變壓器畢業(yè)設(shè)計(jì)論文

變壓器1）介紹

要從遠(yuǎn)端發(fā)電廠送出電能，必須應(yīng)用高壓輸電。因?yàn)樽罱K的負(fù)荷，在一些點(diǎn)高電壓必須降低。變壓器能使電力系統(tǒng)各個(gè)部分運(yùn)行在電壓不同的等級。本文我們討論的原則和電力變壓器的應(yīng)用。

2）雙繞組變壓器

變壓器的最簡單形式包括兩個(gè)磁通相互耦合的固定線圈。兩個(gè)線圈之所以相互耦合，是因?yàn)樗鼈冞B接著共同的磁通。

在電力應(yīng)用中，使用層式鐵芯變壓器(本文中提到的)。變壓器是高效率的，因?yàn)樗鼪]有旋轉(zhuǎn)損失，因此在電壓等級轉(zhuǎn)換的過程中，能量損失比較少。典型的效率范圍在92到99%，上限值適用于大功率變壓器。

從交流電源流入電流的一側(cè)被稱為變壓器的一次側(cè)繞組或者是原邊。它在鐵圈中建立了磁通φ，它的幅值和方向都會發(fā)生周期性的變化。磁通連接的第二個(gè)繞組被稱為變壓器的二次側(cè)繞組或者是副邊。磁通是變化的；因此依據(jù)楞次定律，電磁感應(yīng)在二次側(cè)產(chǎn)生了電壓。變壓器在原邊接收電能的同時(shí)也在向副邊所帶的負(fù)荷輸送電能。這就是變壓器的作用。

3）變壓器的工作原理

當(dāng)二次側(cè)電路開路是，即使原邊被施以正弦電壓Vp，也是沒有能量轉(zhuǎn)移的。外加電壓在一次側(cè)繞組中產(chǎn)生一個(gè)小電流Iθ。這個(gè)空載電流有兩項(xiàng)功能為在鐵芯中產(chǎn)生電磁通，該磁通在零和φm之間做正弦變化，φm是φm鐵芯磁通的最大值；它的一個(gè)分量說明了鐵芯中的渦流和磁滯損耗。這兩種相關(guān)的損耗被稱為鐵芯損耗。

變壓器空載電流Iθ一般大約只有滿載電流的2%—5%。因?yàn)樵诳蛰d時(shí)，原邊繞組中的鐵芯相當(dāng)于一個(gè)很大的電抗，空載電流的相位大約將滯后于原邊電壓相位90o。顯然可見電流分量Im=I0sinθ0，被稱做勵(lì)磁電流，它在相位上滯后于原邊電壓VP90o。就是這個(gè)分量在鐵芯中建立了磁通；因此磁通φ與Im同相。

第二個(gè)分量Ie=I0sinθ0，與原邊電壓同相。這個(gè)電流分量向鐵芯提供用于損耗的電流。兩個(gè)相量的分量和代表空載電流，即應(yīng)注意的是空載電流是畸變和非正弦形的。這種情況是非線性鐵芯材料造成的。

如果假定變壓器中沒有其他的電能損耗一次側(cè)的感應(yīng)電動(dòng)勢Ep和二次側(cè)的感應(yīng)電壓Es可以表示出來。因?yàn)橐淮蝹?cè)繞組中的磁通會通過二次繞組，依據(jù)法拉第電磁感應(yīng)定律，二次側(cè)繞組中將產(chǎn)生一個(gè)電動(dòng)勢E，即E=NΔφ/Δt。相同的磁通會通過原邊自身，產(chǎn)生一個(gè)電動(dòng)勢Ep。正如前文中討論到的，所產(chǎn)生的電壓必定滯后于磁通90o，因此，它于施加的電壓有180o的相位差。因?yàn)闆]有電流流過二次側(cè)繞組，Es=Vs。一次側(cè)空載電流很小，僅為滿載電流的百分之幾。因此原邊電壓很小，并且Vp的值近乎等于Ep。原邊的電壓和它產(chǎn)生的磁通波形是正弦形的；因此產(chǎn)生電動(dòng)勢Ep和Es的值是做正弦變化的。產(chǎn)生電壓的平均值如下：即是法拉第定律在瞬時(shí)時(shí)間里的應(yīng)用，它遵循：其中N是指線圈的匝數(shù)，從交流電原理可知，有效值是一個(gè)正弦波，其值為平均電壓的1.11倍，因此因?yàn)橐淮蝹?cè)繞組和二次側(cè)繞組的磁通相等，所以繞組中每匝的電壓也相同。因此并且其中Np和Es是一次側(cè)繞組和二次側(cè)繞組的匝數(shù)。一次側(cè)和二次側(cè)電壓增長的比率稱做變比。用字母a來表示這個(gè)比率，如下式

