Embed Size (px)
Citation preview
אאא
אאאא
0
ص٢ش ،א،אאא
W، אאאאאאאאא
אא،אאאאאאאאאא
אאאאאאאKאאאWאא
א א א אא ،אאאאאאאא،א
א אא ،אאא א אאאאאאא
،אאאאאאאאאאא،אא
Kא אא?אאא??
אא?אאאאKאא
אאאאאא א ،א אאא
،א א א אKאא
אאא؛אKא
אאאא
אא:
אאאEF
אאאא
אאא
אאא
אאאא
1
،،א א،א
W אאאאאאאאא
אא،אאאאאאאאאא
אאאאאאאאKאאא
א א א אא אא،אאא
אאא،אא ،אאא א אא א א
אאאאא،אאאאאאאאא،אאאא
אK ? א א א א א J ??אאאאאאא?
אאKאאאאאא אאאאאא
،א א אא א אאא،א
Kאא אWאאא
Kא
אאאא
אאא
אאאא
2
א
א א
١
٨
אאאWא١٠ א
١ J١אאא ١٣
١ J٢אאאאאא١٧
١ J٢ J١אאאאאא١٩ א
١ J٣אא٢٠ א
١ J٤אאאאא ٢٢
١ J٤ J١אאאאא ٢٢
١ J٤ J٢אאאאאאK ٢٣
אא ٢٨
אאאWאא ٣٠
٢ J١אא ٣٢
٢ J١ J١אאאאא ٣٦
٢ J٢אא ٣٩
٢ J٢ J١אא ٤٠
٢ J٢ J٢אאא ٤٢
٢ J٢ J٢ J١א ٤٥
אאא
אאאא
3
א א٢ J٣א ٤٧
٢ J٤אא ٤٨
٢ J٤ J١אאאאא ٤٨
٢ J٤ J٢אאאא ٥١ ٢ J٤ J٢ J١אאא ٥٢
٢ J٤ J٢ J٢אאאא ٥٤
٢ J٤ J٢ J٣אאא ٥٧
٢ J٥אאאאא ٦٠ ٢ J٥ J١אאאאא ٦١
٢ J٥ J٢אאאאא ٦٤
٢ J٥ J٢ J١אאאאא ٦٥
٢ J٥ J٢ J٢אאאאא ٦٦
٢ J٥ J٢ J٣אאאא ٦٧
٢ J٦אאאאא ٦٩
٢ J٦ J١EאFאאא٦٩
٢ J٦ J٢EאFאאא ٧٠
٢ J٦ J٣אEאFא ٧٠
٢ J٦ J٤א ٧١
٢ J٦ J٥אא ٧٢
אא ٧٥
אאWאא ٧٩
٣ J١אא ٨١
א א
אאא
אאאא
4
٣ J٢אאאאא ٨٣
٣ J٣אאא ٨٥
٣ J٤אאא ٨٩
٣ J٤ J١אא ٨٩
٣ J٤ J٢אאא ٩٣ ٣ J٤ J٢ J١אא ٩٣
٣ J٤ J٢ J٢א ٩٧ ٣ J٤ J٢ J٣א١٠٢ א
٣ J٥א ١٠٨
٣ J٥ J١אא ١٠٨
٣ J٥ J٢אא ١٠٩
٣ J٦א ١١١
٣ J٧אאא ١١٣
٣ J٨אא١١٤
٣ J٨ J١אאא ١١٤
٣ J٨ J٢א ١١٤
אא ١١٨
אWאא א אא ١٢١
٤ J١אאא ١٢٣
٤ J٢א ١٢٥
٤ J٣א ١٢٦
٤ J٤א ١٣٣
א א
٤ J٤ J١אא١٣٣ א
אאא
אאאא
5
٤ J٤ J٢אאא ١٣٤
٤ J٥אאאא ١٣٥
٤ J٦אאאאא ١٣٨
٤ J٦ J١אא ١٣٨
٤ J٦ J٢אאא ١٤١
٤ J٧א ١٤٩ ٤ J٧ J١אא ١٤٩
٤ J٧ J٢אא ١٥٠
٤ J٨א ١٥٢
٤ J٩אאא ١٥٣
٤ J٩ J١אא ١٥٣
٤ J٩ J٢אא ١٥٤
٤ J١٠אא١٥٦
٤ J١٠ J١אא ١٥٦
٤ J١٠ J٢א ١٥٧
٤ J١١אאא١٥٩
٤ J١٢אאאא١٦١
٤ J١٢ J١א ١٦١
٤ J١٢ J٢אאא ١٦٢
אאא ١٦٤
א א
Wאא אאא ١٦٧ ٥ J١אא ١٦٩
אאא
אאאא
6
٥ J١ J١אא ١٧٠
٥ J١ J٢EאFאא١٧٠
٥ J٢א ١٧٢
٥ J٢ J١ J(Y-Y)١٧٢
٥ J٢ J٢ J(Δ-Δ) ١٧٤ ٥ J٢ J٣ J(Y-Δ) ١٧٦
٥ J٢ J٤ J (Δ- Y) ١٧٧
٥ J٣אא ١٧٩
٥ J٤אאאא ١٨١
٥ J٤ J١אאא١٨١
٥ J٤ J٢אאאא ١٨٩
٥ J٥א١٩٠
٥ J٥ J١Wאא١٩٠
٥ J٥ J٢Wאאא ١٩٠
٥ J٦א ١٩٣
٥ J٦ J١ א ١٩٣
٥ J٦ J٢א ١٩٥
٥ J٦ J٣ א ١٩٦
٥ J٦ J٤א ١٩٦
٥ J٦ J٥א ١٩٨
א א
אאא
אאאא
7
٥ J٦ J٦אא ١٩٨
٥ J٧א ٢٠٠
٥ J٧ J١אא٢٠١
٥ J٧ J٢אא٢٠١
٥ J٧ J٣אא٢٠٢
٥ J٧ J٤אא٢٠٣
٥ J 8EאFא ٢٠٥ ٥ J٩אא ٢٠٧
٥ J٩ J١א٢٠٧
٥ J٩ J٢אא٢٠٨
אא ٢٠٩
אאא
אאא
אאאא
8
אאאאאאאאאאאאאK
א אא אא אא Kא א אא א א א א
א K אא אא ،אא אאאא
Kאאאאא אאאאאאאא
א א א ، אאא،אא
،א אאאא،א K
אא א א אא Kא אאאאאא،
א א ،א א א אאאאאKאא
אא א א א אאאKאאאאא
אKאאא ،א א א א א א
א א א ،א אא א אאאאאאאKאאא Kאא א א א אא א
אאאKא א א א א א א
Kאא،אאאאא
אאא
אאאא
9
Kאאאאאאא،אאאאא
אאKא א א אא א א ،
א א אא א א KאאKאאאאאאא
Kאא אא א אא א Kא א א
א א א K ،אא א א
KאאאאאאK א א א א א א
א א ، א ،אאאאאאא
אאK אאאא،
אאאא،אאא א א K א
אאאאאאאK
אאאאWא אאKאאא
Kאאאאא
Kאאאאא
Kאאאא
Kאאאאאא
אKאאא
אאאKאא
אאא
אאאא
10
אאאMagnetic Circuits
אא
אאא
אאאא
11
אאאWאא
א א Wא אאאאא.
אאאW
١K אKאאאא
٢K אאאאאאאK
٣K א אא א אא א א אKא
אאא
אאאא
12
אאא
א א אא
א אאא א א א א ، א ،א א אא א K
אאאא(Permanent Magnet) אא א א(Ferrait) ، (Niodenum
Boron Iron) א(Smarum Cobalt) ،א אא א Kא
،אאא،אאא،אאא
א،אאאא א א א K א
א א אא א א Kאאאא،אא،א
Kא א אאאאאאאאא
אאאאKאאאאאאKאאא
אאא
אאאא
13
١ J١ אאא
אאאEאFא،אאאאKאאKא
- אאW Magnetic Field
אא،אא א אא، א
אאKאאKאא
- אאWMagnetic Field line א א א
، א א ،א א א ،א א א א א א א
Kא -אא: μ Permeability
א א א א אאאאאאא Kא א ، אא א
אאKאאאאאאא μא א (Magnetic
permeability) ،אא אKאאאא(Magnetization Curve)א א ،א א א
אאא،،אאא Kא א א א א
אKאאאאW 1-1 r o
אאא
אאאא
14
μoאא(Absolute permeability)אא
אאW
μrאא(Relative Permeability)אK
-אאФ: Magnetic Flux
،אאאאאאאאא א א אK א
Kאאאאאא אאאאאאאא
א אאא א א א א Kאא אא אK א א (weber)Wb
א10-8K JאאMagnetic Flux Density :B
א א אאא אKLFteslaETW
1-2 2m/WbA
B
Jאא:H Magnetic Field Intensity
א K אאאאLא
W
1-3 m/AtBH
μo=4π 10-7 h/m
אאא
אאאא
15
-אאאאmmf :Magnetomotive Force
N אאאא،אא
Kא אא א א א א א א א א א،א א
K(ampere-turn) W 1-4 AtI Nmmf
אאאא J١אאIאאHWאא
1-5 L HI Nmmf
-אא: Rmag Magnetic Reluctance א ، א אא
אאאאאWאא
1-6 Wb/AtI NmmfR mag
אKאאא
אאא،א אאLAאμאW
1-7 A LR mag
אאאא אאKא،
אא אא א א א K א א،
Kא١ J١LאIBאאאK
אאא
אאאא
16
אF א א א א א
Wאא 1-8 N I L BF
אא،אאא א א א א א Kא
א ،א א א ،א א אאKאא
١ J١
אאא
אאאא
17
١ J٢Wאאאאאא
אא א א א אא א אא א א אא ،א
אאאא،אאאאאK
א אאא אאא א א א Kא אא
אאאאא٧ J١،אא א א K
אאאאאאא K١ J٢ א א ABCDEF
אאA,FאאKAB, BC, CD, DE, EFאKאאאCD
NIKΦאKאאאא
١ J٢אא
אאא
אאאא
18
אא٧ J١Wאאאא
CDCD
CDCD mag A
LR
BCBC
BCBC mag A
LR
ABAB
ABAB mag A
LR
gapo
gap)gap(mag A
LR
EFEF
EFEF mag A
LR
DEDE
DEDE mag A
LR
אאאFRmag(tW
1-9 gapo
gap
EFEF
EF
DEDE
DE
CDCD
CD
BCBC
BC
ABAB
AB)t(mag A
LA
LA
LA
LA
LA
LR
אאאФאאאאFEN.IאאאFRmag(t،
٦ J١Wאא
1-10 )t(magR
I N
١ J٣אאאאאאאאא،א אא אאאא א אא
אאאא،א،אא א אא אא K
אאאאK١ J١Kאאא
١ J٣אאאאאאאאא١ J٢
אאא
אאאא
19
אאא אאא אאאאe.m.f אאאאmmf
אאALR אא
A LR mag
אאREI אא
magRmmf
אAIJ א
AB
١ J١אאאאאאא
١ J٢ J١Wאאאאאאא ١K אאאאא،
Kאאא ٢K א،אא
Kאאאאא ٣K אאאאאאאא
אאKאא
אאא
אאאא
20
١ J٣אאא
١ J٤אKאאאאאKאאאאאאאא Kא א
אpא،g،אאא t ،א y ،א אac א Kא
، א אא Kא א١ J٢אאאKא
١ J٤אאא
אא אΦ
אB
אA
אH
אL
אאאא
mmf
אאא Φm Bg Ag Hg 2Lg Fg
א Φm Bt At Ht 2Lt Ft
א Φac=Φm/2 Bac Aac Hac Lac Fac
א Φm Bp Ap Hp 2Lp Fp
אא Φy= Φm/2 By Ay Hy Ly Fy
١ J٢אאאאאא
אאא
אאאא
21
א א א א אא א ٦ J1
،אאאאאאא Wא
1-11 yy
ym
pp
pm
acac
acm
tt
tm
go
gmtotal A
L2A
L2A
L2A
L2AL2
Fmmf
11א J١אאאא אא אאאBא٢ J١
١١א J١W
1-12 y
yy
p
pp
ac
acac
t
tt
o
ggtotal
LBLB2LBLB2LB2F
W
yA2
m
yB
،acA
2m
acB
א٣ J١א١٢ J١ 1-13 yLyHpLpH2acLacHtLtH2gLgH2totalF
1-14 yFpFacFtFgFtotalF
14א J١אאאאאאKאאאאאאאא
אאא
אאאא
22
١ J٤אאאאא
א א W א א א
אאאאא Kאאא אא א Kא
Kאאאא ١ J٤ J١אאאאא
١ J٥L،אאVBאאאEW
1-15 Volt )sin( V L BE
θאאא،אאאאאאאאאאאK
١ J٥אאאא
אאא
אאאא
23
א١ J٦Kאאאאא
א א،אאאא א א א ،א א א א
Kאאאאאאאא
١ J٤ J٢אאאאאאK אא،א(Faraday) Wאאא
1-16 )dt
d(NE
אאאאאאאאאא א Kאאאא
א ،אא א ١ J٧،א א אא א אא (Self-
Inductance)אKאאא א אא אא (Mutual Inductance)
