diff options
Diffstat (limited to 'Electric_Machines_by_Nagrath_&_Kothari/Chapter09_1.ipynb')
| -rwxr-xr-x | Electric_Machines_by_Nagrath_&_Kothari/Chapter09_1.ipynb | 1141 |
1 files changed, 1141 insertions, 0 deletions
diff --git a/Electric_Machines_by_Nagrath_&_Kothari/Chapter09_1.ipynb b/Electric_Machines_by_Nagrath_&_Kothari/Chapter09_1.ipynb new file mode 100755 index 00000000..c3b55239 --- /dev/null +++ b/Electric_Machines_by_Nagrath_&_Kothari/Chapter09_1.ipynb @@ -0,0 +1,1141 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 09 : Induction Machine"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.1, Page No 148"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "# to campute cu loss in rotoe windings, input to the motor, efficiency\n",
+ "\n",
+ " \n",
+ "f_s=120.0/60 #cycles/min\n",
+ "f=50.0\n",
+ "s=f_s/f \n",
+ "n_s=1000.0 \n",
+ "\n",
+ "#Calculations\n",
+ "n=(1-s)*n_s \n",
+ "w=n*2*math.pi/60.0 \n",
+ "T=160.0 \n",
+ "P=T*w \n",
+ "T_L=10 \n",
+ "P_m=(T+T_L)*w \n",
+ "cu=P_m*(s/(1.0-s)) \n",
+ "print(cu,'rotor cu loss(W)') \n",
+ "P_sl=800.0 #stator loss\n",
+ "P_in=P_m+cu+P_sl \n",
+ "print(P_in,'power i/p to motor(W)') \n",
+ "\n",
+ "eff=P/P_in \n",
+ "\n",
+ "#Results\n",
+ "print(eff*100.0,'efficiency(%)') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(712.0943348136864, 'rotor cu loss(W)')\n",
+ "(18602.358370342157, 'power i/p to motor(W)')\n",
+ "(86.46728584706803, 'efficiency(%)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to calculate torque,resitance to be added to rotor ckt\n",
+ "\n",
+ "f=50.0\n",
+ "P=6.0 \n",
+ "n_s=120.0*f/P \n",
+ "w_s=2*math.pi*n_s/60 \n",
+ "n=875.0 \n",
+ "s_maxT=(n_s-n)/n_s \n",
+ "R_2=.25 \n",
+ "X_2=R_2/s_maxT \n",
+ "T_max=10.0 \n",
+ "#v=V/a\n",
+ "\n",
+ "#Calculations\n",
+ "v=math.sqrt((T_max*w_s*X_2)/(3*.5)) \n",
+ "T=((3.0)*v**2*(R_2/s))/(w_s*((R_2/s)**2+(X_2)**2)) \n",
+ "print(T,'torque(Nm)') \n",
+ "\n",
+ "#from eqn(T_start/T_max)=(R2+Rext)*(X2/.5)/((R2+Rext)**2+X2**2)\n",
+ "#after solving\n",
+ "#Rt**2-6.67*Rt+4=0\n",
+ "def quad(a,b,c):\n",
+ " d=math.sqrt(b**2-4*a*c)\n",
+ " x1=(-b+d)/(2*a) \n",
+ " x2=(-b-d)/(2*a) \n",
+ " if(x1>x2):\n",
+ " x=x2\n",
+ " else:\n",
+ " x=x1 \n",
+ " return x\n",
+ "Rt=quad(1,-6.67,4) \n",
+ "r2=.25 \n",
+ "\n",
+ "#Results\n",
+ "print(Rt-r2,'external resistance(ohm)') \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(5.805515239477503, 'torque(Nm)')\n",
+ "(0.41625029274006264, 'external resistance(ohm)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.3, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to find slip at max torque,full load slip and rotor current at starting\n",
+ "\n",
+ " \n",
+ "#Tfl=(3/w_s)*(V**2*Rs/s_fl)/((R2/s_fl)**2+X2**2) (i)\n",
+ "#Ts=(3/w_s)*(V**2*R2)/(R2**2+X2**2) (ii)\n",
+ "#Tmax=(3/w_s)*(.5*V**2)/X2**2 (iii)\n",
