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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter01 - Poly phase ac machines"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1 Page 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"# Given data\n",
"Zinner=0.01+0.5*1J #Impedence at standstill of inner cage in ohm\n",
"Zouter=0.05+0.1*1J #Impedence at standstill of outer cage in ohm\n",
"\n",
"#Calculations\n",
"#Part (a) : at starting\n",
"R1=Zinner.real #in ohm\n",
"R2=Zouter.real #in ohm\n",
"X1=Zinner.imag #in ohm\n",
"X2=Zouter.imag #in ohm\n",
"#Formula : Ts=3/ws*V_dash**2*R2/(R2**2+X2**2)\n",
"TsoBYTsi=(R2/(R2**2+X2**2))/(R1/(R1**2+X1**2))\n",
"print \"Part(a) Ratio of Torque : \" ,round(TsoBYTsi)\n",
"#Part(b) : slip =5%\n",
"S=5/100 #slip\n",
"#Formula : T=3/ws*V_dash**2*(R2/S)**2/((R2/S)+X2**2)\n",
"ToBYTi=((R2/S)/((R2/S)**2+X2**2))/((R1/S)/((R1/S)**2+X1**2))\n",
"print \"Part(b) Ratio of Torque : \" ,round(ToBYTi,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Part(a) Ratio of Torque : 100.0\n",
"Part(b) Ratio of Torque : 1.436\n"
]
}
],
"prompt_number": 99
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1 Page: 41 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"# Given data\n",
"P=4 #No. of poles\n",
"f=50 #in Hz\n",
"N=1410 #in rpm\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in r\n",
"print \"Synchronous speed = %0.f rpm\" %Ns\n",
"S=(Ns-N)/Ns #Full load slip\n",
"S=S*100 #in %\n",
"print \"Full load slip = %0.f %% \"%S "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Synchronous speed = 1500 rpm\n",
"Full load slip = 6 % \n"
]
}
],
"prompt_number": 100
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.2 Page 42"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=2 #No. of poles\n",
"f=50 #in Hz\n",
"S=2 #in %#Calculations\n",
"S=S/100 #unitless\n",
"Ns=120*f/P #in rpm\n",
"N=Ns*(1-S)\n",
"print \"Speed of motor = %0.f rpm \" %N"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Speed of motor = 2940 rpm \n"
]
}
],
"prompt_number": 101
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.3 Page 42"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #No. of poles\n",
"f=50 #in Hz\n",
"N=1470 #in rpm\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #Slip\n",
"fr=S*f #induced emf frequency in Hz\n",
"print \"Induced emf frequency = %0.2f Hz\" %fr"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Induced emf frequency = 1.00 Hz\n"
]
}
],
"prompt_number": 102
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.4 Page 42"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math as mh\n",
"# Given data\n",
"P=4 #No. of poles\n",
"f=50 #in Hz\n",
"K=1/2 #rotor to stator turns\n",
"N=1455 #in rpm\n",
"E1_line=415 #in volt#Calculations\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #Slip\n",
"fr=S*f #induced emf frequency in Hz\n",
"print \"(i) Frequency of rotor emf in running condition = %0.2f Hz\" %fr\n",
"N2BYN1=K #rotor to stator turns\n",
"N1BYN2=1/K #stator to rotor turns\n",
"E1ph=E1_line/mh.sqrt(3) #\n",
"#Formula : E2ph/E1ph=K\n",
"E2ph=E1ph*K #in volt\n",
"print \"(ii) Rotor induced emf at standstill = %0.2f V\"%E2ph\n",
"E2r=S*E2ph #in volt\n",
"print \"(iii) Rotor induced emf at running condition = %0.3f V\" %E2r"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Frequency of rotor emf in running condition = 1.50 Hz\n",
"(ii) Rotor induced emf at standstill = 119.80 V\n",
"(iii) Rotor induced emf at running condition = 3.594 V\n"
]
}
],
"prompt_number": 103
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.5 Page 43"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math as mh\n",
"# Given data\n",
"P=4 #No. of poles\n",
"f=50 #in Hz\n",
"R2=0.2 #in ohm\n",
"X2=1 #in ohm\n",
"N=1440 #in rpm\n",
"E2_line=120 #in volt#Calculations\n",
"E2ph=E2_line/mh.sqrt(3) #\n",
"cosfi_2=R2/mh.sqrt(R2**2+X2**2) #lagging power factor\n",
"I2=E2ph/mh.sqrt(R2**2+X2**2) #in Ampere/phase\n",
"print \"(i) Rotor power factor = %0.3f lagging\" %cosfi_2\n",
"print \"(i) Rotor Current = %0.2f Ampere per phase\" %I2\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #Slip\n",
"cosfi_2r=R2/mh.sqrt(R2**2+(S*X2)**2) #lagging power factor\n",
"I2r=S*E2ph/mh.sqrt(R2**2+(S*X2)**2) #in Ampere\n",
"print \"(ii) Rotor power factor = %0.4f lagging\" %cosfi_2r\n",
"print \"(ii) Rotor Current = %0.3f Ampere\" %I2r"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Rotor power factor = 0.196 lagging\n",
"(i) Rotor Current = 67.94 Ampere per phase\n",
"(ii) Rotor power factor = 0.9806 lagging\n",
"(ii) Rotor Current = 13.587 Ampere\n"
]
}
],
"prompt_number": 104
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.6 Page 44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math as mh\n",
"# Given data\n",
"P=4 #No. of poles\n",
"f=50 #in Hz\n",
"R2=0.1 #in ohm\n",
"X2=1 #in ohm\n",
"N=1440 #in rpm\n",
"E1_line=400 #in volt\n",
"Kdash=2 #stator turns by rotor turns\n",
"\n",
"#Calculations\n",
"K=1/Kdash #rotor turns by stator turns\n",
"Ns=120*f/P #in rpm\n",
"E1ph=E1_line/mh.sqrt(3) #\n",
"#Formula : E2ph/E1ph=K\n",
"E2ph=E1ph*K #in volt\n",
"S=(Ns-N)/Ns #Slip\n",
"ns=Ns/60 #synchronous speed in rps\n",
"T=3/(2*mh.pi*ns)*(S*E2ph**2*R2)/(R2**2+(S*X2)**2) #in N-m\n",
"print \"Torque devloped on full load = %0.2f N-m \"%T "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Torque devloped on full load = 87.81 N-m \n"
]
}
],
"prompt_number": 105
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.7 Page 45"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, pi\n",
"# Given data\n",
"P=4 #No. of poles\n",
"f=50 #in Hz\n",
"Kdash=4 #stator turns by rotor turn\n",
"R2=0.01 #in ohm\n",
"X2=0.1 #in ohm\n",
"E1_line=400 #in volt\n",
"\n",
"#Calculations\n",
"K=1/Kdash #rotor turns by stator turns\n",
"Ns=120*f/P #in rpm\n",
"E1ph=E1_line/sqrt(3) #\n",
"#Formula : E2ph/E1ph=K\n",
"E2ph=E1ph*K #in volt\n",
"#(i) at start S=1\n",
"ns=Ns/60 #in rps\n",
"K=3/2/pi/ns \n",
"Tst=K*E2ph**2*R2/(R2**2+X2**2) #in N-m\n",
"print \"(i) Starting Torque = %0.2f N-m\" %Tst\n",
"#part (ii) \n",
"Sm=R2/X2 #slip for max torque\n",
"print \"(ii) Slip at which max torque devloped = %0.2f %% \"%(Sm*100) \n",
"#Part (iii)\n",
"N=Ns*(1-Sm) #in rpm\n",
"print \"(iii) Speed at which max torque occur = %0.2f rpm\" %N\n",
"#Part (iv)\n",
"Tm=K*E2ph**2/2/X2 #in N-m\n",
"print \"(iv) Maximum torque = %0.2f N-m\" %Tm\n",
"#Part (v)\n",
"Sf=4 #in %\n",
"Sf=Sf/100 #slip\n",
"Tfl=K*Sf*E2ph**2*R2/(R2**2+(Sf*X2)**2) #in N-m\n",
"print \"(v) Full load Torque devloped = %0.2f N-m \"%Tfl "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Starting Torque = 63.03 N-m\n",
"(ii) Slip at which max torque devloped = 10.00 % \n",
"(iii) Speed at which max torque occur = 1350.00 rpm\n",
"(iv) Maximum torque = 318.31 N-m\n",
"(v) Full load Torque devloped = 219.52 N-m \n"
]
}
],
"prompt_number": 106
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.8 Page 46"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=24 #No. of poles\n",
"f=50 #in Hz\n",
"R2=0.016 #in ohm\n",
"X2=0.265 #in ohm\n",
"N=247 #in rpm\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"Sf=(Ns-N)/Ns #full load slip\n",
"Sm=R2/X2 #max slip\n",
"Tfl_BY_Tm=2*Sm*Sf/(Sm**2+Sf**2) #unitless\n",
"print \"Ratio of full load torque to max torque : \" ,round(Tfl_BY_Tm,4)\n",
"Tst_BY_Tm=2*Sm/(1+Sm**2) #unitless\n",
"print \"Ratio of starting torque to max torque : \" ,round(Tst_BY_Tm,4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio of full load torque to max torque : 0.3824\n",
"Ratio of starting torque to max torque : 0.1203\n"
]
}
],
"prompt_number": 107
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.9 Page 47"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"R2=0.04 #in ohm\n",
"X2=0.2 #in ohm\n",
"\n",
"#Calculations\n",
"R2dash=X2 #in ohm (for Tm=Tst)\n",
"#formula : R2dash=R2+rex\n",
"Rex=R2dash-R2 #in ohm/phase\n",
"print \"(i) External resistance required = %0.2f ohm/phase\"%Rex \n",
"from sympy import symbols, solve\n",
"k, E2, R2dash = symbols('k, E2, R2dash')\n",
"# For Tst = 1/2*Tm\n",
"Tm = k*E2**2/2/X2\n",
"Tst = k*E2**2*R2/(R2**2+X2**2)\n",
"#R2dash = R2+Rex\n",
"##Putting R2 dash in place of R2\n",
"Tst = k*E2**2*R2dash/(R2dash**2+X2**2)\n",
"#Equating Tst = 1/2*Tm gives\n",
"expr = R2dash**2-4*X2*R2dash+X2**2\n",
"R2dash = solve(expr, R2dash)\n",
"R2dash = R2dash[0] #ohm as R2 can't >X2\n",
"Rex = R2dash-R2\n",
"print \"(ii) External resistance required = %0.4f ohm/phase\" %Rex"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) External resistance required = 0.16 ohm/phase\n",
"(ii) External resistance required = 0.0136 ohm/phase"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 108
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.10 Page 48"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"f=50 #in Hz\n",
"P=8 #no. of poles\n",
"Tsh=190 #in N-m\n",
"fr=1.5 #in Hz\n",
"MechLoss=700 #in watts\n",
"\n",
"#Calculations\n",
"S=fr/f #Slip\n",
"Ns=120*f/P #in rpm\n",
"N=Ns*(1-S) #in rpm\n",
"Pout=Tsh*2*pi*N/60 #in watts\n",
"Pm=Pout+MechLoss #in watts\n",
"#formula-: P2:Pc:Pm=1:S:1-S\n",
"Pc=Pm*S/(1-S) #in watts\n",
"print \"Rotor Copper loss = %0.3f W\" %Pc"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rotor Copper loss = 469.326 W\n"
]
}
],
"prompt_number": 109
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.11 Page 49"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"f=50 #in Hz\n",
"P=4 #no. of poles\n",
"Pin=50 #in kW\n",
"N=1440 #in rpm\n",
"StatorLoss=1000 #in watts\n",
"FrictionalLoss=650 #in watts\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #Slip\n",
"\n",
"N=Ns*(1-S) #in rpm\n",
"P2=Pin-StatorLoss/1000 #in KW\n",
"#formula-: P2:Pc:Pm=1:S:1-S\n",
"Pc=S*P2 #in KW\n",
"Pm=P2-Pc #in KW\n",
"Pout=Pm-FrictionalLoss/1000 #in KW\n",
"Eff=Pout/Pin*100 #in %\n",
"print \"Full load efficiency = %0.2f %%\" %Eff"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Full load efficiency = 92.78 %\n"
]
}
],
"prompt_number": 110
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.12 Page 50"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"f=50 #in Hz\n",
"phase=3 #no. of phase\n",
"P=4 #no. of poles\n",
"Tsh=300 #in N-m\n",
"Tlost=50 #in N-m\n",
"fr=120 #in cycles/min\n",
"fr=fr/60 #in Hz\n",
