Curs masini electrice

93
Noiuni generale 3.1.3. Înfáçurári de curent alternativ y ! " # $ ! % % m 2 & ’ ( zona de dus) zon de întors. & c N mpq N c 2 = *+ # înfurarea întreag $ % , ! ! # - c N p 2 = # ! / # ! . ) , ( p N c / = mt N c 0 1# *2 # " ) = m N c # ) = m N c 2 # " *3 4 !

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Curs masini electrice

Transcript of Curs masini electrice

Page 1: Curs masini electrice

Noţiuni generale

3.1.3. Înfáçurári de curent alternativ ă ăşă ă ţ ş ă ă τy ăşă ! "#ă $ ! ăşă ăşă ă ţ%ă

şă ă ă %ş mπ2

& ' ă ă (ţ ă 'şzona de dus) ă ' ă ş ă zonă de întors. &ă ă cN şă ă

mpqNc 2= * + 'ă #înfăşurareaşîntreagă

$ ă % ă ăşă ,ăşă ă ţ ă ş !!#-ţăş ă ă

cNpπα 2

= #ă ă!

/α #ă ! . ),( pNc ă/ţ

=mtNc 01#* 2

ţ#ăşă"ş ă )

=mNc ă #ăşă )

=mNc2

ă #ăş"* 3

4ţăşă!

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0 5

3.1.3.2. Înfáçurári trifazate íntr-un singur strat $ă %ăş"#

24=cN 2=p 3=m ) ă 2=t ă 5

$!ă ţ* 2ş * 3ăşă)

5$ş624

22/ ππαα =⋅

== #*5*

*$ ă 42

=mNc ă ă)

ă ă ă -4# 5 * 6ă %ă

$ # ! ! ă

!3

2πăă

7+2 3 8/9 :5 556/ ă ă

# /A /B /C 6 ! ă % ş ţ /ă ăş ă ă %ă

; # ş ă ţă !ţă ă ş #!-%ăşă#ăăşă<

– ă ş = ă!ţ ţ)

Fig. 3.23. Steaua t.e.m. pentru înfăsurarea analizată.

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*

– # #

>#*56?ăş"#ă >#*5+(ă=ă#*5* =ăţ

3.1.3.3. Înfáçurári trifazate ín douá straturi , ăşă ă ă ş ă ă, τyy = ş ă!ţş =ăă ş ţ

@ţă#/ă ăă ş ă #ă ă

/mNc #

ă ăţ ă # # ţ ? # *58 ă ăşă ăşă

18=cN 2=p 3=m 2/3=q 4ş ăş

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0 6

>#*58$ăşă ăşăă ş

3.1.3.4. Înfáçurári ín colivie

;ăş!ă "ă cN ă ă #*59 ă ăş ă ş ă ţ ăş ă ăş >ăă ă<ă ă 2/1=N

cNm = ă!#

3.2.2. T.e.m. indusá íntr-o ínfáçurare de curent alternativ$0 A B#

#**5 / !0 0 v 100 A0 B # 0 !0 1 - 1" 10 0 AB1A00$1!101#010

Fig.3.29. Înfăşurare în colivie.

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+

T.e.m. indusá de armonica fundamentalá de spaþiu A# 1B C!01!A0

pnf =1 *52

#cNpπα 2

=

$ 0 1ecU ! !0 01"0## ,il

vlBU iec 11 21

= *53

B npDnv ⋅== τπ 2

nplBU iec ⋅= τ22

111 *58

>%0

∫ ∫ ===Φτ τ

τπτ

π

0 01111

2sin)( iii lBxdxBldxlxB *59

111 2Φ= fUec

π**:

1=0 0 1 0 # #**5 0 10 #%0(0 0 ! # x∆ 0# 1B 1AB#

> 1 0 1 ,x∆ 0# 1B 1 A B#

1 A0# 1 x∆ 0A##)0#***0 1eciU 47(=1% τπβ c=

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0 2

>#**5/AA>#***C01"#01A00101#

&B@ă

2sin211

ββ RURU eciec == **

111 iececi KUU ⋅= **5

τπ

τπ

22sin1

ccKi = ***

10B0 10

C 0 1" 0 1esU A 0 1 D#5*:

# πτyy

#**6

1111 22

sin2 seciecies KUyyUU ⋅==τ

π**6

/ τ

πyyKs 2

sin1 =

100 τyy = ).11 =sKT.e.m. indusá íntr-o bobiná cu bs spire

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3

11 esbeb UsU = **+

>#**6C01"0>#**+C01 0

C' 1 00

∑=

=q

kebkeq UU

111 )( (10#

111211 )(...)(...)()( ebqebkebeb UUUU ===== **2

cNpπα 2

= ) /#AA011"

0@

2

sin2;2

sin2 11αα qRURU eqeb == **3

111 rebeq KqUU ⋅=

2sin

2sin

1 α

α

q

qKr =

/ 1rK 0 B " 1eqU 0 , 10 1#0 1 0 #

11 2 eqe pUU = *6:

111111 24 Φ= fKKKpqsU rsibe

π*6

&00 bpqsN 2=

1111 rsiB KKKK = 100

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0 8

1111 2 Φ= Be NKfU π *65@A!01001"

11 eqe pUU = bpqsN =2. T.e.m. indusá de armonica de ordinul ν B

τν

τυ1

= ) pp νυ =

ναπναυ ==cNp2

*62

>!A0

1fpnnpf ννυυ === *63

ννυν π Φ= Be NKfU 2 *68 3. T.e.m. indusá pe o fazá0A

∑∞

=

=1

2

υνee UU *+5

-0y 10c ! A 0 !A10

$ 1 ! 00!c By B τy

Cãmpul magnetic pulsatoriu (000

txBtxB ωτπ

δδ sinsin),( 11 = *29

!0 0 ! B # 1 A ! 10 # 0 0 !B##**9 @A 0 <

++

−= xtBxtBtxB

τπω

τπω δδδ sin

21sin

21),( 111 *3:

>#**9 /B #

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9

$"A0B#1!B#!#1!)BA!

τfvpfn dd 2== *3

!!<

τfvpfn ii 2−=−= *35

3.3.2. Cãmpul magnetic ínvãrtitor circular 1. Cãmpul magnetic ínvãrtitor circular produs pe cale electricá $ 0 0 0 0 0 0

10 0 1 - 100 0 A<

−=

−=

=

34sin2

32sin2

sin2

πω

πω

ω

tIi

tIi

tIi

C

B

A

*3*

/B 0 10 0 1 - 1 1 A % #*6: B B #!00B1!B<

−++

−=

−++

−=

++

−=

38sin

21sin

21),(

34sin

21sin

21),(

sin21sin

21),(

πτπω

τπω

πτπω

τπω

τπω

τπω

δδδ

δδδ

δδδ

xtBxtBtxB

xtBxtBtxB

xtBxtBtxB

C

B

A

*36

>#*6:-B#1!B

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0 :

$" # A 1 % 4 .: 0

/BA1!<

−= xtBtxB

τπωδδ sin

23),( *3+

0 0 0 0 1 (0 ! B A <

),(),( ttxxBtxB ∆+∆+= δδ *320<

( ) ( )xxttxt ∆+−∆+=−τπω

τπω *33

(0A<

pfnf

txv ==∆∆

= τ2 *38

( !E: B # 01!%;%#*6 (00010A"0<

+= xtBtxB

τπωδδ sin

23),( *39

000!01!(0A<

pfnf

txv ii −=−=∆∆

−= τ2 *8:

( 0<iv B#!01#!%;%#*6

2. Cãmpul magnetic ínvãrtitor circular produs pe cale mecanicá$000A#*65

10 %A 0 0 (0 1B#A#1

0 0 A 0 " A0 % A0

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4@ #*65 % B # -A%A0#!<

gReR pBBxB αα δδδ sinsin)( ==

eRα "#% A0 4@ % )

gRα "##$ 0

A0 % A0 4$ 0 gSRα " # #

% 0 ) gSα "##1A04$B<

gRgSRgS ααα += *85(00%

% A !0#0 Ω 0 B# A4$A*8 *85!AB#A<

)(sin)( gSRgSpBxB ααδδ −= *8*/B0.:1A<

xptSARA eSgSgSR τπααα ==Ω=≡ .... *86

1A<

−=Ω−= txBtppBtxB gS ωτπα δδδ sin)sin(),( *8+

$" A B # 1!B 0!#0Ω 110 F B 0 A 0 1B 0

1. MAÇINA SINCRONÁ

1.PÁRÞI COMPONENTE ÇI MATERIALE UTILIZATE 00!00A#0A pfn /60 11 = ,

>#*65-B#1!B0

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0 5

00B#0 10 0 1 0 10 %A

0 0 # (0 !0 ! 1AA

# 0 A !0 0"0A

# 5 0 A !0 0"01A-AA1

># $A!00># 5$A!00"00A"001A

A0#1A

# turbogenerator 0 0 0 hidrogenerator000

C##1AAA0##0A1A 0 ! <(. "5– ).2"3"##

G##AAA01A!00%!!

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* <(. 6" 2– ) . "5 " ## Statorul 0%0 ! 0 0A! Rotorul0 B 1 0 ! !< A!1A

1.1.1. Párþile componente ale statorului Carcasa # A 0 A 1A00

Miezul feromagnetic al statorului B#!10000%#:+

(0 # 0 H5:"5+ 0 # !A % 0 0-#0!!!# ! !A 0 0 , # 00

C!000 Înfáçurarea statorului e 10 0 1" 1

!%00010

> 100 0 AA0,!F.*" +IJ,1000B"

1.1.2. Párþile componente ale rotorului A.Rotorul cu poli aparenþi$0A

+:: K B!

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0 6

, 1 !100%A @A1#=#10%A Miezul feromagnetic al polilor %010A# "5+#

># -00< "00)

5"00)*"=0B#)6"0)+"#.

-=#110 B0 # 0 01C00

/BBAA0%0000= Infáçurarea de amortizare (de pornire în asincron) 0 1 0 10 0 7 A 0 #0 %0 "10#0"10

Infáçurarea de excitaþie %00

B.Rotorul cu poli înecaþi$01A00%0

!!#Miezul feromagnetic al rotoruluiB0

::: IJ4 %0 A

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+1%0!# 5

CA1 A 0 0 5K* K* - A # !# * %0 A = A00AB"0 0AB# 6

Infáçurarea de excitaþie0%!5K* %0 0 1 0 / 100 1=%

Infáçurarea de amortizare 0 ! 100

1.2. PROCESUL DE REACÞIE AL INDUSULUI

, A 1 # 10 %0 B# 10 %A /B A0 1 0 B A $ A A 0 B < "!) "A0#) "100) "A100) "A1000) #0 0 1.2.1. Reacþia indusului la maçina cu poli plini Cãmpul magnetic inductor , 0 0 10 %A 0 10 0 5K* A %A

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0 2

A 0 ( 1 !B 1 ! A A A#0<

)(2)(

)( // xpx

xB EoE δ

θµ=

0 A B # A0< )(xEθ "A%A0) "0) )(// xδ "1! 0 1 ! A A 0 / Ck # A sk <

)()(// xkkx Cs δδ = 5 # +0A 0 00 # 00 1 10 %A EI B / # # $ 1 0 0 EB B00 0 1EB ( 1 0 00#=0$0%#0%'%!0 Reacţia transversalá a indusului ! 10 !0 ( ) 0, == IU eEψ -# # 2 L )0( == dq III L

aϑ 0 L0 L Eϑ 2/π 0 0 !0 '1 1 % 21 , dd

># + $A B#

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3# 2 , M # L 1 # # /@ 1 0 ! L0 M # ( ! L 0=ψ L!0

># 2@L!0< – A0AB

A0)"#

N # 2 0 !L L L0!1%!%01%' (01 .,ct=δ L0BA0#0<

)(2)(

)( // xpx

xB aqoaq δ

θµ= +

;!0 0 # 0 A L 10 A B ! 2θ 0#AA! 1θ # 3# 3 #A#A<

a) Maçiná nesaturatá #0# 3A#0110! EB

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0 8

, # A 0 1θ 0 0A#! minB 00A! 2θ 0A maxM

># 3A!100<"00)"00

>% A 1#A

abcdS A10 ABcdS ( # 0 A0

#G7#0#G4 #0 0 0 0 0 0 # # % 0 A 1 0 # A1# EΦ=Φ

b) Maçiná saturatá # 0# 3!$A#$!00A0# # 0 A

ABcdabcd SS ≠ 0 % 0 A 1 0 B A 1 # EΦ<Φ Efectele reacþiei transversale sunt urmátoarele: -##)" % 1 ! 0 A0 % 0#0)

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9"0 % 0 A 10A01#0A#

Reacþia longitudinalá a indusului ín cazul 2/πψ = 0 !0 #

80 )0( == qd III $!000

L# 8 '1 1%! ,ML1/@##1B

># 8@L#0 2/πψ = – A0ABA#0)"#

/%#0%0BA

! 2/π=ϕ L #0$L0ML π = ), EII 0ML/ 0 # 8 M L # N #0 ! !L L L0 Reacþia longitudinalá a indusului ín cazul 2/πψ −=

0 !0 # 9 0 1 )0( == qd III $ !0 00A00!

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0 5:

, M L 1 # # 1 B

># 9@L#0 2/πψ −= – A0ABA#0)"#

@L##1

# 9!00L0 rθ

1.3. ECUAÞIILE DE TENSIUNI §I DIAGRAMELE FAZORIALE 1.3.1. Generatorul sincron cu poli ínecaþi -A

0 10 0 $ 0 "O1 Γ 0 % 100 /B 0##0A<

euuRi Σ=+ "< @"A1000) ")

># 5* 0

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5

") euΣ "110 - 0 # A#

dtdueψ

−=Σ 5

ψ "%010 $1!0%0<

σψψψψ ++= aE * Eψ "%) aψ "%A) σψ "% 4%00A<

iLiL

Nk

aa

EBE

σσψψψ

==

Φ= 6

&"00100) Bk "=) EΦ "%) aL "!0BA) σL "!0B -1%1A88A<

σeeaeEe uuuu ++=Σ + eEu "0B)

eau "0B)

σeu "0B 0 A 1 ! 0 00<

Riuuuu eeaeE −++= σ 2 - A 0 0 0 ! 1 1 3/2π! 3/4π

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0 55

# 1%AA00<

IRUUUU eeaeE −++= σ 3!!!A<

IjXUIjXUfNKjU

e

aea

EBeE

σσ

π

−=−=

Φ−= 2 8

aX "A0BA) σX "A0B 4!B 0A 3 1 # 56" #0 0 ! !0 1 # 5+#0!!0

># 56(#0 ># 5+(#00!!0 0!!0

Ecuaþia de tensiuni çi diagrama fazorialá transformatá $1!A<

IXXjUU aeea )( σσ +−=+ 9

σXXX as += 5: sX "A0 /

IjXU ses −= 5

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5*A0<

IRUUU eseE −+= 55 (#01# 520!!0

Ecuaþia de tensiuni çi diagrama fazorialá simplificatá #=00A0

eseE UUU += 5* (#0001# 53

># 52(#0 ># 53(#00 0

1.3.2. Generatorul sincron cu poli aparenþi 00 # 1A

0 10 # 5* $ 0 "O1Γ

euuRi Σ=+ 56

dtdueψ

−=Σ 5+

ψ "%010 σψψψψψ +++= aqadE 52

Eψ "%) adψ "%A0%#0) aqψ "%A0%!0)

σψ "% adL "!0BA#)

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0 56

aqL "!0BA!)

di "#0)

qi "!0 -1%1A 5+A<

σeeaqeadeEe uuuuu +++=Σ 58

eadu "0BA#)

eaqu "0B! 0A1!0

Riuuuuu eeaqeadeE −+++= σ 59 # 1%AA00<

IRUUUUU eeaqeadeE −+++= σ *:!!!A<

IjXU

IjXUIjXUfNKjU

e

qaqeaq

dadead

EBeE

σσ

π

−=

−=

−=

Φ−= 2

*

adX "A 0 B A #) aqX "A0BA!