+ "#Tmax/Ts=2 k=R2/X2 (iii)/(ii)and solving\n",
+ "#k**2-4*k+1=0 \n",
+ "\n",
+ "#Calculations\n",
+ "def quad(a,b,c):\n",
+ " d=math.sqrt(b**2-4*a*c)\n",
+ " x1=(-b+d)/(2*a) \n",
+ " x2=(-b-d)/(2*a) \n",
+ " if(x1>x2):\n",
+ " x=x2\n",
+ " else:\n",
+ " x=x1 \n",
+ " return x\n",
+ "k=quad(1,-4,1) \n",
+ "print(k,'s_max_T') \n",
+ "\n",
+ "#(iii)/(i)and solving\n",
+ "#s_fl**2-1.072*s_fl+.072=0\n",
+ "s_fl=quad(1,-1.072,.072) \n",
+ "print(s_fl,'s_fl') \n",
+ "\n",
+ "#a=I2_start/I2_fullload\n",
+ "a=math.sqrt((k/s_fl)**2+1)/(k**2+1) \n",
+ "\n",
+ "#Results\n",
+ "print(a,'I2_start/I2_fullload') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(0.2679491924311228, 's_max_T')\n",
+ "(0.07200000000000001, 's_fl')\n",
+ "(3.59539147554005, 'I2_start/I2_fullload')\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5 Page No 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to determine ckt model parameters,parameters of thevenin equivalent, max torque and slip, stator current, pf and eff\n",
+ "\n",
+ " \n",
+ "j=math.sqrt(1.0) \n",
+ "#NL test\n",
+ "V=3300.0 \n",
+ "f=50.0 \n",
+ "Inl=5.0 \n",
+ "Po=2500.0 \n",
+ "Zo=V/(math.sqrt(3.0)*Inl) \n",
+ "Ro=Po/(3*Inl**2) \n",
+ "print(Ro,'Ro(ohm)') \n",
+ "Xo=math.sqrt(Zo**2-Ro**2) \n",
+ "print(Xo,'Xo(ohm)') \n",
+ "#BR test\n",
+ "V_BR=400.0 \n",
+ "I_BR=27.0 \n",
+ "ff=15.0 \n",
+ "P_BR=15000.0\n",
+ "\n",
+ "#Calculations\n",
+ "Z_BR=V_BR/(math.sqrt(3.0)*I_BR) \n",
+ "R_BR=P_BR/(3*I_BR**2) \n",
+ "X_BR=math.sqrt(Z_BR**2-R_BR**2) \n",
+ "x1=X_BR/2 #at 15 Hz\n",
+ "X1=x1*f/ff #at 50Hz\n",
+ "print(X1,'X1(ohm)') \n",
+ "Xm=Xo-X1 \n",
+ "print(Xm,'Xm(ohm)') \n",
+ "R1=3.75 \n",
+ "R2=(R_BR-R1)*((Xm+X1)/Xm)**2 \n",
+ "print(R2,'R2(ohm)') \n",
+ "\n",
+ "V_TH=(V/math.sqrt(3))*complex(math.cos(math.radians(0)),math.sin(math.radians(0)))*complex(0,Xm)/complex(R1,X1+Xm) \n",
+ "print(V_TH,'V_TH(V)') \n",
+ "Z_TH=complex(0,Xm)*complex(R1,X1)/complex(R1,X1+Xm) \n",
+ "print((Z_TH.real),'R_TH(ohm)') \n",
+ "print((Z_TH.imag),'X_TH(ohm)') \n",
+ "\n",
+ "a=(math.sqrt((Z_TH.real)**2+(X1+(Z_TH.imag))**2)) \n",
+ "s_max_T=R2/a \n",
+ "n_s=1000.0\n",
+ "Z_tot=complex((Z_TH.real)+a,X1+(Z_TH.imag)) \n",
+ "I2=abs(V_TH)/abs(Z_tot) \n",
+ "T_max=3*(I2**2)*R2/(s_max_T*(2*math.pi*n_s/60)) \n",
+ "print(T_max,'T_max(Nm)') \n",
+ "\n",
+ "Z_f=complex(0,Xm)*complex(81.25,X1)/complex(81.25,X1+Xm) \n",
+ "Z_in=Z_f+complex(R1,X1) \n",
+ "I1=V/(math.sqrt(3)*abs(Z_in)) \n",
+ "pf=math.cos(math.radians(math.degrees(math.atan((Z_in.imag)/(Z_in.real)))))\n",
+ "s=.04 \n",
+ "Pmechg=(1-s)*3*I1**2*(Z_f.real) \n",
+ "Prot=Po-Inl**2*R1 \n",
+ "Pip=math.sqrt(3.0)*V*I1*pf \n",
+ "Pop=Pmechg-Prot \n",
+ "eff=Pop/Pip \n",
+ "print(eff,'efficiency') \n",
+ "Tint=Pmechg/((1-s)*2*math.pi*n_s/60) \n",
+ "\n",
+ "#Results\n",
