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A Elements_of_electrical_science_by_Mukopadhyay,_Pant/Chapter2.ipynb A Elements_of_electrical_science_by_Mukopadhyay,_Pant/Chapter3.ipynb A Elements_of_electrical_science_by_Mukopadhyay,_Pant/Chapter4.ipynb A Elements_of_electrical_science_by_Mukopadhyay,_Pant/Chapter5.ipynb A Elements_of_electrical_science_by_Mukopadhyay,_Pant/Chapter6.ipynb A Elements_of_electrical_science_by_Mukopadhyay,_Pant/Chapter7.ipynb A Elements_of_electrical_science_by_Mukopadhyay,_Pant/screenshots/chapter2.png A Elements_of_electrical_science_by_Mukopadhyay,_Pant/screenshots/chapter3.png A Elements_of_electrical_science_by_Mukopadhyay,_Pant/screenshots/chapter4.png A sample_notebooks/Harshitgarg/Chapter_1-INTRODUCTION_TO_MECHANICS_OF_SOLIDS__1.ipynb
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 6 : Rotating electrical machine"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1 : pg 105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Terminal voltage,(V) = 459.25\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.1# Terminal voltage \n",
+ "#calculate the terminal voltage\n",
+ "#given data :\n",
+ "Z=440.;# number of lap\n",
+ "N=900.;# revolutions in rpm\n",
+ "fi=0.07;#fluxin Wb\n",
+ "P=4.;# number of pole\n",
+ "A=4.;#constant\n",
+ "Ia=50.;# armature current in Amperes\n",
+ "E=462.;#voltage in V\n",
+ "#calculations\n",
+ "E=(P*fi*Z*N)/(60*A);#general voltage in volts\n",
+ "R=0.002;# resistance in ohm\n",
+ "C=110.;# conductors\n",
+ "Re=C*R;#resistance of each path in ohm\n",
+ "Ra=Re/A;#armature resistance in ohm\n",
+ "V=E-(Ia*Ra);#terminal voltage in volts\n",
+ "#results\n",
+ "print \"Terminal voltage,(V) = \",V"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2 : pg 105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "emf when machine acts as generator,(V) = 205.0\n",
+ "emf when machine acts as motor,(V) = 195.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.2# e.m.f \n",
+ "#calculate the emf in all cases\n",
+ "#given data :\n",
+ "V=200.;#voltage\n",
+ "Ra=0.1;#resistance in ohm\n",
+ "Ia=50.;#armature current in Amperes\n",
+ "#calculations\n",
+ "E=V+(Ia*Ra);#generator voltage in volts\n",
+ "Eb=V-(Ia*Ra);#motor voltage in volts\n",
+ "#results\n",
+ "print \"emf when machine acts as generator,(V) = \",E\n",
+ "print \"emf when machine acts as motor,(V) = \",Eb\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3 : pg 106"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed is,(rpm)= 623.944\n",
+ "armature torque is, (N-m)= 323.76\n",
+ "full load motor efficiency is ,(%)= 79.2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.3\n",
+ "#calculate the speed ,torque and efficiency\n",
+ "v=200.;#voltage in volts\n",
+ "r=100.;#resistance in ohms\n",
+ "#calculations\n",
+ "ish=v/r;#shunt current in amperes\n",
+ "i=4;#current in amperes\n",
+ "nla=i-ish;#no load armature current in amperes\n",
+ "w=8.;#powerin kW\n",
+ "ifl=(w*10**3)/v;#full load current in amperes\n",
+ "fla=ifl-ish;#full load armature current in amperes\n",
+ "r1=0.6;#internal resistance in ohms\n",