># 58(#0 ># 59(#00!!0 0!!0

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5+

4!B0A *:1# 58"#0 0 ! !0 1 # 59#0!!0

Ecuaþia de tensiuni çi diagrama fazorialá transformatá /B 0 0 %A00<

)( qdqaqdadeeaqead IIjXIjXIjXUUU +−−−=++ σσ *50

σ

σ

XXXXXX

aqq

add

+=

+= **

dX "A0#0) qX "A0!0 /0

qqeq

dded

IjXUIjXU

−=

−= *6

IRUUUU eqedeE −++= *+ - A # 001# *:0!!0

Ecuaþia de tensiuni çi diagrama fazorialá simplificatá #=00A0

eqedeE UUUU ++= *2 (#0001# *

># *:(#0 ># * (#00 0

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0 52

1.4. CUPLAREA ÍN PARALEL A GENERATOARELOR SINCRONE

&01#<" # B 0 )" A0 # 1 10A1AB#B!!)"0!A N ! !0 1 1 10O 0 # L# *5# **010A<

J!#A0#5 $#A0* #!A#A6 00

#00 Verificarea condiþiilor çi modul de índeplinire al acestora

- A # !0 0!=000#A(0A 10 0 %A # UU g < 0 UU g > B0BA#

5-!A!#A!= 0 0 = # 1!B

Montajul la stingere 0 # *5

# # A 1# *5 (0 0

321 ,, UUU ∆∆∆ 01# *5##

(0 10 L 10N1O1L0

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53 L L M 1#L

># *5<"=##L)"#0

#L 321 ,, UUU ∆∆∆ 0

- % 1 = # *5 !0

L # " ! 7/$!00! 541 ,, UUU ∆∆∆ 0!#!

/1A!!0#A!0L

Montajul la foc ínvãrtitor $ 0 # ** #

#A1# ** - 0 321 ,, UUU ∆∆∆ 00B1!B

(0 10 L 1 0 $ !0 0 ! 541 ,, UUU ∆∆∆ #

-1A!!0#A!0L

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0 58

># **<"=1!B#L)"#0#L 321 ,, UUU ∆∆∆

0*JA#!A#A

=(0!L#1%L!0%0000

(0 !L 0 0 ! !#0 gr ωω − gr ωω , LL#$

!00 U∆ !0100- 1 A 0 A

!A#B0BA#064A 10

!0 montajului la stingere 11O 1# 0 =0 # / M!L M 01M1L

montajului la foc ínvãrtitor A 10 B 0 0 0A# Consecinþe ín cazul nerespectárii condiþiile

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59

0 A # 10 # 0 A A A !(0 UU g > #0A0!0A! UU g < !0

54A! A010010#0AA1(0A

*(0 !A # A # 1A0A0!00

6 & A 6 0 # B # 0 10 A 0 A (0#0BA

1.5. CUPLUL ELECTROMAGNETIC AL MA§INII SINCRONE

1.5.1. Bilanþul puterilor active la generatorul sincron # *6AA

0< 1P "00 ) MP " #0 0) 2P "00) vmp + "!A) FeP " 1 1

#) CuP "110

Ecuaþia de miçcare ín regim staþionar 7A!<

># *6 7A ! #

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0 *:

vmM pPP ++=1 *9(00A1Ω "!#00

AA1#A<01 MMM += 6:

1.5.2. Cuplul çi puterea electromagneticá $#=0110

ϕcos2 mUIPPM =≈ 6 ( # 0 0

A# *+0θψϕ −= 65

A A 6 0A<

θψθψ

sinsincoscos

mUImUIPM

++=

6*

$1!0ψψ cossin IIsiII qd == 66

( # 0 1# *+A00%

q

qd

eEd X

UIXUU

I θθ sincos=

−=

N L0 A 6* 66 6+ A 0#<

θθ 2sin112

sin2

−+=

dqd

eEM XX

mUX

mUUP 62

/ # 0 10A A!#0Ω

−+= θθ

ω2sin11

2sin

2

dqd

eE

XXmU

XmUUpM 63

$ !0 0 ! #0 B0<

># *+(#00A

Page 31: Curs masini electrice

*

-Componenta principalá %0 0 0%A

θω

sin/

d

eE

XmUUpM = 63

"Componenta auxiliará %0A000%<

θω

2sin112

2//

−=

dq XXmUpM 63

00!0

ψθθψθψϕcossincossin

)sin(sinmUImUI

mUImUIQ−=

=−== 68

1 qd II , A<

qdqd

eE

XmU

XXmU

XmUU

Q22

2cos112

cos −

−+= θθ 69

$!00!000%A 0%0000%100

Caracteristica unghiular staticá <

===

=.

.

.)(,

ctIctfctU

fMP

E

M θ +:

La maçina cu poli ínecaþi 1A00%!#A0

sqd XXX == + /#00

θω

sin/

s

eE

XmUUpMM == +5

#001# *20 La maçina cu poli aparenþi 0 #0# *2

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0 *5

># *2/#0 )(θfM = #< " 1A)"A

;!0# *20θ

#0 1#!

1.6. CARACTERISTICILE DE FUNCÞIONARE ALE GENERATORULUI SINCRON 1.6.1. Caracteristicile generatorului sincron autonom 1.Caracteristica de funcþionare ín gol4000A0<

===

=0

..

)(0

Ictfctn

IfU E +*

0U A1# eEUU =0 ( eEU

L0 % %A#A 1 # )(0 EIfU = 0 00 #

)( mmUf=Φ

- 0 <

># *3 / A1#

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**%A!0A0/B=#1A0B%!0000%A(00#10 0 %A ! ! 0 $000B#000

2.Caracteristica de scurtcircuit0=L

==

=0

.)(

Uctf

IfI Esc +6

,A1000BAPEE@!1 2/π

@L # NMM#1LL0L1# 0 M# @L )( Esc IfI = 00! 0 1 1 L ,! ! L 0M 0 NM L # L 0 ) %L ++!0

3. Caracteristicile de funcþionare ín sarcináL

===

=.cos

..

)(ct

ctfctI

IfU E

ϕ +3

; L000 1 0 !0 0=ϕ /1#0 ..:010

Page 34: Curs masini electrice

0 *6

! ϕ 0 . " G 0

># 6:/10 ># 6 /%# #

4. Caracteristicile externeL

===

=.cos

..

)(ct

ctfctI

IfUE

ϕ +8

(0%01M#! NN IU , ! )2/πϕ = 1M L #0 0 0 M11F

, 0 !0 # M 1 !01#

5. Caracteristicile de reglare 4L

Page 35: Curs masini electrice

*+

===

=.cos

..

)(ct

ctfctU

IfI E

ϕ +9

>0E

I %L #LM 1 # !F0N# 65" F . !ϕ

(0 !

)2/( πϕ = 10 # L #0#0 '

eU F / #0LF.00 %L

1.6.2. Caracteristicile de funcþionare ale generatorului sincron cuplat la reþea 1.6.2.1. Funcþionarea generatorului sincron la cuplu constant çi curent de excitaþie variabil a) Funcþionarea ín gol > 0 0

L L0 0L .: UU eE = 0=θ ## 6* $" EoI " %A A 1 ##0 UUeE =

(0 %L EoE II > eEU 1#=0A0 sR

># 65 / # #

># 6*" !L100!

Page 36: Curs masini electrice

0 *2

ss

eE

jXU

jXUU

I ∆=

−= 2:

10L0### 6* # 0 !0 1 L !0!%A=#1A (0L0L1#%L EoE II < I L01

eEU #

!0L#0# 6*40!A#

1JA1# 02 =P 01# 6+N 0 0 %L 00

0 1 !0 %L000!1A 8,0cos =ϕ

c) Caracteristicile ín V -1

J <

===

=...

)(ctPctfctU

IfI E 2

N #0 " 10 L 0 0 0/ )( EIfI = L J /01 !M 1J 0 ! 100! L0 #%QH:#%QE:

># 6+ / 1 J !!-.

Page 37: Curs masini electrice

*3

1.6.2.2. Funcþionarea generatorului sincron la cuplu variabil çi curent de excitaþie constant (0 L 0 # #

2 8 0 L UU eE , 0 eEU 10 0≠I 00 ≠ϑ (#0001# 62/ I 0!00U L0 # !0L

(0 0L eEU 0 1 0 L0 U # 0θ " # 0! # 62 $!0 0 00 !0 #!0 !0 L0L01#

, %L B 0110!00001## a) Stabilitatea staticá a maçinii sincrone $ 0 0# L1L )(θfP = M!0 - 0 0 #1A# 63 4 A 0 # 0θ A1#A!<

01 MMM += 25 (0 1M

/1M 0# 0θ /

0θ 0

># 62JA100!

Page 38: Curs masini electrice

0 *8

0#D/#A14DA

0//

1 MMM += 2*

># 63$0<!1A)!A

0 1M

//1M D 0 0 # 0θ //

0θ 0 0 # R A!#A14RA0

0////

1 MMM += 26$ 0 A7

# 1θ A1#A 25 # 0 B

1M /1M D0# 1θ

/1θ 00# ///M

/ # 1 /B 0 1A0

zona de funcþionare stabilá#0# )2/0( πθ ÷= zona instabilá )2/( ππθ ÷= # 63 63 " 0 A 0 # 10 0( !0 0 # θ oo 3020 ÷ B10)

5,22sin

1max ÷===NMN

Mm P

PK

θ 2+

Page 39: Curs masini electrice

*9

1.8. FUNCÞIONAREA GENERATORULUI SINCRON ÍN REGIM STAÞIONAR NESIMETRIC

A % # !

ABA"A B 0 0A!B! $#1 0 A 0<

#=0A1A0) # 0

A0< A0 CBA III ,, A ClBlAl III ,, )

0 CBA UUU ,, # 01!0A0!00

hhiidd jXRZjXRZjXRZ +=+=+= 39 dZ "A 0 A BBA1) iZ "A !0 A BB1) hZ "A0 AB#B%0B# 4#A01A< "0) "!00) " >A0#010010 @A

cba VVV ,, 1<

Page 40: Curs masini electrice

0 6:

=

c

b

a

i

d

h

VVV

aaaa

VVV

2

2

11

111

31 8:

!!0

=

i

d

h

c

b

a

VVV

aaaa

VVV

2

2

11

111 8

F#0 %5≤Ad

Ai

II

1.8.1. Regimul de scurtcircuit bifazat al generatorului sincron /0 0 01%AB1" # 0 # +5 00 0 1

AA<0=AI ) 2kCB III =−=

0=−= CBBC UUU 8* - A 0 001!04<

( ) ( )

( ) [ ]

( ) [ ]

++=++=

++=++=

==++=

)(31

31

)(31

31

231

31

22

22

aaUUUaUaUU

aaUUUaUaUU

UUUUUU

BACBAAi

BACBAAd

BACBAAh

86

(A 86!00 AiAd UU =

># +5$#

Page 41: Curs masini electrice

6

( )

( )

( )

−=−=++=

−=−=++=

=++=

)(31)(

31

31

)(31)(

31

31

031

22

22

22

22

aaIaaIIaIaII

aaIaaIIaIaII

IIII

kBCBAAi

kBCBAAd

CBAAh

82

$!00!00<

AiAd II −= 83(A#10

eEses UIjXUUU =+=− 8840A040

0 B B 0!A<

00=+=+=+

AhhAh

AiiAi

eAAddAd

IjXUIjXU

UIjXU 89

(0 0 A 89 1 !A 8+0<

eAAiiAdd UIjXIjX =− 9: AA 830<

id

eA

id

eAAd XX

Uj

XXjU

I+

−=+

=)(

9

41!!0!<

id

eAd XX

UI

+= 0 95

># +*(#<")"A0!0

Page 42: Curs masini electrice

0 65

# +*"#01100/0 10

2/π A0 0 1 4 B # A 0 !0 # +* # +*

-A#0<

)(0 222

aaIIaIaIIIII

AdAiAd

BhBiBdBk

−=++=

=++== 9*

$1!A<

23

21

23

21

34

2

32

jea

jea

j

j

−−==

+−==

π

π

96

11 9*AB 9 A<

id

eAAdk XX

UIjI

+−=−= 332 9+

/!!0!<

id

ek XX

UI

+= 0

2 3 92

1.10. MOTORUL SINCRON

0 !0 1

L#

(0 0 % L0 0M0 1A0% M 1!M

"#θ L # /#A 630 B A0 #

># 26 0 !

Page 43: Curs masini electrice

6*0 ! !40 0M 100M0 arbMM =

1.10.1.Ecuaþia de tensiuni çi diagrama fazorialá # 26 " 10 ! " 00 # A0 4B "O0A1!<

euuRi Σ=− 6: (#A#A<

dtdueψ

−=Σ 6

%0100<

σψψψψψ +++= aqadE 65

Eψ "%10%A) adψ "%A0%#0) aqψ "%A0%!0)

σψ "% A A A 00<

Riuuuuu eeaqeadeE +−−−−= σ 6* #1%

IRUUUUU eeaqeadeE +−−−−= σ 66 / = A 0 # 0 ! 0 !0 1A# 2+!!# 22

-!00A 0cos1 >= ϕmUIP # 0<θ 0 eEU 1U

# # ! 0 0 L L 0%L 0 !0 1 L

0sin <= ϕmUIQ B%0# 2+!00sin >= ϕmUIQ B%0# 22

Page 44: Curs masini electrice

0 66

># 2+(#0 ># 22(#00!0 0!0

1.10.2. Bilanþul puterilor active la motorul sincron # 23AA

0A< 1P "0!00A) MP "#00)

># 237A! ># 28$A0 A

Page 45: Curs masini electrice

6+

2P "00) vmp + "!A) FeP "11#) CuP "110

Ecuaþia de miçcare ín regim staþionar 7A!<

FevmM ppPP ++= +2 6+$1AΩ AA1#A<

02 MMM += 62 Avantajele motorului sincron faþá de cel asincron "L0" ϕcos !L0 L 1 = ! 100A)

"A0#%1A%!L

Dezavantajele motorului sincron faþá de cel asincron "0L # L !L0

#0)"L 0

0L1L)1.10.3. Pornirea motorului sincron

-! L 0 0 # L0!!0 A. Pornirea cu motor auxiliar /L0%0L01L# B. Pornirea cu frecvenþá reglabilá -!0 !L0 #0 !L 0 ,!A 0 .5"* G A B #100 min/)65(1 rotn −=

Page 46: Curs masini electrice

0 62

(010%A0!0 B1

-! !L LLL0!L0LL0

! 0 !A 0 C. Pornirea ín asincron 400 0 100 1 colivie de pornire 04B10A0B#1!B01!

A A ! B# 0# asM 1

/B =# A 0 195,09,0 nn −= 10 L rezas MM = 010%A

-M#0LL! sM !0A$ 0 0 ! M %A A 1A0 @ 1 M L 00

, L 1 1 L %L4%0L#00#0%'-100A<a) Se scurtcircuiteazá ínfáçurarea de excitaþie

-0 1 10 %A! 0%A0! B # !0 0B # 1!B 0 !041A0A<

Page 47: Curs masini electrice

63

nnnnnn

psf

pfn −=

−⋅=== 1

1

11

122

6060 63

/BA0A<

12 nnnnd =+= 68 !0 B / # dM

/B!A0A<)21()1(22 11112 snnsnnnnnni −=−−=−=−= 69

A B A 10 0 ! .:+ -A ! 0 0 0

># 3 /<"10%A01)"10%00

(0 sM 0 01047A %A 0 1 A B0 =# 1 7 0 !

15,0 nn = A 1 0A- A 0 ! A000A0=#014(0%Ab) Se lasá deschisá ínfáçurarea de excitaþie

Page 48: Curs masini electrice

0 68

10 0 1 10 0%00#A&00!0 c) Se conecteazá ínfáçurarea de excitaþie pe o rezistenþá

0 10 %A A0 0! exs RR )108( −= !10%A! iM # 3 A dM 0! $ ! 0 1 0 A 14!1 4A01

1.10.4. Caracteristicile de funcþionare ale motorului sincron 4<

===

=.

.

.)(cos,,,,, 2

ctIctfctU

PfnMIP

E

ϕη +:

1# 3*

># 3*/ ># 36/ )(cos 2Pf=ϕ

)(,,, 2PfIMn =η !L%A

Page 49: Curs masini electrice

69

NML0 ,1nn = 0caracteristica ! )( 2Pfn = 00 %

/ # 20 MMM += Ω

= 22

PM 1M

)( 2PfM = 0# 0M / )( 2Pf=η 0 00

L/ )(cos 2Pf=ϕ ! ! .ctI E = "

1 # 36 $ !0 0 1 L %L ϕcos !000(0%%0

1EI 1M1#0

10L 1cos =ϕ 00 %L ϕcos !! A1!0A /5%0

12 EE II > 0 0 10 L 1cos =ϕ , 0100 ! ϕcos 00 ! 1 #!001L!%0

( #0 %L 0 %0 !

23 EE II > * 0 0L ! 1 ! #0 L0 # !01L / 6 0 0

14 EE II > -1#!L 2P !0 N ! 01MLL!0L!0

1.10.5. Compensatorul sincron N#1

!0 100A 0

@# # 0 % A0 1#0 !0

Page 50: Curs masini electrice

0 +:

1A 00A1

!0 0 1 A ! !01A!

/!0 /aI 0

A 10 !0 /rI 0

/I # 3+ $ !0 0 0 !0 00

( 10 ! /

rI 0BA rI !000 //

rI 0

!000A

># 3+$100AB00!0

/!

0!=100A"#=! Observaþie. /#A!0"A

2. MA§INA DE CURENT CONTINUU !0 B 0

# B % = 0 # 0 1 A 1 # B

Page 51: Curs masini electrice

+ 0A00(0100%A!0<

" %A 0 B 10 %A 000)

" %A!AB 10%A0)

" %A B 10 %A 01)

"%A%0B!0100%A!A0

2.1.1. Párþile componenete ale statorului $ %0 0 inductoare

B#0 Carcasa00%0%0%0A=

,==#1!=##>0B#111#0 # ! A 1A00

,!0 %0 0 0 10A# "5+0A#:+1 % # 0!0

Polii principali %0A# "5+ A 1 # %A 0A0AA0

4 A 100 %A %0 0N!A# B # A !0 1 01

Page 52: Curs masini electrice

0 +5

Polii auxiliari 1 # 1 A !0 A A # A 0 A1%%100AA Infáçurárile de excitaþie % %0 0 # 1 A 0 7 0 1 " 1B 0 A0 B#

,A0!BA0#=!01#!înfáçurarea de compensaþie, 0101

2.1.2. Párþile componenete ale rotorului @Miezul feromagnetic A

0 C A0000#:+ 0 % 1! 1#

( ! ! # 0 # 0 cml 20≤ B 0 0 0 !0!A%

# # 000A!0!A

Infáçurarea indusului 0 100#01000#1C1000000000 1 0100

410010 ínfáçurári de curent continuu. $A 0 1 A 0

Page 53: Curs masini electrice

+*

Colectorul 0A0B1BA0B##0100

@1#1%101

2.3.1.Tensiunea electromotoare indusá @Al S0

medesbie UNU α= 55 A0!#5 8

aKNb 2

= 555

!0S"0

medecsmedes UwU 2= 55*

iα A00) O – 0 # 0 S00) 5–00S) sw "00) medecU "!S" (#A#0<

aimedmedec vLBU δ= 556

medBδ !A#SS) iL "#0) av –!0 ,!A<

60Dnvaπ

= 55+

(") "SK (0S!A)

Page 54: Curs masini electrice

0 +6

pD

2πτ = 552

0!

602 npvaτ

= 553

-AS0Φ= nKU ee 558

apNKe 60

= 559

00L)

medii BL δτα=Φ 5*:%

2.3.2. Cuplul electromagnetic al maçinii de current continuu ,L10 # L M#10<

Ω== MIUP aeM 5* 0!BS!A558559<

ama

aae IKI

apN

n

nIa

pNIU

M Φ=Φ=Φ

=ππ 2

602

60 5*5

apNKm π2

= 5**

00L / # L 0 % Φ L L# aI

In concluzie # B A0 # ! ! #

Page 55: Curs masini electrice

++

2.4. GENERATOARE DE CURENT CONTINUU ; 0 L0 generator M

000

2.4.1. Bilanþul de puteri çi ecuaþiile generatorului de curent continuu separata

$ 0 % # %A0 ABS0A# 552 0 A A<" Ω= 11 MP puterea mecanicá 0 )" UIP =2 puterea electricá 0)" aeM IUMP =Ω= puterea electromagneticá, !"0S)" vmp + !L)" Fep 11L =# L0 1 0 0)" eexex IUp = 1 10 %)" 2

aaCua IRp = 1 10)" aR AS00)" apect IUp ∆= 10 Ecuaþia de miçcare

(A L

FevmM ppPP ++= +1 5*6&0 vmFe ppp ++=0 0 #

AS#SS0#001 =−− pPP M 5*+

>#552 7A #

Page 56: Curs masini electrice

0 +2

-S0AAΩ "!#0AAS#A!T"<

001 =−− MMM 5*2" 1M ) "M #) " 0M

Ecuaþia de tensiuni la generatorul de curent contiuu - "#552!0A<

ctCuaM ppPP −−=2 5*8%!<

apeaaae IUIRIUUI ∆−−= 2 5*9

( # %A 0 aII = 0 # S0A A AA<

peaae UIRUU ∆−−= 56:

000"S aa IR

aae IRUU −= 56 2.4.2. Curbele caracteristice ale generatorului cu excitaþie separatá

N#55301#

%L0

Fig.2.27. Schema pentru ridicarea experimentalá a caracteristicilor generatorului de curent continuu cu excitaþie separatá.

Page 57: Curs masini electrice

+3

Caracteristica de funcþionare ín gol

==

=.

0)(0 ctnI

IfU e 56*

, A S # 0 00 eUU = 00 Φ≡eU ! eemme INU 2==θ )(0 eIfU = 0 0 0 #0

)(0 mmUf=Φ (0 0 # 00 ≠U

0=eI /M %L %L M ,cR L 0 ##558 , 0 0 %L #0 0 0 N0 ! 0 #00 !0 %L 000-0%0 remU % remΦ ( 0 # M0 +" 5 NU -LL-00##0,0=0-0

Caractersitica de sarciná0A0<

==

=..

)(ctnctI

IfU e 56+

$0% #5531!!L0 sR 0%L cR 00 .

>#558/AS#

Page 58: Curs masini electrice

0 +8

/#0 001 .: > 0 5 0 1 # 5* L0 #0 0 0 # 0 . !M40#)!M/00

>#5* /0 >#5*5/%0

Caractersitica externá $A<

==

=..

)(ctnctI

IfU e 562

01#5*5 $ !0 0 0< " # A ! AS0) "0L aR

/ %L 0 !

NN IU , %L (0L001-#5*50M01#! 0U JL0#L<

%1000

N

N

UUU

U−

=∆ 563

N )%105( −=∆U

Page 59: Curs masini electrice

+9

>#5**/%ă >#5*6/#=

N # 5** 0 #0 % # #-! #0!M40#)!M / ctI e = 0 0

Caracteristica de reglare $A<

==

=..

)(ctnctU

IfI e 568

#5*60#0S# 5*6 #0 (# # 0 ! L 0 0 1M !M / 0 F. N #0 " #= NUU =

$ !0 0 %L 1M 0 0 0 0 0

2.4.3. Curbele caracteristice ale generatorului cu excitaþie derivaþie

U %L !L 1# 5*+ N0 %L 000 )%52( −=eI 0 10 0

Page 60: Curs masini electrice

0 2:

#010%L0

>#5*+$%0

#%L!L

Procesul de autoexcitaþie 1 0 0#L1O0 # 1 10 eu ! 0 1 1010%,!001001M% 10 %L 0 1 % eu !0 0 10%L (L569!M01 ea ii = L

dtdi

LLiRRRu eeaeece )()( ++++= 5+:

N # 5*2 0 #)( ee IfU = 50%L0

).()( eeec IfIRRR =++-%L0M01-L

5 0=dtdie

$!0 0 0 eU 00# α L ec RRRtg ++=α M cR >L0M

Page 61: Curs masini electrice

2 L-L-L00 ccrR 1M 5 0 L 5D0 L 1

crα #%0 # - LL ! 0)

ccrc RR > 5VV 0%L (000 %L 0 S0A<

" 0 % M #S0)

5" %S0%A0S)

*" A0%A00B!0 ccrc RR <

(0! A S !0 A B # %A<

$ ! A cR B0 SA ccrc RR < (0SAS00AS0

0#0A "S0S0%A ! % 0!0

(0 A 0S0 0 S 0 B # / B 0 10 %L00B!

Observaþii: C 0U 1 # #0 eU 0 L 100 L! ea II = #=)

>#5*2 %!0 %L

Page 62: Curs masini electrice

0 25

L-0 # C # !L L 0 L M ( # L0 0 #= M cR

4%L 0 1 O 1 N # L L L #!L56900

ea

eec

aae

IIIIRRUIRUU

+=

+=

−=

)(;

5+

Caracteristica de funcþionare in gol

==

=.

0)(0 ctnI

IfU e 5+5

NM

00 eUU = 1#00 # %A 0 0 S 0%#ML cR 1 ( )∞,0

Caracteristica externá

==

=.

.)(

ctnctR

IfU c 5+*

( %0 cR 0 NU

0 NI N # 5*8 ! % # % !L 05$!00L010#!L<M#00#%L0S<

>#5*3/ AS#

Page 63: Curs masini electrice

2*

"%

+

=ce

e RRUI

%( ! 0 0 L 0 sR

# M0 ! %0 crI curent critic 0 0MM L0 sR 0 L 01)

scI 00!#00-L# %L 0 0

Naesc IRUI )2010(/ ÷== %L 0M" %0 eU

Caracteristica de sarciná

==

=..

)(ctnctI

IfU e 5+6

çi cracteristica de reglare

..

)(ctnctU

IfI e ==

= 5++

0 # %L 0 !L

Caracteristica de scurtcircuit 0 #!L1M010%L0%%0

2.4.5. Caracteristicile generatorului cu excitaþie mixtá $#%%00 1 #565U00100%L!L% %(0% 100%%

>#5*8 /%#% !L 0

Page 64: Curs masini electrice

0 26

#excitaþie mixtá adiþionalá diferenþialá (#010 !L 10 %L 0 10000!

>#565$%0#%L%0

0 1 M caracteristica externá #

% , 1 # 0 # !LM # 10 % N 010M! 0 " L #!L N # 56* " %0 # !L(0 0 NI 0 0 1# 1000L 0 1M 0 0 0 5 $ 0 # normal compundat(0 100 0NI 0 0 1 # *

#supracompundat, L0 100 A S

0 % # 6#anticompundat

>#56*/%!

Page 65: Curs masini electrice

2+

- 0 0 L # 0 0 %

2.5. MOTOARE DE CURENT CONTINUU

;0L0M000, 0 #

2.5.1. Bilanþul de puteri çi ecuaþiile motorului de curent continuu $ 0 % %A0#56+0A<" UIP =1 puterea electricá 0A)" Ω= 22 MP puterea mecanicá 0)" aeM IUMP =Ω= puterea electromagneticá, !"0S)" vmp + !L)" Fep 1 1 L =# L0 1 0 0)" eexex IUp = 1 10 %A)

" 2aaCua IRp = 1 10

)" aR A0S00)" apect IUp ∆= " Ecuaþia de miçcare

(A L

FevmM ppPP ++= +2 5+8&0 vmFe ppp ++=0 0 #

AS#SS0002 =−− pPPM 5+9

>#56+ 7A

Page 66: Curs masini electrice

0 22

- S0A A Ω AA S #A!T"<

002 =−− MMM 52:" 2M )"M #)" 0M #A!<

dtdJMMM Ω

=−− 02 52

Ecuaþia de tensiuni la motorul de curent contiuu -#56+!0A<

ctCuaM ppPP ++=1 525

apeaaae IUIRIUUI ∆++= 2 52*

(%A0 aII = S0A

peaae UIRUU ∆++= 526

aae IRUU += 52+

2.5.2. Caracteristicile motorului derivaþie

>#562$%0!A

0 %A 000

Ne II )%52( ÷= AAS#A<

ea

eec

aae

IIIIRRUIRUU

+=+=+=

)(;

523

Page 67: Curs masini electrice

23

Caracteristicile de funcþionare ale motorului derivaþie 1) Caracteristica vitezei $A<

Φ=Φ=

=

=

N

s

N

RUU

Pfn 0)( 2 528

aae IRnKU +Φ= 52940A00A<

se

aa

ee

aa nnKIR

KU

KIRU

n ∆−=Φ

−Φ

−= 0 53:

0n "AS#0)

Φ=

eKUn0 53

sn∆ "0AAS0)

Φ=∆

e

aas K

IRn 535

4B A 53: S B #=0 A .ct=Φ !0 )( aIfn = 0A0#!00 0 (0#=0 A %! A aIP ≈2 A ! )( 2Pfn = 0 0#!0 0S#563 , !A 0 A 0 0 0 )%85( ÷=∆ sn

Observaþie $ A #0 0 B 0 0 %

>#563/!

Page 68: Curs masini electrice

0 28

L 2P 54! 1#1M0L0

5Caracteristica cuplului

Φ=Φ=

=

=

N

s

N

RUU

PfM 0)( 2 53*

$!M1!A S #A 20 MMM += A< 2M " 0)

Ω= 2

2PM 536

0M "S0)

Ω+

= +vmFe pppM 00 53+

( ! 0 A S0 .ct=Ω BA0 #568,0!!0SBA5

*Caracteristica curentului

Φ=Φ=

=

=

N

s

N

RUU

PfI 0)( 2 532

$!M1!A#

am IKM Φ= A ea III += $!00 )( 2PfIa = A00 )( 2PfIe =0@#00S#569" "0 .ct=Φ 5"0

>#568/

Page 69: Curs masini electrice

29

>#569/>#5+:/

6Caracteristica randamentului

Φ=Φ=

=

=

N

s

N

RUU

Pf 0)( 2η 533

-!A<

11

2 1Pp

PP Σ

−==η 538

pΣ "0

)%9475( ÷=η 0#5+:

Caracteristicile mecanice ale motorului derivaþie ; L0 0 0 1 L0 caracteristica mecanicá0<

=Φ==

=..

.)(

ctctRctU

Mfn s 539

-A0A1Φ

=m

a KMI

sme

a

enn

KKMR

KUn ∆−=

Φ−

Φ= 02 58:

Page 70: Curs masini electrice

0 3:

0n "AS#0053 ) sn∆ "0AAS0)

2Φ=∆

me

as KK

MRn 58

B #=0 A .ct=Φ !0 0 )(Mfn =0 A 0#!0001) Caracteristica mecanicá naturalá

Φ=Φ=

=

=

N

s

N

RUU

Mfn 0)( 585

,!A0A 0 0 0

)%85( ÷=∆ sn B 00 #0 # 5+ " 001B0!!AB .ct≈Φ

1) Caracteristicile mecanice artificiale de tensiune

Φ=Φ=

≠=

=

N

s

N

RUctU

Mfn 0.

)( 58*

AA<

sme

a

enn

KKMR

KUn ∆−=

Φ−

Φ= /

02

/586

!00 sn∆ .0AS#0

Φ=

eKUn

//0 58+

/ ! ! 0 000$00<

/ NUU > <

>#5+ /00

Page 71: Curs masini electrice

3

"S AB) " 0 A 0#/ NUU < 0 #5+5

2) Caracteristicile mecanice artificiale reostatice

Φ=Φ≠=

=

=

N

s

N

ctRUU

Mfn 0.)( 582

-ASA<

/02

)(s

me

sa

e

nnKK

MRRKUn ∆−=

Φ+

−Φ

= 583

AS#0 0n "0A

2/ )(

Φ+

=∆me

sas KK

MRRn 588

4 ! ! A 0 0 " sR 0 0#5+* 2) Caracteristicile mecanice artificiale de flux

>#5+5/

>#5+*/

Page 72: Curs masini electrice

0 35

Φ≠=Φ=

=

=

N

s

N

ctR

UUMfn

.0)( 582

-%A0A<

//02//

)(s

me

sa

e

nnKK

MRRKUn ∆−=

Φ

+−

Φ= 583

!00"AS#0

//0 Φ=

eKUn 588

0A

2//

Φ=∆

me

as KK

MRn 588

/ !!A0A / % NΦ<Φ şi 0 #5++

2.5.3. Caracteristicile motorului serie 0 %A 000 ae II = 0 S S0 (0 0A AS#00%0

>#5+2$%0

Page 73: Curs masini electrice

3*

AS#A0<

ea

aae

IIIIRUU

==

+= ;59:

- A 52+ !B S ! A558!AAA<

Φ−

Φ=

Φ−

=e

aa

ee

aa

KIR

KU

KIRU

n 595

Caracteristicile mecanice ale motorului serie

L0 caracteristicile mecanice<

=Φ==

=..

.)(

ctctRctU

Mfn s 592

,0 2amKIKM =

0KK

MIm

a = A5950

21 KR

MKU

KKR

KKMKK

Un a

e

a

me

−=−= 593

- 0 ct≅Φ !

asm IKM Φ= 0sm

a KMIΦ

= -SA

2sme

a

se KKMR

KUn

Φ−

Φ= 598

0 )(Mfn = 0A593

00598

1) Caracteristica mecanicá naturalá # 5+9 " 0 0

0 " A 0 0 0 ; 0elasticá (moale

Page 74: Curs masini electrice

0 36

Φ=Φ=

=

=

N

s

N

RUU

Mfn 0)( 599

, L !0 # ! " #0 1L 0 1 L0 #) ! 0 L! 00L1#

5) Caracteristicile mecanice artificiale de tensiune

Φ=Φ=

≠=

=

N

s

N

RUctU

Mfn 0.

)( 5 ::

AA<

"A21

/

KR

MKUn a−= 5 :

"A 2

/

sme

a

se kKMR

KUn

Φ−

Φ= 5 :5

!A 0 NUU < B 00%! 1 #52:

2) Caracteristicile mecanice artificiale reostatice

>#5+9/00

>#52:/

Page 75: Curs masini electrice

3+

Φ=Φ≠=

=

=

N

s

N

ctRUU

Mfn 0.)( 5 :*

-ASA<

"A21 KRR

MKUn sa +−= 5 :6

"A

2

)(

sme

sa

se kKMRR

KUn

Φ+

−Φ

= 5 :+

/ #52 0 0 A sR 1AA

3) Caracteristicile mecanice artificiale de flux

Φ≠=Φ==

=

N

s

N

ctR

UUMfn

.0)( 5 :2

( % 0 0 # 100 %A # A10!0A0W NΦ<Φ %1A01A#525

2.5.4. Caracteristicile motorului mixt %A %0 S# 52* >% 0

>#52 /

>#525/%

Page 76: Curs masini electrice

0 32

100!A%% 01000=AB%00AB% = A 0 1 0 A100A0

>#52*$%0

Caracteristicile mecanice ale motorului mixt

0-%!A 1 # 526 " < " !A) " 5 ) " * % A !A0 0 #00010) " 6 % 0 0 10!A!BAA1#) "+%A $ 0 0 0 100 %L!L0 0 L 0 !%#10

>#526/%

Page 77: Curs masini electrice

33

2.6. PORNIREA MOTORULUI DE CURENT CONTINUU -0 10

0 ) A0 0 00#!# N 0 #!!L1!L!

2.6.1. Pornirea prin cuplare directá la reþea 40 0 0 0M02IXA

=ΦΦ=

Ω=−

+=

Φ=

++=

)(

);(

)(

e

am

r

eeeEex

ee

eaaaaa

ifiKmdtdJmm

iLdtdiRu

nKu

uiLdtdiRu

5 :3

$1!motorul derivaþie0N .Uuu exa == !0L ea LL , 100100%L0!0L $ !0 0 M#0 regimul tranzitoriu mecanic !L L regim tranzitoriu electromagnetic!LL%"regim tranzitoriu unic electromecanic.

/M 0, =< nmm r L

dtdiLiRU a

aaa += 5 :8

$L L 0!L %L0

a

aa R

LT = 0 ! 0 ap RUI /max = 4

Page 78: Curs masini electrice

0 38

!LL00 - rmm > 0 1 L M M L 1 L Y) 0≠n

0≠eu / pI 10 0 0 !

Φ=

M

rf K

MI ! #52+

rmm = CL fn 1 #

0 52+

Φ

−=

e

faf K

IRUn / M

M pI100!0 maxpI /#

M ai M%Φ ( ! %L !L

1 10 %L 0 0 1M M# !%L pI , motorul serie 0 %Φ ! - 0 1 L 0 Np II )1510( −= 1"

.::5 0=rM pt .: ":*

NM1# pI M

0 pI #

>#52+/ L 1 0L

Page 79: Curs masini electrice

39

pM 0 4 ! #=1L

2.6.2. Pornirea reostaticá ,0 10 pR M00001LN0%L0L cR0LL00#523NL%Φ ! %0 # ! $#=000.:.:10

p

p RUI =max 5 56

pR L0(01B

0 ! 1 0 ) Np II )7,15,1(max −=

Np II )2,11,1(min −=

;p

ea R

nKUI

Φ−= 5 5+

!0 L 0 pR #528 0

!0 fI 00

>#523$0!L

Page 80: Curs masini electrice

0 8:

@L L0 1 !0 N #523 L 0 1 iC /M ! 00 1 1C A ! 1R 1MA0! 1pR

ai !L0 maxpI N0<

!0L 1pR M0

! minpI M0!L1M

0 !0 maxpI $ 1

L iR 0 ! 1 ), minmax pp II / L iR

minmax , pp II #00< "A52+014

max0 ppe IRKU +Φ⋅⋅= 5 52

0A pR 0!<

maxpp I

UR = 5 53

" A 0 7 pR !/ 1pR

max11

min1

ppe

ppe

IRnKUIRnKU

+Φ=

+Φ=5 58

(A0A

pp

pp R

II

Rmin

max1 = 5 59

4B=0A<

np

np

RRRRRRRRR

+++=

++++=

...

