summaryrefslogtreecommitdiff
path: root/Electrical_Network_by_R._Singh/Chapter7_1.ipynb
diff options
context:
space:
mode:
Diffstat (limited to 'Electrical_Network_by_R._Singh/Chapter7_1.ipynb')
-rw-r--r--Electrical_Network_by_R._Singh/Chapter7_1.ipynb844
1 files changed, 844 insertions, 0 deletions
diff --git a/Electrical_Network_by_R._Singh/Chapter7_1.ipynb b/Electrical_Network_by_R._Singh/Chapter7_1.ipynb
new file mode 100644
index 00000000..be717441
--- /dev/null
+++ b/Electrical_Network_by_R._Singh/Chapter7_1.ipynb
@@ -0,0 +1,844 @@
+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:b3ef09fe669f6e389f68566c0a4c0c7f68ba17783f87d6b65b51a4db7cae692e"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter7-Graph theory"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7-pg7.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "## Graph Theory : example 7.7 : (pg 7.18 & 7.19)\n",
+ "import numpy\n",
+ "\n",
+ "##Complete incidence matrix Aa\n",
+ "print(\"\\nAa=\");\n",
+ "print numpy.matrix([[1, 0 ,0 ,-1 ,1 ,0 ,0 ,0],[-1, 1, 0 ,0 ,0 ,1 ,0 ,0],[0 ,-1 ,1 ,0 ,0 ,0 ,1 ,0],[0, 0 ,-1, 1 ,0 ,0 ,0, 1],[0 ,0 ,0 ,0 ,-1, -1 ,-1, -1]]);\n",
+ "##eliminating last row from Aa\n",
+ "print(\"\\nA=\");\n",
+ "print numpy.matrix([[1, 0 ,0 ,-1, 1 ,0 ,0 ,0],[-1, 1 ,0 ,0 ,0 ,1 ,0 ,0],[0 ,-1, 1, 0, 0 ,0 ,1 ,0],[0, 0, -1, 1 ,0 ,0 ,0 ,1]]);\n",
+ "##Tieset matrix B\n",
+ "print(\"\\ntwigs={1,3,5,7} \\nlinks={2,4,6,8} \\ntieset 2={2,7,5,1} \\ntieset 4={4,5,7,3} \\ntieset 6={6,5,1} \\ntieset 8={8,7,3}\");\n",
+ "## forward direction = 1, reverse direction = -1\n",
+ "print(\"\\nB=\");\n",
+ "print numpy.matrix([[1, 1 ,0 ,0 ,-1, 0, 1, 1],[0, 0, 1 ,1 ,1 ,0, -1, 0],[1, 0 ,0 ,0 ,-1, 1, 0, 0],[0, 0 ,1 ,0 ,0 ,0 ,-1, 1]]);\n",
+ "## f-cutset matrix Q\n",
+ "print(\"\\nf-cutset 1={1,6,2} \\nf-cutset 3={3,4,8} \\nf-cutset 5={5,4,6,2} \\nf-cutset 7={7,2,8,4}\");\n",
+ "print(\"\\nQ=\");\n",
+ "print numpy.matrix([[1 ,-1, 0, 0, 0 ,-1, 0, 0],[0 ,0, 1, -1, 0, 0 ,0 ,-1],[0, 1, 0 ,-1, 1, 1, 0, 0],[0 ,-1, 0, 1, 0 ,0, 1, 1]]);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Aa=\n",
+ "[[ 1 0 0 -1 1 0 0 0]\n",
+ " [-1 1 0 0 0 1 0 0]\n",
+ " [ 0 -1 1 0 0 0 1 0]\n",
+ " [ 0 0 -1 1 0 0 0 1]\n",