假設(shè)變壓器輸出電能等于其輸入電能——這個(gè)假設(shè)適用于高效率的變壓器。實(shí)際上我們是考慮一臺理想狀態(tài)下的變壓器；這意味著它沒有任何損耗。因此或者這里PF代表功率因素。在上面公式中一次側(cè)和二次側(cè)的功率因素是相等的；因此從上式我們可以得知它表明端電壓比等于匝數(shù)比，換句話說，一次側(cè)和二次側(cè)電流比與匝數(shù)比成反比。匝數(shù)比可以衡量二次側(cè)電壓相對于一次惻電壓是升高或者是降低。為了計(jì)算電壓，我們需要更多數(shù)據(jù)。

終端電壓的比率變化有些根據(jù)負(fù)載和它的功率因素。實(shí)際上,變比從標(biāo)識牌數(shù)據(jù)獲得,列出在滿載情況下原邊和副邊電壓。

當(dāng)副邊電壓Vs相對于原邊電壓減小時(shí)，這個(gè)變壓器就叫做降壓變壓器。如果這個(gè)電壓是升高的，它就是一個(gè)升壓變壓器。在一個(gè)降壓變壓器中傳輸變比a遠(yuǎn)大于1(a>1.0)，同樣的，一個(gè)升壓變壓器的變比小于1(a<1.0)。當(dāng)a=1時(shí)，變壓器的二次側(cè)電壓就等于起一次側(cè)電壓。這是一種特殊類型的變壓器，可被應(yīng)用于當(dāng)一次側(cè)和二次側(cè)需要相互絕緣以維持相同的電壓等級的狀況下。因此，我們把這種類型的變壓器稱為絕緣型變壓器。

顯然，鐵芯中的電磁通形成了連接原邊和副邊的回路。在第四部分我們會了解到當(dāng)變壓器帶負(fù)荷運(yùn)行時(shí)一次側(cè)繞組電流是如何隨著二次側(cè)負(fù)荷電流變化而變化的。

從電源側(cè)來看變壓器，其阻抗可認(rèn)為等于Vp

/

Ip。從等式中我們可知Vp

=

aVs并且Ip

=

Is/a。根據(jù)Vs和Is，可得Vp和Ip的比例是但是Vs

/

Is

負(fù)荷阻抗ZL，因此我們可以這樣表示這個(gè)等式表明二次側(cè)連接的阻抗折算到電源側(cè)，其值為原來的a2倍。我們把這種折算方式稱為負(fù)載阻抗向一次側(cè)的折算。這個(gè)公式應(yīng)用于變壓器的阻抗匹配。

4.有載情況下的變壓器

一次側(cè)電壓和二次側(cè)電壓有著相同的極性，一般習(xí)慣上用點(diǎn)記號表示。如果點(diǎn)號同在線圈的上端，就意味著它們的極性相同。因此當(dāng)二次側(cè)連接著一個(gè)負(fù)載時(shí)，在瞬間就有一個(gè)負(fù)荷電流沿著這個(gè)方向產(chǎn)生。換句話說，極性的標(biāo)注可以表明當(dāng)電流流過兩側(cè)的線圈時(shí)，線圈中的磁動(dòng)勢會增加。

