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2 (Coupled) 2 1. (Power Transformer) 2. (Variable Frequency Transformer) (Coil) (Ferromagnetic Core) 2 (Primary Winding) (Secondary Winding) 2.1

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Page 1: บทที่ - iee.eng.kmutnb.ac.thiee.eng.kmutnb.ac.th/web/personal/swr/ElectricalMachinelesson2.pdf · ®¨´ µ¦Á ¦ºÉ° ´ ¦ ¨Å¢¢oµ Á¨n¤ 1 50 »ª´ r ¦° ¨

2

(Coupled) 2

1. (Power Transformer)

2. (Variable Frequency Transformer)

“ ”

(Coil) (Ferromagnetic Core)

2 (Primary Winding)

(Secondary Winding)

2.1

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1 50

.1885

William Stanley ( .1858-1916) 2.1

2.1

( )

(Lenz’s Law) (Faraday’s Law)

2.2

2.2 Coil 1

Coil 2

Coil 2

1 1 (+)

Coil 1 ( )

( )

1.8 1

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2 51

= = (Volt) (2.1)

2.2

(Volt) (2.2)

2.2

-

( 2.1)

2.2 1

(Primary Winding)

(Secondary Winding) 1 2.3

2.3 1

2.3

(Leakage Flux)

1 2 Core-type

Shell-type 2.4 2.5

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1 52

2.4 1

(Laminated Core)

Core-type L 2.5 .

Shell-type E I 2.5 .

. Core-type

. Shell-type

2.5 1

HV

LV

LV

HV

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2 53

2.3

2.6

2.6 .

(Exciting Current ; )

2 - 5% ( 5% )

Mutual

Flux ( )

Primary =

2.6 . ( )

( = )

2.1 ( )

+, - (Dot, )

(+) (-) ( ) + 2.6

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1 54

2.4

2.7

(Ideal Transformer)

(No Load Test)

(Open Circuit Test)

(Short Circuit Test)

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2 55

2.5

2.8

2.8 . (Leakage Flux)

= +

=

1 1.8

1 1.8 ( 1.20)

= , = (2.3)

Page 8: บทที่ - iee.eng.kmutnb.ac.thiee.eng.kmutnb.ac.th/web/personal/swr/ElectricalMachinelesson2.pdf · ®¨´ µ¦Á ¦ºÉ° ´ ¦ ¨Å¢¢oµ Á¨n¤ 1 50 »ª´ r ¦° ¨

1 56

. . 1.21 1

.

2

( ) Core-loss

Current Magnetizing Current

2.8 .

= + , = , = , = + (2.4)

cos (Power Factor ; )

(Core Loss ; )

= = = = (2.5)

2.1 2.8 . ( ) 264

( ) 220 50

Leakage Flux

. ( ) 25 .

( )

. ( ) 50 W, Apparent Power [S, (VI)rms] 500 VA

Exciting Current ( ), Core-loss Current ( ), Magnetizing Current ( )

.

. = 25 cm

= = 220 V

2.3 ; = 2 =

= 2

= 2 = 220 2 (264)(50)(25 × 10 ) = 1.5 T

= .

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2 57

. , , = 50 W, ( ) = 500 VA

2.8 . 2.8 .

= ( ) = = 2.273 A

= , = = = 0.2273 A

= = 2.273 0.2273 = 2.262 A

=( )

= = 0.1

= . , = . , = . , = .

.

= =.

= 968 , = =.

= 97.3

= , = .

2.6

(Transfer)

Leakage Flux

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1 58

2.9

2.3

= = 2 ……………….. (1)

= = 2 ……………….. (2)

( )( )

; = = = …………………. (3)

Turn Ratio Voltage Ratio

2.9 .

2.9 . + + = 0

( = 0) =

= ……………………………… (4)

(3) (4)

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2 59

= = = = (2.6)

2.6 Referred

2.6 ; = =

( ) = ( ) (2.7)

Referred Referred

(Impedance ; ) (Admittance ; )

2.10 Referred

2.10 Referred

. Referred

.