١ J٨ .
١ J٦א
אאא
אאאא
24
١ J٧א
١ J٨א
١ J١
א20×30cm،5cmאKturns٢٥2Ω
24VאאאאK 0.008
Tא،W ١K אא IK ٢K אאHK ٣K אאΦK
אאא
אאאא
25
א
١ J٩،א אא אX,Y ،אאא LWא
١ J٩אאאא
L 2 X 5 Y 5 L 2 20 5 30 5 80cm 0.8m
A=(5×10-2)×(5×10-2) =25×10 -4 m2 , B=0.008 tesla , R=2Ω V=24V
N=25 turns ،
١. A122
24RVI
٢. m/At3758.01225
LI NH
٣. Wb 20Wb 00002.041025008.0A B
אאא
אאאא
26
١ J٢
א א 25cm 3cm2 Kturns٢٥א2AאKאא1500K
אW
١K Kאא ٢K אאאאK ٣K אאK
٤K אאK ٥K אאK
אW
١ J١٠ ،א אא א r ،אאא LWא
١ J١٠אאאא
2 2 25 10 1.57
A= 3×10-4 m2 μr=1500 μo=4π×10-7 h/m N=600 turns I = 2 A
Wb/At61078.2)4103)(7104(1500
57.1A o r
LRmag
١.
At 12002600I Nmmf ٢.
אאא
אאאא
27
m/At33.76457.1
1200
LmmfH
٣.
wb41032.461078.2
1200
Rmmf
mag
٤.
tesla44.14103
41032.4
AB
٥.
אאא
אאאא
28
אא
١K אאאאאאK
٢K א א א אא א א אK
٣K אאKאאאאאא
٤K ؟אאא
٥K Kא
٦K אאאאK
٧K Kאאאאאא
٨K א א 6µWb א א ،12At/mא א K
0.5אmא 0.00015m2Kאא א אKאא،אאא
٩K א 20cm ،3×5cmאK
15 turns 1.4Ω 12V א Kאאא0.006 teslaא،W
aK אא
bK אא cK Kאא
١٠K א א 0.0002Wbא א100אcmא5cm2אאאאK
א א א ،א א א٥٠٠אK
אאא
אאאא
29
אאא
אא
אאא
אאאא
30
Wאאא אא
Direct Current Generators
אאWאאאאאאאאאאאKא
אאאW
١K אאאK
٢K אEאאאFאא
٣K אאאאאאKא
٤K אKאאאא
٥K אKאאא
٦K אאKא
٧K אKאאאאא
אאא
אאאא
31
א אא DC Generators א אא Direct Current Generators
אאא Kאא א،אאאאאאאא
אאאאאאKאאאאאאא
אאאאאאאאאKאאאאKאאאא
אKאא א א א א
א א א K א א אא א א Kא א
א אא א אא א א אא א Kא א א
אKא ٢ J١אא
، א א א א א א א א א (Prime Mover)
?אא?אK، א א ?אאאא?אא
אאאאאאאKאאא א א ،
אאא٢ J١
אאא
אאאא
32
א א א א אא אKאאאאאא
٢ J١אא
٢ J٢K אא א אאאא٢ J١אא
אF א אF א א א EאאאאEEאאFא
א א א א א אא א אאאאא،A א0°
٢ J٢אBא90°אאאאB אאאאא،
א אB א א א ،אא א
אאאאאאאאאאKאא
אאא
אאאא
33
א אא א B א 90° א Cא
180° א אאא אCאאאאא،
Bא א C א א א אאאKאאאאא
אאאCא 180° אDא270°אאאאאאאאאאאאאא
٢ J٢K
٢ J٢אאאאא
אאאאאאא(Sine wave) ٢ J٢א א E F א א
א(DC) Kאא אאאאFאאא
E٢ J٣אאA
אאא
אאאא
34
אאאאא B ٢ J
3אא،(abcd)١٨٠،٢ J٣אאAא א א א
אאאB،٢ J٤אא١٨٠אא،١٨٠٣٦٠א
א א א ٢ J١א א א K
FאאאKEא א K א
Kאא
EF EF
٢ J٣EFאאאא
٢ J٤ א א א אא א Kא א א א
אאאא١א J٢K ٢-١ volt v L Be
אאא
אאאא
35
B אא (Wb/m2)،Lא(m)، vא
א א א(m/sec) א אא א K(e)א (volt)אאKK
٢ J٤אאאאאא
٢ J١ J١אאאאא א א א
K א א א B
א v א א٢ J٥אאאe K
٢ J٥אאאא
אאא
אאאא
36
Wאא
2-2
אrWאא
2-3 260
nאא\(r.p.m)،ω אאא(rad/sec)،Wאאאאא
2-4 2 ⁄
A،אא٢ J٣א٢ J٤א٢ J٢Wאאאאא
2-5
2 2 60
א٢ J٥W
2-6 60
אאאZאאאaאאאאא Wאאא
2-7 60
אאא
אאאא
37
٢ J١
٦ אא٢٥٠، 1200 rpm א א K٤א ،
Kאאאא אW
p = 6 , a=2 [] , Z= 250 , n=1200 rpm , =4 mega lines/pole
=4×106 ×10-8 =0.04 Wb/pole (1 line = 10-8 Wb)
60
6 0.04 1200 2502 60
600
٢ J٢ ٨אא٩٦٠א،
600 rpmאאאאאאK220 V،Kאא
Wא p = 8 , a=p=8 [א] , Z=960 , n=600 rpm , Ea=220 V
60
≫≫ 60
220 8 608 600 960
0.023 /
א
Kאא
אאא
אאא
אא J٧
א
א٢J
(أ)
א
אא
38
א
Kא
א
א
٢ J٦
٢ J٧
א
אאאא
א
J٦
(ب)
א
٢א
K٢J
K
)
אא
٢ J٢
אאא
אאאא
39
٢ J٢ J١אאStator
אאאאאYokeאא(Main Poles)א (Commutating Poles)
K א א(Yoke)Wא א א א
אא א ،،א א ، א א ٢ J٨א אא
אאאK
٢ J٨אא
א א(Main Poles)Wא א א א א א(Pole Face or Pole shoe)
אאאא אא א אא אא א
אא אא א (Main Field Coils)W
אאא
אאאא
40
J א(Shunt Field Coil)א
אאאK
J א(Series Field Coil) Kאא
אאאאאאאא،
אאאאאאא،א٢ J٩Kא
٢ J ٩א
אoles)P(Commutating אWאאאא 2kW،א
אא א Kא א אאKאא
אאא
אאאא
41
٢ J٢ J٢אאאRotor
א א ،א א אאא אאא א
אאאאאאאKאא،אאאא٢א J١٠Wאאא
אא
א
نامرلا( قالزنالا تاقلح)يلب
אאא
אא
א
אא
אאאא
٢ J١٠אאא
א ore)C(Armature W אא א א א אא א אא א א א
א،אאאאאאא(High Permeability)
א א ،א Kאאא٢א J١١א
(Slots) אK
אאא
אאאא
42
EF א
EF א
EF אא
٢ J١١EאFאאא
אindings)W(Armature W،אאאאא ٢ J١١א
٢ J١١ א א א א א אאאאאאא
Kאאאאאא א אאא א ،
אאאאאאאאאאאאאאאאאאאא
אאK
אEאF)(CommutatorWאאאKEאF א א א א
אא ٢ J١٢א א ، א א א א
،אאאאאאאאאאאKאאאא
אאא
אאאא
43
٢ J١٢EאFא
אאolder)H(Brushes W א אאאאאאאא
EאFאאאאאאK Kאא٢ J١٣
Kאאאא
٢ J١٣אא
א
Armatuא
K
א 2
אא
١٥א
אאא
ure Win
א
אא
K
א
1אא
א
٢ J٥
nding
אא
אאW
١٥،א
אא
K
אאא
אא
א
אא א
٢ J٥1,2E
א א Kא
א
44
א
אאא
٢ J١٤(LWא
F2,3
3א
אא
אאא
א א
אאא
א
inWLap
א א3
אא Kא א
א
אא
nding)
2 Kא
א
א
٢ J٢ J١
Kאא
אא١٤
א
א
א א
אא
٢ J٢
אKא
٢ J٤
Jא
אאא
א
،
אאא
אא
(Com،
אאmmutator
א
א
EF
א
אא
Pitch)
אא
א
א
45
(WW אאא
אא
א
inWWave
אאאאאKא
٢ J١٦א
٢ J١٥א
א
nding)
אא
א١٦ Kא
א
E
א
א
אא،
٢ J٦
EF
אא
Jא
א
א
،אאא א
א
،
K
K
אאא
א
א א
W
א א
א
א
א אא א א
א ،
،
אא
אאאא
א א
،
אא אא א א
א
אא
46
(Armatא
א
א ،
א
Kא
א
א ٢ J١٧
ture Rea
א א
אא א
K
אא א אא
א
Kאא
א
J١٧
א
action)
א א
אא אא אא
אא
א א ،א
٢
א
٣אא
אא ،א
א
אאאאא
א
K
אא
٢ J٣
١K
٢K א٣K
א
אKא
אאא
אאאא
47
٢ J٤אא(Methods of Excitation) אאאא(Field Windings)
אאאאאאאKאא א א א א
אאאאאאא،W ١K אאא(Separately-excited)
Kא
٢K אאא(Self-excited)،אאאאאאאא
K
٢ J٤ J١אאאאא(Separately excited generators)
٢ J١٨א אא אא، א א א אא
،א א א אא א א Kא א ،א א א
אאK
Loa
d
٢ J١٨אא
אאא
אאאא
48
Wאא אאL
Wאאאא ٢-٨
W VfWKא IfKאW
RfKאW WאאL
(Kirechhoff’s Law)א א א Wא
٢-٩ 2-10 2-11 W
VLWאאאFאKE
IaKאW RaKא ILאKא
EaWאאאאאאאWא
k Kא אא א א א אא א
KEאFאא 2-14
2-12 60
٢-١٣
אאא
אאאא
49
אאאאאא،אאאא
Kא ٢ J٣
א،1200 rpm 200 A125 VאK0.04 אא
אאאאאאאאאK Wא
Wא VL = 125 V , IL = 200 A , n = 1200 rpm
200
125 200 0.04 133 V
125200
0.625Ω
125 200 25
٢ J٤ א אא1000 rpmאאא
KאאאאאאאאK Wא
If = const. , n2 =1000 rpm אאאאאא
133 12001000
Ea2 = 110.83V
110.83
0.04 0.625166.66
110.83 166.66 0.04 104.16V Or 166.66 0.625 104.16 V
110.83 166.66 12.264
אאא
אאאא
50
٢ J٥
א٢ J٣אאאאא١٠אK٪Kאאאאאאא
Wא If2 = 1.10 × If1 , n2 = constant
אאאאאא
133 11.10
Ea2 = 146.3
146.3
0.04 0.625220
146.3 220 0.04 137.5 V Or 220 0.625 137.5
137.5 220 30.25 ٢ J٤ J٢אאאא(Self -excited Generators)
אאאאאWא ١K א(Series Excitation)אאאא ٢K א(Shunt Excitation)אאא
٣K (Compound Excitation)אאא
אאא
אאאא
51
٢ J٤ J٢ J١אאא(Series Excited Generator)
א א א א א E אא F א ،א א א א
אא٢א J١٩Kאאאא
٢ J١٩אאא
אא:
