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| author | root | 2014-07-07 17:05:00 +0530 |
|---|---|---|
| committer | root | 2014-07-07 17:05:00 +0530 |
| commit | 64874ad005ac7fea242828c5094fc827e7736851 (patch) | |
| tree | d3626c9cac8ce51b6b1c3e0ec85608eb14c4f047 /Fundamentals_of_Electric_Drives_and_Control/Chapter_4.ipynb | |
| parent | 1b0d935754549d175d2bad3d5eb5dc541bd7a0d4 (diff) | |
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diff --git a/Fundamentals_of_Electric_Drives_and_Control/Chapter_4.ipynb b/Fundamentals_of_Electric_Drives_and_Control/Chapter_4.ipynb new file mode 100644 index 00000000..e3ec0b71 --- /dev/null +++ b/Fundamentals_of_Electric_Drives_and_Control/Chapter_4.ipynb @@ -0,0 +1,622 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4:Selection of Motor Power Rating"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.1,Page no:49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "from scipy.optimize import fsolve\n",
+ "#Variable declaration\n",
+ "P=30.0 #[Power KW\n",
+ "theta1=30.0 #Temperature degree C\n",
+ "t1=40.0 # time in min\n",
+ "theta2=45.0 #Final temperature in degree C\n",
+ "\n",
+ "#Calculation\n",
+ "t2=80.0 #min(t2=2*t1)\n",
+ "#theta=theta_f*(1-exp(-t/T))\"\n",
+ "def f(T):\n",
+ " return((1-math.exp(-80.0/T))/(1-math.exp(-40/T))-(theta2/theta1))\n",
+ "T=fsolve(f,1)\n",
+ "theta_f=theta1/(1.0-math.exp(-t1/T)) #degreeC\n",
+ "#Result\n",
+ "print\"(a).Thermal time constant: \",round(T[0],2),\"minutes\"\n",
+ "print\"(b).Final temperature rise: \",theta_f,\"degrees\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " (a).Thermal time constant: 57.71 minutes\n",
+ "(b).Final temperature rise: 60.0 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.2,Page no:50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "P=30.0 #Power in KW\n",
+ "theta1=20.0 #Temerature degree C\n",
+ "t1=30.0 #Time in min\n",
+ "theta2=30.0 #Temperature in degree C\n",
+ "t2=60.0 #Final time innmin(t2=2*t1)\n",
+ "\n",
+ "#Calculation\n",
+ "#Let exp(-t1/T)=x then exp(-t2/T)=x**2\n",
+ "#theta1/theta2=(1-x)/(1-x**2)\n",
+ "#x**2*theta1-x*theta2+theta2-theta1=0\n",
+ "def f(T):\n",
+ " return(((1-math.exp(-t2/T))/(1-math.exp(-t1/T)))-theta2/theta1)\n",
+ "T=fsolve(f,1)\n",
+ "theta_f=theta1/(1-math.exp(-t1/T)) #degreeC\n",
+ "\n",
+ "#Result\n",
+ "print\"Thermal time constant : \",round(T[0],2),\"minutes\"\n",
+ "print\"Final temperature rise : \",theta_f,\"C\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Thermal time constant : 43.28 minutes\n",
+ "Final temperature rise : 40.0 C\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3,Page no:51"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "T_ambient=30 #Ambient tmeperature in dgree C\n",
+ "P=30.0 #Power in KW\n",
+ "theta1=54.0-T_ambient #Temperature durin g full load operation degree C\n",
+ "t1=1.0 #Time in hour\n",
+ "theta2=67.0-T_ambient #Temperature in degree C\n",
+ "t2=2.0 #Time in hour(t2=2*t1)\n",
+ "\n",
+ "#Calculation\n",
+ "def f(T):\n",
+ " return(((1-math.exp(-2/T))/(1-math.exp(-1/T)))-theta2/theta1)\n",
+ "T=fsolve(f,1)\n",
+ "theta_f=theta1/(1-math.exp(-t1/T)) #degreeC\n",
+ "theta_steady=theta_f+30 #degreeC\n",
+ "\n",
+ "#Result\n",
+ "print\"(a) Final steady state temperature : \",round(theta_steady,2),\"C\"\n",
+ "print\"(b) Heating time constant :\",round(T[0],2),\"hour\"\n",
+ "theta2=theta_f #degree C\n",
+ "t=2.7 #hour\n",
+ "theta=40-30 #degree C\n",
+ "Tdash=-t/math.log(theta/theta2) #hour\n",
+ "print\"(c) Cooling time constant: \",round(Tdash,2),\"hour\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " (a) Final steady state temperature : 82.36 C\n",
+ "(b) Heating time constant : 1.63 hour\n",
+ "(c) Cooling time constant: 1.63 hour\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4,Page no:52"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "T=110.0 #Time in min\n",
+ "Tdash=150.0 #Final time in min\n",
+ "t=30.0 #Run time of motor min\n",
+ "tdash=45.0 #Switch off time in min\n",
+ "theta_f=50.0 #final temperature rise in degree C\n",
+ "\n",