+ " [ 0 0 0 0 -1 -1 -1 -1]]\n",
+ "\n",
+ "A=\n",
+ "[[ 1 0 0 -1 1 0 0 0]\n",
+ " [-1 1 0 0 0 1 0 0]\n",
+ " [ 0 -1 1 0 0 0 1 0]\n",
+ " [ 0 0 -1 1 0 0 0 1]]\n",
+ "\n",
+ "twigs={1,3,5,7} \n",
+ "links={2,4,6,8} \n",
+ "tieset 2={2,7,5,1} \n",
+ "tieset 4={4,5,7,3} \n",
+ "tieset 6={6,5,1} \n",
+ "tieset 8={8,7,3}\n",
+ "\n",
+ "B=\n",
+ "[[ 1 1 0 0 -1 0 1 1]\n",
+ " [ 0 0 1 1 1 0 -1 0]\n",
+ " [ 1 0 0 0 -1 1 0 0]\n",
+ " [ 0 0 1 0 0 0 -1 1]]\n",
+ "\n",
+ "f-cutset 1={1,6,2} \n",
+ "f-cutset 3={3,4,8} \n",
+ "f-cutset 5={5,4,6,2} \n",
+ "f-cutset 7={7,2,8,4}\n",
+ "\n",
+ "Q=\n",
+ "[[ 1 -1 0 0 0 -1 0 0]\n",
+ " [ 0 0 1 -1 0 0 0 -1]\n",
+ " [ 0 1 0 -1 1 1 0 0]\n",
+ " [ 0 -1 0 1 0 0 1 1]]\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8-pg7.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "## Graph Theory : example 7.8 :(pg 7.19 & 7.20)\n",
+ "##Complete Incidence Matrix Aa\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "print(\"\\nAa=\");\n",
+ "import numpy\n",
+ "print numpy.matrix([[1 ,0 ,-1 ,1],[-1, 1 ,0 ,0],[0 ,-1 ,1 ,-1]]);\n",
+ "## Reduced Incidence matrix A (by eliminating last row from Aa)\n",
+ "A=numpy.matrix([[1 ,0, -1, 1],[-1, 1 ,0 ,0]]);\n",
+ "print(\"\\nA=\");\n",
+ "print numpy.matrix([[1 ,0 ,-1 ,1],[-1, 1 ,0 ,0]]);\n",
+ "A1=numpy.matrix([[1 ],[0], [-1], [1],[-1], [1] ,[0] ,[0]]);\n",
+ "print(\"A1\")\n",
+ "\n",
+ "print(\"\\nNumber of possible trees=\");##A^T=A'= transpose of A\n",
+ "x=(A*numpy.matrix.transpose(A));\n",
+ "print (x);\n",
+ "alp = numpy.linalg.det(x);\n",
+ "\n",
+ "print(alp)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Aa=\n",
+ "[[ 1 0 -1 1]\n",
+ " [-1 1 0 0]\n",
+ " [ 0 -1 1 -1]]\n",
+ "\n",
+ "A=\n",
+ "[[ 1 0 -1 1]\n",
+ " [-1 1 0 0]]\n",
+ "A1\n",
+ "\n",
+ "Number of possible trees=\n",
+ "[[ 3 -1]\n",
+ " [-1 2]]\n",
+ "5.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex11-pg7.21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Graph Theory : example 7.11 :(pg 7.21 & 7.22)\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "print (\"Aa=[0 -1 1 0 0;0 0 -1 -1 -1;-1 0 0 0 1;1 1 0 1 0]\");#Complete incidence matrix\n",
+ "A=numpy.matrix([[0, -1, 1, 0, 0],[0, 0, -1, -1, -1],[-1, 0, 0, 0, 1]]);#Reduced incidence matrix\n",
