第次課Symmetricalcomponents(對稱分量法)

1、Symmetrical components(對稱分量法)Content 1 Definition of symmetrical components2 Sequence networks of impedance loads3 Sequence networks of series impedance4 Sequence networks of three-phase lines5 Sequence networks of rotating machines6 Per-unit sequence models of three-phase two-winding transformers7

2、Per-unit sequence models of three-phase three-winding transformers8 Power in sequence networkThe three-phase voltages designated: Ua,Ub,Uc are resolved into the following three sets sequence components:1.positive-sequence components:(正序分量組):consisting of three phasors with equal magnitudes,1200 phas

3、e displacement, and positive sequence.(三個分量的量值相等，相位相差120度，相序與原有相系統(tǒng)的相序相同。下角用注1表示。)Ua1Ub1Uc1正序分量1 Definition of symmetrical componentspositive-sequence components1 Definition of symmetrical components2.negative-sequence components( 負序分量組：) consisting of three phasors with equal magnitudes,1200 phase d

4、isplacement, and negative sequence.(三個分量的量值相等，相位相差120度，相序與原有相系統(tǒng)的相序相反。下角用注2表示。)Uc2Ub2Ua2負序分量negative-sequence components1 Definition of symmetrical components3.zero-sequence components(零序分量組)： consisting of three phasors with equal magnitudes and zero phase displacement.(三個分量的量值相等，相位相差0(360)度，三個分量為同相

5、。下角用注0表示。)Ua0Ub0Uc0zero-sequence components1 Definition of symmetrical componentsThree unsymmetrical components are the compose of three symmetrical components(三個不對稱相量可用三個對稱分量表示)compose of three symmetrical componentsUa1Ub1Uc1Uc2Ub2Ua2Ua0Ub0Uc0UcUbUaUa2Uc2Ub2Uc0Ua0Ub0Uc1Ua1Ub11 Definition of symmetr

6、ical components取運算符號a,則有：UcUbUaUa1Ub1Uc1Ua0Ub0Uc0Ua2Uc2Ub2三相不對稱分量寫成矩陣形式為：1 Definition of symmetrical components1 Definition of symmetrical componentsThe symmetrical component transformation can also be applied to currents.In a three-phase Y-connected system, the neutral current In is the sum of the

7、line current: In=Ia+Ib+Ic=3I0 The neutral current equals three times the zero-sequence current.Example 8.1,8.2,8.3The balance three-phase systems with abc sequence(or positive sequence) have no zero-sequence or negative-sequence components.The balance three-phase systems with abc sequence(or negativ

8、e-sequence) have no zero-sequence or positive sequence components.The unbalanced three-phase systems have nonzero values for all sequence components.The neutral current equals three times the zero- sequence current.2 Sequence networks of impedance loadsA balanced-Y impedance load, the impedance of e

9、ach phase is designated ZY, and a neutral impedance Zn is connected between the load neutral and ground. The line-to-ground voltage UagZYZnacbgUagUcgUbgIaIcIb2 Sequence networks of impedance loadsZs is called the sequence impedance matrix.Z0 is called zero-sequence impedance.Z1 is called positive-se

10、quence impedance.Z2 is called negative-sequence impedance.2 Sequence networks of impedance loadsZ0=ZY+3ZnZ1=ZY positive-sequence networkZ2=Z1=ZY negative-sequence networkzero-sequence networkSequence networks:U0U1U2I0I1I2Each sequence networks is separate, uncoupled from the other two.2 Sequence net

11、works of impedance loadsFor a general three-phase linear impedance load. The load could represent a balanced load such as the balanced-Y or balanced- load, or an unbalanced impedance load. 2 Sequence networks of impedance loadsThe general relationship between the line-to-ground voltages and line cur

12、rents for this load can be written as:Up is line-to-neutral (or phase) voltagesIp is line (or phase) currentsZp is called 3*3 phase impedance matrix.2 Sequence networks of impedance loadsZ0,Z1,Z2 is diagonal sequence impedancesOff-diagonal sequence impedancesA symmetrical load is defined as a load w

