{
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"name": ""
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER 8: STARTING, CONTROL AND TESTING OF AN INDUCTION MOTOR"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.1, Page number 273"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"T_st = '1.5*T_f' #Starting torque\n",
"s = 0.03 #Slip\n",
"\n",
"#Calculation\n",
"I_sc_I_f = (1.5/s)**0.5 #I_sc/I_f\n",
"\n",
"#Result\n",
"print('Short circuit current , I_sc = %.2f*I_f' %I_sc_I_f)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Short circuit current , I_sc = 7.07*I_f\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.2, Page number 274-275"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"T_ratio = 50.0/100 #Ratio of starting torque to full load torque T_st/T_f\n",
"s_f = 0.03 #Full load slip\n",
"I_ratio = 5.0 #Ratio of short circuit current to full load current I_sc/I_f\n",
"\n",
"#Calculation\n",
"x = (1/I_ratio)*(T_ratio/s_f)**0.5 #Percentage of taping\n",
"\n",
"#Result\n",
"print('Percentage tapings required on the autotransformer , x = %.3f ' %x)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Percentage tapings required on the autotransformer , x = 0.816 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.3, Page number 277"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"T_ratio = 25.0/100 #Ratio of starting torque to full load torque T_st/T_f\n",
"I_ratio = 3.0*120/100 #Ratio of short circuit current to full load current I_sc/I_f\n",
"\n",
"#Calculation\n",
"s_f = T_ratio*3/I_ratio**2 #Full load slip\n",
"\n",
"#Result\n",
"print('Full load slip , s_f = %.2f ' %s_f)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Full load slip , s_f = 0.06 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4, Page number 281-282"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Z_icr = complex(0.04,0.5) #Inner cage impedance per phase at standstill(ohm)\n",
"Z_ocr = complex(0.4,0.2) #Outer cage impedance per phase at standstill(ohm)\n",
"V = 120.0 #Per phase rotor induced voltage at standstill(V)\n",
"\n",
"#Calculation\n",
"#For case(i)\n",
"Z_com = (Z_icr*Z_ocr)/(Z_icr+Z_ocr) #Combined impedance(ohm)\n",
"I_2 = V/abs(Z_com) #Rotor current per phase(A)\n",
"R_2 = Z_com.real #Combined rotor resistance(ohm)\n",
"T = I_2**2*R_2 #Torque at stand still condition(synchronous watts)\n",
"#For case(ii)\n",
"s = 0.06 #Slip\n",
"R_ocr = Z_ocr.real\n",
"X_ocr = Z_ocr.imag\n",
"R_icr = Z_icr.real\n",
"X_icr = Z_icr.imag\n",
"Z_com6 = complex(R_ocr/s,X_ocr)*complex(R_icr/s,X_icr)/complex(R_ocr/s+R_icr/s,X_ocr+X_icr) #Combined impedance(ohm)\n",
"I2_6 = V/abs(Z_com6) #Rotor current per phase(A)\n",
"R2_6 = Z_com6.real #Combined rotor resistance(ohm)\n",
"T_6 = I2_6**2*R2_6 #Torque at 6% slip(synhronous watts)\n",
"\n",
"#Result\n",
"print('(i) Torque at standstill condition , T = %.2f syn.watt' %T)\n",
"print('(ii) Torque at 6 percent slip , T_6 = %.2f syn.watt' %T_6)\n",
"print('\\nNOTE : Changes in answer is due to precision i.e more number of decimal places')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Torque at standstill condition , T = 31089.35 syn.watt\n",
"(ii) Torque at 6 percent slip , T_6 = 15982.06 syn.watt\n",
"\n",
"NOTE : Changes in answer is due to precision i.e more number of decimal places\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.5, Page number 285"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"V = 210.0 #Supply voltage(V)\n",
"f = 50.0 #Supply frequency(Hz)\n",