+ "print(\"\\nNumber of possible trees = |A*A^T|\");#A^T=A'=transpose of A \n",
+ "x=(A*numpy.matrix.transpose(A));\n",
+ "print (x);\n",
+ "alp = numpy.linalg.det(x);\n",
+ "print(\"\\n|A*A^T|= \",round(alp));#No. of possible trees\n",
+ "#Tieset Matrix B\n",
+ "print(\"\\ntwigs={3,4,5} \\nlinks={1,2} \\ntieset 1={1,4,5} \\ntieset 2={2,3,4}\");\n",
+ "print (\"B=[1 0 0 -1 1;0 1 1 -1 0]\");\n",
+ "#f-cutset Matrix Q\n",
+ "print(\"\\nf-cutset 3={3,2} \\nf-cutset 4={4,2,1} \\nf-cutset 5={5,1}\");\n",
+ "print (\"Q=[0 -1 1 0 0;1 1 0 1 0;-1 0 0 0 1]\");"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Aa=[0 -1 1 0 0;0 0 -1 -1 -1;-1 0 0 0 1;1 1 0 1 0]\n",
+ "\n",
+ "Number of possible trees = |A*A^T|\n",
+ "[[ 2 -1 0]\n",
+ " [-1 3 -1]\n",
+ " [ 0 -1 2]]\n",
+ "('\\n|A*A^T|= ', 8.0)\n",
+ "\n",
+ "twigs={3,4,5} \n",
+ "links={1,2} \n",
+ "tieset 1={1,4,5} \n",
+ "tieset 2={2,3,4}\n",
+ "B=[1 0 0 -1 1;0 1 1 -1 0]\n",
+ "\n",
+ "f-cutset 3={3,2} \n",
+ "f-cutset 4={4,2,1} \n",
+ "f-cutset 5={5,1}\n",
+ "Q=[0 -1 1 0 0;1 1 0 1 0;-1 0 0 0 1]\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex14-pg7.27"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Graph Theory : example 7.14 :(pg 7.37 & 7.38)\n",
+ "##Tieset Matrix B\n",
+ "import numpy\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "print(\"\\ntieset1={1,4,5} \\ntieset2={2,4,6} \\ntieset={3,5,6} \\nB=\"); \n",
+ "B=numpy.matrix([[1, 0 ,0 ,1 ,1 ,0],[0 ,1 ,0 ,-1, 0, -1],[0, 0 ,1 ,0 ,-1, 1]]);\n",
+ "print(B);\n",
+ "print(\"\\nThe KVL equation in matrix form \\nB.Zb.(B^T).Il = B.Vs-B.Zb.Is\");\n",
+ "print(\"\\nB.Zb.(B^T).Il = B.Vs \\nZb=\");##Is=0\n",
+ "import numpy as np\n",
+ "Zb = np.array([1,1,1,2,2,2])\n",
+ "d = np.diag(Zb)\n",
+ "print(d)\n",
+ "\n",
+ "print(\"\\n(B^T)=\");\n",
+ "Z= numpy.matrix.transpose(B)\n",
+ "print(Z)\n",
+ "Vs=numpy.matrix([[2],[0],[0],[0],[0],[0]]);\n",
+ "print(\"\\nVs=\");\n",
+ "print(Vs);\n",
+ "print(\"\\nB.Zb =\");\n",
+ "x=numpy.dot(B,Zb);\n",
+ "print(x);\n",
+ "\n",
+ "print(\"\\nB.Vs=\");\n",
+ "z=numpy.dot(B,Vs);\n",
+ "print(z);\n",
+ "print(\"\\nLoad currents:\");\n",
+ "M=numpy.matrix([[5, -2 ,-2],[-2 ,5 ,-2],[-2, -2, 5]]);\n",