2.10 . ; = , =

2.6 ; = , =

= = =

= (2.8)

Referred Referred

Referred

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1 60

= (2.9)

Referred

2.8, 2.9 ,

Referred , Referred 2.10

= , = (2.10)

2.7

(Polarity)

(Dot, )

1 3

2.11

2.11 ( ) . ( 1

3 ) 2 4 ,

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2 61

1

3 (+) ( ) .

( ) ( )

.

.

(Subtractive Polarity)

= | | (2.11)

2.12

2.12 ( ) . ( 1

4 ) 2 4 ,

1 4

(+) ( ) .

( ) ( )

.

.

(Additive Polarity)

= | + | (2.12)

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1 62

2.11 2.12

2.13

2.13 2 4

1

,

1. = | | ( ) 3 (

2.11)

2. = | + | ( ) 4 (

2.12)

1

2.14

( ) .

2.14

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2 63

2.8

(Practical Transformer)

2.15

N2

.

+

-

+

-

+

-V1 E1 E2

+

-V2Load

Ideal Transformer

.

l1 l2

+

-

E1

+

-

+

-

V2

+

-

V1

R2R1 X l1 X l2

Primary Secondary

Primary Secondary

R c1 X m1

Im1Ic1

I

E2

I 2

I2

I 1

N : N or E : E or a1 21 2

m

N1

I 1 I 2

2.15

,

(Reactance) Leakage Flux

(Reactance) Leakage Flux

, Referred

(Ideal Transformer)

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1 64

Referred

Referred , Referred

,

2.15 . Referred

2.16

Ideal Transformer

+

- a

+

-

V2

+

-

V1

R1 X l1

Primary Secondary

X l2 R2

V2

R c1 X m1

Im1Ic1

I I 2I2I 1

. Referred

Ideal Transformer

+

-a

+

-

V2

+

-

V1

Primary Secondary

I 2I 1

. Referred

R1 X l1 R2X l2

I1

Ic2 Im2

R c2 X m2

V1

I

2.16 Referred

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2 65

2.15 . Referred (Parameter) -

Referred ,

2.16 .

Referred 2.8

= , =

2.15 . Referred (Parameter) -

Referred , ,

, 2.16 .

Referred 2.10

= = , = =

= , =

2.2 (Distribution Transformer)

50 kVA, 2200 220 V, 50 Hz (HV) 0.75 + 0.95

(LV) 0.007 + 0.009 = 310 + 44.6

(Referred LV)

. Referred HV

. Referred LV

= 2200 220 = 10

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1 66

. Referred HV

Referred 2.8

+ = ( + ) = 10 (0.007 + 0.009) = 0.7 + 0.9

= =

= ( + ) = 10 (310 + 44.6) = (31 + 4.46) × 10

. Referred LV

Referred 2.10

+ = ( + ) = (0.75 + 0.95) 10 = 0.0075 + 0.0095

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2 67

2.9

2.8 Referred

2.16

T-Circuit

(Approximate Equivalent Circuit)

Referred 2.16 .

2.17 .

( , ) 2.17 .

+

-

+

-

V1

R1 X l1 X l2 R2

V2R c1 X m1

Im1Ic1

I I 2I 1

. Referred

+

-

+

-

V1

R1 X l1 X l2R2

V2R c1

Im1Ic1

II 2

I 1

. , Xm1R c1 V1

X m1

2.17

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1 68

2.17 . 2.18 . + = , + = , + =

(Equivalent Resistance) Referred

(Equivalent Reactance) Referred

(Equivalent Impedance) Referred

.

.

2.18 Referred

2.19 Referred

2.19 Referred

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2 69

2.10

2.18 .

2.19 .

Referred ( 2.18 .)

Referred ( 2.19 .)

