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1、a Date: 19 October 2006 Origin: International Latest date for receipt of comments: 31 January 2007 Project no.: 2005/03199 Responsible committee: SS/7 General metrology, quantities, units and symbols Interested committees: Title: Draft BS EN 62428 Electric power engineering - Modal components in thr
2、ee-phase AC systems- Quantities and transformations (25/335/CDV) (Note: This is IEC 62428 and is subject to parallel vote in CLC/SR 25 as an EN) Supersession information: If this document is published as a standard, the UK implementation of it will supersede NONE and partially supersede NONE . If yo
3、u are aware of a current national standard which may be affected, please notify the secretary (contact details below). WARNING: THIS IS A DRAFT AND MUST NOT BE REGARDED OR USED AS A BRITISH STANDARD. THIS DRAFT IS NOT CURRENT BEYOND 31 January 2007. This draft is issued to allow comments from intere
4、sted parties; all comments will be given consideration prior to publication. No acknowledgement will normally be sent. See overleaf for information on commenting. No copying is allowed, in any form, without prior written permission from BSI except as permitted under the Copyright, Designs and Patent
5、 Act 1988 or for circulation within a nominating organization for briefing purposes. Electronic circulation is limited to dissemination by e-mail within such an organization by committee members. Further copies of this draft may be purchased from BSI Customer Services, Tel: +44(0) 20 8996 9001 or em
6、ail ordersbsi-. British, International and foreign standards are also available from BSI Customer Services. British Standards on CD or Online are available from British Standards Publishing Sales Limited. Tel: 01344 404409 or email bsonlinetechindex.co.uk. Information on the co-operating organizatio
7、ns represented on the committees referenced above may be obtained from the responsible committee secretary. Cross-references The British Standards which implement International or European publications referred to in this draft may be found via the British Standards Online Service on the BSI web sit
8、e http:/www.bsi-. Direct tel: 020 8996 7411 Responsible Committee Secretary: Mr G H Williams (BSI) E-mail: geoff.williamsbsi- Draft for Public Comment Head Office 389 Chiswick High Road London W4 4AL Telephone: +44(0)20 8996 9000 Fax: +44(0)20 8996 7001 Form 36 Version 6.1 DPC: 06/30143616 DC Licens
9、ed Copy: London South Bank University, London South Bank University, Sun Dec 24 04:17:00 GMT+00:00 2006, Uncontrolled Copy, (c) BSI b Introduction This draft standard is based on international discussions in which the UK has taken an active part. Your comments on this draft are welcome and will assi
10、st in the preparation of the consequent standard. If no comments are received to the contrary, then the UK will approve this draft. There is a high probability that this text could be adopted by CENELEC as a reference document for harmonization or as a European Standard. Recipients of this draft are
11、 requested to comment on the text bearing in mind this possibility. UK Vote Please indicate whether you consider the UK should submit a negative (with reasons) or positive vote on this draft. Submission The guidance given below is intended to ensure that all comments receive efficient and appropriat
12、e attention by the responsible BSI committee. Annotated drafts are not acceptable and will be rejected. All comments must be submitted, preferably electronically, to the Responsible Committee Secretary at the address given on the front cover. Comments should be compatible with Version 6.0 or Version
13、 97 of Microsoft Word for Windows, if possible; otherwise comments in ASCII text format are acceptable. Any comments not submitted electronically should still adhere to these format requirements. All comments submitted should be presented as given in the example below. Further information on submitt
14、ing comments and how to obtain a blank electronic version of a comment form are available from the BSI web site at:http:/www.bsi- Template for comments and secretariat observations Date: xx/xx/200x Document: ISO/DIS xxxxx 1 2 (3) 4 5 (6) (7) MB Clause No./ Subclause No./ Annex (e.g. 3.1) Paragraph/
15、Figure/Table/ Note (e.g. Table 1) Type of com- ment Comment (justification for change) by the MB Proposed change by the MB Secretariat observations on each comment submitted 3.1 Definition 1 ed Definition is ambiguous and needs clarifying. Amend to read . so that the mains connector to which no conn
16、ection . 6.4 Paragraph 2 te The use of the UV photometer as an alternative cannot be supported as serious problems have been encountered in its use in the UK. Delete reference to UV photometer. Microsoft and MS-DOS are registered trademarks, and Windows is a trademark of Microsoft Corporation. Licen