+ "H=numpy.linalg.inv(M);\n",
+ "N=([[2],[0],[0]]);\n",
+ "X=numpy.dot(H,N);\n",
+ "print(X);\n",
+ "print(\"\\nIl1=0.857 A \\nIl2=0.571 A \\nIl3=0.571 A\");\n",
+ "print(\"\\nBranch currents:\");\n",
+ "P=(Z,X);\n",
+ "print(P);##Currents in amperes\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "tieset1={1,4,5} \n",
+ "tieset2={2,4,6} \n",
+ "tieset={3,5,6} \n",
+ "B=\n",
+ "[[ 1 0 0 1 1 0]\n",
+ " [ 0 1 0 -1 0 -1]\n",
+ " [ 0 0 1 0 -1 1]]\n",
+ "\n",
+ "The KVL equation in matrix form \n",
+ "B.Zb.(B^T).Il = B.Vs-B.Zb.Is\n",
+ "\n",
+ "B.Zb.(B^T).Il = B.Vs \n",
+ "Zb=\n",
+ "[[1 0 0 0 0 0]\n",
+ " [0 1 0 0 0 0]\n",
+ " [0 0 1 0 0 0]\n",
+ " [0 0 0 2 0 0]\n",
+ " [0 0 0 0 2 0]\n",
+ " [0 0 0 0 0 2]]\n",
+ "\n",
+ "(B^T)=\n",
+ "[[ 1 0 0]\n",
+ " [ 0 1 0]\n",
+ " [ 0 0 1]\n",
+ " [ 1 -1 0]\n",
+ " [ 1 0 -1]\n",
+ " [ 0 -1 1]]\n",
+ "\n",
+ "Vs=\n",
+ "[[2]\n",
+ " [0]\n",
+ " [0]\n",
+ " [0]\n",
+ " [0]\n",
+ " [0]]\n",
+ "\n",
+ "B.Zb =\n",
+ "[[ 5 -3 1]]\n",
+ "\n",
+ "B.Vs=\n",
+ "[[2]\n",
+ " [0]\n",
+ " [0]]\n",
+ "\n",
+ "Load currents:\n",
+ "[[ 0.85714286]\n",
+ " [ 0.57142857]\n",
+ " [ 0.57142857]]\n",
+ "\n",
+ "Il1=0.857 A \n",
+ "Il2=0.571 A \n",
+ "Il3=0.571 A\n",
+ "\n",
+ "Branch currents:\n",
+ "(matrix([[ 1, 0, 0],\n",
+ " [ 0, 1, 0],\n",
+ " [ 0, 0, 1],\n",
+ " [ 1, -1, 0],\n",
+ " [ 1, 0, -1],\n",
+ " [ 0, -1, 1]]), matrix([[ 0.85714286],\n",
+ " [ 0.57142857],\n",
+ " [ 0.57142857]]))\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex15-pg7.28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Graph Theory : example 7.15 :(pg 7.38 & 7.39)\n",
+ "##Tieset Matrix B\n",
+ "import numpy\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "print(\"\\ntieset1={1,4,6} \\ntieset2={2,5,6} \\ntieset={3,5,4} \\nB=\"); \n",
+ "B=numpy.matrix([[1, 0 ,0 ,1 ,0 ,1],[0, 1, 0, 0, 1 ,-1],[0 ,0 ,1 ,-1 ,-1 ,0]]);\n",
+ "print(B);\n",
+ "print(\"\\nThe KVL equation in matrix form \\nB.Zb.(B^T).Il = B.Vs-B.Zb.Is\");\n",
+ "print(\"\\nB.Zb.(B^T).Il = B.Vs \\nZb=\");##Is=0\n",
+ "Zb = numpy.array([6,4,3,4,6,2])\n",
+ "d = numpy.diag(Zb)\n",
+ "print(d)\n",
+ "XY=numpy.matrix.transpose(B)\n",
+ "print(\"\\n(B^T)=\");\n",
+ "print(XY);\n",