+ "ebo=(v-(ish*r1));#voltage in volts\n",
+ "eb=(v-(fla*r1));#voltage in volts\n",
+ "no=700.;#number of rpm\n",
+ "n=no*(eb/ebo);#number of rpm\n",
+ "ta=((eb*fla*60)/(2*n));#armature torque in N-m\n",
+ "nlpi=v*i;#no load power input in watts\n",
+ "cl=(ish**2*r1);#copper losses in watts\n",
+ "cl=nlpi-cl;#total copper lossses in Watts\n",
+ "flacl=(fla**2*r1);#full load armmature copper losses in Watts\n",
+ "tfll=flacl+cl;#total full load losses in Watts\n",
+ "flo=(w*10**3)-tfll;#full load output in Watts\n",
+ "ef=((flo)/(w*10**3))*100;#efficiency\n",
+ "#results\n",
+ "print \"speed is,(rpm)=\",round(n,3)\n",
+ "print \"armature torque is, (N-m)=\",ta\n",
+ "print \"full load motor efficiency is ,(%)=\",ef\n",
+ "#armature torque is calculated wrong in the textbook\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4 : pg 108"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The speed of the machine,(rpm) = 1003.51\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.4# speed\n",
+ "#calculate the speed of the machine\n",
+ "#given data :\n",
+ "fi=0.02# flux in Wb\n",
+ "P=4.;# number of poles\n",
+ "A=2.;#constant\n",
+ "Z=151.*A;#turns\n",
+ "V=200.;# in volts\n",
+ "Rsh=50.;#shunt resistance in ohm\n",
+ "Ra=0.01;# armature resistance in ohm\n",
+ "Pr=40000.;#power required in Watts\n",
+ "#calculations\n",
+ "Il=Pr/V;#load current in amperes\n",
+ "Ish=V/Rsh;#shunt current in amperes\n",
+ "Ia=Il+Ish;#armature current in amperes\n",
+ "E=V+(Ia*Ra);#generated voltage\n",
+ "N=(60*A*E)/(fi*P*Z);#rpm\n",
+ "#results\n",
+ "print \"The speed of the machine,(rpm) = \",round(N,3)\n",
+ "#answer is wrong in the textbook\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5 : pg 112"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Power consumed is,(W)= 5154.127\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.5# Power\n",
+ "#calculate the power consumed\n",
+ "#given data :\n",
+ "fp=0.024;# flux per pole\n",
+ "lf=1.2;# leakage factor\n",
+ "fi=fp/lf;# in Wb\n",
+ "Z=756;#turns\n",
+ "P=4;# number of pole\n",
+ "N=1000;# in rpm\n",
+ "A=4;#constant\n",
+ "#calculations\n",
+ "E=(fi*Z*N*P)/(60*A);#generated voltage\n",
+ "il=1/10.;#load current in amperes\n",
+ "ish=1/100.;#shunt current in amperes\n",
+ "ra=1;#armature resistance in ohms\n",
+ "isa=il+ish;#current in amperes\n",
+ "v=((E)/(1+(ra*isa)));#volts\n",
+ "r2=10;#ohms\n",
+ "il=v/r2;#amperes\n",
+ "pc=il*v;#Watts\n",
+ "#results\n",
+ "print \"Power consumed is,(W)=\",round(pc,3)\n",
+ "#answer is wrong in the textbook\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6 : pg 115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "part (a)\n",
+ "emf genereted,(V) = 254.0\n",
+ "part (b)\n",
+ "Total copper losses,(kW) = 3.3\n",
+ "Output of the prime mover,(W) = 51750.0\n",
+ "part (c)\n",
+ "Mechanical efficiency,(%) = 98.164\n",
+ "Electrical efficiency,(%) = 93.504\n",
+ "Commercial efficiency,(%) = 91.787\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.6: \n",