2-1٥
2-1٦
אאא
אאאא
52
٢ J٦
،אא٤אא18 kW150 Vא1200 rpmא0.12 Ωא0.18 ΩK
אאא1250א rpmא125 AאאאK30 %K
אW
Pout =18 kW , VL1 =150 V , n1=1200 rpm , Rf = 0.12Ω
Ra = 0.18Ω , n2 =1250rpm , IL2 =125 Amp. , 2= 1.٣٠1
18000150
120 Amp.
150 120 0.18 0.12 186V
א(2-14)
1.30 1200 186
1250232.128
– 232.128 – 125 0.18 0.12 194.628 V
אאא
אאאא
53
٢ J٤ J٢ J٢אאאא(Shunt excited generators)
א א א א ٢ J٢٠אKאא
אאא،אאאא א אא
Kאאאאאא١٪
٥٪Kא
٢ J٢٠אאא
אא:
2-1٧
2-1٨
2-1٩
אאא
אאאא
54
٢ J٧
א350 Aא240 Vא،אאא0.02Ω 55 Ω Kאאאאא
Kא אW
IL = 350 A , VL =240 V , Ra = 0.02Ω , Rf = 55Ω
24055
4.36
350 4.36 354.36 240 354.36 0.02 247.1
אאא
אאאא
55
٢ J٨
אא א א ٥٠٠،א0.01 Ωא95 Ω،٢٠٠
60 W120 VאאאאאK0.02 WbK
אW p = a [ألنه لف انطباقي], Z = 500 , Ra= 0.01Ω , Rf = 95Ω , VL=120 V
Φ = 0.02 Wb/pole Pout =200×60=12000W
≫≫12000120
100
12095
1.26
100 1.26 101.26
120 101.26 0.01 121.01
60
121.01 0.02500
60
n = 746 rpm
אאא
אאאא
56
٢ J٤ J٢ J٣אאא(Compound Excited Generators)
אאאאאאא(Series Windings) אא(Shunt Windings) ،א א אא
،אא א א א אא א א א א א א א
א א ،אא אא(Cumulative
Compound ) א א א א א א א א ،אא
א(Differential Compound)K
אא אא א א אאאאא
א אא(Short-Shunt)، א א אא אא אאאאEאאאF(Long-Shunt)،
٢ J٢١א אא א אא א ،אאseאאshK
EF EF ٢ J٢١אא
אאא
אאאא
57
Wאאא
2-20
2-٢١
2-٢٢
אאא: 2-٢٣
2-٢٤
2-2٥
אא Kא א א א א אא אאאאא
א א ،א אא(Demagnetize The Machine)Kאא
אאא
אאאא
58
٢ J٩
60 A230 VKאאאאא ،א א 0.04 Ω،א אא 0.01 Ω
אא125Ω K אW
VL = 230 V , IL = 60 A , Ra = 0.04 Ω , Rse = 0.01Ω , Rsh =125Ω 230125
1.84
60 1.84 61.84
230 61.84 0.04 0.01 233.1
אאא
אאאא
59
٢ J٥אאאאא
(Characteristic Curves of DC Generators) א א א א Jא
אאאאא J א ، א א ،א
א א ، א א Kא א אא א א א
،אאa , pאאאאEaאאΦאא،nK
E א אא א ، א
אאאאאVLK Wאאאאא
١K אאNo-load Characteristics
א א אא(o.c.c)אאאאאאאא(Eo)א(If) Kא
٢K אאLoad Characteristics
אא א א (VL) א (If)א Kאא
٣K אאאExternal Characteristics
אאאא(VL)א(IL)אKא
٤K אאאאInternal Characteristics
א א א א אא א א אא אא Kאאאא
אאא
אאאא
60
א א אא א א
Kאאאאאאא
٢ J٥ J١אאאאא אאNo-load Characteristics
، א א א אאאאאאEaWאאא
E אאאאא،(If)
E
אאאאאאא
אאEoאא،אא א ٢ J٢٢אא א א ،
אאא، א،אאאאא
אVfאאאKאאאאאאאEoאIfא،٢ J
٢٢א(a)،א(b)،אאאאאאאK
EFאא אEF
٢ J٢٢אא
אאא
אאאא
61
אאLoad Characteristics
אאאאאאאאא(Armature Reaction)א،
אVLאאאאEaאאאא (Ia Ra) אא،א
אא RLאאVL ، VLא E אF E אF
Kאאאאא،א٢ J٢٢،אאא٢ J٢٢ Kא
٢א J٢٢، IIIאאIאאא،אאAB (Ia Ra)אIIIא،II
א،אאאאאאאCBאאאא،אאVL
א אEo א א CD א Kאא
אאEF אEF
٢ J٢٢אא
אאא
אאאא
62
אאאExternal Characteristics
٢ J٢٣،אאאאאאאאאאאא(II)Ea
אאא،אאא(I)אEoאאאKאאאאאאאאאאאאאא
א(III)אאאא،VLאILKאא
אאאאInternal Characteristics
א II ٢ J٢٣ א ، אא אא א א אא אEa א א Ia א
אIL אאKאא،אאאאאאAB،אאאEaא
Kאאאאאאאאאא
٢ J٢٣אאא
אאא
אאאא
63
،אאא٢ J٢٣א،ε
Wאא
٢ J٥ J٢אאאאא
א אא א ، א א א א א א אא א Kא
א א ، EאFא אאאאאא،אאאא א א K אאא؟ Wא
א،א א،אא א Kאא
،אא،אאא א٢ J٢٤א (Magnetization curve)א
אאIf،אאא אאא Eo א אא Kא א א
אאאא،א Erאא א א
אאא א א K א Lfא Rfא אא א ،
אא א Kא אאא אאא א א א
אאאאא(Residual magnetism) ErK
2-2٦100
אאא
אאאא
64
٢ J٥ J٢ J١אאאאא
א א א א א אא אא אא אא K٢ J٢٥א אא א א
אאאאאא KRLאאאאKא
א Ia ، א א א אא אא א E א VL א K٢ J٢٥
אאאאא،Iא א אא،אIII א אאI(Ra+Rf)אא K
אIIא א א א אא אKא אא אא ،א א א
אא،אאאאILK
٢ J٢٤אאאא
אאא
אאאא
65
אאEF אאאEF ٢ J٢٥אאא
٢ J٥ J٢ J٢אאאאא
אI ٢ J٢٦אאאאאאIIא،אאאאIIIKאאא
אא ،א א א א אאאKא IV א
א א אאEo K א Wאא
2-2٧100
אאא
אאאא
66
אאEF אאאEF ٢ J٢٦אאא
٢ J٥ J٢ J٣אאאא א א א ،א א Long-
shunt א א א Short-shuntK،א אאאא
אא،אאא،אאKא
אאאא Jאא J א א ،אא אא
Kאאא ١K Wא א א אא
א א ،אא אאאאאאא
אאאVL٢ J٢٧K ٢K Wאא
אאאאאאא
אאא
אאאא
67
٣K א א ،א ،א
אVLKא ٤K WEFאא אאא
א א ،אאאא،אאאאאא
٢ J٢٧K
٢ J٢٧אאאא
אאא
אאאא
68
٢ J٦אאאאא Energy Losses and Efficiency of DC Generators
אאאא،א א א ،א אא ،א א
אאאאאאאאאאא،א،
אא،EFKא
אא،אאא אא א אא א ،
א א א א Kא אK
١K EאFאאאMagnetic losses (Iron losses) ٢K EאFאאאElectrical losses (Cupper losses) ٣K EאF)Mechanical losses (Friction losses
٢ J٦ J١EאFאאא אאW
אאHysteresis loss:אאאאאWאאאאא
2-2٨
EאF אאאאEddy Current loss Wא אא
2-2٩
אאאאאאאא א Kאאאא
،אאאאאאKאא
fgBhW 6.1
fgBeW 2
אאא
אאאא
69
٢ J٦ J٢FאאאאE אאאאאאא
אא א א אאא،אאאW
אא W א א
2-30 Armature Cupper Losses
אאאאא א אW א
Kא 2-31 Field Cupper Losses
אאאאאאאKאאאא
2-32 Field Cupper Losses אאW
2-33 Loss due to brush contact resistance ∆
VKאאא،אאא
٢ J٦ J٣אאאFE אאאא Bearingאא،
אאאאאאאKאאKאאאא
אאא
אאאא
70
٢ J٦ J٤א
א א א אאPrime Moverאאאאא
אInput Power ٢ J٢٨אא א ،Pin H.Pא
746Watt. א K א א PmechאאPi א PgPgא
אW
2-٣4
א א אPg א אאאאאאPout
אPLK
٢ J28אאאא
אאא
אאאא
71
٢ J٦ J٥אאEfficiency
אא،אאאW
Wאא
2-35 746
אאW
2-36 η
Wאא
2-37 η746
Wאאא
2-38 η 100
אאא
אאאא
72
٢ J١٠
א، 1000 rpm 45kW240 Vאא،0.05 Ωא 65 Ω،
א א א K א א א א אאאא3500 WK
אW
n =1000 rpm , Pout = 10 kW , VL=240 V , Ra= 0.05Ω , Rf =65Ω
Pi+Pmech = 3500 W
10 10240
4.167
24065
3.7
Ia=IL+If =4.167+3.7 =7.867 A
7.867 0.05 3.7 65 893
893 3500 4483
10045 10
45 10 4483100 91%
אאא
אאאא
73
٢ J١١ ٨ ،١٢٠٠
600 rpmא،60Aאא0.022 WbKא0.06 Ωאא،0.04 Ωאא250
ΩאאKאא3500א WK אW
p=8 , a=2 [ألنه لف تموجي] , Z=1200 , n=600 rpm , Ia=60 A , Φ=0.022 Wb
Ra=0.06Ω , Rse=0.04Ω , Rsh=250Ω , Pi+Pmech=٣500W
60
8 0.022 600 12002 60
1056
1056 60 0.06 1052.4 1052.4250
4.21
60 4.21 55.79 1052.4 55.79 0.04 1052.17
Pout=VL IL=1050.17×55.79=58589 W
2 2 2 602 0.06 4.212 250 55.792 0.04 4771.5
Plosses=Pcu+Pi+Pmech = 4771.5+3500=8271.5 W
10058589
58589 8271.5100 87.6 %
אאא
אאאא
74
אא
١ J אKאאאאא ٢ J Kאאא
٣ J אאאK
٤ J Kאא؟אאאא
٥ J א א؟ א א ؟
٦ J Kאאא
٧ J אאKאא
٨ J ؟אא؟אא
٩ J ؟אא
١٠ J אאאאאK
١١ J אאאKאא
١٢ J Kאאאא
١٣ J א אא א،א 230א Vא1000 rpm 1.25 AKW
aK אאאאאא1200 rpmא1.1 AK
bK אאאאאא210 Vא1.2 AK
cK א1200 rpmאא205 VK
١٤ J א אא א אא א120 V،אאאאא95 %אאא110 %א120 VK
אאא
אאאא
75
١٥ J א30 kW250 V،0.125א ΩאאאאאK256 VK
אא ،א105 Aא א אא אKא
١٦ J א٨٩٦٠،500 rpm6.5 Ω280 Vאא
0.25 Ωא175 ΩW
aK א
bK אאאאא
cK Kאא
١٧ J א٤אא،0.8 Ω،100
Ω،א٣٠٠אא،א0.03א Wbא،12Ωאא1000
rpmKא
١٨ J ٤א 25 kWא500 Vאא،0.03 Ωאא0.04
Ωאא200 ΩW
aK אאאא
bK אא א א 1200 rpmא א0.02 WbK
١٩ J 250 Vא80 Aאאאא،אא0.05 Ω،0.03 Ω،100 Ω
אאאא،אKא
אאא
אאאא
76
٢٠ J א1500 rpm א30 A א א150 Vא א אא א ،
1800 rpmאא60 Aאא؟60 Aאא50%אא 0.1 Ω،0.15ΩKא
٢١ J 1000rpm25kW 250 V אא אא ،א א
0.05Ω،0.06Ω،110Ωאאא،א88%W
aK אאK
bK אKאא
٢٢ J 1000rpm45kW 240V א א ،0.05Ωאא
0.02Ω אא 65Ω א א א א אאא3500אWK
אאא
אאאא
77
אא
אא
אאא
אאאא
78
אאWאא Direct Current Motors
א אאא WאאאאאאאKאא
א.
