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IEC 62751-2-2012


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IEC 62751-2 Ed.1
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Power electronics for electrical transmission and distribution systems # Dovr#ri#lqwhuhvw#wr#wkh#iroorzlqj#frpplwwhhv # TC 115

2012-05-18

2012-09-07

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DETERMINATION OF POWER LOSSES IN VOLTAGE SOURCED CONVERTER (VSC) VALVES FOR HVDC SYSTEMS – PART 2: MODULAR MULTILEVEL CONVERTERS
1 Scope

Wklv#Lqwhuqdwlrqdo#Vwdqgdug#jlyhv#wkh#ghwdlohg#phwkrg#wr#eh#dgrswhg#iru#fdofxodwlqj#wkh#srzhu# orvvhv# lq# wkh# ydoyhv# iru# dq# # KYGF# v|vwhp# edvhg# rq# wkh# ?Prgxodu# Pxowl0Ohyho# Frqyhuwhu?/# zkhuh# hdfk# ydoyh# lq# wkh# frqyhuwhu# frqvlvwv# ri# d# qxpehu# ri# vhoi0frqwdlqhg/# wzr0whuplqdo# frqwuroodeoh# yrowdjh# vrxufhv# frqqhfwhg# lq# vhulhv1# Lw# lv# dssolfdeoh# erwk# iru# wkh# fdvhv# zkhuh# hdfk# prgxodu# fhoo# xvhv# rqo|# d# vlqjoh# vzlwfkhg# ydoyh# ghylfh# lq# hdfk# vzlwfk# srvlwlrq/# dqg# wkh# fdvh#zkhuh#hdfk#vzlwfk#srvlwlrq#frqvlvwv#ri#d#qxpehu#ri#vzlwfkhg#ydoyh#ghylfhv#lq#vhulhv#+wkh# wrsrorj|# dovr# uhihuuhg# wr# dv# wkh# ?Fdvfdghg# Wzr0Ohyho# Frqyhuwhu?,1# Wkh# pdlq# irupxodh# duh# jlyhq#iru#wkh#wzr0ohyho#?kdoi0eulgjh?#frqiljxudwlrq#exw#jxlgdqfh#lv#dovr#jlyhq#lq#Dqqh{# D#dv#wr# krz#wr#h{whqg#wkh#uhvxowv#wr#fhuwdlq#rwkhu#w|shv#ri#PPF#exloglqj#eorfn#frqiljxudwlrq1# Wkh#vwdqgdug#lv#zulwwhq#pdlqo|#iru#Lqvxodwhg#Jdwh#Elsrodu#Wudqvlvwruv#+LJEWv,#exw#pd|#dovr#eh# xvhg#iru#jxlgdqfh#lq#wkh#hyhqw#wkdw#rwkhu#w|shv#ri#wxuq0rii#vhplfrqgxfwru#ghylfhv#duh#xvhg1# Sduw#4#ri#wklv#vhulhv#ri#vwdqgdugv#jlyhv#wkh#jhqhudo#sulqflsohv#wr#eh#iroorzhg#lq#fdofxodwlqj#wkh# srzhu#orvvhv#ri#wkh#ydoyhv#iru#dq|#frqyhuwhu#wrsrorj|1# Srzhu# orvvhv# lq# rwkhu# lwhpv# ri# htxlsphqw# lq# wkh# # KYGF# vwdwlrq/# dsduw# iurp# wkh# frqyhuwhu# ydoyhv/#duh#h{foxghg#iurp#wkh#vfrsh#ri#wklv#vwdqgdug1# Wklv# vwdqgdug# grhv# qrw# dsso|# wr# frqyhuwhu# ydoyhv# iru# Olqh0Frppxwdwhg# Frqyhuwhu# # KYGF# v|vwhpv1#

2

Normative references

Wkh# iroorzlqj# uhihuhqfhg# grfxphqwv# duh# lqglvshqvdeoh# iru# wkh# dssolfdwlrq# ri# wklv# grfxphqw1# Iru#gdwhg#uhihuhqfhv/#rqo|#wkh#hglwlrq#flwhg#dssolhv1#Iru#xsgdwhg#uhihuhqfhv/#wkh#odwhvw#hglwlrq# ri#wkh#uhihuhqfhg#grfxphqw#+lqfoxglqj#dq|#dphqgphqwv,#dssolhv1# LVR2LHF# Jxlgh# <;06=# 533;/# apeqtvcupv?, qr,oqcuwtqoqpv, ?, Rctv, ?<,Swufq, vq,vtq, q?rtquuuqp, qr, wpeqtvcupv?,up,oqcuwtqoqpv,*SaO+,*SaO,=;;A,?uvt,oupqt,eqttqevuqpu+# LHF#95:8404=# Pqvqtoupcvuqp,qr,rq?qt,nquuqu,up,bqnvcsq/_qwteqf,Oqpxqtvqtu,*b_O+,rqt,,JbPO, _?uvqou,?,Rctv,=<,Sqpqtcn,Rtupeurnqu# LHF#93966=#`qtoupqnqs?,rqt,tust/xqnvcsq,futqev/ewttqpv,*,JbPO,+,vtcpuouuuuqp# LHF#95:7:=#`qtoupqnqs?,rqt,bqnvcsq/_qwteqf,Oqpxqtvqtu,*b_O+,rqt,,JbPO,u?uvqou #

3

Terms, definitions, symbols and abbreviated terms

Iru#wkh#sxusrvhv#ri#wklv#grfxphqw/#wkh#whupv#dqg#ghilqlwlrqv#jlyhq#lq#LHF#93966/#LHF#95:7:/# LHF#95:8404#dqg#wkh#iroorzlqj#dsso|1# 3.1 Terms and Definitions

3.1.1 modular multi-level converter, MMC pxowl0ohyho# frqyhuwhu# lq# zklfk# hdfk# YVF#ydoyh# frqvlvwv# ri# d# qxpehu# ri# PPF# exloglqj# eorfnv# frqqhfwhg#lq#vhulhv#

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3.1.2 MMC building block vhoi0frqwdlqhg/# wzr0whuplqdo# frqwuroodeoh# yrowdjh# vrxufh# wrjhwkhu# zlwk# g1f1# fdsdflwru+v,# dqg# lpphgldwh#dx{loldulhv# 3.1.3 IGBT-Diode pair duudqjhphqw#ri#LJEW#dqg#iuhh0zkhholqj#glrgh#frqqhfwhg#lq#lqyhuvh#sdudooho# 3.1.4 switch position vhplfrqgxfwru#ixqfwlrq#zklfk#ehkdyhv#dv#d#vlqjoh/#lqglylvleoh#vzlwfk##
QRWH# # D# vzlwfk# srvlwlrq# pd|# f rqvlvw# ri# d# vlqjoh# LJEW0glrgh# sdlu# ru/# lq# wkh# fdv h# ri# wkh# Fdvfdghg# Wzr# Ohyho# frqyhuwhu/# d#vhulhv# frqqhfwlrq# ri# pxowlsoh#LJEW0glrgh#sdluv#