+ "print(Tint,'internal torque developed(Nm)') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(33.333333333333336, 'Ro(ohm)')\n",
+ "(379.5904225463136, 'Xo(ohm)')\n",
+ "(8.517574764607758, 'X1(ohm)')\n",
+ "(371.07284778170583, 'Xm(ohm)')\n",
+ "(3.2530626454410436, 'R2(ohm)')\n",
+ "((1862.3223709107285+18.39801131985398j), 'V_TH(V)')\n",
+ "(3.583247004147812, 'R_TH(ohm)')\n",
+ "(8.36184927709782, 'X_TH(ohm)')\n",
+ "(2384.194780011334, 'T_max(Nm)')\n",
+ "(0.8935727897525297, 'efficiency')\n",
+ "(1079.130406010449, 'internal torque developed(Nm)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6, Page No 151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to calculate starting torque and current,full load current,pf, torque , internal and overall eff,slip and max torque\n",
+ "\n",
+ " \n",
+ "R1=.3 \n",
+ "R2=.25 \n",
+ "X1=.6 \n",
+ "X2=.6 \n",
+ "Xm=35 \n",
+ "Prot=1500.0 \n",
+ "V=231.0 \n",
+ "Z_TH=complex(0,Xm)*complex(R1,X1)/complex(R1,X1+Xm) \n",
+ "V_TH=(V*complex(0,Xm))/complex(R1,X1+Xm) \n",
+ "n_s=1500.0 \n",
+ "w_s=2*math.pi*n_s/60 \n",
+ "\n",
+ "s=1 \n",
+ "Z_f=complex(0,Xm)*complex(R2,X2)/complex(R2,X2+Xm) \n",
+ "R_f=(Z_f.real) \n",
+ "Z_in=Z_f+complex(R1,X1) \n",
+ "I1=V/abs(Z_in) \n",
+ "print(I1,'starting current(A)') \n",
+ "Tstart=3*I1**2*R_f/w_s \n",
+ "print(Tstart,'starting torque(Nm)') \n",
+ "\n",
+ "n=1450.0 \n",
+ "s=1-n/n_s \n",
+ "a=R2/s \n",
+ "Z_f=complex(0,Xm)*complex(a,X2)/complex(a,X2+Xm) \n",
+ "R_f=(Z_f.real) \n",
+ "Z_in=Z_f+complex(R1,X1) \n",
+ "I1=V/abs(Z_in) \n",
+ "print(I1,'full load current(A)') \n",
+ "\n",
+ "#Calculations\n",
+ "pf=math.cos(math.radians(math.degrees(math.atan((Z_in.imag)/(Z_in.real)))))\n",
+ "print(pf,'pf') \n",
+ "P_G=3*I1**2*R_f \n",
+ "Popg=P_G*(1-s) \n",
+ "Pop=Popg-Prot \n",
+ "Tnet=Pop/((1.0-s)*w_s) \n",
+ "print(Tnet,'net torque(Nm)') \n",
+ "Vt=400 \n",
+ "Pip=math.sqrt(3)*Vt*I1*pf \n",
+ "eff=Pop/Pip \n",
+ "print(eff*100,'efficiency(%)') \n",
+ "int_eff=Popg/Pip \n",
+ "print(int_eff*100,'internal eff(%)') \n",
+ "\n",
+ "s_max_T=1/(math.sqrt((Z_TH.real)**2+((Z_TH.imag)+X1)**2)/R2) \n",
+ "print(s_max_T,'max slip') \n",
+ "Z_tot=Z_TH+complex(R2/s_max_T,X2) \n",
+ "I2=abs(V_TH)/abs(Z_tot) \n",
+ "T_max=3*I2**2*(R2/s_max_T)/w_s \n",
+ "\n",
+ "#Results\n",
+ "print(T_max,'max torque(Nm)') \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(176.48305256673922, 'starting current(A)')\n",
+ "(143.73484876981178, 'starting torque(Nm)')\n",
+ "(29.954582094223984, 'full load current(A)')\n",
+ "(0.9389975693602858, 'pf')\n",
+ "(109.07162925039286, 'net torque(Nm)')\n",
+ "(84.9884813377422, 'efficiency(%)')\n",
+ "(92.6858609868727, 'internal eff(%)')\n",
+ "(0.2037356745317859, 'max slip')\n",
+ "(324.6427710199817, 'max torque(Nm)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9, Page No 152"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to determine the line current,pf, power ip, shaft torque, mech op and efficiency\n",