+ "#Calculation\n",
+ "#theta=theta_f-(theta_f-theta1)*exp(-t/T)\n",
+ "#theta1=theta*exp(-tdash/Tdash) \n",
+ "theta=(theta_f-theta_f*math.exp(-t/T))/(1-math.exp(-tdash/Tdash)*math.exp(-t/T)) #degreeC\n",
+ "\n",
+ "#Result\n",
+ "print\"Maximum temperature rise of the motor: \",round(theta,2),\"C\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum temperature rise of the motor: 27.37 C\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5,Page no:52"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "theta1=20.0 #Initial temperature in degreeC\n",
+ "theta2=28.0 #Final temperature in degreeC\n",
+ "dthetaBYdt1=0.08 #Rate of temp rise in degreeC/min\n",
+ "dthetaBYdt2=0.06 #Rate of temp rise in degreeC/min\n",
+ "\n",
+ "#Calculation\n",
+ "#theta=theta_f-(theta_f-theta1)*exp(-t/T)\n",
+ "#dtheta/dt=(theta_f-theta)/T\n",
+ "#dthetaBYdt1/dthetaBYdt2=(theta_f-theta1)/(theta_f-theta2)\n",
+ "theta_f=(theta2*dthetaBYdt1-theta1*dthetaBYdt2)/(dthetaBYdt1-dthetaBYdt2)\n",
+ "T=(theta_f-theta1)/dthetaBYdt1 #min\n",
+ "\n",
+ "#Result\n",
+ "print\"Final temperature rise,theta_f= : \",theta_f,\"C\"\n",
+ "print\"Heating time constant: \",T,\"minutes\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Final temperature rise,theta_f= : 52.0 C\n",
+ "Heating time constant: 400.0 minutes\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.6,Page no:59"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "cycle1=50.0 #Duty cycle hp\n",
+ "t1=20.0 #Time in sec\n",
+ "cycle2=100.0 #Duty cycle in hp\n",
+ "t2=20.0 #Time in sec\n",
+ "cycle3=150.0 #3rd duty cycle in hp\n",
+ "t3=10.0 #time sec\n",
+ "cycle4=120.0 #4th duty cyclein hp\n",
+ "t4=20.0 #time sec\n",
+ "cycle5=0.0 #th duty cycle in hp\n",
+ "t5=15.0 #sec\n",
+ "\n",
+ "#Calculation\n",
+ "hp_rms=math.sqrt((cycle1**2*t1+cycle2**2*t2+cycle3**2*t3+cycle4**2*t4+cycle5**2*t5)/(t1+t2+t3+t4+t5)) #hp\n",
+ "\n",
+ "#Result\n",
+ "print\"hp(rms) for the motor : \",round(hp_rms,2),\"hp\"\n",
+ "print\"We should choose 100hp motor.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "hp(rms) for the motor : 94.74 hp\n",
+ "We should choose 100hp motor.\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.7,Page no:61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "t_on=15.0 #Time for full load [min]\n",
+ "t_off=25.0 #time for off load in [min]\n",
+ "T=100.0 #Heating time constant in [min]\n",
+ "Tdash=140.0 #Cooling time constant in [min]\n",
+ "theta_f=55.0 #Continuous full load operation time in [degree C]\n",
+ "\n",
+ "#Calculation\n",
+ "#theta=theta_f-(theta_f-theta1)*exp(-t/T)\n",
+ "#theta1=theta*exp(-tdash/Tdash) \n",
+ "theta_max=theta_f*(1-math.exp(-t_on/T))/(1-math.exp(-(t_off/Tdash+t_on/T))) #degreeC\n",
+ "\n",
+ "#Result\n",
+ "print\"Maximum temperature rise: \",round(theta_max,2),\"C\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum temperature rise: 27.36 C\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.8,Page no:62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "\n",
+ "#Variable declaration\n",
+ "Rating=100.0 #Rating in KW\n",
+ "alfa=0.9 #Ratio rating unitless\n",
+ "ts=20.0 #Running time in min\n",
+ "T=100.0 #Heating time constant in min\n",
+ "\n",
+ "#Calculation\n",
+ "S=math.sqrt((1.0+alfa)/(1.0-math.exp(-ts/T))) \n",
+ "ShortTimeRating=S*Rating #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Short time rating: \",round(ShortTimeRating,1),\"kW\"\n",
+ "print\"NOTE:Answer is wrong in the textbook.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Short time rating: 323.8 kW\n",
+ "NOTE:Answer is wrong in the textbook.\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.9,Page no:62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "T=80.0 #Heating time constant in min\n",
+ "Tdash=110.0 #cooling time constant in min\n",
+ "Rating=50.0 #Full load rating in [KW]\n",
+ "ts=15.0 #Runt time in [min]\n",
+ "\n",
+ "#Calculation\n",
+ "S=math.sqrt(1.0/(1.0-math.exp(-ts/T))) \n",
+ "ShortTimeRating=S*Rating #KW\n",
+ "t_off=20.0 #min\n",
+ "S=math.sqrt((1.0-math.exp(-(ts/T+t_off/Tdash)))/(1.0-math.exp(-(ts/T))))\n",
