{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER 10: SYNCHRONOUS MOTOR"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.1, Page number 335"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"V = 2.5*10**3 #Supply voltage(V)\n",
"R_r = 0.12 #Per phase resistance(ohm)\n",
"X_r = 3.2 #Syncronous reactance(ohm)\n",
"I_a = 185.0 #Line current(A)\n",
"pf = 0.8 #Leading power factor\n",
"\n",
"#Calculation\n",
"phi = math.acos(pf) #Angle(radians)\n",
"phi_deg = phi*180/math.pi #Angle(degree)\n",
"V_t = V/3**0.5 #Terminal voltage per phase(V)\n",
"Z_s = complex(R_r,X_r) #Impedance per phase(ohm)\n",
"beta = math.atan(X_r/R_r) #Angle(radians)\n",
"beta_deg = beta*180/math.pi #Angle(degree)\n",
"E_r = I_a*abs(Z_s) #Resultant voltage due to impedance(V)\n",
"E_f = (V_t**2+E_r**2-2*V_t*E_r*math.cos(beta+phi))**0.5 #Excitation voltage per phase(V)\n",
"\n",
"#Result\n",
"print('Excitation voltage per phase , E = %.2f V' %E_f)\n",
"print('\\nNOTE : Changes in answer is due to precision i.e more number of decimal places')\n",
"print(' ERROR : Line current I_a = 185 A not 180 A as given in textbook question')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Excitation voltage per phase , E = 1846.18 V\n",
"\n",
"NOTE : Changes in answer is due to precision i.e more number of decimal places\n",
" ERROR : Line current I_a = 185 A not 180 A as given in textbook question\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.2, Page number 335-337"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"kVA = 1200.0 #kVA ratings\n",
"V = 14.0*10**3 #Supply voltage(V)\n",
"R_r = 4.8 #Per phase resistance(ohm)\n",
"X_r = 35.0 #Syncronous reactance(ohm)\n",
"pf = 0.95 #Leading power factor\n",
"\n",
"#Calculation\n",
"phi = math.acos(pf) #Angle(radians)\n",
"phi_deg = phi*180/math.pi #Angle(degree)\n",
"Z_s = complex(R_r,X_r) #Impedance per phase(ohm)\n",
"I_a = kVA*10**3/(3**0.5*V) #Armature current(A)\n",
"E_r = I_a*abs(Z_s) #Resultant voltage due to impedance(V)\n",
"V_t = V/3**0.5 #Terminal voltage per phase(V)\n",
"b = math.atan(X_r/R_r) #Beta value(radians)\n",
"b_deg = b*180/math.pi #Beta value(degree)\n",
"E_f = (V_t**2+E_r**2-2*V_t*E_r*math.cos(b-phi))**0.5 #Excitation voltage per phase(V)\n",
"sin_delta = (E_r/E_f)*math.sin(b-phi)\n",
"delta = math.asin(sin_delta)*180/math.pi #Torque angle(degree)\n",
"\n",
"#Result\n",
"print('Excitation voltage per phase , E_f = %.2f V' %E_f)\n",
"print('Torque angle , \u03b4 = %.2f\u00b0' %delta)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Excitation voltage per phase , E_f = 7483.23 V\n",
"Torque angle , \u03b4 = 12.12\u00b0\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.3, Page number 343-344"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"V = 440.0 #Supply voltage(V)\n",
"R_a = 1.5 #Per phase armature resistance(ohm)\n",
"X_a = 8.0 #Synchronous reactance(ohm)\n",
"P = 4.0 #Number of poles\n",
"f = 50.0 #Supply frequency(Hz)\n",
"pf = 0.9 #Leading power factor\n",
"I_a = 50.0 #Armature current(A)\n",
"\n",
"#Calculation\n",
"V_t = V/3**0.5 #Terminal voltage per phase(V)\n",
"phi = math.acos(pf) #Angle(radians)\n",
"phi_deg = phi*180/math.pi #Angle(degree)\n",
"Z_s = complex(R_a,X_a) #Impedance per phase(ohm)\n",
"E_r = I_a*abs(Z_s) #Resultant voltage due to impedance(V)\n",
"beta = math.atan(X_a/R_a) #Beta value(radians)\n",
"beta_deg = beta*180/math.pi #Beta value(degree)\n",
"E_f = (V_t**2+E_r**2-2*V_t*E_r*math.cos(beta+phi))**0.5 #Excitation voltage per phase(V)\n",
"P_dm = (((E_f*V_t)/abs(Z_s))-((E_f**2*R_a)/abs(Z_s)**2)) #Maximum power per phase(W)\n",
"\n",
"#Result \n",
"print('Maximum power per phase , P_dm = %.1f W' %P_dm)\n",
"print('\\nNOTE : ERROR : In textbook solution E_f = 513.5 V is taken instead of 533.337089826 V')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum power per phase , P_dm = 10205.3 W\n",
"\n",
"NOTE : ERROR : In textbook solution E_f = 513.5 V is taken instead of 533.337089826 V\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.4, Page number 344"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"P = 4.0 #Number of poles\n",
"f = 50.0 #Supply frequency(Hz)\n",
"V_t = 1500.0 #Terminal voltage per phase(V)\n",
"E_f = 1000.0 #Excitation voltage per phase(V)\n",
"Z_s = 12.0 #Synchronous impedance per phase(ohm)\n",
"R_a = 1.5 #Armature resistance(ohm)\n",
"\n",
"#Caclulation\n",
"P_dm = ((E_f*V_t/Z_s)-(E_f**2*R_a/Z_s**2)) #Maximum power(W)\n",
"N_s = 120*f/P #Synchronous speed(rpm)\n",
"T_dm = 9.55*P_dm/N_s #Maximum torque(N-m)\n",
"\n",
"#Result \n",
"print('Maximum power developed , P_dm = %.f W' %P_dm)\n",
"print('Maximum toruqe , T_dm = %.1f N-m' %T_dm)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum power developed , P_dm = 114583 W\n",
"Maximum toruqe , T_dm = 729.5 N-m\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}