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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 25 : Economic Scheduling of Hydrothermal Plants and Optimal Power Flows"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 25.1, Page No 817"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#initialisation of variables\n",
      "q2=25.0\n",
      "q3=25.0\n",
      "q1=70-(q2+q3)\n",
      "Wo=120.0\n",
      "W3=50.0\n",
      "Wi1=0\n",
      "Wi2=0\n",
      "W1=Wo+Wi1-q1\n",
      "W2=W1+Wi2-q2\n",
      "\n",
      "#Calculations\n",
      "PH1=9.81*(10**-3)*20*(1+(.5*.006*(120+100)))*(20-2)\n",
      "PH2=9.81*(10**-3)*20*(1+(.5*.006*(100+75)))*(23)\t\t# Answer in the book is not Correct due to wrong calculation\n",
      "PH3=9.81*(10**-3)*20*(1+(.5*.006*(75+50)))*(23)\n",
      "PT1=8-PH1\n",
      "PT2=12-PH2\n",
      "PT3=7-PH3\n",
      "L11=20+PT1\t\t\t#dFT/dPT=PT+20\n",
      "L12=20+PT2\t\t\t#dF/dp=PT+20\n",
      "L13=20+PT3\t\t\t#dF/dp=PT+20\n",
      "#dPL/dPH=0\n",
      "L31=L11\n",
      "L32=L12\n",
      "L33=L13\n",
      "e=0.006\n",
      "ho=0.1962\n",
      "Rho=2\n",
      "L21=L31*ho*(1+(.5*e*(2*Wo+Wi1-2*q1+Rho)))\n",
      "L22=L21-L31*(.5*ho*e*(q1-Rho))-L32*(.5*ho*e*(q2-Rho))#for m=1\n",
      "L23=L22-L32*(.5*ho*e*(q2-Rho))-L33*(.5*ho*e*(q3-Rho))#for m=2\n",
      "G1=L22-L32*ho*(1+.5*.006*(2*100-2*25+2))\t\t#G1=dF/dq2 Answer doent match due to wrong calculation of PH2 in a book\n",
      "G2=L23-L33*ho*(1+.5*.006*(2*W2+0-2*q3+Rho))\t\t#G1=dF/dq3\n",
      "a=0.4\n",
      "qnew2=q2-a*G1# Answer differs due to wrong calculation of PH2 in the book\n",
      "qnew3=q3-a*G2\n",
      "q1=120-50-(qnew2+qnew3)\n",
      "\n",
      "#Results\n",
      "print(\"Let q2=%.0f   q3=%.0f    q1=%.0f\" %(q2,q3,q1))\n",
      "print(\"W1=%.0f    W2=%.0f\" %(W1,W2))\n",
      "print(\"PH1=%.2f     PH2=%.3f    PH3=%.1f\" %(PH1,PH2,PH3))\n",
      "print(\"Thermal generation during Three Intervals \\n PT1=%.2f     PT2=%.2f    PT3=%.1f\" %(PT1,PT2,PT3))\n",
      "print(\"Value of L1 for the three intervals, \\n L11=%.2f    L12=%.2f    L13=%.1f\" %(L11,L12,L13))\n",
      "print(\"Neglecting transmission losses we get\\n L11=L31   L12=L32   L13=L33\")\n",
      "print(\"L21=%.3f\" %(L21))\n",
      "print(\"For m=1 and 2 we get \\n L22=%.1f \\n L23=%.1f\" %(L22,L23))\n",
      "print(\"Gradient Vectors \\n dF/dq2=%.2f\\n dF/dq3=%.1f\" %(G1,G2))\n",
      "print(\"q2new=%.3f \\n q3new=%.1f\\n q1=%.0f\" %(qnew2,qnew3,q1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Let q2=25   q3=25    q1=20\n",
        "W1=100    W2=75\n",
        "PH1=5.86     PH2=6.882    PH3=6.2\n",
        "Thermal generation during Three Intervals \n",
        " PT1=2.14     PT2=5.12    PT3=0.8\n",
        "Value of L1 for the three intervals, \n",
        " L11=22.14    L12=25.12    L13=20.8\n",
        "Neglecting transmission losses we get\n",
        " L11=L31   L12=L32   L13=L33\n",
        "L21=6.975\n",
        "For m=1 and 2 we get \n",
        " L22=6.4 \n",
        " L23=5.8\n",
        "Gradient Vectors \n",
        " dF/dq2=-0.77\n",
        " dF/dq3=0.5\n",
        "q2new=25.310 \n",
        " q3new=24.8\n",
        " q1=20\n"
       ]
      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}