+ "Vs=([[12],[-6],[-8],[0],[0],[0]]);\n",
+ "print(\"\\nVs=\");\n",
+ "print(Vs);\n",
+ "print(\"\\nB.Zb=\");\n",
+ "x=numpy.dot(B,Zb);\n",
+ "print(x);\n",
+ "print(\"\\nB.Zb.(B^T)=\");\n",
+ "#y=numpy.dot(XY,x);\n",
+ "#print(y);\n",
+ "print(\"\\nB.Vs=\");\n",
+ "z=numpy.dot(B,Vs);\n",
+ "print(z);\n",
+ "print(\"\\nLoad currents:\");\n",
+ "M=numpy.matrix([[12 ,-2 ,-4],[-2, 12, -6],[-4, -6, 12]]);\n",
+ "H=numpy.linalg.inv(M);\n",
+ "N=([[12],[-6],[-8]]);\n",
+ "X=numpy.dot(H,N);\n",
+ "print(X);\n",
+ "print(\"\\nIl1=0.55 A \\nIl2=-0.866 A \\nIl3=-0.916 A\");\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "tieset1={1,4,6} \n",
+ "tieset2={2,5,6} \n",
+ "tieset={3,5,4} \n",
+ "B=\n",
+ "[[ 1 0 0 1 0 1]\n",
+ " [ 0 1 0 0 1 -1]\n",
+ " [ 0 0 1 -1 -1 0]]\n",
+ "\n",
+ "The KVL equation in matrix form \n",
+ "B.Zb.(B^T).Il = B.Vs-B.Zb.Is\n",
+ "\n",
+ "B.Zb.(B^T).Il = B.Vs \n",
+ "Zb=\n",
+ "[[6 0 0 0 0 0]\n",
+ " [0 4 0 0 0 0]\n",
+ " [0 0 3 0 0 0]\n",
+ " [0 0 0 4 0 0]\n",
+ " [0 0 0 0 6 0]\n",
+ " [0 0 0 0 0 2]]\n",
+ "\n",
+ "(B^T)=\n",
+ "[[ 1 0 0]\n",
+ " [ 0 1 0]\n",
+ " [ 0 0 1]\n",
+ " [ 1 0 -1]\n",
+ " [ 0 1 -1]\n",
+ " [ 1 -1 0]]\n",
+ "\n",
+ "Vs=\n",
+ "[[12], [-6], [-8], [0], [0], [0]]\n",
+ "\n",
+ "B.Zb=\n",
+ "[[12 8 -7]]\n",
+ "\n",
+ "B.Zb.(B^T)=\n",
+ "\n",
+ "B.Vs=\n",
+ "[[12]\n",
+ " [-6]\n",
+ " [-8]]\n",
+ "\n",
+ "Load currents:\n",
+ "[[ 0.55 ]\n",
+ " [-0.86666667]\n",
+ " [-0.91666667]]\n",
+ "\n",
+ "Il1=0.55 A \n",
+ "Il2=-0.866 A \n",
+ "Il3=-0.916 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex19-pg7.34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Graph Theory : example 7.19 \n",
+ "import math\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "Q=numpy.matrix([[1, -1, 0, 0],[0 ,-1 ,1 ,1]]);\n",
+ "print(\"\\nQ=\");\n",
+ "print(Q);\n",
+ "print(\"\\nThe KCL equation in matrix form is given by\");\n",
+ "print(\"\\nQ.Yb.(Q^T).Vl=Q.Is-Q.Yb.Vs\");\n",
+ "print(\"\\nQ.Yb.(Q^T).Vl=Q.Is\");##Vs=0\n",
+ "Yb=numpy.array([5,5,5,10]);\n",
+ "d=numpy.diag(Yb)\n",
+ "Is=numpy.matrix([[-10],[0],[0],[0]]);\n",
+ "print(\"\\nYb=\");\n",
+ "print(d);\n",
+ "print(\"\\n(Q^T)=\");\n",
+ "ZZ=numpy.matrix.transpose(Q)\n",
+ "print(ZZ);\n",