"I2r=60 #in Ampere/phase\n",
"\n",
"#Calculations\n",
"S=fr/f #slip\n",
"print \"(i) Slip = %0.2f %%\" %(S*100)\n",
"Ns=120*f/P #in rpm\n",
"N=Ns*(1-S) #in rpm\n",
"Pout=Tsh*2*pi*N/60 #watts\n",
"print \"(ii) Net output Power = %0.3f kW\" %(Pout/1000)\n",
"FricLoss=Tlost*2*pi*N/60 #in watts\n",
"Pm=Pout+FricLoss #in watts\n",
"#formula-: P2:Pc:Pm=1:S:1-S\n",
"Pc=S*Pm/(1-S) #copper loss in Watts\n",
"PcPERphase=Pc/phase #Copper loss per phase in watts\n",
"print \"(iii) Rotor copper loss per phase = %0.4f W\"%PcPERphase \n",
"P2=Pc/S #in watts\n",
"Eff=Pm/P2*100 #in %\n",
"print \"(iv) Rotor efficiency = %0.2f %% \"%Eff \n",
"#Formula : CuLossPerPhase=I2r**2*R2 #in watts\n",
"R2=PcPERphase/I2r**2 #in ohm/phase\n",
"print \"(v) Rotor resistance per phase = %0.4f W/phase \"%R2 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Slip = 4.00 %\n",
"(ii) Net output Power = 45.239 kW\n",
"(iii) Rotor copper loss per phase = 733.0383 W\n",
"(iv) Rotor efficiency = 96.00 % \n",
"(v) Rotor resistance per phase = 0.2036 W/phase \n"
]
}
],
"prompt_number": 111
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.13 Page 51"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"Pout=25 #in KW\n",
"f=50 #in Hz\n",
"phase=3 #no. of phase\n",
"P=4 #no. of poles\n",
"N=1410 #in rpm\n",
"MechLoss=850 #in watts\n",
"StatLossBYCuLoss=1.17 \n",
"I2r=65 #in Ampere\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #slip\n",
"Pm=Pout*1000+MechLoss #in watts\n",
"print \"Gross mechanical power devloped = %0.2f W\" %Pm\n",
"#formula-: P2:Pc:Pm=1:S:1-S\n",
"Pc=S*Pm/(1-S) #copper loss in Watts\n",
"print \"Rotor Copper Losses = %0.2f W\"%Pc\n",
"R2=Pc/phase/I2r**2 #in ohm/phase\n",
"print \"Rotor resistance per phase = %0.2f ohm\" %R2\n",
"StatorLoss=1.7*Pc #in watts\n",
"P2=Pc/S #in Watts\n",
"Pin=P2+StatorLoss #in watts\n",
"Eff=Pout*1000/Pin*100 #in %\n",
"print \"Full laod Efficiency = %0.2f %%\" %Eff"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Gross mechanical power devloped = 25850.00 W\n",
"Rotor Copper Losses = 1650.00 W\n",
"Rotor resistance per phase = 0.13 ohm\n",
"Full laod Efficiency = 82.49 %\n"
]
}
],
"prompt_number": 112
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.14 Page 52"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"Pout=24 #in KW\n",
"P=8 #no. of poles\n",
"N=720 #in rpm\n",
"VL=415 #in volt\n",
"IL=57 #in Ampere\n",
"f=50 #in Hz\n",
"phase=3 #no. of phase\n",
"cosfi=0.707 #power factor\n",
"MechLoss=1000 #in watts\n",
"Rs=0.1 #in ohm/phase\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #slip\n",
"Pm=Pout*1000+MechLoss #in watts\n",
"#formula-: P2:Pc:Pm=1:S:1-S\n",
"#Pc=S*Pm/(1-S) #copper loss in Watts\n",
"Tsh=Pout*10**3/(2*pi*N/60) #in N-m\n",
"print \"Shaft Torque = %0.3f N-m\" %Tsh\n",
"T=Pm/((2*pi*N/60)) #in N-m\n",
"print \"Gross torque devloped = %0.3f N-m\"%T\n",
"Pc=S*Pm/(1-S) #copper loss in Watts\n",
"print \"Rotor Cu losses = %0.2f W\" %Pc\n",
"P2=Pc/S #in watts\n",
"Pin=sqrt(3)*VL*IL*cosfi #in watts\n",
"Is=IL #stator current per phase in Ampere\n",
"StatorCuLoss=3*Is**2*Rs #in watts\n",
"print \"Stator Copper losses = %0.2f W\" %StatorCuLoss\n",
"StatorLosses=Pin-P2 #in watts\n",
"StatorIronLoss=StatorLosses-StatorCuLoss #in watts\n",
"print \"Stator Iron losses = %0.2f W\" %StatorIronLoss\n",
"Eff=Pout*10**3/Pin*100 #in %\n",
"print \"Efficiency = %0.2f %%\" %Eff"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Shaft Torque = 318.310 N-m\n",
"Gross torque devloped = 331.573 N-m\n",
"Rotor Cu losses = 1041.67 W\n",
"Stator Copper losses = 974.70 W\n",
"Stator Iron losses = 1950.60 W\n",
"Efficiency = 82.85 %\n"
]
}
],
"prompt_number": 113
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.15 Page 54"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import cmath\n",
"from numpy import array, sqrt, pi\n",
"from math import degrees, cos\n",
"# Given data\n",
"Poles=12 #no. of poles\n",
"V1=420 #in volt\n",
"f=50 #in Hz\n",
"r1=2.95 #in watts\n",
"x1=6.82 #in watts\n",
"r2dash=2.08 #in watts\n",
"x2dash=4.11 #in ohm/phase\n",
"ImLine=6.7 #in Ampere\n",
"TcoreLoss=269 #in watts\n",
"S=3 #slip in %\n",
"\n",
"#Calculations\n",
"S=S/100 #slip\n",
"Im=ImLine/sqrt(3) #in Ampere\n",
"Im_bar=Im*cmath.exp(1J*(-pi/2))*(r1+1J*x1) #in Ampere\n",
"\n",
"\n",
"from sympy import symbols, solve\n",
"E1 = symbols('E1')\n",
"V1 = E1+Im_bar\n",
"#V1=(E1+real(Im_bar))+imag(Im_bar) \n",
"#Equating magnitude of both sides gives a polynomial for E1\n",
"V1=420 # Volt\n",
"poly = (E1+Im_bar.real)**2+Im_bar.imag**2-V1**2\n",
"E1 = solve(poly, E1)\n",
"E1 = E1[1] # V # #discarding -ve value\n",
"Xo=E1/Im #in ohm\n",
"\n",
"#Zeq=Xo*exp(1J*(pi/2))*(r2dash/S)/(1J*Xo+1J*x2dash+r2dash/S) \n",
"Zeq = complex(0,Xo)*complex(r2dash/S,x2dash)/(complex(0,Xo)+complex(r2dash/S,x2dash))\n",
"Zin=r1+1J*x1+Zeq #in ohm\n",
"I1=V1/Zin #in Ampere\n",
"print \"Input current : Magnitude =\",round(abs(I1),3),\" & phase =\",round(degrees(cmath.phase(I1)),2) ,\"degree\"\n",
"# Note : In the textbook +ve sign of phase is shown by mistake.\n",
"cosfi=cos(round(degrees(cmath.phase(I1)),2)*pi/180) #lagging power factor\n",
"print \"Power factor =\",round(cosfi,4),\"lagging\" \n",
"I2r_dash=I1*complex(0,Xo)/complex(r2dash,(Xo+x2dash)) #in Ampere\n",
"print \"Rotor current : Magnitude =\",round(abs(I2r_dash),3),\" & phase =\",round(degrees(cmath.phase(I2r_dash)),2) ,\"degree\"\n",
"Ns=120*f/Poles #in rpm\n",
"T=9.55*3*I2r_dash.real**2*r2dash/S/Ns #in N-m\n",
"print \"Torque developed =\",round(T,3),\"N-m\" \n",
"Zth=complex(r1,x1)*complex(0,Xo)/(complex(r1,x1)+complex(0,Xo)) #in Ohm\n",
"Rth=Zth.real #in ohm\n",
"Xth=Zth.imag #in ohm\n",
"Vth=V1*complex(0,Xo)/complex(r1,(Xth+Xo)) #in Volt\n",
"Ws=(2*pi*Ns/60) #in rad/sec\n",
"Tm=(3/Ws)*0.5*(Vth.real)**2/(Rth+sqrt(Rth**2+(Xth+x2dash)**2)) #in N-m\n",
"print \"Maximum torque devloped = %0.2f N-m \"%(Tm) \n",
"Sm=r2dash/sqrt(Rth**2+(Xth+x2dash)**2) #slip\n",
"Nm=Ns*(1-Sm) #\n",
"print \"Speed at maximum torque = %0.1f rpm\" %Nm \n",
"#Answer for rotor equivalent Current and Torque developed is wrong in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Input current : Magnitude = 6.732 & phase = -40.04 degree\n",
"Power factor = 0.7656 lagging\n",
"Rotor current : Magnitude = 6.469 & phase = -38.91 degree\n",
"Torque developed = 100.678 N-m\n",
"Maximum torque devloped = 331.11 N-m \n",
"Speed at maximum torque = 404.4 rpm\n"
]
}
],
"prompt_number": 114
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.16 Page 57"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import acos, atan\n",
"from cmath import exp\n",
"# Given data\n",
"V=440 #in volt\n",
"P=8 #no. of poles\n",
"Pout=40 #in KW\n",
"f=50 #in Hz\n",
"phase=3 #no. of phase\n",
"R1=0.1 #in ohm\n",
"X1=0.4 #in ohm\n",
"R2dash=0.15 #Equivalent rotor resistance in ohm\n",
"X2dash=0.44 #Equivalent rotor reactance in ohm\n",
"I0=20*exp(1J*-acos(0.09)) #in Ampere\n",
"N=727.5 #in rpm\n",
"MechLoss=1000 #in watts\n",
"CoreLoss=1250 #in watts\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #slip\n",
"RLdash=R2dash*(1-S)/S\n",
"V1=V/sqrt(3) #in volt\n",
"R1e=R1+R2dash #in ohm\n",
"X1e=X1+X2dash #in ohm\n",
"I2rdash=V1/(R1e+RLdash+1J*X1e) #in Ampere\n",
"I1bar=I0+I2rdash #in Ampere\n",
"InputCurrent=abs(I1bar) #in Ampere\n",
"InputPF=cos(atan((I1bar.imag)/(I1bar.real))) #\n",
"print \"(i) Input Current = %0.3f Ampere & PF = %0.4f lagging\" %(InputCurrent,InputPF)\n",
"T=3*abs(I2rdash)**2*R2dash/S/(2*pi*Ns/60) #in N-m\n",
"print \"(ii) Torque Developed = %0.4f N-m\"%T\n",
"P2=3*abs(I2rdash)**2*R2dash/S #in Watts\n",
"#Formula : P2:Pc:Pm=1:S:1-S\n",
"Pm=(1-S)*P2 #in Watts\n",
"TotPout=Pm-MechLoss #in watts\n",
"print \"(iii) Output power = %0.2f Watts\" %TotPout\n",
"TotCuLoss=3*abs(I2rdash)**2*R1e #in watts\n",
"Eff=TotPout/(TotPout+TotCuLoss+CoreLoss+MechLoss)*100 #in %\n",
"print \"(iv) Efficiency = %0.2f %%\" %Eff"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Input Current = 57.518 Ampere & PF = 0.8744 lagging\n",
"(ii) Torque Developed = 461.3394 N-m\n",
"(iii) Output power = 34146.51 Watts\n",
"(iv) Efficiency = 89.37 %\n"
]
}
],
"prompt_number": 115
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.17 Page 59"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"Z1=0.07+1J*0.4 #in ohm\n",
"Z2dash=0.08+1J*0.2 #in ohm\n",
"V1_line=200 #in volt\n",
"\n",
"#Calculations\n",
"R1=Z1.real #in ohm\n",
"X1=Z1.imag #in ohm\n",
"R2dash=Z2dash.real #in ohm\n",
"X2dash=Z2dash.imag #in ohm\n",
"R1e=R1+R2dash #in ohm\n",
"X1e=X1+X2dash #in ohm\n",
"Z1e=R1e+1J*X1e #in ohm\n",
"Z1e_mag=abs(Z1e) #magnitude of Z1e in ohm\n",
"V1PerPhase=V1_line/sqrt(3) #in volt\n",
"Pout_max=3*V1PerPhase**2/2/(R1e+Z1e) #\n",
"S=R2dash/(R2dash+Z1e_mag) #\n",
"print \"Slip = %0.2f %% \"%(S*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slip = 11.45 % \n"
]
}
],
"prompt_number": 116
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.18 Page 59"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #in poles\n",
"f=50 #in Hz\n",
"Pout=30 #in HP\n",
"VL=400 #in volt\n",
"Eta=0.8 #Efficiency\n",
"cosfi=0.75 #lagging power factor\n",
"\n",
"#Calculations\n",
"Pout=Pout*735.5 #in Watts\n",
"Pin=Pout/Eta #in Watts\n",
"#Formula : Pin=sqrt(3)*VL*IL*cosfi\n",
"IL=Pin/sqrt(3)/VL/cosfi #in Ampere\n",
"print \"Current by the mains = %0.2f A\" %IL"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current by the mains = 53.08 A\n"
]
}
],
"prompt_number": 117
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.19 Page 60"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #in poles\n",
"Pout=37 #in HP\n",
"f=50 #in Hz\n",
"N=1425 #in rpm\n",
"MechLoss=3 #in HP\n",
"StatorLoss=2500 #in watts\n",
"VL=500 #in volt\n",
"cosfi=0.9 #power factor\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #slip\n",
"print \"(i) Slip is : \" ,S\n",
"Pout=Pout*735.5 #in Watts\n",
"MechLoss=MechLoss*735.5 #in Watts\n",
"Pin=Pout+MechLoss #in Watts\n",
"#Formula : P2:Pc:Pin=1:5:1-S\n",
"Pc=(S/(1-S))*Pin #in watts\n",
"print \"(ii) Rotor Cu Loss = %0.2f W\" %Pc\n",
"P2=Pc/S #in Watts\n",
"Pin=P2+StatorLoss #in watts\n",
"print \"(iii) Total power input = %0.2f W\" %Pin\n",
"Eta=Pout/Pin*100 #in %\n",
"print \"(iv) Efficiency = %0.2f %% \"%Eta \n",
"fr=S*f #in Hz\n",
"fr=fr*60 #in cycles/min\n",
