א
א
א
DC
Generators
אאאא
K
אא
א
א
אאאא،א
אאאאאאאאא
א
K
אאאאא
אאאא
K
אאאאאאאאא
אאאא
K
אא
אא
K
אאאא
א
א
K
אא
א
אא
K
אא א אא א א
א
אא
א
א
אא
א
K
א
אאאאא
K
٢
J
١
אא
٢
J
١
J
١
אאא
אאאא
א،
א
،،א
K
אאאאא
W
א
F
E
אא
J
אאאא
J
א א א א
א
K
،
א
(abcd)
(N)
א
(S)
٢
J
١
،אאאא
א
،אא
אא
אא،אאא
אאאאאאא
W
e=BLv
١ ٢
B(wb/m
٢
)
،אא
L(m)
א
،
v(m/sec)
אא
א
א
K
א אא א
(e)
א
(volt)
K
א
(ab)
א
א
(cd)
א
א
٢
J
١
K
F
E
F
FE
E
٢
J
١
אא
א
(abcd)
٢
J
١
א א
F
אא
٠٩
o
E
אאא،
٠٩
o
א
א
K
אא
٠٩
o
א
אאא
אא
٠٧٢
٠
،אא
אאאאאאא
(sinewave)
٢
J
١
،
אא
F
E
אא
(DC)
א א
אא
K
א א
א
F
א
E
A, B
٢
J
٢
K
אאא
A
٢
J
٢
אא،
(abcd)
٠٨١
،
٢
J
٢
אאא
B
،
٢
J
٢
אא
٠٨١
א،
א
٠٨١
٠٦٣
אאא
א
٢
J
١
K
אאא
F
E
K
אאא
א
K
אא
אא
K
F
E
F
E
F
E
٢
J
٢
אאא
d
a
b
c
٢
J
١
J
٢
אא
א א א ، א א
א
אאאא
א
אא،א
אאאא
K
،אאאאאאאא
٢
J
٣
אא
K
אאאאא
W
•
אא
(Yoke)
W
אא
אאאא
אאא،א
،א
K
٢
J
٤
אא
K
אא
(Main poles)
W
אאא
אאא
(Pole face or shoe)
אא
אאא
K
אאא
(Field coils)
W
א
(shunt field coil)
א
(series field coil)
،
אא
א
א
K
אאאא
K
א
،אאא
F
٢
J
٥
E
א
K
٢
J
٣
•
א
(Commutating poles)
W
אא
אאא
F
٢
א
E
א،
אא
אא
K
אאא
א
אא
K
٢
J
٤
אא
٢
J
٥
א
א
אא
F
א
E
א
W
•
א
(Armature core)
W
אא
אאאא،אא
K
א
א
K
،אא
٢
J
٦K
•
א
(Armature windings)
W
אאא
אא
K
אאאאא
אאא
אאא
K
אאאא
א
א
א
K
•
א
F
א
E
)
(Commutator
W
אאאא
אאאא
K
אאאאא
א
F
א
KE
אא א
אאא،א
K
•
א א
(Brushes holder)
W
א א א
א
א
אאאא
א
א
F
א
E
אאא
K
K
٢
J
١
J
٣
א
Armature winding
W
אאאאאאאאא
אאאא
٢
J
٦
א
אא
F
א
E
א
אאא
K
אאאאא
א א א
K
א א א
J
אא
J
אאאאא
אא،אא א
אא
(commutator segments)
אא،
א
א
W
J
אא
(Lap winding)
W
אאא
٢
J
٧
א،
F
١{٢{٣
E
א
١
אא
٢
א
٢
אא
٣
אאא
K
א
אא
אא
K
אאא
אאאאא
אא
K
٢
J
٧
א
אאאא
K
J
אא
(Wave winding)
W
אאא אא א אא
،