אאאW
١K אאאK
٢K אאאאאאKאא
٣K אKאאא
٤K אKאאאא
٥K אאאאא
٦K אאאK
٧K אאאאאK
אאא
אאאא
79
אאDirectCurrentMotors א א Kא א א א
אאאא٦٠אא٪אKאאא אאאא א אא אא א א Kא
אא א אא א א א ،א
א א Kא א א א Kא א א א
אאאאאאאאKאKאאאא
אKאא ٣ J١אא
אאא אאא א א א ، F
א א KEאא א EאFא
אא،אאאאאאאאאאאא
Kאא א א א א ٣ J١K
אאא
אאאא
80
٣ J١אאאא
א א א א א?אא?א،א
Kא٣ J٢BIאאא
،אFא،אא אאLאא B א א
W
١ J٣ F=B I L
אאאאאאאאאאאא אאא א EאFא
אאאאאK
אאא
אאאא
81
٣ J٢אא
٣ J٢Wאאאאא
א א א א א אא אEb (Back e.m.f)א
אאא:
3-2 60
אאאאאא א Fאא א
א א F E ،Eאאאא،אאאאאא٣ J٣،
א،א א א א א אאא אאאאא
אא אא،Kאאאא
א
Ea = VL
א
Eb = VL
א א K
Fא
אאא
א
א
+ Ia Ra
J
- Ia Ra
א א
אאא،EאF
אא
אאא
אאEא
א
א
אא
אא
א אא
F
KאאH
ZE
J٣ KE
،אא
א
(
82
אאא
אF
٣ J٣F،E٤
אא א
אא
א אאאא
(3-4)
٣
אZ
א אא
א F٣
א אאא
אא א
א
א
א
אא٣ J٣
אאא
א W
אא
א ،
אאא
א
EF
אאאWא
א א
א
א אאא א אא
E
אא
3-٣
3-٤
אא
אאא
א
אאא
אאאא
83
אאאאא
Eb א(3-4)אא(3-5) 3-5 Ia =
א ،אא אאאאא
אא(3-6)א אאKא
3-6 Iast =
א Rst א א א א אא א א א Kא א
Kאא ٣ J٣Wאאא
אא אאא٣ J٤א xx'אא،r
אאאאIcאאא1 J3W
F=B L IC
אאא
אאאא
84
٣ J٤אאא
Wאאאא
אאW 3-٧2
2
Tcאא rL א א א א א
אאאF٨ J٣WE 3-٨p =B(2πrL)
p،אBF٨א J٣אE7 J٣Wאאא
3-٩∅2
אאאאIaאא ZאאאaWאאאא
3-١٠
2
אאא
אאאא
85
אאאIcWאאאאא
3-١١
א١١ J٣ א١٠ J٣ אא אWאאא
3-١٢2
Wאאא 3-١٣
kאW 3-14
2πa
١٣א J٣אאאא،IaK
W 3-15
Eb Fא،אאא١٥א J٣אE F١٣ J٣EW
3-1٦
2 60
PאωאKאא
אאא
אאאא
86
٣ J١
٨ אא ٢٤٠، 1000 rpmא א K٥אא א ،
אKאאאאא200 AK אW
p = 8 , a = 2[ألنه لف تموجي] , Z=240 , n =1000 rpm
ϕ =4 megalines /pole=5 10 10 0.05 Wb/pole 60
8 0.05 240 1000
2 60600
ω 2 60
2 1000
60 104.72 rad/sec
600 200104.72
1145.9 N.m
٣ J٢ ٨אא٩٦٠،א
600 rpmאאאאאאK250 Vא،אKאאאאא1000 N.mK
אW p=8 a =p=8 , Z=960 , n=600 rpm , Eb = 250 V
60
8 960 600
8 60250 V
∴ 0.026
ω 2 60
2 600
60 62.83 rad/s
≫≫ 1000 62.83
250251.32
אאא
אאאא
87
٣ J٤אאא Types of DC Motors
א א WEאאFא
אאאEאFאא אאאאאא
٣ J٤ J١אא
אאאאא٣ J٥K
Eb
Ra
+ _
Ia
Vf
A1
A2 If
n
I
Rf
V +_
٣ J٥אאאאא
אאא 3-1٧V = Eb +IaRa
3-1٨Eb = kv If 3-1٩Vf = If Rf
3-٢٠Td= kt If Ia
3-21Td= TL +B
אא(3-21) W
3-22 Td = TL
אאא
אאאא
88
W
V א(V) Eb אאאאא(V) Ra א() Ia א(A) Vf אאא(V) Rf א() If א(A) kv א
kt א Td אא(N.m) TL א(N.m) אאא (rad/sec) B א(N.m/rad./sec)
אא
אאא
אאאא
89
٣ J٣W
אאאאאאא 440 VאאK0.15 Ω
300א Ω א1.15 V/A·rad/sא،100 N.mKאאKאאא
אW V = 440 V Vf = 440 V Rf = 300 Ω Ra = 0.15 Ω
TL = 100 N.m kv = 1.15 V/A.rad./sec.
Td = TL = 100 N.m 440300
1.467
אאא= אW
100
1.15 1.46759.28
Eb = V –Ia Ra= 440-59.28 ×0.15 = 431.107 V
ω
431.1071.15 1.467
255.54 /
602
60 255.542
2440.217
אאא
אאאא
90
אא
אאאאWא אאn=f(Ia)
אא T=f(Ia)
אא n=f(T) א(3-17)א(3-18)אא
Wאאא
א א א אא
א א
א
אEאFאא F٣ J٦א א KE
אKאאאאאKא
א(3-13)FאאאFאאאאאE٣ J٦KE
אאאאאאא،Kאא
א
א א
DC Shא אא
אאא
א
א
א
אא א K
hunt Mo
א
،
אא
א
otor
א
א
אאא
،א
אאאא
א אא
91
אא
אא א
אא
א
א
J6א:
א
א
א
אא
אא אא
אK
א
3Jא
אא
אא K
אאאא
W
٤ J٢ J١٣ J7
אאK
א
א
،א
K
٤ J٢אאא
٣ J٤
אא
א
אא
٣ J٤
א
אאא
אאאא
92
٣ J7אאאאא
אאא 3-23 V = Eb +Ia Ra
3-24 I = Ia +If
3-25 Eb = kv If
3-26 V=Vf = If Rf
3-27 Td= kt If Ia
3-28 Td = TL +B
אא(3-28) W 3-29 Td = TL
אאא
אאאא
93
٣ J٤
א240V750 rpmא30 A ، א 0.05Ωא ، א V/A.rad./sec٥٢١
W
aK אK
bK Kא
cK Kא אW
V= Vf = 240 V , n = 750 rpm , Ia= 30 A , Ra= 0.05Ω ,
kv =1.52 V/A.rad./sec
Eb=V - Ia Ra =240 - 30×0.05 = 238.5 V
2 60
2 750
60 78.54 rad/s
238.5 3078.54
91.1 N.m
Eb = kv If ω
238.5
1.52 78.542
2402
120Ω
אאא
אאאא
94
٣ J5
א 500 V א ،٩٦٠אK52 A אא
٣אאאK0.04 Ω200 ΩKאאאאK
אW p =4 V = Vf = 500v Z =960 , I = 52 Amp Ra= 0.04 Ω Rf =200 Ω , =3megalines = 0.03 Wb , a= 2
500200
2.5
Ia = I – If = 52 – 2.5 = 49.5 A Eb=V - Ia Ra = 500 - 49.5×0.04 = 498.02 V
60
60
498.02 2 604 960 0.03
512.77
2 ∙60
2 512.7760
54.33 rad/s
498.03 49.554.33
453.75 .
אאא
אאאא
95
אאאא
אאאאאאאא א א
Kאאאא
٣ J٤ J٢ J٢אDC Series Motor ٣ J8 א אאא ،אא
אא،אאא
٣ J8אאאאא
אאא
3-28 I = If = Ia
3-29 V = Eb +Ia(Ra +Rf)
3-30 Eb = kv If
3-31 Td= kt If Ia = kt Ia 2 = kt If
2
3-32 Td= TL +B
אא(3-32) W
3-33 Td = TL
אאא
אאאא
96
٣ J٦
אא220 V א50 Aא1000 rpmא، 0.15 Ω א0.1 ΩK
W aK אא bK אאאא cK א
אW V = 220 V, Ia= 50 Amp., n =1000 rpm, Ra=0.15 Ω, Rf =0.1Ω ,
Eb =V - Ia ·(Ra+Rf) = 220 - 50 (0.15+ 0.1) = 207.5 V
260
2 100060
104.72 rad/sec.
207.5 50104.72
99.07 N.m
T=Kt Ia2
299.0750
0.0396
٣ J٧ אאא،אא25 %Kאא
Wא T = 1.25 (99.07) = 123.84 N.m
T=Kt Ia2
123.840.0396
55.92 A
אאא
אאאא
97
٣ J٨
אא 220V אא52 AKאאא٦٣٠א
0.018אWbאאא،0.2 Ω0.1 ΩKאKאאאא
אW
p=4, V =220 V, Ia=52 Amp., Z=630, = 0.018 Wb, Ra=0.2Ω
Rf = 0.1Ω a= 2 , T2= 0.6T1
Eb=V - Ia (Ra+Rf) = 220 - 52 (0.2+0.1) =204.4 V
60
4 630 0.0182 60
204.4
∴ 541
260
2 54160
56.65 rad/sec.
