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diff --git a/backup/Fundamentals_of_Electrical_Drives_version_backup/Chapter7.ipynb b/backup/Fundamentals_of_Electrical_Drives_version_backup/Chapter7.ipynb new file mode 100755 index 00000000..63650d6e --- /dev/null +++ b/backup/Fundamentals_of_Electrical_Drives_version_backup/Chapter7.ipynb @@ -0,0 +1,416 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7: Synchronous Motor and Brushless dc Motor Drives" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example no:7.1,Page no:247" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import cmath\n", + "\n", + "#variable declaration\n", + "#ratings of the synchronous motor\n", + "Pm1=500*1000 # power rating in W\n", + "f=50 # frequency in HZ\n", + "Vl=3.3*1000 # line voltage in V\n", + "pf=0.8 # power factor lagging\n", + "P=4 # number of poles\n", + "I=10 # field current in A\n", + "Xs=15 # reactance of the windings in ohm\n", + "Rs=0 # resistance of the windings in ohm\n", + "Wms=50*math.pi # synchronous speed in rad/sec\n", + "Pm=Pm1/2 # power at half the rated torque when the losses are neglected\n", + "\n", + "#calculation\n", + "V=Vl/math.sqrt(3) #phase voltage\n", + "Is=Pm1/(math.sqrt(3)*Vl*pf) #rated current\n", + "rad=math.acos(pf)\n", + "\n", + "Is=cmath.rect(Is,-rad) #rated current in vector form\n", + "V=cmath.rect(V,0) #rated phase voltage in rectangular form\n", + "E=V-Is*1j*Xs #back emf\n", + "\n", + "#(i) when field current has not changed\n", + "sin_delta=Pm*Xs/(3*abs(V)*abs(E)) \n", + "delta=math.asin(sin_delta) #angle delta\n", + "Is=(V-cmath.rect(abs(E),-delta))/(1j*Xs) #armature current\n", + "Is1=cmath.polar(Is)\n", + "x=math.degrees(Is1[1]) #where x=Is which is the required armature current \n", + "power_factor=math.cos(Is1[1]) #power factor \n", + "\n", + "#(ii) At unity power factor and rated torque\n", + "cos_phi=1\n", + "Is=Pm1/(3*V) #since Pm1=3*V*Is\n", + "E1=V-Is*1j*Xs\n", + "If=abs(E1)/abs(E)*I #field current\n", + "\n", + "#(iii) At the field current of 12.5 A\n", + "If1=12.5 #field current \n", + "E2=If1/I*abs(E)\n", + "Is=math.sqrt(E2**2-abs(V)**2)/Xs #since E2=abs(V-Is*1j*Xs)\n", + "Pm=3*abs(V)*Is*cos_phi #power output at the given field current\n", + "T=Pm/Wms #required torque\n", + "\n", + "#results\n", + "print\"i)armature current :\",round(Is1[0],2),round(x),\"\u00b0\",\"A\"\n", + "print\" power factor\",round(power_factor,2),\"lagging\"\n", + "print\"\\nii)field current at unity power factor at rated torque:\",round(If,2),\"A\"\n", + "print\"\\niii)Required torque is:\",round(T,1),\"N-m\"\n", + "print\"Note: there is a slight difference in the answer due to the decimal place\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)armature current : 52.76 -34.0 \u00b0 A\n", + " power factor 0.83 lagging\n", + "\n", + "ii)field current at unity power factor at rated torque: 14.43 A\n", + "\n", + "iii)Required torque is: 1507.2 N-m\n", + "Note: there is a slight difference in the answer due to the decimal place\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example no:7.2,Page no:249" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from __future__ import division\n", + "import cmath\n", + "\n", + "#variable declaration\n", + "#ratings of the synchronous motor is same as that of