第三章
3.14 C398e=
pN3⨯60a
=60⨯3
=6.63
EC-2
a=eφn=6.63⨯1500⨯2.1⨯10=208.8VEa=Ceφn=6.63⨯500⨯2.1⨯10-2
=23.2V
TpNe=
2πa
φIa=9.55Ce⨯2.1⨯10
-2
⨯10=13.3N.m
3.15 T2
60002=
PΩ
=
2πn60
=57.3N.mTP0
0=Ω
=
3952πn60
=3.77N.m
PΩ=61.07⨯
2π⨯1000
e=Te60
=6395W
P1=Pe+pcua+pcuf=6395+500+100=6995W
η=60006995
=0.857
3.16
IPNa=IN+If
=
U
+
UNN
I
=365.2A
f
Ea=U
N
+Iara+2∆U2=230+365.2⨯0.0259+2=241.46V
Pe=EaIa=241.46⨯365.2=88180W
P1=Pe+p0=88180+4300+0.005⨯82000=92980WTPe
88180e=
868.5N.mη=82000Ω
=2πn60
=92980
=88.2%
3.18
额定负载时电枢电流为：
Ia=80-
110138
=79.2A
（1）接入电阻瞬间
E'a
=110-79.2⨯0.078=103.8VI'=110-103.8
a
0.078+0.4=12.97A
TE'aI'a103.8⨯12.97e'=Ω=2π⨯1470/60=8.75N⋅m
（2）Ia=79.2A （3）
Te=T2+T0=61.07N.m
n''nN
=
''EaEaN
''=U-79.2⨯0.478=72.1VEa
n''=1470⨯
72.1103.8
=1021r/min
第四章
4.10
（1）ns=1500r/min（3）
2p=4 （2）Q=2mpq=2⨯3⨯2⨯3=36
α1=
p⨯360Qy1
=
2⨯36036=sinsin
89
=20⨯90
20
ky1=sin
sinkq1=
τ
90=0.9848
qα
3⨯200202
=0.9598
qsin
α
2
=3sin
kw1=ky1kd1=0.9848⨯0.9598=0.9452
（4）
E1φ=4.44fNkE1L=
w1
Φ1=4.44⨯50⨯108⨯0.9452⨯1.015⨯10
-2
=230.02V
3⨯230.02=398.39V
4.11
q=
Q2mp
=
542⨯3
=936054=sin
α=
p⨯360Qy1
=90
=6.66672227⨯90
ky1=sin
sinkq1=
τ
2
=0.9579
qα
sin=
9⨯6.666726.6667
2
2
qsin
α
2
=0.9936
9sin
kw1=ky1kd1=0.9579⨯0.9936=0.9517E1φ=N=
63001.732
C
=3637.4V=
2⨯1⨯9⨯1
1=
w1
2pqNa
=183637.4
=0.9556Wb
Φ=4.12 (1)q=
E1φ4.44fNk
4.44⨯50⨯18⨯0.9517
Q2mp
=
362⨯3⨯2
=3
α=
p⨯360Qy1
=90
2⨯36036=sinsin
79
=20⨯90
20
ky1=sin
sinkq1=
τ=0.9396
qα
3⨯200202
qsin
α2
=3sin
=0.9598
kw1=ky1kd1=0.9848⨯0.9598=0.9018N=
2pqNa
C
=
2⨯2⨯3⨯3
1
w1
=36
E1φ=4.44fNkE1L=
Φ1=4.44⨯50⨯36⨯0.9018⨯0.75=5405.38V
3⨯5405.38=9362.1V
(2)ky5=sin5
sin
kq5=
qsin
y1
τ
25α2
90
=sin5sin
79
⨯90
=-0.1736
5qα
=
5⨯3⨯202
5⨯20
2
=0.2176
3sin
kw5=ky5kd5=-0.1736⨯0.2176=-0.03778E5=4.44f5Nk合成相电动势线电动势E=4.13
(1)q=
Q2mp
=
362⨯3⨯2
w5
φ5=4.44⨯250⨯36⨯0.03778⨯0.03=-45.29V
E1φ+E5φ=
2
2
Eφ=
5405.38
2
