!!"# ! $#% &' !!#

#! (%) # * ! # ! + $!

, -.&!'// 01% !!&' 2 343-&3 '5 0 2

3&'430

67

&'&'

Φ= $8!!2

&'4# 0 #403$"

9

#) 5 ! !/ ! 2

&'4:&'0: 0 5 ! #$%

#9 ! # # 2 *8 !*!8 * 89;<# !*!8 *8$ 9;°49= 1># * 8 *8$ 9?;°4?=1>

# θ *8 !*!8 * 8

3&-'43-3!&-'43&-@9=1>'3 &-'43&-@?=1>'

Eje del arrollamiento de la

fase a

Eje del arrollamiento de la fase b

Eje del arrollamiento de la fase c

>

5 01 2

3&'430 &'4# 0

3!&'43&0@9=1>' !&'4# &0*9=1>'

3 &'43&0@?=1>' &'4# &0*?=1>'

#403A 2

#;## =+=•

## >19!

π=•

&'

## >19*

π=•

B9;°2 !#•

#•9;° #

• #

•9?;°

?

2

###### >19

>19 !

ππ ++=++•••

;'&# >1?*>19* =++= ππ &9'

# 9;C 9&'!&' &'9;C % ) & & ' ># D E) "()E &(5

?

A A+ 9;CF F 2

)*#

B2 9?;C4&9;C'9492 >49•4&9;G9;'4>H;4 ?4>•4 # 9;C/ # 9;C/.

$ E#• )#

• 2

)9

E ####••••

== $&9' " ! 2

;'&####### 9

9)E =++=++=++

••••••

+$%'*&'

5 7?# 7I 5 & F! F' 2

••

••

••

6 2

;JJJ ! =++•••

I

# +! 7H/! &9' ! 6%'

,-' %

5+ + 5!! $ # &' &' $!+ , &E)'&KEK)K'# $ ./0 & '+ + &7 L' # $ & .10

H

, ! ! & M' , / !E)

! " $ $

;'& 9 =++=++••••

#$%#

A &' $!2

! $ * N

#7O $@ 2

&

+

+

+

VB

a

b

c

vAVC vA

VB

VC

L

# + 2" 2 # P, ! ! ! E ) 3 3

.% & ' #% / #7; /4/7/41

#79 $@.14/07> $*.1510

Q!7;> 7 ? /! &7IH') !! "

M

, $ # /! $ &7 9' , % & "%

• , ! ! %67%&#.J'

• , &! E E ) ) ' / 7 3&.'J'

• : 7I&' $ &J4J'&.≠.'# ! $&7I!' *! &.4.' &J≠J'

&'&!'

O

6 , )E E) A 8 9;°5 ! 8&89 ( %7 3

()*** *+* *,*

# 7 H & $%# ---••• '

O ! A+/!

;JJJJ D)E ==++••••

! & ', 2

&I'.*...*...*.. )))EE)EE

•••••••••===

9;°, H# ! $ $ &I' QEEQ))Q

&'5 &!'5

;

QE QE9;° & ' >;° # !2

9

>9>; .9QE .9. E #-===

∧

5

---•

∠

•== >;, >>.

# 2

, E) > >;°# >;C()** *+ *,*

#7L $#%$#% •••

7& '6 ! / / 6R // E) 2

E)))EE)E)E J*JJJ*JJJ*JJ•••••••••

===

&'5 &!'5

!

6 / ! R // ! 2

J,4√>J7 •

−∠

•= >;, >J

# E) > >;°# >;C

.*/* / 0* ,* ** * / 123.Ω 4 **5.*'.**/ $/*)*' *+ *,* (5*'# **/ #'! '#

.*)**,*%+*/ */*/ * H;9; 0∠ 4

/*#%$'/6 •

%$0 7

(5 O;MI9;L 0∠

.*)*$/* * * * H;HH; 0∠ 4

/***6'/6 •

#%0 7

(5 ;I?> 0−∠

: %

. # ! , // ! # / # & ' $ *8)*9 **/ 1 .'5 O Q8Q!, 2

$

$$

%

%%

#

##

••

••

••

===

9

6,R)2

$

$

%

%

#

#$%#:

•••••••

++=++=

B2

! &N4NE4N)' ;=•

:

5 ! /!