+ "print(\"\\nIs=\");\n",
+ "print(Is);##current entering into nodes is taken as negative\n",
+ "x=numpy.dot(Q,Yb);\n",
+ "print(\"\\nQ.Yb=\");\n",
+ "print(x);\n",
+ "#y=numpy.dot(x[0],ZZ);\n",
+ "print(\"\\nQ.Yb.(Q^T)=\");\n",
+ "#print(y);\n",
+ "z=numpy.dot(Q,Is);\n",
+ "print(\"\\nQ.Is=\");\n",
+ "print(z);\n",
+ "print(\"\\nLoad voltages:\");\n",
+ "M=numpy.matrix([[10, 5],[5, 20]]);\n",
+ "P=numpy.linalg.inv(M);\n",
+ "N=numpy.matrix([[-10],[0]]);\n",
+ "X=numpy.dot(P,N);\n",
+ "print(X);\n",
+ "print(\"\\nvl1=-1.14 V \\nvl2=0.28 V\");\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Q=\n",
+ "[[ 1 -1 0 0]\n",
+ " [ 0 -1 1 1]]\n",
+ "\n",
+ "The KCL equation in matrix form is given by\n",
+ "\n",
+ "Q.Yb.(Q^T).Vl=Q.Is-Q.Yb.Vs\n",
+ "\n",
+ "Q.Yb.(Q^T).Vl=Q.Is\n",
+ "\n",
+ "Yb=\n",
+ "[[ 5 0 0 0]\n",
+ " [ 0 5 0 0]\n",
+ " [ 0 0 5 0]\n",
+ " [ 0 0 0 10]]\n",
+ "\n",
+ "(Q^T)=\n",
+ "[[ 1 0]\n",
+ " [-1 -1]\n",
+ " [ 0 1]\n",
+ " [ 0 1]]\n",
+ "\n",
+ "Is=\n",
+ "[[-10]\n",
+ " [ 0]\n",
+ " [ 0]\n",
+ " [ 0]]\n",
+ "\n",
+ "Q.Yb=\n",
+ "[[ 0 10]]\n",
+ "\n",
+ "Q.Yb.(Q^T)=\n",
+ "\n",
+ "Q.Is=\n",
+ "[[-10]\n",
+ " [ 0]]\n",
+ "\n",
+ "Load voltages:\n",
+ "[[-1.14285714]\n",
+ " [ 0.28571429]]\n",
+ "\n",
+ "vl1=-1.14 V \n",
+ "vl2=0.28 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex20-pg7.35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Graph Theory : example 7.20 :(pg 7.35 & 7.36)\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "print(\"\\nf-cutset1={1,4,5,6} \\nf-cutset2={2,4,5} \\nf-cutset3={3,4,6}\");\n",
+ "Q=numpy.matrix([[1, 0 ,0 ,-1, -1, 1],[0 ,1 ,0 ,-1, -1 ,0],[0 ,0, 1, -1 ,0 ,1]]);\n",
+ "print(\"\\nQ=\");\n",
+ "print(Q);\n",
+ "print(\"\\nThe KCL equation in matrix form is given by\");\n",
+ "print(\"\\nQ.Yb.(Q^T).Vl=Q.Is-Q.Yb.Vs\");\n",
+ "print(\"\\nQ.Yb.(Q^T).Vl=Q.Is\");##Is=0\n",
+ "Yb=numpy.array([0.2,0.2,0.2,0.1,0.5,0.1]);\n",
+ "yz=numpy.diag(Yb)\n",
+ "Vs=numpy.matrix([[910],[0],[0],[0],[0],[0]]);\n",
+ "Is=numpy.matrix([[0],[0],[0],[0],[0],[0]]);\n",
+ "print(\"\\nyz=\");\n",
+ "print(yz);\n",
+ "print(\"\\nVs=\");\n",
+ "print(Vs);\n",
+ "print(\"\\nIs=\");\n",
+ "print(Is);\n",
+ "x=numpy.dot(Q,yz);\n",
+ "print(\"\\nQ.Yb=\");\n",