+ "#calculate the e.m.f ,copper losses ,output of the prime mover ,commercial, mechanical and electrical efficiencies\n",
+ "#given data :\n",
+ "Il=190;#load current in Amperes\n",
+ "V=250;# voltage in volts\n",
+ "Ra=0.02;#armature resistance in ohm\n",
+ "Rsh=25.;#shunt resistance in ohm\n",
+ "#calculations and results\n",
+ "Ish=V/Rsh;#shunt current in amperes\n",
+ "Ia=Ish+Il;#armature current in amperes\n",
+ "E=V+(Ia*Ra);#generated voltage\n",
+ "print \"part (a)\"\n",
+ "print \"emf genereted,(V) = \",E\n",
+ "Cl=(Ia**2*Ra);# armeture copper losses\n",
+ "Sl=Ish*V;# shunt copper losses\n",
+ "T=(Cl+Sl)*10**-3;#copper losses in k-Watt\n",
+ "print \"part (b)\"\n",
+ "print \"Total copper losses,(kW) = \",T\n",
+ "Eo=V*Il;#output voltage in volts\n",
+ "I_l=950.;#iron loss in watt\n",
+ "O=Eo+I_l+(T*10**3);#output in watt\n",
+ "print \"Output of the prime mover,(W) = \",O\n",
+ "Ep=O-I_l;# electrical power in W\n",
+ "Me=(Ep/O)*100;#Mechanical efficiency\n",
+ "print \"part (c)\"\n",
+ "print \"Mechanical efficiency,(%) = \",round(Me,3)\n",
+ "Ee=(Eo/Ep)*100;#Electrical efficiency\n",
+ "print \"Electrical efficiency,(%) = \",round(Ee,3)\n",
+ "Ce=(Eo/O)*100;#Commercial efficiency\n",
+ "print \"Commercial efficiency,(%) = \",round(Ce,3)\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7 : pg 117"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "additional resistance required is,(Ohm)= 9.162\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.7# resistance \n",
+ "#calculate the resistance\n",
+ "#given:\n",
+ "n=1000;#turns in rpm\n",
+ "ra=0.3;#armature resistance in ohms\n",
+ "rf=40;#field resistance in ohms\n",
+ "it=5;#field current in amperes\n",
+ "if1=4;#field current in amperes\n",
+ "e1=220.;#emf in volts\n",
+ "e2=200.;#emf in volts\n",
+ "ia=35.;#armature current in amperes\n",
+ "#calculations\n",
+ "eb=(e1-(ia*ra));#emf in volts\n",
+ "x=((eb-e2)/(it*if1));#additional field current in amperes\n",
+ "ce=e1-e2;#change in emf in volts\n",
+ "ix=if1+x;#total current in amperes\n",
+ "rt=(e1/ix);#total resistance in ohms\n",
+ "adr=rt-rf;#additional resistance required in ohms\n",
+ "#results\n",
+ "print \"additional resistance required is,(Ohm)=\",round(adr,3)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8 : pg 120"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "part (a)\n",
+ "resistance to be added is,(Ohm)= 18.644\n",
+ "part (b)\n",
+ "resistance to be added is,(Ohm)= 1.519\n",
+ "speed is,(rpm)= 1500.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.8# resistance and speed\n",
+ "#calculate the resistance and speed\n",
+ "from math import ceil\n",
+ "#given:\n",
+ "v1=240.;#primary voltage\n",
+ "r1=0.2;#primary resistance in ohm\n",
+ "i1=40.;#primary current in volts\n",
+ "#calculations and results\n",
+ "eb1=(v1-i1*r1);#primary emf\n",
+ "n11=1800.;#number of turns on primary side in rpm\n",
+ "n21=1600.;#number of turns on secondary side in rpm\n",
+ "i2=10.;#secondary current in amperes\n",
+ "x=((n21/n11)*(i2/i1)*eb1);#variable\n",
+ "r=((v1-(i2*r1))-x)/i2;#resistance in ohm\n",
+ "print \"part (a)\"\n",
