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diff --git a/Principles_of_Power_System/chapter9.ipynb b/Principles_of_Power_System/chapter9.ipynb new file mode 100755 index 00000000..925aa356 --- /dev/null +++ b/Principles_of_Power_System/chapter9.ipynb @@ -0,0 +1,740 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:1c5f89ed0470787a153a235132b85821455bc93d217ca226b9eba94372c90683"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 9: Electrical Design of Overhead\n",
+ "Lines"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.1, Page Number: 214"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "d = 200 #Spacing of conductors(cm)\n",
+ "r = 1.2/2 #Radius of conductor(cm)\n",
+ "\n",
+ "\n",
+ "#Calculation:\n",
+ "L = 10**-7*(1+4*math.log(d/r))*10**3 #Loop inductance per m length of the line(H)\n",
+ "\n",
+ "\n",
+ "#Result:\n",
+ "print \" The loop inductance per km of the line is\",round(L*1000,3),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " The loop inductance per km of the line is 2.424 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.2, Page Number: 214"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "d = 300 #Spacing of conductors(cm)\n",
+ "r = 1 #Radius of conductor(cm)\n",
+ "u1 = 1 #relative permeability of copper\n",
+ "u2 = 100 #relative permeability of steel\n",
+ "\n",
+ "#Calculation:\n",
+ "#(i) With copper conductors,\n",
+ "Lc = 10**-7*(u1+4*math.log(d/r))*10**3 #Loop inductance/km\n",
+ "\n",
+ "#(ii) With steel conductors,\n",
+ "Ls = 10**-7*(u2+4*math.log(d/r))*10**3 ##Loop inductance/km\n",
+ "\n",
+ "\n",
+ "#Result:\n",
+ "print \"The loop inductance per km length of the line are:\"\n",
+ "print \"(i) for copper, Lc\",round(Lc*1000,2),\"mH and\"\n",
+ "print \"(ii) for steel line, Ls =\",round(Ls*1000,2),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The loop inductance per km length of the line are:\n",
+ "(i) for copper, Lc 2.38 mH and\n",
+ "(ii) for steel line, Ls = 12.28 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.3, Page Number: 214"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "d = 200 #cm\n",
+ "r = 0.62 #conductor radius(cm)\n",
+ "\n",
+ "\n",
+ "#Calculation:\n",
+ "L = 10**-7*(0.5+2*math.log(d/r))*10**3 #Inductance/phase/km\n",
+ "\n",
+ "#Result:\n",
+ "print \"The inductance per km of a 3-ph transmission line is\",round(L*10**3,1),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The inductance per km of a 3-ph transmission line is 1.2 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.4, Page Number: 214"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "D12 = 2 #m\n",
+ "D23 = 2.5 #m\n",
+ "D13 = 4.5 #m\n",
+ "r = 0.62 #m\n",
+ "\n",
+ "#Calculation:\n",
+ "Deq = (D12*D23*D13)**(1/3)*100 #Equivalent equilateral spacing(cm)\n",
+ "L = 10**-7*(0.5+2*math.log(Deq/r))*10**3\n",
+ "\n",
+ "\n",
+ "#Result:\n",
+ "print \"The inductance per km of the line is\",round(L*1000,3),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The inductance per km of the line is 1.274 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.5, Page Number: 214"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "r = 1.25 #cm\n",