+ "print(x);\n",
+ "z=numpy.dot(x,Vs);\n",
+ "print(\"\\nQ.Yb.Vs=\");\n",
+ "print(z);\n",
+ "print(\"\\nQ.Is=\");\n",
+ "u=numpy.dot(Q,Is);\n",
+ "print(u);\n",
+ "v=(u-z);\n",
+ "print(\"\\nQ.Is-Q.Yb.Vs=\");\n",
+ "print(v);\n",
+ "print(\"\\nLoad voltages:\");\n",
+ "M=([[0.9, 0.6, 0.2],[0.6, 0.8, 0.1],[0.2 ,0.1 ,0.3]]);\n",
+ "P=numpy.linalg.inv(M);\n",
+ "N=([[-182],[0],[0]]);\n",
+ "X=numpy.dot(P,N);\n",
+ "print(X);\n",
+ "print(\"\\nvl1=-460 V \\nvl2=320 V \\nvl3=200 V\");\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "f-cutset1={1,4,5,6} \n",
+ "f-cutset2={2,4,5} \n",
+ "f-cutset3={3,4,6}\n",
+ "\n",
+ "Q=\n",
+ "[[ 1 0 0 -1 -1 1]\n",
+ " [ 0 1 0 -1 -1 0]\n",
+ " [ 0 0 1 -1 0 1]]\n",
+ "\n",
+ "The KCL equation in matrix form is given by\n",
+ "\n",
+ "Q.Yb.(Q^T).Vl=Q.Is-Q.Yb.Vs\n",
+ "\n",
+ "Q.Yb.(Q^T).Vl=Q.Is\n",
+ "\n",
+ "yz=\n",
+ "[[ 0.2 0. 0. 0. 0. 0. ]\n",
+ " [ 0. 0.2 0. 0. 0. 0. ]\n",
+ " [ 0. 0. 0.2 0. 0. 0. ]\n",
+ " [ 0. 0. 0. 0.1 0. 0. ]\n",
+ " [ 0. 0. 0. 0. 0.5 0. ]\n",
+ " [ 0. 0. 0. 0. 0. 0.1]]\n",
+ "\n",
+ "Vs=\n",
+ "[[910]\n",
+ " [ 0]\n",
+ " [ 0]\n",
+ " [ 0]\n",
+ " [ 0]\n",
+ " [ 0]]\n",
+ "\n",
+ "Is=\n",
+ "[[0]\n",
+ " [0]\n",
+ " [0]\n",
+ " [0]\n",
+ " [0]\n",
+ " [0]]\n",
+ "\n",
+ "Q.Yb=\n",
+ "[[ 0.2 0. 0. -0.1 -0.5 0.1]\n",
+ " [ 0. 0.2 0. -0.1 -0.5 0. ]\n",
+ " [ 0. 0. 0.2 -0.1 0. 0.1]]\n",
+ "\n",
+ "Q.Yb.Vs=\n",
+ "[[ 182.]\n",
+ " [ 0.]\n",
+ " [ 0.]]\n",
+ "\n",
+ "Q.Is=\n",
+ "[[0]\n",
+ " [0]\n",
+ " [0]]\n",
+ "\n",
+ "Q.Is-Q.Yb.Vs=\n",
+ "[[-182.]\n",
+ " [ 0.]\n",
+ " [ 0.]]\n",
+ "\n",
+ "Load voltages:\n",
+ "[[-460.]\n",
+ " [ 320.]\n",
+ " [ 200.]]\n",
+ "\n",
+ "vl1=-460 V \n",
+ "vl2=320 V \n",
+ "vl3=200 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex21-pg7.36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Graph Theory : example 7.21 :(pg 7.38 & 7.39)\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "print(\"\\ntwigs={1,2} \\nf-cutset1={1,4} \\nf-cutset2={2,3}\");\n",
+ "Q=numpy.matrix([[1, 0, 0 ,-1],[0 ,1 ,-1, 0]]);\n",
+ "print(\"\\nQ=\");\n",
+ "print(Q);\n",
+ "print(\"\\nThe KCL equation in matrix form is given by\");\n",
+ "print(\"\\nQ.Yb.(Q^T).Vl=Q.Is-Q.Yb.Vs\");\n",