因?yàn)槎蝹?cè)電壓的大小取決于鐵芯磁通大小φ0，所以很顯然當(dāng)正常情況下負(fù)載電勢Es沒有變化時(shí)，二次電壓也不會有明顯的變化。當(dāng)變壓器帶負(fù)荷運(yùn)行時(shí)，將有電流Is流過二次側(cè)，因?yàn)镋s產(chǎn)生的感應(yīng)電動(dòng)勢相當(dāng)于一個(gè)電壓源。二次側(cè)電流產(chǎn)生的磁動(dòng)勢NsIs會產(chǎn)生一個(gè)勵(lì)磁。這個(gè)磁通的方向在任何一個(gè)時(shí)刻都和主磁通反向。當(dāng)然，這是楞次定律的體現(xiàn)。因此，NsIs所產(chǎn)生的磁動(dòng)勢會使主磁通φ0減小。這意味著一次側(cè)線圈中的磁通減少，因而它的電壓Ep將會增大。感應(yīng)電壓的減小將使外施電壓和感應(yīng)電動(dòng)勢之間的差值更大，它將使初級線圈中流過更大的電流。初級線圈中的電流Ip的增大，意味著前面所說明的兩個(gè)條件都滿足：1）輸出功率將隨著輸出功率的增加而增加2）初級線圈中的磁動(dòng)勢將增加，以此來抵消二次側(cè)中的磁動(dòng)勢減小磁通的趨勢。

總的來說，變壓器為了保持磁通是常數(shù)，對磁通變化的響應(yīng)是瞬時(shí)的。更重要的是，在空載和滿載時(shí)，主磁通φ0的降落是很少的（一般在）1至3%。其需要的條件是E降落很多來使電流Ip增加。

在一次側(cè)，電流Ip’在一次側(cè)流過以平衡Is產(chǎn)生的影響。它的磁動(dòng)勢NpIp’只停留在一次側(cè)。因?yàn)殍F芯的磁通φ0保持不變，變壓器空載時(shí)空載電流I0必定會為其提供能量，故一次側(cè)電流Ip是電流Ip’與I0’的和。

因?yàn)榭蛰d電流相對較小，那么一次側(cè)的安匝數(shù)與二次側(cè)的安匝數(shù)相等的假設(shè)是成立的。因?yàn)樵谶@種狀況下鐵芯的磁通是恒定的。因此我們?nèi)耘f可以認(rèn)定空載電流I0相對于滿載電流是極其小的。

當(dāng)一個(gè)電流流過二次側(cè)繞組，它的磁動(dòng)勢（NsIs）將產(chǎn)生一個(gè)磁通，于空載電流I0產(chǎn)生的磁通φ0不同，它只停留在二次側(cè)繞組中，因?yàn)檫@個(gè)磁通不流過一次側(cè)繞組，所以它不是一個(gè)公共磁通。

另外，流過一次側(cè)繞組的負(fù)載電流只在一次側(cè)繞組中產(chǎn)生磁通，這個(gè)磁通被稱為一次側(cè)的漏磁。二次側(cè)漏磁將使電壓增大以保持兩側(cè)電壓的平衡。一次側(cè)漏磁也一樣。因此，這兩個(gè)增大的電壓具有電壓降的性質(zhì)，總稱為漏電抗電壓降。另外，兩側(cè)繞組同樣具有阻抗，這也將產(chǎn)生一個(gè)電阻壓降。把這些附加的電壓降也考慮在內(nèi)，這樣一個(gè)實(shí)際的變壓器的等值電路圖就完成了。由于分支勵(lì)磁體現(xiàn)在電流里，為了分析我們可以將它忽略。這就符我們前面計(jì)算中可以忽略空載電流的假設(shè)。這證明了它對我們分析變壓器時(shí)所產(chǎn)生的影響微乎其微。因?yàn)殡妷航蹬c負(fù)載電流成比例關(guān)系，這就意味著空載情況下一次側(cè)和二次側(cè)繞組的電壓降都為零。TRANSFORMER1)INTRODUCTIONThe

high-voltage

transmission

was

need

for

the

case

electrical

power

is

to

be

provided

at

considerable

distance

from

a

generating

station.