אא
،אאא
אאאא
(commutator pitch)
٢
J
٨
K
אאאאאא
א
אא،
K
F
FE
E
٢
J
٧
אא
אא
٢
J
٨
אאאא
٢
J
٢
אאאאא
אא
א
אא
K
L (m)
B (tesla)
א
v (m/sec)
א
א
F
٢
J
٩
E
אאא
e (volt)
א
W
e=BLv volt
٢ ٢
א
r meter
אא
W
٣ ٢
r
n
r
v
60
2
π
ω
=
=
(rpm) n
אא
L
،
ω
(rad/sec)
אאא
F
א
E
אאאאא
٤ ٢
p
rl
A
B
2
/
2
π
φ
φ
=
=
A
،אא
٢
J
٣
א
٢
J
٤
א
٢
J
٢
אאאאא
W
٥ ٢
r
n
l
rl
p
e
60
2
2
2
π
π
φ
=
א
٢
J
٥
٦ ٢
60
2 pn
e
φ
=
אאא
Z
a
אאא
٢a
אאאא
א
אאא
W
٧ ٢
60
2
2
n
Z
a
p
E
a
a
φ
=
٢
J
١
٦
אא
٠٥٢
،
٠٠٢١
L
K
א
א
٤
א אא א ،
א
K
א
٢p=٦ ٢a=٢[wave winding] Z
a
=
٠٥٢n=١٢٠٠ rpm Φ=٤ megalines/pole
Φ=
٤*١٠
٦
*
٠١
٨
=
٠{٠٤ wb/pole
60
2
2
n
Z
a
p
E
a
a
φ
=
volt
E
a
600
60
1200
*
250
*
04
.
0
*
2
6
=
=
٢
J
٢
٨
אא
٠٦٩
،
א
٠٠٦
L
K
א א אא א א
٠٢٢
א ،
א
K
א
٢p=٨ ٢a=٢p[lap winding] Z
a
=
٠٦٩n=٦٠٠ rpm E
a
=
٠٢٢V
60
2
2
n
Z
a
p
E
a
a
φ
=
60
600
*
960
*
*
8
8
220
φ
=
Φ=٠٢٢*٦٠/(٦٠٠*٩٦٠)=٠٫٠٢٣ wb/pole
٢
J
٩
אאא
٢
J
٣
א
(Armature Reaction)
،א א א א
א
א
אא،א،אא
אאאא
א،אאא،א
אאא
א،
אאאאא
(Lenz Law)
אאאאאאאא
אאאא
،
א
،אאא
א
אאאא
K
אאאאאא
אא
א
אא
K
אא
א
K
א
K
،א
אאאא
א
K
٢
J
٠١
א א א א א
א
F
א
KE
א
(M.M.F
f
)
א
،
אא
F
אא
א
KE
אאאא
(G.M.A)
א
א
(M.N.A)
K
٢
J
٠١
אאאאא
א
K
אאאאא
אאאא،
אאא
،א
x
א
K
א
אא،אאא
אאאאא
א
א א
אאאאא،א
(M.M.F
a
)
א
אא
K
אא
אאא
א
،אא،א
٢
J
٠١
K
א א אא א
(M.M.F
t
)
א
θ
אא
(M.M.F
f
)
אא،
(M.N.A)
אאאא
(G.M.A)
K
٢
J
٠١
א
א
٢
J
٠١
K
אאא
א
(ab)
K
٢
J
٠١
אאאאא
א،אא
(bc)
אא
א
אא
٢
J
٠١
K
א
אאאאא
K
א
א
،אאאאא
،אא
א،א
אאאאאא
F
א
E
،אא
א
אאאא
אאאא
(Demagnetizing effect)
אאא
אאא
W
J
،אאאא
אאא
K
J
אאאא
אא
K
J
אאאאאאאאא
אא
K
F
FE
E
F
E
٢
J
٠١
אאא
אאא
א
K
א
א
א
א
א
K
א
،אאאאאאאאא
٢
J
١١
،אאא
٢
J
٢١
א
אאאאאאא
(F
c
)
א
(F
a
)
K
א
אאאא
K
אאא
א
אאא