+ "print \"resistance to be added is,(Ohm)=\",round(r,3)\n",
+ "print \"part (b)\"\n",
+ "n11=1800.;#number of turns on primary side\n",
+ "n21=900.;#number of turns on secondary side in rpm\n",
+ "i2=60.;#secondary current in amperes\n",
+ "x=((n21/n11)*(1.18)*eb1);#variable\n",
+ "r=((v1-(i2*r1))-x)/i2;#resistance in ohms\n",
+ "print \"resistance to be added is,(Ohm)=\",round(r,3)\n",
+ "eb2=228.;#secondary emf in volts\n",
+ "eb1=232.;#primary emf in volts\n",
+ "p1=100.;#primary power in watt\n",
+ "p2=118.;#secondary power in watt\n",
+ "n2=((eb2/eb1)*(p1/p2)*n11);#speed in rpm\n",
+ "print \"speed is,(rpm)=\",ceil(n2)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 9 : pg 121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "speed is,(rpm)= 1433.938\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.9# speed\n",
+ "#calculate the speed\n",
+ "from math import sqrt\n",
+ "#given:\n",
+ "i1=50.;#primary current in amperes\n",
+ "i2=i1/(sqrt(2));#secondary current in amperes\n",
+ "r1=0.2;#primary resistance in ohms\n",
+ "v1=220.;#primary voltage in volts\n",
+ "#calculations\n",
+ "eb1=((v1-(i1*r1)));#primary emf in volts\n",
+ "eb2=((v1-(i2*r1)));#secondary emf in volts\n",
+ "n1=1000#primary speed in rpm\n",
+ "n2=(n1*(eb2/eb1)*(i1/i2));#seconadry speed in rpm\n",
+ "#results\n",
+ "print \"speed is,(rpm)=\",round(n2,3)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10 : pg 124"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "part (a)\n",
+ " The speed of rotating magnetic field,(rpm) = 1500.0\n",
+ "part (b)\n",
+ "Motor speed,(rpm) = 1447.5\n",
+ "part (c)\n",
+ "Frequency 2.0 Hz or 120 rpm \n",
+ "part (d)\n",
+ "Frequency of rotor current,(Hz) = 50.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.10# \n",
+ "#calculate the Speed ,motor speed,and frequency \n",
+ "#given data :\n",
+ "print \"part (a)\"\n",
+ "f=50.;#frquency in Hz\n",
+ "P=4;# number of pole\n",
+ "#calculations and results\n",
+ "Ns=(120*f)/P;#speed in rom\n",
+ "print \" The speed of rotating magnetic field,(rpm) = \",Ns\n",
+ "print \"part (b)\"\n",
+ "S=0.035;# slip\n",
+ "N=Ns*(1-S);#motor speed in rpm\n",
+ "print \"Motor speed,(rpm) = \",N\n",
+ "print \"part (c)\"\n",
+ "S=0.04;# slip\n",
+ "F=S*f;#frequency in Hz\n",
+ "print \"Frequency \",F,\" Hz or \",120,\" rpm \"\n",
+ "print \"part (d)\"\n",
+ "f=50.;# in Hz\n",
+ "F=f;#frequency in Hz\n",
+ "print \"Frequency of rotor current,(Hz) = \",F\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11 : pg 125"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "part (a)\n",
+ "rotor current per phase is,(A)= 14.003\n",
+ "power factor is,= 0.243\n",
+ "part (b)\n",
+ "rotor current per phase is,(A)= 10.206\n",
+ "power factor is,= 0.707\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.11# \n",
+ "#calculate the current per phase and power factor\n",
+ "from math import sqrt\n",
+ "#given:\n",
+ "v1=100.;#emf in volts\n",
+ "vi=v1/sqrt(3);#induced emf in volts\n",
+ "r1=1.;#rotor resistance ohms per phase\n",
+ "r2=4.;#rotor reactance ohms per phase\n",
+ "#calculations and results\n",