;≠•

: !'5 N!

A DQQ8 ..••

= 2

:$%#

$$%%##:;<

====

-=-=-=--

+++++

==•••

••

SSES) A2

'&

'&

'&

:$$$

:%%%

:###

--=

--=

--=

•••

•••

•••

−=

−=

−=

B ND4;

5 ;>'& =

+++====

••••

:$%#;<$%# ==

=----====

) $ *8)*9**/ # 7;6 !2

$%#

$%##

$%#

$$%%##><

===

===

===

===-

++++

=++

++=

••••• 9&

5 ! &S4SE4S)' 2

;>

'& 9

=++

=•

•

#

##

;< =

=-

>

2

5 ! ;B QQ8 =•

2 BQF4#*BQ8Q BEQ84#E*BQ8Q B)Q84#)*BQ8Q

, 2

$

$<$

%

%<%

#

#<#

0

0

0

PPP

••

••

••

===

N!4N)TN 2

$ ***/

57I&!' EJ•! EB

•*

NE, E)J• E)B

• )J

•

)B•

, 2

9

9

9

%$$#$

#%%$%

$##%#

5 ! J,4U>J75 ! U>J7;%

B ;H ! .D4; # ! 9;C 6 7M / # %

000 $$%%<##< ′′′

;9

'&=

+−

=•

•

#%

%##

;< ==

==-

?

"

/! P7MJP ! # ! # !

!$/ / 6?/ *

5 7O

&

# !

00•

∠

•= >;>

I

/! +E) 2

.@ * **)*#* 0#23'/+8*/* /**/50#'0AB'0''(45#9%9$(0AB &' C9' D'0'&C9"' D'E'" C&' D'E("'!!C9"' D

+

+

+

A

B

VA

VB

VC-j6

-j6

-j6

G

H

I

10

I3

IGI

10 10

C

2+j2

2+j2

2+j2

2+j2

2+j2

2+j2

D

E

F

IRE

I1

H

.@*123.Ω ****/ */*,**)*/+ */ **/**1'23'.Ω/* 4 *)*,*)** 0. $/ *,*. $/* * *'*6 F. $/** *)*(5E"'C9 '&DG '&C9&'DηH! '!H

@ * *)*,*** *.-* /*#%$+*)*0'* * /+, *5

I5JK ϕ'"I5"JK ϕ'!I5 JK ϕ'!&

* * *+*/ $/ *F */ *(5*&!C'D

<

# ! B/ , 2

B 5V2

ω.9 = '>

9*&.9 7E

πω= '>

9&.9 7)

πω +=

'&J9 7 ϕω −= '>

9&J9 7E ϕπω −−= '

>

9&J9 7) ϕπω −+=

Potencia media por fase (Pa, Pb o Pc)

Potencia instantánea total pa+pb+pc

L

,$ 2'9& J.&' 77 ϕωϕ −−== -

'>

?9& J.&' 77EEE ϕπωϕ −−−== -

'>

?9& J.&' 77))) ϕπωϕ −+−== -

, 2

22 $%# '&'&'&'&

5! 2

L-22 $%# ϕ '&'&'&'&

# $ , ! , ! $ !

=(6(7"%

# 6

646G6EG6) 64>6, 2

W4WGWEGW) W4>W6 2

W6W6X

+=+=4

2

M2L4

M

5$ 2 646E46)4BJ V W4WE4W)4BJVV 6 2

64>BJ V W4>BJV 54>BJ

,$ 2

64√>BJ V W4√>BJV 54√>BJ# ! $ !

