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"source": [
"# Chapter 2 Transmission Lines"
]
},
{
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"metadata": {},
"source": [
"## Example 2_1 pgno:65"
]
},
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"text": [
"Maximum field = V/m per volt 42064315640.1\n"
]
}
],
"source": [
"#Chapter 2, Example 1, page 65\n",
"#Calculate the maximum field at the sphere surface\n",
"\n",
"#Calulating Field at surface E based on figure 2.31 and table 2.3\n",
"from math import pi\n",
"Q1 = 0.25\n",
"e0 = 8.85418*10**-12 #Epselon nought\n",
"RV1= ((1/0.25**2)+(0.067/(0.25-0.067)**2)+(0.0048/(0.25-0.067)**2))\n",
"RV2= ((0.25+0.01795+0.00128)/(0.75-0.067)**2)\n",
"RV= RV1+RV2\n",
"E = (Q1*RV)/(4*pi*e0)\n",
"print\"Maximum field = V/m per volt\",E\n",
"\n",
"#Answers vary due to round off error\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2_2 pgno:66"
]
},
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"Part a\t\n",
"Equivalent radius = m \t0.0887411967465\n",
"Charge per bundle = uC/m \t4.88704086264e-06\n",
"Charge per sunconducter = uC/m \t2.44352043132e-06\n",
"\tPart b\n",
"\tSub part 1\t\n",
"Maximum feild = kV/m \t2607466.95017\n",
"Maximum feild = kV/m \t2412255.52075\n",
"Maximum feild = kV/m \t2509861.23546\n",
"\tSub part 2\t\n",
"EO1 = kV/m \t2597956.83558\n",
"EO2 = kV/m \t2597429.47744\n",
"EI1 = kV/m \t2402709.21273\n",
"EI2 = kV/m \t2402258.0563\n",
"\tPart c\t\n",
"The average of the maximum gradient = kV/m \t2597693.15651\n"
]
}
],
"source": [
"#Chapter 2, Exmaple 2, page 66\n",
"\n",
"\n",
"#calculation based on figure 2.32\n",
"from math import sqrt,pi,log\n",
"\n",
"#(a)Charge on each bundle\n",
"print\"Part a\\t\"\n",
"req = sqrt(0.0175*0.45)\n",
"print\"Equivalent radius = m \\t\", req\n",
"V = 400*10**3 #Voltage\n",
"H = 12. #bundle height in m\n",
"d = 9. #pole to pole spacing in m\n",
"e0 = 8.85418*10**-12 #Epselon nought\n",
"Hd = sqrt((2*H)**2+d**2)#2*H**2 + d**2\n",
"Q = V*2*pi*e0/(log((2*H/req))-log((Hd/d)))\n",
"q = Q/2\n",
"print\"Charge per bundle = uC/m \\t\",Q #micro C/m\n",
"print\"Charge per sunconducter = uC/m \\t\",q #micro C/m\n",
"\n",
"#(b part i)Maximim & average surface feild\n",
"print\"\\tPart b\"\n",
"print\"\\tSub part 1\\t\"\n",
"r = 0.0175 #subconductor radius\n",
"R = 0.45 #conductor to subconductor spacing\n",
"MF = (q/(2*pi*e0))*((1/r)+(1/R)) # maximum feild\n",
"print\"Maximum feild = kV/m \\t\",MF\n",
"MSF = (q/(2*pi*e0))*((1/r)-(1/R)) # maximum surface feild\n",
"print\"Maximum feild = kV/m \\t\",MSF\n",
"ASF = (q/(2*pi*e0))*(1/r) # Average surface feild\n",
"print\"Maximum feild = kV/m \\t\",ASF\n",
"\n",
"#(b part ii) Considering the two sunconductors on the left\n",
"print\"\\tSub part 2\\t\"\n",
"#field at the outer point of subconductor #1 \n",
"drO1 = 1/(d+r)\n",
"dRrO1 = 1/(d+R+r)\n",
"EO1 = MF -((q/(2*pi*e0))*(drO1+dRrO1))\n",