2.10.1

(No Load Test, Open Circuit

Test) ( )

, 2.20 .

+

-

. .

Primary Secondary

Transformer

WA

VVoc

IocPoc

P = Pc oc

Voc

Ioc

R c1 X m1

Y

2.20

2.20 . ( )

( )

( , , )

, .

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1 70

.

= , = , = (2.13)

= , =

2.10.2

(Short Circuit Test)

, Referred

, 2.21 .

2.21

2.21 .

, , ,

.

= , = , = (2.14)

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2 71

2.3 1 10 kVA, 200 1000 V, 50 Hz

= 0.04 + 0.3 (Referred )

1000

. = 1 . = 0.8

= 200 1000 = 1 5

( ) = 1000 V, ( ) = , ( ) = 10000 1000 = 10 A

= = (1000) = 200 V, = = = = 50 A

. = 1

= cos ( ) = cos 1 = 0° = 1000 0° V, = 10 0° A = 200 0° V, = 50 0° A

1 Complex Number

= + + = 200 0° + (0.04 + 0.3)(50 0°)

= 200 + 2 + 15 = 202 + 15 = 202.56 4.25° V

= .

2 Phasor Diagram

Phasor Diagram

= + + = + +

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1 72

V2

V1

R eq1I2

I 2 Xeq1

I 2

= (50)(0.04) = 2 V

= (50)(0.3) = 15 V

Phasor Diagram

= + + = (200 + 2) + (15) = 202.56 V

= .

. = 0.8

= cos ( ) = cos (0.8) = 36.87°

= 1000 0° V, = 10 36.87° A

= 200 0° V, = 50 36.87° A

1 Complex Number

= + + = 200 0° + (0.04 + 0.3)(50 36.87°)

= 200 + (0.3027 82.41°)(50 36.87°) = 200 + 15.135 45.54°

= 200 + 10.6 + 10.802 = 210.6 + 10.802 = 210.88 2.94°

= .

2 Phasor Diagram

Phasor Diagram

= + +

Req1

I2

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2 73

= cos = (50)(0.04) cos 36.87° = 1.6

= = sin = (50)(0.04) sin 36.87° = 1.2

= = sin = (50)(0.3) sin 36.87° = 9

= cos = (50)(0.3) cos 36.87° = 12

Phasor Diagram

= ( + + ) + ( )

= (200 + 1.6 + 9) + (12 1.2) = 210.88 V

= .

2.4 1 50 kVA, 2200 220 V, 50 Hz

= 0.0272 + 0.0348 (Referred )

= 0.9

(Feeder) 1.68 + 3.12

2200

= 2200 220 = 10

Referred Feeder

= = = 10 (0.0272 + 0.0348) = 2.72 + 3.48

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1 74

+

-

a = 10

1.68 + j3.12 +

-

Load

Primary Secondary

V2

I 1

I 2I 2Feeder

(2200 V) 0.9 Leading

2.72 + j3.48Vs V2

+

-

Req1 Xeq1

a = 10

+

-

Load

Primary Secondary

V2

I 2I 2

0.9 Leading

4.4 + j6.6

V2

+

-

+

-

I 1

(2200 V)Vs

R X

( ) = 220 V, ( ) = , ( ) = 50000 220 = 227.3 A

= = (10) , = 10, = = = . = 22.73 A

= cos ( ) = cos (0.9) = 25.84°

= 0° V, = 227.3 25.84° A

= 0° V, = 22.73 25.84° A

1 Phasor Diagram

Phasor Diagram

= + +

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2 75

= cos = (22.73)(4.4) cos 25.84° = 90

= = sin = (22.73)(4.4) sin 25.84° = 43.6

= = sin = (22.73)(6.6) sin 25.84° = 65.4

= cos = (22.73)(6.6) cos 25.84° = 135

= ( + ) + ( + )

(2200) = ( + 90 65.4) + (43.6 + 135) = ( + 24.6) + (178.6)

= (2200) (178.6) 24.6 = 2168 = 10 = 2168 10 = 216.8 V

= .

