1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI British StandardsWB9423_BSI_StandardColCov_noK_AW:BSI FRONT COVERS 5/9/08 12:55 Page 1Electric power engineering Modal components in three-phase a.c. systems Quantities and transformationsBS EN 62428
2、:2008NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LALicensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSINational forewordThis British Standard is the UK implementation of EN 62428:2008. It is identi-cal to IEC 62428:2008.The UK par
3、ticipation in its preparation was entrusted to Technical CommitteeSS/7, General metrology, quantities, units and symbols.A list of organizations represented on this committee can be obtained onrequest to its secretary.This publication does not purport to include all the necessary provisions of acont
4、ract. Users are responsible for its correct application. BSI 2009ISBN 978 0 580 56247 1ICS 01.060; 29.020Compliance with a British Standard cannot confer immunity fromlegal obligations.Amendments issued since publicationAmd. No. Date Text affectedBRITISH STANDARDBS EN 62428:2008This Draft for Develo
5、pment was published under the authority of the Standards Policy and Strategy Committee on 31 January 2009Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSIEUROPEAN STANDARD EN 62428 NORME EUROPENNE EUROPISCHE NORM September 2008 CENELEC European Commi
6、ttee for Electrotechnical Standardization Comit Europen de Normalisation Electrotechnique Europisches Komitee fr Elektrotechnische Normung Central Secretariat: rue de Stassart 35, B - 1050 Brussels 2008 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC
7、members. Ref. No. EN 62428:2008 E ICS 01.060; 29.020 English version Electric power engineering - Modal components in three-phase a.c. systems - Quantities and transformations (IEC 62428:2008) Energie lectrique - Composantes modales dans les systmes a.c. triphass - Grandeurs et transformations (CEI
8、62428:2008) Elektrische Energietechnik - Modale Komponenten in Drehstromsystemen - Gren und Transformationen (IEC 62428:2008) This European Standard was approved by CENELEC on 2008-08-01. CENELEC members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for
9、 giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CENELEC member. This European Standard exists in three offic
10、ial versions (English, French, German). A version in any other language made by translation under the responsibility of a CENELEC member into its own language and notified to the Central Secretariat has the same status as the official versions. CENELEC members are the national electrotechnical commi
11、ttees of Austria, Belgium, Bulgaria, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the Unit
12、ed Kingdom. BS EN 62428:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSIEN 62428:2008 - 2 - Foreword The text of document 25/382/FDIS, future edition 1 of IEC 62428, prepared by IEC TC 25, Quantities and units, was submitted to the IEC-CENELEC p
13、arallel vote and was approved by CENELEC as EN 62428 on 2008-08-01. The following dates were fixed: latest date by which the EN has to be implemented at national level by publication of an identical national standard or by endorsement (dop) 2009-05-01 latest date by which the national standards conf
14、licting with the EN have to be withdrawn (dow) 2011-08-01 Annex ZA has been added by CENELEC. _ Endorsement notice The text of the International Standard IEC 62428:2008 was approved by CENELEC as a European Standard without any modification. In the official version, for Bibliography, the following n
15、otes have to be added for the standards indicated: IEC 60909-0 NOTE Harmonized as EN 60909-0:2001 (not modified). IEC 61660 NOTE Harmonized in EN 61660 series (not modified). _ BS EN 62428:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSI- 3 - EN
16、 62428:2008 Annex ZA (normative) Normative references to international publications with their corresponding European publications The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references,
17、the latest edition of the referenced document (including any amendments) applies. NOTE When an international publication has been modified by common modifications, indicated by (mod), the relevant EN/HD applies. Publication Year Title EN/HD Year IEC 60050-141 -1)International Electrotechnical Vocabu
18、lary (IEV) - Part 141: Polyphase systems and circuits - - 1)Undated reference. BS EN 62428:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSIThis page deliberately left blankLicensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10,
19、Uncontrolled Copy, (c) BSI 2 62428 IEC:2008 CONTENTS FOREWORD.3 1 Scope.5 2 Normative references .5 3 Terms, definitions, quantities and concepts 5 3.1 General .5 3.2 Terms and definitions 5 4 Modal transformation7 4.1 General .7 4.2 Power in modal components8 4.3 Established transformations 10 5 De
20、coupling in three-phase a.c. systems .16 5.1 Decoupling in case of steady-state operation with sinusoidal quantities.16 5.2 Decoupling under transient conditions .19 Bibliography23 Figure 1 Circuit, fed by a three-phase voltage source with L1QU , L2QU , L3QU at the connection point Q and earthed at
21、the neutral point N via the impedance NNNj XRZ += 16 Figure 2 Three decoupled systems which replace the coupled three-phase a.c. system of Figure 1 under the described conditions (see text) 19 Table 1 Power-variant form of modal components and transformation matrices11 Table 2 Power-invariant form o
22、f modal components and transformation matrices.12 Table 3 Clark, Park and space phasor components modal transformations in the power-variant form13 Table 4 Clark, Park and space phasor components Modal transformations in the power-invariant form .14 Table 5 Transformation matrices in the power-varia
23、nt form for phasor quantities .15 Table 6 Transformation matrices in the power-invariant form for phasor quantities.15 Table 7 Modal voltages and impedances in case of phasor quantities18 Table 8 Modal voltages and inductances under transient conditions.22 BS EN 62428:2008Licensed Copy: Wang Bin, IS
24、O/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSI62428 IEC:2008 3 INTERNATIONAL ELECTROTECHNICAL COMMISSION _ ELECTRIC POWER ENGINEERING MODAL COMPONENTS IN THREE-PHASE AC SYSTEMS QUANTITIES AND TRANSFORMATIONS FOREWORD 1) The International Electrotechnical Commission (IEC) is