+ "DutyRating=S*Rating #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"(a) Short time rating of motor: \",round(ShortTimeRating,1),\"kW\"\n",
+ "print\"(b) Intermittent periodic duty rating: \",round(DutyRating,2),\"kW\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a) Short time rating of motor: 120.9 kW\n",
+ "(b) Intermittent periodic duty rating: 67.2 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.10,Page no:63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "T=90.0 #Heating time constant in [min]\n",
+ "t=25.0 #time in min \n",
+ "ShortTimeRating=50.0 #Short time rating in KW\n",
+ "Eff=80/100.0 #Efficiency\n",
+ "\n",
+ "#Calculation\n",
+ "#Let full load rating is P KW and Losses=Pc\n",
+ "#CuLoss=(P/(P*Eff))**2 & alfa=Pc/CuLoss\n",
+ "alfa=(Eff)**2 #unitless\n",
+ "S=math.sqrt(((1.0+alfa)/(1.0-math.exp(-t/T))-alfa)) \n",
+ "ContinuousRating_fl=ShortTimeRating/S #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Full load continuous rating: \",round(ContinuousRating_fl,1),\"kW\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Full load continuous rating: 20.2 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.11,Page no:63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "Rating=25.0 #Rating in [KW]\n",
+ "T=90.0 #Heating time constant in min\n",
+ "ts=30.0 #time in min\n",
+ "\n",
+ "#Calculation\n",
+ "S=math.sqrt(1.0/(1.0-math.exp(-ts/T))) \n",
+ "HalfHourRating=S*Rating #KW\n",
+ "\n",
+ "#Result\n",
+ "print\"Half hour rating of motor: \",round(HalfHourRating,2),\"kW\"\n",
+ "print\"Answer wrong in textbook.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Half hour rating of motor: 46.96 kW\n",
+ "Answer wrong in textbook.\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.12,Page no:63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration:\n",
+ "ts=20 #rating itme in [min]\n",
+ "W=300 #rating in [W]\n",
+ "T=60 #time constant in [minutes]\n",
+ "max_eff_load=0.8 #Maximum effeciency of motor at load\n",
+ "\n",
+ "#Calculations\n",
+ "import sympy\n",
+ "P=sympy.Symbol('P')\n",
+ "pc=sympy.Symbol('pc')\n",
+ "Full_load_CL=(P/(0.8*P))**2*pc\n",
+ "alpha=pc/Full_load_CL\n",
+ "S=math.sqrt((1.0+alpha)/(1-math.exp(-ts/64.0))-alpha)\n",
+ "Cont_rating=W/round(S,1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Continuous rating of motor is :\",round(Cont_rating,1),\"W\"\n",
+ "print\"NOTE:There is a slight error in book in calculation of S,approximate value is taken\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Continuous rating of motor is : 130.4 W\n",
+ "NOTE:There is a slight error in book in calculation of S,approximate value is taken\n"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Continuous rating of motor is : 130.4 W\n",
+ "NOTE:There is a slight error in book in calculation of S,approximate value is taken\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.13,Page no:67"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#Variable declaration\n",
+ "P=6.0 #poles\n",
+ "f=50.0 #Frequency in [Hz]\n",
+ "MoI=9.5 #Moment of inertia in [Kg-m**2]\n",
+ "Tr=550.0 #Torque in [N-m]\n",
+ "S=5.0/100.0 #Slip\n",
+ "Tmax=720.0 #MAximum torque in [N-m]\n",
+ "T_LH=1020.0 #Torque requirement in [N-m]\n",
+ "th=12.0 #Time in [sec]\n",
+ "Tmin=220.0 #Light torque req in [N-m]\n",
+ "Snl=3.0/100.0 #No load slip\n",
+ "Ns=120.0*f/P #Speed in rpm\n",
+ "\n",
+ "#Calculation\n",
+ "Nnl=Ns-Ns*Snl #rpm\n",
+ "Nrated=Ns-Ns*S #rpm\n",
+ "omega_mo=Nnl*2.0*math.pi/60.0 #rad/s\n",
+ "omega_mr=Nrated*2.0*math.pi/60.0 #rad/s\n",
+ "J=(Tr/(omega_mo-omega_mr))*(th/math.log((T_LH-Tmin)/(T_LH-Tmax))) #Kg-m**2\n",
+ "MoI_flywheel=J-MoI #Kg-m**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Moment of inertia of flywheel : \",MoI_flywheel,\"kg-m^2\"\n",
+ "print\"NOTE:Answer in the book is wrong.\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Moment of inertia of flywheel : 3203.36081501 kg-m^2\n",
+ "NOTE:Answer in the book is wrong.\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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