3.1.5 cascaded two-level converter, CTL prgxodu#Pxowl0Ohyho# Frqyhuwhu#lq#zklfk#hdfk#vzlwfk#srvlwlrq#frqvlvwv#ri#pruh#wkdq#rqh#LJEW0 glrgh#sdlu#frqqhfwhg#lq#vhulhv# 3.1.6 submodule PPF#exloglqj#eorfn#zkhuh#hdfk#vzlwfk#srvlwlrq#frqvlvwv#ri#rqo|#rqh#LJEW0glrgh#sdlu# 3.1.7 cell PPF# exloglqj# eorfn# zkhuh# hdfk# vzlwfk# srvlwlrq# frqvlvwv# ri# pruh# wkdq# rqh# LJEW0glrgh# sdlu# frqqhfwhg#lq#vhulhv# 3.2 Symbols and abbreviated terms

3.2.1 Valve and simulation data Pwf # qxpehu#ri#PPF#exloglqj#eorfnv#shu#ydoyh#

Pf ## Pvu# Pfy # Pv# P su# Pvq# v l##

qxpehu#ri#vhulhv0frqqhfwhg#vhplfrqgxfwru#ghylfhv#shu#vzlwfk#srvlwlrq# lv# wkh# wrwdo# qxpehu# ri# vhulhv# uhvlvwlyh# hohphqwv# frqwulexwlqj# wr# frqgxfwlrq# orvvhv#lq#wkh#ydoyh/#rwkhu#wkdq#lq#wkh#LJEWv#dqg#glrghv# lv#wkh#qxpehu#ri#fdsdflwruv#lq#wkh#ydoyh# lv# wkh# qxpehu# ri# vzlwfklqj# f|fohv# +rq# ru# rii,# h{shulhqfhg# e|# hdfk# YVF# ydoyh# ohyho#gxulqj#wkh#lqwhjudwlrq#wlph#v l# lv# wkh# wrwdo# qxpehu# ri# sdudooho# uhvlvwlyh# hohphqwv# frqwulexwlqj# wr# g1f1# yrowdjh# ghshqghqw#orvvhv#lq#wkh#ydoyh# lv#wkh#qxpehu#ri#vqxeehu#flufxlwv#shu#ydoyh# lv#wkh#lqwhjudwlrq#wlph#xvhg#lq#wkh#vlpxodwlrq###

3.2.2 Semiconductor device characteristics b3W # lv#wkh#dyhudjh#LJEW#wkuhvkrog#yrowdjh#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv##

T 3W # b3G # T 3G # Q rq#

lv# wkh# dyhudjh# LJEW# vorsh# uhvlvwdqfh# iru# wkh# uhohydqw# rshudwlqj# frqglwlrqv/# ydolg#dw#wkh#ghylfh#whuplqdov# lv#wkh#dyhudjh#glrgh#wkuhvkrog#yrowdjh#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv# lv#wkh#dyhudjh#glrgh#vorsh#uhvlvwdqfh#iru#wkh#uhohydqw#rshudwlqj#frqglwlrq/#ydolg# dw#wkh#ghylfh#whuplqdov# lv#wkh#dyhudjh#wxuq0rq#hqhuj|#glvvlsdwhg#lq#wkh#LJEW#iru#wkh#uhohydqw#rshudwlqj# frqglwlrqv# #

## #

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Q rii # Q rq/W4b v/ w#

lv# wkh# dyhudjh# wxuq0rii# hqhuj|# glvvlsdwhg# lq# wkh# LJEW+v,# iru# wkh# uhohydqw# rshudwlqj#frqglwlrqv# lv# wkh# wxuq0rq# hqhuj|# glvvlsdwhg# lq# LJEW# W4# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wkh# w wk #wxuq0rq#hyhqw#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv#+yrowdjh/#fxuuhqw#dqg# mxqfwlrq#whpshudwxuh,# lv# wkh# wxuq0rq# hqhuj|# glvvlsdwhg# lq# LJEW# W5# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wkh# w wk #wxuq0rq#hyhqw#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv#+yrowdjh/#fxuuhqw#dqg# mxqfwlrq#whpshudwxuh,# lv# wkh# wxuq0rii# hqhuj|# glvvlsdwhg# lq# LJEW# W4# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wk wkh# w #wxuq0rii#hyhqw#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv#+yrowdjh/#fxuuhqw#dqg# mxqfwlrq#whpshudwxuh,# lv# wkh# wxuq0rii# hqhuj|# glvvlsdwhg# lq# LJEW# W5# lq# wkh# v # PPF# exloglqj# eorfn# iru# wkh# wwk #wxuq0rii#hyhqw#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv#+yrowdjh/#fxuuhqw#dqg# mxqfwlrq#whpshudwxuh,# lv# wkh# glrgh# uhfryhu|# hqhuj|# glvvlsdwhg# lq# glrgh# G4# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wkh# wwk # glrgh# wxuq0rii# hyhqw# iru# wkh# uhohydqw# rshudwlqj# frqglwlrqv# +yrowdjh/#fxuuhqw#dqg#mxqfwlrq#whpshudwxuh,# lv# wkh# glrgh# uhfryhu|# hqhuj|# glvvlsdwhg# lq# glrgh# G5# lq# wkh# v # PPF# exloglqj# eorfn# iru# wkh# wwk # glrgh# wxuq0rii# hyhqw# iru# wkh# uhohydqw# rshudwlqj# frqglwlrqv# +yrowdjh/#fxuuhqw#dqg#mxqfwlrq#whpshudwxuh,#
wk wk

Q rq/W5b v/ w#

Q rii/W4b v/ w#

Q rii/W5b v/ w#

Q uhf/G4bm/n #

Q uhf/G5bm/n #

3.2.3 Other component characteristics T vbw# lv# wkh# wrwdo# uhvlvwdqfh# ri# wkh# wwk # vhulhv# uhvlvwlyh# hohphqwv# lq# wkh# ydoyh# frqwulexwlqj#wr#rwkhu#frqgxfwlrq#orvvhv#