2 Complex Number

= + + , = 0° + ( + ) 25.84°

2200 = 0° + (4.4 + 6.6)(22.73 25.84°)

2200 = 0° + (7.932 56.31°)(22.73 25.84°)

2200 = 0° + 180.294 82.15°

2200 cos + 2200 sin = ( + 24.625) + 178.6

+ 24.625 = 2200 cos ………………………….. (1)

2200 sin = 178.6 ………………………………………. (2)

(2) ; sin = 178.6 2200 , = 4.66°

(1) ; + 24.625 = 2200 cos 4.66° , = 2168

= 10 = 2168 10 = 216.8 V

= .

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1 76

2.11 Voltage Regulation

Voltage Regulation

(

) Voltage Regulation

2.22 Voltage Regulation

% = , ,

,× % (2.15)

,

,

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2 77

2.22 . Referred

% = , ,

,× 100%

2.22 . = 0 = 0

, = % Voltage Regulation 2.16

% = | | ,

,× % (2.16)

2.16 % Voltage Regulation | |

2.22 . (Locus)

PF + = 0

% Voltage Regulation PF

Lagging PF ( ) )

% Voltage Regulation PF (cos )

% Voltage Regulation ±5%

% Voltage Regulation PF 2.23

2.23 %Voltage Regulation PF

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1 78

2.5 1 10 kVA, 2200 220 V, 50 Hz

= 10 + 30 (Referred )

( , ) 220 % Voltage Regulation

. 80% = 0.6

. = 0.6

= 2200 220 = 10

. 80% = 0.6

= (0.8) (10 × 10 ) 2200 = 3.636 A

= cos ( ) = cos (0.6) = 53.13°

= = (10)(220) = 2200 V

= 0° = 2200 0°, = 53.13° = 3.636 53.13°

= + + = 2200 0° + (10 + 30)(3.636 53.13°)

= 2200 0° + 36.36 53.13° + 109.08 90° 53.13°

= 2200 + 21.816 29.089 + 87.264 + 65.448

= 2309.08 + 36.359 = 2309.37 0.9°

= 2309.37 V

% = | | ,

,× 100% = . × 100% = 4.97%

% = . %

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2 79

. = 0.6 = (10 × 10 ) 2200 = 4.545 A

= cos ( ) = cos (0.6) = 53.13°

= = (10)(220) = 2200 V

= 0° = 2200 0°, = 53.13° = 4.545 53.13°

= + + = 2200 0° + (10 + 30)(4.545 53.13°)

= 2200 0° + 45.45 53.13° + 136.35 90° + 53.13°

= 2200 + 27.27 + 36.36 109.08 + 81.81

= 2118.19 + 118.17 = 2121.48 3.19°

= 2121.48 V

% = | | ,

,× 100% = . × 100%

3.57%

% . %

2.12

( -

) (Efficiency ; )

95%

= × % = × % (2.17)

2.24 Referred

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1 80

2.24

= ( ) 2.25 .

= 2.25 .

= cos

= × % (2.18)

2.25 .

. .

2.25

2.12.1

2.25

( )

= = cos

=( )

= 0 = 0 =

c

cu

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2 81

( )

2.19 = 2.25 .

= = , , (2.19)

= =

= ( ) ( )

= 0 sin = 0, = 0°

= cos 0° = 1

( )

2.20

= , , (2.20)

=

=

2.6 1 10 kVA, 2200 220 V, 50 Hz

(Referred ) = 100 W

80% PF = 0.6 Lagging

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1 82

= %%

( ) ( ) = (0.8)(10000) 220 = 36.36 A

= %%

( ) ( ) = %%

(10000)(0.6) = 4800 W

= 100 W

= = 36.36 (0.104) = 137.5 W

= × 100% =.