F
א
E
،אא،א
אאאא
٢
J
٣١
אאאאא
K
٢
J
١١
א
א
٢
J
٢١
אאאאאאאא
٢
J
٣١
א
٢
J
٤
א
F
א
E
אא
(Methods of Excitation)
א א א
F
E
אא א א
אאאאאאאאאא
K
א
אא
אאאא
אא،
א
א
KW
J
אא
F
E
(Separately excited)
א
F
א
KE
J
אאא
(Self excited)
،אא
אא
אא
א
א
K
٢
J
٤
J
١
אאאאא
(Separately excited generators)
٢
J
٤١
א ،אאא אא
אא
אאא
K
אא
א،אאאאא
אא،אאא
K
٢
J
٤١
אא
אא
W
(Kirechhoff’s Law)
אאאא
W
٨ ٢
a
a
L
a
R
I
V
E
+
=
V
L
אאא
F
א
E
،
E
a
אאאאאא
אא
W
٩ ٢
60
/
2
2
N
Z
a
p
E
a
a
φ
=
I
a
،א
R
a
،א
I
L
אא
K
٠١ ٢
L
a
I
I
=
٢
J
٣
،א
٠٠٢١
L
א
٠٠٢
٥٢١
K
א
אאאא
٠٠٠١
L
א،
K
א
٤٠
{
٠
K
א
n
١
=
٠٠٢١rpm I
L١
=
٠٠٢A V
L١
=
٥٢١V n
٢
=
٠٠٠١rpm R
a
=
٠{٠٤ Ω
E
a
α n as I
f
is constant
E
a١
=V
L١
+I
L١
R
a
=
٥٢١H٢٠٠*٠{٠٤=١٣٣ V
2
1
2
1
n
n
E
E
a
a
=
1000
1200
133
2
=
a
E
V
E
a
8
.
110
1200
133
*
1000
2
=
=
E
a٢
=V
L٢
+I
L٢
R
a
=I
L٢
R
L
+ I
L٢
R
a
Ω
=
=
=
625
.
0
200
125
L
L
L
I
V
R
٠١١{٨=I
L٢
[
٠{٦٢٥H٠{٠٤]=I
L٢
[
٠{٦٦٥]
.
62
.
166
665
.
0
8
.
110
2
Amp
I
L
=
=
٢
J
٤
J
٢
אאאא
(Self excited generators)
אאאאא
א
W
J
א
(series excitation)
אאאא
J
א
(shunt excitation)
אאא
J
(compound excitation)
אאא
٢
J
٤
J
٢
J
١
אאא
(series excited generator)
אאאא
٢
J
٥١
K
٢
J
٥١
אאא
אא
:
١١ ٢
(
)
f
a
a
L
a
R
R
I
V
E
+
+
=
٢١ ٢
f
L
a
I
I
I
=
=
٢
J
٤
א
،
٤
אא
٥١
א
٥٢١
א
٠٥١١
L
K
א
٥١
,
א
٤٢
,
Kא
א
אא
٠٠٢١
L
א
٥٢١
K
אאא
٠٣
K٪
א
P
out
=
٥١Kw V
L١
=
٥٢١V n
١
=
٠٥١١rpm R
f
=
٠{١٥Ω R
a
=
٠{٢٤Ω n
٢
=
٠٠٢١rpm I
L٢
=
٥٢١A
Φ
٢
= ٣٫١Φ
١
.
120
125
3
10
*
15
1
1
Amp
V
P
I
L
out
L
=
=
=
E
a١
=V
L١
+I
L١
R
f
+I
a
R
a
=V
L١
+I
L١
[R
f
+R
a
] as I
L
=I
a
E
a١
=٥٢١+١٢٠[٠٫١٥+٠٫٢٤]=١٧١٫٨ V
2
2
1
1
2
1
n
n
E
E
a
a
φ
φ
=
V
n
E
n
E
a
a
05
.
233
1150
*
8
.
171
*
1200
*
3
.
