KOMPONEN SIMETRISISTEM TIGA FASA SEIMBANGSISTEM TIGA FASA TIDAK SEIMBANGSISTEM SATU FASASISTEM 3 FASASEIMBANGKOMPONEN SEIMBANG KOMPONEN IMETRI

PHASA SQUENCE1. Sistem 3 fasa SeimbangR = R1 + R2 + R3

Y = Y1 + Y2 + Y3

B = B1 + B2 + B3

BalanceSupplayHubungan BintangHubungan Delta

Balance Load

2. Sistem 3 fasa Tidak SeimbangJika Znetral = 0

Jika Znetral 0

ARUS (I) DAN TEGANGAN (V)URUTAN FASA

OPERATOR a / untuk menyatakan komponen simetri Diagram Fasor berbagai tingkat dari Operator a /

Positive Squence (ABC)Negative Squence (CBA)

Zero Squence Dengan menggunakan OPERATOR a , maka urutan positip dapat ditulismenjadi :Demikian juga untuk urutan negatip :

Sehingga untuk fasor tak seimbang dinyatakan dalam :

Atau dalam bentuk matriks dinyatakan sbb :KomponenOperator aKomponenVektor SimetriKomponen Vektor Fasa

Invers of Symetrical component matrix

3. Mencari komponen simetri Komponen simetri didapat dengan menjumlahkan ketiga Fasor, dengan mengingat (1 + a + a2) = 0 , maka :

Dengan cara yang sama yaitu baris 2 x a dan baris 3 x a2, akan diperoleh :

4. Sequence Impedances

a. Impedances Transmission

Symmetrical componentPhasa componentZs = Rs + j.LsZm = M

b. Impedances Y conect Load (a) positive, (b) negative and (c) zero sequence.

c. Impedances conect Loadd. Impedances for Syncrounus GeneratorAsumsi balanced operation which implies Ia + Ib + Ic = 0

Similar expressions can also be written for the other two phases. We therefore haveSince the synchronous generator is operated to supply only balanced voltages we can assume that Ean0 = Ean2 = 0 and Ean1 = Ean .

The sequence diagrams for a synchronous generator are shown in (a) positive, (b) negative and (c) zero sequence.Vn = - 3ZnIa0 Va0 = Van0 + Vn . Since the synchronous generator is operated to supply only balanced voltages we can assume that Ean0 = Ean2 = 0 and Ean1 = Ean

5. Three Phase Power

The three-phase power in the original unbalanced system is given byQ = 3 ( Vao.Iao.Sin 0 + Va1.Ia1.sin1 + Va2.Ia2.sin 2)

Urutan nol dari Transformator dua belitan

Urutan nol dari Transformator tiga belitan

Urutan nol dari Generator

Urutan nol dari Beban

Let us consider a set of balanced voltages given in per unit byExample :These implyAnd then Va1 = Va Vb1 = VbVc1 = Vc

Solusi :

A 25 MVA, 11 kV generator with Xd =20 % is conected throug a transfromer, line and a transformer to bus that supplies a motors as shown in Fig.9,8.with motor has Xd= 25 % and Xd = 30 % on a base of 5 MVA,6,6 kV. The three phase rating of the step up transformer is 25 MVA, 11/66 kVwith a leakage reactance of 10 % and that of the step down transformer is25 MVA, 66/6,6 kV with a leakege reactance of 10 %.The bus voltage at motors is 6,6 kV. Choose a system base of 25 MVAThe system is per unit The shown sequence positive, negative and zero for system

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