+(-45.29)
2
=5405.56V
3⨯5405.56=9362.44V
=3
α=
p⨯360Qy1
=90
2⨯36036=sinsin
79
=20⨯90
20
ky1=sin
sinkq1=
τ
2
=0.9396
qα
3⨯2020202
qsin
α
2
=3sin
=0.9598
kw1=ky1kd1=0.9848⨯0.9598=0.9018(2)N=
2pqNa
C
=
2⨯2⨯3⨯20
1
w1
=240
-3
E1φ=4.44fNkΦ1=4.44⨯50⨯240⨯0.9018⨯7.5⨯10
=360.35V
4.14
(1)q=
Q2mp
=
362⨯3⨯1
=6
α=
p⨯360
Qy1
=90
1⨯360
36=sinsin
=10⨯90
ky1=sin
sin
kq1=
1518
τ
=0.966
qα
6⨯10102
qsin
α
2
=
6sin
=0.9562
kw1=ky1kd1=0.966⨯0.9562=0.9237N=I=
2pqN
aP3Ucosϕ
Nkp
w1C
=
2⨯1⨯6⨯1
1=
6000
=12
=687.34
1.732⨯6.3⨯0.8
12⨯0.9237
1
Fφ1=0.9Iφ=0.9
⨯687.34=6856.8A
(2)ky5=sin5
sinkq5=
qsin
y1
τ
25α2
90
=sin5sin
1518
⨯90
=0.2588
5qα
=
5⨯6⨯102
5⨯102
=0.1020
6sin
kw5=0.2588⨯0.1020=0.0264F1=1.35
Nkp
w1
Iφ=1.35
w5
12⨯0.9237
115⨯
⨯687.34=10285.3A
F5=1.35⨯
1Nk
νp
Iφ=1.35⨯
12⨯0.0264
1
⨯687.34=58.79A
4.16
(1)
τ=
q=
Q2pQ
=
602=
=3060
=10
2mp2⨯3⨯1
α=
p⨯360
Q
=
1⨯360
60
=6
当y1=τ时ky1=sinky5=sin
sin
kq1=
qsinsin
kq5=
qsiny1
ττ
90
=sin90
=1
5y110α2
90=sin5⨯90sin
10⨯6
=1
α
225α2
=10sin
sin=
2=0.95540⨯625⨯10⨯6
2
5⨯62
5⨯10α
=0.1932
10sin
kw1=ky1kd1=0.9554kw5=ky5kd5=0.1932E1φ=4.44fNk（2）y1=τ-ky1=sin
5
w1
Φ1=4.44⨯50⨯200⨯0.9554⨯0.1505=6384V
τ45
=90
45
τ=24=0.951
kw1=ky1kd1=0.951⨯0.9554=0.9086E1φ=4.44fNk
w1
Φ1=4.44⨯50⨯200⨯0.9086⨯0.1505=6071V
4.17
kw1=0.9452kw3=-0.5774kw5=0.1399kw7=0.0607F1=1.35n1=
60fpNkp
w1
Iφ=1.35
108⨯0.9452
2
⨯20=1378.1A
=1500r/min
F3=0F5=1.35⨯n5=
n15
1Nk5
w5
p
Iφ=1.35⨯
15
⨯
108⨯0.1399
2
⨯20=40.79A
=300r/min
1Nk7
w7
F7=1.35⨯n1=
n17
p
Iφ=1.35⨯
1108⨯0.06077
2
⨯20=12.64A
=214r/min
第五章
5.14 (1)ns=
60fp
=750r/min
nN=ns(1-sN)=750(1-0.044)=717r/mins=
750-700750
=0.0666
s=1
5.15
(1)
pFe=P0-mR1I0-pmec=1340-3⨯0.4(Rm=
pFemIU0I0Z
20
2
21.23
)-100=1060W
2
=
10603⨯(380
21.23)
2
=2.36Ω
Z0=
=(
20
21.23
20
=31Ω)=
31-2.76
2
2
X0=
-R=30.87Ω
由短路试验Zk=
UkIkPKmI
2K
=(=
38066.83)
=2.85Ω
Rk=
41403⨯(
66.83)
2
=0.928Ω
X
K