× 100% = 95.29%

= . %

2.12.2

(All-day Efficiency ; ) (Energy)

24

(%Load)

= × % (2.21)

(kWh) ( kW)

( hr)

% = ( )( )

× 100% =,

× 100%,,

= %%

= %%

( ) ( )( )

= +

24 = ( )(24 )

= ( )( ) = ( ) = ,

,( )

= ,

,( ) =

,, ( )

= %% , ( )

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2 83

2.7 1 50 kVA, 2200 220 V, 50 Hz

= 200 W = 500 W

24

% 0% 50% 80% 100% 110%

1 0.8 0.9 1

6 8 5 3 2

( )

24 = (50)(1)(8) + (50)(0.8)(5)

+ (50)(0.9)(3) + (50)(1)(2)

= 605 kWh

24 = (0.2 )(24 ) = 4.8 kWh

24 = (0.5)(8) + (0.5)(5)

+ (0.5)(3) + (0.5)(2)

= 5.31 kWh

24 = 4.8 + 5.31 = 10.11 kWh

= × 100%

=.

× 100% = 98.36%

= . %

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1 84

2.13

(Autotransformer)

2.26

2.26

= = = , = (2.22)

( )

2.8

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2 85

2.8 1 2 100 kVA, 2000 200 V

kVA

= = 2000 V, = + = 2200 V

= = 100 × 10 2000 = 50 A

= = = 100 × 10 200 = 500 A

= + = 50 + 500 = 550 A

= = (2000)(550) = 1100 kVA

= = (2200)(500) = 1100 kVA

= =

kVA 100 kVA

2.8 kVA 1100 kVA

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1 86

2.14 Per-unit

Per-unit (Per-unit ; pu)

(Base, Reference)

= ( ) (2.22)

Per-unit

1.

2. Referred

)

Per-unit 1

1 2.1

2.1 1

, , = = 1

, = = 1 , = = 1

, =,

= 1 , =,

= 1

, = ,

,= , = 1 , = ,

,= , = 1

Referred Referred

, = , = , , , = , = ,

, = , = , , , = , = ,

, = , = , , , = , = ,

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2 87

, ,

= , , = ,

, =,

, , =,

=,

=,

, = , Referred

Referred

, = , , , = , , , = , , , = , , = , , , = ,

Per-unit 100

2.9 1 10 kVA, 2200 220 V, 50 Hz

= 10 + 30 (Referred )

.

.

. 80% = 0.6 -

% Voltage Regulation

= 2200 220 = 10

. , , = = 10 kVA, , = = 2200 V

, = , = = 484

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1 88

, =,

= = 0.02066 + 0.062

.

, = , = , = 1

, = , , = (1) (0.02066) = 0.02066

= , = (0.02066 )(10000) = 206.6 W

, = . , = .

, = ,

. 80% = 0.6 -

% Voltage Regulation

, = , = 1, , = , = , = 0.8

= cos ( ) = cos (0.6) = 53.13°

, = 1 0°, , = 0.8 53.13°

, = , + , , = 1 0° + (0.02066 + 0.062)(0.8 53.13°)

= 1 + 0.01653 53.13° + 0.0496 36.87°

= 1 + 0.00992 0.01322 + 0.03968 + 0.02976

= 1.0496 + 0.01654 = 1.04973 0.9°

% Voltage Regulation ( 2.16)

% = | | ,

,× 100% = , , ,

, ,× 100%

= . × 100% = 4.97%

% = . % 2.5 .)

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2 89

2.15 3

3 120°

2 (Star, Wye ; Y) (Delta ; )

2.27 .

2.27

, , 120°

.

= = =

, , 120°

. 3

= = = = 3

30° . 30°

30° 30°

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1 90

2.28 .

A

C B

VABVABVCA VCA

C

A

BVBC

VBC

. .

2.28

, ,

120°

= = = =

3 1 3

( 3

1 3 3

3

3 3

1.