"P = 50.0 #Input power(W)\n",
"I_br = 2.5 #Line current(A)\n",
"V_L = 25.0 #Line voltage(V)\n",
"R_1 = 2.4 #DC resistance between any two terminal(ohm)\n",
"\n",
"#Calculation\n",
"V_br = V_L/3**0.5 #Phase voltage(V)\n",
"P_br = P/3 #Power per phase(W)\n",
"R_eq = P_br/I_br**2 #Equivalent resistance(ohm)\n",
"R_2 = R_eq-(R_1/2) #Per phase rotor resistance(ohm)\n",
"Z_eq = V_br/I_br #Equivalent impedance(ohm)\n",
"X_eq = (Z_eq**2-R_2**2)**0.5 #Equivalent reactance(ohm)\n",
"X_1 = 0.5*X_eq #For practical cases reactances(ohm)\n",
"\n",
"#Result\n",
"print('Equivalent resistance , R_eq = %.1f ohm' %R_eq)\n",
"print('Equivalent impedance , Z_eq = %.1f ohm' %Z_eq)\n",
"print('Equivalent reactance , X_eq = %.1f ohm' %X_eq)\n",
"print('Per phase rotor resistance , R_2 = %.1f ohm' %R_2)\n",
"print('Reactances for practical cases , X_1 = X_2 = %.1f ohm' %X_1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equivalent resistance , R_eq = 2.7 ohm\n",
"Equivalent impedance , Z_eq = 5.8 ohm\n",
"Equivalent reactance , X_eq = 5.6 ohm\n",
"Per phase rotor resistance , R_2 = 1.5 ohm\n",
"Reactances for practical cases , X_1 = X_2 = 2.8 ohm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.6, Page number 287"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"V = 210.0 #Supply voltage(V)\n",
"f = 50.0 #Supply frequency(Hz)\n",
"P = 4.0 #Number of poles\n",
"P_0 = 400.0 #Input power(W)\n",
"I_0 = 1.2 #Line current(A)\n",
"V_0 = 210.0 #Line voltage(V)\n",
"P_fw = 150.0 #Total friction and windage losses(W)\n",
"R = 2.2 #Stator resistance between any two terminals(ohm)\n",
" \n",
"#Calculation\n",
"R_1 = R/2 #Per phase stator resistance(ohm)\n",
"P_scu = 3*I_0**2*R_1 #Stator copper loss(W)\n",
"P_core = P_0-P_fw-P_scu #Stator core loss(W)\n",
"R_0 = (V_0/3**0.5)**2/(P_core/3) #No-load resistance(ohm)\n",
"#Alternate approach\\n\",\n",
"phi_0 = math.acos(P_core/(3**0.5*V_0*I_0)) #Power factor angle(radians)\n",
"phi_0_deg = phi_0*180/math.pi #Power factor angle(degree)\n",
"R_01 = (V_0/3**0.5)/(I_0*math.cos(phi_0)) #No-load circuit resistance per phase(ohm)\n",
"X_0 = (V_0/3**0.5)/(I_0*math.sin(phi_0)) #Magnetizing reactance per phase(ohm)\n",
" \n",
"#Result\n",
"print('Stator core loss , P_core = %.1f W' %P_core)\n",
"print('No-load circuit resistance per phase , R_0 = %.1f ohm' %R_01)\n",
"print('Magnetizing reactance per phase , X_0 = %.f ohm' %X_0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Stator core loss , P_core = 245.2 W\n",
"No-load circuit resistance per phase , R_0 = 179.8 ohm\n",
"Magnetizing reactance per phase , X_0 = 122 ohm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.7, Page number 290"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"P_1 = 6.0 #Number of pole\n",
"P_2 = 4.0 #Number of pole\n",
"f = 50.0 #Supply frequency(Hz)\n",
"P = 60.0 #Power(kW)\n",
"\n",
"#Calculation\n",
"#For case(i)\n",
"s = P_2/(P_1+P_2) #Combined slip\n",
"#For case(ii)\n",
"N_cs = 120*f/(P_1+P_2) #Combined synchronous speed(rpm)\n",
"#For case(iii)\n",
"P_0 = P*P_2/(P_1+P_2) #Output of 4-pole motor(kW)\n",
"\n",
"#Result\n",
"print('(i) Combined slip , s = %.1f ' %s)\n",
"print('(ii) Combined synchronous speed , N_cs = %.f rpm' %N_cs)\n",
"print('(iii) Output of the 4-pole motor , P_0 = %.f kW' %P_0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Combined slip , s = 0.4 \n",
"(ii) Combined synchronous speed , N_cs = 600 rpm\n",
"(iii) Output of the 4-pole motor , P_0 = 24 kW\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}