"print \"(v) No. of cycles per minute : \" ,fr\n",
"#Part (ii) & (iii) answer is wrong in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Slip is : 0.05\n",
"(ii) Rotor Cu Loss = 1548.42 W\n",
"(iii) Total power input = 33468.42 W\n",
"(iv) Efficiency = 81.31 % \n",
"(v) No. of cycles per minute : 150.0\n"
]
}
],
"prompt_number": 118
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.20 Page 61"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"E2line=60 #in Volt\n",
"R2=0.6 #in ohm\n",
"X2=4 #in ohm\n",
"Rx=5 #in ohm\n",
"Xx=2 #in ohm\n",
"S=4 #in %\n",
"\n",
"#Calculations\n",
"E2ph=E2line/sqrt(3) #in volt\n",
"ZT=R2+1J*X2+Rx+1J*Xx #\n",
"I2=E2ph/abs(ZT) #in Ampere\n",
"print \"(i) Rotor Current per phase = %0.4f A\" %I2\n",
"S=S/100 #slip\n",
"Z2r=R2+1J*S*X2 #in ohm\n",
"I2r=S*E2ph/abs(Z2r) #in Ampere\n",
"print \"(ii) Rotor Current per phase = %0.4f Ampere \"%I2r "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Rotor Current per phase = 4.2207 A\n",
"(ii) Rotor Current per phase = 2.2314 Ampere \n"
]
}
],
"prompt_number": 119
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.21 Page 62"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"f=50 #in Hz\n",
"P2=3000 #in watts\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"T=P2/(2*pi*Ns/60) #in N-m\n",
"print \"Torque Devloped = %0.3f N-m \"%T \n",
"T=T*(2*pi*Ns/60) #in syn. Watt\n",
"print \"Torque Devloped = %0.f syn. Watt \"%T "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Torque Devloped = 19.099 N-m \n",
"Torque Devloped = 3000 syn. Watt \n"
]
}
],
"prompt_number": 120
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.22 Page 62"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"E1Line=1000 #in volt\n",
"R2=0.01 #in ohm\n",
"X2=0.2 #in ohm\n",
"I2st=200 #in Ampere\n",
"ratio=3.6 #ratio of stator to rotor turns\n",
"\n",
"#Calculations\n",
"K=1/ratio #ratio of rotor to stator turns\n",
"E1ph=E1Line/sqrt(3) #in Volt\n",
"E2ph=K*E1ph #in volt\n",
"#Let R2dash=R2+Rx\n",
"#Formula : I2st=E2ph/sqrt(R2dash**2+X2**2) \n",
"R2dash=sqrt((E2ph/I2st)**2-X2**2)\n",
"Rx=R2dash-R2 #in ohm\n",
"print \"External resistance required per phase = %0.4f ohm \"%Rx "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"External resistance required per phase = 0.7665 ohm \n"
]
}
],
"prompt_number": 121
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.23 Page 63"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"VL=400 #in volt\n",
"E1Line=VL #in volt\n",
"P=4 #no. of poles\n",
"S=5 #in %\n",
"f=50 #in Hz\n",
"R2=0.15 #in ohm\n",
"X2=1 #in ohm\n",
"ratio=2 #ratio of stator to rotor turns\n",
"\n",
"#Calculations\n",
"S=S/100 #slip\n",
"E1ph=E1Line/sqrt(3) #in Volt\n",
"K=1/ratio #ratio of rotor to stator turns\n",
"E2ph=K*E1ph #in volt\n",
"Ns=120*f/P #in rpm\n",
"ns=Ns/60 #in rps\n",
"T=(3/2/pi/ns)*S*E2ph**2*R2/(R2**2+(S*X2)**2) #in N-m\n",
"print \"(i) Total Torque devloped = %0.2f N-m \"%T \n",
"Tm=(3/2/pi/ns)*E2ph**2/2/X2 #in N-m\n",
"print \"(ii) Maximum Torque = %0.2f N-m\"%Tm \n",
"Sm=R2/X2 #maximum slip\n",
"N=Ns*(1-Sm) #in rpm\n",
"print \"(iii) Speed at maximum torque = %0.2f rpm \"%N "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Total Torque devloped = 76.39 N-m \n",
"(ii) Maximum Torque = 127.32 N-m\n",
"(iii) Speed at maximum torque = 1275.00 rpm \n"
]
}
],
"prompt_number": 122
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.24 Page 64"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import cos, atan\n",
"# Given data\n",
"VL=400 #in volt\n",
"f=50 #in Hz\n",
"P=6 #no. of poles\n",
"Z1=0.3+1J*0.4 #in ohm\n",
"Z2dash=0.2+1j*0.4 #in ohm\n",
"X0=20 #Magnetic reactance in ohm\n",
"R0=100 #resistance for core loss in ohm\n",
"S=4 #in %\n",
"StatorLoss=2 #in KW\n",
"MechLoss=2 #in KW\n",
"#Calculations\n",
"R1=Z1.real #in ohm\n",
"R2dash=Z2dash.real #in ohm\n",
"X1=Z1.imag #in ohm\n",
"X2dash=Z2dash.imag #in ohm\n",
"S=S/100 #slip\n",
"V1=VL/sqrt(3) #in volt\n",
"Ns=120*f/P #in rpm\n",
"Ri=R2dash*(1-S)/S #in ohm\n",
"R1e=R1+R2dash #in ohm\n",
"X1e=X1+X2dash #in ohm\n",
"I2rdash=V1/(R1e+Ri+1J*X1e) #in Ampere\n",
"Ic=V1/R0 #in Ampere\n",
"Im=V1/(1J*X0) #in Ampere\n",
"I0=(Ic+Im) #in Ampere\n",
"CoreLoss=Ic**2*R0 #Core loss per phase in Watts\n",
"I1=I0+I2rdash #in Ampere\n",
"Istator=abs(I1) #in Ampere\n",
"cosfi=cos(atan(I1.imag/I1.real)*pi/180) #lagging power factor\n",
"\n",
"Pc=3*abs(I2rdash)**2*R2dash #in Watts\n",
"#Here P2:P0:Pm=1:S:1-S\n",
"Pm=Pc*(1-S)/S #in watts\n",
"Pout=Pm-MechLoss*1000 #in watts\n",
"StatorCuLoss=3*abs(I1)**2*R1 #in watts\n",
"TotLoss=CoreLoss*3+StatorCuLoss+Pc+MechLoss*1000 #in watts\n",
"Eff=Pout/(Pout+TotLoss)*100 #in %\n",
"N=Ns*(1-S) #in rpm\n",
"print \"(a) Motor Speed = %0.2f rpm \"%N\n",
"print \"(b) Stator current = %0.2f Ampere \"%Istator \n",
"print \"(c) Power factor lagging : \" ,round(cosfi,5)\n",
"print \"(d) Motor Output = %0.2f W\" %Pout\n",
"print \"(e) Efficiency = %0.2f %% \"%Eff \n",
"#Answer of Pout & PF is wrong in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Motor Speed = 960.00 rpm \n",
"(b) Stator current = 48.38 Ampere \n",
"(c) Power factor lagging : 0.99998\n",
"(d) Motor Output = 24731.64 W\n",
"(e) Efficiency = 78.38 % \n"
]
}
],
"prompt_number": 123
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.25 Page 66"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"V=440 #in volt\n",
"f=50 #in Hz\n",
"P=4 #no. of poles\n",
"X1=5.2 #in ohm\n",
"R2dash=1.2 #in ohm\n",
"X2dash=4.5 #in ohm\n",
"\n",
"#Calculations\n",
"#Rth=R1 #in ohm\n",
"#Xth=X1 #in ohm\n",
"#Formula : R2dash/Sm=sqrt(X1**2+X2dash**2)\n",
"Sm=R2dash/(X1+X2dash) #Maximum Slip\n",
"I1=V/sqrt(3)/sqrt((R2dash/Sm)**2+(X1+X2dash)**2) #in Ampere\n",
"I2dash=I1 #in Ampere(Neglecting I0)\n",
"Ns=120*f/P #in rpm\n",
"Tmax=3*I2dash**2*R2dash/Sm/2/pi/Ns*60 #in N-m\n",
"print \"Maximum Torque = %0.2f N-m \"%Tmax \n",
"print \"Maximum Slip = %0.2f %% \"%(Sm*100) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum Torque = 63.53 N-m \n",
"Maximum Slip = 12.37 % \n"
]
}
],
"prompt_number": 124
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.26 Page 67"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import symbols, solve\n",
"R2dash = symbols('R2dash')\n",
"# Given data\n",
"f=50 #in Hz\n",
"P=4 #no. of poles\n",
"X2=0.1 #in ohm\n",
"R2=0.02 #in ohm\n",
"#Tst=2/3*Tmax\n",
"TstByTm=2/3 #ratio\n",
"#Calculations\n",
"#Tm proportional to E2**2/(2*X2)\n",
"#formula : TstByTm=(E2**2*R2dash/(R2dash**2+X2**2))/(E2**2/(2*X2))\n",
"expr = (R2dash**2)*TstByTm-2*X2*R2dash+TstByTm*X2**2\n",
"R2dash=solve(expr, R2dash) #\n",
"R2dash=R2dash[0] #discarding higher value bcoc R2dash < X2\n",
"Rex=R2dash-R2 #in ohm\n",
"print \"Extra resistance required = %0.3f ohm \"%Rex "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Extra resistance required = 0.018 ohm \n"
]
}
],
"prompt_number": 125
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.27 Page 68"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"VL=3300 #in volt\n",
"f=50 #in Hz\n",
"P=10 #no. of poles\n",
"X2=0.25 #in ohm\n",
"R2=0.015 #in ohm\n",
"Sfl=2.5 #Slip in %\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"N=Ns*(1-Sfl/100) #in rpm\n",
"print \"(1.) The speed of motor, N = %0.2f rpm \"% N \n",
"Sm=R2/X2 #Max Slip\n",
"Nm=Ns*(1-Sm) #Max speed in rpm\n",
"print \"(2.) Speed of motor, Ns = %0.2f rpm\"%Nm \n",
"TmByTfl=Sm*R2/(R2**2+(Sm*X2)**2)*(R2**2+(Sfl/100*X2)**2)/(Sfl/100)/R2 #ratio\n",
"print \"(3.) Ratio of max torque to full load torque : \" ,round(TmByTfl,4)\n",
"#Answer of 1st part is wrong in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(1.) The speed of motor, N = 585.00 rpm \n",
"(2.) Speed of motor, Ns = 564.00 rpm\n",
"(3.) Ratio of max torque to full load torque : 1.4083\n"
]
}
],
"prompt_number": 126
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.28 Page 69"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sin, acos, degrees\n",
"from cmath import phase\n",
"# Given data\n",
"\n",
"V0=400 #in volt\n",
"f=50 #in Hz\n",
"P=10 #no. of poles\n",
"R1=1.75 #in ohm\n",
"X1=5.5 #in ohm\n",
"R2dash=2.25 #in ohm\n",
"X2dash=6.6 #in ohm\n",
"I0=3.8 #in Ampere\n",
"W0=310 #in watts\n",
"S=4 #in %\n",
"\n",
"#Calculations\n",
"S=S/100 #slip in ratio\n",
"#Formula : W0=sqrt(3)*V0*I0*cos_fi0\n",
"cos_fi0=W0/sqrt(3)/V0/I0 #power factor\n",
"sin_fi0=sin(acos(cos_fi0)*pi/180) \n",
"Ic=I0*cos_fi0 #in Ampere\n",
"Im=I0*sin_fi0 #in Ampere\n",
"Vph=V0/sqrt(3) #in Volt\n",
"R0=Vph/Ic #in ohm\n",
"X0=Vph/Im #in ohm\n",
"Ns=120*f/P #in rpm\n",
"RLdash=R2dash*(1-S)/S #in ohm\n",
"R1e=R1+R2dash #in ohm\n",
"X1e=X1+X2dash #in ohm\n",
"I2rdash=Vph/(R1e+RLdash+1J*X1e) #in Ampere\n",
"print \"Rotor Current : Magnitude =\",round(abs(I2rdash),3),\"A & Phase =\",round(degrees(phase(I2rdash)),2),\"degree\"\n",
"I0_bar=Ic-1J*Im #in Ampere\n",
"I1_bar=I0_bar+I2rdash #Supply current in Ampere\n",
"print \"Supply Current : Magnitude =\",round(abs(I1_bar),3),\"A & Phase =\",round(degrees(phase(I1_bar)),2),\"degree\"\n",
"cosfi=cos(pi/180*atan((I1_bar.imag)/(I1_bar.real))) #Lagging power factor\n",
"print \"Power factor = %0.4f lagging \"%cosfi\n",
"Pc=3*abs(I2rdash)**2*R2dash #in watts\n",
"#Formula : P2:Pc:Pm=1:S:1-S\n",
"Pm=Pc*(1-S)/S ##in watts\n",
"print \"Mechanical power devloped = %0.2f N-m \"%Pm \n",
"N=Ns*(1-S) #in rpm\n",
"w=2*pi*N/60 #in rad/sec\n",
"T=Pm/w #in N-m\n",
"print \"Gross load torque = %0.3f N-m \"%T \n",
"# Supply current and power factor ans is wrong in te textbook."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rotor Current : Magnitude = 3.898 A & Phase = -11.78 degree\n",
"Supply Current : Magnitude = 4.356 A & Phase = -11.82 degree\n",
"Power factor = 1.0000 lagging \n",
"Mechanical power devloped = 2461.25 N-m \n",
"Gross load torque = 40.804 N-m \n"
]
}
],
"prompt_number": 127
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.29 Page 70\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"PA=12 #no. of poles\n",
"Ns=500 #in rpm\n",
"N=1440 #in rpm\n",
"\n",
"#Calculations\n",
"#Formula : Ns=120*f/PA\n",
"f=Ns/120*PA #in Hz\n",
"PM=4 #assumed for motor\n",
"Ns=120*f/PM #in rpm(For motor)\n",
"S=(Ns-N)/Ns*100 #slip in %\n",
"print \"Slip = %0.2f %% \"%S "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slip = 4.00 % \n"
]
}
],
