{
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"name": ""
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 23 : State Estimation In Power Systems"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 23.1, Page No 148"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#initialisation of variables\n",
"C1=0.02*100\n",
"C2=0.05\n",
"Fs=100\n",
"S1=complex(0.41,-0.11)\n",
"S2=complex(-0.4, 0.10)\n",
"S3=complex(-.105,0.11)\n",
"S4=complex(-.105,.11)\n",
"S5=complex(0.14,-.14)\n",
"S6=complex(-0.7,.35)\n",
"Z12=complex(0.08,.24)\n",
"Z23=complex(0.06,.18)\n",
"Z31=complex(0.02,.06)\n",
"Z21=Z12\n",
"Z32=Z23\n",
"Z13=Z31\n",
"\n",
"#Calculations\n",
"W1=(50*10**(-6))/((C1*abs(S1)+(C2*(Fs)))**2)\n",
"W2=(50*10**(-6))/((C1*abs(S2)+C2*(Fs))**2)\n",
"W3=(50*10**(-6))/((C1*abs(S3)+C2*(Fs))**2)\n",
"W4=(50*10**(-6))/((C1*abs(S4)+C2*(Fs))**2)\n",
"W5=(50*10**(-6))/((C1*abs(S5)+C2*(Fs))**2)\n",
"W6=(50*10**(-6))/((C1*abs(S6)+C2*(Fs))**2)\n",
"print(\"W1= %.2f\" %W1)\t\t\t#Answers for W1,W2,W3,W4,W5,W6 in the book is wrongly Calculated\n",
"print(\"W2= %.2f\" %W2)\t\n",
"print(\"W3= %.2f\" %W3)\t\n",
"print(\"W4= %.2f\" %W4)\t\n",
"print(\"W5= %.2f\" %W5)\t\n",
"print(\"W6= %.2f\" %W6)\t\n",
"a1=W1/(abs(13)**2)\n",
"[D]=diag([W1/(abs(Z13)**2)W2/(abs(Z31)**2)W3/(abs(Z12)**2)W4/(abs(Z21)**2)W5/(abs(Z23)**2)W6/(abs(Z32)**2)])\n",
"A=[-1 0 11 0 -11 -1 0-1 1 00 1 -10 -1 1]\n",
"B=[-1 01 01 -1-1 10 10 -1]\n",
"b=[1-100-11]\n",
"C=(B')*D#Assuming Transpose(B)D=C\n",
"F=(B')*D*B#Assuming Transpose(B)*D*B=F\n",
"G=(inv(F))*C#Assuming(BTDB)-1*(BT)*D=F\n",
"E1=1.05\n",
"E2=E1\n",
"E3=E1\n",
"invH=diag([Z31/E3Z13/E1Z12/E1Z21/E2Z23/E2Z32/E2])\n",
"Sm=[.41+%i*.11-.4-%i*.1-.105-%i*.11.14+%i*.14.72+%i*.37-.7+%i*.35]\n",
"EMo=invH*Sm\n",
"a=EMo-b*E1\n",
"E=G*a\n",
"\n",
"#Results\n",
"print(E,\"E=\") #Answers differs due to wrong calculation of W1,W2,W3,W4,W5,W6"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) For p.f unity , Eth= 1.34000+0.00000i\n",
"(i) For p.f .8 , Eth= 1.59500+0.00000i\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 22.3, Page No 149"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#initialisation of variables\n",
"X=.625\n",
"P=1.0\n",
"Q=0.6\n",
"V=1.0\n",
"\n",
"#Calculations\n",
"Eth=V+(Q*X/V)+complex(P*X/V)\n",
"Phase_Eth=math.degrees(math.atan(Eth.imag/Eth.real))\n",
"\n",
"#Results\n",
"print(\"Eth=%.2f at an angle %.0f degrees\" %(abs(Eth),Phase_Eth))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Eth=2.00 at an angle 0 degrees\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 22.4, Page No 149"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#initialisation of variables\n",
"P=0.5\n",
"toff=4.0\n",
"\n",
"#Calculations\n",
"ton=(P*toff-0*toff)/(0.8-P)\n",
"\n",
"#Results\n",
"print(\"Toff= 4min .\")\n",
"print(\"ton(min.)=%.3f min.\" %ton)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Toff= 4min .\n",
"ton(min.)=6.667 min.\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 22.6 Page No 150"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#initialisation of variables\n",
"V=1.0\n",
"Qload=1.0*V\n",
"Qcap=-0.75*V**2\n",
"\n",
"#Calculations\n",
"Qnet=Qload+Qcap\n",
"VS=1-0.75*2*V # voltage sensitivity\n",
"\n",
"#Results\n",
"print(\"Voltage sensitivity=%.3f\" %VS)\n",
"print(\"since the voltage sensitivity is negative,\\nvoltage regulation by tap changing will reduce net reactive load and improive voltage stability \")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Voltage sensitivity=-0.500\n",
"since the voltage sensitivity is negative,\n",
"voltage regulation by tap changing will reduce net reactive load and improive voltage stability \n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 22.7, Page No 151"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#initialisation of variables\n",
"Y=complex(-10)\n",
"n=1+0.1\n",
"\n",
"#Calculations\n",
"Y1=n*(n-1)*Y\n",
"Y2=(1-n)*Y\n",
"\n",
"#Results\n",
"print(\"Y1= {0:.2f}+{1:.2f}i\".format(Y1.real, Y1.imag))\n",
"print(\"Y2= {0:.2f}+{1:.2f}i\".format(Y2.real, Y2.imag))\n",
"print(\"The shunt elements equal to a reactor of 1.1V1^2 size oin the primary side and a capacitive of sixe 1V2**2 on the secondary side\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Y1= -1.10+0.00i\n",
"Y2= 1.00+-0.00i\n",
"The shunt elements equal to a reactor of 1.1V1^2 size oin the primary side and a capacitive of sixe 1V2**2 on the secondary side\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 22.8, Page No 152"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#initialisation of variables\n",
"P=1.0\t\t#assuming\n",
"S1=P/.95\t#For pf .95\n",
"S2=P/.8\t\t#For pf .8\n",
"\n",
"#Calculations\n",
"dMVA=(S2-S1)*100.0/P\t\t#Increase in MVA rating \n",
"Q1=P*math.tan(math.radians(math.degrees(math.acos(0.95))))\t\t#Q for pf .95\n",
"Q2=P*math.tan(math.radians(math.degrees(math.acos(0.8))))\t\t#Q for pf .8\n",
"dPc=(Q2-Q1)*100.0/Q1\t\t#Percent additional Reactive Power Capability \n",
"\n",
"#Results\n",
"print(\"Percent additional Reactive Power Capability is %.2f\" %dPc)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Percent additional Reactive Power Capability is 128.18\n"
]
}
],
"prompt_number": 17
}
],
"metadata": {}
}
]
}