+ "D12 = 2 #m\n",
+ "D23 = 2 #m\n",
+ "D13 = 4 #m\n",
+ "\n",
+ "\n",
+ "#Calculation:\n",
+ "Deq = (D12*D23*D13)**(1/3)*100 #Equivalent equilateral spacing(m)\n",
+ "L = 10**-7*(0.5+2*math.log(Deq/r))*10**3\n",
+ "\n",
+ "\n",
+ "#Result:\n",
+ "print \"The inductance per km of the line is\",round(L*1000,2),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The inductance per km of the line is 1.11 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.6, Page Number: 214"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "r = 0.5 #radius of conductor(m)\n",
+ "Dab = 25 #cm\n",
+ "Daa1 = 100 #cm\n",
+ "Dbb1 = 100 #cm\n",
+ "Dab1 = 103 #cm\n",
+ "Da1b = 103 #cm\n",
+ "Da1b1 = 25 #cm\n",
+ "\n",
+ "#Calculation:\n",
+ "GMR = 0.7788*r #G.M.R. of conductor(cm)\n",
+ "Ds = (GMR*Daa1)**(1/2) #Self G.M.D. of aa1 combination(cm)\n",
+ "Dm = (Dab*Dab1*Da1b*Da1b1)**(1/4) #Mutual G.M.D. between a and b(cm)\n",
+ "L1 = 2*10**-7*math.log(Dm/Ds) #Loop inductance per conductor per m(H)\n",
+ "L = 2*L1*1000\n",
+ "\n",
+ "#Result:\n",
+ "print \"The inductance per km of the line is\",round(L*1000,2),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The inductance per km of the line is 0.84 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.7, Page Number: 216"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "\n",
+ "#Variable declaration:\n",
+ "r = 1.3 #conuctor radius(cm)\n",
+ "Dab = 3 #m\n",
+ "Dab1 = 6.7 #m\n",
+ "Da1b = 6.7 #m\n",
+ "Da1b1 = 3 #m\n",
+ "Daa1 = 8.48 #m\n",
+ "Da1a = 8.48 #m\n",
+ "Dbb1 = 6 #m\n",
+ "Db1b = 6 #m\n",
+ "Dca = 6 #m\n",
+ "Dc1a = 6 #m\n",
+ "Dca1 = 6 #m\n",
+ "Dc1a1 = 6 #m\n",
+ "\n",
+ "#Calculation:\n",
+ "GMR = 1.3*0.7788/100 #m\n",
+ "Daa = GMR\n",
+ "Da1a1 = GMR\n",
+ "Dbb = GMR\n",
+ "Db1b1 = GMR\n",
+ "Ds1 = (Daa*Daa1*Da1a1*Da1a)**(1/4) #m\n",
+ "Ds2 = (Dbb*Dbb1*Db1b1*Db1b)**(1/4) #m\n",
+ "Ds = (Ds1*Ds2*Ds1)**(1/3) #m\n",
+ "DAB = (Dab*Dab1*Da1b*Da1b1)**(1/4) #m\n",
+ "DBC = DAB\n",
+ "DCA = (Dca*Dc1a*Dca1*Dc1a1)**(1/4) #m\n",
+ "Dm = (DAB*DBC*DCA)**(1/3) #Equivalent mutual G.M.D(m)\n",
+ "\n",
+ "L1 = 2*10**-7*math.log(Dm/Ds) #Loop inductance per conductor per m(H)\n",
+ "L = L1*1000\n",
+ "\n",
+ "#Result:\n",
+ "print \"The inductance per km of the line is\",round(L*1000,2),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The inductance per km of the line is 0.58 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.8, Page Number: 217"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable Declaration:\n",
+ "r = 0.75 #conductor radius(cm)\n",
+ "Db1b = 5.5 #m\n",
+ "Dca = 6 #m\n",
+ "Dca1 = 4 #m\n",
+ "Dc1a = 4 #m\n",
+ "Dc1a1 = 6 #m\n",
+ "\n",
+ "\n",
+ "#Calculation:\n",
+ "GMR = 0.7788*r #m\n",
+ "Dab = (3**2+0.75**2)**0.5 #m\n",
+ "Dab1 = (3**2+4.75**2)**0.5 #m\n",
+ "Daa1 = (6**2+4**2)**0.5 #m\n",
+ "Daa = GMR/100 #m\n",
+ "Da1a1 = Daa #m\n",
+ "Da1a = Daa1 #m\n",
+ "Dbb = GMR/100 #m\n",
+ "Dbb1 = 5.5 #m\n",
