SyncGenCapCurveGenerator.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "####################################################################################################\n",
    "# SYNCHRONOUS GENERATOR CAPABILITY CURVES GENERATOR\n",
    "####################################################################################################\n",
    "# This program was designed to create the capability curves of a synchronous generator\n",
    "# given the machines' nominal parameters.\n",
    "# It comprises two functions:\n",
    "# 1) Capability Curve Generator:\n",
    "#       generates the capability curve from the current limit curves for the rotor and stator\n",
    "# 2) Generator Capability Verification:\n",
    "#       verify wheter a certain load condition can be achieved by a generator\n",
    "####################################################################################################\n",
    "# This code was developed using the concepts and electric machinery modeling from Chapman's\n",
    "# \"Electric Machinery Fundamentals\", 5th edition and Uman's \"Fitzgerald & Kingsley's Electric\n",
    "#  Machinery\", 7th edition.\n",
    "# The sections used were, respectively, 4.11 (Synchronous Generator Ratings - Synchronous Generator\n",
    "# Capability Curves, p.254) and 5.5 (Steady-state Operating Characteristics, p.293)\n",
    "# Along with several mathematical and programming ideas that will be cited when approriate\n",
    "#  throught the code.\n",
    "####################################################################################################\n",
    "# Developed by\n",
    "#       Felipe Baldner (https://github.com/fbaldner) and\n",
    "#       Júlia Avellar ()\n",
    "####################################################################################################\n",
    "# version 0.1 (2021-12-09):\n",
    "#      - Initial release\n",
    "#      - Defines generator input parameters and calculates both curves' data\n",
    "#      - Plot both curves overlapping each other and prime-mover max power"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Needed libraries\n",
    "import math as mt\n",
    "import numpy as np\n",
    "import cmath as cm\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sym"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generator input parameters\n",
    "Vterminal   = 480       # Terminal voltage, in volt (line voltage)\n",
    "freq        = 50        # Electrical frequency, in hertz\n",
    "Srated      = 50e3      # Rated apparent power, in volt-ampere\n",
    "poles       = 6         # Number of poles\n",
    "PowerFactor = 0.8       # Power factor, lagging (inductive)\n",
    "Xsync       = 1         # Synchronous reactance, in ohm per phase\n",
    "\n",
    "# Load parameters\n",
    "Pload       = 45e3      # Load that is being supplied by the generator, in watt\n",
    "\n",
    "# Generator's Losses\n",
    "Pmech_loss  = 1.5e3     # Mechanical (friction and windage) Losses, in watt\n",
    "Pcore_loss  = 1e3       # Core Losses, in watt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculations\n",
    "# Phase voltage, in volt\n",
    "Vphase          = Vterminal/mt.sqrt(3)\n",
    "\n",
    "# Maximum armature current, in ampere - absolute value and phasor\n",
    "Iarm_max        = Srated/(3 * Vphase)\n",
    "Iarm_max_phasor = Iarm_max*cm.exp(-1j * mt.acos(PowerFactor))\n",
    "\n",
    "# Origin of rotor current curve\n",
    "Qrotor          = -(3 * Vphase**2)/Xsync\n",
    "\n",
    "# Generator's internal generated voltage, in volt\n",
    "Ea              = Vphase + 1j * Xsync * Iarm_max_phasor\n",
    "\n",
    "# Apparent power that is the radius of the rotor curve, in volt-ampere\n",
    "D_E             = (3 * abs(Ea) * Vphase)/Xsync\n",
    "\n",
    "# Prime-mover maximum output real power, in watt\n",
    "Pmax_out        = Pload - Pmech_loss - Pcore_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Stator current limit curve\n",
    "# A circle centered in (0,0) with radius Srated\n",
    "x_stator_o = 0\n",
    "y_stator_o = 0\n",
    "r_stator   = Srated\n",
    "\n",
    "# Rotor current limit curve\n",
    "# A circle centered in (0,Q) with radius D_E\n",
    "x_stator_o = 0\n",
    "y_stator_o = Qrotor\n",
    "r_stator   = D_E\n",
    "\n",
    "# Prime-mover power limit\n",
    "x_prime = Pmax_out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Circle at 0x242ef15c0a0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot both curves overlapping each other\n",
    "stator_curve = plt.Circle((0 , 0)      , Srated , color='r' , fill=False)\n",
    "rotor_curve  = plt.Circle((0 , Qrotor) , D_E    , color='b' , fill=False)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Plot prime-mover real power limit\n",
    "maxpower_curve = plt.axvline(x=Pmax_out , color='g' )\n",
    "\n",
    "xlim_pos = 4*Srated\n",
    "ylim_neg = -1.5*Srated\n",
    "ylim_pos =  1.5*Srated\n",
    "\n",
    "ax.set_xlim((0        , xlim_pos))\n",
    "ax.set_ylim((ylim_neg , ylim_pos))\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "plt.legend((stator_curve           , rotor_curve           , maxpower_curve) ,\n",
    "           ('Stator current limit' , 'Rotor current limit' , 'Prime-mover maximum power') ,\n",
    "           numpoints=1,\n",
    "           loc=1)\n",
    "\n",
    "plt.xlabel(\"P, W\")\n",
    "plt.ylabel(\"Q, var\")\n",
    "\n",
    "ax.add_patch(stator_curve)\n",
    "ax.add_patch(rotor_curve)"
   ]
  }
 ],
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