+ "ZZ=numpy.matrix.transpose(Q)\n",
+ "\n",
+ "yxx=numpy.array([0.25,0.5,0.25,0.5]);\n",
+ "Yb=numpy.diag(yxx)\n",
+ "Vs=numpy.matrix([[1],[1],[0],[0]]);\n",
+ "Is=numpy.matrix([[0],[0],[0.5],[-0.5]]);\n",
+ "print(\"\\nYb=\");\n",
+ "print(Yb);\n",
+ "print(\"\\n(Q^T)=\");\n",
+ "print(ZZ);\n",
+ "print(\"\\nVs=\");\n",
+ "print(Vs);\n",
+ "print(\"\\nIs=\");\n",
+ "print(Is);\n",
+ "x=numpy.dot(Q,Yb);\n",
+ "print(\"\\nQ.Yb=\");\n",
+ "print(x);\n",
+ "y=numpy.dot(x,ZZ);\n",
+ "print(\"\\nQ.Yb.(Q^T)=\");\n",
+ "print(y);\n",
+ "print(\"\\nQ.Is=\");\n",
+ "u=numpy.dot(Q,Is);\n",
+ "print(Q*Is);\n",
+ "z=numpy.dot(x,Vs);\n",
+ "print(\"\\nQ.Yb.Vs=\");\n",
+ "print(z);\n",
+ "v=(u-z);\n",
+ "print(\"\\nQ.Is-Q.Yb.Vs=\");\n",
+ "print(v);\n",
+ "print(\"\\nLoad voltages:\");\n",
+ "M=([[0.75, 0],[0 ,0.75]]);\n",
+ "P=numpy.linalg.inv(M);\n",
+ "N=([[0.25],[-1]]);\n",
+ "X=numpy.dot(P,N);\n",
+ "print(X);\n",
+ "print(\"\\nvl1=0.33 V \\nvl2=-1.33 V\");\n",
+ "vl2=-1.33;\n",
+ "v=1.+vl2;\n",
+ "print\"%s %.2f %s\"%(\"\\nV=\",v,\"\");\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "twigs={1,2} \n",
+ "f-cutset1={1,4} \n",
+ "f-cutset2={2,3}\n",
+ "\n",
+ "Q=\n",
+ "[[ 1 0 0 -1]\n",
+ " [ 0 1 -1 0]]\n",
+ "\n",
+ "The KCL equation in matrix form is given by\n",
+ "\n",
+ "Q.Yb.(Q^T).Vl=Q.Is-Q.Yb.Vs\n",
+ "\n",
+ "Yb=\n",
+ "[[ 0.25 0. 0. 0. ]\n",
+ " [ 0. 0.5 0. 0. ]\n",
+ " [ 0. 0. 0.25 0. ]\n",
+ " [ 0. 0. 0. 0.5 ]]\n",
+ "\n",
+ "(Q^T)=\n",
+ "[[ 1 0]\n",
+ " [ 0 1]\n",
+ " [ 0 -1]\n",
+ " [-1 0]]\n",
+ "\n",
+ "Vs=\n",
+ "[[1]\n",
+ " [1]\n",
+ " [0]\n",
+ " [0]]\n",
+ "\n",
+ "Is=\n",
+ "[[ 0. ]\n",
+ " [ 0. ]\n",
+ " [ 0.5]\n",
+ " [-0.5]]\n",
+ "\n",
+ "Q.Yb=\n",
+ "[[ 0.25 0. 0. -0.5 ]\n",
+ " [ 0. 0.5 -0.25 0. ]]\n",
+ "\n",
+ "Q.Yb.(Q^T)=\n",
+ "[[ 0.75 0. ]\n",
+ " [ 0. 0.75]]\n",
+ "\n",
+ "Q.Is=\n",
+ "[[ 0.5]\n",
+ " [-0.5]]\n",
+ "\n",
+ "Q.Yb.Vs=\n",
+ "[[ 0.25]\n",
+ " [ 0.5 ]]\n",
+ "\n",
+ "Q.Is-Q.Yb.Vs=\n",
+ "[[ 0.25]\n",
+ " [-1. ]]\n",
+ "\n",
+ "Load voltages:\n",
+ "[[ 0.33333333]\n",
+ " [-1.33333333]]\n",
+ "\n",
+ "vl1=0.33 V \n",
+ "vl2=-1.33 V\n",
+ "\n",
+ "V= -0.33 \n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-21 02:31:57 +0000