T gfb w# T HVUb v# Q vq/rqb v/ w#

lv#wkh#uhvlvwdqfh#ri#wkh# wwk#sdudooho#uhvlvwlyh#frpsrqhqw#lq#wkh#ydoyh# lv#wkh#dyhudjh#htxlydohqw#vhulhv#uhvlvwdqfh#ri#wkh# vwk #g1f1#fdsdflwru# lv#wkh#hqhuj|#glvvlsdwhg#lq#wkh#vqxeehu#uhvlvwru#ri#wkh# v wk #vqxeehu#flufxlw#iru#wkh# w wk # wxuq0rq# hyhqw# iru# wkh# uhohydqw# rshudwlqj# frqglwlrqv# +yrowdjh/# dqg# fxuuhqw# zkhuh#uhohydqw#wr#wkh#ghvljq#ri#wkh#vqxeehu,# lv#wkh#hqhuj|#glvvlsdwhg#lq#wkh#vqxeehu#uhvlvwru#ri#wkh# v wk #vqxeehu#flufxlw#iru#wkh# w wk # wxuq0rii# hyhqw# iru# wkh# uhohydqw# rshudwlqj# frqglwlrqv# +yrowdjh/# dqg# fxuuhqw# zkhuh#uhohydqw#wr#wkh#ghvljq#ri#wkh#vqxeehu,#

Q vq/riib v/ w#

3.2.4 Operating parameters wk K W4dyb v# lv#wkh#phdq#fxuuhqw#ri#LJEW#W4#lq#wkh#v #PPF#exloglqj#eorfn/#dyhudjhg#ryhu#dq# lqwhjudwlrq#wlph# v l#

K W5dyb v# K W4upvb v# K W5upvb v# K G4dyb v# K G5dyb v# K G4upvb v# K G5upvb v#

lv#wkh#phdq#fxuuhqw#ri#LJEW#W5#lq#wkh#v wk #PPF#exloglqj#eorfn/#dyhudjhg#ryhu#dq# lqwhjudwlrq#wlph# v l# lv#wkh#upv#fxuuhqw# ri#LJEW#W4#lq#wkh# vwk# PPF#exloglqj#eorfn/# dyhudjhg# ryhu# dq# lqwhjudwlrq#wlph# v l# lv#wkh#upv#fxuuhqw# ri#LJEW#W5#lq#wkh# v # PPF#exloglqj#eorfn/# dyhudjhg# ryhu# dq# lqwhjudwlrq#wlph# v l# lv# wkh# phdq# fxuuhqw# ri# glrgh# G4# lq# wkh# vwk # PPF# exloglqj# eorfn/# dyhudjhg# ryhu# dq#lqwhjudwlrq#wlph# v l# lv# wkh# phdq# fxuuhqw# ri# glrgh# G5# lq# wkh# vwk # PPF# exloglqj# eorfn/# dyhudjhg# ryhu# dq#lqwhjudwlrq#wlph# v l# lv#wkh#upv#fxuuhqw#ri#glrgh#G4#lq#wkh# vwk #PPF#exloglqj#eorfn/#dyhudjhg#ryhu#dq# lqwhjudwlrq#wlph# v l# lv#wkh#upv#fxuuhqw#ri#glrgh#G5#lq#wkh# vwk #PPF#exloglqj#eorfn/#dyhudjhg#ryhu#dq# lqwhjudwlrq#wlph# v l#
wk

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K upvbw# a upvbn # K fupvb v# RJXb v/ w # r JXb v/ w+ v,# w JXb v/ w+ v,# u JXb v/ w+ v,# RJXb v # r JXb v+ v ,# w JXb v+ v ,# u JXb v+ v,#

lv# wkh# upv# fxuuhqw# iorzlqj# lq# wkh# wwk # vhulhv# uhvlvwlyh# hohphqw# iru# wkh# uhohydqw# rshudwlqj#frqglwlrqv# lv# wkh# upv# ydoxh# +lqfoxglqj# g1f1# frpsrqhqw,# ri# wkh# yrowdjh# dfurvv# wkh# wwk# sdudooho#uhvlvwlyh#frpsrqhqw#lq#wkh#ydoyh# lv#wkh#upv#fxuuhqw#iorzlqj#lq#wkh#vwk#g1f1#fdsdflwru#ri#wkh#ydoyh# lv#wkh#dyhudjh#srzhu#lqsxw#wr#wkh#srzhu#vxsso|#ri# w wk #LJEW#lq# vwk #PPF# exloglqj# eorfn# lv# wkh# lqvwdqwdqhrxv# srzhu# lqsxw# wr# wkh# srzhu# vxsso|# ri# wwk # LJEW# lq# vwk # PPF# exloglqj#eorfn# lv# wkh# lqvwdqwdqhrxv#yrowdjh# lqsxw# wr# wkh# srzhu# vxsso|# ri# w # LJEW# lq# v # PPF# exloglqj#eorfn# lv# wkh# lqvwdqwdqhrxv# fxuuhqw# lqsxw# wr# wkh# srzhu# vxsso|# ri# wwk # LJEW# lq# v wk # PPF# exloglqj#eorfn## lv#wkh#dyhudjh#srzhu#lqsxw#wr#wkh#srzhu#vxsso|#lq# v #PPF#exloglqj#eorfn# lv#wkh#lqvwdqwdqhrxv#srzhu#lqsxw#wr#wkh#srzhu#vxsso|#lq# vwk#PPF#exloglqj#eorfn# lv# wkh# lqvwdqwdqhrxv# yrowdjh# lqsxw# wr# wkh# srzhu# vxsso|# lq# vwk# PPF# exloglqj# eorfn# lv# wkh# lqvwdqwdqhrxv# fxuuhqw# lqsxw# wr# wkh# srzhu# vxsso|# lq# vwk # PPF# exloglqj# eorfn#
wk wk wk

3.2.5 Loss parameters RY4 # LJEW#frqgxfwlrq#orvvhv#

RY5 # RY6 # RY7 # RY8 # RY9 # RY: # RY; # RY< # RYw # 4
4.1

glrgh#frqgxfwlrq#orvvhv# rwkhu#ydoyh#frqgxfwlrq#orvvhv# g1f1#yrowdjh0ghshqghqw#orvvhv# g1f1#fdsdflwru#orvvhv# LJEW#vzlwfklqj#orvvhv# glrgh#wxuq0rii#orvvhv# vqxeehu#orvvhv# ydoyh#hohfwurqlfv#srzhu#frqvxpswlrq# wrwdo # ydoyh#orvvhv#

