Geometry of the transformer phasor diagram

Appendix 2 Geometry of the transformer phasor diagram

The following diagrams and equations apply equally well to single-phase transformers and to the individual phases of polyphase transformers. Specification data V1

V2 Ii

/2 n (=N1/N2=E1/E2) COS~2

primary terminal voltage secondary terminal voltage load component of total primary current total primary current secondary load current turns ratio secondary load power factor

Test data RI R2 I'2Z'e 12Z"e

/0 I"0

Pf

primary resistance secondary resistance total equivalent impedance voltage drop (referred to the primary side) total equivalent impedance voltage drop (referred to the secondary side) primary no-load current secondary no-load current iron loss

For the phasor diagram see Fig. A2.1. Voltage drops due to no-load current are ignored. 833

834

Appendix 2

V~

Z~R~

REFERRED TO PRIMARY SIDE /I

i,,f•, 7",<"Io

'I c

I

REFERRED TO SECONDARY

"" '

SIDE

V2

~[v;,

12X'~

Figure A2.1 Phasor diagram for no-load and for load conditions

f,

~

u

e5

i!

N

......

~o 'Jr--

~

,A u

a

,.,,

U u.J

'-"

Appendix 2

I-"

~.0 u.J aC.

835

rb. u

e.,

u

or) tO -0 cO 0 0

0

s_ .m

s._ 0 cOO

E

o

01

0

-0

in o4

cD

o4

LL

836

co

-~ ~_ ~ >,

II

~

Appendix 2

~,-

II .~'-

~

E

.C_

'-'~I

c

o

O0

+

+

+

.c_

o

O0

+

+

+

II

a; I

-o IIo

..o

o~

-~

II

o

II

o

o

c

~' O0 0

~ "~II

+

+

0

+

+

.o +

C 9- -

I1."II ~o ~-.v o

~

.o

II

E

0

T

--~

m

._~

o

m

T

+

~

--

00~176176

o

~0

+

~ - -II

o

o

~

~~

~0

II

~II

oo

~_

~--~

II

~~

_,_

,_._

8 ~00 ~

~0 .~-o~, -o~, ~,~ -Oo ~ d~o o ~,o~_>, >,o ~ ~> , > , - ~ , _ o _

~.-o

II

~ ~ ~II

~ ~~ c

~, ~9 --

_

II -.o

-~ ~, o

=o_._.,..~:E.~176162176

II + ~,,.-

CC

Ix

II

II

II

~ed

~:[x

o r

>,~.___

~

~cy

~ II

II -~

>

>,-~=~176176

~

~"

~

~

~

II

II

I1

II

~

~1

~

~

I~

>

5 ~ -~

>

5o ~

~3

I'--

O4 I--

+ O4

o

II

nL

#.8

I

C

~

To ~

~-,__

.C

§

o o

I

c o

c~

,-*

CO

E o.~-~.~.~8--~ 8--~ XS- ~ 0_00 .. .~ ,~-S#- ,~-S .E-S:~ (Xi CO

c~

#-$c$ INN

c

c

T T 4--

!,...

Od

o o

ss?.7

o o

T T o o

(1)

+

O

-.

0

7

It- TC

"

v

~-(XI

~

:2~ o

lot)

"--

o

oo

I

~

O~ 0 ~-- 04 v

Appendix 2

(3 v

837

838

1}

8

P: {:} {,3 {b (O

{,3

8

Appendix

o o

2

+

NBJ

+

II

{1} ~

N

+

~

~

-t-

--.Oa

--

II

"~

oi

(6

II

~

{d

{5

II

:~}

{d

{6

II

~

G T '" T '"

~

~

~

~

~.

::} +

~ "-

~-_.

T

.~ e} "~ O

r

o ~ o ~

II I::I:: ~

v

O

T

~~

";"

T .~ o

o

o

(I) i... i._

..i.-, (-.

o~

o {.-

(I) i,..

{~ 0

IN

--. {xl

+

";"

.,~ ~ . . . .

t":"

o

..{~

"-

-a} .~

v

G} O'}

+

v

~

-:3

!:::: {1}

I"-

~

I:~

(1}

{3

~ .--

v

a}

{l}

~

~

{O

o {~

{l}

~ .

~o

v

~ ~

~-"

~

~

.

-a

~

o {~

Bl {{ "-i.l_

.~

.

v

.~_

o

.

~"

{-

~

v

-~

.

.~ -a

Or)

o

v

~O4

~ -a .~, ~--a ~ ~--a v