...

32

3215 *:

0000A0<

11 pp RRR −= 5 *

Page 81: Curs masini electrice

8

Observaþie - A !A1 0 00 !A 01#53 -000!=< "00) "A) "!0 /!=< "#

2.6.3. Pornirea cu tensiune redusá ,

!0/ ! 0 !0 #! 00 0 1AB0=# !0$ 1!A0

N0 %L 0 L cR 0LL00#535 NL% Φ !%0#!

>#529/ )( aIfn = 0!A

Page 82: Curs masini electrice

0 85

;/

a

ea R

nKUI Φ−= 5 *8

>#535$0!L

$01B Np II )7,15,1(max −=

Np II )2,11,1(min −=

A 0 0 1U 0 1 0 maxpI $A!AA!0 0 1U /M !0000001B ai !L0 maxpI N$1B0!1 ), minmax pp II /

iU minmax , pp II #00< "A52+014

max1 0 pae IRKU +Φ⋅⋅= 5 *90!01) " A 0 7 0 1U !/ 2U

max12

min11

pae

pae

IRnKUIRnKU

+Φ=

+Φ=5 6:

(A0A

app RIIUU )( minmax12 −+= 5 6

Page 83: Curs masini electrice

8*

-B 1#0

>#53*/ )( aIfn = 0!0!A

Observaþie. - !A 1 0 00 !A 0 1 -00!=< "000) "=0) "# (!=< "#0

2.7. REGLAJUL VITEZEI MOTOARELOR DE CURENT CONTINUU #L#L

Φ

−=

e

aaa

KIRU

n 5 *:

0< aU ) 5 A)*%Φ 40L#=!M

.ctM r = 0"<

Page 84: Curs masini electrice

0 86

U#! minmax / nn=γ5 (#=* /#=6 4

2.7.1. Reglajul vitezei prin variaþia tensiunii

0 #0 A0 NUU <

>#536/#=!!A< !A)

/ # .ctM r = 1 #536 !A 1 # 536 A0

Indici tehnico- economici00< U # ! 108/ minmax ÷== nnγ

0A5 ( #=< 0

0* / #=< 1 A

64<" !A !=0

#00) " # !=0 1B #0

Page 85: Curs masini electrice

8+

2.7.2. Reglajul vitezei prin metoda restaticá 1 " A0

# 0>sR A @A0##00!0A00# $ 0 0 1 #!"##=

>#53+/#=!0<!A)

/ # .ctM r = 1 #

53+ !A 1 # 53+ 1A0

Indici tehnico- economici< U#! 32/ minmax ÷== nnγ 0

#5 ( #=< 0

0*/#=<1

0!A064<" !A !=0 A

)

Page 86: Curs masini electrice

0 82

" # !=0 1B 0#

2.7.3. Reglajul vitezei prin variaþia fluxului de excitaþie A0 % $ ! 1 otorul derivaþie %%A!L eI =B cR <

ceee RR

UIIf+

==Φ )( 5 *9

, !A ! % " 0 0 # 0% / % NΦ<Φ L

//02// s

me

a

e

nnKKMR

KUn ∆−=

Φ−

Φ= 5 6:

0L1# 0 L ;/

sn∆ 0 0 1#532

>#532/#=!%< !A)

C ! 10 0 %

,ctMM r == ! L

Page 87: Curs masini electrice

83

)am IKM Φ= 0 00 ! 0 N #532 " 0 0 @0 0 =0LM#0M ctM r =

La motorul serie B#;#A%A<

m

ee

m

e

RIw

R2

==Φθ

5 6

eθ "A%A)

mR "A#00%)

ew "0100%A)

eI "%A4B 0 A 0 0 0

%< " 0 10 %A0 0 # ) " 100 %A #533 0 #0B0 %A A 0 0 BOB<

aed

de I

RRR

I+

= 5 65

Indici de relare 0: U # ! 32/ minmax ÷== nnγ 0

0A0%0<"100LL

101L)" 0 A0 B # 0

0 L ! 0 A0000)

>#533$=%A

Page 88: Curs masini electrice

0 88

5(#=

*/#="1)!AA cR ! dR 64<

" !A !=0 1%A)

" # != 0 #

2.8. FRÃNAREA MOTOARELOR DE CURENT CONTINUU $0B<

"B!0) "B)

"B02.8.1. Frãnarea recuperativá ; 0 # 1 #

B0!0B01 ! 1A A B #0A ! A 0 0

Frãnarea recuperativá la motorul derivaþie $0 0 %

!0 L0 1 4 0 0#538 /B 0 0 0 1 ! aM #A0 #0A 1A

/ A A 0 0 /B "

>#538/M!0!A

Page 89: Curs masini electrice

890 A 1 # 0 0n 0 A 1 !00!B$=# A0 17#538 B 0 A0 1 00 fa MM =

(0 0 0 B !0 A0B fR 17D

40 0 M 0 != 1L0M

Cazul motorului serie ( A 1 # 0 0 0 1 B!0

Frãnarea recuperativá la motorul mixt ,%00A1A=A%0100<

sd Φ+Φ=Φ 533 /B1#B0!00 0<aI 0%10 0)( <=Φ as If / = ! A %00B(A!B010B0

Bilanþul de puteri: 1 # 0 00"B010000001 A 0 $ B !=00 #0!=00B0A 0nn > 0MM0000

2.8.2. Frãnarea contacurent (electromagneticá) - # 1#B0#00A<

Page 90: Curs masini electrice

0 9:

" 0 10 A 0 !0)

"1AB- A B L

#0 M <

fa

ef RR

nKUI

+Φ+

−= 5 6*

@ 0 1 ! # L # M0#0

Frãnarea contracurent la motorul derivaþie

# 539 0 L 4 0 00 L0 1700B 1fR

/ # LM0B A0B0$!0000AB

(0 B 0 0 B B =# ! 0 minfM 0 A BA0 2fR 0!%0 maxfM B

N !0 1 0 L0 rMM > -L L01!

40 0 M M0 00

>#539 / B !A

Page 91: Curs masini electrice

9

Frãnarea contracurent la motorul serie , 0 0 10 % )( as If=Φ / # 0!A1 - 1#B0!! 10 10 %A ! A B 1 $ !A A ! B1 000

Frãnarea contracurent la motorul mixt ,% A 1 # B0 0 = 0 %A /!B%010#

Bilanþul de puteri:A0 0 " B0 N L0 L M0 #0 0!#N#000 1 00(0 A B 10 # ! ))3020( Nf II ÷= B A 10

1 ( L fR01M#=0000011%

2.8.3. Frânarea dinamicá -!100L0 A0 B 10 %A 0B01

/0L0!

fa

ef RR

nKI

−= 5 69

Page 92: Curs masini electrice

0 95

1 # # %A 0 !B0 1 A !0 1 L0 #M Frãnarea dinamicá la motorul derivaþie /#M<

nRR

KKIKMfa

mefm +

Φ−=Φ=

2

5 +:

!0A.0A0#!0# #585B1 0 A 4 000A017B 1fR

$!000B00A00 B 0 B 0 B =# !0 minfM ! A B A 0 2fR 0 !%0

maxfM B - 0!0 L fR L # M M 1M0L >ML Frãnarea dinamicá la motorul serie , M 1 # #%1A<

" 0 10 %A ! 0 eremU L0A"##)

>#585/B0!A

Page 93: Curs masini electrice

9*

"LB0!0 crff RR < / B 1

0 Frãnarea dinamicá la motorul mixt , % A 1 # B0 00 = 0 %A /!B%010# Bilanþul de puteri< 1B " B00 0100000 0 1 00 A B $ B!=00A

-!AB0!B0