2. Y

3. 1

58% Open-delta (V )

4. Y 3

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2 91

2.15.1

. .

A

C

B

a

b

c

A

a b c

B C

A

B

C

a

bc

VAN

VBN

VCN

VABVCA

N

CC

AA

B BVBC

VAB

30

. . .

N

Vab

Vbc

Vca Vab

a

b

c

V2V1

I

aIV

V3 V

3 a

3 aI

2.29

3 Voltage Ratio 2 ( , )

( ) Voltage Ratio Voltage Ratio 1

2.29 . ( )

= =

= = 3 = 3

= ( ) (2.23)

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1 92

Referred 3

Referred Voltage Ratio ( , ) Referred

Voltage Ratio ( )

Referred Voltage Ratio

Voltage Ratio Referred

2.29 .

30° Polarity 2.29 .)

2.15.2

. .

A

C

B

a

b

c

A

a b c

B C

A

B

C

a

bc

VAB

VCA

C

A

BVBC

VAB

30

. . .

n

Vab

Vbc

Vca

Vaba

bc

V2V1

I

V I3 V

a

aI3

aI3

3 Va

Van

Vbn

Vcn

a

c b

n

2.30 Y

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2 93

2.30 . ( )

= =

= = 3 = 3

= ( Y) (2.24)

2.30 .

30° ( Polarity 2.30 .)

2.15.3

2.31

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1 94

2.31 . ( )

= =

= = =

= ( ) (2.25)

2.31 .

( Polarity 2.31 .)

2.15.4

. .

A

C

B

a

b

c

A

a b c

B C

A

B

C

a

bc

VAN

VBNVCN

VABVCA

N

CC

AA

B BVBC

VAB

. . .

N

Vbc

Vca

Vab

a

b c

V2V1

I aI

V

V3

V3 a

n

Va

a

c

Vab

b

Van

VbnVcnn

2.32 Y

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2 95

2.32 . ( )

= =

= = 3 3 =

= ( Y) (2.26)

2.32 .

Polarity 2.32 .)

2.15.5 Referred

Referred 3 1

2 Referred Referred

1. Referred Voltage Ratio -

( ) Referred

2. Referred Voltage Ratio -

( ) Referred

.

A

B

C

a

b

c

. Referred

A

B

C

a

b

c

Z eq2Z eq2

Z eq2Z L

Z L

Z L

Z eq1

Z eq1

Z eq1

Z L

Z L

Z L

2.33 Referred 3

Voltage Ratio ; = =

Voltage Ratio ; = = 3

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1 96

2.15.6

3

(Y)

( )

. .3

2.34 Y

= (2.27)

2.15.7 3

3 1

3

3

2 Core-type Shell-type

1. Core-type

Core-type 2.35 1 Core-

type 3 .

, , 120° + + = 0

. B

. .

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2 97

. .

. .

2.35 3 Core-type

2. Shell-type

Shell-type 1 Shell-type 3

2.36

2.36 3 Shell-type

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1 98

1 Shell-type

2.36 2.37 Shell-type 5-leg

2.37 3 Shell-type 5-leg

2.2 3

Connection Connection

Voltage Magnitude = 3 =

Current Magnitude = = 3

Apparent Power (S) VA = 3 = 3

Active Power (P) W = 3 cos = 3 cos

Reactive Power (Q) VAR = 3 sin = 3 sin

Equivalent Y (Balanced Phase) = 3

3-phase Y Transformer = 3 , , , , 30°

3-phase Y Transformer = 3, , , , 30°

3-phase , Y Y Transformer = , , ,

Polarity 30° 0°, 30°, 150°, 180°,

330° Vector Group)

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2 99

2.10 1 40 kVA, 2400 240 V

= 1.83 (Referred )

3 3

Feeder 3 -

= 0.8 /phase ( Feeder) Feeder

3 , 500 kVA, 24000 2400 V( )

= 2.76 /phase (Referred )

24000 V( )

3 240 V ( )

Feeder 2400 V 2400 240 V

240 V

.