=
ZK-RK=2.69Ω
X0X0-X
k
k
22
'=(Rk-R1)R2
=(0.928-0.4)⨯
30.8730.87-2.69
=0.578Ω30.87-2.69
30.87
'σ=X0-X1σ=X2X
m
X0-XX0
(R'
2
2
+X0
2
)=30.87-
⨯(0.578
2
+30.87)=1.37Ω
2
=X0-X1σ=30.87-1.37=29.5Ω
5.16
(1)sm='=RstRst=
'R2
'σR+(X1σ+X2
2
1
2
'σR1+(X1σ+X2
)
2
=1
2
2
)2
'=-R2
0.143+(0.262+0.328)-0.134=0.472Ω
'Rstkikem12πf1
=
0.4721.342
2
=0.262ΩpU
21
Tst='=Ist(2)Tst='=Ist
⨯
'+Rst')(R2
(R1
'+Rst'+R2
U1
)2
'σ+(X1σ+X2
)2
=
3⨯4⨯220314⨯(0.749220
22
⨯0.606+0.59)
2
=1232.9N.m
(R1
m12πf1
'+Rst'+R2
)
2
'σ+(X1σ+X2
212
)
2
=
(0.749
2
+0.59)
2
=230.7A
⨯
pU
'R2
(R1
'+Rst'+R2
U1
2
)
'σ+(X1σ+X2
)
2
=
3⨯4⨯220314⨯(0.277
22
⨯0.134+0.59)
2
=583.5N.m
(R1')+(X1σ+X2'σ+R2
)2
=
220(0.277
2
+0.59)
2
=337.5A
5.17
2p=4sN=
15000
ns=1500r/min=0.0493
f2=sf1=2.465Hz
1500-1426
用等效电路求解Z=
5.18 (1)s=
1500-1450
1500
T20.9
=0.0333
T2=
P2
Ω
=
750002π⨯1450
60
=494.2N.m
Pe=TeΩs=ΩS=
494.20.9
⨯
2π⨯1500
60
=86210W
pcu2=sPem=2870W
P1=Pe+pFe+pcu1=86210+2100+2870=91180Wcosϕ1=
P13UNIN
=
911801.732⨯380⨯160
=0.86
5.19
Pe=P1-pcu1-pFe=10700-450-200=10050Wpcu2=sPe=10050⨯0.029=291.45WPΩ=Pe(1-s)=9758.55W
5.20
(1)s=
1000-9601000PΩ1-s
=0.04
f2=sf1=2Hz
PΩ=P2+pmec+pad=7500+45+37.5=7582.5WPe=
=7582.51-0.04
=7898W
pcu2=sPe=7898⨯0.04=316W
P1=Pe+pcu1+pFe=7898+316+231=8603WI1=
P1
3UP2P1
=
N
cosϕN
=
8603
1.732⨯380⨯0.824
=15.86A
η=5.21
75008603
=87.17%
PN=∴IN=
U
N
INcosϕNηPN
cosϕNη
=
28000
1.732⨯380⨯0.9⨯0.88
=53.7A
3U
N
Ist=6⨯53.7=322.2AIst∆=
322.23
=107.4A
5.22
R2sN
=
R2+RΩ
s15001500
=0.0133
sN=s=
1500-1480
1500-1100
=0.26660.020.0133
-0.02=0.38Ω
RΩ=0.2666⨯
5.23
(1)sN=(2)
PΩ=P2+Pmec+pad=7500+45+80=7625WPe=
PΩ1-s
=
76251-0.038
=7926.2W
pcu2=sPe=0.038⨯7926.2=301W
1000-9621000
=0.038
f2=sf1=1.9Hz
P1=P2+
∑
p=7500+470+234+45+80+301=8630.2W
=86.9%
η=(3)I1=(4)T2=
P2P1
=
75008630.2
P13U1cosϕ1P2
=
8630.21.732⨯380⨯0.827
=15.85A
Ω
=74.44N.m
Te=
Pe
Ωs