"prompt_number": 128
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.30 Page 71"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"R2=0.04 #in ohm\n",
"X2=0.2 #in ohm\n",
"TstByTm=50 #in %\n",
"\n",
"#Calculations\n",
"Sm=1 #slip for max Torque\n",
"R2dash=Sm*X2 #in ohm\n",
"Rx=R2dash-R2 #in ohm\n",
"print \"(i) External resistance required for max Torque = %0.2f ohm\"%Rx \n",
"TstByTm=TstByTm/100 #in ratio\n",
"#Formula : Tst proportional to E2**2*R2dash/(R2dash**2+X2**2)\n",
"#Formula : Tm Proportional to E2**2/2/X2\n",
"from sympy import symbols, solve\n",
"R2dash = symbols('R2dash')\n",
"expr = R2dash**2+X2**2-2*X2*R2dash/TstByTm#Polynomial for R2dash\n",
"R2dash=solve(expr, R2dash) #\n",
"R2dash=R2dash[0] #discarding higher value bcoc R2dash < X2\n",
"Rx=R2dash-R2 #in ohm\n",
"print \"(ii) Extra resistance required for 50%% max Torque at start = %0.4f ohm\"%Rx "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) External resistance required for max Torque = 0.16 ohm\n",
"(ii) Extra resistance required for 50% max Torque at start = 0.0136 ohm"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 129
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.31 Page 72"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"f=50 #in Hz\n",
"P=8 #no. of poles\n",
"Sf=40 #in %\n",
"R2=0.001 #in ohm/phase\n",
"X2=0.005 #in ohm/phase\n",
"\n",
"#Calculations\n",
"Sf=Sf/100 #slip\n",
"#Formula : T proportional to S*R2/(R2**2+(S*X2)**2)\n",
"Sm=R2/X2 #slip for max Torque\n",
"TmByTfl=Sm*R2/(R2**2+(Sm*X2)**2)*(R2**2+(Sf*X2)**2)/Sf/R2 #in ratio\n",
"print \"Ratio of max torque to full load torque : \" ,TmByTfl\n",
"Ns=120*f/P #in rpm\n",
"N=Ns*(1-Sm) #in rpm\n",
"print \"Speed for maximum torque = %0.2f rpm \"%N "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio of max torque to full load torque : 1.25\n",
"Speed for maximum torque = 600.00 rpm \n"
]
}
],
"prompt_number": 130
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.32 Page 73"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"f=50 #in Hz\n",
"P=4 #no. of poles\n",
"VL=400 #in volt\n",
"E2=100 #in volt\n",
"R2=50 #in milli ohm\n",
"X2=0.5 #in ohm\n",
"\n",
"#Calculations\n",
"R2=R2*10**-3 #in ohm\n",
"Sm=R2/X2 #Maximum Slip\n",
"ns=(120*f/P)/60 #in rpS\n",
"Tmax=3/2/pi/ns*Sm*E2**2*R2/(R2**2+(Sm*X2)**2) #in N-m\n",
"print \"Maximum Torque = %0.2f N-m \"%Tmax \n",
"print \"Slip at which Tmax occur : \" ,Sm"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum Torque = 190.99 N-m \n",
"Slip at which Tmax occur : 0.1\n"
]
}
],
"prompt_number": 131
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.33 Page 73"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"#Tst=100% of Tfl #in %\n",
"#Tm=100% of Tfl #in %\n",
"TstByTfl=100/100 #ratio\n",
"TmByTfl=200/100 #ratio\n",
"\n",
"#Calculations\n",
"#Formula : T proportional to S*E2**2*R2/(R2**2+(S*X2)**2)\n",
"#Formula : TstByTm=2*Sm/(Sm**2+1)\n",
"TstByTm=TstByTfl/TmByTfl #Calculating TstByTm\n",
"\n",
"\n",
"from sympy import symbols, solve, N\n",
"Sm, Sfl = symbols('sm, Sfl')\n",
"expr = Sm**2-4*Sm+1#Polynomial for R2dash\n",
"Sm=solve(expr, Sm) #\n",
"Sm=Sm[0] #Discarding value > 1\n",
"print \"Slip at which max Torque occurs = %0.2f %%\"%(Sm*100) \n",
"#Formula : 1/TstByTm=(Sm**2+Sfl**2)/(2*Sm*Sfl)\n",
"Expr = Sm**2+Sfl**2-2*(2*Sm*Sfl)\n",
"Sfl=solve(Expr,Sfl) \n",
"Sfl=Sfl[0] #Discarding value >= 1\n",
"print \"Full load slip = \",N(Sfl*100,4) ,\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slip at which max Torque occurs = 26.79 %\n",
"Full load slip = "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 7.180 %\n"
]
}
],
"prompt_number": 132
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.34 Page 74"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=8 #no. of Poles\n",
"f=50 #in Hz\n",
"Tm=150 #in N-m\n",
"N=650 #in rpm\n",
"R2=0.6 #in ohm\n",
"S=4 #in %\n",
"\n",
"#Calculations\n",
"S=S/100 #Slip\n",
"Ns=120*f/P #in rpm\n",
"Sm=(Ns-N)/Ns #Maximum Slip\n",
"#Formula : T proportional to S*E2**2*R2/(R2**2+(S*X2)**2)\n",
"X2=R2/Sm #in ohm\n",
"T=Tm*S*(R2**2+(Sm*X2)**2)/Sm/(R2**2+(S*X2)**2) #In N-m\n",
"print \"Torque at 4%% slip = %0.4f N-m \"%T "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Torque at 4% slip = 82.5688 N-m \n"
]
}
],
"prompt_number": 133
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.35 Page 75"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import atan, cos\n",
"# Given data\n",
"V=400 #in volts\n",
"P=4 #no. of Poles\n",
"f=50 #in Hz\n",
"r1=0.15 #in ohm\n",
"x1=0.44 #in ohm\n",
"r2dash=0.12 #in ohm\n",
"x2dash=0.44 #in ohm\n",
"xm=30 #in ohm\n",
"S=4 #in %\n",
"\n",
"#Calculations\n",
"S=S/100 #Slip\n",
"RLdash=r2dash*(1-S)/S #in ohm\n",
"V1=V/sqrt(3) #in volt\n",
"I2rdash=V1/(r1+r2dash+RLdash+1J*(x1+x2dash)) #in Ampere\n",
"I0=V1/(1J*xm) #in Ampere\n",
"I1=I0+I2rdash #in Ampere\n",
"print \"Stator Current in Ampere : \" \n",
"print \"Magnitude is %0.3f A\"%(abs(I1)),\" & angle = %0.2f degree\"%degrees((atan((I1.imag)/(I1.real))) )\n",
"cosfi=cos(atan((I1.imag)/(I1.real))) #lagging power factor\n",
"print \"Power factor = %0.4f lagging \"%cosfi "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Stator Current in Ampere : \n",
"Magnitude is 73.059 A & angle = -21.43 degree\n",
"Power factor = 0.9308 lagging \n"
]
}
],
"prompt_number": 134
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.36 Page 76"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"VL=440 #in volts\n",
"P=4 #no. of Poles\n",
"f=50 #in Hz\n",
"#Zleak=0.3+%i*5.5+0.25/S #in ohm/phase\n",
"K=2.5 #Stator to rotor voltage ratio\n",
"T=150 #in N-m\n",
"N=1250 #in rpm\n",
"R1 = 0.1 # ohm\n",
"X1e = 1.83 # ohm\n",
"\n",
"\n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"S=(Ns-N)/Ns #slip\n",
"Zleakage=1/3*(0.3+1J*5.5+0.25/S) #in ohm/phase\n",
"V1=VL/sqrt(3) #in volt\n",
"\n",
"from sympy import symbols, solve\n",
"R2x = symbols('R2x')\n",
"#expr = R2x**2*T*S*2*pi*ns/S**2+R2x*T*S*(2*pi*ns*0.2/S+T*S*2*pi*ns*0.01+T*S*2*pi*ns*1.83**2-3*(V1**2)*R2x) #equating\n",
"#R2x**2*T*S*2*pi*ns/S**2+R2x*T*S*2*pi*ns*0.2/S+T*S*2*pi*ns*0.01+T*S*2*pi*ns*1.83**2-3*(V1**2)*R2x=0 #equating\n",
"Idash_2r_sqr = V1**2/((R1*R2x/S)**2+X1e**2)\n",
"expr = 35.856*R2x**2-48*R2x+3.3589\n",
"R2x = solve(expr, R2x)\n",
"R2x = R2x[1] # discarding lower value\n",
"ns=Ns/60 #in rps\n",
"#P=[T*S*2*pi*ns/S**2 T*S*2*pi*ns*0.2/S-3*(V1**2) T*S*2*pi*ns*0.01+T*S*2*pi*ns*1.83**2] #polynomial for value of R2xdash\n",
"Rx_stator=R2x-0.083 #in ohm\n",
"print \"External resistance referred to stator = %0.4f ohm \"%Rx_stator \n",
"Rx_rotor=Rx_stator/K**2 #in ohm/phase\n",
"print \"External resistance rotor side = %0.3f ohm/phase \"%Rx_rotor "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"External resistance referred to stator = 1.1816 ohm \n",
"External resistance rotor side = 0.189 ohm/phase \n"
]
}
],
"prompt_number": 135
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.37 Page 77"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"Nnl=1485 #in rpm\n",
"Nfl=1350 #in rpm\n",
"f=50 #in Hz\n",
"\n",
"#Calculations\n",
"Ns=1500 #nearest syn speed to Nfl in rpm(Assumed)\n",
"#Formula : Ns=120*f/P\n",
"P=120*f/Ns #no. of poles\n",
"print \"Part (i)\" \n",
"print \"No. of poles : \" ,P\n",
"Snl=(Ns-Nnl)/Ns #slip\n",
"print \"Part (ii)\" \n",
"print \"No load Slip = %0.2f %%\"%(Snl*100) \n",
"Sfl=(Ns-Nfl)/Ns #slip\n",
"print \"No load Slip = %0.2f %% \"%(Sfl*100) \n",
"fr_nl=f*Snl #in Hz\n",
"fr_fl=f*Sfl #in Hz\n",
"print \"Part (iii)\" \n",
"print \"No load frequency = %0.2f Hz \"%fr_nl \n",
"print \"Full load frequency = %0.2f Hz \"%fr_fl \n",
"#Part (iv)\n",
"print \"On No Load : \" \n",
"N1=120*fr_nl/P #speed of rotor field with respect to rotor conductor in rpm\n",
"print \"Speed of rotor field with respect to rotor conductor = %0.2f rpm \"%N1 \n",
"Rf_wrtS=1500 #in rpm\n",
"Rf_wrtSF=0 #in rpm\n",
"print \"Rotor field with respect to stator = %0.2f rpm\"%Rf_wrtS \n",
"print \"Rotor field with respect to stator field = %0.2f rpm \"%Rf_wrtSF \n",
"print \"On Full Load : \" \n",
"N2=120*fr_fl/P #speed of rotor field with respect to rotor conductor in rpm\n",
"print \"Speed of rotor field with respect to rotor conductor = %0.2f rpm \"%N2 \n",
"Rf_wrtS=1500 #in rpm\n",
"Rf_wrtSF=0 #in rpm\n",
"print \"Rotor field with respect to stator = %0.2f rpm \"% Rf_wrtS \n",
"print \"Rotor field with respect to stator field = %0.2f rpm \"%Rf_wrtSF \n",
"#Answer of no load slip is wrong in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Part (i)\n",
"No. of poles : 4.0\n",
"Part (ii)\n",
"No load Slip = 1.00 %\n",
"No load Slip = 10.00 % \n",
"Part (iii)\n",
"No load frequency = 0.50 Hz \n",
"Full load frequency = 5.00 Hz \n",
"On No Load : \n",
"Speed of rotor field with respect to rotor conductor = 15.00 rpm \n",
"Rotor field with respect to stator = 1500.00 rpm\n",
"Rotor field with respect to stator field = 0.00 rpm \n",
"On Full Load : \n",
"Speed of rotor field with respect to rotor conductor = 150.00 rpm \n",
"Rotor field with respect to stator = 1500.00 rpm \n",
"Rotor field with respect to stator field = 0.00 rpm \n"
]
}
],
"prompt_number": 136
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.38 Page 78"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"VL=3.3 #in KV\n",
"P=20 #no of poles\n",
"f=50 #in Hz\n",
"R2=0.025 #in ohm/phase\n",
"X2=0.28 #in ohm/phase\n",
"N=294 #Full load speed in rpm\n",
"\n",
"#Calculations\n",
"Sm=R2/X2 #Max Slip\n",
"print \"Slip at max torque = %0.2f %%\" %(Sm*100)\n",
"Ns=120*f/P #in rpm\n",
"Sfl=(Ns-N)/Ns #Full load slip\n",
"#Formula : T proportional to S*E2**2*R2/(R2**2+(S*X2)**2)\n",
"TmByTfl=Sm/(R2**2+(Sm*X2)**2)*((R2**2+(Sfl*X2)**2))/Sfl #ratio\n",
"print \"Ratio of max to full load torqiue : \" ,round(TmByTfl,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slip at max torque = 8.93 %\n",
"Ratio of max to full load torqiue : 2.344\n"
]
}
],
"prompt_number": 137
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.39 Page 79"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"Pin=50 #in KW\n",
"StatorLoss=800 #in watts\n",
"f=50 #in Hz\n",
"fr=90 #cycles/min\n",
"\n",
"#Calculations\n",
"fr=fr/60 #in Hz\n",
"S=fr/f #slip\n",
"P2=Pin*1000-StatorLoss #watts\n",
"#Formula : P2:Pc:Pm=1:S:1-S\n",