1
1
1
1
1
1
2
2
2
=
=
=
φ
φ
φ
φ
E
a٢
=V
L٢
+I
L٢
R
f
+I
a
R
a
=V
L٢
+I
L٢
[R
f
+R
a
]
V
L٢
=E
a٢
-I
L٢
[R
f
+R
a
]=٥٠٫٣٣٢-١٢٥[٠٫١٥+٠٫٢٤]=١٨٤٫٣ volt
-
٤٣
-
٢
J
٤
J
٢
J
٢
אאאא
(Shunt excited generators)
אאאא
٢
J
٦١
K
א
א א א א
،אא
אא،אא
אא
K
אא
:
٣١ ٢
a
a
L
a
R
I
V
E
+
=
٤١ ٢
f
f
L
f
R
I
V
V
=
=
٥١ ٢
f
L
a
I
I
I
+
=
אאאא
١
٪
٥
٪
אא،א
אא
K
٢
J
٦١
אאא
٢
J
٥
א
٠٥٣
א
٠٤٢
א،
אאא
٢٠
,
٠
٥٥
Kא
אאאא
K
א
I
L
=
٠٥٣A V
L
=
٠٤٢V R
a
=
٠{٠٢Ω R
f
=
٥٥Ω
Amp
R
V
R
V
I
f
L
f
f
f
36
.
4
55
240 =
=
=
=
I
a
=I
L
+I
f
=
٠٥٣H٤{٣٦=٣٥٤{٣٦ Amp
E
a
=V
L
+I
a
R
a
=
٠٤٢H٣٥٤{٣٦*٠{٠٢=٢٤٧{١ V
٢
J
٦
אא
אא
٠٠٥
،
א
١٠
{
٠
א
٥٩
،
٠٠٢
٠٦
א
٠٢١
K
אאאאא
٢٠
,
٠
K
א
٢p=٢a [lap winding] Z
a
=
٠٠٥R
a
=
٠{٠١Ω R
f
=
٥٩Ω P
out
=
٠٠٢*٦٠=١٠٠٢٠W V
L
=
٠٢١
V Φ=
٠{٠٢ wb/pole
P
out
=V
L
*I
L
A
V
P
I
L
out
L
100
120
60
*
200
=
=
=
A
R
V
I
f
f
f
26
.
1
95
120 =
=
=
I
a
=I
L
+I
f
=
٠٠١H١{٢٦=١٠١{٢٦ A
E
a
=V
L
+I
a
R
a
=
٠٢١H١٠١{٢٦*٠{٠١=١٢١{٠١ V
60
/
2
2
n
Z
a
p
E
a
a
φ
=
60
/
*
500
*
02
.
0
*
2
2
01
.
121
n
p
p
=
n=
١٢١{٠١*٦٠/(٠{٠٢*٥٠٠)=٧٢٦ rpm
٢
J
٤
J
٢
J
٣
אאא
(Compound excited generators)
،אאאאאאאאא
אא
א
אאאאא
אא
אאאא،אא
(cumulative compound )
א،אאא
אא
(differential compound)
K
א א א אא ،א א
אאא
(short-shunt)
،
אאאאאא
F
א
אא
E
אאא א
(long-shunt)
א א ،
א
٢
J
٧١
אא،
٢
J
٧١
،
אא
se
אא
sh
K
אאא
W
٦١ ٢
se
L
a
a
L
a
R
I
R
I
V
E
+
+
=
٧١ ٢
sh
L
a
I
I
I
+
=
٨١ ٢
L
se
I
I
=
א
אא
:
٩١ ٢
)
(
se
a
a
L
a
R
R
I
V
E
+
+
=
٠٢ ٢
sh
L
a
I
I
I
+
=
١٢ ٢
a
se
I
I
=
F
FE
E
٢
J
٧١
אא
F
E
F
E
אא
אאאאא
K
אא
אאא
،אאאא
אאא
(demagnetize the machine)
אא
K
٢
J
٧
٠٦
٠٣٢
K
א
א
אא،אאאא
٤٠
{
٠
אא،
١٠
{
٠
אא
٥٢١
K
א
V
L
=
٠٣٢V I
L
=
٠٦A R
a
=
٠{٠٤ Ω R
se
=
٠{٠١Ω R
sh
=
٥٢١Ω
A
R
V
R
V
I
sh
L
sh
sh
sh
84
.