+ "\n",
+ " \n",
+ "R1=1.4 \n",
+ "R2=.6 \n",
+ "X1=2 \n",
+ "X2=1 \n",
+ "Xm=50.0 \n",
+ "V=400.0 \n",
+ "Prot=275.0 \n",
+ "n_s=1000.0 \n",
+ "\n",
+ "#Calculations\n",
+ "w_s=2*math.pi*n_s/60.0 \n",
+ "\n",
+ "print('slip=0.03') \n",
+ "s=0.03 \n",
+ "I2=(V/math.sqrt(3.0))/complex(R1+R2/s,X1+X2) \n",
+ "Im=(V/math.sqrt(3.0))/(Xm*complex(math.cos(math.radians(90)),math.sin(math.radians(90)))) \n",
+ "I1=Im+I2 \n",
+ "I_L=abs(I1) \n",
+ "print(I_L,'line current(A)') \n",
+ "pf=math.cos(math.radians(math.degrees(math.atan((Z_in.imag)/(Z_in.real)))))\n",
+ "print(pf,'pf') \n",
+ "Pip=math.sqrt(3.0)*V*abs(I1)*math.cos(math.radians(math.degrees(math.atan((I1.imag)/(I1.real)))))\n",
+ "print(Pip,'power i/p(W)') \n",
+ "\n",
+ "P_G=3*abs(I2)**2*R2/s \n",
+ "Pmechg=(1-s)*P_G \n",
+ "print(Pmechg,'mech power op(W)') \n",
+ "Popnet=Pmechg-Prot \n",
+ "Tnet=Popnet/(w_s*(1.0-s)) \n",
+ "print(Tnet,'shaft torque(Nm)') \n",
+ "eff=Popnet/Pip \n",
+ "print(eff,'efficiency') \n",
+ "\n",
+ "print('slip= -0.03') \n",
+ "s=-0.03 \n",
+ "I2=(V/math.sqrt(3))/complex(R1+R2/s,X1+X2) \n",
+ "Im=(V/math.sqrt(3))/(Xm*complex(math.cos(math.radians(90)),math.sin(math.radians(90)))) \n",
+ "I1=-(Im+I2) \n",
+ "I_L=abs(I1) \n",
+ "print(I_L,'line current(A)') \n",
+ "pf=math.cos(math.radians(math.degrees(math.atan((I1.imag)/(I1.real)))))\n",
+ "print(pf,'pf') \n",
+ "Pip=math.sqrt(3.0)*V*abs(I1)*math.cos(math.radians(math.degrees(math.atan((I1.imag)/(I1.real)))))\n",
+ "print(Pip,'power i/p(W)') \n",
+ "\n",
+ "P_G=3*abs(I2)**2*R2/s \n",
+ "Pmechop=(1-s)*P_G \n",
+ "Pmechipnet=-Pmechop \n",
+ "Pmechipg=Pmechipnet+Prot \n",
+ "print(Pmechipg,'mech power op(W)') \n",
+ "Tnet=Pmechipg/(w_s*(1-s)) \n",
+ "print(Tnet,'shaft torque(Nm)') \n",
+ "eff=Pip/Pmechipg \n",
+ "print(eff,'efficiency') \n",
+ "\n",
+ "print('slip= 1.2') \n",
+ "s=1.2 \n",
+ "I2=(V/math.sqrt(3))/complex(R1+R2/s,X1+X2) \n",
+ "Im=(V/math.sqrt(3))/(Xm*complex(math.cos(math.radians(90)),math.sin(math.radians(90)))) \n",
+ "I1=Im+I2 \n",
+ "I_L=abs(I1) \n",
+ "print(I_L,'line current(A)') \n",
+ "pf=math.cos(math.radians(math.degrees(math.atan((I1.imag)/(I1.real)))))\n",
+ "print(pf,'pf') \n",
+ "Pip=math.sqrt(3)*V*abs(I1)*pf \n",
+ "print(Pip,'power i/p(W)') \n",
+ "\n",
+ "P_G=3*abs(I2)**2*.5/s \n",
+ "Pmechg=(1-s)*P_G \n",
+ "print(Pmechg,'mech power op(W)') \n",
+ "Pmechabs=-Pmechg \n",
+ "n=n_s*(1-s) \n",
+ "w=2*math.pi*n/60 \n",
+ "Tnet=Pmechg/w \n",
+ "\n",
+ "#Results\n",
+ "print(Tnet,'torque developed(Nm)') \n",
+ "P=Pmechabs+Pip \n",
+ "print(P,'power disipated(W)') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "slip=0.03\n",
+ "(12.216911505440674, 'line current(A)')\n",
+ "(0.9389975693602858, 'pf')\n",
+ "(7332.533835874596, 'power i/p(W)')\n",