.<**/ / * 34+*)*-N/**

I 5L3 BL

ϕ'"*η'!#

$5LKO/' *123.Ω123.Ω

541!&!'23!'. -&'"0

ZL1

ZL1

ZL1

ZL2

ZL2

ZL2

MGenerador

U

I2

Z

Z Z

O

. A /* '5

ZC1

ZC1 ZC1

ZL1

ZL1

ZL1

ZL2

ZL2

ZL2

Zc2

Zc2

Zc2

ILCVBC

CARGA 1

CARGA 2

A

B

C

A 5123.Ω$1&93.Ω$123 .Ω0#0%0$0

' Q!J,)BE) B499;BY;Z!' ) ! J,)4M?HYOM>IZ BE)4>IL>Y*O>IZ 6)94;L[ W)949LI?>B 5)949OII9B 94;>H96)4>M9IO[ W)4*9LI>B 5)4?;>9OB 4;O?M .*/ /*5

. 6 (. * ' ** *8)*' 6 ' / ** -

**. -/ *

MZL

ZL

ZL

UUp

A

B

C

RR R

Zc

Zc Zc

CARGA

264?I\[ 4;L;Lη4O;]N,4&;G;>'ΩN 4IΩ4I;^.4I;;B6 4;;\[

2_4IΩ )49L7.4I9>?IB

9;

.*/ /'/5

. $ *,*#1F.. @*)*-* ,*. *. (**/* 'I$'#'-P%$'+- * -P#% *

ZL

ZL

ZL

3*U50Hz

IA

U'AB

U'BC

IMC

IZZ

Z

Z

A

B

C

M

A25 *E*)N,4&G'ΩN4&9?GM'Ω64;^6η4M;]4;H.KE4I9;B

J4?HM .4H>?LB )4;L>?

! 2'!') '

• , _ G ` &6,4_,J

9', 64BJ ϕ 2

(0

L(L

ϕ

, _, B ! $

• ,

• , 2

' ! ! /!

!' ) & !'

' !/ / ! /

9

' # / : .)

UR

MZL=3+j3

ZL=3+j3

ZL=3+j3

Uc

ILIR

IMA

UG

A

B

C

RR R

A:Q525 *E*) _4?;Ω a 4>;;Y;ZBb4?MIY*LIILZ

b_4?>>Y*I;Za_4L>9Y*>;Zb,4IHIY?LMHZac4HLLIYd9?Z9'# 2

' ) .J,5

!' 5J,;%.9 &'Q!. / $ #

M

U2=450V

IL

10Ω 10Ω 10Ω

50uF50uF 50uF

CARGA

ZL

ZL

ZL

U1

A

B

C

A:Q52264I;;[ 4;Oη4;MN,4&9Ω9 'ω4;;;1

2

a4?>OOBJ,4HH5)4O;O>B )4Lµ7 .K4?>II9B K4;??9

99

>'# 2

' 5cJ,

!' ^. .

' 5+ e # .

Z2

Z2 Z2

Z1

Z1

Z1

UoUG

IL

Scfpc

A2.c4H;;B.4?I;B5)4>I\B)4;OHN4&;;?MG;?M'ΩN94*9LΩ

25c4?;;IIHB J,4>?M J,K4L>9?' # 2 .9 4 H;U> B 5 ! 6,4?M;[ W,4?M;BA2

' J N,!' , 4 $.9

' , .

ZL=RL+jXL

3xU1

A

B

C

ZL=RL+jXL

ZL=RL+jXL

20Ω 20Ω

20Ω

20Ω 20Ω

20Ω

60Ω 60Ω

60Ω

CARGA

U2

2N,4&G'Ω `,4?;Ω .49O9?B .49OMLB

9>

I' : ! 2J,.cEJEJ) 5c

-j30Ω

-j30Ω -j30Ω

MZL

ZL

ZL

U=380V IMBUGAB

A

B

C

ILA

I1C

A:Q525 *E*)N,49G9Ω264L;;[ ϕ4;Oη4;M

b,49;HYI;OZ acE4>>Y?>Z bE4>HY*LIM?Z b)49O?YM;Z