=75.7N.m
T0=Te-T2=1.26N.m
5.24 (1)sN=
1500-1442
1500m1
=0.0386U1
22
'R2s
1σ
Te=
Ωs⎛
=
'σ+cX2
3⨯22πf
380
⨯(4.47+
3.18
2
3.180.0386
)+(6.7+9.85)
2
2
'⎫R2
R1+c⎪+(X
s⎝⎭
=29N.m
)
2
0.0386
(2)Tmax=±
m1
U1
2
2
Ωs2c⎡±R+
1
⎢⎣
'σR1+(X1σ+cX2
)
2
⎤
⎥⎦
=
4πf(4.47+
2
3⨯2⨯3804.47
2
2
2
+(6.7+9.85)
=65.6N.m
(3)Tst=
m12πf1
⨯
pU
2
21
'R2
(R1+R2')+(X1σ+X2'σ
)
2
=
3⨯2⨯380314⨯(7.65
2
⨯3.18
2
+16.55)
=26.4N.m
第六章
6-8 （1）p=2
IN=
SN3U
N
=
2⨯10
3
1.732⨯400
=28.87A
(2) PN=0.8⨯20=16KW6-9
QN=0.6⨯20=12Kvar
U
N
=
63003
=3637.3V
IN=
00
P3U
N
cosϕ
=45.82A
δ=60-36.87
00
=23.13
Id=INsinψIq=INcosψXX
d
=45.82sin60=39.68A=22.91A
=45.82cos60
=102.2Ω
==
E0-Ucosδ
Id
UsinδIq
q
=62.36Ω
6-10
ϕ=arccosψ
=arctan
*
PNSN
*
=31
Usinϕ+IX
Ucosϕ
00
*
**
q
=54.8
Id=I
*
sinψ
=sin54.8=0.8171A
δ=54.8-31=23.8
E0=Ucosδ+IdX
*
*
*
*d
=1.732
6-11
U
N
=
630031375E0IE0I=
=3637.3V
IN=
sN3U
N
=1375A
Zb=(1)X
s
3637.3
=2.646Ω
==
8000/8875.22.646=
3
=5.2Ω
X
*s
===1.97Ω
3
X
E0I=
6300/887
s(饱和）
=4.1Ω
X
*
4.12.646
s(饱1和）
=1.55Ω
(2)KC=(3)E
*0
11.55
*
=0.645
=U
+jIX
Nϕ*
*s
=2.689∠35.8
E0=E0⨯U
*
=2.689⨯3637.3=9780V
6-12
I
fN
=259A∆u=26%
6-22 (1)U
N
=
60003
=3464V
3464⨯0.6+57.8⨯40.8
3464⨯0.8
ψ
=arctan=58.01
ϕ=36.87∴δ=58.01
-36.87
=21.14
IdM=INMsinψ
mE0UX
d
=57.8⨯sin58.01
d2
=49.02A
E0=UcosδM+IdMXPe=Pe=TeM=
sinδ+
mU2
=6378V(1X
q
-
1X
d
)=480.5⨯10W
3
3UPeΩs
N
INMcosϕ=480.5KW
=15288.4N.M
(2)若负载转矩不变，调励'=IM
Pe3U
N
磁电流使cosϕ=1
=46.24A
cosϕ
=
4805003⨯6000
ψ
=arctan
46.24⨯40.8
3464
=28.57
'=28.570δ=ψ0
'=IM'sin28.57IdM
=22.11A
d
'=UcosδM'+IdM'XE0
=3464⨯cos28.57+22.11⨯64.2=4462V
6-25 (1)
未接入同步电机时
ϕ=arccos0.7=45.57
S1=
P1cosϕ
=
45000.7
=6428.6KVA
Q1=S1sinϕ=4590Kvar(2)接入同步电动机后，总的有功功率总的无功功率
ϕ'=arccos0.9=25.84
P=P1+PM=4500+500=5000KWP=P⨯tgϕ'=5000⨯tg25.84=2421.6Kvar
率为：QM=Q1-Q=4590-2421.6=2168.4Kvar
则同步电动机的无功功SM=
2
2
PM+QM=2226.3KVAPMQM
=50002226.3
=0.2246
cosϕm=
