Determination of power losses in voltage sourced converter (VSC) valves for high voltage direct current (HVDC) systems - Part 2: Modular multilevel converters

This part of IEC 62751 gives the detailed method to be adopted for calculating the power
losses in the valves for an HVDC system based on the “modular multi-level converter”, where
each valve in the converter consists of a number of self-contained, two-terminal controllable
voltage sources connected in series. It is applicable both for the cases where each modular
cell uses only a single turn-off semiconductor device in each switch position, and the case
where each switch position consists of a number of turn-off semiconductor devices in series
(topology also referred to as “cascaded two-level converter”). The main formulae are given for
the two-level “half-bridge” configuration but guidance is also given in Annex A as to how to
extend the results to certain other types of MMC building block configuration.
The standard is written mainly for insulated gate bipolar transistors (IGBTs) but may also be
used for guidance in the event that other types of turn-off semiconductor devices are used.
Power losses in other items of equipment in the HVDC station, apart from the converter
valves, are excluded from the scope of this standard.
This standard does not apply to converter valves for line-commutated converter HVDC
systems.

Bestimmung der Leistungsverluste in Spannungszwischenkreis-Stromrichtern (VSC) für Hochspannungsgleichstrom(HGÜ)-Systeme -- Teil 2: Modulare Mehrstufen-Stromrichter

Determination des pertes de puissance dans les valves à convertisseur de source de tension (VSC) des systemes en courant continu a haute tension (CCHT) -- Partie 2: Convertisseurs multiniveaux modulaires

L'IEC 62571-2:2014 donne la méthode détaillée à adopter pour calculer les pertes de puissance dans les valves d'un système CCHT doté d'un "convertisseur multiniveaux modulaire" dont chaque valve est composée d'un certain nombre de sources de tension indépendantes commandables à deux bornes connectées en série. Elle s'applique lorsque chaque cellule modulaire n'utilise qu'un seul dispositif à semi-conducteur blocable dans chaque position de commutation, et lorsque chaque position de commutation est composée d'un certain nombre de dispositifs à semi-conducteur blocables en série (cette topologie étant également appelée "convertisseur à deux niveaux monté en cascade"). Les principales formules sont données pour la configuration "en demi-pont" à deux niveaux. Des lignes directrices sont également données pour indiquer l'étendue des résultats de certains autres types de configurations de bloc module MMC.

Ugotavljanje izgub moči v napetostnih pretvorniških ventilih za visokonapetostne enosmerne sisteme - 2. del: Modularni večnivojski pretvorniki (IEC 62751-2:2014)

Ta del standarda IEC 62751 podaja podrobno metodo, ki naj bi se sprejela za izračun izgub moči v ventilih za sistem HVDC na osnovi »modularnega večnivojskega pretvornika«, pri katerem je vsak ventil v pretvorniku sestavljen iz številnih zaporedno vezanih samostojnih, krmiljenih napetostnih virov z dvema priključkoma. Uporablja se v primerih, kjer je posamezna modularna celica uporablja samo eno izklopno polprevodniško napravo pri vsakem stikalnem položaju, in v primerih, kjer posamezni stikalni položaj vsebuje več zaporedno vezanih izklopnih polprevodniških naprav (topologija: imenovan tudi »kaskadni dvonivojski pretvornik«). Glavne formule so podane za dvonivojsko »pol mostično« konfiguracijo, vendar so v dodatku A podane tudi smernice, kako rezultate razširiti na določene druge vrste konfiguracije gradnikov MMC. Standard je zapisan zlasti za bipolarne tranzistorje z izoliranimi vrati (IGBT), vendar se lahko uporablja tudi za navodila v primeru, da se uporabljajo druge vrste izklopnih polprevodniškh naprav.
Izgube moči v drugih elementih opreme v napravi HVDC, razen pretvorniških ventilov, so izključene iz področja uporabe tega standarda. Ta standard se ne uporablja za pretvorniške ventile za sisteme HVDC s pretvorniki z linijsko komutacijo.

