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 LANational forewordThis British Standard is the UK implementation of EN 62428:2008. It is identi-cal to IEC 62428:2008.The UK participation in its preparation was entrusted to Technical CommitteeSS/7, General metrology, quantiti
3、es, 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 acontract. Users are responsible for its correct application. BSI 2009ISBN 978 0 580 56247 1ICS 01.060;
4、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 Development was published under the authority of the Standards Policy and Strategy Committee on 31 Januar
5、y 2009EUROPEAN STANDARD EN 62428 NORME EUROPENNE EUROPISCHE NORM September 2008 CENELEC European Committee for Electrotechnical Standardization Comit Europen de Normalisation Electrotechnique Europisches Komitee fr Elektrotechnische Normung Central Secretariat: rue de Stassart 35, B - 1050 Brussels
6、2008 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC 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) Energ
7、ie lectrique - Composantes modales dans les systmes a.c. triphass - Grandeurs et transformations (CEI 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 me
8、mbers are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for 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 applica
9、tion to the Central Secretariat or to any CENELEC member. This European Standard exists in three official 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
10、 has the same status as the official versions. CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Nethe
11、rlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom. BS EN 62428:2008EN 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-CENELE
12、C parallel 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 c
13、onflicting 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 followin
14、g notes 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 62428:2008- 3 - EN 62428:2008 Annex ZA (normative) Normative references to international publications with their c
15、orresponding 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, the latest edition of the referenced document (including any amendments) applies. NOTE When an i
16、nternational 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 Vocabulary (IEV) - Part 141: Polyphase systems and circuits - - 1)Undated reference. BS EN 62428:2008T
17、his page deliberately left blank 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 1
18、0 5 Decoupling 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 earth
19、ed at 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
20、form of 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
21、variant 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 62428:200862428 IEC:2008 3 INTE
22、RNATIONAL ELECTROTECHNICAL COMMISSION _ ELECTRIC POWER ENGINEERING MODAL COMPONENTS IN THREE-PHASE AC SYSTEMS QUANTITIES AND TRANSFORMATIONS FOREWORD 1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising all national electrotechnical commit
23、tees (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 other activities, IEC publishes International Standards, Technical Specifications, Technical
24、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 the subject dealt with may participate in this preparatory work. International, governmental a
25、nd 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 conditions determined by agreement between the two organizations. 2) The formal decisions or agreeme
26、nts 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 National Committees. 3) IEC Publications have the form of recommendations for international use and
27、 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 in which they are used or for any misinterpretation by any end user. 4) In order to promote i
28、nternational 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 Publication and the corresponding national or regional publication shall be clearly indicated
29、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 ensure that they have the latest edition of this publication. 7) No liability shall attach to IE
30、C 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 any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and ex
31、penses 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 referenced publications is indispensable for the correct application of this publication. 9) At
32、tention 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. International Standard IEC 62428 has been prepared by IEC technical committee 25: Quantities and
33、 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 on voting indicated in the above table. This publication has been drafted in accordance with
34、 the ISO/IEC Directives, Part 2. BS EN 62428:2008 4 62428 IEC:2008 The committee has decided that the contents 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 t
35、his date, the publication will be reconfirmed; withdrawn; replaced by a revised edition; or amended. BS EN 62428:200862428 IEC:2008 5 ELECTRIC POWER ENGINEERING MODAL COMPONENTS IN THREE-PHASE AC SYSTEMS QUANTITIES AND TRANSFORMATIONS 1 Scope This International Standard deals with transformations fr
36、om original 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
37、between the 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 lea
38、ds to decoupled 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 refe
39、renced documents 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
40、 141: Polyphase 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 gene
41、ral letter 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
42、and column 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 genera
43、lly used 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 62428:2008 6 62428 IEC:2008 3.2.2 modal components quantities Mg , Mg or MG found by a transformation from the original quantities according to Clause 3 NOTE
44、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 described by g or Mg and G or MG , respectively. 3.2.4 modal transformation matrix equation T gM=
45、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 be power-variant or power-invariant, see Tables 1 and 2. 3.2.5 inverse modal transformatio
46、n 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 tr
47、ansformation linear modal transformation with constant complex coefficients, the solution of which converts the three original phasors of a three-phase a.c. system into the reference phasors of three symmetric three-phase a.c. systems the so-called symmetrical components , the first system being a p
48、ositive-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 of asymmetric steady-state conditions in three-phase a.c. systems. NOTE 2 See Ta
49、bles 1 and 2. 3.2.7 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-phase a.c. 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 for “space phasor”. NOTE