Example-7.1\n", + "Pm1=500*1000 # power rating in W\n", + "f=50 # frequency in HZ\n", + "Vl=3.3*1000 # line voltage in V\n", + "pf=0.8 # power factor lagging\n", + "P=4 # number of poles\n", + "I=10 # field current in A\n", + "Xs=15 # reactance of the windings in ohm\n", + "Rs=0 # resistance of the windings in ohm\n", + "Pm=Pm1/2 # power at half the rated torque when the losses are neglected\n", + "\n", + "#calculation\n", + "Wms=50*math.pi # synchronous speed in rad/sec\n", + "V=Vl/math.sqrt(3) # phase voltage\n", + "Is=Pm1/(math.sqrt(3)*Vl*pf) #rated current\n", + "rad=math.acos(pf)\n", + "\n", + "Is=cmath.rect(Is,-rad) #rated current in vector form\n", + "V=cmath.rect(V,0) \n", + "E=V-Is*1j*Xs #back emf\n", + "\n", + "#(i) at rated current and unity power factor\n", + "E1=V-abs(Is)*1j*Xs\n", + "delta=cmath.phase(E1) #phase angle of E1\n", + "Pm=3*abs(V)*abs(E1)*math.sin(delta)/Xs #mechanical power developed\n", + "T=Pm/Wms #braking torque\n", + "If=abs(E1)/abs(E)*I #field current\n", + "\n", + "#(ii) at field current of 15A and 500kW output\n", + "If1=15 #field current\n", + "Pm=-500*1000 #output power \n", + "E2=If1/I*abs(E)\n", + "sin_delta=Pm*Xs/(3*abs(V)*abs(E2)) \n", + "delta=math.asin(sin_delta) #angle delta\n", + "Is=(cmath.rect(E2,abs(delta))-V)/(1j*Xs) #armature current\n", + "Is=cmath.polar(Is)\n", + "x=(Is[1])*180/math.pi #phase angle of Is\n", + "power_factor=math.cos(Is[1]) #power factor\n", + "\n", + "\n", + "#results\n", + "print\"i)braking torque :\",round(T,1),\"N-m\"\n", + "print\" Field current\",round(If,2),\"A\"\n", + "print\"\\nii)armature current :\",round(Is[0],2),round(x,2),\"\u00b0\",\"A\"\n", + "print\" power factor\",round(power_factor,3),\"lagging\"\n", + "print\"\\nNote :There is a slight difference in the answers due to the decimal place\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)braking torque : -3978.9 N-m\n", + " Field current 15.68 A\n", + "\n", + "ii)armature current : 87.78 -4.79 \u00b0 A\n", + " power factor 0.997 lagging\n", + "\n", + "Note :There is a slight difference in the answers due to the decimal place\n" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example no:7.3,Page no:257" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from __future__ import division\n", + "import cmath\n", + "from sympy import *\n", + "\n", + "#variable declaration\n", + "#ratings of the synchronous motor\n", + "Pm1=6*10**6 # power rating in W\n", + "f=50 # frequency in HZ\n", + "Vl=11*1000 # line voltage in V\n", + "pf=0.9 # power factor leading\n", + "P=6 # number of poles\n", + "I=10 # rated field current in A\n", + "Xs=9 # reactance of the windings in ohm\n", + "Rs=0 # resistance of the windings in ohm\n", + "N=120*f/P # synchronous speed\n", + "\n", + "#calculation\n", + "V=Vl/math.sqrt(3) #phase voltage\n", + "Is=Pm1/(math.sqrt(3)*Vl*pf) #rated current\n", + "rad=math.acos(pf)\n", + "\n", + "#(i)to find torque and field current at rated armature current\n", + "# at 750 rpm and 0.8 leading power factor\n", + "Is=cmath.rect(Is,rad) #rated current in vector form\n", + "V=cmath.rect(V,0)\n", + "E=V-Is*1j*Xs #back emf\n", + "\n", + "N1=750 #speeed in rpm\n", + "pf1=0.8 #given leading power factor\n", + "f1=N1/N*f #required frequency\n", + "V1=abs(V)*f1/f #required voltage\n", + "Xs1=Xs*f1/f #required