204.4 5256.65
187.61 N.m
אאא
אאאא
98
٣ J٩
אאאאאאא60%،אאאאא
Wא
T α Ia2
0.6
52
0.6
Ia2 = √0.6 52 = 40.3 A
Eb2=V - Ia2(Ra+Rf) = 220 - 40.3(0.2+0.1)= 208 V
208204.4
40.3541 52
n2 =710 rpm
אא א(3-29)א(3-30)אאא
אאאאאאW
א א א א אא∞אאא
אאא
אאאא
99
אאאאאא
Fאאא٣ J9KE א(3-31)אא،
א א א F٣ J9KE א٣ J١٠אא א א א
אאאK
٣ J9אאאאאא
٣ J١٠אאאאא
אאא
אאאא
100
אאאא
אאאEאFא א א א EאF א
Kאאאאאא،אאאאא
אאאאאKאאאאאאאא،،א
א אאאאאא א אאאאאאאאא
KאאאאאאאK
٣ J٤ J٢ J٣אאDC Compound Motor א אא א א א(Series Windings)
אא (Shunt Windings) ، א א ،אאאאאאאא
אאאאאאאא אא א א ،אא
(Cumulative Compound ) א א א אאאא،אאא
א(Differential Compound)K
אא אא א א אאאאא
א אא(Short-shunt)، אא אא א אאאאאEאאאF(Long-shunt)،
٣ J١١،א אא א אא א אאse אאshK
אאא
אאאא
101
EF (ب)
٣ J١١אא EFEF אאWא
(3-34)
(3-35)
(3-36)
(3-37)
(3-38)
אאא: (3-39)
(3-40)
(3-41)
(3-42)
(3-43)
אאא
אאאא
102
٣ J١٠
50A220VK1200rpm אא אא א א א א ،0.04Ω ،
אא0.01Ωאא125ΩKKאאא
אW V=220 V, I = 50 Amp, Ra=0.04 Ω, Rse=0.01Ω, Rsh=125Ω n= 1200 rpm
220125
1.76
Ia=I-Ish = 50 -1.76 = 48.24 A
Eb=V - Ia(Ra+Rse)= 220 - 48.24(0.04+ 0.01) = 217.588 V
260
2 120060
125.66 rad/sec.
217.588 48.2456.65
83.53 N.m
אאא
אאאא
103
٣ J١١
50A 220V Kא א0.04Ωאא،0.01Ωאא125Ωא K1200א rpmא 85 %אW
١K אאאאאK
٢K Kא
٣K Kא
٤K Kאאא אW
V = 220 v, I =50 Amp, Ra=0.04 Ω, Rse=0.01Ω, Rsh =125Ω, n = 1200 rpm, = 0.85
220125
1.76A
Ia=I-Ish=50-1.76= 48.24 A
Eb=V - Ia(Ra+Rse)=220 - 51.76(0.04+0.01)= 217.588 V
Pin = V I = 220×50 = 11kW
= ηPin = 0.85 ×11×103 = 9.35 kW
ω260
2 120060
125.66 /
9350125.66
74.41 N.m
אאא
אאאא
104
٣ J١٢
50 A220 V Kא0.04א Ωאא،0.01 Ωאא125ΩאK
א1200 rpmא90%אW ١K אאאאאK
٢K Kא
٣K Kא
٤K Kאאא אW
V = 220 v, I= Ise =50Amp, Ra=0.04 Ω, Rse=0.01Ω,
Rsh=125Ω, n = 1200 rpm, = 0.85
220 50 0.01 219.5 V
219.5125
1.756 A
Ia= I - Ish = 50-1.756 = 48.244 A
Eb=V – Ise Rse - Ia Ra=220-50 × 0.01 – 48.244 × 0.04 = 217.57 V Pin = V I = 220(50) = 11 kW
= η∙Pin = 0.9 (11) = 9.9 kW
ω260
2 ∙ 120060
125.66 rad/s
9900125.66
78.78 N.m
א
אאא אא
אאא
٣ J١٢
א
אא
אאא
א
א
:(C אא
א
W
א אא ١٢K
אאא E
Cumulati
אאא א،א
(L :
א
א
(Differeא
٣J
א
אאא
א
ive Com
אא
אא
Level Co
א אא ،
١٢K ential Co
א
א
א
105
אא
אF
mpound M
אא
ompound
א
א ٣J
ompoun
א
אא
K
Motor)
א א
Kא
d Motor)
אא א
d Motor
אא Kא
٣ J١٢
א
אא א
אא
א
)
אא
،
r)
א
א
אאאא
אא א
אW
א
،אאא
אא
א ،אא א
אא
אא
אאא
J
Jאא
J
א
אאא
אאאא
106
Wאאאא
אאאא،אאאאאאאKאא
א (Rolling mills )אאא،אאא،א،א
אאאאאK
٣ J٥ אStarting Methods
EאאFאאאאאא א א F א
אאאא،EאאZא א א א א א א א א Kאא א אא א
א א Kא Kא א א א א
אאא(Starter) א א א אא א
אאEFאא،אא אא
אKא ٣ J٥ J١אא
א א אאאא ،אאא
אאא،אאKא٣ J١٣אאאא،
אא(A) א א אRstא אא(B)אאאאאאא
אאא
אאאא
107
אא،אאאא(A)١א٢٣אon
אאאאאאאאאאאאאאKאא
(S) א א אא א (on)א א א
אאאא(off)K
٣ J١٣אא
٣ J٥ J٢אא א אאאא א٢٠
אEF(Overload)אאא א (Circuit Breaker)א
א(S)אKאא٣ J١٤ אאKאאאאאAאoffא،
א
אAא
אC
אאA
אA
א
K
אאא
א،Kא
D א א
אD
(Sp
א א
א
אE
א
א K
אא
pring)
F
אא
א
אא
C
onK
אא
אא
108
א
אא
אAא
אא
אoff
E א א א
אC
א
אאא
S
א
CאA
٣ J١٤
א
Bא
אCאA
א
on
א
א C
א
א
אאB
אא
אRstאא
אC
אKא
E،
D
אא
S
אא
א
F ،
א
אאא
אאאא
109
٣ J٦אSpeed Control א א א אאאאאKא
Wאא אאW
Wאאאאא
אאאW Wאאאאא
אאאאאאאאאאא
אאKאא JאאWאאא
،אאאאאאאאאאאאאא
א א א א א Kאאאא
JאאאWאא אאאאא
،אאאאאאאא א א א א א א א א אא א ،
،Eא؟F א א ? ? א א א ٣ J١٥אאא،MG،
אאאM’،
א
א Kא
?
א
אאא
א א
K
אאאאאא
?א
א
אאא
110
א א א
אא
א
א
K
١٦،
אא
א
א
א
א
א٣J
٣ J١٥
١٦
א
אא
א
א
٣J
אא
אא
אאא
אאאא
111
JאאW(Flux Control)
א א א א א ،אא א ، א
אאאאאא א א א
Kא א אא Kאא
٣ J٧אאא א אא אא א א
אא אאא Kאא Kא א א ،א א
אאאאKאאא אא ٣ J١٧ א
Kא،א
٣ J١٧אא
אאא
אאאא
112
٣ J٨אאLosses and Efficiency
אאאא אא Wא ١K אאMechanical Loss ٢K אאCopper Loss ٣K אIron Loss
א،אאאא א K א א
Kא
٣ J٨ J١אאא אאאא
אאאאInput PowerאאאאF(W
אאא אPg،PgאW
3-4٣Pg=Pin - Pcu= Ea ·Ia
אאאPg א PmechPi אאאא א Pout K ٣ J١٨ א א
Kא ٣ J٨ J٢Wא
א،אאאאאאW
١K אא
3-44 I V
746HP
P
P
in
out
אאא
אאאא
113
אאא
3-45 lossesP
P
out
out
in
in
P
lossesP 3-46
٣ J١٨אאא
אאא
אאאא
114
٣ J١٣
אא150 HPאא960 rpm،550 VאK91%
אא275Ωא0.1ΩKW ١K אאאאאאאK ٢K אאאא60%אאא
0.2ΩKאאא אW
HP=150 n=960rpm V=550V η=91% Rsh=275Ω Ra=0.1Ω
in
out
P
P
inP
74615091.0
WPin 12296791.0
746150
I VPin I550122967
A6.223550
122967I
A 2275
550
R
V
R
VI
shsh
shsh
A6.22126.223III sha W6011275)2(1.0)6.221(R IR IP 22
sh2sha
2acu
WPPP outinlosses 11067)746150(122967
cuimechlosses PPPP
WPPPP culossesimech 5056601111067 V84.5271.06.221550R IVE aab
m.N5.116360/9602
6.22184.527
60/n2
I EI ET abab
אאΦ aIT
אאא
אאאא
115
aIT
6.011 a
a
I
I
T
T
AII aa 96.1326.2216.06.01 V1.510)2.01.0(96.132550)RR(IVE ada1a1b
60/2
96.1321.5105.11636.0
1n
rpmn 9285.11636.02
6096.1321.5101
60/2 1
11
1
111 n
IEIET abab
אאא
אאאא
116
אא
١ J Kאאא ٢ J Kאא؟אאא
٣ J אאאאאKאא
٤ J אאא،אאא
Kאא
٥ J Kאאאא
٦ J ؟אאK
٧ J ؟אאאא
٨ J אאאאא א؟
٩ J א א אא א K؟א
١٠ J א٤220Vא٥٤٠ א א ،32A 6kW א ،
א 1A א 0.9Ω א א0.03WbאKאא
١١ J א 220V 500 rpmא50AאKאאאאאא،א
א0.2Ω
١٢ J א ٤ 220V א٧٨٤א א Kאא
0.5Ω ،0.25Ω א א25 mWbא ،אאא40AK
אאא
אאאא
117
١٣ J א240V850 rpmא100
Aאאא א ،0.15Ω ،0.1Ω ، א א א 30א Aא א ،
Kאאא
١٤ J א0 V٥٠אאא55A21 HPאא،0.8Ωא٢٤٥ΩאKאKאאאא
١٥ J א٤א٨٢٠ א א ٢ ، א
1200 rpmאא6 Aאאא،120
Aאאאאאא א K0.15Ω،0.05Ω،120 Ω،W
aK אאא bK Kאאא
אאא
אאאא
118
אאא
אאא
אאא
אאאא
119
Wאאא א אאSingle-Phase Transformers
אאWאא،א
אאאאאאאאאאאאKאא
אאאW
١K אאאKא
٢K אאאאאאKא
٣K אKאאא
٤K אKאאאאאא
٥K אאאKא
٦K אא
٧K אKאאאא
٨K אאKא
٩K אKאאאאא
١٠K אKאאאא
אאא
אאאא
120
אאאSingle Phase Transformers אאאאאא
א א אא א ،א א אא א
אאאKאאא אאאF
EאאאאאאאאאאאאK
א א א ?אא? א אאאאאאאא
Kא א א א אאאKאאא
אאKאאאאאאאKאאא
אאאאאאאK ٤ J١Wאאא
אאאWא
אPower TransformersWאאאאאאאא٤ J١K
٤ J١
אאא
אאאא
121
א Distribution TransformersW א א אאאאא
K٤ J٢Kאא
٤ J٢
א Instrument TransformersW א א א ٤ J٣ ،א א
א א א א K
K K
٤ J٣ א ing TransformershEartW
אא Kא אKאאאא
אאא
אאאא
122
Wאאאאאאאאא
אK
Wא א א א א א א אא٤א J٤K
٤ J٤אא
٤ J٢א
אאאא
(core) א א ٤ J٥א ،א א א K א א
א(Magnetic flux)א،אא א אאא א
אאאא،אאאKאאאא(primary winding) N1א،
אאאא(secondary winding)N2K א א א א א
،אאאאאאא א Kא א א א א
אאאאאאאauto transformerK
אאא
אאאא
123
א،אאאאאא
א؟
٤ J٥
٤ J٣א
אאWאאאא(core)א،(windings)אאאאאא
Kא Jאא(core) Wאא
א א א אאKKא(legs)
אא (yoke) Kא אא א (laminations)אFאא،Eאאא
0.35mm 0.5mm א א א 0.02mm0.03mmא، אא