At

some

point

this

high

voltage

must

be

reduced,

because

ultimately

is

must

supply

a

load.

The

transformer

makes

it

possible

for

various

parts

of

a

power

system

to

operate

at

different

voltage

levels.

In

this

paper

we

discuss

power

transformer

principles

and

applications.2)TOW-WINDING

TRANSFORMERSA

transformer

in

its

simplest

form

consists

of

two

stationary

coils

coupled

by

a

mutual

magnetic

flux.

The

coils

are

said

to

be

mutually

coupled

because

they

link

acommon

flux.In

power

applications,

laminated

steel

core

transformers

(to

which

this

paper

is

restrictedare

used.

Transformers

are

efficient

because

the

rotational

losses

normally

associated

with

rotating

machine

are

absent,

so

relatively

little

power

is

lost

when

transforming

power

from

one

voltage

level

to

another.

Typical

efficiencies

are

in

the

range

92

to

99%,

the

higher

values

applying

to

the

larger

power

transformers.The

current

flowing

in

the

coil

connected

to

the

ac

source

is

called

the

primary

winding

or

simply

the

primary.

It

sets

up

the

flux

φ

in

the

core,

which

varies

periodically

both

in

magnitudeand

direction.

The

flux

links

the

second

coil,

called

the

secondary

winding

or

simply

secondary.The

flux

is

changing;

therefore,

it

induces

a

voltage

in

the

secondary

by

electromagnetic

induction

in

accordance

with

Lenz’s

law.

Thus

the

primary

receives

its

power

from

the

source

while

the

secondary

supplies

this

power

to

the

load.

This

action

is

known

as

transformer

action.3)TRANSFORMER

PRINCIPLESWhen

a

sinusoidal

voltage

Vp

is

applied

to

the

primary

with

the

secondary

open-circuited,

there

will

be

no

energy

transfer.

The

impressed

voltage

causes

a

small

current

Iθ

to

flow

in

the

primary

winding.

This

no-load

current

has

two

functions:

(1)

it

produces

the

magnetic

flux

in

the

core,

which

varies

sinusoidally

between

zero

and

φm,

where

φm

is

the

maximum

value

of

the

core

flux;

and

(2)

it

provides

a

component

to

account

for

the

hysteresis

and

eddy

current

losses

in

the

core.

There

combined

losses

arenormally

referred

to

as

the

core

losses.The

no-load

current

Iθ

is

usually

few

percent

of

the

rated

full-load

current

of

the

transformer

(about

2

to

5%).

Since

at

no-load

the

primary

winding

acts

as

a

large

reactance

due

to

the

iron

core,

the

no-load

current

will

lag

the

primary

voltage

by

nearly

90o.

It

is

readily

seen

that

the

current

component

Im=

I0sinθ0,

called

the

magnetizing

current,

is

90o

in

phase

behind

the

primary

voltage

VP.

It

is

this

component

that

sets

up

the

flux

in

the

core;

φ

is

therefore

in

phase

with

Im.The

second

component,

Ie=I0sinθ0,

is

in

phase

with

the

primary

voltage.

It

is

the

current

component

that

supplies

the

core

losses.

The

phasor

sum

of

these

two

components

represents

the

no-load

current,

orIt

should

be

noted

that

the

no-load

current

is

distortes

and

nonsinusoidal.

This

is

the

result

of

the

nonlinear

behavior

of

the

core

material.If

it

is

assumed

that

there

are

no

other

losses

in

the

transformer,

the

induced

voltage

In

the

primary,

Ep

and

that

in

the

secondary,

Es

can

be

shown.