+ "(6647.250299811549, 'mech power op(W)')\n",
+ "(62.732482505184755, 'shaft torque(Nm)')\n",
+ "(0.8690379672897196, 'efficiency')\n",
+ "slip= -0.03\n",
+ "(13.770083713222693, 'line current(A)')\n",
+ "(0.8788126748308187, 'pf')\n",
+ "(8384.043272481405, 'power i/p(W)')\n",
+ "(9560.553301780481, 'mech power op(W)')\n",
+ "(88.63743592263522, 'shaft torque(Nm)')\n",
+ "(0.8769412195965717, 'efficiency')\n",
+ "slip= 1.2\n",
+ "(68.98053758242195, 'line current(A)')\n",
+ "(0.5044420753093245, 'pf')\n",
+ "(24107.85091197462, 'power i/p(W)')\n",
+ "(-1057.3618821041503, 'mech power op(W)')\n",
+ "(50.48531105214763, 'torque developed(Nm)')\n",
+ "(25165.21279407877, 'power disipated(W)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.10 Page No 163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to calculate max torque and slip, starting torque\n",
+ "\n",
+ " \n",
+ "k=5.0 #k=I_s/I_fl\n",
+ "s_fl=0.04 \n",
+ "\n",
+ "#Calculations\n",
+ "s_max_T=math.sqrt((s_fl**2*(1-k**2))/((k*s_fl)**2-1)) \n",
+ "print(s_max_T,'slip') \n",
+ "T_max=.5*(s_max_T**2+s_fl**2)/(s_fl*s_max_T) \n",
+ "print(T_max,'max torque(pu)') \n",
+ "\n",
+ "T_s=k**2*s_fl \n",
+ "\n",
+ "#Results\n",
+ "print(T_s,'starting torque(pu)') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(0.2, 'slip')\n",
+ "(2.6, 'max torque(pu)')\n",
+ "(1.0, 'starting torque(pu)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.11, Page No 164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to find starting current and torque, necessary exteranl resistance and corresponding starting torque\n",
+ "\n",
+ " \n",
+ "f=50.0 \n",
+ "R2=.1 \n",
+ "X2=2*math.pi*f*3.61*10**-3 \n",
+ "a=3.6 \n",
+ "R22=a**2*R2 \n",
+ "X22=a**2*X2 \n",
+ "V=3000.0 \n",
+ "n_s=1000.0 \n",
+ "\n",
+ "#Calculations\n",
+ "w_s=2*math.pi*n_s/60 \n",
+ "I_s=(V/math.sqrt(3.0))/math.sqrt(R22**2+X22**2) \n",
+ "print(I_s,'starting current(A)') \n",
+ "T_s=(3/w_s)*(V/math.sqrt(3.0))**2*R22/(R22**2+X22**2) \n",
+ "print(T_s,'torque(Nm)') \n",
+ "\n",
+ "Iss=30 \n",
+ "Rext=math.sqrt(((V/math.sqrt(3.0)/Iss)**2-X22**2)-R22) \n",
+ "print(Rext,'external resistance(ohm)') \n",
+ "T_s=(3/w_s)*(V/math.sqrt(3.0))**2*(R22+Rext)/((R22+Rext)**2+X22**2) \n",
+ "\n",
+ "#Results\n",
+ "print(T_s,'torque(Nm)') \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(117.38613867026375, 'starting current(A)')\n",
+ "(511.600867712354, 'torque(Nm)')\n",
+ "(55.821163691822676, 'external resistance(ohm)')\n",
+ "(1411.238212203274, 'torque(Nm)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.12 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#find line current and starting torque with direct switching, stator resistance starting, autotransformer starting, star delta starting, autotransformer ratio give 1 pu\n",
+ "\n",
+ " \n",
+ "#I_s/I_fl=6 \n",