"Pm=P2*(1-S) #in watts\n",
"print \"Total Mechanical power devloped = %.f W\" %Pm"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total Mechanical power devloped = 47724 W\n"
]
}
],
"prompt_number": 138
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.40 Page 79"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"VL=200 #in volt\n",
"f=50 #in Hz\n",
"R2=0.1 #in ohm/phase\n",
"X2=0.9 #in ohm/phase\n",
"S=4 #in %\n",
"K=0.67 #rotor to stator turns \n",
"\n",
"#Calculations\n",
"S=S/100 #slip\n",
"E1ph=VL/sqrt(3) #in volt\n",
"E2ph=K*E1ph #in volt\n",
"Ns=120*f/P #in rpm\n",
"ns=Ns/60 #in rps\n",
"T=3/2/pi/ns*S*E2ph**2*R2/(R2**2+(S*X2)**2) #in N-m\n",
"print \"Total torque at 4%% slip = %0.4f N-m \"%T\n",
"Tm=3/2/pi/ns*E2ph**2/2/X2 #in N-m\n",
"print \"Maximum torque developed = %0.4f N-m \"%Tm\n",
"Sm=R2/X2 #Max Slip\n",
"Nm=Ns*(1-Sm) #in rpm\n",
"print \"Speed at max Torque = %0.3f rpm \"%Nm \n",
"Pmax=Tm*2*pi*Nm/60 #in watts\n",
"print \"Maximum mechanical power = %0.4f W\" %Pmax"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total torque at 4% slip = 40.4786 N-m \n",
"Maximum torque developed = 63.5064 N-m \n",
"Speed at max Torque = 1333.333 rpm \n",
"Maximum mechanical power = 8867.1605 W\n"
]
}
],
"prompt_number": 139
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.41 Page 80"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=6 #no. of poles\n",
"f=50 #in Hz\n",
"Tsh=150 #in N-m\n",
"fr=1.5 #in Hz\n",
"Tlost=10 #in N-m\n",
"\n",
"#Calculations\n",
"S=fr/f #slip\n",
"Ns=120*f/P #in rpm\n",
"N=Ns*(1-S) #in rpm\n",
"RotationalLoss=Tlost*2*pi*N/60 #in watts\n",
"Pout=Tsh*2*pi*N/60 #in watts\n",
"Pm=Pout+RotationalLoss #in watts\n",
"#Formula : P2:Pc:Pm=1:S:1-S\n",
"Pc=Pm*S/(1-S) #in watts\n",
"print \"Rotor Copper Loss = %0.4f W\" %Pc\n",
"P2=Pc/S #in watts\n",
"print \"Input to the rotor = %0.2f W\" %P2\n",
"StatorLoss=700 #in watts(assumed)\n",
"Pin=P2+StatorLoss #in watts]\n",
"Eff=Pout/Pin*100 #in %\n",
"print \"Efficiency = %0.2f %%\" %Eff"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rotor Copper Loss = 502.6548 W\n",
"Input to the rotor = 16755.16 W\n",
"Efficiency = 87.29 %\n"
]
}
],
"prompt_number": 140
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.42 Page 81"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"Sfl=5 #in %\n",
"IscByIfl=6 #ratio\n",
"\n",
"#Calculations\n",
"Sfl=Sfl/100 #slip\n",
"TstByTfl=1 #as Tfl=Tst\n",
"#Let X= tapping on transformer\n",
"X=sqrt(TstByTfl/(IscByIfl**2)/Sfl) #Tapping on transformer\n",
"print \"Tapping on auto transformer : \" ,round(X,4)\n",
"IstByIfl=X**2*IscByIfl #supply starting current to full load current \n",
"print \"The supply starting current is\",round(IstByIfl,2),\"times of full load current.\" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Tapping on auto transformer : 0.7454\n",
"The supply starting current is 3.33 times of full load current.\n"
]
}
],
"prompt_number": 141
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.43 Page 81"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"TmByTfl=2.5 #ratio\n",
"R2=0.4 #in ohm/phase\n",
"X2=4 #in ohm/phase\n",
"\n",
"#Calculations\n",
"#Formula : Tm=K*E2**2/2/X2 and Tst=K*E2**2*R2/(R2**2+X2**2)\n",
"#E2=E2/sqrt(3) #for star delta starter\n",
"TstByTfl=(TmByTfl*2*X2)*R2/(R2**2+X2**2)/3 #calculated from above equations\n",
"print \"ratio of starting torque to full load torque is : \" ,round(TstByTfl,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"ratio of starting torque to full load torque is : 0.165\n"
]
}
],
"prompt_number": 142
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.44 Page 82"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"Zouter=0.05+1J*0.10 #in ohm\n",
"Zinner=0.01+1J*0.60 #in ohm\n",
"S=3 #in %\n",
"\n",
"#Calculations\n",
"R2o=(Zouter.real) #in ohm\n",
"R2i=(Zinner.real) #in ohm\n",
"X2o=(Zouter.imag) #in ohm\n",
"X2i=(Zinner.imag) #in ohm\n",
"S=S/100 #slip\n",
"#Formula : T=3/2/pi/ns*(S*E2**2*R2/(R2**2+(S*X2)**2))\n",
"S=1 #at starting\n",
"TouterByTinner=R2o/R2i*(R2i**2+X2i**2)/(R2o**2+X2o**2) #\n",
"print \"(i) Ratio of torque due to two cages at starting : \" ,round(TouterByTinner)\n",
"S=3/100 #Slip at running\n",
"TouterByTinner=R2o/R2i*(R2i**2+(S*X2i)**2)/(R2o**2+(S*X2o)**2) #\n",
"print \"(ii) Ratio of torque due to two cages when running at 3% slip : \",round(TouterByTinner,5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Ratio of torque due to two cages at starting : 144.0\n",
"(ii) Ratio of torque due to two cages when running at 3% slip : 0.84496\n"
]
}
],
"prompt_number": 143
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.45 Page 83"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"Zi=0.6+1J*7 #in ohm\n",
"Zo=3.5+1J*1.5 #in ohm\n",
"Sfl=6 #in %\n",
"\n",
"#Calculations\n",
"#At starting S=1\n",
"Ro=(Zo.real) #in ohm\n",
"Ri=(Zi.real) #in ohm\n",
"Xo=(Zo.imag) #in ohm\n",
"Xi=(Zi.imag) #in ohm\n",
"Zeq1=Zi*Zo/(Zi+Zo) #equivalent impedence in ohm\n",
"Req1=(Zeq1.real) #in ohm\n",
"#I2=V/Zeq\n",
"#Tst=I2**2*R2 #in N-m\n",
"\n",
"#During full load\n",
"S=Sfl/100 #slip \n",
"Zi=Ri/S+1J*Xi #in ohm\n",
"Zo=Ro/S+1J*Xo #in ohm\n",
"Zeq2=Zi*Zo/(Zi+Zo) #equivalent impedence in ohm\n",
"Req2=(Zeq2.real) #in ohm\n",
"#I2=V/Zeq\n",
"#Tfl=I2**2*R2 #in N-m\n",
"TstByTfl=(1/abs(Zeq1)**2)/(1/abs(Zeq2)**2)*Req1/Req2 #ratio\n",
"print \"Starting torque is\",round(TstByTfl*100,0),\"% of full load torque.\" \n",
"#Answer in the book is not accurate."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Starting torque is 301.0 % of full load torque.\n"
]
}
],
"prompt_number": 144
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.46 Page 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"f=50 #in Hz\n",
"R2=0.2 #in ohm per phase\n",
"X2=1 #in ohm per phase\n",
"Sf=4 #full load slip in %\n",
"N2=1260 #reduced speed in rpm\n",
"\n",
"#Calculations\n",
"Sf=Sf/100 #full load slip\n",
"Ns=120*f/P #in rpm\n",
"S2=(Ns-N2)/Ns #new value of slip\n",
"#Let new resistance is R2dash\n",
"#Formula : T proportional to S*E2**2*R2/(R2**2+(S*X2)**2)\n",
"#T1=T2 as load is same\n",
"from sympy import symbols, solve\n",
"R2dash = symbols('R2dash')\n",
"expr = (R2dash**2)*Sf*(E2**2)*R2-R2dash*(R2**2+(Sf*X2)**2)*(S2*E2**2)+Sf*(E2**2)*R2*(S2*X2)**2\n",
"#P=[Sf*R2 -[R2**2+(Sf*X2)**2]*(S2) Sf*R2*(S2*X2)**2] #polynomial for R2dash\n",
"R2dash=solve(expr,R2dash) \n",
"R2dash=R2dash[1] #discarding smaller value as R2dash cant be < R2\n",
"Rex=R2dash-R2\n",
"print \"Extra resistance required = %0.2f ohm per phase \"%Rex "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Extra resistance required = 0.60 ohm per phase \n"
]
}
],
"prompt_number": 145
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.47 Page 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"P=4 #no. of poles\n",
"V2=415 #in volt\n",
"f=50 #in Hz\n",
"E2ByE1=1.75 #stator to rotor turn ratio\n",
"Z2=0.1+1J*0.9 #in ohm\n",
"I2=60 #in Ampere at startX2=1 #in ohm per phase\n",
"Sf=4 #full load slip in %\n",
"N2=1260 #reduced speed in rpm\n",
"\n",
"#Calculations\n",
"R2=(Z2.real) #in ohm\n",
"X2=(Z2.imag) #in ohm\n",
"E1ph=V2/sqrt(3) #in volt\n",
"E2ph=E1ph/E2ByE1 #in Volt\n",
"#Formula : I2=E2ph/sqrt(R2dash**2+X2**2)\n",
"R2dash=sqrt((E2ph/I2)**2-X2**2) #in ohm\n",
"Rex=R2dash-R2 #in ohm per phase\n",
"print \"Extra resiatance required = %0.3f ohm\"%Rex "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Extra resiatance required = 1.997 ohm\n"
]
}
],
"prompt_number": 146
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.48 Page 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=16 #no. of poles\n",
"PM=4 #no. of poles of modulating function\n",
"n=1 #assumed\n",
"r=4 #assumed\n",
"f=50 #in Hz\n",
"\n",
"#Calculations\n",
"check=n/r==1/3*(1-PM/P) \n",
"if check :\n",
" print \"Equation is satisfied with -ve sign.\" \n",
" P2=P+PM \n",
"\n",
"check=n/r==1/3*(1+PM/P) \n",
"if check :\n",
" print \"Equation is satisfied with +ve sign.\"\n",
" P2=P-PM \n",
"\n",
"Ns1=120*f/P #in rpm\n",
"Ns2=120*f/P2 #in rpm\n",
"print \"Two speeds = %0.2f rpm & %0.2f rpm\"%(Ns1,Ns2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equation is satisfied with -ve sign.\n",
"Two speeds = 375.00 rpm & 300.00 rpm\n"
]
}
],
"prompt_number": 147
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.49 Page 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"PA=4 #no. of poles\n",
"PB=6 #no. of poles\n",
"f=50 #in Hz\n",
"\n",
"#Calculations\n",
"Ns=120*f/PA #in rpm, A running alone\n",
"print \"(1.) If A running alone, Speed = %0.2f rpm\" %Ns\n",
"Ns=120*f/PB #in rpm, B running alone\n",
"print \"(2.) If B running alone, Speed = %0.2f rpm\" %Ns\n",
"Ns=120*f/(PA+PB) #in rpm, Cumulative cascade\n",
"print \"(3.) For Cumulative cascade, Speed = %0.2f rpm\"%Ns\n",
"Ns=120*f/(PA-PB) #in rpm, Differential cascade\n",
"print \"(4.) Differential cascade, Speed = %0.2f rpm\"%Ns"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(1.) If A running alone, Speed = 1500.00 rpm\n",
"(2.) If B running alone, Speed = 1000.00 rpm\n",
"(3.) For Cumulative cascade, Speed = 600.00 rpm\n",
"(4.) Differential cascade, Speed = -3000.00 rpm\n"
]
}
],
"prompt_number": 148
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.50 Page 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"PA=4 #no. of poles\n",
"PB=6 #no. of poles\n",
"f=50 #in Hz\n",
"fr2=1 #in Hz\n",
"\n",
"#Calculations\n",
"Nsc=120*f/(PA+PB) #synchronous speed of set in rpm\n",
"S=1 #Slip\n",
"N=Nsc-(S/f)*Nsc #combined speed of set in rpm\n",
"print \"Combibned speed of set = %0.2f rpm\"%N \n",
"NSA=120*f/PA #in rpm\n",
"SA=(NSA-N)/NSA #slip \n",
"print \"Slip of machine A = %0.2f %% \"%(SA*100) \n",
"fr1=SA*f #in Hz\n",
"NSB=120*fr1/PB #in rpm\n",
"SB=(NSB-N)/NSB #slip\n",
"print \"Slip of machine B = %0.1f %%\"%(SB*100) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Combibned speed of set = 588.00 rpm\n",
"Slip of machine A = 60.80 % \n",
"Slip of machine B = 3.3 %\n"
]
}
],
"prompt_number": 149
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.51 Page 88"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"f=50 #in Hz\n",
"R2=0.25 #in ohm per phase\n",
"X2=2 #in ohm per phase\n",
"N1=1455 #ion rpm\n",
"N2=N1*83/100 #in rpm\n",
" \n",
"#Calculations\n",