א א א Kא א אא،אKא
،אאאאKא٤ J٦ K
אאא
אאאא
124
אאאא א
،אאאאאאKאKאאאא
٤ J٦(Leg)
א،אאא:
K אא ype TransformerTCore W٤ J٧ א ،א אא א א
א Kא א אא אאאאאאא،א
Kאאאאאא
א ٤אאא J٧אא،אאL
٤ J٨ אא٤ J٩אא،،אא،אאאא
Kא
א
אאא
א
אא
J١٠
א
א
W٤אKא
א
א
TShell א
125
٧אא
א
ype TraT
٤ J٧
٨אא
א
ansform
א
٤ J٨
٤ J٩
mer
אא
א
٤
K א א
אא
אא
א
٤ J١١،I،
א א
אאא
J١٢،
،
אI
E ٤J
א
א
אE
E
Eא אא
אK
א
126
١٠א
،א
אאאא
א
٤J
אא א
א
٤ J١١א
א
א
I
א א K
א
אאא
אא
אא
א
אא
א
א א אא
א ،
אאא
אא
א א Kא א
א
א א אא
Wא א,א
א
א
אא
אא
Kא א
א
127
א
א
PWאא
אKאא
א
א א
אא אאKancake T
א
٤ J١٣
א
J١٢
(WindinWא א אאא
،E
Type
K
א
٤J
ngs)
אאא
אFא
K אאא א
٤ J١٣
אא
Jא
א
K
א
אא
J١٥
אאא
אא
E
K٤J
א
א
אא
אא
א
אK
١٤
א
אא
א
א
128
croWאא
٤ J٤
HeWאאא
٣٣
ossover
אא
٤ J١٤
elical Ty
F
٣
٤ J١٥
א
Type
ype
אאKא
א
K אא
K אאאאא
אא
א
א K
אאא
אאאא א
א
א Kא
א
אא אא
א
129
אא א
K
Disc TWא אא
א
٤ J١٦
א
ype
،א
אא
א
K אאא
א
٤ J١٦
אא
אאא
אאאא
130
٤ J٤א
א א ، אא(Sandwich) K
٤ J٤ J١אאא
א אאאאא Kא٤ J١٧،א א
אאאא، א ،א א א
אאא0.05mmא0.1mmKא
אאאאאאא،אאאאאאאא
،אKאאאKאא
٤ J١٧אא
אאא
אאאא
131
٤ J٤ J٢אאא ،אאאאא
،אאאא، אאאאאא
،אאאא،אאא٤ J١٨K
٤ J١٨אא
אאא،אאאא
אKאאאאאא
א
،אא Fאא
א
אאא
א א
K
א
אאKE
א א אאא
א
W
132
אאFאאאא
١٩אאא
אא
W
א
،א١٩אאאא،א
٤ J٩
א
א
א
א
אאאא א
٤J
אא
W
אאאא
א
א
א
א אEאא
(
(
א
(
אא
אא
٤ J٥
א
4-1)
א
4-2)
א
4-3)
אאא
אאאא
133
(t) =m sin(ωt) (4-4)
m אאאK·f ،fKא
(4-4)אאא (4-1)אWא e1(t) =N1m ω cosωt=N1 m f cost (4-5)
Wאאא 1 √2 cos
E1Wאאאאאא
fNE m 112
2
אאאאאאE1 W
E1=4.44 N1 m f (4-6)
א ،א א א א א א אWא
E2=4.44 N2 m f (4-7)
א(4-6)א(4-7)אאאאאאאאאאאאאאא
W
(4-8)
אא אאאא א אא א אאאאא א אא
אאKאא“S”KVA
אאאאאאאאWאאאאא
(4-9)
אאא
אאאא
134
٤ J١ א60 Hzאאא،
א20cmאאא אא10000א lines/cm2–אאאא
אאאא3000/220 VK אW
B=10000lines/cm2, A=20x20=400cm2, E1=3000 V, E2=220V, f=60Hz m =Bm A=10000 400 10-8=0.04 WbE1=4.44 f Φm N1
4.44 3000
4.44600.04282
E2=4.44 f Φm N2
4.44 220
4.44600.0421
א
אא
א
V1 = E1
אאא
Kא
אא
;
אאא
W אא
א
V2= E2
Kא
א
אאא
W
135
אאא
א
4-8א
אW
א
א
אאא
4-10א
א א
٢٠אא
א
אאא
Wאאאא
א
א
א0
א א
W
٤J
א
٦אא
٦ J١אאא
٢٠،
،
(4
(4
א
(4
א
אא
٤ J٦
٤J
٤ J٠
א
4-10)
-11)
-12)
א
אאא
אאאא
136
٤ J٢ א 25kVA א٥٠٠אא٥٠
אאא3000V،Wא ١K אKאא ٢K אאאאK ٣K אאאאאK ٤K Kאאא
אW
S =25 kVA , N1=500 turns, N2=50 turns, V1=3000V
300050050
3000 50500
300
250003000
8.33
25000300
83 ∙ 3 8.33 500
5083.3
E1=4.44 f m N1
4.443000
4.44 50 5000.027 Wb
אאא
אאאא
137
٤ J٣א5kVA،440/110V60Hz א 35A 0.8 Kא א
،אW ١K Kאאא ٢K Kאאא ٣K Kא
אW S=5kVA , 4 , f=60 Hz , I2=35 A,P.F= 0.8 leading
V2 = 1100 volt I2 = 35 0.8=3536.87 Amp.
∴ 110 35∠36.87°
4408.75∠36.87°
2
2
11003536.87°
3.1436.87°Ω
אאא
אאאא
138
٤ J٦ J٢אאא א א א אא א אא א
אאאאאאKאאאאאאא
٤ J٢٠ אא،אאאאאאאאאאא
،אאאאאW LאאאאWV1אR1אא
X1אאאאE1אאאI1
Lא א אW א אא א E2 א
א אR2 א אX2 א Z2אאI2V2K
LWא א א אא א א א Kא א א א אא א
אאRCXCאאאאKKאאאא
٤ J٢١ אא א א אKאאא
א
אאא
אא
אא
א
א
א
אא
א
אאאא
א
א
139
٢١אא
א
אאא
א
א
אאאא
٤J
אאאא
אא
אא
אא
א
אא
אא
א
אא
אא
אאא
אא
אאא
אא
א
W R1W R2W X1W X2W RcW אXcW ZLW I1W אI2W אIOW IcW אImW אV1W V2W אE1W אE2W א
אא
א
א
א א
אאא
א
א
א
א
א
א W
א א
אאא
140
א
א٤ J٢٢
אK
אא
אא
א
אא
אאאאא
א
א
W
אא א
אא
אא
J٢٢אא
א
אא א
(4
אאא אאא
א אא
٤
אא
א
-13)
א
אאא
אאאא
141
٤ J٢٢ א א אא א א
אאאאאאא אאאאאWאאאאאאא
(4-14)
(4-15)
(4-16)
(4-17)
(4-18)
W
R2’W אאאא
X2’W אא אא
I2’W אאאאאא
V2’W אאאאא
E2’W אאאאאאאא
אאאאאאאאאאאאאאאאאאאא
אא٤א J٢٣K אאא
אאא
אאאא
142
٤ J٢٣אאאאאא
W
ZL'Wאאא א אא ٤ J٢٤ א
אאאא א אא אK
٤ J٢٤אאאאאא
W (4-19) (4-20)
אאא
אאאא
143
אאאא٤ J٢٣א
Wא I1 = Io + (4-21)
V1 = V2’ + I2
’ (Req1 + jXeq1) (4-22)
٤ J٤
א120kVA400/2000VאאאW
R1=0.01 Ω , X1=0.03 Ω , R2=0.25 Ω , X2=0.75 Ω,
Rc=500Ω , Xc=150 Ω , =
100kVAא2000V٨0.Kאאאאאא٤א J٢٤
אW אאW،אאא
R1=0.015Ω, X1=0.035 Ω,
= 0.25 = 0.01 Ω
= 0.75 = 0.03 Ω
= 0.015 +.01 = 0.025 Ω = 0.035 + 0.03 = 0.065 Ω
Wאאא I2 = = = 60 A
= 60 = 300 A
א0.8W = 300 36.87 = 240 – j 180
Wא Im = =
90 = 2.66 90 A
א
Ic = =
Io = Ic +
I1 = Io +
א
V1 = V2
= 40 = 400 =400V1 = 417
אא
אאא
= = 0
Im = 0.8
+ = 2.7 = 0.8 = 30
36.78o
’ + I2’ (R
0 0 +0 0 + 0+21327.79 + j1
אאא
٢K
אא
.8 A
8 – j 2.66
78 738 – j 2.660.64 א
eq1 + jXeq
3003002.09 1.16 = 4
אאאא
٤ J٢٥
= 2.78W
3.26 + 36 + 240 –36.78300.64
W q1)36.8736.87
17.941
א
144
73.2
300 –j180 = 2
4
א
(0.025+j 0.07
1.5 V
אא
א
א
6 Aא36.87
240.8 – j
אאא
j0.065)68.96
א
אא
א
א
180.8
אאא
אא،אא
٤ J٢٥א
א
א
א
אא
אא
א
א
א
1
21 V
N
NV
2
11 I
N
NI
11
NRR
11 XX
12 RReq
2 XX eq
= I2
= V2
אאא
א
٤ J٢٦
א
1V
1I
2
1
2
N
N
2
1
2
N
N
2R
21 XX
+ I2 (Req
W א
q2 + jXeq2)
אאא
2)
145
٤ J٢٥
K א
א
W
٤אא
א
٢אאא
א
אא
אאא
٤ J٢٦
א
א
אאI1 =
אא
א
(4
(4
(4
(4
(4
(4
-٤(
-٤(
אא
א
=
א
-23)
-24)
-25)
-26)
-27)
-28)
)٢٩-
)٣٠-
אאא
אאאא
146
٤ J٧א Transformer Operation ٤ J٧ J١אאNo load operation
א אא א א א א א ٤א J٢٧K
AC
Im Ic
Xc Rc
I1
Io
V1 E1=E2'
Req1 Xeq1
V2'V1
I2'
٤ J٢٧אאאאאא
אאאFאאא،אאEאאIo
אImאאאIcאאאאPoWאאא
Po = ·V1·Io·cos (4-٣١)
א א א א א א 90o
א א א א א א א א א א ٤ J٢٨ K
Wאאאאא
Im = Io· cos
Ic = Io· sin(4-٣٢)
oאאאIoאאאאאK
אאא
אאאא
147
٤ J٢٨אאא
٤ J٧ J٢אאLoad operation
ZLEFא א א אא I2 א אא
אא Kא א אא א ٤א J٢٤Wאא
(4-٣٣)
(4-٣٤)
אאאאאאא٤ J٢٤K٤ J٢٩K
אאא
אאאא
148
٤ J٢٩אאא
אאא
אאאא
149
٤ J٨אTransformer Regulation אאאאKא،
אאאאKאאWא
.| | | |
| | (4-٣٥)
W V.RWא
V2noloadאאאאאW V2rated אאאאאאWא
Wא
. .| | | |
| |100 (4-٣٦)
W V.RPKאאאW
אאWאא
.| | | |
| | (4-٣٧)
. .| | | |
| |100 (4-٣٨)
א
א W
No L
אאא א K
Po = Vo
cos o =
Ic = Io c
Rc =
Im = Io s
Xc =
אאא
Load Tes
א KאאKא
W Io cos
=
oso
sin ϕo
אst
א אא ،
Ioא
אRo
o
אא ،
א אא
אo
א , Xo
אא
150
،א
אאא אאא א
٤ J٣٠
אE
א
א א
(Open אא
PoKאא
א
אא אאא
J١א
Circuit
א א
א
אאאא אF
٤ J٩Jאא
Test)
٣٠ ،
אא
אא
٤ J٩
א
א
٤ J٠א
אא
אאא
אאאא
151
٤ J٩ J٢אאShort Circuit Test א א א א א
٤ J٣١،אאאאאאאאאאא
אאאאאאאאאאאאא،אאאאFPscא
Isc، אאVsc،E אאא Req , Xeqאאא:
Psc = Isc2 Req (4-٣٩)
Zsc = = (4-٤٠)
ReqXeqR1R2'Req٢X1X2'אאR2 X2K
٤ J٣١אא
אאא
אאאא
152
٤ J٥
א 500kVA 2300/230V K אאאא،אאאאK2250אWא9.4A א ،2300V אא א K8220Wאאאא94.5VKאKאאא
אW Open Circuit Test: Vo=2300V, Io=9.4A, Po=2250W
Short Circuit Test: Vsc=94.5V, Isc=Irated , Psc=8220W
oooo VIP cos
1156.023004.9
2250
V I
Pcos
oo
oo
o
o 36.83)1156.0(cos 1
21161156.04.9
2300
cosI
V
I
VR
oo
o
c
1c
33.2469933.04.9
2300
sin1
oo
o
mc I
V
I
VX
AII lfsc 39.2172300
10500 3
.