2400 V 24000 V 240 V

24000 V

j0.8

j0.8

j0.8

I1 I4I3

I2

j1.83

j1.83

j1.83j2.76

j2.76

j2.76

Trans.1Trans.2

.

Trans.1 = = 2400 240 = 10

Y , = 1.83 3 = 0.61

Trans.2 = 24000 2400 = 10

Y , = 2.76 3 = 0.92

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1 100

.

2400 V 24000 V 240 V

24000 V

j0.8

j0.8

j0.8

I1 I4I3

j0.61j0.92

Trans.1Trans.2

j0.61

j0.61j0.92

j0.92

2400 V N

.

j2.33

I1

0 V0 V

0 V

.

2400 V3

2400 V3

Trans.2 24000 2400 V( )

24000 V( ) 2400 V( ) Y

2400 3 V .

Feeder 2400 V Y 2 Neutral (

) Neutral

0.92 + 0.8 + 0.61 = 2.33 .

= 2400 3 2.33 = 594.7 A

, , .

= 3 = 594.7 3 = 343.35 A

= = (10)(343.35) = 3433.5 A

= 3 = 3(3433.5) = 5947 A

= . , = . , = . , =

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2 101

2

1. ( ) 55

( ) 220 ( ) 2

Leakage Flux

. , Core-loss Current ( ) Magnetizing Current ( )

.

. = 0.125 , = 0.25 A, = 1.984 A

. = 880 , = 110.9

2. 1 100 kVA, 220 1100 V, 50 Hz

(LV) 0.011 + 0.031 (HV) 0.25 + 0.75

= 440 + 260 (Referred LV)

. Referred HV

. Referred LV

+

-

+

-

V2

+

-

V1

R1 X l1 X l2 R2

V2

R c1

Primary (LV) Secondary (HV)

0.011 + j0.031 0.01 + j0.03

Xm1

a = 1/5

440 + j260

.

.

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1 102

3. 1 440 220 V, 50 Hz

Test Voltage (V) Current (A) Power (W)

Open Circuit 220 2.5 100 220 V

Short Circuit 30 22.75 209.1 440 V

. Referred . Referred

. .

4. 1 10 kVA, 2400 240 V, 50 Hz

= 6 + 30 (Referred )

= 0.8

240 % Voltage Regulation

2347.8 2.81° V, 2.175%

5. 1 24 kVA, 2400 240 V, 50 Hz

= 6 + 30 (Referred )

= 1

2400 % Voltage Regulation

232.12 V, 3.4%

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2 103

6. 1 500 kVA, 2300 230 V, 50 Hz

= 0.174 + 0.4 (Referred HV)

= 2351 + 246 (Referred HV) = 1

HV 2300

1137 A, 98.3%

7. 1 10 kVA, 2400 240 V, 50 Hz

= 100 W = 240 W

24

% 0% 70% 90%

0.8 0.9

6 10 8

( )

95.93%

8. 4 pu (Referred

) 4 % Voltage

Regulation 4

2.175%

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1 104

9. 1 440 110 V 3 3 Y

Feeder 3 = 1.6 /phase (

Feeder) (Resistive

Load) (Line) 50

= 0.5 (Referred )

Feeder 432 V( )

173.76 V( )

10. 1 2200 220 V 3 3

Feeder 3 = 2 /phase (

Feeder) R-L (Line)

433 218 V( )

Feeder 3880 V( ) = 0.01

(Referred )

PF

0.606

11. 1 10 kVA, 1330 230 V 3 3

Feeder 3 = 0.8 +

5 /phase Feeder 3 = 0.003 +

0.015 /phase 3 27 kVA, 0.9

230 V( ) = 0.12 + 0.25

(Referred )

Feeder

2437 V( )