General Information

Status
Published
Publication Date
23-Nov-2014
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
10-Nov-2014
Due Date
15-Jan-2015
Completion Date
24-Nov-2014

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SLOVENSKI STANDARD
SIST EN 62751-2:2014
01-december-2014
8JRWDYOMDQMHL]JXEPRþLYQDSHWRVWQLKSUHWYRUQLãNLKYHQWLOLK]DYLVRNRQDSHWRVWQH
HQRVPHUQHVLVWHPHGHO0RGXODUQLYHþQLYRMVNLSUHWYRUQLNL ,(&
Determination of power losses in voltage sourced converter (VSC) valves for high
voltage direct current (HVDC) systems - Part 2: Modular multilevel converters
Bestimmung der Leistungsverluste in Spannungszwischenkreis-Stromrichtern (VSC) für
Hochspannungsgleichstrom(HGÜ)-Systeme -- Teil 2: Modulare Mehrstufen-Stromrichter
Determination des pertes de puissance dans les valves à convertisseur de source de
tension (VSC) des systemes en courant continu a haute tension (CCHT) -- Partie 2:
Convertisseurs multiniveaux modulaires
Ta slovenski standard je istoveten z: EN 62751-2:2014
ICS:
29.200 8VPHUQLNL3UHWYRUQLNL Rectifiers. Convertors.
6WDELOL]LUDQRHOHNWULþQR Stabilized power supply
QDSDMDQMH
29.240.01 2PUHåMD]DSUHQRVLQ Power transmission and
GLVWULEXFLMRHOHNWULþQHHQHUJLMH distribution networks in
QDVSORãQR general
SIST EN 62751-2:2014 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST EN 62751-2:2014

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SIST EN 62751-2:2014


EUROPEAN STANDARD EN 62751-2

NORME EUROPÉENNE

EUROPÄISCHE NORM
October 2014
ICS 29.200; 29.240

English Version
Power losses in voltage sourced converter (VSC) valves for
high-voltage direct current (HVDC) systems - Part 2: Modular
multilevel converters
(IEC 62751-2:2014)
Pertes de puissance dans les valves à convertisseur de Bestimmung der Leistungsverluste in
source de tension (VSC) des systèmes en courant continu Spannungszwischenkreis-Stromrichtern (VSC) für
à haute tension (CCHT) - Partie 2: Convertisseurs Hochspannungsgleichstrom(HGÜ)-Systeme - Teil 2:
multiniveaux modulaires Modulare Mehrstufen-Stromrichter
(CEI 62751-2:2014) (IEC 62751-2:2014)
This European Standard was approved by CENELEC on 2014-10-01. 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 CEN-CENELEC
Management Centre 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 CEN-CENELEC Management Centre has the
same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic,
Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.


European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2014 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.
 Ref. No. EN 62751-2:2014 E

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SIST EN 62751-2:2014
EN 62751-2:2014 - 2 -
Foreword
The text of document 22F/303/CDV, future edition 1 of IEC 62751-2, prepared by SC 22F "Power
electronics for electrical transmission and distribution systems", of IEC/TC 22 "Power electronic
systems and equipment" was submitted to the IEC-CENELEC parallel vote and approved by
CENELEC as EN 62751-2:2014.
The following dates are fixed:
– latest date by which the document has to be implemented at (dop) 2015-07-01
national level by publication of an identical national
standard or by endorsement
– latest date by which the national standards conflicting with (dow) 2017-10-01
the document have to be withdrawn

Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CENELEC [and/or CEN] shall not be held responsible for identifying any or all such
patent rights.
Endorsement notice
The text of the International Standard IEC 62751-2:2014 was approved by CENELEC as a European
Standard without any modification.
In the official version, for Bibliography, the following note has to be added for the standard indicated:
IEC 61803:1999 NOTE Harmonised as EN 61803:1999.

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SIST EN 62751-2:2014
- 3 - EN 62751-2:2014
Annex ZA
(normative)

Normative references to international publications
with their corresponding European publications
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
NOTE 1 When an International Publication has been modified by common modifications, indicated by (mod),
the relevant EN/HD applies.
NOTE 2 Up-to-date information on the latest versions of the European Standards listed in this annex is
available here: www.cenelec.eu.
Publication Year Title EN/HD Year
IEC 60633 -  Terminology for high-voltage direct current EN 60633 -
(HVDC) transmission
IEC 62747 -  Terminology for voltage-sourced EN 62747 -
converters (VSC) for high-voltage direct
current (HVDC) systems
IEC 62751-1 2014 Determination of power losses in voltage EN 62751-1 2014
sourced converter (VSC) valves for high-
voltage direct current (HVDC) systems --
Part 1: General requirements
ISO/IEC Guide 98-3 -  Uncertainty of measurement -- Part-3: - -
Guide to the expression of uncertainty in
measurement (GUM:1995)

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SIST EN 62751-2:2014

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SIST EN 62751-2:2014




IEC 62751-2

®


Edition 1.0 2014-08




INTERNATIONAL



STANDARD




NORME



INTERNATIONALE
colour

inside










Power losses in voltage sourced converter (VSC) valves for high-voltage direct

current (HVDC) systems –

Part 2: Modular multilevel converters




Pertes de puissance dans les valves à convertisseur de source de tension (VSC)

des systèmes en courant continu à haute tension (CCHT) –


Partie 2: Convertisseurs multiniveaux modulaires












INTERNATIONAL

ELECTROTECHNICAL

COMMISSION


COMMISSION

ELECTROTECHNIQUE

PRICE CODE
INTERNATIONALE

CODE PRIX XA


ICS 29.200; 29.240 ISBN 978-2-8322-1836-5



Warning! Make sure that you obtained this publication from an authorized distributor.

Attention! Veuillez vous assurer que vous avez obtenu cette publication via un distributeur agréé.

® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale

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SIST EN 62751-2:2014
– 2 – IEC 62751-2:2014 © IEC 2014
CONTENTS
FOREWORD . 5
1 Scope . 7
2 Normative references . 7
3 Terms, definitions, symbols and abbreviated terms . 7
3.1 Terms and definitions . 8
3.2 Symbols and abbreviated terms . 9
3.2.1 Valve and simulation data . 9
3.2.2 Semiconductor device characteristics . 10
3.2.3 Other component characteristics. 10
3.2.4 Operating parameters . 10
3.2.5 Loss parameters . 11
4 General conditions. 11
4.1 General . 11
4.2 Principles for loss determination . 12
4.3 Categories of valve losses . 12
4.4 Loss calculation method . 13
4.5 Input parameters . 13
4.5.1 General . 13
4.5.2 Input data for numerical simulations . 13
4.5.3 Input data coming from numerical simulations . 14
4.5.4 Converter station data . 14
4.5.5 Operating conditions . 15
5 Conduction losses . 15
5.1 General . 15
5.2 IGBT conduction losses . 16
5.3 Diode conduction losses . 17
5.4 Other conduction losses . 18
6 DC voltage-dependent losses . 19
7 Losses in d.c. capacitors of the valve . 19
8 Switching losses . 20
8.1 General . 20
8.2 IGBT switching losses . 20
8.3 Diode switching losses . 21
9 Other losses . 21
9.1 Snubber circuit losses . 21
9.2 Valve electronics power consumption. 22
9.2.1 General . 22
9.2.2 Power supply from off-state voltage across each IGBT . 23
9.2.3 Power supply from the d.c. capacitor . 23
10 Total valve losses per HVDC substation . 24
Annex A (informative) Description of power loss mechanisms in MMC valves . 26
A.1 Introduction to MMC Converter topology . 26
A.2 Valve voltage and current stresses . 29
A.2.1 Simplified analysis with voltage and current in phase . 29
A.2.2 Generalised analysis with voltage and current out of phase . 30

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SIST EN 62751-2:2014
IEC 62751-2:2014 © IEC 2014 – 3 –
A.2.3 Effects of third harmonic injection . 31
A.3 Conduction losses in MMC building blocks . 32
A.3.1 Description of conduction paths . 32
A.3.2 Conduction losses in semiconductors . 38
A.3.3 MMC building block d.c. capacitor losses . 42
A.3.4 Other conduction losses . 42
A.4 Switching losses . 42
A.4.1 Description of state changes . 42
A.4.2 Analysis of state changes during cycle . 44
A.4.3 Worked example of switching losses . 44
A.5 Other losses . 47
A.5.1 Snubber losses . 47
A.5.2 DC voltage-dependent losses . 47
A.5.3 Valve electronics power consumption . 50
A.6 Application to other variants of valve. 52
A.6.1 General . 52
A.6.2 Two-level full-bridge MMC building block . 52
A.6.3 Multi-level MMC building blocks . 53
Bibliography . 55

Figure 1 – Two basic versions of MMC building block designs . 15
Figure 2 – Conduction paths in MMC building blocks . 16
Figure A.1 – Phase unit of the modular multi-level converter (MMC) in basic half-
bridge, two-level arrangement, with submodules . 27
Figure A.2 – Phase unit of the cascaded two-level converter (CTL) in half-bridge form . 28
Figure A.3 – Basic operation of the MMC converters . 29
Figure A.4 – MMC converters showing composition of valve current . 30
Figure A.5 – Phasor diagram showing a.c. system voltage, converter a.c. voltage and
converter a.c. current . 31
rd
Figure A.6 – Effect of 3 harmonic injection on converter voltage and current . 32
Figure A.7 – Two functionally equivalent variants of a “half-bridge”, two-level MMC
building block . 33
Figure A.8 – Conducting states in “half-bridge”, two-level MMC building block . 34
Figure A.9 – Typical patterns of conduction for inverter operation (left) and rectifier
operation (right) . 35
Figure A.10 – Example of converter with only one MMC building block per valve to
illustrate switching behaviour . 36
Figure A.11 – Inverter operation example of switching events . 36
Figure A.12 – Rectifier operation example of switching events . 37
Figure A.13 – Valve current and mean rectified valve current . 39
Figure A.14 – IGBT and diode switching energy as a function of collector current . 43
Figure A.15 – Valve voltage, current and switching behaviour for a hypothetical MMC
valve consisting of 5 submodules . 45
Figure A.16 – Power supply from IGBT terminals . 50
Figure A.17 – Power supply from IGBT terminals in cell . 51
Figure A.18 – Power supply from d.c. capacitor in submodule . 52
Figure A.19 – One “full-bridge”, two-level MMC building block . 52

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SIST EN 62751-2:2014
– 4 – IEC 62751-2:2014 © IEC 2014
Figure A.20 – Four possible variants of three-level MMC building block . 54

Table 1 – Contributions to valve losses in different operating modes . 25
Table A.1 – Hard switching events . 42
Table A.2 – Soft switching events . 44
Table A.3 – Summary of switching events from Figure A.15 . 46

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SIST EN 62751-2:2014
IEC 62751-2:2014 © IEC 2014 – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________

POWER LOSSES IN VOLTAGE SOURCED
CONVERTER (VSC) VALVES FOR HIGH-VOLTAGE
DIRECT CURRENT (HVDC) SYSTEMS –

Part 2: Modular multilevel converters

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,
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 the 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 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 itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure 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 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 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 62751-2 has been prepared by subcommittee 22F: Power
electronics for electrical transmission and distribution systems, of IEC technical committee 22:
Power electronic systems and equipment.
The text of this standard is based on the following documents:
CDV Report on voting
22F/303/CDV 22F/322A/RVC

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.

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SIST EN 62751-2:2014
– 6 – IEC 62751-2:2014 © IEC 2014
A list of all parts in the IEC 62751series, published under the general title Power losses in
voltage sourced converter (VSC) valves for high-voltage direct current (HVDC) systems, can
be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the stability 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.

IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.

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SIST EN 62751-2:2014
IEC 62751-2:2014 © IEC 2014 – 7 –
POWER LOSSES IN VOLTAGE SOURCED
CONVERTER (VSC) VALVES FOR HIGH-VOLTAGE
DIRECT CURRENT (HVDC) SYSTEMS –

Part 2: Modular multilevel converters



1 Scope
This part of IEC 62751 gives the detailed method to be adopted for calculating the power
losses in the valves for an HVDC system based on the “modular multi-level converter”, where
each valve in the converter consists of a number of self-contained, two-terminal controllable
voltage sources connected in series. It is applicable both for the cases where each modular
cell uses only a single turn-off semiconductor device in each switch position, and the case
where each switch position consists of a number of turn-off semiconductor devices in series
(topology also referred to as “cascaded two-level converter”). The main formulae are given for
the two-level “half-bridge” configuration but guidance is also given in Annex A as to how to
extend the results to certain other types of MMC building block configuration.
The standard is written mainly for insulated gate bipolar transistors (IGBTs) but may also be
used for guidance in the event that other types of turn-off semiconductor devices are used.
Power losses in other items of equipment in the HVDC station, apart from the converter
valves, are excluded from the scope of this standard.
This standard does not apply to converter valves for line-commutated converter HVDC
systems.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60633, Terminology for high-voltage direct-current (HVDC) transmission
IEC 62747, Terminology for voltage-sourced converters (VSC) for high-voltage direct current
(HVDC) systems
IEC 62751-1:2014, Power losses in voltage sourced converter (VSC) valves for high-voltage
direct current (HVDC) systems – Part 1: General requirements
ISO/IEC Guide 98-3, Uncertainty of measurement – Part 3: Guide to the expression of
uncertainty in measurement (GUM:1995)
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the terms and definitions given in IEC 60633, IEC 62747,
IEC 62751-1, as well as the following apply.

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SIST EN 62751-2:2014
– 8 – IEC 62751-2:2014 © IEC 2014
3.1 Terms and definitions
3.1.1
modular multi-level converter
MMC
multi-level converter in which each VSC valve consists of a number of MMC building blocks
connected in series
Note 1 to entry: This note applies to the French language only.
3.1.2
MMC building block
self-contained, two-terminal controllable voltage source together with d.c. capacitor(s) and
immediate auxiliaries, forming part of a MMC
3.1.3
IGBT-diode pair
arrangement of IGBT and free-wheeling diode connected in inverse parallel
3.1.4
switch position
semiconductor function which behaves as a single, indivisible switch
Note 1 to entry: A switch position may consist of a single IGBT-diode pair or, in the case of the cascaded two
level converter, a series connection of multiple IGBT-diode pairs.
3.1.5
cascaded two-level converter
CTL
modular multi-level converter in which each switch position consists of more than one
IGBT-diode pair connected in series
Note 1 to entry: This note applies to the French language only.
3.1.6
submodule
MMC building block where each switch position consists of only one IGBT-diode pair
3.1.7
cell
MMC building block where each switch position consists of more than one IGBT-diode pair
connected in series
3.1.8
turn-off semiconductor device
controllable semiconductor device which may be turned on and off by a control signal, for
example an IGBT
3.1.9
insulated gate bipolar transistor
IGBT
turn-off semiconductor device with three terminals: a gate terminal (G) and two load terminals
emitter (E) and collector (C)
Note 1 to entry: This note applies to the French language only.
3.1.10
operating state
condition in which the HVDC substation is energized and the converters are de-blocked

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SIST EN 62751-2:2014
IEC 62751-2:2014 © IEC 2014 – 9 –
Note 1 to entry: Unlike line-commutated converter, VSC can operate with zero active/reactive power output.
3.1.11
no-load operating state
condition in which the HVDC substation is energized but the IGBTs are blocked and all
necessary substation service loads and auxiliary equipment are connected
3.1.12
idling operating state
condition in which the HVDC substation is energized and the IGBTs are de-blocked but with
no active or reactive power output at the point of common connection to the a.c. network
Note 1 to entry: The “idling operating” and “no-load” conditions are similar but from the no-load state, several
seconds may be needed before power can be transmitted, while from the idling operating state, power transmission
may be commenced almost immediately (less than 3 power frequency cycles).
Note 2 to entry: In the idling operating state, the converter is capable of actively controlling the d.c. voltage, in
contrast to the no-load state where the behavior of the converter is essentially “passive”.
Note 3 to entry: Losses will generally be slightly lower in the no-load state than in the idling operating state,
therefore this operating mode is preferred where the arrangement of the VSC system permits it.
3.1.13
modulation index of PWM converters
M
ratio of the peak line to ground a.c. converter voltage, to half of the converter d.c. terminal to
terminal voltage
2 ⋅U
c1
M =
U
dc
3 ⋅
2
where
U is the r.m.s value of the fundamental frequency component of the line-to-line voltage U ;
c1 c
U is the output voltag
...

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