi}{3}}+ v_c e^{j\\frac{4\\pi}{3}}\\right)$',\n",
        "        size=24,ha='center')\n",
        "\n",
        "\n",
        "lines = [] #array containing all the line segments\n",
        "lines.append(ax.plot([], [], '-', lw=5, color='tab:orange',alpha=0.7)[0]) #v_sv trajectory\n",
        "for i in range(3):\n",
        "  lines.append(ax1.plot([], [], '-', lw=3-i*.8, color=clst[i],alpha=0.8)[0]) #v_a,v_b,v_c PWM\n",
        "  lines.append(ax1.plot([], [], '--', lw=3-i*.8, color=clst[i])[0]) #v_a,v_b,v_c modulation\n",
        "lines.append(ax1.plot([], [], '-', lw=1, color='k')[0]) #carrier\n",
        "\n",
        "ax1.text(0,xymax*6/9,r'$v_a$',size=40,color=clst[0]) #va label\n",
        "ax1.text(1,xymax*6/9,r'$v_b$',size=40,color=clst[1]) #vb label\n",
        "ax1.text(2,xymax*6/9,r'$v_c$',size=40,color=clst[2]) #vc label\n",
        "text_waveforms=ax1.text(3,xymax*6/9,r'Sinusoidal PWM',size=22)\n",
        "\n",
        "ax1.text(2*xymax-.1,-.03,r'$\\omega t$',size=24,va='top',ha='right') #x-axis label\n",
        "\n",
        "def drawVectors(ax,xymax,v_sv,vabc,clst):\n",
        "  theta = np.angle(v_sv)\n",
        "  if theta<0:\n",
        "    theta = 2*pi+theta\n",
        "  ax.clear()\n",
        "  ax.set_xlim([-xymax,xymax])\n",
        "  ax.set_ylim([-xymax,xymax])\n",
        "  ax.axis('off')\n",
        "  arr = mp.FancyArrow(0,0,v_sv.real, v_sv.imag, width=.06,length_includes_head=True,\n",
        "                   color='k') #space vector v_sv\n",
        "  ax.add_patch(arr)\n",
        "  for i in range(3):\n",
        "    v=0\n",
        "    for ii in range(i):\n",
        "      v+=vabc[ii]*exp(1j*2*pi/3**ii)*2/3\n",
        "    arr = mp.FancyArrow(v.real,v.imag,(vabc[i]*exp(1j*i*2*pi/3)).real*2/3,\n",
        "     (vabc[i]*exp(1j*i*2*pi/3)).imag*2/3, width=.03,length_includes_head=True,\n",
        "     color=clst[i]) #v_a,v_b,v_c\n",
        "    ax.add_patch(arr)\n",
        "  t1 = ax.text(v_sv.real,v_sv.imag,r'$v\\underbar$', size = 40)\n",
        "  if theta>pi/2 and theta<3*pi/2:\n",
        "    t1.set_ha('right')\n",
        "  if theta>pi:\n",
        "    t1.set_va('top')\n",
        "  return\n",
        "\n",
        "# animation function. This is called sequentially\n",
        "def animate(i):\n",
        "  if i%30==0: #for monitoring the progress\n",
        "    print(i)\n",
        "  # i=800\n",
        "\n",
        "  #plot\n",
        "  lines[0].set_data(v_sv[:i+1].real,v_sv[:i+1].imag) #v_sv trajectory\n",
        "  for k in range(3):\n",
        "    lines[2*k+1].set_data(t[:i+1]/T*xymax*1.9,vabc_pwm[k][:i+1]) #v_a,v_b,v_c PWM\n",
        "    lines[2*k+2].set_data(t[:i+1]/T*xymax*1.9,vabc_modulation[k][:i+1]) #v_a,v_b,v_c PWM\n",
        "  lines[7].set_data(t[:i+1]/T*xymax*1.9,carr[:i+1]) #carrier\n",
        "\n",
        "  drawVectors(ax0,xymax,v_sv[i],[va2[i],vb2[i],vc2[i]],clst)\n",
        "  return\n",
        "anim = animation.FuncAnimation(fig, animate, frames=Nf, interval=50)\n",
        "fn = r\"SpaceVector_SPWM.mp4\"\n",
        "writervideo = animation.FFMpegWriter(fps=20)\n",
        "anim.save(fn, writer=writervideo,dpi = 200)"
      ]
    }
  ]
}