第三章
3.14 C398e=
pN3⨯60a
=60⨯3
=6.63
EC-2
a=eφn=6.63⨯1500⨯2.1⨯10=208.8VEa=Ceφn=6.63⨯500⨯2.1⨯10-2
=23.2V
TpNe=
2πa
φIa=9.55Ce⨯2.1⨯10
-2
⨯10=13.3N.m
3.15 T2
60002=
PΩ
=
2πn60
=57.3N.mTP0
0=Ω
=
3952πn60
=3.77N.m
PΩ=61.07⨯
2π⨯1000
e=Te60
=6395W
P1=Pe+pcua+pcuf=6395+500+100=6995W
η=60006995
=0.857
3.16
IPNa=IN+If
=
U
+
UNN
I
=365.2A
f
Ea=U
N
+Iara+2∆U2=230+365.2⨯0.0259+2=241.46V
Pe=EaIa=241.46⨯365.2=88180W
P1=Pe+p0=88180+4300+0.005⨯82000=92980WTPe
88180e=
868.5N.mη=82000Ω
=2πn60
=92980
=88.2%
3.18
额定负载时电枢电流为：
Ia=80-
110138
=79.2A
（1）接入电阻瞬间
E'a
=110-79.2⨯0.078=103.8VI'=110-103.8
a
0.078+0.4=12.97A
TE'aI'a103.8⨯12.97e'=Ω=2π⨯1470/60=8.75N⋅m
（2）Ia=79.2A （3）
Te=T2+T0=61.07N.m
n''nN
=
''EaEaN
''=U-79.2⨯0.478=72.1VEa
n''=1470⨯
72.1103.8
=1021r/min
第四章
4.10
（1）ns=1500r/min（3）
2p=4 （2）Q=2mpq=2⨯3⨯2⨯3=36
α1=
p⨯360Qy1
=
2⨯36036=sinsin
89
=20⨯90
20
ky1=sin
sinkq1=
τ
90=0.9848
qα
3⨯200202
=0.9598
qsin
α
2
=3sin
kw1=ky1kd1=0.9848⨯0.9598=0.9452
（4）
E1φ=4.44fNkE1L=
w1
Φ1=4.44⨯50⨯108⨯0.9452⨯1.015⨯10
-2
=230.02V
3⨯230.02=398.39V
4.11
q=
Q2mp
=
542⨯3
=936054=sin
α=
p⨯360Qy1
=90
=6.66672227⨯90
ky1=sin
sinkq1=
τ
2
=0.9579
qα
sin=
9⨯6.666726.6667
2
2
qsin
α
2
=0.9936
9sin
kw1=ky1kd1=0.9579⨯0.9936=0.9517E1φ=N=
63001.732
C
=3637.4V=
2⨯1⨯9⨯1
1=
w1
2pqNa
=183637.4
=0.9556Wb
Φ=4.12 (1)q=
E1φ4.44fNk
4.44⨯50⨯18⨯0.9517
Q2mp
=
362⨯3⨯2
=3
α=
p⨯360Qy1
=90
2⨯36036=sinsin
79
=20⨯90
20
ky1=sin
sinkq1=
τ=0.9396
qα
3⨯200202
qsin
α2
=3sin
=0.9598
kw1=ky1kd1=0.9848⨯0.9598=0.9018N=
2pqNa
C
=
2⨯2⨯3⨯3
1
w1
=36
E1φ=4.44fNkE1L=
Φ1=4.44⨯50⨯36⨯0.9018⨯0.75=5405.38V
3⨯5405.38=9362.1V
(2)ky5=sin5
sin
kq5=
qsin
y1
τ
25α2
90
=sin5sin
79
⨯90
=-0.1736
5qα
=
5⨯3⨯202
5⨯20
2
=0.2176
3sin
kw5=ky5kd5=-0.1736⨯0.2176=-0.03778E5=4.44f5Nk合成相电动势线电动势E=4.13
(1)q=
Q2mp
=
362⨯3⨯2
w5
φ5=4.44⨯250⨯36⨯0.03778⨯0.03=-45.29V
E1φ+E5φ=
2
2
Eφ=
5405.38
