EN 62428:2008
(Main)Electric power engineering - Modal components in three-phase a.c. systems - Quantities and transformations
Electric power engineering - Modal components in three-phase a.c. systems - Quantities and transformations
IEC 62428:2008 deals with transformations from 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 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 leads 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.
Elektrische Energietechnik - Modale Komponenten in Drehstromsystemen - Größen und Transformationen
Energie électrique - Composantes modales dans les systèmes a.c. triphasés - Grandeurs et transformations
La CEI 62428:2008 traite des transformations des grandeurs originales en grandeurs modales pour les systèmes a.c. triphasés qui sont largement utilisés dans le domaine de l'énergie électrique. L'étude des conditions de fonctionnement et des régimes transitoires dans les systèmes a.c. triphasés est rendue difficile du fait des couplages résistifs, inductifs ou capacitifs entre les éléments de phase et entre les conducteurs de ligne. Le calcul et la description de ces phénomènes dans les systèmes a.c. triphasés est plus facile si les grandeurs concernant les éléments de phase et les conducteurs de ligne sont transformées en grandeurs modales. Le calcul devient très facile si la transformation conduit à des systèmes modaux découplés. Les matrices d'impédances et d'admittances originales sont transformées en matrices d'impédances et d'admittances modales. Dans le cas où les grandeurs modales sont découplées, les matrices d'impédances et d'admittances deviennent diagonales.
Elektroenergetsko inženirstvo - Modalne komponente v trifaznih izmeničnih sistemih - Veličine in transformacije (IEC 62428:2008)
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-januar-2009
(OHNWURHQHUJHWVNRLQåHQLUVWYR0RGDOQHNRPSRQHQWHYWULID]QLKL]PHQLþQLK
VLVWHPLK9HOLþLQHLQWUDQVIRUPDFLMH ,(&
Electric power engineering - Modal components in three-phase a.c. systems - Quantities
and transformations (IEC 62428:2008)
Elektrische Energietechnik - Modale Komponenten in Drehstromsystemen - Größen und
Transformationen (IEC 62428:2008)
Energie électrique - Composantes modales dans les systèmes a.c. triphasés -
Grandeurs et transformations (CEI 62428:2008)
Ta slovenski standard je istoveten z: EN 62428:2008
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
29.020 Elektrotehnika na splošno Electrical engineering in
general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EUROPEAN STANDARD
EN 62428
NORME EUROPÉENNE
September 2008
EUROPÄISCHE NORM
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 électrique - Elektrische Energietechnik -
Composantes modales Modale Komponenten
dans les systèmes a.c. triphasés - in Drehstromsystemen -
Grandeurs et transformations Größen und Transformationen
(CEI 62428:2008) (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 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 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 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 Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für 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 members.
Ref. No. EN 62428:2008 E
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 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 conflicting
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 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).
__________
- 3 - EN 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, 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
1)
IEC 60050-141 - International Electrotechnical Vocabulary - -
(IEV) -
Part 141: Polyphase systems and circuits
1)
Undated reference.
IEC 62428
Edition 1.0 2008-07
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Electric power engineering – Modal components in three-phase a.c. systems –
Quantities and transformations
Energie électrique – Composantes modales dans les systèmes a.c. triphasés –
Grandeurs et transformations
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
S
CODE PRIX
ICS 01.060; 29.020 ISBN 2-8318-9921-4
– 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 transformation.7
4.1 General .7
4.2 Power in modal components.8
4.3 Established transformations .10
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
Bibliography.23
Figure 1 – Circuit, fed by a three-phase voltage source with U , U , U at the
L1Q L2Q L3Q
connection point Q and earthed at the neutral point N via the impedance
Z = R + j X .16
N N
N
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 matrices.11
Table 2 – Power-invariant form of modal components and transformation matrices.12
Table 3 – Clark, Park and space phasor components – modal transformations in the
power-variant form.13
Table 4 – Clark, Park and space phasor components – Modal transformations in the
power-invariant form .14
Table 5 – Transformation matrices in the power-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 quantities .18
Table 8 – Modal voltages and inductances under transient conditions.22
62428 © 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 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 other activities, IEC publishes International Standards, Technical Specifications,
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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 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 National 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 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 Publication 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 ensure that they have the latest edition of this publication.
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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 referenced 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.
International 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 on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
– 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 this date, the publication will be
• reconfirmed;
• withdrawn;
• replaced by a revised edition; or
• amended.
62428 © 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 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 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 leads 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 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.
IEC 60050-141, International Electrotechnical Vocabulary (IEV) – Part 141: Polyphase
systems and circuits
3 Terms, definitions, quantities and concepts
3.1 General
Quantities in this stand
...
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