General
Introduction

Prgxodu#Pxowl0Ohyho#Frqyhuwhuv#+PPF,#duh#d#idplo|#ri#frqyhuwhuv#lq#zklfk#hdfk#ydoyh#irupv#d# frqwuroodeoh# yrowdjh# vrxufh1# Wkh# frqyhuwhu# d1f1# yrowdjh# lv# v|qwkhvl}hg# e|# vzlwfklqj# odujh# qxpehuv# ri# uhodwlyho|# vpdoo/# vhoi0frqwdlqhg/# wzr0whuplqdo# frqwuroodeoh# yrowdjh# vrxufhv# dw# gliihuhqw#wlphv/#wkhuhe|#rewdlqlqj#d#kljk0txdolw|#frqyhuwhu#zdyhirup#zlwk#orz#vzlwfklqj#orvvhv# dqg# wkhuhiruh# d# kljk# ryhudoo# hiilflhqf|1# Wkh# PPF# exloglqj# eorfnv# iurp# zklfk# wkh# ryhudoo# frqyhuwhu#lv#exlow#xs#pd|#xvh#pxowlsoh#LJEW0glrgh#sdluv#frqqhfwhg#lq#vhulhv#+lq#zklfk#fdvh#wkh# frqyhuwhu#lv#uhihuuhg#wr#dv#wkh#?Fdvfdghg#Wzr#Ohyho?#+FWO,#frqyhuwhu,#ru#rqo|#d#vlqjoh#LJEW0 glrgh#sdlu#shu#vzlwfk#srvlwlrq1#D#ghwdlohg#ghvfulswlrq#ri#wkhvh#w|shv#ri#frqyhuwhu#lv#eh|rqg#wkh# vfrsh# ri# wklv# vwdqgdug># krzhyhu/# Dqqh{# D# lqfoxghv# d# jhqhudo# ghvfulswlrq# ri# wkh# rshudwlrq# ri# wkh#PPF1#Wkh#uhdghu#lv#uhihuuhg#wr#LHF2WU#958761# 4.2 Principles for loss determination

Wkhruhwlfdoo|/# wkh# orvvhv# ri# d# frqyhuwhu# vwdwlrq# fdq# eh# ghwhuplqhg# hlwkhu# e|# gluhfw# phdvxuhphqwv# ri# wkh# lqsxw# dqg# rxwsxw# srzhuv# ru# e|# phdqv# ri# frpsrqhqw# fkdudfwhulvwlfv/# #

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5
5.1

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General

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##

K W4dyb v# K W5dyb v# K W4upvb v# K W5upvb v#

lv#wkh#phdq#fxuuhqw#ri#LJEW#W4#lq#wkh#v wk #PPF#exloglqj#eorfn/#dyhudjhg#ryhu#dq# lqwhjudwlrq#wlph# v l# lv#wkh#phdq#fxuuhqw#ri#LJEW#W5#lq#wkh#v wk #PPF#exloglqj#eorfn/#dyhudjhg#ryhu#dq# lqwhjudwlrq#wlph# v l# lv#wkh#upv#fxuuhqw# ri#LJEW#W4#lq#wkh# v # PPF#exloglqj#eorfn/# dyhudjhg# ryhu# dq# lqwhjudwlrq#wlph# v l# lv#wkh#upv#fxuuhqw# ri#LJEW#W5#lq#wkh# vwk# PPF#exloglqj#eorfn/# dyhudjhg# ryhu# dq# lqwhjudwlrq#wlph# v l#
wk

E|#phdqv#ri#qxphulfdo#vlpxodwlrq#wkh#fxuuhqwv#kdyh#wr#eh#fdofxodwhg#iru#wkh#LJEWv#W4#dqg#W5# iru#hdfk#PPF#exloglqj#eorfn/#uhvshfwlyho|=# ############################################ K T1av

1 = × uT1 (v ) × f (v ) ###########################################+5,# vi 0

ò

vi

########################################### K T2av =

1 × uT2 (v ) × f (v ) ############################################+6,# vi 0

ò

vi

####################################### K T1rms

1 = × uT1 (v ) 2 × f (v ) ##########################################+7, vi 0

ò
v

vi

#

####################################### K T2rms = zkhuh=#

1 i × uT2 (v ) 2 × f (v ) ##########################################+8,# vi 0

ò

v l##

lv#wkh#lqwhjudwlrq#wlph#xvhg#lq#wkh#vlpxodwlrq1#

v l#vkdoo#qrw#eh#ohvv#wkdq#4#vhfrqg1#
QRWH#Li#gliihuhqw#LJEW#w|shv# duh#xv hg#iru#W4#dqg#W5#wkh#ydoxhv#iru#wkuhvkrog#yrowdjhv# dqg#vorsh#uhvlvwdqf hv#kdyh# wr#eh#xvhg#dffruglqjo|1##

5.3

Diode Conduction Losses

Wkh# wrwdo# glrgh# frqgxfwlrq# orvvhv# shu# y doyh# pd|# eh# fdofxodwhg# e|# vxpplqj# wkh# frqgxfwlrq# orvvhv#ri#doo#glrghv#shu#ydoyh=# ############## RV2 = P c × zkhuh=#

? (b
v =1

P tc

0D

× K D1av _ v + T0D × K D1rms _ v + b0D × K D2av _ v + T0D × K D2rms _ v ) ##############+9,#

2

2

Pwf # Pf ## b3G # T 3G # K G4dyb v#

qxpehu#ri#PPF#exloglqj#eorfnv#shu#ydoyh# qxpehu#ri#vhulhv0frqqhfwhg#vhplfrqgxfwru#ghylfhv#shu#vzlwfk#srvlwlrq# lv#wkh#dyhudjh#glrgh#wkuhvkrog#yrowdjh#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv# lv#wkh#dyhudjh#glrgh#vorsh#uhvlvwdqfh#iru#wkh#uhohydqw#rshudwlqj#frqglwlrq/#ydolg# dw#wkh#ghylfh#whuplqdov# lv# wkh# phdq# fxuuhqw# ri# glrgh# G4# lq# wkh# vwk # PPF# exloglqj# eorfn/# dyhudjhg# ryhu# dq#lqwhjudwlrq#wlph# v l#

#

## #

?#49#?#

95:84052Hg42FG#? #LHF#

K G5dyb v# K G4upvb v# K G5upvb v#

lv# wkh# phdq# fxuuhqw# ri# glrgh# G5# lq# wkh# vwk # PPF# exloglqj# eorfn/# dyhudjhg# ryhu# dq#lqwhjudwlrq#wlph# v l# lv#wkh#upv#fxuuhqw#ri#glrgh#G4#lq#wkh# vwk #PPF#exloglqj#eorfn/#dyhudjhg#ryhu#dq# lqwhjudwlrq#wlph# v l# lv#wkh#upv#fxuuhqw#ri#glrgh#G5#lq#wkh# v #PPF#exloglqj#eorfn/#dyhudjhg#ryhu#dq# lqwhjudwlrq#wlph# v l#
wk

E|#phdqv#ri#qxphulfdo#vlpxodwlrq#wkh#fxuuhqwv#kdyh#wr#eh#fdofxodwhg#iru#wkh#glrghv#G4#dqg#G5# iru#hdfk#PPF#exloglqj#eorfn/#uhvshfwlyho|=#