1
125
230 =
=
=
=
I
a
=I
L
+I
sh
=
٠٦H١{٨٤=٦١{٨٤ A
E
a
=V
L
+I
a
(R
a
+R
se
)=
٠٣٢H٦١{٨٤*(٠{٠٤H٠{٠١)=٢٣٣{٠٩٢ Volt
٢
J
٥
אאאאא
(Characteristic Curves of DC Generators
)
אאאא
J
א
אאא
א
א
J
א
אא،א
،אא،
א
אא،אא،אא
א
K
אאאא
אא
א
،א
٢a,٢P
א אא א
E
a
אא
Φ
אא،
N
K
N
k
a
E
φ
=
،א אא א
א אא א
אא
V
L
K
אאאאא
W
J
אא
No-load characteristic, E
o
=f(I
f
), N=constant
א
אאא
(o.c.c)
אא
אאא
אא
א
(E
o
)
א
(I
f
)
א
K
J
אא
Load characteristic, V
L
=f(I
f
), I
a
and N=constant
אאאא
(V
L
)
א
(I
f
)
א
אא
K
J
אאא
External characteristic, V
L
=f(I
L
), I
f
and N=constant
אאאא
(V
L
)
א
(I
L
)
אא
K
J
אאאא
Internal characteristic, E
a
=f(I
a
), I
f
and N=constant
א
אאאאאאאאאאאא
אאא
K
אאאאאאאא
אאא
אא
K
٢
J
٥
J
١
אאאאא
J
אא
No-load characteristic
،אאאאא
אאאא
E
a
אאא
W
φ
k
E
a
=
א
אאא،
(I
f
)
f
a
I
k
E
′
=
א
אאאאאאא
א
E
o
א
אאא،א
٢
J
٨١
אא א א ،
אאאאאאא،
א
אא אא ،
א
K
אאאאאא
E
o
א
I
f
א،
٢
J
٨١
א
(a)
،
א
(b)
א א
،א
אאאא
K
F
FE
E
٢
J
٨١
אא
F
E
א
F
E
אא
J
אא
Load characteristic
א א א אא א א
א
(E
o
)
א
(armature reaction)
א،
א
(V
L
)
אאאא
(E
a
)
אאאא
(I
a
R
a
)
אא،
F
א
E
אא
א
(R
L
)
אא
V
L
،
V
L
F
א
E
א
F
א
E
אאא،א
אא
K
٢
J
٩١
،אאא
٢
J
٩١
א
K
א
٢
J
٩١
،
III
אא
I
א
א
אא،א
AB
(I
a
R
a
)
א
III
א،
II
א،אאאאאאא
CB
א
אאא،אא
(V
L
)
א
א
(E
o
)
אא
(CD)
אא
א
K
F
FE
E
٢
J
٩١
אא
F
E
א
F
E
אא
J
אאא
(External characteristic)
٢
J
٠٢
،אאא
אאא
אאאאאא
(II)
E
a
،אאא
אאא
(I)
א
E
o
אאא
אאאא
K
אאאאאא
אאאאא
(III)
،
א
אאא
(V
L
)
א
(I
L
)
אא
K
J
אאאא
Internal characteristic)
(
א
II
٢
J
٠٢
אאאא
E
a
=f(I
a
)
אא،
אאאא
(E
a
)
אא
(I
a
)
אא
(I
L
)
א
אא،אא
K
אאאא
א
AB
،אאא
E
a
אאאאאא
אאאאא
K
،אאא
٢
J
٠٢
א،
ε
אא
W
٢٢ ٢
100
%
∗
−
=
L
L
o
V
V
E
ε
٢
J
٠٢
א
אא
٢
J
٥
J
٢
אאאאא
،אאאא
אאאא
אאאאא
א
K
אא
א
F
א
E
،
אא،אאאא
אאאאא
W
א
؟אא
K
א א א
،
אאא
K
،אאא
א
،א
א
אא
א،א
٢
J
١٢
א