2
+(-45.29)
2
=5405.56V
3⨯5405.56=9362.44V
=3
α=
p⨯360Qy1
=90
2⨯36036=sinsin
79
=20⨯90
20
ky1=sin
sinkq1=
τ
2
=0.9396
qα
3⨯2020202
qsin
α
2
=3sin
=0.9598
kw1=ky1kd1=0.9848⨯0.9598=0.9018(2)N=
2pqNa
C
=
2⨯2⨯3⨯20
1
w1
=240
-3
E1φ=4.44fNkΦ1=4.44⨯50⨯240⨯0.9018⨯7.5⨯10
=360.35V
4.14
(1)q=
Q2mp
=
362⨯3⨯1
=6
α=
p⨯360
Qy1
=90
1⨯360
36=sinsin
=10⨯90
ky1=sin
sin
kq1=
1518
τ
=0.966
qα
6⨯10102
qsin
α
2
=
6sin
=0.9562
kw1=ky1kd1=0.966⨯0.9562=0.9237N=I=
2pqN
aP3Ucosϕ
Nkp
w1C
=
2⨯1⨯6⨯1
1=
6000
=12
=687.34
1.732⨯6.3⨯0.8
12⨯0.9237
1
Fφ1=0.9Iφ=0.9
⨯687.34=6856.8A
(2)ky5=sin5
sinkq5=
qsin
y1
τ
25α2
90
=sin5sin
1518
⨯90
=0.2588
5qα
=
5⨯6⨯102
5⨯102
=0.1020
6sin
kw5=0.2588⨯0.1020=0.0264F1=1.35
Nkp
w1
Iφ=1.35
w5
12⨯0.9237
115⨯
⨯687.34=10285.3A
F5=1.35⨯
1Nk
νp
Iφ=1.35⨯
12⨯0.0264
1
⨯687.34=58.79A
4.16
(1)
τ=
q=
Q2pQ
=
602=
=3060
=10
2mp2⨯3⨯1
α=
p⨯360
Q
=
1⨯360
60
=6
当y1=τ时ky1=sinky5=sin
sin
kq1=
qsinsin
kq5=
qsiny1
ττ
90
=sin90
=1
5y110α2
90=sin5⨯90sin
10⨯6
=1
α
225α2
=10sin
sin=
2=0.95540⨯625⨯10⨯6
2
5⨯62
5⨯10α
=0.1932
10sin
kw1=ky1kd1=0.9554kw5=ky5kd5=0.1932E1φ=4.44fNk（2）y1=τ-ky1=sin
5
w1
Φ1=4.44⨯50⨯200⨯0.9554⨯0.1505=6384V
τ45
=90
45
τ=24=0.951
kw1=ky1kd1=0.951⨯0.9554=0.9086E1φ=4.44fNk
w1
Φ1=4.44⨯50⨯200⨯0.9086⨯0.1505=6071V
4.17
kw1=0.9452kw3=-0.5774kw5=0.1399kw7=0.0607F1=1.35n1=
60fpNkp
w1
Iφ=1.35
108⨯0.9452
2
⨯20=1378.1A
=1500r/min
F3=0F5=1.35⨯n5=
n15
1Nk5
w5
p
Iφ=1.35⨯
15
⨯
108⨯0.1399
2
⨯20=40.79A
=300r/min
1Nk7
w7
F7=1.35⨯n1=
n17
p
Iφ=1.35⨯
1108⨯0.06077
2
⨯20=12.64A
=214r/min
第五章
5.14 (1)ns=
60fp
=750r/min
nN=ns(1-sN)=750(1-0.044)=717r/mins=
750-700750
=0.0666
s=1
5.15
(1)
pFe=P0-mR1I0-pmec=1340-3⨯0.4(Rm=
pFemIU0I0Z
20
2
21.23
)-100=1060W
2
=
10603⨯(380
21.23)
2
=2.36Ω
Z0=
=(
20
21.23
20
=31Ω)=
31-2.76
2
2
X0=
-R=30.87Ω
由短路试验Zk=
UkIkPKmI
2K
=(=
38066.83)
=2.85Ω
Rk=
41403⨯(
66.83)
2
=0.928Ω
X
K
=
ZK-RK=2.69Ω
X0X0-X
k
k
22
'=(Rk-R1)R2
=(0.928-0.4)⨯
30.8730.87-2.69
=0.578Ω30.87-2.69
30.87
'σ=X0-X1σ=X2X
m
X0-XX0
(R'
2
2
+X0
2
)=30.87-
⨯(0.578
2
+30.87)=1.37Ω
2
=X0-X1σ=30.87-1.37=29.5Ω
5.16
(1)sm='=RstRst=
'R2
'σR+(X1σ+X2
2
1
2
'σR1+(X1σ+X2
)
2
=1
2
2
)2
'=-R2
0.143+(0.262+0.328)-0.134=0.472Ω
'Rstkikem12πf1
=
0.4721.342
2
=0.262ΩpU
21
Tst='=Ist(2)Tst='=Ist
⨯
'+Rst')(R2
(R1
'+Rst'+R2
U1
)2
'σ+(X1σ+X2
)2
=
3⨯4⨯220314⨯(0.749220
22
⨯0.606+0.59)
2
=1232.9N.m
(R1
m12πf1
'+Rst'+R2
)
2
'σ+(X1σ+X2
212
)
2
=
(0.749
2
+0.59)
2
=230.7A
⨯
pU
'R2
(R1
'+Rst'+R2
U1
2
)
'σ+(X1σ+X2
)
2
=
3⨯4⨯220314⨯(0.277
22
⨯0.134+0.59)
2
=583.5N.m
(R1')+(X1σ+X2'σ+R2
)2
=
220(0.277
2
+0.59)
2
=337.5A
5.17
2p=4sN=
15000
ns=1500r/min=0.0493
f2=sf1=2.465Hz
1500-1426
用等效电路求解Z=
5.18 (1)s=
1500-1450
1500
T20.9
=0.0333
T2=
P2
Ω
=
750002π⨯1450
60
=494.2N.m
Pe=TeΩs=ΩS=
494.20.9
⨯
2π⨯1500
60
=86210W
pcu2=sPem=2870W
P1=Pe+pFe+pcu1=86210+2100+2870=91180Wcosϕ1=
P13UNIN
=
911801.732⨯380⨯160
=0.86
5.19
Pe=P1-pcu1-pFe=10700-450-200=10050Wpcu2=sPe=10050⨯0.029=291.45WPΩ=Pe(1-s)=9758.55W
5.20
(1)s=
1000-9601000PΩ1-s
=0.04
f2=sf1=2Hz
PΩ=P2+pmec+pad=7500+45+37.5=7582.5WPe=
=7582.51-0.04
=7898W
pcu2=sPe=7898⨯0.04=316W
P1=Pe+pcu1+pFe=7898+316+231=8603WI1=
P1
3UP2P1
=
N
cosϕN
=
8603
1.732⨯380⨯0.824
=15.86A
η=5.21
75008603
=87.17%
PN=∴IN=
U
N
INcosϕNηPN
cosϕNη
=
28000
1.732⨯380⨯0.9⨯0.88
=53.7A
3U
N
Ist=6⨯53.7=322.2AIst∆=
322.23
=107.4A
5.22
R2sN
=
R2+RΩ
s15001500
=0.0133
sN=s=
1500-1480
1500-1100
=0.26660.020.0133
-0.02=0.38Ω
RΩ=0.2666⨯
5.23
(1)sN=(2)
PΩ=P2+Pmec+pad=7500+45+80=7625WPe=
PΩ1-s
=
76251-0.038
=7926.2W
pcu2=sPe=0.038⨯7926.2=301W
1000-9621000
=0.038
f2=sf1=1.9Hz
P1=P2+
∑
p=7500+470+234+45+80+301=8630.2W
=86.9%
η=(3)I1=(4)T2=
P2P1
=
75008630.2
P13U1cosϕ1P2
=
8630.21.732⨯380⨯0.827
=15.85A
Ω
=74.44N.m
Te=
Pe
Ωs
=75.7N.m
T0=Te-T2=1.26N.m
5.24 (1)sN=
1500-1442
1500m1
=0.0386U1
22
'R2s
1σ
Te=
Ωs⎛
=
'σ+cX2
3⨯22πf
380
⨯(4.47+
3.18
2
3.180.0386
)+(6.7+9.85)
2
2
'⎫R2
R1+c⎪+(X
s⎝⎭
=29N.m
)
2
0.0386
(2)Tmax=±
m1
U1
2
2
Ωs2c⎡±R+
1
⎢⎣
'σR1+(X1σ+cX2
)
2
⎤
⎥⎦
=
4πf(4.47+
2
3⨯2⨯3804.47
2
2
2
+(6.7+9.85)
=65.6N.m
(3)Tst=
m12πf1
⨯
pU
2
21
'R2
(R1+R2')+(X1σ+X2'σ
)
2
=
3⨯2⨯380314⨯(7.65
2
⨯3.18
2
+16.55)
=26.4N.m
第六章
6-8 （1）p=2
IN=
SN3U
N
=
2⨯10
3
1.732⨯400
=28.87A
(2) PN=0.8⨯20=16KW6-9
QN=0.6⨯20=12Kvar
U
N
=
63003
=3637.3V
IN=
00
P3U
N
cosϕ
=45.82A
δ=60-36.87
00
=23.13
Id=INsinψIq=INcosψXX
d
=45.82sin60=39.68A=22.91A
=45.82cos60
=102.2Ω
==
E0-Ucosδ
Id
UsinδIq
q
=62.36Ω
6-10
ϕ=arccosψ
=arctan
*
PNSN
*
=31
Usinϕ+IX
Ucosϕ
00
*
**
q
=54.8
Id=I
*
sinψ
=sin54.8=0.8171A
δ=54.8-31=23.8
E0=Ucosδ+IdX
*
*
*
*d
=1.732
6-11
U
N
=
630031375E0IE0I=
=3637.3V
IN=
sN3U
N
=1375A
Zb=(1)X
s
3637.3
=2.646Ω
==
8000/8875.22.646=
3
=5.2Ω
X
*s
===1.97Ω
3
X
E0I=
6300/887
s(饱和）
=4.1Ω
X
*
4.12.646
s(饱1和）
=1.55Ω
(2)KC=(3)E
*0
11.55
*
=0.645
=U
+jIX
Nϕ*
*s
=2.689∠35.8
E0=E0⨯U
*
=2.689⨯3637.3=9780V
6-12
I
fN
=259A∆u=26%
6-22 (1)U
N
=
60003
=3464V
3464⨯0.6+57.8⨯40.8
3464⨯0.8
ψ
=arctan=58.01
ϕ=36.87∴δ=58.01
-36.87
=21.14
IdM=INMsinψ
mE0UX
d
=57.8⨯sin58.01
d2
=49.02A
E0=UcosδM+IdMXPe=Pe=TeM=
sinδ+
mU2
=6378V(1X
q
-
1X
d
)=480.5⨯10W
3
3UPeΩs
N
INMcosϕ=480.5KW
=15288.4N.M
(2)若负载转矩不变，调励'=IM
Pe3U
N
磁电流使cosϕ=1
=46.24A
cosϕ
=
4805003⨯6000
ψ
=arctan
46.24⨯40.8
3464
=28.57
'=28.570δ=ψ0
'=IM'sin28.57IdM
=22.11A
d
'=UcosδM'+IdM'XE0
=3464⨯cos28.57+22.11⨯64.2=4462V
6-25 (1)
未接入同步电机时
ϕ=arccos0.7=45.57
S1=
P1cosϕ
=
45000.7
=6428.6KVA
Q1=S1sinϕ=4590Kvar(2)接入同步电动机后，总的有功功率总的无功功率
ϕ'=arccos0.9=25.84
P=P1+PM=4500+500=5000KWP=P⨯tgϕ'=5000⨯tg25.84=2421.6Kvar
率为：QM=Q1-Q=4590-2421.6=2168.4Kvar
则同步电动机的无功功SM=
2
2
PM+QM=2226.3KVAPMQM
=50002226.3
=0.2246
cosϕm=