{
"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": {}
}
]
}