1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
|
// Example 5.2
// Determine (a) Slip (b) Line current (c) Apparent power, active power,
// reactive power and power factor of the motor (d) Equivalent rotor curret
// (e) Stator copper loss (f) Rotor copper loss (g) Core loss (h) Air-gap
// power (i) Mechanical power developed (j) Developed torque (k) Shaft
// horsepower (l) Shaft torque (m) Effiency
// Page No. 180
clc;
clear;
close;
// Given data
f=60; // Frequency
P=6; // Number of poles
nr=1185;
R1=0.200; // Motor resistance
R2=0.250;
X1=1.20; // Motor reactance
X2=1.29;
Rfe=317; // Field resistance
XM=42; // Motor reactance
V=460; // Voltage rating
PFPS=166; // Stray loss
// (a) Slip
ns=(120*f)/P;
s=(ns-nr)/ns; // Speed difference
// (b) Line current
Z2=(R2/s)+%i*X2;
// Complex to Polar form...
Z2_Mag=sqrt(real(Z2)^2+imag(Z2)^2); // Magnitude part
Z2_Ang = atan(imag(Z2),real(Z2))*180/%pi; // Angle part
Z0_Num_Mag=Rfe*XM; // Z0 numerator
Z0_Num_Ang=0+90;
Z0_Den_R=Rfe; // Z0 denominator
Z0_Den_I=XM;
Z0_Den=Z0_Den_R+%i*Z0_Den_I;
// Complex to Polar form...
Z0_Den_Mag=sqrt(real(Z0_Den)^2+imag(Z0_Den)^2); // Magnitude part
Z0_Den_Ang = atan(imag(Z0_Den),real(Z0_Den))*180/%pi; // Angle part
Z0_Mag=Z0_Num_Mag/Z0_Den_Mag; // Magnitude of Z0
Z0_Ang=Z0_Num_Ang-Z0_Den_Ang; // Angle of Z0
// Polar to Complex form
Z0_R=Z0_Mag*cos(-Z0_Ang*%pi/180); // Real part of complex number
Z0_I=Z0_Mag*sin(Z0_Ang*%pi/180); // Imaginary part of complex number
// ZP computation
ZP_Num_Mag=Z2_Mag*Z0_Mag; // ZP numerator magnitude
ZP_Num_Ang=Z2_Ang+Z0_Ang; // ZP numerator angle
ZP_Den_R=real(Z2)+Z0_R; // Real part of ZP denominator
ZP_Den_I=imag(Z2)+Z0_I;
ZP_Den=ZP_Den_R+%i*ZP_Den_I; // ZP in complex form
// Complex to Polar form...
ZP_Den_Mag=sqrt(real(ZP_Den)^2+imag(ZP_Den)^2); // Magnitude part
ZP_Den_Ang = atan(imag(ZP_Den),real(ZP_Den))*180/%pi; // Angle part
ZP_Mag=ZP_Num_Mag/ZP_Den_Mag; // Final vlaue of ZP in polar form
ZP_Ang=ZP_Num_Ang-ZP_Den_Ang;
// Polar to Complex form
ZP_R=ZP_Mag*cos(-ZP_Ang*%pi/180); // Real part of complex number
ZP_I=ZP_Mag*sin(ZP_Ang*%pi/180); // Imaginary part of complex number
// Zin computation
ZP=ZP_R+%i*ZP_I; // Parallel impedance
Z1=R1+%i*X1;
Zin=Z1+ZP; // Input impedance
// Complex to Polar form...
Zin_Mag=sqrt(real(Zin)^2+imag(Zin)^2); // Magnitude part
Zin_Ang = atan(imag(Zin),real(Zin))*180/%pi; // Angle part
// I1 computation
I1_Mag=(V/sqrt(3))/Zin_Mag; // I1 magnitude
I1_Ang=0-Zin_Ang; // I1 angle
// (c) Apparent power, active power, reactive power and power factor of the motor
S_Mag=3*(V/sqrt(3))*I1_Mag; // S magnitude
S_Ang=0-(-Zin_Ang); // S angle
// Polar to Complex form
S_R=S_Mag*cos(-S_Ang*%pi/180); // Real part of complex number
S_I=S_Mag*sin(S_Ang*%pi/180); // Imaginary part of complex number
FP=cosd(S_Ang); // Power factor
// (d) Equivalent rotor curret
E2_Mag=I1_Mag*ZP_Mag; // E2 magnitude
E2_Ang=I1_Ang+ZP_Ang; // E2 angle
I2_Mag=E2_Mag/Z2_Mag; // I2 magnitude
I2_Ang=E2_Ang-Z2_Ang; // I2 angle
// (e) Stator copper loss
Pscl=3*I1_Mag^2*R1;
// (f) Rotor copper loss
Prel=3*I2_Mag^2*R2;
// (g) Core loss
Pcore=3*(E2_Mag^2/Rfe);
// (h) Air-gap power
Pgap=Prel/s;
// (i) Mechanical power developed
Pmech=Prel*(1-s)/s;
// (j) Developed torque
TD=(21.12*I2_Mag^2*R2)/(s*ns);
// (k) Shaft horsepower
LOSS=Pscl+Prel+Pcore+PFPS;
Pshaft=(S_R-LOSS)/746;
// (l) Shaft torque
T=5252*Pshaft/nr;
// (m) Effiency
eta=Pshaft/S_R*746;
// Display result on command window
printf("\n Slip = %0.4f ",s);
printf("\n Line current magnitude = %0.4f A",I1_Mag);
printf("\n Line current angle = %0.4f deg",I1_Ang);
printf("\n Apparent power = %0.0f W",S_R);
printf("\n Active power = %0.0f var",S_I);
printf("\n Reactive power = %0.0f VA",S_Mag);
printf("\n Power factor of the motor = %0.3f ",FP);
printf("\n Equivalent rotor curret magnitude = %0.4f A",I2_Mag);
printf("\n Equivalent rotor curret angle = %0.4f deg",I2_Ang);
printf("\n Stator copper loss = %0.0f W",Pscl);
printf("\n Rotor copper loss = %0.0f W",Prel);
printf("\n Core loss = %0.0f W",Pcore);
printf("\n Air-gap power = %0.0f W",Pgap);
printf("\n Mechanical power developed = %0.0f W",Pmech);
printf("\n Developed torque = %0.2f lb-ft",TD);
printf("\n Shaft horsepower = %0.2f hp",Pshaft);
printf("\n Shaft torque = %0.1f lb-ft",T);
printf("\n Effiency = %0.3f",eta);
|