17、sed Copy: London South Bank University, London South Bank University, Sun Dec 24 04:17:00 GMT+00:00 2006, Uncontrolled Copy, (c) BSI FORM CDV (IEC) 2005-09-23 25/335/CDV COMMITTEE DRAFT FOR VOTE (CDV) PROJET DE COMIT POUR VOTE (CDV) Project number Numro de projet IEC 62428 Ed.1 IEC/TC or SC: CEI/CE
18、ou SC: 25 Secretariat/ Secrtariat Italy Submitted for parallel voting in CENELEC Soumis au vote parallle au CENELEC Date of circulation Date de diffusion 2006-09-29 Closing date for voting (Voting mandatory for P-members) Date de clture du vote (Vote obligatoire pour les membres(P) 2007-03-02 Also o
19、f interest to the following committees Intresse galement les comits suivants - Supersedes document Remplace le document 25/320/CD additional letters may be put, for instance L1, L2, L3 at it is established in IEC 60909, IEC 60865 and IEC 61660. 2.2.2 modal components quantities M g, M g or M G found
20、 by a transformation from the original quantities according to clause 3 NOTE Additional subscripts 1, 2, 3 are used. 2.2.3 column vector of quantities column matrix containing the three original quantities or modal components of a three-phase AC system NOTE Column vectors are described by g or M g a
21、nd G or M G, respectively. 2.2.4 modal transformation matrix equation T gM = g for a column vector gM containing the three unknown modal quantities, where g is a column vector containing the three given original quantities and T is a 33 transformation matrix NOTE The transformation can be power-vari
22、ant or power-invariant , see tables 1 and 2. 2.2.5 inverse modal transformation solution gM = T 1 g of the modal transformation that expresses a column vector gM containing the three modal quantities as a matrix product of the inverse transformation matrix T 1 by a column vector g containing the thr
23、ee original quantities 2.2.6 transformation into symmetrical components Fortescue transformation linear modal transformation with constant complex coefficients, the solution of which converts the three original phasors of a three-phase AC system into the reference phasors of three symmetric three-ph
24、ase AC systems the so called symmetrical components , the first system being a positive-sequence system, the second system being a negative-sequence system and the third system being a zero-sequence system NOTE 1 The transformation into symmetrical components is used for example for the description
25、of asymmetric steady-state conditions in three-phase AC systems. NOTE 2 See tables 1 and 2. 2.2.7 transformation into space phasor components linear modal transformation with constant or angle-dependent coefficients, the solution of which replaces the instantaneous original quantities of a three-pha
26、se AC system by the complex space phasor in a rotating or a non-rotating frame of reference, its conjugate complex value and the real zero-sequence component NOTE 1 The term space vector is also used. NOTE 2 The space phasor transformation is used for example for the description of transients in thr
27、ee-phase AC systems and machines. NOTE 3 See tables 1 and 2. Licensed Copy: London South Bank University, London South Bank University, Sun Dec 24 04:17:00 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 62428 Ed.1/CDV IEC:200X 4 2.2.8 transformation into 00 components Clarke transformation linear modal
28、transformation with constant real coefficients, the solution of which replaces the instantaneous original quantities of a three-phase AC system by the real part and the imaginary part of a complex space phasor in a non-rotating frame of reference and a real zero-sequence component or replaces the th
29、ree original phasors of the three-phase AC system by two phasors ( and phasor) and a zero-sequence phasor NOTE 1 The power-variant form of the space phasor is given by s jggg+= and the power-invariant form is given by)j( 2 1 s ggg+=. NOTE 2 The 0 transformation is used for example for the descriptio
30、n of asymmetric transients in three-phase AC systems. NOTE 3 See tables 1 and 2. 2.2.9 transformation into dq0 components Park transformation linear modal transformation with coefficients sinusoidally depending on the angle of rotation, the solution of which replaces the instantaneous original quant
31、ities of a three-phase AC system by the real part and the imaginary part of a complex space phasor in a rotating frame of reference and a real zero-sequence component NOTE 1 The power-variant form of the space phasor is given by qd r jggg+= and the power-invariant form is given by )j( qd 2 1 r ggg+=
32、. NOTE 2 The dq0 transformation is used for the description of transients in synchronous machines. NOTE 3 See tables 1 and 2. 3 Modal transformation 3.1 General The original quantities 321 ,ggg and the modal components M3M2M1 ,ggg are related to each other by the following transformation equations:
