path: root/sample_notebooks/ShantanuBhosale/chapter40_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CHAPTER 40: D.C TRANSMISSION AND DISTRIBUTION\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.1 ,Page No :- 1574"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage saving in copper is = 50.0 %.\n"
     ]
    }
   ],
   "source": [
    "#A DC 2-wire feeder supplies a constant load with a sending-end voltage of 220V.Calculate the saving in copper\n",
    "#if this voltage is doubled with power transmitted remaining the same.\n",
    "##################################################################################################################\n",
    "\n",
    "\n",
    "\n",
    "#Given\n",
    "V1 = 220.0\n",
    "V2 = 440.0\n",
    "##Let us assume the wire has##\n",
    "#length -> length \n",
    "#area   -> area\n",
    "#current density -> cd\n",
    "#power  -> P\n",
    "P = 10000.0   #assumption\n",
    "length = 1000.0    #assumption \n",
    "cd = 5.0    #assumption\n",
    "#The values are assumed as these terms cancel out while calculating percentage.\n",
    "I1 = P/V1\n",
    "area  = I1/cd\n",
    "#Vol of Cu required for 220V ->vol1\n",
    "vol1 = 2*area*length\n",
    "\n",
    "\n",
    "I2 = P/V2\n",
    "area  = I2/cd\n",
    "#Vol of Cu required for 440V ->vol2\n",
    "vol2 = 2*area*length\n",
    "\n",
    "#percentage saving of copper is\n",
    "per_cent = ((vol1-vol2)/vol1)*100\n",
    "print 'percentage saving in copper is ',per_cent,'%.'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.2 ,Page No :- 1577"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum voltage drop from one end is =  12.0 V.\n",
      "Maximum voltage drop from both end is =  3.0 V.\n"
     ]
    }
   ],
   "source": [
    "#A uniform 2-wire d.c distributor 200 metres long is loaded with 2 amperes/metre.Resistance of\n",
    "#single wire is 0.3 ohm/kilometre.Calculate the maximum voltage drop if the distributor is fed\n",
    "#(a)from one end (b)from both ends with equal voltages.\n",
    "#################################################################################################\n",
    "\n",
    "#Given\n",
    "length = 200.0        #metres\n",
    "#current per unit length is\n",
    "cur = 2.0             #amp/metre\n",
    "#resistance per unit length is\n",
    "res = 0.3/1000        #ohm/metre\n",
    "\n",
    "#total resistance is\n",
    "R = res*length        #ohm\n",
    "#total current is\n",
    "I = cur*length        #amp\n",
    "#Total drop over a distributor fed from one end is given by\n",
    "drop1 = (1/2.0)*I*R        #volts\n",
    "#Total drop over a distributor fed from both ends is given by\n",
    "drop2 = (1/8.0)*I*R\n",
    "print 'Maximum voltage drop from one end is = ',drop1,'V.'\n",
    "print 'Maximum voltage drop from both end is = ',drop2,'V.'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.3 ,Page No :- 1577"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross sectional area of distributor = 116.412 cm^2\n"
     ]
    }
   ],
   "source": [
    "#A 2-wire d.c distributor AB is 300 metres long.It is fed at point A.The various loads and\n",
    "#their positions are given below.\n",
    "#      At point       distance from A in metres     concentrated load in A\n",
    "#         C                     40                             30\n",
    "#         D                     100                            40                \n",
    "#         E                     150                            100\n",
    "#         F                     250                            50\n",
    "#If the maximum permissible voltage drop is not to exceed 10V,find the cross-sectional\n",
    "#area of the distributor.Take resistivity = 1.78*10^(-8) ohm-m.\n",
    "###########################################################################################\n",
    "\n",
    "\n",
    "#Given\n",
    "resistivity = 1.78e-8     #ohm-m\n",
    "drop_max    = 10.0          #V\n",
    "#loads and their positions\n",
    "I1 = 30.0    #A\n",
    "l1 = 40.0    #m\n",
    "I2 = 40.0    #A\n",
    "l2 = 100.0   #m\n",
    "I3 = 100.0   #A\n",
    "l3 = 150.0   #m\n",
    "I4 = 50   #A\n",
    "l4 = 250   #m\n",
    "#We know that R = resistivity*length/Area\n",
    "#Also max drop = I1*R1 + I2*R2 + I3*R3 + I4*R4 , using this\n",
    "area = 2*(I1*l1 + I2*l2 + I3*l3 + I4*l4)*resistivity/drop_max   #m^2\n",
    "area = area*1000000    #cm^2                 \n",
    "print 'Cross sectional area of distributor =',area,'cm^2'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.4 ,Page No :- 1578"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hence drop at minimum potential where load is 70 A is = 48.4 V.\n"
     ]
    }
   ],
   "source": [
    "#A 2-wire d.c distributor F1F2 1000 metres long is loaded as under:\n",
    "#Distance from F1(in metres): 100    250    500    600    700    800    850    920\n",
    "#Load in amperes:              20     80     50     70     40     30     10     15\n",
    "#The feeding points F1 and F2 are maintained at the same potential.Find which point will have the\n",
    "#minimum potential and what will be the drop at this point?Take the cross-section of the conductors\n",
    "#as 0.35 cm^2 and specific resistance of copper as 1.764*10^(-6) ohm-cm\n",
    "#####################################################################################################\n",
    "\n",
    "#Given\n",
    "import numpy as np\n",
    "resistivity = 1.764e-8           #ohm-m\n",
    "area = 0.35e-4                      #m^2 \n",
    "#loads and their positions taking from F1\n",
    "I1 = 20         #A\n",
    "l1 = 100        #m\n",
    "I2 = 80         #A\n",
    "l2 = 150        #m\n",
    "I3 = 50         #A\n",
    "l3 = 250        #m\n",
    "I4 = 70        #A\n",
    "l4 = 100        #m\n",
    "I5 = 40         #A\n",
    "l5 = 100        #m\n",
    "I6 = 30         #A\n",
    "l6 = 50        #m\n",
    "I7 = 10         #A\n",
    "l7 = 70        #m\n",
    "I8 = 15         #A\n",
    "l8 = 80       #m \n",
    "\n",
    "#sum of loads from F1\n",
    "load1 = I1*l1 + I2*(l1+l2) + I3*(l1+l2+l3)                          #A-m\n",
    "load2 = I8*l8 + I7*(l7+l8) + I6*(l6+l7+l8) + I5*(l5+l6+l7+l8)       #A-m\n",
    "\n",
    "#guessing the point of minimum potential\n",
    "if load1>load2:\n",
    "    load2_new = load2 + I4*(l4+l5+l6+l7+l8)\n",
    "    if load2_new>load1:\n",
    "        pivot = I4\n",
    "\n",
    "#solving 2 equations simultaneously\n",
    "# x + y = 70(pivot) & 47000(load1) + 600(l1+l2+l3)x = 20,700(load2) + 400(l5+l6+l7+l8)y)\n",
    "line1 = l1+l2+l3+l4                   #m\n",
    "line2 = l4+l5+l6+l7+l8                #m \n",
    "\n",
    "a = [[1,1],[line1,-line2]]\n",
    "b = [pivot,load2-load1]\n",
    "soln = np.linalg.solve(a,b)            #soln is array with its elements[x,y]\n",
    "#drop at minimum potential per conductor (in A-m)\n",
    "drop_m = load1 + soln[0]*line1   #A-m\n",
    "\n",
    "#resistance per metre = resistivity/Area\n",
    "res = resistivity/area     #ohm/m\n",
    "\n",
    "#Hence, drop in voltage per conductor is\n",
    "drop = drop_m*res          #V  \n",
    "#drop due to both is\n",
    "drop = drop*2              #V\n",
    "\n",
    "print 'Hence drop at minimum potential where load is',pivot,'A is =',round(drop,2),'V.'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.5 ,Page No :- 1579"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The current entering at A is =  88.6 A \n",
      "The current entering at B is =  211.4 A.\n"
     ]
    }
   ],
   "source": [
    "#The resistance of a cable is 0.1ohm per 1000 metre for both conductors.It is loaded as shown in Fig.40.14(a).\n",
    "#Find the current supplied at A and at B.If both the ends are supplied at 200 V\n",
    "##############################################################################################################\n",