field resistance\n", + "E1=V1-Xs1*1j*cmath.rect(abs(Is),math.acos(pf1)) #rated back emf in complex form \n", + "E1_polar=cmath.polar(E1) #rated back emf in rectangular form \n", + "#at rated field current and 750 rpm\n", + "E2=abs(E)*N1/N #back emf at the given speed N1 \n", + "If=abs(E1)/E2*f #field current at the given speed N1 \n", + "Pm=3*abs(V1)*abs(Is)*pf1 #power input at the given speed N1\n", + "Wm1=2*math.pi*N1/60 #angular motor speed in rad/s\n", + "T=Pm/Wm1\n", + "\n", + "#(ii) at half the rated motor torque and 1500 rpm and rated field current\n", + "Pm=6*10**6 #rated power rating in W\n", + "N1=1500 #speeed in rpm\n", + "f1=N1/N*f #required frequency\n", + "Xs1=f1/f*Xs #required field resistance\n", + "E1=abs(E)*f1/f #back emf at rated field current \n", + "\n", + "Wms = Symbol('Wms') #rated speed in rad/sec\n", + "T_rated = Symbol('T_rated') #rated torque\n", + "Wms=Pm/T_rated\n", + "Wms_=N1/N*Wms\n", + "Pm_= (0.5*T_rated)*Wms_ #required power developed at N1=1500 rpm \n", + "\n", + "sin_delta=Pm_*Xs1/(3*abs(V)*abs(E1)) #since Pm=3*abs(V)*abs(E1)*math.sin(delta)/Xs \n", + "delta=math.asin(sin_delta) #angle delta\n", + "Is=(abs(V)-cmath.rect(E1,-delta))/(1j*Xs1) #armature current\n", + "Is1=cmath.polar(Is) #aramture current in rectangular form\n", + "x1=math.degrees(Is1[1])\n", + "power_factor1=math.cos(Is1[1]) #power factor\n", + " \n", + "#(iii) at 750 rpm and rated field current from part(i)\n", + "N1=750 #speeed in rpm\n", + "pf1=0.8 #given leading power factor\n", + "f1=N1/N*f #required frequency at N1=750 rpm\n", + "V1=abs(V)*f1/f #required voltage at N1=750 rpm\n", + "Xs1=Xs*f1/f #required field resistance\n", + "E2=abs(E)*N1/N \n", + "\n", + "Pm=-4.2*10**6 #braking power output\n", + "sin_delta=Pm*Xs1/(3*abs(V1)*abs(E2)) #since Pm=3*abs(V)*abs(E1)*math.sin(delta)/Xs \n", + "delta=math.asin(sin_delta) #angle delta\n", + "Is=(cmath.rect(E2,abs(delta))-V1)/(1j*Xs1) #armature current \n", + "Is2=cmath.polar(Is) #aramture current in rectangular form\n", + "x2=math.degrees(Is2[1]) \n", + "power_factor2=math.cos(Is2[1]) #power factor\n", + "\n", + "#(iv)from part (ii) at 1500 rpm and from part(iii) the armature current of 349.9 A is taken\n", + "Is=Pm1/(math.sqrt(3)*Vl*pf) #armature current as given from (i)\n", + "N1=1500 #speeed in rpm\n", + "f1=N1/N*f #required frequency at N1=1500 rpm\n", + "Xs1=f1/f*Xs #required field resistance\n", + "E1=abs(E)*f1/f #at rated field current \n", + "E2=V-1j*Xs1*Is\n", + "E2=cmath.polar(E2)\n", + "\n", + "If1=E2[0]/abs(E1)*f #required field current\n", + "Pm=3*abs(V)*E2[0]*math.sin(abs(E2[1]))/Xs1 #power input\n", + "Wm1=2*math.pi*N1/60 #motor speed in rad/sec\n", + "T1=Pm/Wm1\n", + "\n", + "#results\n", + "print\"\\ni)Required torque is:\",round(T,1),\"N-m\"\n", + "print\" Field current :\",round(If,2),\"A\"\n", + "print\"\\nii)armature current :\",round(Is1[0],1),round(x1,2),\"\u00b0\",\"A\"\n", + "print\" power factor :\",round(power_factor1,1),\"leading\"\n", + "print\"\\niii)armature current :\",round(Is2[0],2),round(x2,2),\"\u00b0\",\"A\"\n", + "print\" power factor :\",round(power_factor2,3),\"lagging\"\n", + "print\"\\niv)Field current :\",round(If1,2),\"A\"\n", + "print\" Required torque is:\",round(T1),\"N-m\"\n", + "print\"\\nNote :There is a slight difference in the answers