33、= 3M 2M 1M 333231 232221 131211 3 2 1 g g g ttt ttt ttt g g g (1) or in a shortened form: M gTg= (2) The coefficients ik t of the transformation matrix T can all be real or some of them can be complex. It is necessary that the transformation matrix T is non-singular, so that the inverse relationship
34、 of equation (2) is valid. Licensed Copy: London South Bank University, London South Bank University, Sun Dec 24 04:17:00 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 62428 Ed.1/CDV IEC:200X 5 gTg 1 M = (3) If the original quantities are sinusoidal quantities of the same frequency, it is possible to e
35、xpress them as phasors and to write the transformation equations (2) and (3) in an analogue form with constant coefficients: = 3M 2M 1M 333231 232221 131211 3 2 1 G G G ttt ttt ttt G G G (4) M GTG= (5) GTG 1 M = (6) 3.2 Power in modal components Transformation relations are used either in the power-
36、variant form as given in table 1 or in the power- invariant form as given in table 2. For the power-invariant form of transformation, the power calculated with the three modal components is equal to the power calculated from the original quantities of a three-phase AC system with three line conducto
37、rs and a neutral conductor, where 1 u, 2 u and 3 u are the line-to-neutral voltages and 1 i, 2 i and 3 i are the currents of the line conductors at a given location of the network. In a three-phase AC system with only three line conductors, 1 u, 2 u and 3 u are the voltages between the line conducto
38、rs and a virtual star point at a given location of the network. The instantaneous power p expressed in terms of the original quantities is defined by: () = =+=iuT 3 2 1 321332211 i i i uuuiuiuiup (7) NOTE The asterisks denote formally the complex conjugate of the currents 1 i, 2 i, 3 i. If these are
39、 real, 1 i, 2 i, 3 i are identical to 1 i, 2 i, 3 i. If the relationship between the original quantities and the modal components given in equation (2) is introduced for the voltages as well as for the currents: M uTu= and M iTi= (7) taking into account () TT M T M T TuuTu=, (9) the power p expresse
40、d in terms of modal components is found as: = M TT M iTTup. (10) For the power-variant case where TT T is not equal to the unity matrix an example is given at the end of this section. In case of Licensed Copy: London South Bank University, London South Bank University, Sun Dec 24 04:17:00 GMT+00:00
41、2006, Uncontrolled Copy, (c) BSI 62428 Ed.1/CDV IEC:200X 6 T =T TE (11) with the matrix E being the unity matrix of third order, equation (10) changes to () += = 3M3M2M2M1M1M 3M 2M 1M 3M2M1MM T M iuiuiu i i i uuupiu. (12) The condition T =T TE or = T1 TT means that the transformation matrix T is a u
42、nitary matrix. Because the equations (7) and (12) have identical structure, the transformation relationship with a unitary matrix is called the power invariant form of transformation. Licensed Copy: London South Bank University, London South Bank University, Sun Dec 24 04:17:00 GMT+00:00 2006, Uncon
43、trolled Copy, (c) BSI 62428 Ed.1/CDV IEC:200X 7 In connection with table 2 the following examples can be given: 000 iuiuiup+= 00qqdd0dq iuiuiup+= 00 ss 00 ssss 0ss Re2iuiuiuiuiup+=+= 00 rr 00 rrrr 0rr Re2iuiuiuiuiup+=+= In case of symmetrical three-phase systems of voltages and currents the complex
44、apparent power is given in original phasor quantities as follows: () = =+=IU T 3 2 1 321332211 I I I UUUIUIUIUS (13) Substituting the modal components by () TT M T M T TUUTU= and = M ITI the complex apparent power is found as: = M TT M ITTUS (14) In case of power invariance, the condition T =T TE mu
45、st also be valid. Then equation (14) leads to the power invariant expression: () =+= 3M 2M 1M 3M2M1M3M3M2M2M1M1MM T M I I I UUUIUIUIUSIU (15) The power-variant forms of transformation matrices are given in the tables 3 and 5. They are also known as reference-component-invariant transformations, beca
46、use, under balanced symmetrical conditions, the reference component (the first component) of the modal components is equal to the reference component of the original quantities or its complex phasors, respectively. This is not the case for transformations in a rotating frame. EXAMPLE According to ta
47、ble 2 for the power-invariant form of the transformation matrix it follows: = 2 2 111 1 aa1 3 aa1 T, = 2 T2 1 aa 1 1aa 3 111 T, = 2 T2 1aa 1 1 aa 3 111 T, showing that = T1 TT or T =T TE, fulfilling the condition for power invariance. Licensed Copy: London South Bank University, London South Bank University, Sun Dec 24 04:17:00 GMT+00:00 2006, Uncontrolled Copy, (c) BSI 62428 Ed.1/CDV IEC:200X 8 If the transformation matrix T from table 1 for the power-variant transformation is used, then the following results are found: = 2 2 111 aa1 aa1 T, = 2 T2 1 aa 1aa 111 T, = 2 T2 1aa 1
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