IEC 62428:2008

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
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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
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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 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 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. valu
...