due to the decimal place\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "i)Required torque is: 50929.6 N-m\n", + " Field current : 52.37 A\n", + "\n", + "ii)armature current : 475.5 60.21 \u00b0 A\n", + " power factor : 0.5 leading\n", + "\n", + "iii)armature current : 334.62 -28.55 \u00b0 A\n", + " power factor : 0.878 lagging\n", + "\n", + "iv)Field current : 32.07 A\n", + " Required torque is: 42441.0 N-m\n", + "\n", + "Note :There is a slight difference in the answers due to the decimal place\n" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example no:7.4,Page no:265" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from __future__ import division\n", + "import cmath\n", + "\n", + "#variable declaration\n", + "#ratings of the synchronous motor\n", + "Pm=8*10**6 # power rating in W\n", + "f=50 # frequency in HZ\n", + "Vl=6600 # line voltage in V\n", + "pf=1 # unity power factor \n", + "P=6 # number of poles\n", + "I=10 # rated field current in A\n", + "Xs=2.8 # reactance of the windings in ohm\n", + "Rs=0 # resistance of the windings in ohm\n", + "Rd=0.1 # Dc link inductor resistance\n", + "alpha=140 # constant firing angle in degrees \n", + "\n", + "#calculation\n", + "N=120*f/P #synchronous speed\n", + "V=Vl/math.sqrt(3) #phase voltage\n", + "Is=Pm/(math.sqrt(3)*Vl*pf) #rated current\n", + "\n", + "Id=math.pi/math.sqrt(6)*Is #Dc line current\n", + "phi=180-alpha #phase angle between Is and V in degrees\n", + "\n", + "#(i) when motor operates at rated current and 500rpm\n", + "N1=500 #motor speed in rpm\n", + "f1=N1/N*f #frequency at N1\n", + "V1=f1/f*V #voltge at N1\n", + "Pm1=3*V1*Is*math.cos(math.radians(phi)) #power developed by the motor\n", + "#for the 3-phase load commutated inverter\n", + "Vdl=(3*math.sqrt(6)/math.pi)*V1*math.cos(math.radians(alpha))\n", + "Vds=-Vdl+Id*Rd\n", + "cos_alpha_s=Vds/(3*math.sqrt(6)/math.pi*V)\n", + "alpha_s=math.acos(cos_alpha_s) #in radian\n", + "alpha_s1=math.degrees(alpha_s) #in degrees\n", + "\n", + "#(ii) regenerative braking at 500rpm and at rated motor current\n", + "alpha=0 #firing angle\n", + "#when firng angle is zero then power factor is unity\n", + "pf=1\n", + "\n", + "Pm2=3*V1*Is*pf #power developed by the motor\n", + "Ps=Pm2-Id**2*Rd #power supplied to the source\n", + "Vdl=(3*math.sqrt(6)/math.pi)*V1*math.cos(math.radians(alpha))\n", + "Vds=-Vdl+Id*Rd\n", + "cos_alpha_s=Vds/(3*math.sqrt(6)/math.pi*V)\n", + "alpha_s=math.acos(cos_alpha_s) #in radian\n", + "alpha_s2=math.degrees(alpha_s) #in degrees\n", + "\n", + "#results\n", + "print\"i)power developed by the motor is:\",round(Pm1/10**6,3),\"MW\"\n", + "print\" Source side converter firing angle is\",round(alpha_s1,2),\"\u00b0\"\n", + "print\"\\nii)power supplied to the source is:\",round(Ps/10**6,3),\"MW\"\n", + "print\" Source side converter firing angle is\",round(alpha_s2,2),\"\u00b0\"\n", + "#answer for firing angle in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)power developed by the motor is: 3.064 MW\n", + " Source side converter firing angle is 66.85 \u00b0\n", + "\n", + "ii)power supplied to the source is: 3.919 MW\n", + " Source side converter firing angle is 119.34 \u00b0\n" + ] + } + ], + "prompt_number": 65 + } + ], + "metadata": {} + } + ] +}
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