1739.0)39.217(
822022
sc
sceq I
PR
2eq
22
2eq
2eq
sc
scsc
X)1739.0(39.217
5.94
)XR(I
VZ
Xeq=0.3984 Ω
אאא
אאאא
153
08695.02
1739.0
221
eqRRR
1992.02
3984.0
221
eqXXX
0008695.2300
23008695.0
22
1
222
2
2
122
N
NRR
N
NRR
٤ J١٠אאLosses and Efficiency
٤ J١٠ J١אא אאאאא
אIron lossאCupper loss، אא אא،א
א א ،א א א KאאאאPoאאאא
אאאאאאאאאאאKא
Pi =Po (4-٤١)
אאאאאאאאWאאאא
Pcu.f.l =I1f.l2 Req1 = I2f.l
2 Req2 (4-٤٢)
א א א א א Kא א א א א א
Kא Pcu(x)= x2 Pcu.f.l = x2 I1f.l
2 Req1 = x2 I2f.l2 Req2 (4-٤٣)
אאא
אאאא
154
א א א א Kא
א אא א،Kאאאאאא
אאאאאאאFא٣٥KאE٪א
א א K אאאאאKאאאאא
Pcu.f.l =Psc (4-٤٤)
٤ J١٠ J٢א אאOutput Powerאא
אאאא،אWא
100xPPP
P
cuiout
out
(4-٤٥)
100xP
P
in
out (4-٤٦)
W PinWאאאK
PoutWאEאF،Wא )٤-٤٧( )٤-٤٨( P P P P
cos2אPower FactorK PoutPcuא4-37אאא
WEאאאFאא
100RIPcosIV
cosIV
eq
2
2i222
222
(4-٤٩)
222out cos I VP
אאא
אאאא
155
٤ J٦ א 500kVA א א ،2500Wא
אא7500אWKאאאאא ٨٠K
אW S=500 kVA, Pi =2500W, Pcu.f.l.=7500 W, cosϕ2=0.8 Pout =500 103 0.8=400000 W
%56.97100x25007500400000
400000100x
PPP
P
cuiout
out
Wא Pout(1/2)=0.5 500 103 0.8=200000W
Pcu(0.5)=(0.5)2Pcu.f.l. =0.25 (7500) = 1875 W
%86.97100x25001875200000
200000100x
PPP
P
)2/1(cui)2/1(out
)2/1(out
א
Auto-tr
ABE
א
א
א אא
١W ٥,٢
אאא
ransform
אאF
אאאאא
אאא Kא
אא
١
א
mer
א
BCE
BCE٣٣K
א
אK
א א א
אאא
K
אF ٤ J٣٢K
אFC
٤ J
א
א
אאאא
“VKאאא
156
אא
٣٢א
אאK
אVariac”
אאא
א א
٤ J٢
א א
??
Kא
א
אא
אאאא
אא
Cא
א א
אא
א
٤ J١١א
א
אא
ABEא
א
אC
א א א
אא
אא
אאאFאא
אאא
אא
א
Kא
אאא
א
א
א
א
אKא
אא
157
א
٣٣
אא
٤J
א
א א א
אאK
א
א
אא
א
א
אאא
אאאא
158
٤ J١٢אאאאPolarity and Parallel Operation
٤ J١٢ J١א אאאאאאאא
אאאadditive subtractiveKאאWא
١K אK
٢K Kאאא
٣K Kאאא א א א א אאאא
Wא אאWH1-H2-H3אאא
X1-X2-X3Kאאא
א אאא WA2-B2-C2 א א א a1-b1-c1Kאאא
א א WU1-V1-W1 א א א U2-V2-W2Kאאא
אאאאאאאאאאא א א אא א א
אאKא ٤ J٣٤ א א אא א
א א א א א א א א ،א א
א א Kא א א א (Additive)אאאאאאא
אא،א(Subtractive)אאKאאאאאאא
א
אאא
E= EP+
K
K
+Es
א
א
אאא
א
אא
א
159
א
אאא
E= EP-
٤ J٣٤
אא
Wא אא
א
Es
٤
אא
א
א
אא
א
אא
א
١٢ J٢א
אא
אא
אא
א
א
א
א
٤ J٢
א١K ٢K
אאא
אאאא
160
٣K א א א אא
אא אאא אא אא אאא אאא
אאא٤א J٣٥K
٤ J٣٥אא
Wאאאאא aK Kא
bK א(Per Unit System)
cK Kא
אאאאאא אא א K א
אאא،א א א א א 5% 10%א
Kאא
אאא
אאאא
161
אאא
١ J אאKא
٢ J אאאאאK
٣ J אאאאK ٤ J אאאאK
٥ J אאאK؟
٦ J אאאאאאK
٧ J אאא؟אא
٨ J א؟אאאאK
٩ J ؟אאאאאאא
١٠ J אא؟
١١ J אאאאא؟
١٢ J אאאK
١٣ J אאא؟
١٤ J אאאאאK
١٥ J אאאאא؟
١٦ J אאאא
١٧ J ؟אא
١٨ J אאאאא
١٩ J א60Hzאאא، א cm٢٠٢٥ א א
א0.0001 א cm2/Wbאאא،אאאאא3000/220V
٢٠ J א 50kVAא ،400/2000V K 40kVA 2000V 0.8א KW
aK אK
אאא
אאאא
162
bK אאK
٢١ J אא١W٤אK10Ωא30°،א120אV،אאK
W
aK אאאאאK
bK אאאK
cK אאK
٢٢ J א 200 kVA א ،6000/660Vאא WאR1=1.56Ω R2=0.016Ω X1=4.67Ω X2=0.048Ω
א א א 0.96A 0.263KKאאאאאא
٢٣ J א500kVAא،2300/230V،
Wאאאאא
אאW Vo=230V Io=94A Po=2250W
אאWVsc=100V Isc=228A Psc=9.2KW
אאאאאאK
٢٤ J אא25kVAא3300/200VWאא
Vo=3300V Io=0.8A Po=300W
Vo=100V Io=7.5A Po=580W
אא،אאאאאא א א א0.8 א ،
Kאא
אאא
אאאא
163
אאא
אא
אאא
אאאא
164
Wאא אאא
Three-Phase Transformers אאWאאא
Kאאאאא،א
אאאW ١K אאאKא
٢K אKא
٣K אKאא
٤. אאאא.
אאא
אאאא
165
אאאThree Phase Transformers
W אאאאאאא
EאאאאFאאאא، א א א Kא א א א א א א א א
אאאאאאאא Kאא
Kאאא ٥ J١אא
אאאאKאאאא،אא
א Kא א א א א א א א אKא א א א א
٥ J١Kא
٥ J١א
אאא
אאאא
166
א א א א אאאאאאא
אאאאאאאאאאא ،א א א
א א א אא א א KEאFאא
٥ J١ J١Wאא Core Type אאאאאאא
500 kVA 100MVA K٥ J٢،א אא א ،א
אKאא
אא
אא
אא
٥ J٢אא
٥ J١ J٢WEאFאאShell Type
Kאאאאאאאא٥ J٣אא،א
،א٥ J٣،אאא ،אא א א אא
Kאאא
אאא
אאאא
167
٥ J٣EאFאא
א אאאאאCore and Shell Type Transformer،
Kאא٥ J٤אאK
٥ J٤
אאא
אאאא
168
٥ J٢א
אאאאאאא א א،אאאא
אאאאאאאאאאא،אאאא
א KE F א א א אאאאאא אאאאא
(phase shift)א א א KWא
J אא JאStar-Star Y-Y
Jאא–א Δ-Δ Delta-Delta
Jאא–א Y-Δ Star-Delta Jאא–א Δ-Y Delta-Star
٥ J٢ J١ J(Y-Y)
٥ J٥א Jאא،YאYK
٥ J٥Y-Y
אאא
אאאא
169
א JWאא
١K א)( √
א)( א
Kאאאאאאאאא
٢K אאאאאאKאאא
٣K אא Jא K
٤K א א K
٥K ،אא אא א ، א
אא،אאאא א Kאאא
K
٦K אאאאאאא W
√⁄
√⁄ = = =
אאא Jא א א K
אאאאאאKא
אאא
אאאא
170
٥ J١
א א Lאאא66kV6.6kVאאאאאאאK
1000 kVA6.6kV K אW
= = =
S = √3 V2 I2
I2 = √
= 87.477 Amp.
= = .
=
I1 = 874.77 Amp.
٥ J٢ J٢ J(Δ-Δ)
،אאא،אאא٥ J٦אאאאK
Kאאאאא
٥ J٦Δ-Δ
אאא
אאאא
171
אWאאאא
١K אאאא א א)(
א)(√א
Kאאאאאאאאא
٢K אא JאאאKאאא
٣K אאאאאאאKא
٤K א א Kא
٥K אאאאK
٦K אאאאאאאW
= =
אאא J א אאאא،א
K
אאא
אאאא
172
٥ J٢
Lא13.8 kV150AאKאאאאאאאאאאאא
אאאאאא٧٨٢٦٤K א
= = = 4.7826
V1 = 66 kV
I2ph = √
= √
= 86.6 Amp.
= = .
=.
.
I1ph = 18.11 Amp.
I1 = I1ph √3 = 31.36 Amp.