(Magnetization curve)
א
אא
(I
f
)
،
אאאא
א
א
(E
o
)
א
אאאא
K
א
،א
אאאא
(E
r
)
אאאאא
K
א
אאאא
(L
f
)
א
(R
f
)
،
אאאאאאא
אא
K
אאאאא
אאא
אאאאא
(Residual magnetism) E
r
K
٢
J
١٢
אאאא
٢
J
٥
J
٢
J
١
אאאאא
א
א
אאאאאאאאאאא
K
٢
J
٢٢
א א אא
אא א
א
K
אאא
(R
L
)
K
אאא
א
אא
(I
a
)
،
אא
אא
אאאאאא
(V
L
)
K
א
٢
J
٢٢
א،אאאא
I
א
،אאא
III
א א א א א אא
I
א
A.C
K
אאאאא
،אאא
אאא،א
אא
I
L
K
OP
א
אאא
٢
J
٢٢
K
אאא
I
a
R
a
אאא
F
III
E
אאאא
F
II
E
א
אאא
E
a
אא
F
א
א
E
אאאא،
I
אאאא،
II
א
אא
K
F
FE
E
٢
J
٢٢
אאא
J
אאא
J
אא
٢
J
٥
J
٢
J
٢
אאאאא
א
I
٢
J
٣٢
א אא אא
א
II
א،אאאא
III
אאא
K
א
אאא،אאא
א
א
K
א
IV
אאאאא
E
o
K
אאא
W
٣٢ ٢
100
%
∗
−
=
AA
AA
o
E
ε
F
FE
E
٢
J
٣٢
אאא
J
אאא
J
אא
٢
J
٥
J
٢
J
٣
אאאא
אאא،אא
(long-shunt )
אאא
(short-shunt)
K
،א
אאאא
אא،א
אאאא،א
K
אאאא
F
אא
E
א،אאאא
אאאא
K
J
א
W
אאאאא
א א ،אא
א א
אאאאא
אא
V
L
אא
٢
J
٤٢
K
J
W
אא
،א א אא א א א א
،א
אאא
V
L
א
K
J
W
،אאאאאאא
א
אאאאאא
א
אא،א
٢
J
٤٢
K
٢
J
٤٢
אאאא
٢
J
٦
אאאאא
Energy Losses and Efficiency of DC Generators
אאאא
،א
אא،א
אאאא،אא
אאאאא
א
،א
א
،אא
F
E
אא،
א
K
אא
אאא،אא
،א אא א
F
א
KE
אאאא
א
K
J
אאא
F
א
E
Magnetic losses (Iron losses)
J
אאא
F
א
E
Electrical losses (Cupper losses)
J
F
א
E
)
Mechanical losses (Friction losses
٢
J
٦
J
١
אאא
F
א
E
אא
W
J
אא
Hysteresis loss
:
אאאאאא
אאאא
W
٤٢ ٢
f
g
B
h
W
6
.
1
=
J
אאאא
F
א
E
Eddy current loss
W
אאא
٥٢ ٢
f
g
B
e
W
2
=
אאאאא
א
אא
אאא
K
אאאאאא
،אאא
אא
K
٢
J
٦
J
٢
א
אאאאאאא
אאאאא
אא،אא
W
J
אא
W
Armature cupper loss=I
٢
a
R
a
אאאאא
J
אא
W
For shunt machine=I
٢
sh
R
sh
(or VI
sh
)
אא
K
For series machine=I
٢
se
R
se
J
א
א
W
Loss due to brush contact resistance=I
a
V
B
V
B
אאא،אאא
K
٢
J
٦
J
٣
אא
אאא،א
(bearing)
א،
א
אאאא
K
אאאא
אאאאא
K
٢
J
٦
J
٤
אא
אאא
אא
(Prime mover)
אאא
א
א
א
Input power
٢
J
٥٢
،
אאא
H.P
אאאא،
W
H.P=
٦٤٧Watt
.
K
א
אא
P
mech
אא
P
i
א
P
g
P
g
א
F
א
E
W
P
g
=E
a
I
a
P
g
=P
in
-(P
mech
+P
i
)
٦٢ ٢
אא
א
P
g
אאא
אאא
א
P
out
א
P
L
K
٢
J
٦٢
אאא
אא
K
א
P
in
P
g
P
out
א
א
א
P
i
&P
mech
A
B C
א
P
cu
٢
J
٥٢
אאאאא
i/p
o/p
V
L
I
L
P
mech
+P
i
I
2
a
R
I
2
sh
R
sh
I
2
se
R
se
∆VI
a
I
a
E
a
אא
אא
אא
אא
٢
J
٦٢
אא
אאא
٢
J
٦
J
٥
א
א
Efficiency
א א א א
،א א
א
W
J
אא
W
٧٢ ٢
746
*
HP
I
E
A
B
a
a
m
=
=
η
J
אא
W
٨٢ ٢
a
a
L
L
e
I
E
I
V
B
C =
=
η
J
אא
W
٩٢ ٢
746
*
/
/
HP
I
V
A
C
p
i
p
o
L
L
e
m
=
=
=
=
η
η
η
אאא
٠٣ ٢
losses
P
P
out
out
+
=
η
١٣ ٢
in
in
P
losses
P
−
=
η
٢
J
٨
،
٠٠٠١
L
٥٤
א
٠٤٢
K
אא،
٥٠
{٠
אא
٢٠
{٠
אא
٥٦
K
אאאאאאאאא
٠٠٥٣
א
K
א
n=
٠٠٠١rpm P
out
=
٥٤Kw V
L
=
٠٤٢V R
a
=
٠{٠٥Ω R
se
=
٠{٠٢Ω R
sh
=
٥٦Ω
P
i
+P
mech
=
٠٠٥٣W
A
V
P
I
L
out
L
5
.
187
240
3
10
*
45
=
=
=
A
R
V
R
V
I
sh
L
sh
sh
sh
7
.
3
65
240 =
=
=
=
I
a
=I
L
+I
sh
=
٧٨١{٥H٣{٧=١٩١{٢ A
P
cu
=I
٢
a
R
a
+ I
٢
a
R
se
+ I
٢
sh
R
sh
= I
٢
a
(R
a
+R
se
)+ I
٢
sh
R
sh
=(
١٩١{٢)
٢
*(
٠{٠٥H٠{٠٢) + (٣{٧)
٢
*
٥٦=٣٤٤٨{٨٧ W
Losses=P
cu
+P
i
+P
mech
=
٨٤٤٣{٨٧H٣٥٠٠=٦٩٤٨{٨٧ W
%
6
.
86
866
.
0
87
.
6948
3
10
*
45
3
10
*
45
=
=
+
=
+
=
Losses
P
P
out
out
η
٢
J
٩
٨
،
٠٠٢١
٠٠٦
L
א،
٠٦
אא
٢٢٠
{٠
K
א
٦٠
,
אא ،
٤٠
{٠
אא
٠٥٢
K
א א
אאא
א
٠٠٥٤
א
K
א
٢p=٨ ٢a=٢ [wave winding] Z
a
=
٠٠٢١n=٦٠٠ rpm I
a
=
٠٦A Φ=٠{٠٢٢ wb
R
a
=
٠{٠٦Ω R
se
=
٠{٠٤Ω R
sh
=
٠٥٢Ω P
i
+P
mech
=
٠٠٥٣W
60
/
2
2
n
Z
a
p
E
a
a
φ
=
V
E
a
1056
60
/
600
*
1200
*
022
.
0
*
2
8
=
=
E
a
=V
a
+I
a
R
a
V
a
=E
a
-I
a
R
a
=
٠٦ ٦٥٠١*٠{٠٦=١٠٥٢{٤ V
A
R
V
I
sh
a
sh
21
.
4
250
4
.
1052 =
=
=
I
L
=I
a
-I
f
=
٤ ٠٦{٢١=٥٥{٧٩ A
V
L
=V
a
-I
L
R
se
=
٢٥٠١{٤ ٥٥{٧٩*٠{٠٤=١٠٥٠{١٦ V
P
out
=V
L
I
L
=
٠٥٠١{١٦*٥٥{٧٩=٥٨٥٨٩ W
P
cu
=I
٢
a
R
a
+ I
٢
L
R
se
+ I
٢
sh
R
sh
=(
)٠٦
٢
*
٠{٠٦H(٥٥{٧٩)
٢
*
٠{٠٤H(٤{٢١)
٢
*
٠٥٢=٤٧٧١{٥ W
losses=P
cu
+P
i
+P
mech
=
١٧٧٤{٥H٣٥٠٠=٨٢٧١{٥ W
%
6
.
87
876
.
0
5
.
8271
58589
58589
=
=
+
=
+
=
Losses
P
P
out
out
η