Since

the

magnetic

flux

set

up

by

the

primary

windingthere

will

be

an

induced

EMF

E

in

the

secondary

winding

in

accordance

with

Faraday’s

law,

namely,

E=NΔφ/Δt.

This

same

flux

also

links

the

primary

itself,

inducing

in

it

an

EMF,

Ep.

As

discussed

earlier,

the

induced

voltage

must

lag

the

flux

by

90o,

therefore,

they

are

180o

out

of

phase

with

the

applied

voltage.

Since

no

current

flows

in

the

secondary

winding,

Es=Vs.

The

no-load

primary

current

I0

is

small,

a

few

percent

of

full-load

current.

Thus

the

voltage

in

the

primary

is

small

and

Vp

is

nearly

equal

to

Ep.

The

primary

voltage

and

the

resulting

flux

are

sinusoidal;

thus

the

induced

quantities

Ep

and

Es

vary

as

a

sine

function.

The

average

value

of

the

induced

voltage

given

bywhich

is

Faraday’s

law

applied

to

a

finite

time

interval.

It

follows

thatwhich

N

is

the

number

of

turns

on

the

winding.

Form

ac

circuit

theory,

the

effective

or

root-mean-square

(rms)

voltage

for

a

sine

wave

is

1.11

times

the

average

voltage;

thusSince

the

same

flux

links

with

the

primary

and

secondary

windings,

the

voltage

per

turn

in

each

winding

is

the

same.

HenceAndwhere

Ep

and

Es

are

the

number

of

turn

on

the

primary

and

secondary

windings,

respectively.

The

ratio

of

primary

to

secondary

induced

voltage

is

called

the

transformation

ratio.

Denoting

this

ratio

by

a,

it

is

seen

thatAssume

that

the

output

power

of

a

transformer

equals

its

input

power,

not

a

bad

sumption

in

practice

considering

the

high

efficiencies.

What

we

really

are

saying

is

that

we

are

dealing

with

an

ideal

transformer;

that

is,

it

has

no

losses.

ThusOrwhere

PF

is

the

power

factor.

For

the

above-stated

assumption

it

means

that

the

power

factor

on

primary

and

secondary

sides

are

equal;

thereforefrom

which

is

obtainedIt

shows

that

as

an

approximation

the

terminal

voltage

ratio

equals

the

turns

ratio.

The

primary

and

secondary

current,

on

the

other

hand,

are

inversely

related

to

the

turns

ratio.

The

turns

ratio

gives

a

measure

of

how

much

the

secondary

voltage

is

raised

or

lowered

in

relation

to

the

primary

voltage.

To

calculate

the

voltage

regulation,

we

need

more

information.The

ratio

of

the

terminal

voltage

varies

somewhat

depending

on

the

load

and

its

power

factor.

In

practice,

the

transformation

ratio

is

obtained

from

the

nameplate

data,

which

list

the

primary

and

secondary

voltage

under

full-load

condition.When

the

secondary

voltage

Vs

is

reduced

compared

to

the

primary

voltage,

the

transformation

is

said

to

be

a

step-down

transformer:

conversely,

if

this

voltage

is

raised,

it

is

called

a

step-up

transformer.

In

a

step-down

transformer

the

transformation

ratio

a

is

greater

than

unity

(a>1.0),

while

for

a

step-up

transformer

it

is

smaller

than

unity

(a<1.0).

In

the

event

that

a=1,

the

transformer

secondary

voltage

equals

the

primary

voltage.

This

is

a

special

type

of

transformer

used

in

instances

where

electrical

isolation

is

required

between

the

primary

and

secondary

circuit

while

maintaining

the

same

voltage

level.

Therefore,

this

transformer

is

generally

knows

as

an

isolation

transformer.As

is

apparent,

it

is

the

magnetic

flux

in

the

core

that

forms

the

connecting

link

between

primary

and

secondary

circuit.