٥ J٢ J٣ J(Y-Δ) אאאא
٥ J٧K
٥ J٧ J
אאא
אאאא
173
JWאא
١K אאאאאאאאאאK
٢K אאאאK
٣K Kאאאאאאאאא
٤K א JKאא
٥K א Jא אאאאאאK
٦K אאאאאאא W
√⁄ = = √
√⁄ = = √
٥ J٢ J٤ J (Δ- Y) אאא Kא
٥ J٨Kאא
٥ J٨ J
אאא
אאאא
174
א JWא ١K אא א א אאא
אאאאאK
٢K אאאאאאא
אאאאאK
٣K א א א א Kאא
٤K אאאאאאK
٥K א Jא א Kא
٦K אאאאאאא W
√⁄ = =
√
√⁄ = =
√
א
F J
אאא
א
א
א
J
Eא
א
אאא E
א
ZigE אF
٥ J٩
אא
JE
175
gzag Tr
א א
א
אFEא١٠
ransform
א
K
٥ J٩א J
٥J
א
אFmerא
א
JFE K
Kא
א
٣אא א ،א
אאFEJ
א
אא
٥ J٣
אא
א
א
אאא
אJ
176
١٠
٥J
אאאא
אאא
אאאא
177
٥ J٤אאאא ٥ J٤ J١אאא
Phasor diagram-Vector group א phasor diagram א
א אא א ،א אאאאאאא،אא
א E אF א א 180אo א א א אא א א א א
360o א30oאאאאKאא
אאאא F א א – –א א E
אא30oא אאאא אאאאאאא،א
א Kאאאא אאאDz0אאאFאאאE
אFאEאאאאאא،אאאאאאאאא،אKא
א א א Wאאאא
١K אאWאאאWאא
aK Dd0אאאאאאא٥ J١١אאא
bK Yy0אאאאאאא٥ J١٢אאא
א
אא
אאא
א
א J١٢
D
Y
א٥
Dd0
Yy0
178
אא
٥ J١١
٥ J١٢
א
א
Dz0א
א
cK אא
אא
א
א
אK
א א
אאא
א
K
א א
D
אאאאא
אא א
J١٦
Dz0
o180א
אא אא
א ٥J
179
٥ J١٣
אאאא
١٥א
א180o
א
٥ J١٤
٥J
אא
א
WאאDd
180Yyא180o
Dzא
K
א
א d6
א0o
y6
א z6
אא
אא
٢K א
aK
bK
cK
א
אאא
D
Y
Dd6
Yy6
180
٥ J١٤
٥ J١٥
אא
אא
א
א א
א א
אא
אאא
א א
א
א
D
אא
١٧
א ١٨
א J١٩
Dz6
o30א
٥J
א ٥J
א ٥J
181
٥ J١٦
א
א30o
א 30o
אא30o
א
א
אא
א
WאאDy1
א K
Yd1א
K
Yz1א
K
א
אaK
אא
bK אא
cK 1
אא
אא
א
a
b
c
א
אאא
D
Y
Dy1
Yd1
182
٥ J١٧
٥ J١٨
אאאא
א
א א
א א
אא
אאא
٣٠
א
א
א
Y
330
א 20
א 21
א22
Yz1
o0
א ٥J
א ٥J
א ٥J
183
٥ J١٩
א 330o
א 330o
א330אo
א א
אא
אא
אאא
א
א WאW
1Dy א
K
Yd1 א
K
Yz1א
K
א
א א
1
אא
1
אא
1
אא
אא
٣K אא
aK
bK
cK
א
אאא
D
Y
Dy11
Yd11
184
٥ J٢٠
٥ J٢١
אאאא
א
א Kא
אאא
Paral א
אאא
Kא
Y
llel Opeא
א אא
Yz11
אאeration
אא،
185
٥ J٢٢
אof Thre
אא א
אא
אee Phas
א
J٢e Trans
א א
א
א
٥ J٤Jsformer
א
Kא
אא
rs
א
אאא
אאאא
186
٥ J٥א Methods of Cooling
אאאאאאאאאKא
א אא אאאאאKאאאא
Kאאאאאאאאאאאאא
א אא אא א KKאאאW
٥ J٥ J١WאאCooling of Dry Type Transformer
אאאאא(self-cooled)אאאאאא
א א א(KVA) 15kV א א ،AN א אAir Naturalא
א אא א אא א אאאאאא (Self-cooled
with forced-air cooling)אאאAFאא Air ForcedK
٥ J٥ J٢Wאאא
Cooling of liquid immersed Transformer ،אא،אאאאא(container)
KWאא K אW Oil Immersed, self-cooled
א אא א אאאאEFאאאאאאK
אאאאאא،אא
אאא
אאאא
187
Kאא٥ J٢٣אאKא،EFאאאאאא
٥ J٢٤אאKONאOil NaturalK
٥ J٢٣אא
٥ J٢٤אא
K אא
אאא
אאאא
188
Oil Immersed, self-cooled/forced-air cooled אאא
Kא ٥ J٢٥ א Kאאאאאא Kא
אONAFאOil Natural Air Forced
٥ J٢٥אא
K א
Oil immersed, self-cooled/forced-air cooled אאא א אאאאאאאאאאאאאאKא
Kא אאאאא
אאאאאאאאאאאאKא
א א א א אא،אאאאא
א K א OFWF א Oil Forced
Water Forced א א ،אONAN/ONAFK
אאא
אאאא
189
٥ J٦א Power Transformers
א(Power Transformers)אאאאאאא
אStep up transformerאאאאאKאאא
א א (Step down
Transformer)אKאאא א א א5000 kVAא
אאא800kVאא
Kאאאא
٥ J٦ J١א
א א א א א א א א Kא א א א א
א א א א א א א א אאאאאאאאK
אאאאאKאKאאאאא
אאא
אאאא
190
٥ J٢٦אאLow Voltage Bushing
א א אאא א א א א א א(Bushings) א
אאאאאKא א א(Bushings) ٥ J٢٦א א
Kאאא אאאאאאא אא א
Wאא אאא١٠٥א
אאאא١٥٠א
א א אאא١٩٠K
אאאאK
אאאאאK
אאא
אאאא
191
٥ J٦ J٢א
א אאא אא א אא א ، א
אא אאא א א א א K
א אא אא،אאאאא
א אא K K ٥ J٢٧
٥ J٢٨K
٥ J٢٧א
אאא
אאאא
192
٥ J٦ J٣א
א א אא א א א א א א
Kאאאאאאאא
501 kVA100 MVAאאאאKאאאאאאא
٥ J٦ J٤א
،אאאאאאWאאאא
אאאאאאא אKא
אאאאKאאא אF א אא א א א א אאאאאא،Eאא
Kאא
אFאאאאא–EאאאאאאK
٥ J٢٨
אאא
אאאא
193
אאאאducts
אאאאאאאאאKאא א Kא א א א
אאאאWא
١K אאאאאאאW
٢K אאW895 kg/m3
٣K WאKאאאא
٤K אWאאאאאאאאאאKאאאא
אאאא
٥K אאWאK٣٠אא
אא٤٥אKאאאא
٦K א، א א אא W א٠٦٠אא٪אא א
אאK٣٥אKאא
٧K אאאאאWאKאא30 kVא50kVK
٨K א א א א א א א Wאאאא٠٠٥٠K
אאאאאאאא،EאאFאאאאK
אאא
אאאא
194
٥ J٦ J٥א
א א א אא K
אאאאאאאאאאאא
א Kא ،א אא אא א ،אאאאא
אאאKאGaskets אא א ،
Kאא א אא א א אאאאאאא א אא א ، א אאאא א א א
אא א א א K Kא
٥ J٦ J٦אא
אאאאWאKא
Wאאא Step Up Transformer
אא א אאאאאא800 kVאאK
א א KL א א א א א
א٧٥٧א،א٪
אאא
אאאא
195
אאאאאאא K
א א א א א א א אאאא א א א
אאאאאאKאאאא
א Eא א F א א א אאאאאKאא
א א א א א Wא
١K אאא אא אאF א א א
Circuit BreakerKE
٢K אא א א א א א אאאאאאא
EאאFאאKא
٣K אאאא(duct)אאאאK
٥ J٢٩א א 1100 MVA19/345 kVאא
אאא
אאאא
196
٥ J٢٩אאא
Wאא Step Down Transformer
אאאאאאא(On Load Tap Changer)
א 15% א 1% 5%K א אאאא א א ،א א
אאאK ٥ J٧א Distribution Transformers
א א א א א Wא א Kאא א אא
אאKאאאא
אאא
אאאא
197
٥ J٧ J١אאLarge Distribution Transformer
אאאאא א א א א א א אא
א5000 kVA 20 MVA אא א 72.5 kVאאאאאא א א א א א א Kא א א
Kא٥ J٣٠אאא K
٥ J٣٠
٥ J٧ J٢אא Medium Distribution Transformer א אאאא
א5000 kVAאאא36 kVא א א א א א
אאאאאאKאאאאא אא אא אאKאא
אאא
אאאא
198
٥ J٧ J٣אא Small Distribution Transformer
אאאאאא א ٥א J٣١ א
٥ J٣٢ א Kא א א אאאאאK
٥ J٣١א
٥ J٣٢א
אאא
אאאא
199
٥ J٧ J٤אא
Dry-type Distribution Transformer אאאאא(Indoors)א
،א،אאאאא א א א א א א א
א א אא אאא א אא50 א MVA אא35 kVK
אאאאאאאאאאאאK
אאאאאאאאאKW
١K Kאא
٢K Kאא
٣K אאאא KאK
٤K Kאאא
٥K Kאאא
٦K א א אKאאא
٧K K
אאא
אאאא
200
Wאא
١. Wאאאאא א א Kאאא ،אא א
אאאאאאאאאאאא،אא
א א א אא א Kאאאא
٢. WאאאאKאאאאאא
אאKאאאאא ،א א
א א אא א א א א אאאא Kאאא א
Kא٥א J٣٣א
٣. W א א א א א א א،
א K א א א C2F6אאאK
אאאKאאאKאאא
א א א Kא Kא
א א אא א Package unitא א
א א ،אא א א א אא א א
Kא
אאא
אאאא
201
٥ J٣٣אאאא
٥ J8אFאE Voltage Taps אאאא(voltage taps)
א א אא א א א א א אא א א א א א Kא
אאאאאאאאאאאאKאאאאאEאFאאאא
אאא،אא Kאאאאא
(voltage taps) א א אא אאא א KEאFא
א א אא א א אאK٩٥א٪١٠٠אא٪٥٢٪
אKא ٥ J٣٤אאא
Kא
א
א
٢٠ ٥١٩ ١٩
٥١٨
(Termin
אאא
K
אאא
א א J٣٤K
אnal
אא
אאא ٥
א ١٢٠ ١٢٠ ١٢٠ ١٢٠
אא א
א
٤
א א אאא
א
202
٣
א
אא
٢ ٢٣ ٢٢ ٢٢
(No (On Lא
٥ J٤
א אא
אא٤٠٠٣٤٠٢٨٠٢٢٠
אא
Load Ta
Load Tap
א
١א
100%
ap chang
p Change
א
٥Jא
א
%
97.5%
95%92.5%
Bo
ger)
er)
אא
א
אoard)
א
אאא
אאאא
203
٥ J٩אא Tap Changers
אאאאאWאאא
٥ J٩ J١א No Load Tap Changer
אאא אא،א(Off Load)K
KאאאאאאFאEא
א א א K٥ J٣٥אאא
٥ J٣٦אאK
٥ J٣٥אאאא
٥ J٣٥ א א ١אא א א אא،٤א٥אא٢א
אא٤ א٦א٥٦Kא،אאאא
אאא
אאאא
204
٥ J٣٦א
٥ J٩ J٢אא On Load Tap Changer
אאאאאאאאא Kאאאאא
אאאאאאאאא
אאKאאאKאאאא
א א KאKאאא
אאא
אאאא
205
אא
١ J ؟אאאא ٢ J אאא؟אא
٣ J ؟אא
٤ J ؟Lא
٥ J ؟Lאאא
٦ J ؟Lאא
٧ J ؟Lאאא
٨ J ؟Lאא
٩ J ؟Lאאא
١٠ J Lאא؟
١١ J Lאאא؟
١٢ J א؟אאא ١٣ J Kאאא
١٤ J ؟אאאאא
١٥ J ؟א
١٦ J ؟Lאאא
١٧ J אאא؟א
١٨ J אאאא؟
١٩ J Lאאא13.8kV،138kVאאאאא؟א
אא100אAK
٢٠ J אא؟Lאאא
אאא
אאאא
206
אאא
אא א אאא?
،?אא١٩٨٨א L
אאאא١٩٨٨
L
١ J א אאSI،א١٩٨١אK
Jאאאאאא
אאאא אאLLElectrical Technology ISBN:0-07-02134-5Edward Hughes Electrical Machines
, Eddison-Weslley 1980G. R. Slemon and A. Straughan Electric Machinery
West Publishing Company, 1994.M. S. Sarma Electrical Machines and
Transformers –Principles and Applications , Prentice Hall.
P. F. Ryff, D. Platnick and J. A. Karnas
Principles of Electricity B. J. Theraga, and B. K. Theraga Electric Machinery Sixth Edition,2003
McGraw-Hill A.E. Fitzgerald, Charles Kingsely, Jr .
and Stephen D. Umans
Principles of Electric Machines and
Power Electronics,1996 P. C. Sen
