LECTURES 4 AND 5 THREE-PHASE CONNECTIONS (1)

Copyright © 2017 Hassan Sowidan

ECE 330

POWER CIRCUITS AND ELECTROMECHANICS

LECTURES 4 AND 5

THREE-PHASE CONNECTIONS (1)

Acknowledgment-These handouts and lecture notes given in class are based on material from Prof. Peter

Sauer’s ECE 330 lecture notes. Some slides are taken from Ali Bazi’s presentations

Disclaimer- These handouts only provide highlights and should not be used to replace the course textbook.

9/4/2017


WHY THREE-PHASE?

• Most effective in terms of equipment and wires.

• Produces smooth rotating magnetic field.

• Constant instantaneous power.

9/4/2017 2


THREE-PHASE VOLTAGES

• The three phases are usually referred to as abc.

• Another standard notation is RYB (Red-Yellow-Blue).

• Voltages:

– Same magnitude.

– Same frequency.

– Out of phase by 120o.

9/4/2017 3

a

a'

+

-

b

b'

+

-

c

c'

+

-



• Positive-sequence voltages are most common (abc).

• Negative-sequence voltages, flip b and c (acb).

9/4/2017 4

'

'

'

( ) cos ( )

( ) cos ( 120 )

( ) cos ( 120 )

aa m

o

bb m

o

cc m

v t V t

v t V t

v t V t

'

'

'

02

1202

1202

omaa

ombb

omcc

VV

VV

VV

'

'

'

( ) cos( )

( ) cos( 120 )

( ) cos( 120 )

aa m

o

bb m

o

cc m

v t V t

v t V t

v t V t

'

'

'

02

1202

1202

omaa

ombb

omcc

VV

VV

VV



• If phase a has angle θv , the positive sequence is (you

practice the negative sequence):

• Phasor representation:

9/4/2017 5

'

'

'

( ) cos( )

( ) cos( 120 )

( ) cos( 120 )

aa m v

o

bb m v

o

cc m v

v t V t

v t V t

v t V t

'

'

'

2

1202

1202

maa v

ombb v

omcc v

VV

VV

VV

Vaa’

Vbb’

Vcc’

-120o

+120o

+θv

Positive

Sequence

Vaa’

Vcc’

Vbb’

-120o

+120o

+θv

Negative

Sequence


THREE-PHASE CONNECTIONS

• In general, positive sequence is used unless

otherwise specified.

• Two main connections:

– Wye (Y)

– Delta (Δ)

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a

a’

+-

b’ b

+-

c’

c

+

-

Delta

Connection

b

-+

c +-

a

n

+

- Y

Connection


PHASE AND LINE

• Phase voltage (Vø) and phase current (Iø) are

defined across an element:

• Line-to-line (or line) voltage (Vll) and line current

(Il) are defined on the line:

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+

Vφ

-

Iφ

Load

Iφ

Source

+

Vφ

-

+

-

Il+

Vll

-

+

Vll

-

+

Vll

-

Il

Il

a

b

c


THREE-PHASE CONNECTION

WYE CONNECTION:

The three windings are represented by coils. In the wye

connection, terminals , , and are joined and

labeled as terminal , also called the neutral terminal

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a b c

n


THREE-PHASE CONNECTION

DELTA CONNECTION:

In the delta connection, terminal is connected to , and

to Finally, can be connected to terminal .

The voltage across and is

identically equal to zero

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a

= ( ) ( ) ( )ac aa bb ccv v t v t v t

c

b

c

b

a


Y-CONNECTION

• Voltages can be line-to-line (Vll) or line-to-neutral (Vln).

• Currents can be line (Il) or phase (Iø).

• Line-to-line voltages can be referred to as line

voltages (Vl).

• Line-to-neutral voltages can be referred to as phase

voltages (Vø).

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Y-CONNECTION

• Line-to-line voltages are vab , vbc , and vca .

• Line-to-neutral voltages are van , vbn , and vcn which

are also

• Example: and so on.

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0 , 120 , 120 .o o o

an bn cnV V V V V V

b

-+

c +-

a

n

+

-

ia

in

ibic

van

vbn

vcn

ab an bnV V V

bc bn cnV V V

c a cn anV V V


Y-CONNECTION

• Thus:

9/4/2017 12

0 120

120 120

120 0

o o

ab

o o

bc

o o

ca

V V V

V V V

V V V

Vab

Vbc

Vca

+30o

Vbn

Van

Vcn

| | 3 | |ll

l

V V

I I

3 30

3 90

3 150

o

ab

o

bc

o

ca

V V

V V

V V


Y OR ∆ CONNECTION?

9/4/2017 13



In distribution, the secondary winding is often in wye,

as it provides a neutral for single or three phase loads.

The primary is often in delta, as it allows 3rd

harmonics to flow within the transformer and prevent

it flowing into the supply.

9/4/2017 14



• In Y connection, voltage across each coil is smaller than the

line voltage, so it is preferable where high line voltage are

used as in high voltage power systems, to protect coils from

high voltage.

• In delta connection current passing through coils are smaller

than line currents, therefore coils can be rated for smaller

current.

9/4/2017 15


Y-SOURCE, Y-LOAD

9/4/2017 16

: 0 3

an a n n

bn b n n

cn c n n

a b c n n

V I Z I Z

V I Z I Z

V I Z I Z

add I I I Z I Z

-++

-

+

-

nL

Z

Z Z

Zn

Ia

IbIc

In

+

Van

--

Vbn+ -

V cn

+

n

,

3 0

0

, ,

a b c n

n n

n

an bn cna b c

but by KCL I I I I

I Z Z

I

V V VI I I

Z Z Z


Y-SOURCE, Y-LOAD

• For a load impedance

9/4/2017 17

,Z Z

0

120120 120

120120 120

ana l

o

o obnb l

o

o ocnc l

VVI I I

Z Z

VVI I I

Z Z

VVI I I

Z Z


Y-SOURCE, Y-LOAD

9/4/2017 18

3

* * *

* * * *

* *

* *

, 0 . .

( )

a b c n n

an a bn b cn c

an a bn b cn a b

an cn a bn cn b

bc b ca a

S S S S S if S i e balanced load

V I V I V I

V I V I V I I

V V I V V I

V I V I


Y-SOURCE, Y-LOAD

9/4/2017 19

3

3

3

3 90 120 3 150

3 1 30 1 150

3 3 cos 3 sin

3

3

o o o

o o

ll l

S V I V I

V I

V I j

S V I

S V I


Y-SOURCE, Y-LOAD

• Therefore,

• Note that (Vll) can also be written as (Vl).

9/4/2017 20

3

3

3

3

3 cos( )

3 sin( )

ll l

ll l

ll l

S V I

P V I

Q V I


READING MATERIAL

9/4/2017 21

• Reading material: Sections 2.5.1 and 2.5.2.

• Recommended reading for next time: Continue section

2.5.2 and section 2.5.3.

LECTURES 4 AND 5 THREE-PHASE CONNECTIONS (1)

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