In

section

4

it

is

shown

how

the

primary

winding

current

adjusts

itself

to

the

secondary

load

current

when

the

transformer

supplies

a

load.Looking

into

the

transformer

terminals

from

the

source,

an

impedance

is

seen

which

by

definition

equals

Vp

/

Ip.From,we

have

Vp

=

aVs

and

Ip

=

Is/a.In

terms

of

Vs

and

Is

the

ratio

of

Vp

to

Ip

isBut

Vs

/

Is

is

the

load

impedance

ZL

thus

we

can

say

thatThis

equation

tells

us

that

when

an

impedance

is

connected

to

the

secondary

side,

it

appears

from

the

source

as

an

impedance

having

a

magnitude

that

is

a2

times

its

actual

value.

We

say

that

the

load

impedance

is

reflected

or

referred

to

the

primary.

It

is

this

property

of

transformers

that

is

used

in

impedance-matching

applications.4)TRANSFORMERS

UNDER

LOADThe

primary

and

secondary

voltages

shown

have

similar

polarities,

as

indicated

by

the

“dot-making”

convention.

The

dots

near

the

upper

ends

of

the

windings

have

the

same

meaning

as

in

circuit

theory;

the

marked

terminals

have

the

same

polarity.

Thus

when

a

load

is

connected

to

the

secondary,

the

instantaneous

load

current

is

in

the

direction

shown.

In

other

words,

the

polarity

markings

signify

that

when

positive

current

enters

both

windings

at

the

marked

terminals,

the

MMFs

of

the

two

windings

add.Since

the

secondary

voltage

depends

on

the

core

flux

φ0,

it

must

be

clear

that

the

flux

should

not

change

appreciably

if

Es

is

to

remain

essentially

constant

under

normal

loading

conditions.

With

the

load

connected,

a

current

Is

will

flow

in

the

secondary

circuit,

because

the

induced

EMF

Es

will

act

as

a

voltage

source.

The

secondary

current

produces

an

MMF

NsIs

that

creates

a

flux.

This

flux

has

such

a

direction

that

at

anyinstant

in

time

it

opposes

the

main

flux

that

created

it

in

the

first

place.

Of

course,

this

is

Lenz’s

law

in

action.

Thus

the

MMF

represented

by

NsIs

tends

to

reduce

the

core

flux

φ0.

This

means

that

the

flux

linking

the

primary

winding

reduces

and

consequently

the

primary

induced

voltage

Ep,

This

reduction

in

induced

voltage

causes

a

greater

difference

between

the

impressed

voltage

and

the

counter

induced

EMF,

therebyallowing

more

current

to

flow

in

the

primary.

The

fact

that

primary

current

Ip

increases

means

that

the

two

conditions

stated

earlier

are

fulfilled:

the

power

input

increases

to

match

the

power

output,

and

the

primary

MMF

increases

to

offset

the

tendency

of

the

secondary

MMF

to

reduce

the

flux.In

general,

it

will

be

found

that

the

transformer

reacts

almost

instantaneously

to

keep

the

resultant

core

flux

essentially

constant.

Moreover,

the

core

flux

φ0

drops

very

slightly

between

n

o

load

and

full

load

(about

1

to

3%),

a

necessary

condition

if

Ep

is

to

fall

sufficiently

to

allow

an

increase

in

Ip.On

the

primary

side,

Ip’

is

the

current

that

flows

in

the

primary

to

balance

the

demagnetizing

effect

of

Is.

Its

MMF

NpIp’

sets

up

a

flux

linking

the

primary

only.

Since

the

core

flux

φ0

remains

constant.

I0

must

be

the

same

current

that

energizes

the

transformer

at

no

load.

The

primary

current

Ip

is

therefore

the

sum

of

the

current

Ip’

and

I0.Because

the

no-load

current

is

relatively

small,

it

is

correct

to

assume

that

the

primary

ampere-turns

equal

the

secondary

ampere-turns,

since

it

is

under

this

condition

that

the

core

flux

is

essentially

constant.

Thus

we

will

assume

that

I0

is

negligible,

as

itis

only

a

small

component

of

the

full-load

current.When

a

current

flows

in

the

secondary

winding