13、hose sequence impedance(序阻抗) matrix is diagonal, that is, all the mutual impedances（互阻抗） are zero.The following conditions for a symmetrical load are determined : when: Zaa=Zbb=Zcc, Zab=Zbc=Zac then: Z01=Z10=Z02=Z20=Z12=Z21=0 Z0=Zaa+2Zab Z1=Z2=Zaa-Zab2 Sequence networks of impedance loads2 Sequence

14、networks of impedance loadsSequence networks of a three-phase symmetrical impedance load :U0U1U2I0I1I2Z0=Zaa+2Zab Z1=Z2=Zaa-Zab positive-sequence networkZ2=Z1=Zaa-Zabnegative-sequence networkzero-sequence network3 Sequence networks of series impedanceSeries impedance connected between two three-phas

15、e buses denoted abc and abc. Self-impedance of each phase are denoted Zaa,Zbb,Zcc. Ingeneral ,the series network may also have mutual impedances between phases. The voltage drops across the series-phase impedances are given:cba3 Sequence networks of series impedanceThe following conditions for a sym

16、metrical series impedances :Zaa=Zbb=Zcc, Zab=Zbc=Zac Z0=Zaa+2ZabZ1=Z2=Zaa-Zabcba3 Sequence networks of series impedanceSequence networks of three-phase symmetrical series impedance:Z0=Zaa+2Zab Z1=Z2=Zaa-Zab positive-sequence networkZ2=Z1=Zaa-Zabnegative-sequence networkzero-sequence networkU0U1U2U0U

17、1U2I0I1I2The models are suitable for sequence networks of three-phase lines.3 Sequence networks of three-phase linesThe series phase impedance matrix Zp for an untransposed line is:If the line is completely transposed, the diagonal and off-diagonal elements are averaged to obtain:The sequence domain

18、:4 Sequence networks of three-phase lines5 Sequence networks of rotating machineSequence networks of Y-connected synchronous generator:A Y-connected synchronous generator grounded though a neutral impedance Zn is shown in figure. The internal generator voltages are designed Ea, Eb, and Ec, the line

19、currents are designed Ia,Ib,IcEaEb EcIaIbIc5 Sequence networks of rotating machineThe sequence networks of the generator :negative-sequence networkZ2=Zg2(negative-sequence impedance)Z1=Zg1(positive-sequence impedance is called the synchronous impedance)Z0=Zg0+3Znzero-sequence networkzero-sequence im

20、pedancepositive-sequence networkEg1U1U2U0Z2Z0Z15 Sequence networks of rotating machineSequence networks of three-phase motorsZ2=Zm2Z0=Zm0+3Znpositive-sequence networkzero-sequence networknegative-sequence networkZ1=Zm1Em1Synchronous motorZ1=Zm1Z0=Zm0+3ZnZ2=Zm2Induction motor6 Per-unit sequence model

21、s of three-phase two-winding transformersAn ideal Y-Y transformer grounded through neutral impedances ZN and Zn.Per-unit sequence networks of the ideal transformers: 3ZN 3ZnPer-unit zero-sequence networksPer-unit positive-sequence networksPer-unit negative-sequence networks6 Per-unit sequence models

22、 of three-phase two-winding transformers Per-unit sequence networks of Y-Y, Y- , - practical transformers are shown in figure 8.19Per-unit sequence networks of Y-Y transformer3Zn3ZNZTzero-sequencepositive-sequence negative-sequence7 Per-unit sequence models of three-phase three-winding transformersT

23、hree identical single-phase three-winding transformers can be connected to form a three-phase bank.The general per-unit sequence networks of a three-phase three-winding transformer:The letters H,M, and X are used to denote the high-, medium-,and low-voltage windings. HHM MX XPer-unit zero-sequence networks of a three-phase transformer7 Per-unit sequence models of three-phase two-winding transformers For a general zero-sequence networks, the connection between terminals H and H depends on how the high-voltage windi