Electrical_Engine_Parameters_Nata_Rodrigo.ipynb

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      "name": "Electrical-Engine-Parameters-Nata-Rodrigo.ipynb",
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      "name": "python3",
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    "language_info": {
      "name": "python"
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    {
      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/github/HenriqueMAP/electrical-induction-motor/blob/main/Electrical_Engine_Parameters_Nata_Rodrigo.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jnW3z2iOLV_4"
      },
      "source": [
        "## Desenvolvido por Natã Rodrigo Santos Pereira\n",
        "\n",
        "### Link do vídeo: https://youtu.be/GJ_lWGTDPd4\n",
        "\n",
        "### Github: https://github.com/natrodrigo\n",
        "\n",
        "---\n",
        "\n",
        "## Cálculos de Parâmetros de Motores Elétricos\n",
        "\n",
        "### Enunciado\n",
        "\n",
        "> Um motor de indução trifásico ligado em Y, de seis polos, tensão de linha de 460Volts, potência ativa de 20kW e frequência de 60Hz, tem os seguintes valores de parâmetros, referidos ao estator:\n",
        "\n",
        "*   R1 = 0,271 Ohms;\n",
        "*   R2 = 0,188 Ohms;\n",
        "\n",
        "*   X1 = 1,12 Ohms;\n",
        "*   X2 = 1,91 Ohms;\n",
        "\n",
        "*   Xm = 23,10 Ohms;\n",
        "*   Escorregamento = 1,6%;\n",
        "\n",
        "#### Objetivos\n",
        "\n",
        ">Realize um código na linguagem de programação de sua preferência para calcular:\n",
        "\n",
        "*   1 - Velocidade;\n",
        "*   2 - Corrente do estator;\n",
        "*   3 - Fator de potência;\n",
        "*   4 - Corrente de rotor;\n",
        "*   5 - Conjugado de partida;\n",
        "*   6 - Conjugado máximo;\n",
        "*   7 - Escorregamento máximo;\n",
        "*   8 - Velocidade de ocorrência do escorregamento;\n",
        "\n",
        "##### Gráfico\n",
        "\n",
        "> Construa uma curva de Conjugado versus Velocidade.\n",
        ">\n",
        "> Considere que a variação de escorregamento está entre o intervalo de \"0 < s < 1\". Ou seja, considere o intervalo completo de variação de \"s\".\n",
        "\n",
        "### Formato de entrega\n",
        "\n",
        "> Realize um pequeno vídeo mostrando os seus resultados e poste no mural digital que está no seguinte link: https://padlet.com/victoriaalejandrafmu/lle1oyktf0nheqmr\n",
        "\n",
        "#### Datas\n",
        "\n",
        "> Solicitação: 20/09/2021\n",
        "> Prazo máximo de entrega: 04/10/2021\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OlaeRzpvMUS9"
      },
      "source": [
        "## Importação de Bibliotecas\n",
        "\n",
        "### - math: Cálculos matemáticos\n",
        "### - matplotlib: Gerar o gráfico"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fSmkV9vWyVmt"
      },
      "source": [
        "import math\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OI__UzsmMqVz"
      },
      "source": [
        "## Definição de funções de cálculos complexos com números imaginários"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qGjERDb3ylIL"
      },
      "source": [
        "def somacomplex(v1, v2):\n",
        "  return complex(v1.real+v2.real, v1.imag+v2.imag)\n",
        "\n",
        "def subcomplex(v1, v2):\n",
        "  return complex(v1.real-v2.real, v1.imag-v2.imag)\n",
        "\n",
        "def multicomplex(v1, v2):\n",
        "  return complex((v1.real*v2.real)-(v1.imag*v2.imag), (v1.real*v2.imag)+(v1.imag*v2.real))\n",
        "\n",
        "def divcomplex(v1, v2):\n",
        "  numerator = (v1*v2.conjugate())\n",
        "  denominator = (v2*v2.conjugate())\n",
        "  quotientreal = (numerator.real / denominator.real)\n",
        "  quotientimag = (numerator.imag / denominator.real)\n",
        "  return complex(quotientreal, quotientimag)\n",
        "\n",
        "def polar(v1):\n",
        "  return math.sqrt(pow(v1.real, 2) + pow(v1.imag, 2)), math.degrees(math.atan(v1.imag / v1.real))"
      ],
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BzUE6sogM4d_"
      },
      "source": [
        "## Definição de parâmetros elétricos e cálculos"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wPTtbZEsy50t"
      },
      "source": [
        "# Dados do enunciado\n",
        "n_polos = int(6)       # Números de Pólos do Motor\n",
        "v_linha = float(460)   # Tensão de Linha (Volts)\n",
        "potencia = float(20)   # Potência Ativa (kWatts) \n",
        "frequencia = float(60) # Frequência de Operação da Rede (Hz)\n",
        "\n",
        "R1 = float(0.271) # Resistência do Estator (Ohms)\n",
        "R2 = float(0.188) # Resistência do Rotor (Ohms)\n",
        "X1 = float(1.12)  # Indutância do Estator (Ohms)\n",
        "X2 = float(1.91)  # Indutância do Rotor (Ohms)\n",
        "Xm = float(23.10) # Indutância de Magnetização (Ohms)\n",
        "\n",
        "Xm_complex = complex(0, Xm)\n",
        "\n",
        "escorregamento = float(1.6)\n",
        "\n",
        "# Conversão de valor percentual para valor numérico\n",
        "escorregamento = (escorregamento/100)\n",
        "\n",
        "# Constante do valor de PI\n",
        "PI = float(math.pi)\n",
        "\n",
        "# Velocidade Síncrona\n",
        "n_sinc = math.ceil((120 / n_polos) * frequencia)\n",
        "\n",
        "# Velocidade do motor (RPM)\n",
        "nm = math.ceil((1 - escorregamento) * n_sinc)\n",
        "\n",
        "# Velocidade síncrona (RAD/S)\n",
        "w_sinc = n_sinc * (PI / 30)\n",
        "\n",
        "# Velotidade do motor (RAD/S)\n",
        "wm = nm * (PI / 30)\n",
        "\n",
        "# Impedância do Estator (Ohms) Real + jImaginário\n",
        "Z1 = complex(R1, X1)\n",
        "\n",
        "# Impedância do Rotor  (Ohms) Real + jImaginário\n",
        "Z2 = complex((R2 / escorregamento), X2)\n",
        "\n",
        "# Impedância equivalente do motor  (Ohms) Real + jImaginário\n",
        "Zeq = somacomplex(divcomplex(multicomplex(Z2, Xm_complex), somacomplex(Z2, Xm_complex)), Z1)\n",
        "\n",
        "# Tensão de linha (Volts)\n",
        "v_linha = complex(v_linha, 0)\n",
        "\n",
        "# Tensão de fase (Volts)\n",
        "v_fase = complex((v_linha.real / math.sqrt(3)), 0)\n",
        "\n",
        "# Corrente do Estator (Ampére)\n",
        "I1 = divcomplex(v_fase, Zeq)\n",
        "\n",
        "# Módulo da Corrente do Estator (Ampére)\n",
        "I1 = polar(I1)\n",
        "\n",
        "# Fator de Potência (Percentual)\n",
        "FP = math.cos(math.radians(I1[1]))\n",
        "\n",
        "# Tensão de Thevénin (Volts)\n",
        "Vth = ((Xm * v_fase) / (math.sqrt(pow(R1, 2) + pow(X1 + Xm, 2))))\n",
        "\n",
        "# Resistência de Thevénin (Ampére)\n",
        "Rth = (R1 * pow((Xm /(X1 + Xm)), 2))\n",
        "\n",
        "# Indutância de Thevénin (Ohms)\n",
        "Xth = X1\n",
        "\n",
        "# Corrente do Rotor (Ampére)\n",
        "I2 = (Vth / (math.sqrt(pow((Rth + (R2 / escorregamento)), 2) + pow((Xth + X2), 2))))\n",
        "\n",
        "# Rendimento ou Eficiência (Porcentagem)\n",
        "P_EF = (3 * pow(I2, 2) * (R2 / escorregamento))\n",
        "\n",
        "# Escorregamento Máximo\n",
        "s_max = (R2 / math.sqrt(pow(Rth, 2) + pow((Xth + X2), 2)))\n",
        "\n",
        "# Conjugado Induzido (Nm)\n",
        "t_ind = ((3 * pow(Vth, 2) * (R2 / escorregamento)) / (w_sinc * (pow((Rth + (R2 / escorregamento)),2) + pow((Xth + X2), 2))))\n",
        "\n",
        "# Conjugado Máximo (Nm)\n",
        "t_max = ((3 * pow(Vth, 2)) / ((2 * w_sinc) * (Rth + math.sqrt(pow(Rth, 2) + pow((Xth + X2), 2)))))\n",
        "\n",
        "# Conjugado de Partida (Nm)\n",
        "t_partida = ((3 * pow(Vth, 2) * (R2 / 1)) / (w_sinc * (pow((Rth + (R2 / 1)), 2) + pow((Xth + X2), 2))))\n",
        "\n",
        "# Velocidade de ocorrência do escorregamento\n",
        "n_tmax = ((1 - s_max) * n_sinc)"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hfHQpcV8iP9i"
      },
      "source": [
        "## Resultados dos cálculos"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aV4AB2X3d6Z6",
        "outputId": "a9a1498a-00d8-4419-f7c9-b30189ed782f"
      },
      "source": [
        "print(\"\\nVelocidade Síncrona = \" + str(n_sinc) + \" RPM\")\n",
        "print(\"\\nVelocidade do Motor = \" + str(nm) + \" RPM\")\n",
        "\n",
        "print(\"\\n-----------------------------------------------\")\n",
        "\n",
        "print(\"\\nVelocidade Síncrona = \" + str(w_sinc) + \" Rad/s\")\n",
        "print(\"\\nVelocidade do Motor = \" + str(wm) + \" Rad/s\")\n",
        "\n",
        "print(\"\\n-----------------------------------------------\")\n",
        "\n",
        "print(\"\\nImpedância do Estator = \" + str(Z1) + \" Ohms\")\n",
        "print(\"\\nImpedância do Rotor = \" + str(Z2) + \" Ohms\")\n",
        "print(\"\\nImpedância do Equivalente = \" + str(Zeq) + \" Ohms\")\n",
        "\n",
        "print(\"\\n-----------------------------------------------\")\n",
        "\n",
        "print(\"\\nTensão de Linha = \" + str(v_linha) + \" Volts\")\n",
        "print(\"\\nTensão de Fase = \" + str(v_fase) + \" Volts\")\n",
        "\n",
        "print(\"\\n-----------------------------------------------\")\n",
        "\n",
        "print(\"\\nCorrente do Estator = \" + str(I1) + \" Ampère\")\n",
        "print(\"\\nCorrente do Rotor = \" + str(I2) + \" Ampère\")\n",
        "\n",
        "print(\"\\n-----------------------------------------------\")\n",
        "\n",
        "print(\"\\nFator de Potência = \" + str(FP) + \" %\")\n",
        "\n",
        "print(\"\\n-----------------------------------------------\")\n",
        "\n",
        "print(\"\\nTensão de Thevénin = \" + str(Vth) + \" Volts\")\n",
        "print(\"\\nResistência de Thevénin = \" + str(Rth) + \" Ampère\")\n",
        "print(\"\\nIndutância de Thevénin = \" + str(Xth) + \" Ohms\")\n",
        "\n",
        "print(\"\\n-----------------------------------------------\")\n",
        "\n",
        "print(\"\\nRendimento ou Eficiência = \" + str(P_EF) + \" %\")\n",
        "\n",
        "print(\"\\n-----------------------------------------------\")\n",
        "\n",
        "print(\"\\nEscorregamento Máximo = \" + str(s_max) + \" \")\n",
        "print(\"\\nConjugado Máximo = \" + str(t_max) + \" Nm\")\n",
        "\n",
        "print(\"\\nConjugado Induzido = \" + str(t_ind) + \" Nm\")\n",
        "\n",
        "print(\"\\nConjugado de Partida = \" + str(t_partida) + \" Nm\")\n",
        "print(\"\\nVelocidade de Ocorrência do Escorregamento = \" + str(n_tmax) + \" RPM\")"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Velocidade Síncrona = 1200 RPM\n",
            "\n",
            "Velocidade do Motor = 1181 RPM\n",
            "\n",
            "-----------------------------------------------\n",
            "\n",
            "Velocidade Síncrona = 125.66370614359172 Rad/s\n",
            "\n",
            "Velocidade do Motor = 123.67403079631818 Rad/s\n",
            "\n",
            "-----------------------------------------------\n",
            "\n",
            "Impedância do Estator = (0.271+1.12j) Ohms\n",
            "\n",
            "Impedância do Rotor = (11.75+1.91j) Ohms\n",
            "\n",
            "Impedância do Equivalente = (8.48239943208324+6.741948953497722j) Ohms\n",
            "\n",
            "-----------------------------------------------\n",
            "\n",
            "Tensão de Linha = (460+0j) Volts\n",
            "\n",
            "Tensão de Fase = (265.5811238272279+0j) Volts\n",
            "\n",
            "-----------------------------------------------\n",
            "\n",
            "Corrente do Estator = (24.510600566975313, -38.47824811868214) Ampère\n",
            "\n",
            "Corrente do Rotor = (20.470295100346398+0j) Ampère\n",
            "\n",
            "-----------------------------------------------\n",
            "\n",
            "Fator de Potência = 0.7828444331178602 %\n",
            "\n",
            "-----------------------------------------------\n",
            "\n",
            "Tensão de Thevénin = (253.28406121497764+0j) Volts\n",
            "\n",
            "Resistência de Thevénin = 0.24651592101306422 Ampère\n",
            "\n",
            "Indutância de Thevénin = 1.12 Ohms\n",
            "\n",
            "-----------------------------------------------\n",
            "\n",
            "Rendimento ou Eficiência = (14770.912597708118+0j) %\n",
            "\n",
            "-----------------------------------------------\n",
            "\n",
            "Escorregamento Máximo = 0.06184187072236265 \n",
            "\n",
            "Conjugado Máximo = (233.00210967963872+0j) Nm\n",
            "\n",
            "Conjugado Induzido = (117.54318769517978+0j) Nm\n",
            "\n",