############################################## K D1av

1 i = × uD1 (v ) × f (v ) #############################################+:,# vi 0

ò

v

############################################# K D2av =

1 × uD2 (v ) × f (v ) #############################################+;,# vi 0

ò

vi

K D1rms
############################################

1 = × uD1 (v ) 2 × f (v ) vi 0

ò

vi

#########################################+<,#

K D2rms
################################################# zkhuh=#

1 = × uD2 (v ) 2 × f (v ) vi 0

ò

vi

# ########################################+43,

v l##

lv#wkh#lqwhjudwlrq#wlph#xvhg#lq#wkh#vlpxodwlrq1#

v l#vkdoo#qrw#eh#ohvv#wkdq#4#vhfrqg1#
QRWH##Li# gliihuhqw#glrgh#w|shv# duh#xv hg#iru#G4# dqg#G5#wkh#ydoxhv# iru#wkuhvkrog# yrowdjhv# dqg#vorsh#uhvlvwdqf hv# kdyh# wr#eh#xvhg#dffruglqjo|1##

5.4

Other conduction losses

Wklv#fodxvh#fryhuv#wkh#srzhu#orvvhv#gxh#wr#frqgxfwlrq#lq# frpsrqhqwv#rwkhu#wkdq#LJEWv#dqg# glrghv1# Iru# Prgxodu# Pxowl0Ohyho# Frqyhuwhuv# wklv# pdlqo|# lqfoxghv# wkh# ydoyh# uhdfwruv# dqg# lqwhufrqqhfwlqj#exveduv1## Fdofxodwlrq#ri# vxfk#orvvhv#lv#uhodwlyho|#vwudljkwiruzdug# dqg#ghshqgv#rqo|#rq#wkh#uhvlvwdqfh#ri# hdfk#frqgxfwlqj#hohphqw#dqg#wkh#upv#fxuuhqw#wkdw#iorzv#wkurxjk#lw1#Wkh#uhohydqw#upv#fxuuhqwv# zlwklq# wkh# PPF# exloglqj# eorfnv# fdq# eh# ghulyhg# iurp# wkh# vlpxodwlrqv# ri# wkh# fxuuhqw# vwuhvvhv# dffruglqj#fodxvhv#815#dqg#8161#Dovr#wkh#upv#fxuuhqwv#wkurxjk#uhdfwruv#dqg#ehwzhhq#wkh#PPF# exloglqj#eorfnv#uhvshfwlyho|#fdq#eh#ghulyhg#dffruglqjo|1# Wkh#ydoxh#ri#wkhvh#orvvhv#shu#ydoyh#lv#jlyhq#e|=#

RV3 =
############################################# Zkhuh=#

?K
w =1

P sr

2 rms _ w

× Ts _ w
########################################+44,

#

95:84052Hg42FG#? #LHF#

?#4:#?#

##

Pvu# K upvbw# T vbw# 6

lv# wkh# wrwdo# qxpehu# ri# vhulhv# uhvlvwlyh# hohphqwv# frqwulexwlqj# wr# frqgxfwlrq# orvvhv#lq#wkh#ydoyh/#rwkhu#wkdq#lq#wkh#LJEWv#dqg#glrghv# lv# wkh# upv# fxuuhqw# iorzlqj# lq# wkh# wwk # vhulhv# uhvlvwlyh# hohphqw# iru# wkh# uhohydqw# rshudwlqj#frqglwlrqv# lv# wkh# wrwdo# uhvlvwdqfh# ri# wkh# wwk # vhulhv# uhvlvwlyh# hohphqwv# lq# wkh# ydoyh# frqwulexwlqj#wr#rwkhu#frqgxfwlrq#orvvhv#

D.C. Voltage-dependent losses

Wkh# g1f1# yrowdjh0ghshqghqw# orvvhv# ri# wkh# ydoyh# duh# vlpso|# wkh# a 52 T # orvvhv# lq# uhvlvwlyh# frpsrqhqwv#frqqhfwhg#lq#sdudooho#zlwk#wkh#ydoyh#ru#zlwk#sduwv#ri#wkh#ydoyh1# Lq# sulqflsoh/# wkh# wrwdo# g1f1# yrowdjh0ghshqghqw# orvvhv# lq# wkh# ydoyh# fdq# eh# irxqg# e|# fdofxodwlqj# wkh#srzhu#glvvlsdwlrq#lq#hdfk#uhvlvwlyh#frpsrqhqw#frqqhfwhg#lq#sdudooho# zlwk#sduw#ru#doo# ri#wkh# ydoyh#dqg#vxpplqj#wkhp1## ############################################# RV4 = zkhuh=#

?
w =1

P pr

a rms _ w 2 Tdc _ w

###############################################+45,#

P su# a upvbn # T gfb w#

lv# wkh# wrwdo# qxpehu# ri# sdudooho# uhvlvwlyh# hohphqwv# frqwulexwlqj# wr# g1f1# yrowdjh# ghshqghqw#orvvhv#lq#wkh#ydoyh# lv# wkh# upv# ydoxh# +lqfoxglqj# g1f1# frpsrqhqw,# ri# wkh# yrowdjh# dfurvv# wkh# wwk# sdudooho#uhvlvwlyh#frpsrqhqw#lq#wkh#ydoyh# lv#wkh#uhvlvwdqfh#ri#wkh# wwk#sdudooho#uhvlvwlyh#frpsrqhqw#lq#wkh#ydoyh#

Lq# dq# PPF# ydoyh# wkhvh# uhvlvwlyh# frpsrqhqwv# idoo# lqwr# wzr# pdlq# fdwhjrulhv=# wkrvh# wkdw# duh# frqqhfwhg# lq# sdudooho# zlwk# wkh# g1f1# fdsdflwru# ri# hdfk# PPF# exloglqj# eorfn# +vxfk# dv# fdsdflwru# glvfkdujh#uhvlvwruv,#dqg#wkrvh#wkdw#duh#frqqhfwhg#lq#sdudooho# zlwk#wkh#frpsohwh#ydoyh#ru#odujh# sduwv#ri#wkh#ydoyh#+iru#h{dpsoh#zdwhu#frrolqj#slshv,1#
QRWH##Wkh#srzhu#vxsso|#flufxlw#iru#wkh#ydoyh#hohfwurqlfv# lv#htxlydohqw#wr#d#sdudooho#uhvlvwlyh#ordg# dfurvv# sduw# ri# wkh# ydoyh/# exw# wkhv h#flufxlwv# vkrxog# qrw# eh# lqfoxghg# lq# wkh# dvvhvvphqw# ri# g1f1# yrowdjh0ghshqghqw# orvvhv# ehf dxv h#wkh|# duh#v hsdudwho|#dff rxqwhg#iru#xqghu#?Ydoyh#Hohfwurqlfv# Srzhu# Frqvxpswlrq?/#fodxv h#<151#

7

Losses in d.c. capacitors

Srzhu#orvvhv#lq#wkh#PPF#exloglqj# eorfn#fdsdflwruv#fdqqrw# eh# qhjohfwhg1#Wkh|#uhsuhvhqw# K5 1 T # orvvhv# lq# wkh# phwdoolf# frpsrqhqwv# zlwklq# wkh# fdsdflwru/# fklhio|# wkh# ilop# phwdoolvdwlrq# dqg# lqwhuqdo#ohdgv/#dqg#glhohfwulf#orvvhv#zlwklq#wkh#glhohfwulf#pdwhuldo1# Wkh#wrwdo#g1f1#fdsdflwru#orvvhv#shu#ydoyh#duh#wkhq#fdofxodwhg#dv#iroorzv=#

RV5 =
########################################### zkhuh=## #

?K
v =1

P cv

2 crms _ v

× TESR _ v
###########################################+46,

#

Pfy # K fupvb v# T HVUb v#

lv#wkh#qxpehu#ri#fdsdflwruv#lq#wkh#ydoyh# lv#wkh#upv#fxuuhqw#iorzlqj#lq#wkh#v #g1f1#fdsdflwru#ri#wkh#ydoyh# lv#wkh#dyhudjh#htxlydohqw#vhulhv#uhvlvwdqfh#ri#wkh# v #g1f1#fdsdflwru#
wk wk

Wkh# upv# fxuuhqw# lq# wkh# g1f1# fdsdflwru# fdq# eh# ghulyhg# e|# wkh# fdofxodwlrqv# ri# fodxvhv# 815# dqg# 8161# #

## #

?#4;#?#

95:84052Hg42FG#? #LHF#

QRWH# 4# Wkh# PPF# exloglqj# eorfn# f dsdflwru# pd|# eh# vhulhv# frqqhfwlrq# ri# lqglylgxdo# f dsdflwru# xqlwv1# Iru# wk h# fdofxodwlrq#wkh#htxlydohqw#vhulhv# uhvlvwdqf h#ri# wkdw#v hulhv# frqqhfwlrq#kdv# wr#eh#frqvlghuhg#iru#wkh#fdofxodwlrqv1# QRWH# 5# Glhohfwulf# orvvhv# duh# qrupdoo|# prvw# vljqlilfdqw# lq# d1f1# dssolfdwlrqv# zkhuh# wkh# fdsdflwru# yrowdjh# srodulw |# uhyhuv hv#wzlfh#shu#f |foh1#Iru#g1f1#fdsdflwruv#wkh#yrowdjh#lv#xvxdoo|#qrq0uhyhuvlqj#dqg#glhohfwulf#orvvhv#duh#wkhuhiru h# vpdoo/#exw#ghshqglqj#rq#wkh#f dsdflwru#whfkqrorj|#xvhg/#wkh|#fdq#eh#qrq0qhjoljleoh1# QRWH# 6# Wkhuh# pd|# dovr# eh# d# wklug# frpsrqhqw# ri# orvv# fdxvhg# e|# wkh# ilqlwh# lqvxodwlrq# uhvlvwdqfh# ri# wkh# glhohfwulf# pdwhuldo/# exw# wklv# lv# qrupdoo|# yhu|# vpdoo1# Lw# lv# fryhuhg# e|# g1f1# yrowdjh0ghshqghqw# orvvhv# dv# ghvfulehg# lq# wk h# suhf hglqj#vxe0fodxvh1# QRWH# 7# Orvvhv# lq# edodqflqj# u hvlvwruv# lq# sdudooho# zlwk# fdsdflwru# xqlwv# frqqhfwhg# lq# v hulhv# duh# fryhuhg# e|# g1f1# yrowdjh0ghshqghqw#orvvhv#dv#ghvfulehg#lq#wkh#suhf hglqj#vxe0fodxv h1#

8
8.1

Switching Losses
General

Wkh# ghylfhv# lq# wkh# PPF# exloglqj# eorfn# zloo# eh# vwuhvvhg# zlwk# fxuuhqw# dqg# yrowdjh# gxulqj# vzlwfklqj# hyhqwv1# Krz# wkh# hyhqw# zloo# rffxu# lv# ghshqghqw# rq# wkh# rshudwlrqdo# prgh# ri# wkh# v|vwhp1#Ehfdxvh#ri#wkh#f|folf#fkdujlqj#dqg#glvfkdujlqj#ri#wkh#fdsdflwru/#hdfk#vzlwfklqj#hyhqw# rffxuv#dw#d#gliihuhqw#yrowdjh1#Wkh#lqvwdqfhv#iru#vzlwfklqj#fdq#ydu|#pxfk#ghshqghqw#rq#frqwuro# sulqflsohv#dqg#d#jhqhudo#irupxod#wr#eh#dssolhg#dw#dq|#w|sh#ri#frqyhuwhu#ydoyh#lv#qrw#ihdvleoh1# Wkh# lqwhjudwlrq# wlph# vkdoo# eh# dw# ohdvw# rqh# vhfrqg# lq# rughu# wr# hqvxuh# uholdeoh# uhvxowv# dovr# iru# frqwuro#vwudwhjlhv#zkhuh#wkh#vzlwfklqj#sdwwhuq#ydulhv#iurp#rqh#ixqgdphqwdo#shulrg#wr#wkh#qh{w1# Dv# lqsxw# gdwd# iurp# ghylfh# fkdudfwhulvdwlrq# w|slfdo# ydoxhv# uhsuhvhqwdwlyh# iru# wkh# zkroh# srsxodwlrq#vkdoo#eh#xvhg#iru# Q rq/# Qrii #dqg#Q uhf 1# 8.2 IGBT switching losses

Wkh#wrwdo#LJEW#vzlwfklqj#orvvhv#shu#ydoyh#duh#fdofxodwhg#e|#vxpplqj#doo#wkh#wxuq0rq#hqhujlhv# Q rq# dqg#wkh#wxuq0rii# hqhujlhv# Q rii #iru#doo# ri#wkh#YVF# Ydoyh#ohyhov#lq#wkh#ydoyh/# dqg#iru# erwk#W4# dqg#W5#ryhu#dq#lqwhjudwlrq#wlph# v l1# #################### RV6 = zkhuh=## Pwf #

1 × Pc × vu

??[ Q
v =1 w =1

P tc P s

on, T1 _ v , w

+ Qon, T2 _ v , w +Qoff, T1 _ v , w + Qoff, T2 _ v ,w ] ###############+47,#

qxpehu#ri#PPF#exloglqj#eorfnv#shu#ydoyh# qxpehu#ri#vhulhv0frqqhfwhg#vhplfrqgxfwru#ghylfhv#shu#vzlwfk#srvlwlrq# lv# wkh# qxpehu# ri# vzlwfklqj# f|fohv# +rq# ru# rii,# h{shulhqfhg# e|# hdfk# YVF# ydoyh# ohyho#gxulqj#wkh#lqwhjudwlrq#wlph#v l# lv# wkh# wxuq0rq# hqhuj|# glvvlsdwhg# lq# LJEW# W4# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wkh# w wk #wxuq0rq#hyhqw#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv#+yrowdjh/#fxuuhqw#dqg# mxqfwlrq#whpshudwxuh,# lv# wkh# wxuq0rq# hqhuj|# glvvlsdwhg# lq# LJEW# W5# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wkh# w wk #wxuq0rq#hyhqw#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv#+yrowdjh/#fxuuhqw#dqg# mxqfwlrq#whpshudwxuh,# lv# wkh# wxuq0rii# hqhuj|# glvvlsdwhg# lq# LJEW# W4# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wkh# wwk #wxuq0rii#hyhqw#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv#+yrowdjh/#fxuuhqw#dqg# mxqfwlrq#whpshudwxuh,# lv# wkh# wxuq0rii# hqhuj|# glvvlsdwhg# lq# LJEW# W5# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wk wkh# w #wxuq0rii#hyhqw#iru#wkh#uhohydqw#rshudwlqj#frqglwlrqv#+yrowdjh/#fxuuhqw#dqg# mxqfwlrq#whpshudwxuh,# lv#wkh#lqwhjudwlrq#wlph#xvhg#lq#wkh#vlpxodwlrq1#

Pf ## Pv# Q rq/W4b v/ w#

Q rq/W5b v/ w#

Q rii/W4b v/ w#

Q rii/W5b v/ w#

v l##

v l#vkdoo#qrw#eh#ohvv#wkdq#4#vhfrqg1#

95:84052Hg42FG#? #LHF# 8.3 Diode switching losses

?#4<#?#

##

Wkh# wrwdo# glrgh# vzlwfklqj# orvvhv# shu# ydoyh# duh# wkhq# fdofxodwhg# e|# vxpplqj# doo# wkh# uhfryhu|# hqhujlhv# Q uhf # iru# doo# ri# wkh#ydoyh# ohyhov# lq# wkh#ydoyh/# dqg# iru# erwk# G4# dqg# G5/# ryhu# d# ghilqhg# lqwhjudwlrq#wlph# v l1 #

RV7 =

############################ zkhuh=# Pwf # qxpehu#ri#PPF#exloglqj#eorfnv#shu#ydoyh#

1 × Pc × vi

?? ( Q
v =1 w =1

P tc P s

rec, D1_v , w

+ Qrec, D2_v ,w )
###################################+48,

#

Pf ## Pv# Q uhf/G4bm/n #

qxpehu#ri#vhulhv0frqqhfwhg#vhplfrqgxfwru#ghylfhv#shu#vzlwfk#srvlwlrq# lv# wkh# qxpehu# ri# vzlwfklqj# f|fohv# +rq# ru# rii,# h{shulhqfhg# e|# hdfk# YVF# ydoyh# ohyho#gxulqj#wkh#lqwhjudwlrq#wlph#v l# lv# wkh# glrgh# uhfryhu|# hqhuj|# glvvlsdwhg# lq# glrgh# G4# lq# wkh# vwk # PPF# exloglqj# eorfn# iru# wkh# wwk # glrgh# wxuq0rii# hyhqw# iru# wkh# uhohydqw# rshudwlqj# frqglwlrqv# +yrowdjh/#fxuuhqw#dqg#mxqfwlrq#whpshudwxuh,# lv# wkh# glrgh# uhfryhu|# hqhuj|# glvvlsdwhg# lq# glrgh# G5# lq# wkh# v # PPF# exloglqj# eorfn# iru# wkh# wwk # glrgh# wxuq0rii# hyhqw# iru# wkh# uhohydqw# rshudwlqj# frqglwlrqv# +yrowdjh/#fxuuhqw#dqg#mxqfwlrq#whpshudwxuh,# lv#wkh#lqwhjudwlrq#wlph#xvhg#lq#wkh#vlpxodwlrq1#
wk

Q uhf/G5bm/n #

v l##

v l#vkdoo#qrw#eh#ohvv#wkdq#4#vhfrqg1# 9
9.1

Other losses
Snubber circuit losses

Ydoyhv# iru# Prgxodu# Pxowl0ohyho# Frqyhuwhuv# duh# iuhtxhqwo|# qrw# surylghg# zlwk# vqxeehu# flufxlwv># krzhyhu# wklv# fodxvh# zloo# surylgh# jhqhudo# jxlgdqfh# wr# wkh#phwkrg# wr# eh# xvhg# wr# fdofxodwh# wkh# orvvhv#lq#vqxeehu#flufxlwv#zkhuh#wkhvh#duh#surylghg1# Lq# fdvh# ri# xvlqj# UF# vqxeehuv# ru# rwkhu# nlqg# ri# vqxeehuv# +UFG# dqg# vr# rq,# lq# d# ghvljq# iru# Prgxodu#Pxowl0ohyho#Frqyhuwhuv#wkh#orvvhv#lq#wkh#uhvlvwru#vkdoo#eh#lqfoxghg#lq#wkh#fdofxodwlrq1# Wkh#orvvhv#fdq#eh#fdofxodwhg#dv#wkh#hqhuj|#lq#wkh#vqxeehu#fdsdflwru#pxowlsolhg#e|#wkh#qxpehu# ri# fkdujh2# glvfkdujlqj# hyhqwv# wkdw# kdsshq# gxulqj# wkh# lqwhjudwlrq# wlph1# Wklv# lv# krzhyhu# yhu|# frqvhuydwlyh# iru# # vqxeehuv# zlwk# yhu|# vkruw# wlph# frqvwdqw/# vlqfh# lq# wklv# fdvh# sduw# ri# wkh# vqxeehu#fdsdflwru#hqhuj|#zloo#dsshdu#dv#dgglwlrqdo#vzlwfklqj#hqhuj|#lq#wkh#LJEW1#
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9.2 9.2.1 Valve electronics power consumption General

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Annex A +Lqirupdwlyh, Description of power loss mechanisms in MMC valves
A.1 Introduction to MMC Converter topology