+ "s_fl=0.05 \n",
+ "print('by direct switching') \n",
+ "Is=6.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(Is,'line current(pu)') \n",
+ "T=Is**2*s_fl \n",
+ "print(T,'torque(pu)') \n",
+ "\n",
+ "print('by stator resistance starting') \n",
+ "Is=2.0\n",
+ "print(Is,'line current(pu)') #given\n",
+ "T=Is**2*s_fl \n",
+ "print(T,'torque(pu)') \n",
+ "\n",
+ "print('by autotransformer starting') \n",
+ "x=2/6.0 \n",
+ "Is_motor=2 \n",
+ "Is=Is_motor*x \n",
+ "print(Is,'line current(pu)') \n",
+ "T=Is**2*s_fl \n",
+ "print(T,'torque(pu)') \n",
+ "\n",
+ "print('by star delta starting') \n",
+ "Is=(1/3.0)*6 \n",
+ "print(Is,'line current(pu)') \n",
+ "T=Is**2*s_fl*3.0 \n",
+ "\n",
+ "#Results\n",
+ "print(T,'torque(pu)') \n",
+ "\n",
+ "print('by autotransformer starting') \n",
+ "Ts=1.0 \n",
+ "x=math.sqrt(Ts/((6**2)*s_fl)) \n",
+ "print(x,'x') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "by direct switching\n",
+ "(6.0, 'line current(pu)')\n",
+ "(1.8, 'torque(pu)')\n",
+ "by stator resistance starting\n",
+ "(2.0, 'line current(pu)')\n",
+ "(0.2, 'torque(pu)')\n",
+ "by autotransformer starting\n",
+ "(0.6666666666666666, 'line current(pu)')\n",
+ "(0.022222222222222223, 'torque(pu)')\n",
+ "by star delta starting\n",
+ "(2.0, 'line current(pu)')\n",
+ "(0.6000000000000001, 'torque(pu)')\n",
+ "by autotransformer starting\n",
+ "(0.7453559924999299, 'x')\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.13 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to find resistance added to ckt\n",
+ "\n",
+ " \n",
+ "Rrot=.061 \n",
+ "R2=Rrot/2.0 \n",
+ "f=50.0 \n",
+ "P=12.0 \n",
+ "w_s=(120.0*f/P)*(2*math.pi/60.0) \n",
+ "s=0.045 \n",
+ "\n",
+ "#Calculations\n",
+ "w=(1.0-s)*w_s \n",
+ "P=200.0*10.0**3 \n",
+ "T_fan=P/w \n",
+ "I2=math.sqrt(T_fan*w_s*s/(3.0*R2)) \n",
+ "E2=I2*R2/s \n",
+ "n=450.0 \n",
+ "ww=2*math.pi*n/60 \n",
+ "nn=500.0 \n",
+ "ss=(nn-n)/nn \n",
+ "Tnew=T_fan*(ww/w)**2 \n",
+ "Rt=(3.0/w_s)*(E2*ss)**2/(ss*Tnew) \n",
+ "Rext=Rt-R2 \n",
+ "\n",
+ "#Results\n",
+ "print(Rext,'external resistance(ohm)') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(0.04581484910836761, 'external resistance(ohm)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.14 Page No 172"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to find resistance added to ckt\n",
+ "\n",
+ " \n",
+ "n_s=1500.0\n",
+ "w_s=2*math.pi*n_s/60.0 \n",
+ "n=1250.0 \n",
+ "s=1-n/n_s \n",
+ "#Im=(1/3.0)*(0.3+.25/s+j*1.83)ohm/ph\n",
+ "T=150.0 \n",
+ "V=440.0 \n",
+ "\n",
+ "#Calculations\n",
+ "#T=(3.0/w_s)*(V**2*(R_2t/s))/((.1+(R_2t/s))**2+(X1+X2)**2) \n",
+ "#after solving R_2t**2-1.34*R_2t+0.093=0\n",
+ "\n",
+ "def quad(a,b,c):\n",
+ " d=math.sqrt(b**2-4*a*c) \n",
+ " x1=(-b+d)/(2*a) \n",
+ " x2=(-b-d)/(2*a) \n",
+ " if(x1>x2):\n",
+ " x=x1 \n",
+ " else:\n",
+ " x=x2 \n",