+ "Db1b1 = Dbb #m\n",
+ "\n",
+ "Ds1 = (Daa*Daa1*Da1a1*Da1a)**(1/4) #m\n",
+ "Ds2 = (Dbb*Dbb1*Db1b1*Db1b)**(1/4) #m\n",
+ "Ds3 = Ds1\n",
+ "Ds = (Ds1*Ds2*Ds3)**(1/3) #Equivalent self G.M.D. of one phase(m)\n",
+ "DAB = (Dab*Dab1*Da1b*Da1b1)**(1/4) #m\n",
+ "DCA = (Dca*Dca1*Dc1a*Dc1a1)**(1/4) #m\n",
+ "DBC = DAB #m\n",
+ "Dm = (DAB*DBC*DCA)**(1/3) #Equivalent mutual G.M.D.(m)\n",
+ "\n",
+ "\n",
+ "L1 = 2*10**-7*math.log(Dm/Ds) #Loop inductance per conductor per m(H)\n",
+ "L = L1*1000\n",
+ "\n",
+ "#Result:\n",
+ "print \"The inductance per km of the line is\",round(L*1000,3),\"mH\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The inductance per km of the line is 0.627 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.9, Page Number: 218"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable Declaration:\n",
+ "r = 5.3/100 #conductor radius(m)\n",
+ "\n",
+ "#Calculation:\n",
+ "GMR = 0.7788*r #m\n",
+ "DAA = GMR #m\n",
+ "DAA1 = 24 #m\n",
+ "DA1A1 = DAA #m\n",
+ "DA1A = 24 #m\n",
+ "\n",
+ "DBB = GMR #m\n",
+ "DBB1 = 24 #m\n",
+ "DB1B1 = DBB #m\n",
+ "DB1B = 24 #m\n",
+ "Ds1 = (DAA*DAA1*DA1A1*DA1A)**(1/4) #m\n",
+ "Ds2 = (DBB*DBB1*DB1B1*DB1B)**(1/4) #m\n",
+ "#Similarly:\n",
+ "Ds3 = 0.995 #m\n",
+ "Ds = (Ds1*Ds2*Ds3)**(1/3) #Equivalent self-G.M.D. of one phase(m)\n",
+ "#DAB = (DAB \u00d7 DAB\u2032 \u00d7 DA\u2032\u0392 \u00d7 DA\u2032B\u2032)**1/4\n",
+ "DAB = (8*32*16*8)**(1/4) #m\n",
+ "DBC = DAB #m\n",
+ "#DCA = (DCA \u00d7 DCA\u2032 \u00d7 DC\u2032A \u00d7DC\u2032A\u2032)1/4 #m\n",
+ "DCA = (16*8*40*16)**(1/4) #m\n",
+ "\n",
+ "Dm = (DAB*DBC*DCA)**(1/3) #m\n",
+ "\n",
+ "L = 2*10**-7*math.log(Dm/Ds) #Loop inductance per conductor per m(H)\n",
+ "\n",
+ "\n",
+ "#Result:\n",
+ "print \"The inductance per m of the line is\",round(L*10**7,2),\"* 10**-7 H/m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The inductance per m of the line is 5.36 * 10**-7 H/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.10, Page Number: 219"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable Declaration:\n",
+ "r = 1 #consuctor radius(cm)\n",
+ "\n",
+ "#Calculation:\n",
+ "#Mutual G.M.D., Dm = (Dab*Dab'*Da'b*Da'b')**(1/4)\n",
+ "Dm = (120*140*100*120)**(1/4) #m\n",
+ "\n",
+ "#Self G.M.D., Ds = (Daa*Daa'*Da'a'*Da'a)**(1/4)\n",
+ "#Daa = Da'a' = 0.7788 cm; Daa' = Da'a = 20 cm\n",
+ "Ds = (0.7788*20*0.7788*20)**(1/4) #cm\n",
+ "L = 4*10**-4*math.log(Dm/Ds) #H/km\n",
+ "\n",
+ "#Result:\n",
+ "print \"The total inductance of the line per km is\",round(L*1000,2),\"mH/km\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total inductance of the line per km is 1.36 mH/km\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.11, Page Number: 224"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "r = 1 #conductor radius(cm)\n",
+ "d = 300 #conductor spacing(cm)\n",
+ "e = 8.854*10**-12 #permitivity of free space(F/m)\n",
+ "\n",
+ "\n",
+ "#Calculation:\n",
+ "C = math.pi*e/math.log(d/r) #F/m\n",
+ "\n",
+ "#Result:\n",