"Ns=120*f/P #synchronous speed in rpm\n",
"S1=(Ns-N1)/Ns #Slip\n",
"S2=(Ns-N2)/Ns #Slip at reduced speed\n",
"#Formula : T proportional to S*E2**2*R2/(R2**2+(S*X2)**2)\n",
"T1ByT2=1 #as T1=T2 & For T2: R2dash Rex+R2\n",
"from sympy import symbols, solve\n",
"R2dash = symbols('R2dash')\n",
"expr = R2dash**2-1.7067*R2dash+0.1519\n",
"R2dash=solve(expr, R2dash) #in ohjm per phase\n",
"R2dash=R2dash[1] #neglecting lower value\n",
"Rex=R2dash-R2 #in ohm per phase\n",
"print \"External resistance required = %0.4f ohm per phase \"%Rex "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"External resistance required = 1.3625 ohm per phase \n"
]
}
],
"prompt_number": 150
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.52 Page 89"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=6 #no. of poles\n",
"f=50 #in Hz\n",
"Sf=3 #in %\n",
"R2=0.2 #in ohm per phase\n",
" \n",
"#Calculations\n",
"Sf=Sf/100 #Slip \n",
"Ns=120*f/P #in rpm\n",
"N1=Ns*(1-Sf) #in rpm\n",
"N2=N1*90/100 #in rpm\n",
"S2=(Ns-N2)/Ns #new slip\n",
"#Formula : T=K*S*E2**2*R2/R2**2 #S*X2 is neglected\n",
"#Sf/R2=S2/(R2+r) if Tfl=T20\n",
"r=(S2*R2)/Sf-R2 #Extra resistance required in ohm\n",
"print \"Extra resistance necessery in series = %0.2f ohm \"%r "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Extra resistance necessery in series = 0.65 ohm \n"
]
}
],
"prompt_number": 151
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.53 Page 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"IscByIfl=5 #ratio\n",
"Sf=5 #in %\n",
"K=50 #tapping in %\n",
" \n",
"#Calculations\n",
"Sf=Sf/100 #Slip \n",
"#(i) Start delta \n",
"TstByTfl=1/3*IscByIfl**2*Sf #ratio\n",
"print \"(i) Starting torque is\",round(TstByTfl*100,2),\"% of full load torque.\" \n",
"#(ii) Auto Transformer having 50% tapping\n",
"K=K/100 #tapping\n",
"TstByTfl=K**2*IscByIfl**2*Sf #ratio\n",
"print \"(ii) Starting torque is\",(TstByTfl*100),\"% of full load torque.\" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Starting torque is 41.67 % of full load torque.\n",
"(ii) Starting torque is 31.25 % of full load torque.\n"
]
}
],
"prompt_number": 152
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.54 Page 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=6 #no. of poles\n",
"f=50 #in Hz\n",
"Ifl=60 #in Ampere\n",
"N=940 #speed in rpm\n",
"Tfl=150 #in N-m\n",
"Isc=300 #in Ampere\n",
" \n",
"#Calculations\n",
"Ns=120*f/P #in rpm\n",
"Sf=(Ns-N)/Ns #Slip full load\n",
"#Formula : Tst/Tfl=(Isc/Ifl)**2*Sf\n",
"Tst=(Isc/Ifl)**2*Sf*Tfl #in N-m\n",
"print \"Starting Torque = %0.2f N-m \"%Tst \n",
"#For Start delta \n",
"Tst=1/3*(Isc/Ifl)**2*Sf*Tfl #in N-m\n",
"print \"Starting Torque for star delta starter = %0.2f N-m \"%Tst \n",
"Isc=sqrt(3*Tst/Tfl/Sf)*Ifl #in Ampere\n",
"print \"Starting current for star delta starter = %0.2f Ampere \"%Isc "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Starting Torque = 225.00 N-m \n",
"Starting Torque for star delta starter = 75.00 N-m \n",
"Starting current for star delta starter = 300.00 Ampere \n"
]
}
],
"prompt_number": 153
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.55 Page 91"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"TmByTfl=2.2 #ratio\n",
"R2=0.5 #in ohm per phase\n",
"X2=5 #in ohm per phase\n",
"K=70 #tapping in %\n",
" \n",
"#Calculations\n",
"#Formula :Tst proportional to E2**2*R2/(R2**2+X2**2) \n",
"#Formula :Tm proportional to E2**2/(2*X2) \n",
"#Formula :Tfl proportional to 1/4.4*E2**2/X2\n",
"TstByTfl=R2/(R2**2+X2**2)*TmByTfl*2*X2 #ratio for direct on line\n",
"print \"Ratio of starting torque to full load torque for direct on line starter : \" ,round(TstByTfl,4)\n",
"TstByTfl=(1/sqrt(3))**2*R2/(R2**2+X2**2)*TmByTfl*2*X2 #ratio for star delta starting\n",
"print \"Ratio of starting torque to full load torque for star delta starter : \" ,round(TstByTfl,4)\n",
"TstByTfl=(K/100)**2*R2/(R2**2+X2**2)*TmByTfl*2*X2 #ratio for auto transformer starting\n",
"print \"Ratio of starting torque to full load torque for auto transformer starter : \" ,round(TstByTfl,4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio of starting torque to full load torque for direct on line starter : 0.4356\n",
"Ratio of starting torque to full load torque for star delta starter : 0.1452\n",
"Ratio of starting torque to full load torque for auto transformer starter : 0.2135\n"
]
}
],
"prompt_number": 154
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.56 Page 92"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"TmByTfl=3 #ratio\n",
"Sm=0.1 #slip at max Torque\n",
" \n",
"#Calculations\n",
"TstByTfl_dol=2*Sm/(1+Sm**2)*TmByTfl #ratio for D.O.L starter\n",
"print \"Ratio of starting torque to full load torque for D.O.L starter : \" ,round(TstByTfl_dol,3)\n",
"\n",
"TstByTfl=1/3*TstByTfl_dol #ratio for star delta starting\n",
"print \"Ratio of starting torque to full load torque for star delta starter : \" ,round(TstByTfl,3)\n",
"#Anser of first part is not given in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio of starting torque to full load torque for D.O.L starter : 0.594\n",
"Ratio of starting torque to full load torque for star delta starter : 0.198\n"
]
}
],
"prompt_number": 155
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.57 Page 92"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"VL=400 #in volt\n",
"Ist=1200 #in Ampere\n",
"Eff=0.85 #Efficiency\n",
"cosfi=0.8 #power factor\n",
"IstByIrated=5 #ratio\n",
" \n",
"#Calculations\n",
"I2_rated=Ist/IstByIrated #in Ampere\n",
"KWrating=sqrt(3)*VL*I2_rated*cosfi*Eff #in KW\n",
"#To have star delta styarter tapping Xo=1/sqrt(3)\n",
"#Ist=X0**2*IstByIrated*IL\n",
"X0=1/sqrt(3) #tapping\n",
"IL=Ist/X0**2/IstByIrated #in Ampere\n",
"KWmax=sqrt(3)*VL*IL*cosfi*Eff/1000 #in KW\n",
"print \"Maximum KW rating with star delta starter : \" ,round(KWmax,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum KW rating with star delta starter : 339.205\n"
]
}
],
"prompt_number": 156
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.58 Page 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"IscByIfl=3*180/100 #ratio\n",
"TstByTfl=0.35 #ratio\n",
"X=80/100 #tapping\n",
" \n",
"#Calculations\n",
"#Formula : TstByTfl=1/3*(IscByIfl**2)*Sfl\n",
"Sfl=TstByTfl/IscByIfl**2*3 #slip at full load\n",
"IstByIsc=X**2 #ratio\n",
"IstByIfl=IstByIsc*IscByIfl #ratio\n",
"print \"Starting current is\",round(IstByIfl,1),\"imes of full load current.\" \n",
"TstByTfl=X**2*IscByIfl**2*Sfl #ratio\n",
"print \"Starting torque is\",round(TstByTfl*100,2),\"% of full load torque.\" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Starting current is 3.5 imes of full load current.\n",
"Starting torque is 67.2 % of full load torque.\n"
]
}
],
"prompt_number": 157
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.59 Page 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy import real\n",
"# Given data\n",
"Zouter=0.05+1J*0.11 #in ohm\n",
"Zinner=0.015+1J*0.5 #in ohm\n",
" \n",
"#Calculations\n",
"R2odash=(Zouter.real) #in ohm\n",
"X2odash=(Zouter.imag) #in ohm\n",
"R2idash=real(Zinner.real) #in ohm\n",
"X2idash=(Zinner.imag) #in ohm\n",
"TouterByTinner=R2odash/(R2odash**2+X2odash**2)*(R2idash**2+X2idash**2)/R2idash #ratio\n",
"print \"Ratio of Torque due to two windinga : \" ,round(TouterByTinner,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio of Torque due to two windinga : 57.13\n"
]
}
],
"prompt_number": 158
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.60 Page 194"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"PA=4 #no. of poles\n",
"PB=4 #no. of poles\n",
"f=50 #in Hz\n",
"V=440 #in volt\n",
"\n",
"#calculations\n",
"#Independently with A\n",
"Ns=120*f/PA #in rpm\n",
"print \"Independently with A, Synchrpnous speed Ns = %0.2f rpm \" %Ns\n",
"#Independently with B\n",
"Ns=120*f/PB #in rpm\n",
"print \"Independently with B, Synchrpnous speed Ns = %0.2f rpm\"%Ns\n",
"#Running as cumulative cascaded\n",
"Ns=120*f/(PA+PB) #in rpm\n",
"print \"Running as cumulative cascaded, Synchrpnous speed Ns = %0.2f rpm\"%Ns\n",
"#Running as differentially cascaded\n",
"print \"Running as differentially cascaded, Synchrpnous speed Ns is undefined.\" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Independently with A, Synchrpnous speed Ns = 1500.00 rpm \n",
"Independently with B, Synchrpnous speed Ns = 1500.00 rpm\n",
"Running as cumulative cascaded, Synchrpnous speed Ns = 750.00 rpm\n",
"Running as differentially cascaded, Synchrpnous speed Ns is undefined.\n"
]
}
],
"prompt_number": 159
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.61 Page 94"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"IscByIfl=3*180/100 #ratio\n",
"TstByTfl=35/100 #ratio\n",
"X=75 #tapping in %\n",
"\n",
"#calculations\n",
"X=X/100 #tapping\n",
"\n",
"#Star delta starting\n",
"#Formula : TstByTfl=1/3*IscByIfl*Sfl\n",
"Sfl=TstByTfl*3/IscByIfl**2 #slip at full load\n",
"\n",
"#Auto transformer starting\n",
"IstByIsc=X**2 #ratio\n",
"IstByIfl=X**2*IscByIfl #ratio\n",
"print \"Starting current is\",(IstByIfl*100),\"% of fulll load current.\" \n",
"TstByTfl=X**2*IscByIfl**2*Sfl #ratio\n",
"print \"Starting torque is\",(TstByTfl*100),\"% of fulll load torque.\" \n",
"#Answer of starting current in terms of full load curremt is not given in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Starting current is 303.75 % of fulll load current.\n",
"Starting torque is 59.0625 % of fulll load torque.\n"
]
}
],
"prompt_number": 160
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.62 page 95"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"VL=400 #in volt\n",
"f=50 #in Hz\n",
"I=100 #i Ampere\n",
"\n",
"#calculations\n",
"#D.O.L starter\n",
"IL=I*sqrt(3) #in Ampere\n",
"print \"(i) The line current for direct on line starting = %0.3f Ampere \"%IL \n",
"#In star delta starter\n",
"Vph=VL/sqrt(3) #in Volt\n",
"Iph=I/sqrt(3) #in Ampere\n",
"print \"(ii) Starting phase current for star delta starting = %0.3f A\" %Iph\n",
"print \"(ii) Starting line current for star delta starting = %0.3f A\" %Iph\n",
"#Auto transformer starter\n",
"K=70/100 #tapping of auto transformer\n",
"Vph=VL/sqrt(3) #in Volt\n",
"Vline=K*VL #in volt\n",
"Ist_phase=Vline*I/VL #in Ampere\n",
"print \"(iii) Starting phase current of motor = %0.2f A\" %Ist_phase\n",
"Ist_line=Ist_phase*sqrt(3) #in Ampere\n",
"print \"(iii) Starting line current of motor = %0.2f A\" %Ist_line\n",
"IsupplyLine=K*Ist_line #in Ampere\n",
"print \"(iii) Supply line current of motor = %0.2f A\" %IsupplyLine"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) The line current for direct on line starting = 173.205 Ampere \n",
"(ii) Starting phase current for star delta starting = 57.735 A\n",
"(ii) Starting line current for star delta starting = 57.735 A\n",
"(iii) Starting phase current of motor = 70.00 A\n",
"(iii) Starting line current of motor = 121.24 A\n",
"(iii) Supply line current of motor = 84.87 A\n"
]
}
],
"prompt_number": 161
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.63 Page 97"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=12 #no. of poles\n",
"Ns=500 #in rpm\n",
"Nr=1440 #in rpm\n",
"\n",
"#calculations\n",
"f1=P*Ns/120 #in Hz\n",
"Nsm=1500 #in rpm (Assumed closed synchronous speed)\n",
"S=(Nsm-Nr)/Nsm #slip\n",
"print \"Slip of the motor = %0.2f %%\"%(S*100) \n",
"Pm=120*f1/Nsm #no. of poles of the motor\n",
"print \"No. of poles of the motor : \" ,Pm"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slip of the motor = 4.00 %\n",
"No. of poles of the motor : 4.0\n"
]
}
],
"prompt_number": 162
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.64 Page 97"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"f1=50 #in Hz\n",
"f2=1.5 #in Hz\n",
"\n",
"#calculations\n",
"S=f2/f1 #slip\n",
"print \"Slip = %0.2f %% \"%(S*100) \n",
"Ns=120*f1/P #in rpm\n",
"N=(1-S)*Ns #in rpm\n",
"print \"Running speed of motor = %0.2f rpm\"%N "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slip = 3.00 % \n",
"Running speed of motor = 1455.00 rpm\n"
]
}
],
"prompt_number": 163
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
" Example 1.65 Page 97"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=6 #no. of poles\n",
"f1=50 #in Hz\n",
"S0=1 #in %\n",
"Sfl=3 #in %\n",
"\n",
"#calculations\n",
"S0=S0/100 #slip\n",
"Sfl=Sfl/100 #slip\n",
"Ns=120*f1/P #in rpm\n",
"print \"(a) Synchronous speed = %0.2f rpm \"%Ns \n",
"N0=(1-S0)*Ns #in rpm\n",
"print \"(b) No Load speed = %0.2f rpm \"%N0 \n",
"Nfl=(1-Sfl)*Ns #in rpm\n",
"print \"(c) Full load speed = %0.2f rpm \"%Ns \n",
"f2_st=f1*S0 #in Hz\n",
"print \"(d) Frequeny of rotor current at standstill = %0.2f Hz \"%f2_st \n",
"f2_fl=f1*Sfl #in Hz\n",
"print \"(e) Frequeny of rotor current at full load = %0.2f Hz\"%f2_fl \n",
"#Answer of part (c) & part(d) is wrong. Calcultion mistake & slip is not divided by 100."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Synchronous speed = 1000.00 rpm \n",
"(b) No Load speed = 990.00 rpm \n",
"(c) Full load speed = 1000.00 rpm \n",
"(d) Frequeny of rotor current at standstill = 0.50 Hz \n",
"(e) Frequeny of rotor current at full load = 1.50 Hz\n"
]
}
],
"prompt_number": 164
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.66 Page 98"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"f1=50 #in Hz\n",
"S=4 #in %\n",
"R2=1 #in ohm/phase\n",
"X2=4 #in ohm/phase\n",
"\n",
"#calculations\n",
"Ns=120*f1/P #in rpm\n",
"S=S/100 #slip\n",
"#part (a)\n",
"N=(1-S)*Ns #in rpm\n",
"print \"(a) Speed of the motor = %0.2f rpm \"%N \n",
"#part (b)\n",
"f2=S*f1 #in Hz\n",
"print \"(b) Frequency of rotor emf = %0.2f Hz \"%f2 \n",
"#part (i)\n",
"Z2=R2+1J*X2 #in ohm\n",
"cosfi=cos(atan((Z2.imag)/(Z2.real))) #power factor\n",
"print \"(i) Power factor at standstill = %0.4f lag \"%cosfi \n",
"#part (ii)\n",
"N=1400 #speed in rpm (given for this part)\n",
"S1=(Ns-N)/Ns #slip\n",
"Z2s1=R2+1J*S1*X2 #in ohm\n",
"cosfi=cos(atan((Z2s1.imag)/(Z2s1.real))) #power factor at 1400 rpm speed\n",
"print \"(ii) Power factor at 1400 rpm = %0.4f lag \"%cosfi "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Speed of the motor = 1440.00 rpm \n",
"(b) Frequency of rotor emf = 2.00 Hz \n",
"(i) Power factor at standstill = 0.2425 lag \n",
"(ii) Power factor at 1400 rpm = 0.9662 lag \n"
]
}
],
"prompt_number": 165
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.67 Page 99"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy import real, imag\n",
"# Given data\n",
"E=60 #in volt\n",
"Zrotor=0.8+1J*6 #rotor impedence in ohm/phase\n",
"Zstator=4+1J*3 #stator impedence in ohm/phase\n",
"S=5 #in %\n",
"\n",
"#calculations\n",
"E2=E/sqrt(3) #emf induced/phase in volt\n",
"Ztotal=Zstator+Zrotor #in ohm/phase\n",
"#Part (a)\n",
"I2=E2/Ztotal #in Ampere\n",
"print \"Part(a) Magnitude is\",round(abs(I2),3),\"& angle = %0.2f degree\"%degrees(atan((I2.imag)/(I2.real)))\n",
"#Part (b)\n",
"S=S/100 #slip\n",
"R2=real(Zrotor) #in ohm/phase\n",
"X2=imag(Zrotor) #in ohm/phase\n",
"I2s=S*E2/(R2+S*1J*X2) #in ampere\n",
"print \"Part(b) Magnitude is\",round(abs(I2s),2),\"& angle = %0.2f degree \"%degrees(atan((I2s.imag)/(I2s.real)))\n",
"#Answer of part (b) is wrong in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Part(a) Magnitude is 3.396 & angle = -61.93 degree\n",
"Part(b) Magnitude is 2.03 & angle = -20.56 degree \n"
]
}
],
"prompt_number": 166
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.68 Page 99"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"Pis=60 #in KW\n",
"phase=3 #no. of phase\n",
"S=3 #in %\n",
"StatorLaser=1 #in KW\n",
"\n",
"#calculations\n",
"S=S/100 #slip \n",
"StatorOutput=Pis-StatorLaser #in KW\n",
"RotorInput=StatorOutput #in KW\n",
"RotorCuLoss=S*RotorInput #in KW\n",
"RotorCuLoss_phase=S*RotorInput/phase #in KW/phase\n",
"print \"Rotor Copper loss per phase = %0.2f kW \"%RotorCuLoss_phase \n",
"MechPower=RotorInput-RotorCuLoss #in KW\n",
"print \"Total mechanical power devloped = %0.2f kW\"%MechPower"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rotor Copper loss per phase = 0.59 kW \n",
"Total mechanical power devloped = 57.23 kW\n"
]
}
],
"prompt_number": 167
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.69 Page 100"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=6 #no. of poles\n",
"f1=50 #in Hz\n",
"f2=1.5 #in Hz\n",
"Zo=150 #useful Torque in N-m\n",
"FrictionLoss=10 #in N-m\n",
"Psc=700 #stator loss in watt\n",
"\n",
"#calculations\n",
"Ns=120*f1/P #in rpm\n",
"S=f2/f1 #slip\n",
"Nr=(1-S)*Ns #in rpm\n",
"wr=2*pi*Nr/60 #in rad/sec\n",
"Po=Zo*wr #in watts\n",
"Pmd=(Zo+FrictionLoss)*wr #in watts\n",
"#Part (a)\n",
"Prc=S/(1-S)*Pmd #in watts\n",
"print \"(a) Rotor Copper Loss = %0.4f kW \"%(Prc/1000)\n",
"#Part (b)\n",
"Pi=Pmd+Prc+Psc #in watts\n",
"print \"(b) Input to the motor = %0.4f kW\"%(Pi/1000)\n",
"#Part (c)\n",
"Eff=Po/Pi #Effiiency\n",
"print \"(d) Efficiency = %0.2f %%\"%(Eff*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Rotor Copper Loss = 0.5027 kW \n",
"(b) Input to the motor = 17.4552 kW\n",
"(d) Efficiency = 87.29 %\n"
]
}
],
"prompt_number": 168
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.70 Page 100"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"V=440 #in Volt\n",
"f=50 #in Hz\n",
"phase=3 #no. of phase\n",
"P=6 #no. of poles\n",
"Pin=80 #rotor input in KW\n",
"f1=50 #in Hz\n",
"f2=100 #in rotation/min\n",
"I=65 #rotor current in Ampere\n",
"\n",
"#calculations\n",
"f2=f2/60 #in Hz\n",
"S=f2/f1 #slip\n",
"print \"Slip = %0.3f p.u\" %S\n",
"Ns=120*f/P #in rpm\n",
"Nr=Ns*(1-S) #in rpm\n",
"print \"Rotor speed = %0.2f rpm \"%Nr \n",
"RotorCuLoss=S*Pin*1000 #in Watts\n",
"Pmd=Pin*1000-RotorCuLoss #Mechanical powre developed /in watts\n",
"Pmd=Pmd/746 #in HP\n",
"print \"Mechanical power developed = %0.2f HP \"%Pmd \n",
"RotorCuLoss_phase=RotorCuLoss/phase #in watts/phase\n",
"print \"Rotor Coopper Loss per phase = %0.f W\" %RotorCuLoss_phase\n",
"R2=RotorCuLoss_phase/I**2 #in ohm\n",
"print \"Rotor resistance per phase = %0.4f ohm\"%R2 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slip = 0.033 p.u\n",
"Rotor speed = 966.67 rpm \n",
"Mechanical power developed = 103.66 HP \n",
"Rotor Coopper Loss per phase = 889 W\n",
"Rotor resistance per phase = 0.2104 ohm\n"
]
}
],
"prompt_number": 169
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.71 Page 101"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"f1=50 #in Hz\n",
"phase=3 #no. of phase\n",
"P=6 #no. of poles\n",
"Nr=960 #in rpm\n",
"GearCuLoss=250 #in watt\n",
"Power=25 #in HP\n",
"MechLoss=1000 #in watts\n",
"I2=35 #in Ampere\n",
"\n",
"#calculations\n",
"Ns=f1*120/P #in rpm\n",
"S=(Ns-Nr)/Ns #slip\n",
"#Formula : RotorCuLoss=S/(1-S)*MechDevPower\n",
"#3*I2**2*R2+GearCuLoss=S/(1-S)*(Power*746+MechLoss)\n",
"R2=(S/(1-S)*(Power*746+MechLoss)-GearCuLoss)/3/I2**2 #in ohm\n",
"print \"Resistance per phase = %0.5f ohm \"%R2 "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance per phase = 0.15476 ohm \n"
]
}
],
"prompt_number": 170
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.72 Page 101"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"V=500 #in Volt\n",
"f1=50 #in Hz\n",
"phase=3 #no. of phase\n",
"P=6 #no. of poles\n",
"Nr=995 #in rpm\n",
"Pm=20 #mech power in KW\n",
"StatorLoss=1500 #in watts\n",
"pf=0.87 #power facator\n",
"\n",
"#calculations\n",
"Ns=f1*120/P #in rpm\n",
"S=(Ns-Nr)/Ns #slip\n",
"print \"(a) Slip is : \" ,S,'pu'\n",
"Prc=S/(1-S)*Pm*1000 #in watts\n",
"print \"(b) Rotor I**2*R Loss = %0.2f Watts\"%Prc \n",
"RotorInput=Prc/S #in watts\n",
"TotalInput=RotorInput+StatorLoss #in watts\n",
"print \"(c) Total input = %0.2f kW \"%(TotalInput/1000) \n",
"LineCurrent=TotalInput/sqrt(3)/V/pf #in Ampere\n",
"print \"(d) Line current = %0.1f A\" %LineCurrent\n",
"fr=S*f1 #in Hz\n",
"print \"(e) Rotor frequency = %0.2f HZ \"%fr "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Slip is : 0.005 pu\n",
"(b) Rotor I**2*R Loss = 100.50 Watts\n",
"(c) Total input = 21.60 kW \n",
"(d) Line current = 28.7 A\n",
"(e) Rotor frequency = 0.25 HZ \n"
]
}
],
"prompt_number": 171
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.73 Page 102"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"StatorLoss=2 #in KW\n",
"StatorInput=90 #stator input in KW\n",
"S=4 #in %\n",
"\n",
"#calculations\n",
"S=S/100 #slip\n",
"StatorOutput=StatorInput-StatorLoss #in KW\n",
"Pri=StatorOutput #rotor input in KW\n",
"Pcr=S*Pri #in KW\n",
"print \"Rotor Copper Loss = %0.2f kW \"%Pcr \n",
"Pm=Pri-Pcr #in KW\n",
"print \"Rotor mechanical power developed = %0.2f kW\"%Pm "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rotor Copper Loss = 3.52 kW \n",
"Rotor mechanical power developed = 84.48 kW\n"
]
}
],
"prompt_number": 172
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.74 Page 102"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"emf=60 #in volt\n",
"R2=0.6 #in ohm\n",
"X2=4 #in ohm\n",
"Rrh=5 #in ohm\n",
"Xrh=2 #in ohm\n",
"S=4 #in %\n",
"\n",
"#calculations\n",
"S=S/100 #slip\n",
"E2=emf/sqrt(3) #in volt\n",
"Rt=R2+Rrh #in ohm\n",
"Xt=X2+Xrh #in ohm\n",
"I2=E2/sqrt(Rt**2+Xt**2) #in Ampere\n",
"print \"(a) Current per phase in rotor = %0.2f A\" %I2\n",
"E2s=S*E2 #in volt\n",
"Z2s=sqrt(R2**2+(S*X2)**2) #in ohm\n",
"I2s=E2s/Z2s #in Ampere\n",
"print \"(b) Current per phase in rotor = %0.3f A\" %I2s"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Current per phase in rotor = 4.22 A\n",
"(b) Current per phase in rotor = 2.231 A\n"
]
}
],
"prompt_number": 173
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.75 Page 103"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"R2=0.05 #in ohm\n",
"X2=0.1 #in ohm\n",
"\n",
"#calculations\n",
"R2dash=X2 #for max Torque\n",
"r=R2dash-R2 #in ohm\n",
"print \"External resistance per phase required = %0.2f ohm \"%r "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"External resistance per phase required = 0.05 ohm \n"
]
}
],
"prompt_number": 174
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.76 Page 103"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=6 #no. of poles\n",
"f=50 #in Hz\n",
"Sfl=4 #in %\n",
"Z2=0.01+1J*0.05 #in ohm\n",
"\n",
"#calculations\n",
"S=Sfl/100 #slip\n",
"R2=real(Z2) #in ohm\n",
"X2=imag(Z2) #in ohm\n",
"Sm=R2/X2 #slip at max speed\n",
"Ns=120*f/P #in rpm\n",
"Nm=(1-Sm)*Ns #in rpm\n",
"TmaxByTfl=(S**2+Sm**2)/2/S/Sm #ratio\n",
"print \"Maximum Torque is\",(TmaxByTfl),\"times of full load torque.\" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum Torque is 2.6 times of full load torque.\n"
]
}
],
"prompt_number": 175
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.77 Page 103"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=6 #no. of poles\n",
"f=50 #in Hz\n",
"Tmax=30 #in N-m\n",
"Nm=960 #in rpm\n",
"S=5 #in %\n",
"R2=0.6 #in ohm\n",
"\n",
"#calculations\n",
"S=S/100 #slip\n",
"Ns=120*f/P #in rpm\n",
"Sm=(Ns-Nm)/Ns #slip at max speed\n",
"X2=R2/Sm #in ohm\n",
"Tau_s=2*S*Sm/(S**2+Sm**2)*Tmax #in N-m\n",
"print \"Torque exerted by the motor = %0.2f N-m \"%Tau_s "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Torque exerted by the motor = 29.27 N-m \n"
]
}
],
"prompt_number": 176
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.78 Page 104"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"f=50 #in Hz\n",
"Tmax=110 #in N-m\n",
"Nm=1360 #in rpm\n",
"R2=0.25 #in ohm\n",
"TstByTmax=1/2 #ratio\n",
"\n",
"#calculations\n",
"Ns=120*f/P #in rpm\n",
"Sm=(Ns-Nm)/Ns #slip at max speed\n",
"X2=R2/Sm #in ohm\n",
"#Formula : Tmax=K*E2**2/2/X2 and Tst=K*E2**2*(R2+r)/((R2+r)**2+X2**2)\n",
"from sympy import symbols, solve\n",
"RT = symbols('RT')\n",
"expr = TstByTmax*RT**2+TstByTmax*X2**2-RT*2*X2\n",
"\n",
"RT=solve(expr, RT)[0] #in ohm\n",
"r=RT-R2 #in ohm\n",
"r=r #leaving higher value as Tmax goes with S>1 for this value\n",
"print \"Resistance required in series = %0.3f ohm \"%r"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance required in series = 0.468 ohm \n"
]
}
],
"prompt_number": 177
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.79 Page 105"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=16 #no. of poles\n",
"f=50 #in Hz\n",
"Z2=0.02+1J*0.15 #in ohm\n",
"Nr=360 #in rpm\n",
"\n",
"#calculations\n",
"Ns=120*f/P #in rpm\n",
"Sfl=(Ns-Nr)/Ns #slip at full load\n",
"R2=real(Z2) #in ohm\n",
"X2=imag(Z2) #in ohm\n",
"Sm=R2/X2 #slip at max torque\n",
"Nm=(1-Sm)*Ns #in rpm\n",
"print \"(a) Speed at which max Torque occurs = %0.2f rpm \"%Nm \n",
"TmaxByTfl=(Sfl**2+Sm**2)/2/Sfl/Sm #ratio\n",
"print \"(b) Ratio of maximum to full load torque : \" ,round(TmaxByTfl,4)\n",
"R2dash=X2 #for max Torque\n",
"r=R2dash-R2 #in ohm\n",
"print \"(c) External resistance per phase required = %0.2f ohm \"%r "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Speed at which max Torque occurs = 325.00 rpm \n",
"(b) Ratio of maximum to full load torque : 1.8167\n",
"(c) External resistance per phase required = 0.13 ohm \n"
]
}
],
"prompt_number": 178
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.80 Page 106"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=6 #no. of poles\n",
"f=50 #in Hz\n",
"N=940 #in rpm\n",
"Output=7 #in KW\n",
"Nm=800 #in rpm\n",
"TotalLaser=840 #in watts\n",
"\n",
"#calculations\n",
"Ns=120*f/P #in rpm \n",
"S=(Ns-N)/Ns #slip\n",
"Sm=(Ns-Nm)/Ns #slip at max Torque\n",
"Pmd=Output*1000+TotalLaser #in watts\n",
"#Formula : Pmd=2*pi*N*Td/60\n",
"Tdfl=Pmd/2/pi/N*60 #in N-m\n",
"Tst=Tdfl*(S**2+Sm**2)/S/(1+Sm**2) #in N-m\n",
"print \"Starting tiorque = %0.2f N-m \"%Tst"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Starting tiorque = 55.65 N-m \n"
]
}
],
"prompt_number": 179
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.81 Page 107"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"f=50 #in Hz\n",
"VL=200 #in volt\n",
"R2=0.1 #in ohm\n",
"X2=0.9 #in ohm\n",
"Te2ByTe1=0.67 #ratio of rotor to stator turns\n",
"S=4 #in %\n",
"\n",
"#calculations\n",
"S=S/100 #slip\n",
"Ns=120*f/P #in rpm\n",
"E1=VL/sqrt(3) #in volt\n",
"E2=E1*Te2ByTe1 #in volt\n",
"Td=3*S*E2**2*R2/2/pi/(Ns/60)/(R2**2+(S*X2)**2) #in N-m\n",
"print \"(a) Total torque at 4%% slip = %0.2f N-m\"%Td \n",
"Tmax=3*E2**2/2/pi/(Ns/60)/(2*X2) #in N-m\n",
"print \"(b) Total torque at 4%% slip = %0.2f N-m \"%Tmax \n",
"Sm=R2/X2 #slip at max torque\n",
"Nm=(1-Sm)*Ns #speed at Tmax in rpm\n",
"print \"(c) Speed at maximum torque = %0.2f rpm \"%Nm \n",
"Pmd_max=2*pi*Nm/60*Tmax #in N-m\n",
"print \"(d) Maximum mechanical power = %0.2f N-m \"%Pmd_max "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Total torque at 4% slip = 40.48 N-m\n",
"(b) Total torque at 4% slip = 63.51 N-m \n",
"(c) Speed at maximum torque = 1333.33 rpm \n",
"(d) Maximum mechanical power = 8867.16 N-m \n"
]
}
],
"prompt_number": 180
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.82 Page 107"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt\n",
"# Given data\n",
"TstByTfl=1 #ratio\n",
"TmaxByTfl=2 #ratio\n",
"\n",
"#calculations\n",
"TstByTmax=TstByTfl/TmaxByTfl #ratio\n",
"#Formula : TstByTmax=2*Sm/(1+Sm**2)\n",
"\n",
"from sympy import symbols, solve \n",
"Sm, S = symbols('Sm, S')\n",
"expr = TstByTmax*Sm**2-2*Sm+TstByTmax\n",
"Sm=solve(expr, Sm) #slip at max torque\n",
"Sm=Sm[0] #neglecting the higher value\n",
"print \"(a) Slip at which max torque occurs : %0.3f\" %Sm\n",
"#Formula : TflByTmax=2*S*Sm/(S**2+Sm**2) \n",
"expr = S**2-TmaxByTfl*2*S*Sm+Sm**2\n",
"S=solve(expr,S) #slip at max torque\n",
"S=S[0] #neglecting the higher value\n",
"print \"(b) Full load slip : %0.4f\" %S\n",
"#I2stByI2fl**2=(Sm**2+S**2)/S**2/(1+Sm**2)\n",
"I2stByI2fl=sqrt((Sm**2+S**2)/S**2/(1+Sm**2)) #ratio\n",
"print \"(c) Rotor current at starting at full load current : %0.4f\"%I2stByI2fl "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Slip at which max torque occurs : 0.268\n",
"(b) Full load slip : 0.0718"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"(c) Rotor current at starting at full load current : 3.7321\n"
]
}
],
"prompt_number": 181
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.83 Page 109"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"Zst=25 #in N-m\n",
"\n",
"#calculations\n",
"#K=2*Zst*R2\n",
"KbyR2=2*Zst #calculation\n",
"#(a) Tst=K*2*R2/((2*R2)**2+R2**2)\n",
"Tst=KbyR2*2/(2**2+1) #in N-m\n",
"print \"(a) Starting torque = %0.2f N-m \"%Tst \n",
"#(b) Tst=K/2*R2/((R2/2)**2+R2**2)\n",
"Tst=KbyR2/2/((1/2)**2+1) #in N-m\n",
"print \"(b) Starting torque = %0.2f N-m \"%Tst "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Starting torque = 20.00 N-m \n",
"(b) Starting torque = 20.00 N-m \n"
]
}
],
"prompt_number": 182
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.84 Page 109"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given data\n",
"P=4 #no. of poles\n",
"f=50 #in Hz\n",
"R2=0.4 #in ohm\n",
"X2=4 #in ohm\n",
"\n",
"#calculations\n",
"Ns=120*f/P #in rpm\n",
"Sm=R2/X2 #slip at max Torque\n",
"Nm=Ns*(1-Sm) #in rpm\n",
"print \"Speed at Max Torque = %0.2f rpm \"%Nm \n",
"TmaxByTst=(1+Sm**2)/2/Sm #ratio\n",
"print \"Ratio of max Torque to starting Torque : \" ,TmaxByTst\n",
"#After adding additional resistance\n",
"from sympy import symbols, solve\n",
"r = symbols('r')\n",
"TstByTm=1/2 #given ratio\n",
"expr = TstByTm-2*X2*(R2+r)/((R2+r)**2+X2**2) #ratio\n",
"r=solve(expr, r) #in ohm\n",
"r=r[0] #leaving higher value\n",
"print \"Required resistance value = %0.2f ohm \"%r \n",
"#Answer of resistance is wrong in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Speed at Max Torque = 1350.00 rpm \n",
"Ratio of max Torque to starting Torque : 5.05\n",
"Required resistance value = 0.67 ohm "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 183
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.85 Page 110"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Given data\n",
"VL=440 #in volt\n",
"f=50 #in Hz\n",
"X2byR2=3 #ratio\n",
"TmByTfl=4 #ratio\n",
"\n",
"#Calculations\n",
"Sm=1/X2byR2 #Maximum slip\n",
"#Formula : TmByTfl=(Sm**2+S**2)/(2*S*Sm)\n",
"from sympy import symbols, solve, N\n",
"S = symbols('S')\n",
"expr = 9*S**2-24*S+1\n",
"S=solve(expr, S)\n",
"S=N(S[0],3)\n",
"print \"(i) Full load slip : \" ,S\n",
"TstByTfl=(Sm**2+S**2)/(S*(1+Sm**2)) #ratio\n",
"print \"(ii) Ratio of starting torque to full load torque : \" ,round(TstByTfl,4)\n",
"V1=VL/sqrt(3) #in volt\n",
"#Tst=Tfl : K*V11**2R2/(R2**2+X2**2)=R*V1*S*R2/(R2**2+(S*X2)**2)\n",
"V11=sqrt(S*V1**2*(1+X2byR2**2)/(1+(S*X2byR2)**2)) #in volt\n",
"Linevoltage=V11*sqrt(3) #in volt\n",
"print \"(c) Line Voltage = %0.2f Volt\" %Linevoltage\n",
"#Note : Answer of line voltage is wrong in the book due to calculation mistake."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Full load slip : 0.0423\n",
"(ii) Ratio of starting torque to full load torque : 2.4002\n",
"(c) Line Voltage = 284.01 Volt\n"
]
}
],
"prompt_number": 184
}
],
"metadata": {}
}
]
}