"print\"EO1 = kV/m \\t\",EO1\n",
"#field at the outer point of subconductor #2 \n",
"drO2 = 1/(d-r)\n",
"dRrO2 = 1/(d-R-r)\n",
"EO2 = MF -((q/(2*pi*e0))*(dRrO2+drO2))\n",
"print\"EO2 = kV/m \\t\",EO2\n",
"\n",
"#field at the inner point of subconductor #1 \n",
"drI1 = 1/(d-r)\n",
"dRrI1 = 1/(d+R-r)\n",
"EI1 = MSF -((q/(2*pi*e0))*(drI1+dRrI1))\n",
"print\"EI1 = kV/m \\t\",EI1\n",
"#field at the inner point of subconductor #2 \n",
"drI2 = 1/(d+r)\n",
"dRrI2 = 1/(d-R+r)\n",
"EI2 = MSF -((q/(2*pi*e0))*(dRrI2+drI2)) \n",
"print\"EI2 = kV/m \\t\",EI2\n",
"\n",
"#(part c)Average of the maximim gradient\n",
"print\"\\tPart c\\t\"\n",
"Eavg = (EO1+EO2)/2\n",
"print\"The average of the maximum gradient = kV/m \\t\",Eavg\n",
"\n",
"#Answers might vary due to round off error\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2_3 pgno:69"
]
},
{
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"execution_count": 3,
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{
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"text": [
"Electric Feild = V/m \t35950238891.0\n"
]
}
],
"source": [
"#Chapter 2, Exmaple 3, page 69\n",
"#Electric feild induced at x\n",
"from math import pi\n",
"e0 = 8.85418*10**-12 #Epselon nought\n",
"q = 1 # C/m\n",
"C = (q/(2*pi*e0))\n",
"#Based on figure 2.33\n",
"E = C-(C*(1/3+1/7))+(C*(1+1/5+1/9))+(C*(1/5+1/9))-(C*(1/3+1/7))\n",
"print\"Electric Feild = V/m \\t\",E\n",
"\n",
"#Answers might vary due to round off error\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2_4 pgno:70"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
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},
"outputs": [
{
"name": "stdout",
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"text": [
"\tThickness of graded design= cm \t4.24264068712\n",
"Curve = cm**2 \t62.4264068712\n",
"V1 = cm**3 \t47402.906725\n",
"Thickness of regular design = cm \t14.684289433\n",
"V2 = cm**3 \t861.944682812\n"
]
}
],
"source": [
"#Chapter 2, Exmaple 4, page 70\n",
"#Calculate the volume of the insulator\n",
"from math import sqrt,pi,e\n",
"#Thinkness of graded design\n",
"V = 150*sqrt(2)\n",
"Ebd = 50\n",
"T = V/Ebd\n",
"print\"\\tThickness of graded design= cm \\t\",T\n",
"#Based on figure 2.24\n",
"r = 2 # radius of the conductor\n",
"l = 10 #length of graded cylinder; The textbook uses 10 instead of 20\n",
"zr = l*(T+r)\n",
"print\"Curve = cm**2 \\t\",zr\n",
"#Volume of graded design V1\n",
"V1 = 4*pi*zr*(zr-r)\n",
"print\"V1 = cm**3 \\t\",V1 #Unit is wrong in the textbook\n",
"#Thickness of regular design as obtained form Eq.2.77\n",
"pow = V/(2*Ebd)\n",
"t = 2*(e**pow-1)\n",
"print\"Thickness of regular design = cm \\t\",t\n",
"#Volume of regular design V2\n",
"V2 = pi*((2+t)**2-4)\n",
"print\"V2 = cm**3 \\t\",V2#unit not mentioned in textbook\n",
" \n",
"#Answers may vary due to round off error\n"
]
}
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