+ "r=sqrt(r1**2+r2**2);#rotor impedence per phase\n",
+ "rcp=(vi/r);#rotor current per phase\n",
+ "pf=(1./r);#power factor\n",
+ "print \"part (a)\"\n",
+ "print \"rotor current per phase is,(A)=\",round(rcp,3)\n",
+ "print \"power factor is,=\",round(pf,3)\n",
+ "r3=3.;#ohms\n",
+ "r4=r1+r3;#rotor resistance ohms per phase\n",
+ "r2=4.;#rotor reactance ohms per phase\n",
+ "r=sqrt(r4**2+r2**2);#rotor impedence per phase\n",
+ "rcp=(vi/r);#rotor current per phase\n",
+ "pf=(r4/r);#power factor\n",
+ "print \"part (b)\"\n",
+ "print \"rotor current per phase is,(A)=\",round(rcp,3)\n",
+ "print \"power factor is,=\",round(pf,3)\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12 : pg 127"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "part (a) generator \n",
+ "emf when the armature current is full load unit pf is,(V)= 89.444\n",
+ "emf when the armature current is full load 0.8 pf (lag) is,(V)= 112.857\n",
+ "emf when the armature current is full load 0.8 pf (lead) is,(V)= 56.71\n",
+ "part (b) motor\n",
+ "emf when the armature current is full load unit pf is,(V)= 89.444\n",
+ "emf when the armature current is full load 0.8 pf (lag) is,(V)= 56.71\n",
+ "emf when the armature current is full load 0.8 pf (lead) is,(V)= 112.857\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Example 6.12# emf\n",
+ "#calculate the emf\n",
+ "from math import sqrt, pi\n",
+ "#given:\n",
+ "print \"part (a) generator \"\n",
+ "kva=4.;#kVA\n",
+ "v=110.;#volts\n",
+ "re=3.;#syncronous reacrance in ohms\n",
+ "#calculations and results\n",
+ "ip=((kva*10**3)/(sqrt(3)*v));#phase current in Amperes\n",
+ "ep=v/(sqrt(3));#phase voltage in volts\n",
+ "e1=ep+1j*(ip*3);#line voltage in volts\n",
+ "e11=sqrt((e1.real**2)+e1.imag**2);#line voltage per phase in volts\n",
+ "pf=0.8;#power factor\n",
+ "e12=(sqrt((e1.real*pf)**2+(((e1.imag*sqrt(1-pf**2))+e1.imag))**2));#\n",
+ "e13=(sqrt((e1.real*pf)**2+(((e1.imag*sqrt(1-pf**2))-e1.imag))**2));#\n",
+ "print \"emf when the armature current is full load unit pf is,(V)=\",round(e11,3)\n",
+ "print \"emf when the armature current is full load 0.8 pf (lag) is,(V)=\",round(e12,3)\n",
+ "print \"emf when the armature current is full load 0.8 pf (lead) is,(V)=\",round(e13,3)\n",
+ "print \"part (b) motor\"\n",
+ "kva=4;#kVa\n",
+ "v=110;#volts\n",
+ "re=3;#syncronous reacrance in ohms\n",
+ "ip=((kva*10**3)/(sqrt(3)*v));#phase current in Amperes\n",
+ "ep=v/(sqrt(3));#phase voltage in volts\n",
+ "e1=ep-1j*(ip*3);#line voltage in volts\n",
+ "e11=sqrt((e1.real**2)+e1.imag**2);#line voltage per phase in volts\n",
+ "pf=0.8;#power factor\n",
+ "e12=(sqrt((e1.real*pf)**2+(((e1.imag*sqrt(1-pf**2))-e1.imag))**2));#\n",
+ "e13=(sqrt((e1.real*pf)**2+(((e1.imag*sqrt(1-pf**2))+e1.imag))**2));#\n",
+ "print \"emf when the armature current is full load unit pf is,(V)=\",round(e11,3)\n",
+ "print \"emf when the armature current is full load 0.8 pf (lag) is,(V)=\",round(e12,3)\n",
+ "print \"emf when the armature current is full load 0.8 pf (lead) is,(V)=\",round(e13,3)\n"
+ ]
+ }
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