25、 a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and in addition to
26、other activities, IEC publishes International Standards, Technical Specifications, Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested in t
27、he subject dealt with may participate in this preparatory work. International, governmental and non-governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditi
28、ons determined by agreement between the two organizations. 2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested IEC Nation
29、al Committees. 3) IEC Publications have the form of recommendations for international use and are accepted by IEC National Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC Publications is accurate, IEC cannot be held responsible for the way
30、in which they are used or for any misinterpretation by any end user. 4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications transparently to the maximum extent possible in their national and regional publications. Any divergence between any IEC P
31、ublication and the corresponding national or regional publication shall be clearly indicated in the latter. 5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any equipment declared to be in conformity with an IEC Publication. 6) All users should ens
32、ure that they have the latest edition of this publication. 7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and members of its technical committees and IEC National Committees for any personal injury, property damage or other damage of
33、any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC Publications. 8) Attention is drawn to the Normative references cited in this publication. Use of the re
34、ferenced publications is indispensable for the correct application of this publication. 9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent rights. IEC shall not be held responsible for identifying any or all such patent rights. Int
35、ernational Standard IEC 62428 has been prepared by IEC technical committee 25: Quantities and units. The text of this standard is based on the following documents: FDIS Report on voting 25/382/FDIS 25/390/RVD Full information on the voting for the approval of this standard can be found in the report
36、 on voting indicated in the above table. This publication has been drafted in accordance with the ISO/IEC Directives, Part 2. BS EN 62428:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSI 4 62428 IEC:2008 The committee has decided that the conten
37、ts of this publication will remain unchanged until the maintenance result date indicated on the IEC web site under “http:/webstore.iec.ch“ in the data related to the specific publication. At this date, the publication will be reconfirmed; withdrawn; replaced by a revised edition; or amended. BS EN 6
38、2428:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSI62428 IEC:2008 5 ELECTRIC POWER ENGINEERING MODAL COMPONENTS IN THREE-PHASE AC SYSTEMS QUANTITIES AND TRANSFORMATIONS 1 Scope This International Standard deals with transformations from origin
39、al quantities into modal quantities for the widely used three-phase a.c. systems in the field of electric power engineering. The examination of operating conditions and transient phenomena in three-phase a.c. systems becomes more difficult by the resistive, inductive or capacitive coupling between t
40、he phase elements and line conductors. Calculation and description of these phenomena in three-phase a.c. systems are easier if the quantities of the coupled phase elements and line conductors are transformed into modal quantities. The calculation becomes very easy if the transformation leads to dec
41、oupled modal systems. The original impedance and admittance matrices are transformed to modal impedance and admittance matrices. In the case of decoupling of the modal quantities, the modal impedance and admittance matrices become diagonal matrices. 2 Normative references The following referenced do
42、cuments are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. IEC 60050-141, International Electrotechnical Vocabulary (IEV) Part 141: Pol
43、yphase systems and circuits 3 Terms, definitions, quantities and concepts 3.1 General Quantities in this standard are usually time-dependent. These quantities are for instance electric currents, voltages, linked fluxes, current linkages, electric and magnetic fluxes. For quantities the general lette
44、r symbol g in case of real instantaneous values, g in case of complex instantaneous values and G in case of phasors (complex r.m.s. values) are used. NOTE Complex quantities in this standard are underlined. Conjugated complex quantities are indicated by an additional asterisk (*). Matrices and colum
45、n vectors are printed in bold face type, italic. 3.2 Terms and definitions For the purposes of this document, the terms and definitions given in IEC 60050-141 and the following apply. 3.2.1 original quantities quantities g or G of a three-phase a.c. system NOTE Subscripts 1, 2, 3 are generally used
46、in this standard; additional letters may be put, for instance L1, L2, L3 as established in IEC 60909, IEC 60865 and IEC 61660. BS EN 62428:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 31/05/2009 04:10, Uncontrolled Copy, (c) BSI 6 62428 IEC:2008 3.2.2 modal components quantities Mg , M
47、g or MG found by a transformation from the original quantities according to Clause 3 NOTE Additional subscripts 1, 2, 3 are used. 3.2.3 column vector of quantities column matrix containing the three original quantities or modal components of a three-phase a.c. system NOTE Column vectors are describe
48、d by g or Mg and G or MG , respectively. 3.2.4 modal transformation matrix equation T gM= g for a column vector gMcontaining the three unknown modal quantities, where g is a column vector containing the three given original quantities and T is a 3 3 transformation matrix NOTE The transformation can
49、be power-variant or power-invariant, see Tables 1 and 2. 3.2.5 inverse modal transformation solution gM= T1g of the modal transformation that expresses a column vector gMcontaining the three modal quantities as a matrix product of the inverse transformation matrix T1by a column vector g containing the three original quantities 3.2.6 transformation into symmetrical components Fortescue transformation linear modal transformation with constant complex co