+ " return x\n",
+ "x=quad(1,-1.34,0.093) \n",
+ "Rext=x-0.083 \n",
+ "\n",
+ "#Results\n",
+ "print(Rext,'external resitance(ohm)') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(1.1835735495309863, 'external resitance(ohm)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.15, Page No 176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to calculate the min resistance to be added and speed of the motor\n",
+ " \n",
+ "V=400.0 \n",
+ "a=2.5 \n",
+ "X2=.4 \n",
+ "R2=0.08 \n",
+ "n_s=750.0 \n",
+ "\n",
+ "#Calculations\n",
+ "w_s=2*math.pi*n_s/60.0 \n",
+ "T=250.0 \n",
+ "x=[];\n",
+ "#T=(3.0/w_s)*((V/math.sqrt(3))/a)*R2t/(R2t**2+X2**2) \n",
+ "#after solving\n",
+ "#R2t**2-1.304*R2t+0.16=0\n",
+ "\n",
+ "def quad(a,b,c):\n",
+ " d=math.sqrt(b**2-4*a*c) \n",
+ " x1=(-b+d)/(2*a) \n",
+ " x2=(-b-d)/(2*a) \n",
+ " if(x1>x2):\n",
+ " x=x1 \n",
+ " else:\n",
+ " x=x2 \n",
+ " return x1,x2\n",
+ "x=quad(1,-1.304,0.16) \n",
+ "if x[0]>x[1]:\n",
+ " R2t=x[1] \n",
+ "else:\n",
+ " R2t=x[0]\n",
+ "Rext=R2t-R2 \n",
+ "print(Rext,'external resistance(ohm)') \n",
+ "\n",
+ "#T=(3/w_s)*((V/math.sqrt(3))/a)*(R2t/s)/((R2t/s)**2+X2**2) \n",
+ "#after solving\n",
+ "#(R2t/s)**2-1.304*(R2t/s)+0.16=0\n",
+ "x=[0,0]\n",
+ "x=quad(1,-1.304,0.16) \n",
+ "s=x[1]/x[0] \n",
+ "n=n_s*(1-s) \n",
+ "print(n,'speed(rpm)') \n",
+ "\n",
+ "#T=(3/w_s)*((V/math.sqrt(3))/a)*(R2/s)/((R2/s)**2+X2**2) \n",
+ "#after solving\n",
+ "#(R2/s)**2-1.304*(R2/s)+0.16=0\n",
+ "x=quad(1,-1.304,0.16) \n",
+ "R2=0.08 \n",
+ "s1=R2/x[0]\n",
+ "s2=R2/x[1]\n",
+ "if s1>s2:\n",
+ " ss=s2 \n",
+ "else:\n",
+ " ss=s1\n",
+ "\n",
+ "n=n_s*(1-ss) \n",
+ "\n",
+ "#Results\n",
+ "print(n,'speed(rpm)') \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(0.057117489129801594, 'external resistance(ohm)')\n",
+ "(661.8693476940879, 'speed(rpm)')\n",
+ "(698.5809415763244, 'speed(rpm)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.16, Page No 186"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "T_jm=125\n",
+ "th_jc=.15 #degC/W\n",
+ "th_cs=0.075 #degC/W\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "dT=54 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "dT=58 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "V_m=math.sqrt(2)*230\n",
+ "R=2\n",
+ "I_TAV=V_m/(R*math.pi)\n",
+ "P_av=90\n",
+ "th_sa=(T_jm-T_a)/P_av-(th_jc+th_cs)\n",
+ "dT=P_av*th_sa\n",
+ "print(\"for heat sink\") \n",
+ "print(\"T_s-T_a=%.2f degC\" %dT) \n",
+ "print(\"\\nP_av=%.0f W\" %P_av)\n",
+ "P=(V_m/2)**2/R\n",
+ "eff=P/(P+P_av) \n",
+ "print(\"\\nckt efficiency=%.3f pu\" %eff)\n",
+ "a=60 #delay angle\n",
+ "I_TAV=(V_m/(2*math.pi*R))*(1+math.cos(math.radians(a)))\n",
+ "print(\"\\nI_TAV=%.2f A\" %I_TAV)\n",
+ "dT=46\n",
+ "T_s=dT+T_a\n",
+ "T_c=T_s+P_av*th_cs \n",
+ "T_j=T_c+P_av*th_jc \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ncase temp=%.2f degC\" %T_c)\n",