            "Conjugado de Partida = (30.7297542435278+0j) Nm\n",
            "\n",
            "Velocidade de Ocorrência do Escorregamento = 1125.7897551331648 RPM\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U8HpIInSiVRW"
      },
      "source": [
        "## Gráfico: Curva de Conjugado Induzido versus Velocidade Síncrona"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "Fjao5hyTCVPI",
        "outputId": "ace2aa4b-e234-4241-8f11-cee3c4ef6644"
      },
      "source": [
        "induzido = []\n",
        "\n",
        "for index in range(0, 1200):\n",
        "  s = ((1200 - index) / 1200)\n",
        "  induzido.append(((3 * pow(Vth, 2) * (R2 / s)) / (w_sinc * (pow((Rth + (R2 / s)), 2) + pow((Xth + X2), 2)))).real)\n",
        "\n",
        "plt.xlabel(\"Velocidade (rpm)\")\n",
        "plt.ylabel(\"Conjugado Induzido\")\n",
        "plt.plot(induzido)\n",
        "plt.axis([0,1200,0,240])\n",
        "plt.title(\"Gráfico\")\n",
        "plt.show()"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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J/LPbPCK3xykeEZGkeW7NbhZsrOYLZ02gJC+1Zi2M1IEHDhM0CGMkSWQN8GPgeTM7LSiLfx1JRCSB2js6+cHf32RseQEfOXVMssOJ2ttPrSdmcqpIkoi7+2PARcD/M7MbOMxwKF3M7E4zqzKz18PKvm1m28xsWfB6f9h3Xzez9Wa2xszOjeZkRESi9ZelW1m7q56vnTc5YXNxxMOAglASqW1qS8jxIvkvZQDuvg44PXhNi2C7PwDn9VD+c3efEbweBzCzKcCVwPHBNr8xs8wIjiEictRqG9v48ZNrmDVmIOedMDTZ4RyV0mDok5RJIu5+Ytjnene/AjjiDPXu/gJQE2EcFwN/dvcWd98ErAdOiXBbEZGj8vN/rGVfYyvfufj4hPRoiqeu8bP2NSYmiRzxYUMzu/MQX308ymPeYGbXEOo6/O/uvhcYASwMW2drUNZTPNcD1wOMHj06yhBERELe3LGfuxZUMu/UMRw/PLWHeo9ESYKTSCTNWX8Lez0DlAD1UR7vFmA8MIPQyMA/7e0O3P02d5/l7rMGDRoUZRgiIqEuvf/16CpK87P59zR8sLAnmRlGcV5WwpqzIhn25KDJqMzsXuDFaA7m7rvC9vM74LFgcRswKmzVkUGZiEjcPLp8O4s31fD9S6YeuCHdFwwoyE6deyI9mAgMPuJaPTCz8HlILgG6em49ClxpZrlmNi44xuJojiEiEon6lnZ+8PhqThhRwodPHnXkDdJIaX7ikkgk90S6Zji04H0n8LUItrsXOAOoMLOtwH8BZ5jZjGA/lcC/Abj7KjO7H3gDaAc+F/6EvIhIrP3kyTXsqmvmNx+dSWZGet9M725Afg77EvSwYSTNWVENpO/uV/VQfMdh1v8e8L1ojiUi0huvvrWX+QsquWb2GGaOHpjscGKuND+b7bVNCTnW4UbxPez4WO7+auzDERGJr9b2Tr7+4EqGluTxlfMmJzucuCgtyGZ/CjRndfWcygNmAcsJNWlNI9Q9d058QxMRib3bXtjAml113H7NLIpyj9gYk5YG5Gezr7EtISP5HvLGuruf6e5nEuqKOzPoVnsScCLqOSUiaWjD7np++c/1XDB1GGdPGZLscOKmND+b9k6nsTX+t5Yj6Z01yd1Xdi24++vAcfELSUQk9jo6na8/uJK8rAz+66IpyQ4nrgYEQ8DvS0CTViR1uRVmdjtwT7A8D1gRv5BERGLvzhc3sbiyhp98aDqDi/OSHU5cleaHnnnZ19jKiAHxnVgrkiTyMeAzwBeD5RcIPXkuIpIW1uys48dPruGcKUO4bGaPIyr1KYkchDGSLr7NwM+Dl4hIWmlt7+TG+5dRnJfF9y+dmvYDLEaiqzmrNgHjZ0XysOFc4NvAmPD13f2II/mKiCTbr/65jlXb93Pb1SdRUZSb7HASIqVqIoQeEPwysBTQU+QikjZefWsvv352PZfNHMk5x6f3PCG9kWo31mvd/e9xj0REJIZqm9r4wr2vMaw0v8/3xuouPzuTnMyMhAwHH0kSedbMfgw8BByYtFdPrItIqnJ3bnpwBTtrm7n/03MoyctOdkgJZWaU5GdT2xT/8bMiSSKnBu+zwsocOCv24YiIHL17Fr3F31/fyU3nT+6TY2NFoiQ/i/3N7XE/TiS9s86MexQiIjHyxvb9fPexN3jPsYO4/t39t/9PcV42dclMImZ24+E2dPefxT4cEZHo1TW3ccO9rzIgP5ufXTGdjD42xHtvlORlJWQQxsPVRKIaAl5EJBk6O51/v385m6sbuecTp1LeT7rzHkpJXjbb98V/OPhDJhF3/07cjy4iEiO/fnY9T72xi//zgSnMGV+e7HCSrjgvKyHNWdFMjysiklL+uXoXP/vHWj44Yzgfnzs22eGkBCUREZEIbNrTwBf/vIzjhpbwg0un9YthTSJRnJdNU1sHbR2dcT2OkoiIpK39zW1cf9cSsjKM3159Evk5mckOKWWU5IXuVsS7NnLEJGJmpWb2czNbErx+amalcY1KROQI2jo6+ew9r7JpTwO/njeTUWUFyQ4ppRQHD1jWNce3h1YkNZE7gf3AFcFrP/D7eAYlInI47s63Hn6dF9fv4fuXTuW08RXJDinlFCeoJhLJE+vj3f2ysOXvmNmyeAUkInIktz6/kfuWbOGGMydwxaxRyQ4nJXXVROL9rEgkNZEmM3tX10IwNHz8Ox+LiPTgbyt28MMnVnPh9OHc+L5jkx1OyirJD9UR4j30SSQ1kc8A84P7IAbUANfFMygRkZ68tH4PX75vGSeNGciPL5/Wr59IP5KSBN0TiWTsrGXAdDMrCZb3xzUiEZEeLNuyj0/dtYRxFYXcce0s8rLVE+twkn5P5FBjZ3X1wdbYWSKSKOt21XHd7xdTXpTDXZ84hQEFOckOKeUV5XY1ZyWvJtI1dtYk4GTg0WD5QmBxPIMSEemydW8jV9+xmOzMDO75xKkMKclLdkhpISszg8KczOTVRLrGzjKzF4CZ7l4XLH8b+FtcoxIRAbbva+Ijv1tEY2s79396DmPKC5MdUloJDQef/N5ZQ4Dw6bFagzIRkbjZvq+JK29byN6GVuZ//BQmDy1JdkhpJxHjZ0XSO+suYLGZPRwsfxCYH7+QRKS/C08gd3/yVGaMGpDskNJSSX52Uu+JAODu3zOzJ4CuZ0U+5u6vxTUqEem3lEBipzgvi5qG+M6zHklNBHdfamZbgDwAMxvt7m/FNTIR6Xc2Vzfw0TsWsa+hTQkkBorzstlc3RjXY0QyAONFZrYO2AQ8H7z/Pa5RiUi/8+aO/Vx+6wLqmtu5RwkkJkL3RJJ/Y/27wGxgrbuPA84GFsY1KhHpV5ZU1vDh3y4g04wHPj2H6UogMVGSl83+piQPBQ+0uXs1kGFmGe7+LDArrlGJSL/x3JoqPnrHIiqKcnngM3OYMLj4yBtJRIrzsmjt6KS5rSNux4jknsg+MysCXgD+aGZVQEPcIhKRfuP+JVv4xkMrmTysmD987BQqinKTHVKfEj4xVbyGiYmkJnIxoVF7vww8AWwg9NT6YZnZnWZWZWavh5WVmdnTZrYueB8YlJuZ/dLM1pvZCjObGd3piEg66Ox0fvTEar76wArmjC/n3k/NVgKJg0RMTHXEJOLuDe7e4e7t7j7f3X8ZNG8dyR+A87qV3QQ84+4TgWeCZYDzgYnB63rglkhPQETSS3NbB5//82v85rkNXHXKaO687uQDP3YSW4kYDj6S3ll1Zra/22uLmT1sZsccajt3f4HQsPHhLubtBxXnE3pwsav8Lg9ZCAwws2G9Px0RSWV76lu46ncLeXzlDr7x/sl8/5ITyM6MpEFEopGImkgk90T+B9gK/InQfCJXAuOBVwlNnXtGL443xN13BJ938vbwKSOALWHrbQ3KdtCNmV1PqLbC6NGje3FoEUmmFVv38em7l1LT2Mot82Zy3gn6d2K8dY3kW5/Mmghwkbv/1t3r3H2/u98GnOvu9wEDoz2wuzvgUWx3m7vPcvdZgwYNivbwIpJA9y/ZwuW3LsDMeODTpymBJMiBJNISvyQSSU2k0cyuAB4Ili8HmoPPvU0Cu8xsmLvvCJqrqoLybUD4RMkjgzIRSWOt7Z1897E3uHvhZuZOKOdXV82krFBzgSRKVxJpiGMSiaQmMg+4mtAP/q7g80fNLB+4oZfHexS4Nvh8LfBIWPk1QS+t2UBtWLOXiKSh7fuauOp3C7l74Wb+7fRjmP+xU5RAEqwwFWoi7r6RQ3fpffFQ25nZvYTul1SY2Vbgv4CbgfvN7BPAZuCKYPXHgfcD64FG4GMRxi8iKeipVTv5ygMraO/o5FdXnciF04cnO6R+KScrg5zMDOpbkviwoZn9nh6ardz944fbzt2vOsRX7+1hXQc+d6RYRCS1Nbd1cPPfV/OHlys5YUQJv7pqJuMqNJFUMhXmZsa1OSuSeyKPhX3OAy4BtscnHBFJVxt21/P5P73GGzv28/G54/ja+ZPIzYrPU9ISuaK8rKQ3Zz0Yvhw0Ux2yGUtE+pfOTueuBZXc/MRq8rMzuePaWbz3OE1+mioKc5KcRHowERgc60BEJP1sqWnkqw+sYMHGas6YNIibL53G0NK8ZIclYYpys5LbnGVmdYTuiVjwvhP4WtwiEpGU5+7c98oWvvvYGwD88LKpXDFrFGaW5Miku6I4z24YSXOWxmUWkQO21DTyrf99nefX7mbOMeX86PJpjCorSHZYcgiFuVm8VRO/2Q0PmUTMbLK7rz7EiLoO1Lj75rhFJiIppa2jkzte3MT//GMtmWZ856LjuXr2GDIyVPtIZUU5yWvOupHQGFU/PcT35Wa23N2vjn1YIpJKXn1rL994aCWrd9ZxzpQhfPui4xk+ID/ZYUkEivKy4jp21iGTiLtfH7yfeah1zOypeAQlIqlhX2MrP31qLfcs2szQkjx+e/VJnHv80GSHJb1QmJtFQ2sHnZ0el1pjRL2zzOw0YGz4+u5+l7ufE/OIRCTp2js6+dPit/jZ02vZ39TGtXPG8h/nTjowFpOkj6Lc0LM6jW0dcbl+kfTOupvQ0O/LgK5n5x24K+bRiEjSvbhuD//92CrW7qpnzjHl/OeFUzhuWEmyw5IoFeWG5hSpb25PThIBZgFTgqFJRKSPqtzTwPcef5On39jFqLJ8bv3oSZx7/BB1201zhUFNJF4PHEaSRF4HhtLDBFEikv527W/ml8+s475XtpCTlcFXz5vEx+eOIy9bQ5b0BfEeDj6SJFIBvGFmi4GWrkJ3vyguEYlIQtQ2tnHrCxv4/UubaO9wPnLqaG44awKDi/XEeV8S74mpIkki347LkUUkKZpaO/jDy5Xc8tx66lrauXj6cL78vmMZU67RdvuieM8pEskT68+b2RDg5KBosbtXHW4bEUk99S3t3L1gM7f/ayPVDa2cNXkw/3HOJKYM103zvizpzVnB1Lg/Bp4jNH7Wr8zsK+7+wGE3FJGUUNvUxh9equTOlzZR29TG6ccO4gtnTWDW2LJkhyYJUJSX/OasbwInd9U+zGwQ8A/ennNdRFJQTUMrd764ifkvV1LX0s7Zxw3hhrMmMGPUgGSHJgmUCvdEMro1X1UT2dzsIpIEG3fXc8eLm3jw1a20tHdy/glD+dyZEzh+eGmyQ5MkyM3KIDPDkto76wkzexK4N1j+MPD3uEQjIlFxdxZtquH2f23kmdVVZGdmcMmMEXzy3eOYOEQDcfdnZkZhTmbcxs+K5Mb6V8zsUuBdQdFt7v5wXKIRkV5pbe/k76/v4PZ/bWLltlrKCnP4/FkTuXr2GAYV5yY7PEkRxXnZ1Ld0HHnFKBxuKPgJwBB3f8ndHwIeCsrfZWbj3X1DXCISkSPaureRPy16i/uXbGFPfSvHDCrk+5dM5dKZI/SQoLxDYW5mUpqz/gf4eg/ltcF3F8YlIhHpUUen88La3dyzcDP/XFOFAWdNHsJHZ4/m9ImDNK+HHFJhbvzmWT9cEhni7iu7F7r7SjMbG5doROQddtQ28dCr27h38Vts3dtERVEuN5w5gStPGc0IzekhESjKzaIuCfdEDtcPUH+5InHU3NbBU2/s4oGlW3lx3W46HU4dV8ZN50/mnClDyclSB0mJXFFuFjtqm+Oy78MlkSVm9il3/114oZl9Elgal2hE+jF3Z/nWWh5YuoVHl21nf3M7w0vz+NyZE7hs5kjGVmhYEolOYW78psg9XBL5EvCwmc3j7aQxC8gBLolLNCL90KY9DTy2fDuPLN/O+qp6crMyOP+EoVx+0ihOG1+uex1y1IqScU/E3XcBp5nZmcAJQfHf3P2fcYlEpB/Zvq+Jx1Zs56/Ld7ByWy0AJ48dyA8uncoF04ZRkped5AilLykKaiLuHvP5YSJ5TuRZ4NmYHlWkH9pd18LfX9/BX5dv55XKvQBMH1nKty44jgumDWNYqW41SnwU5mbR6dDU1kFBTmxnN9SEySJxtLm6gSdX7eSpVbtY+tZe3GHy0GK+cu4kPjBtmIZfl4QIH4RRSUQkhbk7q7bv56lVO3ly1S7W7KoD4PjhJXzpvcdy/tShHKthSCTBirqmyG1uZ3CM//yURESOUnNbBws3VvPcmt08/cYutu1rIsPg5LFl/OcHpvC+KUMYVVaQ7DClHyvM6ZpTJALF42cAABD2SURBVPZDnyiJiERhc3UDz63ZzbNrqliwoZqW9k5yszJ498QKvnj2RM4+bghlhTnJDlMEiO9w8EoiIhFobutg8aYanl1TxfNrdrNxTwMAY8sLuOqU0ZwxaRCzjynXuFWSkrqmyG1sVRIRSYj2jk5WbKtlwYZqXlq/hyWb99Ia1DZmH1PONXPGcMakwXoAUNJCYXBPpKFVzVkiceHurN1Vz0vr9/Dyhj0s2lhDXVD1P25YCdfMHsPciRXMHldOfo5qG5JeunpkNao5SyQ2OjqdNTvreKWyhsWVNSzaWM2e+lYg1ER14YzhzB1fwexjyigv0rwckt4O3FjvKzURM6sE6oAOoN3dZ5lZGXAfMBaoBK5w973JiE/6nua2DlZuq2Xxphpeqaxh6ea9B0Y1HVaax7smVHDahArmTqjQyLjS53TVnvtaTeRMd98TtnwT8Iy732xmNwXLX0tOaJLuqutbWLZlH0s272VJZQ3Lt9TS2tEJwMTBRVw4fTinjC1j1tiBjByo7rfSt+VkZZCTmdF3aiKHcDFwRvB5PvAcSiISgea2DlZt38+yLfuC11621DQBkJVhTB1ZynVzx3Ly2DJmjRnIQHW9lX6oIDezT/XOcuApM3Pgt+5+G6FJsHYE3+8EhiQpNklhnZ3OpuoGlr2170DSeHPHfto7HYDhpXnMGD2Aq2ePYcaogUwdUaob4SKE7ov0pYcN3+Xu28xsMPC0ma0O/9LdPUgw72Bm1wPXA4wePTr+kUrStHd0smF3A6u21/L6tv2s2l7LG9v3H+g1VZiTybSRA/jU6ccwY9QAThw1gMEleUmOWiQ1FeT0oZqIu28L3qvM7GHgFGCXmQ1z9x1mNgyoOsS2twG3AcyaNavHRCPpp7mtg7W76g4ki9e372f1jv20tIfuY+RlZ3DcsBI+eOIIpo4oZcboAYwfVESm5toQiUhBblbfuCdiZoVAhrvXBZ/PAf4beBS4Frg5eH8k0bFJ/Lk72/Y1sXZXHat31rF2Z+h9fVX9gSap4rwsThheytWzx3DCiFKOH17CMUoYIkelMCezz/TOGkJoxsSu4//J3Z8ws1eA+83sE8Bm4IokxCYxtLehNZQouhLGrlDSqAv7Qx4xIJ9jhxRx9nFDOH54CSeMKGXkwPyYT5wj0t8V5GSxt7Ep5vtNeBJx943A9B7Kq4H3JjoeOTruzp76Vjbsrg+9qhpYV1XHmp11VNW1HFivND+bSUOLuWTmCCYNLWbSkGKOHVqsGfxEEqSoj/XOkjTT1tHJWzWNbKiqZ8PuhrCkUc/+5rf/MPOzMxk/uJB3TxzE5KHFoYQxtJjBxbmqXYgkUUFu3+qdJSnI3amqa6FyTwObqxvZVN3Axt31rK+qZ3N144F7FgCDi3MZP6iIi2YMZ/ygotBrcBHDSvLI0L0LkZRT2Jd6Z0nydHQ6O2qb2FzdGLwaqKxuOLDc1Pb2v1SyMoyxFYVMGFzEuccPPZAojhlUqGYokTRTkJNFY2sHnZ2x7dSqJNIHNbS0s21fE1v3NrKlpumgZLGlpunA8B8QGg5hTFkBY8oLmDuhgrHlBYwpL2RseSHDB+SRlZmRxDMRkVjpGg6+sS22TVpKImmooaWdrXtDSaLrPZQ0Qq+ahtaD1i/IyWRMeSHHDinm7ClDGFteyJjyAsaWFzJUzU8i/UK8hoNXEkkxnZ1OdUMrO2ub2V7bxI59TQcliK17G9nb2HbQNrlZGYwcmM/IgQVMHVHKyIEFwXI+IwbmM6hIN7VF+rt4TUylJJJA3RNE+PuOfc3s2N/ErtqWg5qb4OAkMW3kwUli5MACKopylCRE5LC6aiINqomkpua2Dqr2t1BV18yusPcdtU3sqG1mR23PCSI70xhamsew0nxmjh7IsNJ8hpXmBa98hpbmKUmIyFHrmpiqUTWRxKpvaadqfzNVdS3s2t/M7roWqupaDiqrqms5MMFRuEMliKGleQwPEkR5YY7uSYhI3BUcaM5STeSoNba2U13fyp76lrffG0Lv3ZNET1k7JyuDISW5DC7O49ghxbxrQgWDS/IYXJz79ntxLgMLlCBEJDUcqInE+IHDPpFEOjqdvY2tVNe3Ul3fwp6GVvbUtVDd8HaS2FPfemD5UNW54twsKopzGVScywkjShlcnBdKFkHCCCWHPErys9S8JCJppSBHNZF3WLernln/92lqGlrp6fmZzAyjrDCHiqJcKopyGFteQEVRLuVFuZQX5TAoeC8vyqW8MIe8bE1eJCJ9U2Guuvi+Q05WBu+bMpSKohzKC3OoKM6lvDCUMCqKcinNz1ZzkogI4TURNWcdMKa8gB9cOjXZYYiIpLzcrAyyMizm42dpTAsRkX7AzCjIyYz5SL5KIiIi/URhbpZqIiIiEp2CnMyY3xNREhER6ScKc7Ni3jtLSUREpJ9QTURERKJWmJMV8wEYlURERPqJgtysmA/AqCQiItJPFOZkqiYiIiLR6ZpnPZaURERE+onC3MyYD8CoJCIi0k8U5GThPQxWezSURERE+omuedZjSUlERKSf6JqYKpaURERE+gnVREREJGoFqomIiEi0VBMREZGoqSYiIiJR0411ERGJWoGas0REJFqqiYiISNTysjP49oVTYrpPJRERkX7CzLhu7riY7lNJREREopZyScTMzjOzNWa23sxuSnY8IiJyaCmVRMwsE/g1cD4wBbjKzGLbgCciIjGTUkkEOAVY7+4b3b0V+DNwcZJjEhGRQ4h9f6+jMwLYEra8FTg1fAUzux64PlhsMbPXExRbMlQAe5IdRBzp/NJXXz436PvnNylWO0q1JHJE7n4bcBuAmS1x91lJDiludH7prS+fX18+N+gf5xerfaVac9Y2YFTY8sigTEREUlCqJZFXgIlmNs7McoArgUeTHJOIiBxCSjVnuXu7md0APAlkAne6+6rDbHJbYiJLGp1feuvL59eXzw10fhEzj/Ws7SIi0m+kWnOWiIikESURERGJWtomkXQfHsXMRpnZs2b2hpmtMrMvBuVlZva0ma0L3gcG5WZmvwzOd4WZzUzuGUTGzDLN7DUzeyxYHmdmi4LzuC/oQIGZ5QbL64PvxyYz7kiY2QAze8DMVpvZm2Y2py9dPzP7cvC3+bqZ3Wtmeel8/czsTjOrCn+2LJrrZWbXBuuvM7Nrk3Eu3R3i3H4c/G2uMLOHzWxA2HdfD85tjZmdG1be+99Vd0+7F6Gb7huAY4AcYDkwJdlx9fIchgEzg8/FwFpCQ738CLgpKL8J+GHw+f3A3wEDZgOLkn0OEZ7njcCfgMeC5fuBK4PPtwKfCT5/Frg1+HwlcF+yY4/g3OYDnww+5wAD+sr1I/Tg7yYgP+y6XZfO1w84HZgJvB5W1qvrBZQBG4P3gcHngSl6bucAWcHnH4ad25TgNzMXGBf8lmZG+7ua9Asb5X+wOcCTYctfB76e7LiO8pweAd4HrAGGBWXDgDXB598CV4Wtf2C9VH0Res7nGeAs4LHgf8g9YX/YB64joR55c4LPWcF6luxzOMy5lQY/statvE9cP94ePaIsuB6PAeem+/UDxnb7oe3V9QKuAn4bVn7Qeql0bt2+uwT4Y/D5oN/LrmsX7e9qujZn9TQ8yogkxXLUgqr/icAiYIi77wi+2gkMCT6n4zn/D/BVoDNYLgf2uXt7sBx+DgfOL/i+Nlg/VY0DdgO/D5rrbjezQvrI9XP3bcBPgLeAHYSux1L6zvXr0tvrlVbXMczHCdWsIMbnlq5JpM8wsyLgQeBL7r4//DsP/XMgLftgm9kHgCp3X5rsWOIki1DzwS3ufiLQQKg55IA0v34DCQ1+Og4YDhQC5yU1qDhL5+t1OGb2TaAd+GM89p+uSaRPDI9iZtmEEsgf3f2hoHiXmQ0Lvh8GVAXl6XbOc4GLzKyS0GjMZwG/AAaYWddDruHncOD8gu9LgepEBtxLW4Gt7r4oWH6AUFLpK9fvbGCTu+929zbgIULXtK9cvy69vV5pdR3N7DrgA8C8IElCjM8tXZNI2g+PYmYG3AG86e4/C/vqUaCrx8e1hO6VdJVfE/QamQ3UhlXDU467f93dR7r7WELX55/uPg94Frg8WK37+XWd9+XB+in7r0J33wlsMbOu0VDfC7xBH7l+hJqxZptZQfC32nV+feL6hent9XoSOMfMBga1tXOCspRjZucRak6+yN0bw756FLgy6FE3DpgILCba39Vk3ww6iptI7yfUo2kD8M1kxxNF/O8iVHVeASwLXu8n1I78DLAO+AdQFqxvhCbs2gCsBGYl+xx6ca5n8HbvrGOCP9j1wF+A3KA8L1heH3x/TLLjjuC8ZgBLgmv4v4R66/SZ6wd8B1gNvA7cTag3T9peP+BeQvd32gjVJD8RzfUidH9hffD6WLLP6zDntp7QPY6u35dbw9b/ZnBua4Dzw8p7/buqYU9ERCRq6dqcJSIiKUBJREREoqYkIiIiUVMSERGRqCmJiIhI1JREJK1YaOTjc7uVfcnMbjnMNs+Z2awojnXRoUYyNbP6Xu7r22b2H73c5oNm9p+92aYX+77BzD4ej31L/6IkIunmXkIPQYW7MiiPKXd/1N1vjvV+e+GrwG+6F4Y9MX407gQ+H4P9SD+nJCLp5gHggrB5LMYSGtvpX2Z2jpktMLNXzewvwbhkBzGzq8xsZTBHxg/Dys8LtltuZs8EZdeZ2f8LPo8L9r3SzP5v2HZFZvZMsO1KM7s47LtvmtlaM3sRmBRWPt7MnjCzpWb2LzOb3EOcxwIt7r4nWP6Dmd1qZouAHwU1m7uDmNaZ2aeC9c4ws+fN7BEz22hmN5vZPDNbHMQ3HsBDTzBXmtkpUV8JEZREJM24ew2hJ6LPD4quJDTHRTnwLeBsd59J6EnyG8O3NbPhhOZVOIvQ0+YnB01Gg4DfAZe5+3TgQz0c+heEBlucSujJ4C7NwCXBMc8EfhoMlXFSENsMQk8Bnxy2zW3A5939JOA/6KG2QWicqle7lY0ETnP3rvOaFpzLHOA/g/MDmA58GjgOuBo41t1PAW7n4NrHEuDdPRxbJGKxqBaLJFpXk9YjwfsnCE0cNAV4KTTUEznAgm7bnQw85+67Aczsj4Qm8+kAXnD3TXAgUXU3F7gs+Hw3oWQEoeExvm9mpxMa8n4EoeHE3w08HPyLHzN7NHgvAk4D/hLECaHhRLobRmio+XB/cfeOsOVH3L0JaDKzZ4FTgH3AKx6My2VmG4CngvVXEkp0XaqAd9SCRHpDSUTS0SPAzy00ZWmBuy81swuBp939qjget6cxguYBg4CT3L3NQqMW5x1mHxmE5uSYcYRjNREaCTdcwxHi6VpuCSvrDFvu5OD/5/OC44hETc1ZknbcvZ7QaLJ38vYN9YXAXDObAGBmhcF9hXCLgfeYWYWZZRKape75YNvTgxFNMbOyHg77Em/f0J8XVl5KaN6UNjM7ExgTlL8AfNDM8s2sGLgwiH0/sMnMPhQcy8xseg/HexOYcIT/FBdbaN7zckKDXL5yhPW7O5bQ4IoiUVMSkXR1L6G2/3sBgiaq64B7zWwFoaasg5pqgiaemwgloOXAUnd/JNj2euAhM1sO3NfD8b4IfM7MVnLwbG9/BGYF5dcQGvUWd3812M9yQjPKhf/AzwM+ERxrFaHJn7p7ATjRwtq8erAiOJeFwHfdffth1u3JXODpXm4jchCN4iuSoszsF8Bf3f0fPXz3baDe3X8S5b5PBG5096uPLkrp71QTEUld3wcK4rTvCuD/xGnf0o+oJiIiIlFTTURERKKmJCIiIlFTEhERkagpiYiISNSUREREJGr/HztC+qE7aS/3AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}