    "\n",
    "#Given\n",
    "#resistance per metre\n",
    "res = 0.1/1000         #ohm/m\n",
    "#loads and their positions taking from A\n",
    "I1 = 50.0      #A\n",
    "l1 = 500.0     #m\n",
    "I2 = 100.0     #A\n",
    "l2 = 700.0     #m\n",
    "I3 = 150.0     #A\n",
    "l3 = 300.0    #m\n",
    "l4 = 250.0     #m    \n",
    "\n",
    "#Assuming I flows from A to B\n",
    "# equation is  res*[500*i + 700(i-50) + 300(i-150) + 250(i-300)] = 0\n",
    "current_i = (I1*l2+(I1+I2)*l3 + (I1+I2+I3)*l4)/(l1+l2+l3+l4)\n",
    "current_AC = current_i\n",
    "current_CD = current_i-I1\n",
    "current_DE = current_CD-I2\n",
    "current_EB = current_DE-I3\n",
    "if current_EB<0:\n",
    "    current_EB = -current_EB;\n",
    "print 'The current entering at A is = ',round(current_i,1),'A '\n",
    "print 'The current entering at B is = ',round(current_EB,1),'A.'    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.6 ,Page No :- 1580"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current supplied at A is =  88.6 A.\n",
      "Current supplied at B is =  -211.4 A.\n",
      "Current in AC is =  88.6 A.\n",
      "Current in CD is =  38.6 A.\n",
      "Current in DE is =  -61.4 A.\n",
      "Current in EB is =  -211.4 A.\n",
      "Drop over AC is =  4.4 V.\n",
      "Drop over CD is =  2.7 V.\n",
      "Drop over DE is =  -1.8 V.\n",
      "Voltage at C is =  195.6 V.\n",
      "Voltage at D is = 192.9 V.\n",
      "Voltage at E is =  194.7 V.\n"
     ]
    }
   ],
   "source": [
    "#The resistance of two conductors of a 2-conductor distributor shown in Fig.39.15 is 0.1ohm per 1000m\n",
    "#for both conductors.Find (a)the current supplied at A(b)the current supplied at B\n",
    "#(c)the current in each section (d)the voltages at C,D and E.Both A and B are maintained at 200V.\n",
    "######################################################################################################\n",
    "\n",
    "#Given\n",
    "#resistance per metre\n",
    "res = 0.1/1000         #ohm/m\n",
    "#loads and their positions taking from A\n",
    "I1 = 50.0      #A\n",
    "l1 = 500.0     #m\n",
    "I2 = 100.0     #A\n",
    "l2 = 700.0     #m\n",
    "I3 = 150.0     #A\n",
    "l3 = 300.0    #m\n",
    "l4 = 250.0     #m    \n",
    "\n",
    "#Assuming I flows from A to B\n",
    "# equation is  res*[500*i + 700(i-50) + 300(i-150) + 250(i-300)] = 0\n",
    "current_i = (I1*l2+(I1+I2)*l3 + (I1+I2+I3)*l4)/(l1+l2+l3+l4)\n",
    "current_AC = current_i\n",
    "current_CD = current_i-I1\n",
    "current_DE = current_CD-I2\n",
    "current_EB = current_DE-I3\n",
    "print \"Current supplied at A is = \",round(current_i,1),\"A.\"\n",
    "print \"Current supplied at B is = \",round(current_EB,1),\"A.\"\n",
    "print \"Current in AC is = \",round(current_i,1),\"A.\"\n",
    "print \"Current in CD is = \",round(current_CD,1),\"A.\"\n",
    "print \"Current in DE is = \",round(current_DE,1),\"A.\"\n",
    "print \"Current in EB is = \",round(current_EB,1),\"A.\"\n",
    "#Drop in volts is (resistance/metre)*length*current\n",
    "drop_AC = res*l1*current_AC         #V\n",
    "drop_CD = res*l2*current_CD          #V \n",
    "drop_DE = res*l3*current_DE          #V\n",
    "print \"Drop over AC is = \",round(drop_AC,1),\"V.\"\n",
    "print \"Drop over CD is = \",round(drop_CD,1),\"V.\"\n",
    "print \"Drop over DE is = \",round(drop_DE,1),\"V.\"\n",
    "\n",
    "#Voltages at C,D,E are\n",
    "volt_C = 200-drop_AC        #V\n",
    "volt_D = volt_C-drop_CD     #V\n",
    "volt_E = volt_D-drop_DE     #V\n",
    "print 'Voltage at C is = ',round(volt_C,1),'V.'\n",
    "print 'Voltage at D is =',round(volt_D,1),'V.'\n",
    "print 'Voltage at E is = ',round(volt_E,1),'V.'\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.7 ,Page No :- 1581"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Therefore point of minimum potential is D and minimum potential is =  246.0 V.\n"
     ]
    }
   ],
   "source": [
    "#A 200 m long distributor is fed from both ends A and B at the same voltage of 250V.The\n",
    "#concentrated loads of 50,40,30 and 25 A are coming on the distributor at distances of 50,75,\n",
    "#100 and 150 m respectively from end A.Determine the minimum potential and locate its positions.\n",
    "#Also,determine the current in each section of the distributor.It is given that the resistance\n",
    "#of the distributor is 0.08ohm per 100 metres for go and return.\n",
    "##################################################################################################\n",
    "\n",
    "\n",
    "#Given\n",
    "#resistance per metre\n",
    "res = 0.08/100           #ohm/m\n",
    "V_A = 250.0                #V\n",
    "V_B = 250.0                #V\n",
    "#load currents and their positions\n",
    "I_C  = 50.0   #A\n",
    "I_D  = 40.0   #A\n",
    "I_E  = 30.0   #A\n",
    "I_F  = 25.0   #A\n",
    "l_AC = 50.0        #m\n",
    "l_CD = 75.0 - l_AC   #m\n",
    "l_DE = 100.0 - l_CD - l_AC        #m\n",
    "l_EF = 150.0 - l_DE - l_CD - l_AC #m\n",
    "l_FB = 200.0-150.0\n",
    "#Assuming I flows from A to B\n",
    "# equation is  res*[50*i + 25(i-50) + 25(i-90) + 50(i-120)+50(i-145)] = 0\n",
    "current_i = (l_CD*I_C + l_DE*(I_C+I_D)+l_EF*(I_C+I_D+I_E) + l_FB*(I_C+I_D+I_E+I_F))/200.0\n",
    "current_AC = current_i\n",
    "current_CD = current_i-I_C\n",
    "current_DE = current_CD-I_D\n",
    "current_EF = current_DE-I_E\n",
    "current_FB = current_EF-I_F\n",
    "#As from figure in the book , point D is at minimum potential\n",
    "if (current_CD>0) & (current_DE<0):\n",
    "    point = \"D\"\n",
    "    \n",
    "#drop in volts = resistance/metre*sum(length*current) \n",
    "drop_d = res*(l_AC*current_AC + l_CD*current_CD)\n",
    "min_pot = V_A-drop_d\n",
    "print \"Therefore point of minimum potential is\",point,\"and minimum potential is = \",round(min_pot,1),\"V.\"    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.8 ,Page No :- 1582"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Voltage at point C is =  250.13 V.\n",
      "Voltage at point D is =  247.73 V.\n"
     ]
    }
   ],
   "source": [
    "#Each conductor of a 2-core distributor,500 metres long has a cross-sectional area\n",
    "#of 2 cm^2.The feeding point A is supplied at 255V and the feeding point B at\n",
    "#250V and load currents of 120A and 160A are taken at points C and D which are\n",
    "#150 metres and 350 metres respectively from the feeding point A.Calculate the\n",
    "#voltage at each load.Specific Resistance of copper is 1.7*10^(-6) ohm-cm\n",
    "##################################################################################\n",
    "\n",
    "#Given\n",
    "area = 2e-4             #m^2\n",
    "resistivity = 1.7e-8    #ohm-m\n",
    "#load currents and their positions\n",
    "i_c = 120.0    #A\n",
    "i_d = 160.0    #A\n",
    "l_ac = 150.0   #m\n",
    "l_cd = 200.0   #m\n",
    "l_db = 150.0   #m\n",
    "V_a = 255.0    #V\n",
    "V_b = 250.0    #V\n",
    "#Resistance = resistivity*length/Area\n",
    "#It is a 2 core distributor.Therefore,resistance per metre is\n",
    "res = 2*resistivity/area   #ohm/m\n",
    "#drop over whole distributor is equal to\n",
    "drop = V_a - V_b     #V\n",
    "#Therefore equation of total drop can be written as\n",
    "# resistivity*(150i+200(i-120)+150(i-280))=5\n",
    "current_i = (drop/res + l_cd*i_c + l_db*(i_c+i_d))/(l_ac+l_cd+l_db)   #A\n",
    "current_ac = current_i          #A\n",
    "current_cd = current_ac-i_c     #A\n",
    "current_db = current_cd-i_d     #A\n",
    "\n",
    "#Voltage at C = 255-drop over AC\n",
    "volt_c = V_a-res*l_ac*current_ac    #V\n",
    "#Voltage at D = 250-drop over DB    \n",
    "volt_d = V_b -res*l_db*abs(current_db) #V\n",
    "print \"Voltage at point C is = \",round(volt_c,2),\"V.\"\n",
    "print \"Voltage at point D is = \",round(volt_d,2),\"V.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.9 ,Page No :- 1583"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatge at point Q is =  225.25 V.\n",
      "Voltage at point B is =  236.56 V.\n"
     ]
    }
   ],
   "source": [
    "#A 2-wire distributor 500 metres long is fed at P at 250V and loads of 40A,20A,60A,30A are tapped off\n",
    "#off from points A,B,C and D which are at distances of 100 metres,150 metres,300 metres and 400 metres\n",
    "#from P respectively.The distributor is also uniformly loaded at the rate of 0.1A/m.If the resistance of\n",
    "#the distributor per metre(go and return) is 0.0005 ohm,calculate the voltage at(i)pointQ and(ii)point B.\n",
    "###########################################################################################################\n",
    "\n",
    "#Given\n",
    "V_P = 250.0    #V\n",
    "resistance = 0.0005        #ohm/m\n",
    "\n",
    "#loads and their positions\n",
    "i_a = 40.0     #A\n",
    "i_b = 20.0     #A\n",
    "i_c = 60.0     #A\n",
    "i_d = 30.0     #A\n",
    "l_pa = 100.0     #m\n",
    "l_ab = 150.0-100.0      #m\n",
    "l_bc = 300.0-150.0     #m\n",
    "l_cd = 400.0-300.0     #m\n",
    "#uniform dstributed load\n",
    "cur_uni = 0.1      #A/m\n",
    "\n",
    "\n",
    "#considering drop due to concentrated loading\n",
    "drop_pa = (i_a+i_b+i_c+i_d)*l_pa*resistance      #V\n",
    "drop_ab = (i_b+i_c+i_d)*l_ab*resistance          #V \n",
    "drop_bc = (i_c+i_d)*l_bc*resistance              #V\n",
    "drop_cd = i_d*l_cd*resistance                    #V\n",
    "tot_drop = drop_pa + drop_ab + drop_bc + drop_cd      #V\n",
    "\n",
    "#considering drop due to uniform loading(drop = irl^2/2) l = 500m\n",
    "drop_uni = cur_uni*resistance*(500.0*500.0)/2     #V\n",
    "\n",
    "V_Q = V_P - (tot_drop + drop_uni)   #V\n",
    "#for point B\n",
    "#drop due to concentrated loading\n",
    "drop_b = drop_pa + drop_ab        #V\n",
    "#drop due to uniform loading (drop = ir(lx-x^2/2)) l=500m x=150m\n",
    "drop_ub = cur_uni*resistance*(500*(l_pa+l_ab)-(l_pa+l_ab)*(l_pa+l_ab)/2)   #V\n",
    "\n",
    "V_B = V_P - (drop_b + drop_ub)    #V\n",
    "\n",
    "print \"Volatge at point Q is = \",round(V_Q,2),\"V.\"\n",
    "print \"Voltage at point B is = \",round(V_B,2),\"V.\" "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.10 ,Page No :- 1583"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current in section AC is =  53.75 A.\n",
      "Current in section CD is =  33.75 A.\n",
      "Current in section DE is =  -6.25 A.\n",
      "Current in section EF is =  -31.25 A.\n",
      "Current in section FB is =  -61.25 A.\n",
      "Minimum voltage is at point D and minimum voltage is =  233.18 V.\n"
     ]
    }
   ],
   "source": [
    "#A distributor AB is fed from both ends.At feeding point A,the voltage is maintained at 236V and at B at 237V.\n",
    "#The total length of the distributor is 200 metres and loads are tapped off as under:\n",
    "#(i) 20A at 50 metres from A   (ii) 40A at 75 metres from A. (iii)25A at 100 metres from A (iv)30A at 150 metres from A\n",
    "#The reistance per kilometre of one conductor is 0.4ohm.Calculate the currents in the various sections of the distributor,\n",
    "#the minimum voltage and the point at which it occurs.\n",
    "###########################################################################################################################\n",
    "\n",
    "\n",
    "#Given\n",
    "#resistance per metre\n",
    "res = 2*0.4/1000      #ohm/m\n",
    "V_a = 236.0    #V\n",
    "V_b = 237.0    #V\n",
    "#loads and their positions\n",
    "i_c = 20.0  #A\n",
    "i_d = 40.0  #A\n",
    "i_e = 25.0  #A\n",
    "i_f = 30.0  #A\n",
    "l_ac = 50.0  #m\n",
    "l_cd = 25.0  #m\n",
    "l_de = 25.0  #m\n",
    "l_ef = 50.0  #m\n",
    "l_fb = 50.0  #m\n",
    "#Voltage drop equation  res*(50i + 25(i-20)+25(i-60) + 50(i-85) + 50(i-115)=-1)\n",
    "current_i = ((V_a-V_b)/res + l_cd*(i_c)+l_de*(i_c+i_d)+l_ef*(i_c+i_d+i_e)+l_fb*(i_c+i_d+i_e+i_f))/200.0\n",
    "current_ac = current_i\n",
    "current_cd = current_ac-i_c\n",
    "current_de = current_cd-i_d\n",
    "current_ef = current_de-i_e\n",
    "current_fb= current_ef-i_f\n",
    "if current_cd>0:\n",
    "    if current_de<0:\n",
    "        point = \"D\"\n",
    "#Minimum potential is at D as shown in figure\n",
    "drop = res*(current_ac*l_ac + current_cd*l_cd)\n",
    "V_d = V_a-drop\n",
    "print \"Current in section AC is = \",round(current_ac,2),\"A.\"\n",
    "print \"Current in section CD is = \",round(current_cd,2),\"A.\"\n",
    "print \"Current in section DE is = \",round(current_de,2),\"A.\"\n",
    "print \"Current in section EF is = \",round(current_ef,2),\"A.\"\n",
    "print \"Current in section FB is = \",round(current_fb,2),\"A.\"\n",
    "print \"Minimum voltage is at point\",point,\"and minimum voltage is = \",round(V_d,2),\"V.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.11 ,Page No :- 1584"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current supplied by feeder at point A is 46.29 A and that by point B is 109.71 A.\n",
      "Voltage at point B is =  240.55 V.\n",
      "Voltage at point C is =  239.63 V.\n",
      "Voltage at point D is =  239.42 V.\n",
      "Voltage at point E is =  239.38 V.\n"
     ]
    }
   ],
   "source": [
    "#A distributor cable AB is fed at its ends A and B.Loads of 12,24,72 and 48 A are taken from the cable at\n",
    "#points C,D,E and F.The resistances of sections AC,CD,DE,EF and FB of the cable are 8,6,4,10 and 5 milliohm\n",
    "#respecively(for the go and return conductors together). The potential difference at point A is 240V,the p.d\n",
    "#at the load F is also to be 240V.Calculate the voltages at the feeding point B,the current supplied by each\n",
    "#feeder and the p.d.s at the loads C,D and E.\n",
    "##############################################################################################################\n",
    "\n",
    "#Given\n",
    "V_a = 240.0    #V  \n",
    "V_f = 240.0    #V\n",
    "#loads and their resistances.\n",
    "i_c = 12.0  #A\n",
    "i_d = 24.0  #A\n",
    "i_e = 72.0  #A\n",
    "i_f = 48.0  #A\n",
    "\n",
    "r_ac = 8e-3   #ohm\n",
    "r_cd = 6e-3   #ohm\n",
    "r_de = 4e-3   #ohm\n",
    "r_ef = 10e-3  #ohm\n",
    "r_fb = 5e-3   #ohm\n",
    "\n",
    "#Voltage drop accross AF is zero.Therefore equation 8i +6(i-12) + 4(i-36)+10(i-108)*10^(-3)\n",
    "current_i = (r_cd*i_c + r_de*(i_c+i_d) + r_ef*(i_c+i_d+i_e))/(28.0e-3)   #A\n",
    "#currents in different sections\n",
    "current_ac = current_i        #A\n",
    "current_cd= current_ac-i_c    #A\n",
    "current_de = current_cd-i_d   #A\n",
    "current_ef = current_de-i_e   #A   \n",
    "current_fb = current_ef-i_f   #A\n",
    "#voltage at different points are\n",
    "V_b = V_f - current_fb*r_fb   #V\n",
    "V_c = V_a - current_ac*r_ac   #V\n",
    "V_d = V_c - current_cd*r_cd   #V\n",
    "V_e = V_d - current_de*r_de   #V \n",
    "\n",
    "print \"Current supplied by feeder at point A is\",round(current_ac,2),\"A and that by point B is\",round(abs(current_fb),2),\"A.\"\n",
    "print \"Voltage at point B is = \",round(V_b,2),\"V.\"\n",
    "print \"Voltage at point C is = \",round(V_c,2),\"V.\"\n",
    "print \"Voltage at point D is = \",round(V_d,2),\"V.\"\n",
    "print \"Voltage at point E is = \",round(V_e,2),\"V.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.12 ,Page No :- 1585"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The current supplied at P is =  143.75 A.\n",
      "The current supplied at Q is =  116.25 A.\n",
      "Power dissipated in distributor is = 847.34 W.\n"
     ]
    }
   ],
   "source": [
    "#A two-wire d.c sdistributor PQ,800 metre long is loaded as under:\n",
    "#Distance from P(metres):    100      250      500      600      700\n",
    "#Loads in amperes:            20       80       50       70       40\n",
    "#The feeding point at P is maintained at 248V and that at Q at 245V.The total resistance of\n",
    "#the distributor(lead and return) is 0.1 ohm.Find (a)the current supplied at P and Q and\n",
    "#(b)the power dissipated in the distributor.\n",
    "##################################################################################################\n",
    "\n",
    "#Given\n",
    "V_p  = 248.0     #V\n",
    "V_q  = 245.0     #V\n",
    "res  = 0.1/800    #ohm/m \n",
    "#loads and their positions\n",
    "i1 = 20.0     #A\n",
    "i2 = 80.0     #A\n",
    "i3 = 50.0     #A\n",
    "i4 = 70.0     #A\n",
    "i5 = 40.0     #A\n",
    "l1 = 100.0           #m\n",
    "l2 = 250.0-100.0     #m\n",
    "l3 = 500.0 -250.0    #m\n",
    "l4 = 600.0-500.0     #m\n",
    "l5 = 700.0-600.0     #m\n",
    "l6 = 800.0-700.0     #m\n",
    "#drop accross the distributor :- 1/8000(100i + 150(i-20) + 250(i-100)+ 100(i-150)+100(i-220)+100(i-260) )=3\n",
    "current_i = ((V_p-V_q)/res + l2*i1+l3*(i1+i2)+l4*(i1+i2+i3)+l5*(i1+i2+i3+i4)+l6*(i1+i2+i3+i4+i5))/800.0\n",
    "current_p = current_i       #A\n",
    "current_2 = current_p-i1    #A\n",
    "current_3 = current_2-i2    #A\n",
    "current_4 = current_3-i3    #A\n",
    "current_5 = current_4-i4    #A\n",
    "current_q = current_5-i5    #A\n",
    "#Power loss = sum(I^2R)\n",
    "loss = res*(current_p*current_p*l1 + current_2*current_2*l2 + current_3*current_3*l3 + current_4*current_4*l4 + current_5*current_5*l5 + current_q*current_q*l6)\n",
    "print \"The current supplied at P is = \",round(current_p,2),\"A.\"\n",
    "print \"The current supplied at Q is = \",round(abs(current_q),2),\"A.\"\n",
    "print \"Power dissipated in distributor is =\",round(loss,2),\"W.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.13 ,Page No :- 1586"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The point of minimum potential is D and minimum potential is =  231.76 V.\n",
      "Current fed at the end A is =  366.0 A.\n",
      "Current fed at the end B is =  454.0 A.\n"
     ]
    }
   ],
   "source": [
    "#The two conductors of a d.c distributor cable 1000m long have a total resistance of 0.1 ohm.\n",
    "#The ends A and B are fed at 240V.The cable is uniformly loaded at 0.5 A per metre length\n",
    "#and has concentrated loads of 120A,60A,100A and 40A at points distant 200,400,700 and 900m.\n",
    "#respectively from the end A.Calculate (i)the point of minimum potential on the distributor\n",
    "#(ii)the value of minimum potential and (iii) currents fed at the ends A and B.\n",
    "###############################################################################################\n",
    "\n",
    "#Given\n",
    "V_a = 240.0   #V\n",
    "V_b = 240.0   #V\n",
    "res = 0.1/1000   #ohm/m\n",
    "#concentrated loads and their positions\n",
    "i_c = 120.0       #A\n",
    "i_d = 60.0        #A\n",
    "i_e = 100.0       #A\n",
    "i_f = 40.0        #A\n",
    "l_ac = 200.0      #m\n",
    "l_cd = 400.0-200.0    #m\n",
    "l_de = 700.0-400.0    #m\n",
    "l_ef = 900.0-700.0    #m\n",
    "l_fb = 1000.0-900.0    #m\n",
    "#Uniform loading\n",
    "cur_uni = 0.5     #A/m\n",
    "#Equation for drop from A to B -> (1/10000)*(200i + 200(i-120)+ 300(i-180)+200(i-280)+100(i-320))=0\n",
    "current_i = (l_cd*i_c + l_de*(i_c+i_d)+l_ef*(i_c+i_d+i_e)+l_fb*(i_c+i_d+i_e+i_f))/1000\n",
    "\n",
    "#point of minimum potential\n",
    "current_ac = current_i       #A\n",
    "current_cd = current_ac-i_c    #A\n",
    "current_de = current_cd-i_d    #A\n",
    "current_ef = current_de-i_e    #A\n",
    "current_fb = current_ef-i_f    #A\n",
    "\n",
    "if current_cd>0:\n",
    "    if current_de<0:\n",
    "        point = \"D\"\n",
    "#As from figure it is inferred that point of minimum potential is D.\n",
    "#Therefore,uniform load from point A to D(supplied from A)\n",
    "cur_uni_A = cur_uni*(l_ac + l_cd)    #A\n",
    "cur_A = cur_uni_A + current_ac     #A\n",
    "#Therefore,uniform load from point B to D(supplied from B)\n",
    "cur_uni_B = cur_uni*(l_de + l_ef + l_fb)    #A\n",
    "cur_B = cur_uni_B + abs(current_fb)     #A\n",
    "\n",
    "#drop at D due to concentrated load(from A)\n",
    "drop_con = res*(current_ac*l_ac + current_cd*l_cd)\n",
    "#drop at D due to uniform load(from A)[formula-> irl^2/2]\n",
    "drop_uni = cur_uni*res*(l_ac+l_cd)*(l_ac+l_cd)/2\n",
    "#total drop is\n",
    "drop_tot = drop_con + drop_uni\n",
    "\n",
    "#potential at D is\n",
    "V_d = V_a - drop_tot\n",
    "print \"The point of minimum potential is\",point,\"and minimum potential is = \",round(V_d,2),\"V.\"\n",
    "print \"Current fed at the end A is = \",round(cur_A,2),\"A.\"\n",
    "print \"Current fed at the end B is = \",round(cur_B,2),\"A.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.14 ,Page No :- 1587"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Voltage V is =  8.62 V.\n",
      "Cross-sectional Area A is =  2.78 cm^2.\n",
      "Cross-sectional Area A1 is =  0.26 cm^2.\n",
      "Cross-sectional Area A2 is =  2.24 cm^2.\n"
     ]
    }
   ],
   "source": [
    "#It is proposed to lay out a d.c distribution system comprising three sections-the first section consists\n",
    "#of a cable from the sub-station to a point distant 800 metres from which two cables are taken,one 350 metres\n",
    "#long supplying a load of 22kW and the other 1.5 kilometre long and supplying a load of 44kW.Calculate the\n",
    "#cross-sectional area of each cable so that the total weight of copper required shall be minimum if the maximum\n",
    "#drop of voltage along the cable is not to exceed 5% of the normal voltage of 440V at the consumer's premises.\n",
    "#Take specific resistance of copper at working temperature equal to 2*10e-7 ohm-cm.\n",
    "###################################################################################################################\n",
    "\n",
    "#Given\n",
    "resistivity = 2*10e-7   #ohm-cm\n",
    "dist = 800.0*100          #cm\n",
    "#Current taken from 350m section\n",
    "cur_1 = 22000.0/440\n",
    "#Current taken from 1.5km section\n",
    "cur_2 = 44000.0/440\n",
    "#Therefore,current in first section\n",
    "cur = cur_1 + cur_2\n",
    "#Let us assume\n",
    "#V->voltage drop accross first section\n",
    "#R->resistance of the first section\n",
    "#A->cross-sectional area of te first section\n",
    "\n",
    "from sympy import Eq, var, solve\n",
    "var('V') \n",
    "#Now , R = V/I\n",
    "R = V/cur\n",
    "# A = resistivity*l/R -> A = resistivity*l*I/V \n",
    "A = resistivity*dist/R\n",
    "#Max allowable drop\n",
    "max_drop = (5.0/100)*440.0\n",
    "#Voltage drop along other sections\n",
    "vol_drop = max_drop - V\n",
    "#Cross-sectional area of 350 m   A = resistivity*l/R \n",
    "A1 = resistivity*350.0*100*cur_1/(vol_drop)\n",
    "#Cross-sectional area of 1.5km   A = resistivity*l/R \n",
    "A2 = resistivity*1500.0*100*cur_2/(vol_drop)\n",
    "\n",
    "\n",
    "#Now,Total weight is propotional to total volume \n",
    "W = 800.0*A + 350.0*A1+1500.0*A2\n",
    "Diff = W.diff(V)\n",
    "eq = Eq(Diff,0)\n",
    "\n",
    "V = solve(eq)\n",
    "#We get 2 values of V of which Negative is not possible.Therefore,\n",
    "V = float(V[1])\n",
    "A = resistivity*dist*cur/V\n",
    "vol_drop = max_drop - V\n",
    "A1 = resistivity*350.0*100*cur_1/vol_drop\n",
    "A2 = resistivity*1500.0*100*cur_2/vol_drop\n",
    "print \"Voltage V is = \",round(V,2),\"V.\"\n",
    "print \"Cross-sectional Area A is = \",round(A,2),\"cm^2.\"\n",
    "print \"Cross-sectional Area A1 is = \",round(A1,2),\"cm^2.\"\n",
    "print \"Cross-sectional Area A2 is = \",round(A2,2),\"cm^2.\"\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.15 ,Page No :- 1588"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The point of minimum potential is at 261.74 m from A.\n",
      "The minimum potential is =  247.34 V.\n"
     ]
    }
   ],
   "source": [
    "#A d.c two-wire distributor AB is 450m long and is fed at both ends at 250 volts.It is loaded as follows:20A at 60m from A,\n",
    "#40A at 100m from A and a uniform loading of 1.5A/m from 200 to 450m from A.The resistance of each conductor is\n",
    "#0.05ohm/km.Find the point of minimum potential and its potential.\n",
    "####################################################################################################################\n",
    "\n",
    "#Given\n",
    "V_a = 250.0  #V\n",
    "V_b = 250.0  #V\n",
    "res = 0.05/1000    #ohm/m\n",
    "cur_uni = 1.5      #A/m (uniform loading)\n",
    "#loads and positions\n",
    "i_c = 20.0   #A\n",
    "i_d = 40.0   #A\n",
    "l_ac = 60.0   #m\n",
    "l_cd = 40.0   #m\n",
    "l_de = 100.0  #m\n",
    "l_eb = 250.0  #m\n",
    "\n",
    "#Let us assume that point of minimum potential is D and let i be current in section CD.\n",
    "#Therefore,current from B is (40-i).If r is resistance then\n",
    "#(20+i)*60r + i*40r = (40-i)*350r + 1.5*r*250^2/2   [drop over AD = drop over BD as V_a = V_b]\n",
    "\n",
    "cur_i = (i_d*(l_de+l_eb)*res + cur_uni*res*l_eb*l_eb/2 - i_c*l_ac*res)/((l_ac+l_cd+l_de+l_eb)*res)   #A\n",
    "\n",
    "#cur_i > 40 i.e 40-i is negative,it means D is not point of minimum potential.Let F be point of minimum potential(between DB)\n",
    "#current in section DF is\n",
    "cur_df = cur_i-i_d      #A\n",
    "\n",
    "#distance EF\n",
    "dist_ef = cur_df/cur_uni    #m\n",
    "\n",
    "#distance of F from A is\n",
    "dist = l_ac + l_cd + l_de + dist_ef   #m\n",
    "\n",
    "#total drop over AF is [(20+i)*60r + i*40r+ (i-40)*161.7r - 1.5*r*61.7^2/2\n",
    "drop_af = 2*res*((i_c+cur_i)*l_ac + cur_i*l_cd + cur_df*(l_de+dist_ef)-cur_uni*dist_ef*dist_ef/2)  #V\n",
    "#potential at F\n",
    "V_f = V_a - drop_af      #V\n",
    "print \"The point of minimum potential is at\",round(dist,2),\"m from A.\"\n",
    "print \"The minimum potential is = \",round(V_f,2),\"V.\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.16 ,Page No :- 1588"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current fed at A is =  225.0 A.\n",
      "Current fed at B is =  475.0 A.\n",
      "Point of minimum potential from B is =  475.0 metres.\n",
      "Voltage at minimum potential is =  230.72 V.\n"
     ]
    }
   ],
   "source": [
    "#A two-wire d.c distributor AB,1000 metres long,is supplied from both ends,240V at A and 242V at B.There is a\n",
    "#concentrated load of 200A at a distance of 400 metre from A and a uniformly distrubuted load of 1.0A/m between\n",
    "#the mid-point and end B.Determine (i)the currents fed at A and B(ii)the point of minimum potential and\n",
    "#(iii)voltage at this point.Take cable resistance as 0.005 ohm per 100 metre each core.\n",
    "#####################################################################################################################\n",
    "\n",
    "#Given\n",
    "#resistance per 100 metres\n",
    "res = 2*0.005/100         #ohm/m\n",
    "cur_uni = 1.0           #A/m\n",
    "cur_con = 200.0         #A\n",
    "len_uni = 500.0\n",
    "#Let us assume that Ib current flows from point B.\n",
    "#Considering a element dx in BD(500 metres) at a distance of X units(100 m each)\n",
    "#voltage drop over dx = (1-100*x)*res*dx\n",
    "#voltage drop over BD by integrating is = 0.05*Ib - 12.5\n",
    "#voltage drop over DC = (Ib-500)*0.01\n",
    "#voltage drop over CA = (Ib-700)*0.01*4\n",
    "#total drop over AB = \n",
    "tot_drop = 242.0-240.0\n",
    "#summation of drops from AC + CD + DB\n",
    "from sympy import Eq, var, solve\n",
    "var('Ib') \n",
    "sum =  (Ib-500)*0.01 +(Ib-700)*0.01*4 + 0.05*Ib - 12.5\n",
    "\n",
    "eq = Eq(sum,tot_drop)\n",
    "\n",
    "Ib =  solve(eq)\n",
    "Ib = float(Ib[0])\n",
    "#Total current\n",
    "cur_tot = len_uni*cur_uni + cur_con\n",
    "Ia = cur_tot - Ib                 #A\n",
    "#Current in distributed load\n",
    "cur_dis = Ia-cur_con              #A\n",
    "#point of minimum potential from D is\n",
    "distD = cur_dis/cur_uni\n",
    "#Therefore distance from B is\n",
    "distB = len_uni-distD\n",
    "#Therefore voltage drop is\n",
    "from scipy.integrate import quad\n",
    "\n",
    "def integrand(x):\n",
    "    return (Ib-100*x)*res*100\n",
    "\n",
    "ans, err = quad(integrand, 0, (distB/100))\n",
    "#Therefore potential of M is\n",
    "pot_M = 242.0-ans     #V\n",
    "print \"Current fed at A is = \",Ia,\"A.\"\n",
    "print \"Current fed at B is = \",Ib,\"A.\"\n",
    "print \"Point of minimum potential from B is = \",distB,\"metres.\"\n",
    "print \"Voltage at minimum potential is = \",round(pot_M,2),\"V.\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.17 ,Page No :- 1590"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Voltage at B is =  236.9 V.\n",
      "Voltage at C is =  235.98 V.\n",
      "Voltage at D is =  237.45 V.\n"
     ]
    }
   ],
   "source": [
    "#A 400-metre ring distributor has loads as shown in Fig. 40.29(a) where distances are in metres.The resistance\n",
    "#of each conductor is 0.2 ohm per 1000 metres and the loads tapped off at points B,C,D are as shown.If the\n",
    "#distributor is fed at A,find voltages at B,C and D.\n",
    "#################################################################################################################\n",
    "\n",
    "#Given\n",
    "\n",
    "res = 0.2/1000   #ohm/m\n",
    "V_a = 240.0       #V\n",
    "#loads and positions\n",
    "i_b = 100.0  #A\n",
    "i_c = 70.0   #A\n",
    "i_d = 50.0   #A\n",
    "l_ab = 60.0   #m\n",
    "l_bc = 80.0   #m\n",
    "l_cd = 90.0   #m\n",
    "l_da = 70.0   #m\n",
    "\n",
    "#total drop ->70i + 90(i-50)+80(i-120)+60(i-220)=0\n",
    "cur_i = (l_cd*i_d + l_bc*(i_d+i_c) + l_ab*(i_d+i_c+i_b))/(l_ab+l_bc+l_cd+l_da)\n",
    "#drops in different sections\n",
    "drop_da = 2*cur_i*l_da*res\n",
    "drop_cd = 2*(cur_i-i_d)*l_cd*res\n",
    "drop_bc = 2*abs(cur_i-i_d-i_c)*l_bc*res\n",
    "drop_ab = 2*abs(cur_i-i_d-i_c-i_b)*l_ab*res\n",
    "\n",
    "#voltages at different points\n",
    "V_d = V_a - drop_da\n",
    "V_c = V_d - drop_cd\n",
    "V_b = V_a - drop_ab\n",
    "print \"Voltage at B is = \",round(V_b,2),\"V.\"\n",
    "print \"Voltage at C is = \",round(V_c,2),\"V.\"\n",
    "print \"Voltage at D is = \",round(V_d,2),\"V.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.18 ,Page No :- 1591"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Voltage at B is =  394.2 V.\n",
      "Voltage at C is =  393.42 V.\n",
      "Current in section BC is =  43.33 A.\n"
     ]
    }
   ],
   "source": [
    "#In a direct current ring main,a voltage of 400V is maintained at A.At B,500 metres away from A,a load of 150A is taken\n",
    "#and at C,300 metres from B,a load of 200A is taken.The distance between A and C is 700 metres.The resistance of each\n",
    "#conductor of the mains is 0.03ohm per 1000 metres.Find the voltage at B and C and also find the current in the section BC.\n",
    "##############################################################################################################################\n",
    "\n",
    "#Given\n",
    "V_a = 400.0    #V\n",
    "res = 0.03/1000   #ohm/m\n",
    "#loads and positions\n",
    "i_b = 150.0    #A\n",
    "i_c = 200.0    #A\n",
    "l_ab = 500.0   #m\n",
    "l_bc = 300.0   #m\n",
    "l_ca = 700.0   #m\n",
    "\n",
    "#total drop-> 500i + 300(i-150) + 700(i-350) = 0\n",
    "cur_i = (l_bc*i_b + l_ca*(i_b+i_c))/(l_ab+l_bc+l_ca)\n",
    "#current in different sections\n",
    "cur_ab = cur_i\n",
    "cur_bc = cur_i-i_b\n",
    "cur_ca = abs(cur_bc-i_c)\n",
    "#drops in different sections\n",
    "drop_ab = 2*cur_ab*l_ab*res\n",
    "drop_bc = 2*cur_bc*l_bc*res\n",
    "#voltages in different sections\n",
    "V_b = V_a-drop_ab\n",
    "V_c = V_b-drop_bc\n",
    "print \"Voltage at B is = \",round(V_b,2),\"V.\"\n",
    "print \"Voltage at C is = \",round(V_c,2),\"V.\"\n",
    "print \"Current in section BC is = \",round(cur_bc,2),\"A.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.19 ,Page No :- 1591"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current in AB,BC,CD,DE,EA is 29.04 A, 19.04 A, 0.96 A, 30.96 A, 40.96 A respectively.\n",
      "\n",
      "Voltage at B,C,D,E is 217.1 V, 216.14 V, 216.15 V, 216.93 V respectively\n",
      "\n",
      "Current in AB,BC,DE,CE,EA is 27.72 A, 17.72 A, 32.28 A, 9.76 A, 42.28 A respectively.\n",
      "\n",
      "Voltage at B,C,D,E is 217.23 V, 216.34 V, 216.02 V, 216.83 V respectively\n"
     ]
    }
   ],
   "source": [
    "#A d.c ring main ABCDE is fed at point A from a 220-V supply and the resistances(including both lead and return)\n",
    "#of the various sections are as follows(in ohms):AB=0.1;BC=0.05;CD=0.01;DE=0.025 and EA=0.075.The main supplies\n",
    "#loads of 10A at B; 20A at C; 30A at D and 10A at E.Find the magnitude and direction of the current flowing in each\n",
    "#section and the voltage at each load point.\n",
    "#If the points C and E are further linked together by a conductor of 0.05 ohm resistance and the output currents\n",
    "#from the mains remain unchanged,find the new distribution of the current and voltage in the network.\n",
    "#####################################################################################################################\n",
    "\n",
    "#Given\n",
    "\n",
    "V_a = 220.0      #V\n",
    "#resistances of different sections\n",
    "r_ab = 0.1      #ohm\n",
    "r_bc = 0.05     #ohm\n",
    "r_cd = 0.01     #ohm\n",
    "r_de = 0.025    #ohm\n",
    "r_ea = 0.075    #ohm\n",
    "#loads\n",
    "i_b = 10.0    #A\n",
    "i_c = 20.0    #A\n",
    "i_d = 30.0    #A\n",
    "i_e = 10.0    #A\n",
    "#total drop -> 0.1i + 0.05(i-10) + 0.01(i-30) + 0.025(i-60) + 0.075(i-70)=0\n",
    "cur_i = (r_bc*i_b + r_cd*(i_b+i_c) + r_de*(i_b+i_c+i_d) + r_ea*(i_b+i_c+i_d+i_e))/(r_ab+r_bc+r_cd+r_de+r_ea)\n",
    "#current in different sections\n",
    "cur_ab = cur_i\n",
    "cur_bc = cur_ab-i_b\n",
    "cur_cd = cur_bc-i_c\n",
    "cur_de = cur_cd-i_d\n",
    "cur_ea = cur_de-i_e\n",
    "\n",
    "#drops in different sections\n",
    "drop_ab = cur_ab*r_ab\n",
    "drop_bc = cur_bc*r_bc\n",
    "drop_de = abs(cur_de)*r_de\n",
    "drop_ea = abs(cur_ea)*r_ea\n",
    "#voltages at different points\n",
    "V_b = V_a - drop_ab\n",
    "V_c = V_b - drop_bc\n",
    "V_e = V_a - drop_ea\n",
    "V_d = V_e - drop_de\n",
    "print \"Current in AB,BC,CD,DE,EA is\",round(cur_ab,2),\"A,\",round(cur_bc,2),\"A,\",round(abs(cur_cd),2),\"A,\",round(abs(cur_de),2),\"A,\",round(abs(cur_ea),2),\"A respectively.\" \n",
    "print \"\"\n",
    "print \"Voltage at B,C,D,E is\",round(V_b,2),\"V,\",round(V_c,2),\"V,\",round(V_d,2),\"V,\",round(V_e,2),\"V respectively\"\n",
    "print \"\"\n",
    "#part-2\n",
    "#Potential difference between end points of interconnector(CE)\n",
    "V_ce = V_e-V_c\n",
    "#Resistance between CE ,as shown in figure\n",
    "r1 = r_ab+r_bc+r_ea\n",
    "r2 = r_de + r_cd\n",
    "res_ce = r1*r2/(r1+r2)+ 0.05\n",
    "\n",
    "#Current in interconnector [I = V/R Ohm's Law]\n",
    "cur_ce = V_ce/res_ce\n",
    "#Current goes from E to C as E is at higher potential.\n",
    "\n",
    "#The current in other sections will also change.\n",
    "#let us assume i1 along ED, voltage round the closed mesh EDC is zero.\n",
    "#total drop -> -0.025*i1-0.01*(i1-30)+0.05*9.75 = 0\n",
    "\n",
    "cur_i1 = (0.05*cur_ce + r_cd*i_d)/(r_cd+r_de)\n",
    "\n",
    "current_ea = i_e+cur_i1+cur_ce\n",
    "current_ab = (i_b+i_c+i_d+i_e)-current_ea\n",
    "current_bc = current_ab-i_b\n",
    "current_de = current_ea-i_e\n",
    "#new drops\n",
    "drop_ab = current_ab*r_ab\n",
    "drop_bc = current_bc*r_bc\n",
    "drop_ea = current_ea*r_ea\n",
    "drop_de = current_de*r_de\n",
    "\n",
    "#new potentials\n",
    "V_b = V_a - drop_ab\n",
    "V_c = V_b - drop_bc\n",
    "V_e = V_a - drop_ea\n",
    "V_d = V_e - drop_de\n",
    "\n",
    "print \"Current in AB,BC,DE,CE,EA is\",round(current_ab,2),\"A,\",round(current_bc,2),\"A,\",round(current_de,2),\"A,\",round(cur_ce,2),\"A,\",round(current_ea,2),\"A respectively.\"\n",
    "print \"\"\n",
    "print \"Voltage at B,C,D,E is\",round(V_b,2),\"V,\",round(V_c,2),\"V,\",round(V_d,2),\"V,\",round(V_e,2),\"V respectively\"                                 \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.20 ,Page No :- 1594"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Voltage across 3 ohm load is =  244.9 V.\n",
      "Voltage across 4 ohm load is =  247.9 V.\n"
     ]
    }
   ],
   "source": [
    "#In a 3-wire distribution system,the supply voltage is 250V on each side.The load on one side is a 3 ohm\n",
    "#resistance and on the other, a 4 ohm resistance.The resistance of each of the 3 conductors is 0.05 ohm.\n",
    "#Find the load voltages.\n",
    "#########################################################################################################\n",
    "\n",
    "import numpy as np\n",
    "#Given\n",
    "#Resistances\n",
    "res_1 = 3.0   #ohm\n",
    "res_2 = 4.0   #ohm\n",
    "res_con = 0.05 #ohm\n",
    "V_sup = 250.0  #V\n",
    "\n",
    "#Let the assumed directions of unknown currents be as shown in figure.\n",
    "#KVL for ABCD\n",
    "# (3+0.05)x + 0.05(x-y) = 250  -------------- eqn 1\n",
    "a = res_1 + 2*res_con\n",
    "b = -(res_con)\n",
    "#KVL for DCEFD\n",
    "# 0.05(y-x) + (4+0.05)y = 250  -------------- eqn 2\n",
    "c = res_2+ 2*res_con       \n",
    "#Solving eqn 1 and eqn2\n",
    "m = [[a,b],[b,c]]\n",
    "n = [V_sup,V_sup]\n",
    "soln = np.linalg.solve(m,n)            #soln is array with its elements[x,y]\n",
    "#Calculating the load voltages\n",
    "#V1 = 250-0.05*x-0.05(x-y)\n",
    "vol1 = V_sup - res_con*soln[0]-res_con*(soln[0]-soln[1])    #V\n",
    "#V2 = 250 + 0.05(x-y)- 0.05y\n",
    "vol2 = V_sup + res_con*(soln[0]-soln[1]) - res_con*soln[1]  #V\n",
    "print \"Voltage across 3 ohm load is = \",round(vol1,1),\"V.\"\n",
    "print \"Voltage across 4 ohm load is = \",round(vol2,1),\"V.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.21 ,Page No :- 1594"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Potential Difference across AB is =  248.62 V.\n",
      "Potential Difference across QK is =  247.83 V.\n",
      "Potential Difference across CD is =  248.4 V.\n",
      "Potential Difference across FE is =  247.65 V.\n"
     ]
    }
   ],
   "source": [
    "#A 3-wire d.c distributor PQ,250 metres long,is supplied at end P at 500/250V and is loaded as under:\n",
    "#Positive side: 20A 150 metres from P ; 30A 250 metres from P.\n",
    "#Negative side: 24A 100 metres from P ; 36A 220 metres from P.\n",
    "#The resistance of each outer wire is 0.02 ohm per 100 metres and the cross-section of the middle wire\n",
    "#is one-half of the outer.Find the voltage across each load point.\n",
    "##########################################################################################################\n",
    "\n",
    "#Given\n",
    "V_PN = 250.0 #V\n",
    "V_NR = 250.0 #V\n",
    "res_out = 0.02/100      #ohm/m\n",
    "res_mid = 2*res_out       #ohm/m  (Area of middle wire is half.As, R = rho*l/A .Therefore,Resistance doubles)\n",
    "\n",
    "#Given Currents\n",
    "i_ab = 20.0  #A\n",
    "i_qk = 30.0  #A\n",
    "i_cd = 24.0  #A\n",
    "i_fe = 36.0  #A\n",
    "\n",
    "#Currents in different sections\n",
    "i_pa = i_ab+i_qk   #A\n",
    "i_aq = i_qk        #A\n",
    "i_fk = i_qk        #A\n",
    "i_bf = i_fe-i_qk   #A\n",
    "i_bc = i_ab-i_bf   #A\n",
    "i_cn = i_cd-i_bc   #A\n",
    "i_de = i_fe        #A\n",
    "i_dr = i_cd+i_fe   #A\n",
    "\n",
    "\n",
    "#lengths of different sections\n",
    "l_pa = 150.0 #m\n",
    "l_aq = 100.0 #m\n",
    "l_kf = 250.0-220.0 #m\n",
    "l_bc = 150.0-100.0 #m\n",
    "l_bf = 220.0-150.0 #m\n",
    "l_cn = 100.0 #m\n",
    "l_de = 220.0-100.0 #m\n",
    "l_dr = 100.0  #m\n",
    "\n",
    "#Resistances of different sections\n",
    "r_pa = l_pa*res_out #ohm\n",
    "r_aq = l_aq*res_out #ohm\n",
    "r_kf = l_kf*res_mid #ohm\n",
    "r_bc = l_bc*res_mid #ohm\n",
    "r_bf = l_bf*res_mid #ohm\n",
    "r_cn = l_cn*res_mid #ohm\n",
    "r_de = l_de*res_out #ohm\n",
    "r_dr = l_dr*res_out #ohm\n",
    "\n",
    "#Drop across different sections\n",
    "drop_pa = r_pa*i_pa #V\n",
    "drop_aq = r_aq*i_aq #V\n",
    "drop_kf = r_kf*i_fk #V\n",
    "drop_bc = r_bc*i_bc #V\n",
    "drop_bf = r_bf*i_bf #V\n",
    "drop_cn = r_cn*i_cn #V\n",
    "drop_de = r_de*i_de #V\n",
    "drop_dr = r_dr*i_dr #V\n",
    "\n",
    "#Voltages across different sections\n",
    "vol_ab = V_PN - drop_pa - drop_bc + drop_cn       #V\n",
    "vol_qk = vol_ab - drop_aq - drop_kf + drop_bf     #V\n",
    "vol_cd = V_NR - drop_cn - drop_dr                 #V  \n",
    "vol_fe = vol_cd + drop_bc - drop_bf - drop_de     #V\n",
    "\n",
    "print \"Potential Difference across AB is = \",round(vol_ab,2),\"V.\"\n",
    "print \"Potential Difference across QK is = \",round(vol_qk,2),\"V.\"\n",
    "print \"Potential Difference across CD is = \",round(vol_cd,2),\"V.\"\n",
    "print \"Potential Difference across FE is = \",round(vol_fe,2),\"V.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.22 ,Page No :- 1597"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total load on main generator is =  155.0 kW.\n",
      "Load on Balancer 1 is =  22.5 kW.\n",
      "Load on Balancer 2 is =  27.5 kW.\n"
     ]
    }
   ],
   "source": [
    "#A d.c 3-wire system with 500-V between outers has lighting load of 100kW on the positive and 50kW on the\n",
    "#negative side.If,at this loading,the balancer machines have each a loss of 2.5kW,Calculate the kW loading\n",
    "#of each balancer machine and the total load on the system.\n",
    "###########################################################################################################\n",
    "\n",
    "#Given\n",
    "V_out = 500.0  #V\n",
    "load_p = 100.0 #kW (positive side)\n",
    "load_n = 50.0  #KW (negative side)\n",
    "load_b = 2.5   #kW  (balancer machine)\n",
    "#total load on main generator\n",
    "load_tot = load_p + load_n + 2*load_b  #kW\n",
    "#Output current of main generator\n",
    "cur_out = load_tot*1000/V_out   #W/V->A\n",
    "#load current on positive side\n",
    "cur_p = load_p*1000/(V_out/2)  #A\n",
    "#load current on negative side\n",
    "cur_n = load_n*1000/(V_out/2)  #A\n",
    "#Current through neutral(Out of balance)\n",
    "cur_o = cur_p-cur_n     #A\n",
    "\n",
    "#Currents of balancer\n",
    "cur_b1 = cur_p-cur_out  #A\n",
    "cur_b2 = cur_o - cur_b1 #A\n",
    "\n",
    "#Load on balancer\n",
    "load_b1 = (V_out/2)*cur_b1/1000    #kW\n",
    "load_b2 = (V_out/2)*cur_b2/1000    #kW\n",
    "\n",
    "print \"Total load on main generator is = \",round(load_tot,2),\"kW.\"\n",
    "print \"Load on Balancer 1 is = \",round(load_b1,2),\"kW.\"\n",
    "print \"Load on Balancer 2 is = \",round(load_b2,2),\"kW.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.23 ,Page No :- 1598"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total load on main generator is =  1216.0 kW.\n",
      "Current through Balancer 1 is =  168.0 A.\n",
      "Current through Balancer 2 is =  232.0 A.\n"
     ]
    }
   ],
   "source": [
    "#In a 500/250-V d.c 3-wire system,there is a current of 2000A on the +ve side, 1600A on the negative side\n",
    "#and a load of 300 kW across the outers.The loss in each balancer set is 8 kW.Calculate the current in each\n",
    "#armature of the balancer set and total load on the main generator.\n",
    "#############################################################################################################\n",
    "\n",
    "#Given\n",
    "V_out    = 500.0  #V\n",
    "cur_p    = 2000.0 #A (current on positive side)\n",
    "cur_n    = 1600.0 #A (current on negative side)\n",
    "load_ext = 300.0 #kW (across outers)\n",
    "load_b   = 8.0   #kW  (loss in balancer set)\n",
    "#loading on positive side\n",
    "load_p = (cur_p*(V_out/2))/1000  #kW\n",
    "#loading on negative side\n",
    "load_n = (cur_n*(V_out/2))/1000  #kW\n",
    "#Total loading on main generator\n",
    "load_tot = load_p + load_n + 2*load_b + load_ext   #kW\n",
    "\n",
    "#current on main generator -> I = W/V\n",
    "cur_tot = load_tot*1000/V_out     #A\n",
    "\n",
    "#current through neutral(out of balance)\n",
    "cur_o = cur_p-cur_n    #A\n",
    "\n",
    "#current through external resistance\n",
    "cur_ext = load_ext*1000/V_out    #A\n",
    "\n",
    "#current through balancer sets\n",
    "cur_b1 = (cur_p+cur_ext)-cur_tot      #A\n",
    "cur_b2 = cur_o - cur_b1               #A\n",
    "\n",
    "print \"Total load on main generator is = \",round(load_tot,2),\"kW.\"\n",
    "print \"Current through Balancer 1 is = \",round(cur_b1,2),\"A.\"\n",
    "print \"Current through Balancer 2 is = \",round(cur_b2,2),\"A.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.24 ,Page No :- 1598"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current supplied by generator is =  7000.0 A.\n",
      "Current in positive side is =  6000.0 A.\n",
      "Current in negative side is =  8000.0 A.\n",
      "Current in neutral is =  2000.0 A.\n",
      "Current through armature 1 is =  1000.0 A.\n",
      "Current through armature 2 is =  1000.0 A.\n"
     ]
    }
   ],
   "source": [
    "#On a 3-wire d.c distribution system with 500V between outers,there is a load of 1500kW on the positive\n",
    "#side and 2000 kW on the negative side.Calculate the current in the neutral and in each of the balancer\n",
    "#armatures and the total current supplied by the generator.Neglect losses.\n",
    "##########################################################################################################\n",
    "\n",
    "#Given\n",
    "V_out = 500.0    #V\n",
    "load_p = 1500.0  #kW   (load on positive side)\n",
    "load_n = 2000.0  #kW   (load on negative side)\n",
    "#total loading on main generator\n",
    "load_tot = load_p + load_n    #kW\n",
    "#current supplied by generator\n",
    "cur_tot = load_tot*1000/V_out    #A\n",
    "#current on positive side\n",
    "cur_p = load_p*1000/(V_out/2)    #A\n",
    "#current on negative side\n",
    "cur_n = load_n*1000/(V_out/2)    #A\n",
    "#current in neutral(out of balance)\n",
    "cur_o = abs(cur_p-cur_n)   #A\n",
    "#current through armatures\n",
    "cur_b1 = cur_tot-cur_p  #A\n",
    "cur_b2 = cur_o-cur_b1   #A\n",
    "\n",
    "print \"Current supplied by generator is = \",cur_tot,\"A.\"\n",
    "print \"Current in positive side is = \",cur_p,\"A.\"\n",
    "print \"Current in negative side is = \",cur_n,\"A.\"\n",
    "print \"Current in neutral is = \",cur_o,\"A.\"\n",
    "print \"Current through armature 1 is = \",cur_b1,\"A.\"\n",
    "print \"Current through armature 2 is = \",cur_b2,\"A.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.25 ,Page No :- 1599"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current in balancer set 1 is =  22.0 A.\n",
      "Current in balancer set 2 is =  28.0 A.\n",
      "Output of main generator is =  119.5 kW.\n"
     ]
    }
   ],
   "source": [
    "#A 125/250 V,3-wire distributor has an out-of-balance current of 50 A and larger load of 500 A.The balancer\n",
    "#set has a loss of 375 W in each machine.Calculate the current in each of the balancer machines and output\n",
    "#of main generator.\n",
    "############################################################################################################\n",
    "\n",
    "#Given\n",
    "V_out = 250.0    #V\n",
    "#Currents\n",
    "cur_p = 500.0  #A\n",
    "cur_o = 50.0   #A\n",
    "cur_n = cur_p - cur_o  #A\n",
    "#larger Load\n",
    "load_p = cur_p*(V_out/2)/1000   #kW\n",
    "#smaller Load\n",
    "load_n = cur_n*(V_out/2)/1000   #kW\n",
    "#Balancer loss\n",
    "loss_b = 2*375.0/1000     #kW\n",
    "#total load on generator\n",
    "load_tot = load_p + load_n + loss_b\n",
    "#current from main generator -> VI = W\n",
    "cur_tot = load_tot*1000/V_out   #A\n",
    "\n",
    "#Current in balancer sets\n",
    "cur_b1 = cur_p - cur_tot     #A\n",
    "cur_b2 = cur_o - cur_b1      #A\n",
    "print \"Current in balancer set 1 is = \",cur_b1,\"A.\"\n",
    "print \"Current in balancer set 2 is = \",cur_b2,\"A.\"\n",
    "print \"Output of main generator is = \",load_tot,\"kW.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.26 ,Page No :- 1599"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total load on main generator is =  1210.0 kW.\n",
      "Load on Balancer set 1 is =  20.0 kW.\n",
      "Load on balancer set 2 is =  30.0 kW.\n"
     ]
    }
   ],
   "source": [
    "#The load on d.c 3-wire system with 500 V between outers consists of lighting current of 1500 A on the\n",
    "#positive side and 1300 A on the negative side while motors connected across the outers absorb 500kW.\n",
    "#Assuming that at this loading,the balancer machines have each a loss of 5kW,calculate the load on the\n",
    "#main generator and on each of the balancer machines.\n",
    "##########################################################################################################\n",
    "\n",
    "#Given\n",
    "cur_p = 1500.0   #A\n",
    "cur_n = 1300.0   #A\n",
    "V_out = 500.0    #V\n",
    "load_ext = 500.0   #kW\n",
    "loss_b = 2*5.0     #kW\n",
    "\n",
    "#current through external load\n",
    "cur_ext = load_ext*1000/V_out   #A\n",
    "#larger load\n",
    "load_p = cur_p*(V_out/2)/1000   #kW\n",
    "#smaller load\n",
    "load_n = cur_n*(V_out/2)/1000   #kW\n",
    "#total load on generator\n",
    "load_tot = load_p + load_n + loss_b + load_ext   #kW\n",
    "#current from generator -> VI = W\n",
    "cur_tot = load_tot*1000/V_out     #A\n",
    "#current through neutral(out of balance)\n",
    "cur_o = cur_p-cur_n      #A\n",
    "#current through balancer sets\n",
    "cur_b1 = (cur_p+cur_ext)-cur_tot   #A\n",
    "cur_b2 = cur_o-cur_b1              #A\n",
    "#load of balancer sets\n",
    "load_b1 = cur_b1*(V_out/2)/1000    #kW\n",
    "load_b2 = cur_b2*(V_out/2)/1000    #kW\n",
    "\n",
    "print \"Total load on main generator is = \",load_tot,\"kW.\"\n",
    "print \"Load on Balancer set 1 is = \",load_b1,\"kW.\"\n",
    "print \"Load on balancer set 2 is = \",load_b2,\"kW.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.27 ,Page No :- 1599"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Voltage across Balancer 1 is =  230.0 A.\n",
      "Voltage across Balancer 2 is =  250.0 A.\n",
      "Load current on main generator is =  1110.0 A.\n"
     ]
    }
   ],
   "source": [
    "#A d.c 3-wire system with 480 V across outers supplies 1200 A on the positive and 1000 A on the negative side.\n",
    "#The balancer machines have each an armature resistances of 0.1W and take 10 A on no-load.Find\n",
    "#(a)the voltage across each balancer and\n",
    "#(b)the total load on the main generator and the current loading of each balancer machine.\n",
    "#The balancer field windings are in series across the outers\n",
    "################################################################################################################\n",
    "\n",
    "#Given\n",
    "V_out = 480.0   #V\n",
    "#currents\n",
    "cur_p = 1200.0  #A\n",
    "cur_n = 1000.0  #A\n",
    "cur_o = cur_p - cur_n  #A (out of balance)\n",
    "#armature resistance \n",
    "res_arm = 0.1    #ohm\n",
    "#no-load current\n",
    "cur_nold = 10.0   #A\n",
    "\n",
    "#Let us assume current Im flows through mtoring machine,then (200-Im) flows through generating machine.\n",
    "#Let Vg and Vm be potential difference of 2 machines.\n",
    "\n",
    "#Total losses in sets = no-load losses + Cu losses in two machines\n",
    "#loss_set = V_out*cur_nold  + 0.1*Im^2+ 0.1*(200-Im)^2\n",
    "#Vm*Im = Vg*Ig + loss_set\n",
    "#Now, Vm = Eb+Im*Ra           Vg = Eb-Ig*Ra\n",
    "Eb = V_out/2-res_arm*cur_nold\n",
    "\n",
    "#Therefore, Vm = 239 + Im*0.1              and Vg = 239 - (200-Im)*0.1\n",
    "#Hence,Equation is \n",
    "#(239+0.1*Im)*Im = [239 - (200-Im)*0.1]*(200-Im) + loss_set\n",
    "#Simplified ->  239Im = 239*(200-Im)+4800\n",
    "\n",
    "#Solving this equation\n",
    "from sympy import Eq, var, solve\n",
    "var('Im')    \n",
    "eq = Eq(Eb*(2*Im-cur_o),V_out*cur_nold)\n",
    "Im =  solve(eq)\n",
    "Im = int(Im[0])\n",
    "Ig = cur_o-Im\n",
    "#Voltage across balancers\n",
    "\n",
    "Vm = Eb + Im*res_arm     #V\n",
    "Vg = Eb - Ig*res_arm     #V \n",
    "\n",
    "#Load on main generator\n",
    "cur_load = cur_p - Ig    #A\n",
    "print \"Voltage across Balancer 1 is = \",round(Vg,2),\"A.\"\n",
    "print \"Voltage across Balancer 2 is = \",round(Vm,2),\"A.\"\n",
    "print \"Load current on main generator is = \",round(cur_load,2),\"A.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.28 ,Page No :- 1600"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Voltage on positive side is =  283.0 V.\n",
      "Voltage on negative side is =  177.0 V.\n"
     ]
    }
   ],
   "source": [
    "#A d.c 3-wire system with 460V between outers supplies 250kW on the positive and 400kW on the negative side,\n",
    "#the voltages being balanced.Calculate the voltage on the positive and negative side,the voltages being balanced.\n",
    "#Calculate the voltage on the positive and negative sides repectively,if the neutral wire becomes disconnected\n",
    "#from balancer set.\n",
    "#################################################################################################################\n",
    "\n",
    "#Given\n",
    "V_mid = 230.0   #V\n",
    "V_out = 460.0   #V\n",
    "#loads\n",
    "load_p = 250.0  #kW\n",
    "load_n = 400.0  #kW\n",
    "#resistance on positive side -> (V^2/R) = W\n",
    "res_p = (V_mid*V_mid)/(load_p*1000)    #ohm\n",
    "\n",
    "#resistance on negative side -> (V^2/R) = W\n",
    "res_n = (V_mid*V_mid)/(load_n*1000)    #ohm\n",
    "\n",
    "#Voltages after disconnecting balancer set\n",
    "vol_p = (res_p/(res_p+res_n))*V_out      #V\n",
    "vol_n = V_out - vol_p        #V\n",
    "\n",
    "print \"Voltage on positive side is = \",round(vol_p),\"V.\"\n",
    "print \"Voltage on negative side is = \",round(vol_n),\"V.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EXAMPLE 40.29 ,Page No :- 1601"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal potential difference of the booster is =  180.0 V.\n",
      "Output of booster is =  21.6 kW.\n"
     ]
    }
   ],
   "source": [
    "#A 2-wire system has the voltage at the supply end maintained at 500.The line is 3 km long.If the full-load\n",
    "#current is 120 A,what must be the booster voltage and output in order that the far end voltage may also be 500 V.\n",
    "#Take the resistance of the cable at the working temperature as 0.5ohm/kilometre.\n",
    "####################################################################################################################\n",
    "\n",
    "#Total resistance of line\n",
    "res_tot = 0.5*3     #ohm\n",
    "#Full load current\n",
    "cur_full = 120.0    #A\n",
    "\n",
    "#drop in the line-> V=IR\n",
    "drop = res_tot*cur_full   #V\n",
    "\n",
    "#Output of booster ->VI = W\n",
    "output = drop*cur_full/1000   #kW\n",
    "\n",
    "print \"Terminal potential difference of the booster is = \",drop,\"V.\"\n",
    "print \"Output of booster is = \",round(output,2),\"kW.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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