+ "print(\"\\njunction temp=%.2f degC\" %T_j)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for heat sink\n",
+ "T_s-T_a=-20.25 degC\n",
+ "\n",
+ "P_av=90 W\n",
+ "\n",
+ "ckt efficiency=0.993 pu\n",
+ "\n",
+ "I_TAV=38.83 A\n",
+ "\n",
+ "case temp=92.75 degC\n",
+ "\n",
+ "junction temp=106.25 degC\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.17, Page No 187"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to find the ratio of currents and torques at the starting,V2/V1\n",
+ "\n",
+ " \n",
+ "f1=50.0 \n",
+ "f2=60.0 \n",
+ "f=f2/f1 \n",
+ "V=1 #V=V2/V1\n",
+ "s_max_T=0.2 \n",
+ "#Is=I_s2/I_s1\n",
+ "\n",
+ "#Calculations\n",
+ "Is=V*math.sqrt((s_max_T**2+1)/(s_max_T**2+f**2)) \n",
+ "print(Is,'ratio of currents at starting') \n",
+ "#Ts=T_s2/T_s1\n",
+ "Ts=V**2*((s_max_T**2+1)/(s_max_T**2+f**2)) \n",
+ "print(Ts,'ratio of torques at starting') \n",
+ "#Tmax=Tmax2/Tmax1\n",
+ "Tmax=V**2/f**2 \n",
+ "print(Tmax,'ratio of max torques') \n",
+ "Vr=math.sqrt(1/math.sqrt((s_max_T**2+1)/(s_max_T**2+f**2)))\n",
+ "\n",
+ "#Results\n",
+ "print(Vr,'V2/V1') "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(0.8382736442849094, 'ratio of currents at starting')\n",
+ "(0.7027027027027027, 'ratio of torques at starting')\n",
+ "(0.6944444444444444, 'ratio of max torques')\n",
+ "(1.0922123778851107, 'V2/V1')\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.18, Page No 197"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to calculate ratio of torques at starting and at slip=0.05\n",
+ "\n",
+ " \n",
+ "R1=0.01 \n",
+ "X1=.5 \n",
+ "R2=0.05 \n",
+ "X2=.1 \n",
+ "\n",
+ "#Calculations\n",
+ "Ts=((R1**2+X1**2)/(R2**2+X2**2))*(R2/R1) \n",
+ "print(Ts,'Tso/Tsi') \n",
+ "\n",
+ "s=0.05 \n",
+ "T=(((R1/s)**2+X1**2)/((R2/s)**2+X2**2))*(R2/R1) \n",
+ "\n",
+ "#Results\n",
+ "print(T,'To/Ti')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(100.03999999999998, 'Tso/Tsi')\n",
+ "(1.4356435643564356, 'To/Ti')\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.19, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "#to compute acc time and value of rotor resistance\n",
+ "\n",
+ " \n",
+ "s=1-.96 #load is brought to .96 of n_s\n",
+ "s_max_T=math.sqrt((1.0-s**2)/(2*math.log(1.0/s))) \n",
+ "R=1.5 \n",
+ "R2_opt=R*s_max_T \n",
+ "\n",
+ "#Calculations\n",
+ "print(R2_opt,'rotor resistance(ohm)') \n",
+ "n=1000 \n",
+ "w_s=2*math.pi*n/60 \n",
+ "V=415 \n",
+ "Tmax=(3.0/w_s)*(.5*(V/math.sqrt(3.0))**2)/R \n",
+ "J=11 \n",
+ "t_A=(J*w_s/(2*Tmax))*((1-s**2)/(2*s_max_T)+s_max_T*math.log(1.0/s))\n",
+ "\n",
+ "#Results\n",
+ "print(t_A,'acc time(min)') \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(0.5907128737793668, 'rotor resistance(ohm)')\n",
+ "(2.663571640987115, 'acc time(min)')\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |