電力系統(tǒng)分析-中文電子課件第20-21次課對稱分量法

Content1

Definition

of

symmetrical

components2

Sequence

networks

of

impedanceloads3

Sequence

networks

of

rotating

machines4

Per-unit

sequence

models

of

three-phasetwo-winding

transformers5

Per-unit

sequence

models

of

three-phasethree-winding

transformers6

Power

in

sequence

networkThe

three-phase

voltages

designated:

Ua,Ub,Ucareresolved

into

the

following

three

sets

sequencecomponents:1.positive-sequence

components:(正序分量組):consisting

of

three

phasors

with

equalmagnitudes,±1200

phase

displacement,

and

positivesequence.(三個分量的量值相等，相位相差120度，相序與原有相系統(tǒng)的相序相同。下角用注1表示。)正序分量1

Definition

of

symmetrical

componentspositive-sequence

components.Ua1.Ub1.Uc11

Definition

of

symmetrical

components2.negative-sequence

components(負序分量組：)consisting

of

three

phasors

with

equalmagnitudes,±1200

phase

displacement,

andnegative

sequence.(三個分量的量值相等，相位相差

120度，相序與原有相系統(tǒng)的相序相反。下角用注2表示。)negative-sequence

components負序分量.Ua2.Uc2.Ub21

Definition

of

symmetrical

components3.zero-sequence

components(零序分量組)：consisting

of

threephasors

with

equal

magnitudesandzero

phase

displacement.(三個分量的量值相等，相位相差0(360)度，三個分量為同相。下角用注0表示。)zero-sequencecomponents零序分量組.U

a

0.U

b

0.U

c

01

Definition

of

symmetrical

componentsThree

unsymmetrical

components

are

the

composeof

three

symmetrical

components(三個不對稱相量可用三個對稱分量表示).

.

.

..

.

.

.U

a

U

a

0

U

a1

U

a

2..

.

.U

b

U

b0

U

b1

U

b

2U

c

U

c

0

U

c1

U

c

2compose

of

three

symmetricalcomponents.U

a.U

b.U

c.U

a

0.U

b

0.U

c

0.Ua2.Uc2.Ub2.Ua1.Uc1.Ub1.Ua1.Ua2.Ua01

Definition

of

symmetrical

components022aaa3

e

j

360

1..

.

..

.

.

..

.

.Ub1

a2U

a1

,U

c1

aU

a1Ub

2

aU

a

2

,U

c

2

a2

U

a

2Ub0

U

a

0

U

c0.U

a.U

b.U

c.U

a

0.U

b

0.U

c

0.Ua2.Uc2.Ub2.Ua1.Uc1.Ub1.

.

..

.

..

.

.Ua

Ua

0

Ua1

Ub

Ub0

Ub1

Uc

Uc0

U

c1

取運算符號

,則有：2a

0a

2a1a

0a1a

22UaU

aU

U

U

a

0U

a1

U

a

2U

a

1

U

a0

U

U

aU

1a

U

b

a1

2

U

1

1a21

aa

U

ac

a

231a1UU

a

03

U

a

U

bU

a

23

U

a

U

b

U

c

U

a

0

1

1

U

a

2

1

11

a

a

U

b

a21a

U

U

a

2

c

1

(

U

c)U

a1

3

(U

a

aU

b

a2U

)c

1

(

a2

a

)三相不對稱分量寫成矩陣形式為：Uabc

AU012Up

AUs012

abcs

pU

A1UU

A1U1

Definition

of

symmetrical

components1

Definition

of

symmetrical

componentsThesymmetricalcomponenttransformation

csobe

applied

to

currents.In

a

three-phaseY-connected

system,

theneutral

current

In

is

thesum

ofthe

line

current:lsIn=Ia+Ib+Ic=3I0The

neutral

currentequathree

timesthe

zero-sequence

current.（中線電流為三相電流之和）2a1a

2a1a

22IaII

aI

I

a

2

I

a0I

a1I

a

1

I

a0

I

I

a

I

1a

I

b

a1

1

1a21

aa2

aa0

I

c

I

a

2a0

232a1abI

b

I

cII

aIb

I

c

I

aI

a0

1

I

a

1

1

2

1

1

a

1

a

a

I

b

3

a21a

I

I

a

Ia

2c

I

a

aI

c

Example

8.1,8.2,8.3The

balance

three-phase

systems

with

abcsequence(orpositive

sequence)

have

no

zero-sequenceor

negative-sequencecomponents.正序分量.U

a1.U

b1.U

c1The

balance

three-phase

systems

with

abcsequence(ornegative-sequence)have

nozero-sequence

or

positivesequencecomponents.負序分量.I

a

2.I

c

2.I

b

2The

unbalancedthree-phasesystems

havenonzero

values

forall

sequencecomponents.The

neutral

currentequals

three

timesthe

zero-

sequencecurrent.正序分量.I

a1.I

c1.I

b12

Sequence

networks

of

impedance

loadsZnZnUag

(ZY

Zn

)

ZnZn

(ZY

Zn

)Zn

ZnUbg

Ib

(ZY

Zn

)

Ic

Ucg

U

p

Zp

I

pA

balanced-Y

impedance

load,the

impedance

ofeach

phase

is

designated

ZY,

and

aneutralimpedance

Zn

is

connected

between

the

loadneutral

and

ground.

The

line-to-ground

voltage

UagnnUbgUcgUag

(ZY

Zn

)Ia

Zn

Ia

(ZY

Zn

)Ib

Zn

Ia

Zn

Ib

(ZY

Zn

)IcZYZnacbgUag

Ia

UcgUbgIaIcIb2

Sequence

networks

of

impedanceloadsssU

p

Zp

I

pU

p

AUs

,

I

p

AIsAUs

Zp

AIU

(

A1Z A

Is

pUs

Zs

Is0Yna2a

1

1

aa23

1Z

3Z

00(1

a

a2

0)Z2

is

called

negative-sequence

impedance.YZU

ZY

3Z

I0

0

I

Zs

is

called

the

sequence

impedance

matrix.U

1

1

Z0

is

called

zero-sequence

impedance.U2

0

0ZY

I2

Z1

is

called

positive-sequence

impedance.U0

(ZY

3Zn

)I0

Z0

I0U1

ZY

I1

Z1I1U2

ZY

I2

Z2

I22

Sequence

networks

of

impedance

loads（負載的序網(wǎng)絡）Z1=ZYpositive-sequence

networkZ2=Z1=ZYnegative-sequence

networkZ0=ZY+3Znzero-sequence

networkSequence

networks:U0U1U2I0I1I2Eachsequencenetworks

isseparate,uncoupled

fromthe

other

two.2

Sequence

networks

of

impedance

loads（負載的序網(wǎng)絡）Z1=ZYpositive-sequence

networkZ2=Z1=ZYnegative-sequence

networkZ0=ZY+3Znzero-sequence

networkSequence

networks:U0U1U2I0I1I2Eachsequencenetworks

isseparate,uncoupled

fromthe

other

two.3

Sequencenetworks

of

rotating

machineSequence

networks

of

Y-connected

synchronousgenerator:A

Y-connectedsynchronous

generatorgrounded

though

aneutral

impedance

Zn

isshown

in

figure.

Theinternal

generatorvoltages

are

designedEa,

Eb,

and

Ec,

the

linecurrents

are

designedIa,Ib,IcEaEbEcIaIbIc3

Sequence

networks

of

rotatingmachineerator

:negative-sequencenetworkZ2=Zg2(negative-sequenceimpedance)Z1=Zg1(positive-sequenceimpedance

iscalled

thesynchronousimpedance)Z0=Zg0+3Znzero-sequencenetworkzero-sequenceimpedanceThe

sequence

networks

of

tpositive-sequencenetworkU1U2U0Z2Z0Z1Eg13

Sequence

networks

of

rotating

machineZ2=Zm2Sequence

networks

of

three-phase

motorspositive-sequencenetworkzero-sequence

Z0=Zm0+3Znnetworknegative-sequencenetworkZ1=Zm1Em1Synchronous

motorZ1=Zm1Z0=Zm0+3ZnZ2=Zm2Induction

motor4

Per-unit

sequencemodels

of

three-phase

two-winding

transformers3ZN

3ZnAn

ideal

Y-Y

transformer

grounded

throughneutral

impedances

ZN

and

Zn.Per-unitsequence

networks

of

the

ideal

transformers:Per-unit

zero-sequencenetworksPer-unit

positive-sequencenetworksPer-unit

negative-sequencenetworks4

Per-unit

sequencemodels

of

three-phase

two-winding

transformersPer-unit

sequencenetworks

of

Y-Y,Y-△,

△-△

practicaltransformers

areshown

in

figure

8.193Zn3ZNZtzero-sequencepositive-sequencenegative-sequencePer-unit

sequence

networks

of

Y-Y

transformer5

Per-unit

sequencemodels

of

three-phase

three-winding

transformersThree

identical

single-phase

three-winding

transformerscan

be

connected

to

form

a

three-phasebank.T eral

per-unit

sequence

networks

of

a

three-phasethree-windingtransformer:The

letters

H,M,and

X

are

used

to

denote

thehigh-,medium-,and

low-voltage

windings.HH’M’

MX’

XPer-unit

zero-sequencenetworks

of

athree-phasetransformer5

Per-unit

sequencemodels

of

three-phase

two-winding

transformersH

H’M’

MX’

XFor

a

general

zero-sequence

networks,

the

connectionbetween

terminals

Hand

H’

depends

on

how

the

high-voltage

windings

are

connected,

asfollows:1.

Solidly

ground

Y----

shortHtoH’grounded

Y

through

ZN----

connect

(3ZN)

from

H

toH’ungrounded

Y----

leaveH-H’

open

asshown△-short

H’

to

thereference

buszero-sequence

networks5

Per-unit

sequence

models

ofthree-phase

three-winding

transformersPer-unit

positive-sequence

or

negative-sequence

networks

of

a

three-phasetransformerpositive-sequence

or

negative-sequence6

Power

in

sequence

networksThe

power

deliveredto

three-phasenetwork

can

bedetermined

from

thepower

delivered

to

thesequence

networks.Let

Sp

denote

thetotal

complex

powerdeliver