+ "print \"Capacitance of the line per km is\",round(C*10**11,4),\"* 10**-2 uF/km\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Capacitance of the line per km is 0.4877 * 10**-2 uF/km\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.12, Page Number: 225"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "r = 0.625 #conductor radius(cm)\n",
+ "d = 200 #conductor spacing(cm)\n",
+ "e = 8.854*10**-12 #permitivity of free space(F/m)\n",
+ "\n",
+ "\n",
+ "#Calculation:\n",
+ "C = 2*math.pi*e/math.log(d/r) #F/m\n",
+ "\n",
+ "#Result:\n",
+ "print \"Capacitance of the line per km is\",round(C*10**9,4),\" uF/km\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Capacitance of the line per km is 0.0096 uF/km\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.13, Page Number: 225"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable Declaration:\n",
+ "d1 = 2 #m\n",
+ "d2 = 2.5 #m\n",
+ "d3 = 4.5 #m\n",
+ "r = 0.625 #conductor raius(cm)\n",
+ "l = 100 #line length(km)\n",
+ "Vl = 66000 #line voltage(V)\n",
+ "f = 50 #frequency of current(Hz)\n",
+ "e = 8.854*10**-12 #permitivity of free space(F/m)\n",
+ "\n",
+ "#Calculation:\n",
+ "d = (d1*d2*d3)**(1/3)*100 #cm\n",
+ "\n",
+ "#(i)Line to neutral capacitance,\n",
+ "C1 = 2*math.pi*e/math.log(d/r)*10**9 #uF/km\n",
+ "C11 = C1*100 #uF\n",
+ "\n",
+ "#(ii)Charging current per phase,\n",
+ "Ic = Vl*2*math.pi*f*C11*10**-6/(3**0.5) #A\n",
+ "\n",
+ "\n",
+ "#Result:\n",
+ "print \"Capacitance per phase is\",round(C11,2),\"uF\"\n",
+ "print \"Charging current per phase is\",round(Ic,1),\"A\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Capacitance per phase is 0.91 uF\n",
+ "Charging current per phase is 10.9 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.14, Page Number: 225"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable declaration:\n",
+ "r = 1 #conductor radius(cm)\n",
+ "d = 250 #equilateral conductor spacing(cm)\n",
+ "e = 8.854*10**-12 #permitivity of free space(F/m)\n",
+ "\n",
+ "\n",
+ "#Calculation:\n",
+ "C = 2*math.pi*e/math.log(d/r)*10**9 #uF/km\n",
+ "C1 = C*100 #F\n",
+ "\n",
+ "#Result:\n",
+ "print \"Capacitance of the line per km is\",round(C1,4),\"uF/phase\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Capacitance of the line per km is 1.0075 uF/phase\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.15, Page Number: 226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Variable Declaration:\n",
+ "d1 = 4 #m\n",
+ "d2 = 4 #m\n",
+ "d3 = 8 #m\n",
+ "r = 1 #conductor raius(cm)\n",
+ "l = 100 #line length(km)\n",
+ "Vl = 132000 #line voltage(V)\n",
+ "f = 50 #frequency of current(Hz)\n",
+ "e = 8.854*10**-12 #permitivity of free space(F/m)\n",
+ "\n",
+ "#Calculation:\n",
+ "Deq = (d1*d2*d3)**(1/3)*100 #cm\n",
+ "C = 2*math.pi*e/math.log(Deq/r)*10**9 #uF/km\n",
+ "C1 = C*100 #uF\n",
+ "Ic = Vl*2*math.pi*f*C1*10**-6/(3**0.5) #A\n",
+ "\n",
+ "\n",
+ "#Result:\n",
+ "print \"Charging current per phase is\",round(Ic,2),\"A\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Charging current per phase is 21.41 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |