Несимметричные режимы в трехфазных электрических цепях. Метод симметричных состовляющих.

1. Постановка задачи:

Использовать метод симметричных состояний для решения несимметричных режимов в трехфазных цепях.

2. Текст программы:

>> b=(pi/180);

>> Ua=380; Ub=381; Uc=375;

>> Kua=0*b; Kub=-119*b; Kuc=125*b;

>> XL1=24; XL2=27; XC0=6.9;

>> XC1=40.0; R0=10; X1=8.0;

>> X2=12.9; Rn=0.5; Xn=1/2;

>> X2=12.9; Rn=0.5; Xn=1.2;

>> j=sqrt(-1);

>> Va=Ua*exp(j*Kua);

>> Vb=Ub*exp(j*Kub);

>> Vc=Uc*exp(j*Kuc);

>> Va_Vb-Vc=[Va;Vb;Vc]

>> Va_Vb_Vc=[Va;Vb;Vc]

Va_Vb_Vc =

1.0e+002 *

3.8000

-1.8471 - 3.3323i

-2.1509 + 3.0718i

>> pause,

>> a=exp(j*120*b)

a =

-0.5000 + 0.8660i

>> A=[1 a a^2;1 a^2 a;1 1 1];

>> UU=(1/3)*A*[Va Vb Vc]'

UU =

1.0e+002 *

0.0843 + 0.0443i

3.7817 - 0.1311i

-0.0660 + 0.0868i

>> pause,

>> U1a_U1b_U1c=diag([1 a^2 a])*ones(3,1).*UU(1)

U1a_U1b_U1c =

8.4295 + 4.4282i

-0.3798 - 9.5143i

-8.0497 + 5.0861i

>> UP=U1a_U1b_U1c;

>> U2a_U2b_U2c=diag([1 a^2 a])*ones(3,1).*UU(2)

U2a_U2b_U2c =

1.0e+002 *

3.7817 - 0.1311i

-2.0044 - 3.2095i

-1.7773 + 3.3406i

>> UO=U2a_U2b_U2c;

>> UN=UU(3)

UN =

-6.6012 + 8.6827i

>> pause,

>> Ua1=UP(1)+UO(1)+UN;

>> Ub1=UP(2)+UO(2)+UN;

>> Uc1=UP(3)+UO(3)+UN;

>> Ua1_Ub1_Uc1=[Ua1 Ub1 Uc1]'

Ua1_Ub1_Uc1 =

1.0e+002 *

3.8000 + 0.0000i

-2.0742 + 3.2178i

-1.9238 - 3.4783i

>> Va_Vb_Vc=[Va Vb Vc]'

Va_Vb_Vc =

1.0e+002 *

3.8000

-1.8471 + 3.3323i

-2.1509 - 3.0718i

>> pause,

>> XC21=(XC1*XL1)/(XC1-XL1);

>> XC11=XL2;

>> XC21_XC11=[XC21 XC11]'

XC21_XC11 =

60

27

>> pause,

>> fi0=UU(3)/(1+(-j*XC0/(3*R0)));

>> I0=fi0/R0;

>> Ic0=I0/3;

>> I0_Ic0=[I0 Ic0]'

I0_Ic0 =

-0.8166 - 0.6804i

-0.2722 - 0.2268i

>> pause,

>> W=sqrt(Rn^2+Xn^2);

>> In1=abs(UP(1))/W

In1 =

7.3245

>> cosfi=Rn/W

cosfi =

0.3846

>> pause,

>> Pf1=In1*abs(UP(1))*cosfi;

>> P3f1=3*Pf1

P3f1 =

80.4732

>> pause,

>> zz=Rn+j*Xn;

>> Ia1=UU(1)/zz;

>> Ic1=UP(3)/zz;

>> Uab1=UP(1)-UP(2);

>> Ucb1=UP(3)-UP(2);

>> Ia1_Ic1=[Ia1 Ic1]'

Ia1_Ic1 =

5.6383 + 4.6754i

1.2298 - 7.2205i

>> Uab1_Ucb1=[Uab1 Ucb1]'

Uab1_Ucb1 =

8.8094 -13.9425i

-7.6699 -14.6004i

>> pause,

>> P1=real(Uab1*Ia1');

>> P2=real(Ucb1*Ic1');

>> P1_P2=[P1 P2]'

P1_P2 =

-15.5169

95.9901

>> Pn1=P1+P2

Pn1 =

80.4732

>> pause,

>> Pn1;

>> P3f1

P3f1 =

80.4732

>> pause,

>> tagfi=(P2-P1)*sqrt(3)/(P1+P2)

tagfi =

2.4000

>> pause,

>> R1=X1*sqrt(3);

>> R2=X2*sqrt(3);

>> Uab2=UO(1)-UO(2);

>> Ubc2=UO(2)-UO(3);

>> zz1=R1-j*X1;

>> zz2=R2-j*X2;

>> Iab2=Uab2/zz1;

>> Ibc2=Ubc2/zz2;

>> Iab2_Ibc2=[Iab2 Ibc2]'

Iab2_Ibc2 =

21.6983 -34.7439i

11.9318 +22.4268i

>> Uab2_Ubc2=[Uab2 Ubc2]'

Uab2_Ubc2 =

1.0e+002 *

5.7861 - 3.0784i

-0.2271 + 6.5501i

>> pause,

>> u=Iab2*R1+Ibc2*(-j*X2)

u =

1.1354e+001 +3.2751e+002i

>> Ulin2=UO(1)-UO(3)

Ulin2 =

5.5590e+002 -3.4717e+002i

>> uu=1.5*Ulin2

uu =

8.3385e+002 -5.2076e+002i

>> pause,

>> Upac=abs(u)

Upac =

327.7030

>> Ucon=abs(uu)

Ucon =

983.1091