ТОЕ НАУ ЧАСТИНА ІІ(Сiрий Д.Т)

.

.

6.

, ,

.

.

6.1. ,

( , )

, 120 :

e1 = Em1 sin t,

e2 = Em2 sin ( t - 120 ), e3= Em3 sin ( t - 240 ).

-, -, .

.

.

:

-( 25%),

-.

-

. 1889 .

: , ,

, . 1891 .

175

.

6.2.

, ,

.

2

:

-x: – e = EmA sin t, eA=0.

: .

-y: – e = E sin ( t - 120 ), = - 1200.

-j120°.

-z: – e = E sin ( t - 240 ), = - 2400.

-j240°.

“ :” ; ; .

,

:

– ,

– .

.

, 120 (2 /3),

:

( . 6.2).

,

+ + = 0,

+ + = + -j120°+ -j240°= (1+ -j120°+ -j240°).

= j120° – 120 , 2 = j240° –

240 , :

= j120° = -j240° = cos1200+j sin1200 = - 0,5 + j 3 /2;2 = j240° = -j120° = cos1200-j sin1200 = - 0,5 - j 3 /2;

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:

(1+ -j120°+ -j240°)= (1 + 2 + )= (1 - 0,5 - j 3 /2 – 0,5 + j 3 /2) = 0.

,

(6.1).

, (

) .

,

: ,

: .

. ,

: .

, -

– . , , .

7,5…120 , 200/115 , 400…900 .

6.3.

,

.

.

. 6.3

.

, ,

, . ,

( . 6.3).

,

.

x, y, z N,

– n,

. : .

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N n . ,

N n, .

, .

.

. 6.4

N – .

, , .

, , :, , – .

, ,

: – . = .

:

U , U , U – U ,

U ', U ', U ' – U '.

: U , U , U – U .

:

= , N= + + .

.

.( . 6.5).

900, – 1800.

.

U = U; U = U -j120° ; U = U -j240°.

:

(6.2) U . U .

,

U + U + U = 0.

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.

:

U = U - U = U - U -j120° = U (1 - -j120°) = U (1 + 0,5 + j 3 /2) =

:

-: U = 120 , U = 208 ;

-: U = 115 , U = 200 .

, , .

.

6.4.

A z, B x, C y

, ,

, ( .6.6).

: .

:

EAB+EBC+ECA=0.

.

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:

EAB, EBC, ECA – ;

IA; IB; IC.– , ;

IAB ;IBC; ICA – ,

;

UAB, UBC, UCA – U ;

UA'B'; UB'C'; UC'A' - U' .

, – ,

.

,

U = U .

. 6.6

.

A', B', C':

, ,

: IA+IB+IC=0,

.

( . 6.7).

,

120 .

:

1..

2., IAB

, – ±1200 : IAB=I ;

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6.5.

( , ,

, )

.

.

, ,

, , :

1.A = B = C ; – = – = – =1200;

2.ZA = Z = Z =Z e .

, .

: uA= Um. sin t, u=0;

iA= Im. sin( t- ), = u - =- .

p= = uA iA+ uB iB+ uC iC= Um. sin t Im. sin( t- ) +

+Um. sin( t-120 ) Im. sin( t- -120 ) + Um. sin( t-240 ) Im. sin( t- -240 ).

,

sin sin =1/2[cos( )-cos( )]; Um. Im. =2 U I ,

:

p=U I [cos - cos(2 t- )+ cos - cos(2 t- -240 ) +

+cos - cos(2 t- - 480 )] =3U I cos ,

, , ±240 (

±1200) .

= 3U I cos = P = const,

, ,

.

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, ,

. , ,

.

:

P = =3 =3R 2 =3 U I cos

.

– .

:

Q = Q +Q +Q =3Q =3X 2 =3 U I sin = 3 U I sin .

:

S = S +S +S =3S =3Z 2 =3 U I = 3 U I = P2 Q2 .

, .

:

p = = uA iA+ uB iB+ uC iC = f(t).

.

:

1.P=PA+PB+PC=UAIA cos A+ UBIB cos B + UCIC cos C=RAIA2 + +RBIB2 + RCIC2.

2.Q=QA+QB+QC= UAIA sin A+ UBIB sin B+ UCIC sin C= XAIA2+ +XBIB2+ XCIC2.

3.S=UA I* + UB I*B+ UC I*C =P+jQ.

,

I*A+I*B+I*C = 0, I*C= -I*A - I*B = 0, :

S= UA I*A+ UB I*B - UC I*A - UC I*B=I*A (UA -UC )+I*B (UB -UC ) =

= UAC I*A+ UBC I*B=P + j Q.

S= UAC I*A+ UBC I*B=P+jQ.

:

S= UAC e uAC IA e-j A+UBC e uBC I e-j B= UAC IA ej( uAC- A) +

+ UBC IB ej( uBC- B) = UAC IA cos( uAC A) + UBC IB cos( uBC - B)+

+j(UAC IA sin( uAC - A) + UBC IB sin( uBC B))= P+jQ. P = UAC IA cos( uAC - A) + UBC IB cos( uBC - B),

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6.6.

,

( , ,

).

,

.

.

,

,

.

. , ( .

6.9).

Z

UA

UN

ZN

UB

Z

Z U

. 6.9

, .

:

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1. UA= UB=UC ; – = – = – =1200;

2. ZA= ZB= ZC= Z= Z e –

IA; IB; IC.

: UA= U'A ; UB= U'B ; UC= U'C ,

:

IA=UA /Z; IB=UB /Z=(UA /Z)e-j120°° e-j120°; IC=UC /Z=(UA /Z)e-j240° e-j240°.

,

. , -120-240 .

:

IN = IA+ IB+IC =(1+e-j120°+e-j240°) IA =0.

,

.

.

( . 6.10).

1.

UA, UB, UC.

UA ,

. 6.10

– ±1200 .

2.

IA, IB, IC, ,

:

IB= U /(Z +Z )=UA e-j120/(Z +ZB );

IC= U /(Z +Z )=UA e-j240/(Z +ZC ).

( . 6.11).

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