DynamicPhasorBasics.ipynb 69.2 KB
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{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gS2nKlN7aO71iabaVbIn8fPq3N3JktLgxW1xXM717hwHwREEBr0PpyPDfvgzq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\nMAaMwWAwGAyGkMMYMAaDwWAwGEKO/wMbGf3mgbqHuAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e3e19b1320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This line configures matplotlib to show figures embedded\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Creates time-voltage vectors\n",
    "time = np.linspace(0, 0.1, 1000)\n",
    "voltageFundRe = np.cos(5*np.pi*2*time)\n",
    "voltageFundIm = np.sin(5*np.pi*2*time)\n",
    "voltageSlowRe = np.cos(5*np.pi*(-2)*time)\n",
    "voltageSlowIm = np.sin(5*np.pi*(-2)*time)\n",
    "voltageEmt = voltageRe*np.cos(2*np.pi*50*time) - \\\n",
    "    voltageIm*np.sin(2*np.pi*50*time)\n",
    "\n",
    "# Shift dynamic phasors by 50 Hz\n",
    "voltageFund = voltageFundRe * np.cos(2*np.pi*50*time) - \\\n",
    "    voltageFundIm * np.sin(2*np.pi*50*time)\n",
    "voltageSlow = voltageReSlow*np.cos(2*np.pi*50*time) - \\\n",
    "    voltageImSlow*np.sin(2*np.pi*50*time)\n",
    "\n",
    "# Plot vectors\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(time, voltageEmt, 'k:', label = 'EMT')\n",
    "ax.plot(time, voltageFund, 'b--', label = 'DP fund')\n",
    "ax.plot(time, voltageSlow, 'r--', label = 'DP slow')\n",
    "\n",
    "# Add legend and labels\n",
    "legend = ax.legend(loc='lower right', shadow=True)\n",
    "frame = legend.get_frame()\n",
    "frame.set_facecolor('0.90')\n",
    "ax.set_xlabel('time [s]')\n",
    "ax.set_ylabel('voltage [V]')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}