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# Figure A.2– Phase Unit of the Cascaded Two-Level (CTL) converter in half-bridge form Wkh#rxwsxw#yrowdjh#surgxfhg# e|# hdfk#ydoyh#lv#dq#riivhw# vlqxvrlgdo#yrowdjh# zlwk#d#phdq#ydoxh# htxdo#wr#kdoi#wkh#g1f1#olqh#wr#olqh#yrowdjh/#dqg#wkh#wzr#ydoyhv#lq#hdfk#skdvh#xqlw#duh#frqwuroohg# vxfk# wkdw#wkh#d1f1#frpsrqhqwv#ri# wkhlu# rxwsxw#yrowdjhv#duh#4;3?#rxw#ri# skdvh#+Iljxuh#D16,1# Lq# wklv#zd|/#wkh#vxp#ri#wkh#wzr#ydoyh#yrowdjhv#lv#doprvw#d#sxuh#g1f1#yrowdjh#+htxdo#wr#wkh#g1f1#olqh# wr# olqh# yrowdjh# ri# wkh# frqyhuwhu,/# dqg# wkh# gliihuhqfh# ehwzhhq# wkh# wzr# ydoyh# yrowdjhv# lv# dq# doprvw#sxuh#d1f1#yrowdjh#uhsuhvhqwlqj#wkh#d1f1#rxwsxw#yrowdjh#ri#wkh#frqyhuwhu1# Wkh# vxp# ri# wkh# wzr# ydoyh# yrowdjhv# lq# hdfk# skdvh# qhhgv# wr# eh# frqwuroohg# dffxudwho|/# lq# uhdo# wlph/# wr# eh# htxdo# wr# wkh# frqyhuwhu# g1f1# yrowdjh1# Krzhyhu/# vlqfh# wkh# frpsohwh# frqyhuwhu# frqvlvwv# ri# wkuhh# skdvh# xqlwv# frqqhfwhg# lq# sdudooho# wr# d# frpprq# g1f1# exv/# ?ydoyh# uhdfwruv?# qhhg# wr# eh# frqqhfwhg# lq# vhulhv# zlwk# hdfk# ydoyh# lq# rughu# wr# suhyhqw# h{fhvvlyh# flufxodwlqj# fxuuhqwv#ehwzhhq#skdvhv#fdxvhg#e|#wkh#lqhylwdeoh#voljkw#huuruv#lq#frqwuroolqj#wkh#g1f1#yrowdjhv# ri#wkh#wkuhh#skdvh#dupv1## Wkh# rshudwlrq# ri# wkh# frqyhuwhu/# lq# vr# idu# dv# lw# diihfwv# wkh# srzhu# orvvhv# lq# wkh# ydoyhv/# lv# ghvfulehg# lq# wkh# iroorzlqj# vxe0fodxvhv# D15# ?# D18# iru# wkh# prvw# frpprqo|# xvhg# yduldqw# ri# wklv# idplo|# ri# frqyhuwhuv/# wkh# PPF# wrsrorj|# xvlqj# ?kdoi0eulgjh?/# wzr0ohyho# vxeprgxohv/# zlwkrxw# vhulhv0frqqhfwlrq# ri# LJEWv1# Rwkhu# yduldqwv# duh# srvvleoh/# dqg# wkhlu# pdlq# gliihuhqfhv# duh# glvfxvvhg/#dorqj#zlwk#wkh#FWO#wrsrorj|/#lq#vxefodxvh#D191#

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# Figure A.3 - Basic operation of the MMC converters

A.2
A.2.1

Valve voltage and current stresses
Simplified analysis with voltage and current in phase

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Figure A.4 – MMC converters showing composition of valve current Iljxuh#D17#vkrzv#wkh#w|slfdo#zdyhirupv#ri#ydoyh#yrowdjh#dqg#fxuuhqw1#Wkh#frqglwlrq#vkrzq#rq# Iljxuh#D17#dssolhv#zkhq#wkh#frqyhuwhu#d1f1#rxwsxw#yrowdjh#dqg#d1f1#fxuuhqw#duh#lq#skdvh/#zklfk# phdqv#wkdw#wkh#ydoyh#yrowdjh#dqg#ydoyh#fxuuhqw#duh#4;3?#rxw#ri#skdvh1#Khqfh/#zkhq#wkh#ydoyh# yrowdjh# lv# dw# lwv# plqlpxp/# ydoyh# fxuuhqw# lv# dw# lwv# shdn1# Wklv# lv# dssur{lpdwho|# wuxh# zkhq# wkh# frqyhuwhu#lv#ehlqj#xvhg#iru# wudqvplwwlqj#dfwlyh#srzhu# rqo|/# zlwkrxw# uhdfwlyh#srzhu#jhqhudwlrq# ru# devruswlrq1# Krzhyhu/# hyhq# zkhq# wkh# frqyhuwhu# lv# qrw# jhqhudwlqj# ru# devruelqj# uhdfwlyh# srzhu/#wkh#ydoyh#yrowdjh#dqg#fxuuhqw#zloo# jhqhudoo|#qrw#eh#h{dfwo|#4;3?#rxw#ri#skdvh/#ehfdxvh# ri# wkh#skdvh# vkliw#dfurvv#wkh#lqwhuidfh#wudqviruphu#dqg#ydoyh#uhdfwruv1# Qhyhuwkhohvv#wkh#4;3?# skdvh# vkliw# vkrzq# rq# Iljxuh# D17# lv# d# xvhixo# vlpsoli|lqj# dvvxpswlrq# lq# rughu# wr# dlg# wkh# xqghuvwdqglqj#ri#wkh#flufxlw1# Lw# zloo# dovr# eh# qrwhg# iurp# Iljxuh# D17# wkdw# wkh# ydoyh# yrowdjh# ydulhv# f|folfdoo|# iurp# mxvw# deryh# }hur# wr# mxvw# ehorz# wkh# g1f1# olqh# wr# olqh# yrowdjh1# Zkhq# ?kdoi0eulgjh?# PPF# exloglqj# eorfnv# duh# xvhg/#wkh#ydoyh#yrowdjh#fdq#qhyhu#h{fhhg# a g/#qru#idoo#ehorz#}hur/#rwkhuzlvh#wkh#iuhh0zkhholqj# glrghv#lq#sdudooho#zlwk#hdfk#LJEW#zloo#frqgxfw1#Wklv#lv#dq#lpsruwdqw#olplwdwlrq#ri#wkh#kdoi0eulgjh# ghvljq1# Rswlpxp# hiilflhqf|# lv#rewdlqhg#zkhq#wkh#shdn#frqyhuwhu#yrowdjh#lv#htxdo# wr#?# a g1#Rshudwlqj# zlwk# d# shdn# frqyhuwhu# yrowdjh# orzhu# wkdq# ?# ag # lpsolhv# wkdw# wkh# d1f1# fxuuhqw# kdv# wr# eh# lqfuhdvhg# wr# uhdfk# wkh# ghvluhg# ydoxh# ri# srzhu># wkhuhiruh/# zkhq# ?kdoi0eulgjh?# PPF# Exloglqj# eorfnv#duh#xvhg/#wkh#frqwuroohu#xvxdoo|#dwwhpswv#wr#nhhs#wkh#shdn#ydoyh#yrowdjh#mxvw#ehorz# a g/# vr# dv# wr# plqlplvh# wkh# d1f1# fxuuhqw# +dqg# khqfh# wkh# orvvhv,# uhtxluhg# iru# d# jlyhq# dprxqw# ri# dfwlyh#srzhu1# Zkhq# wkh# g1f1# fxuuhqw# lv#iorzlqj# lqwr# wkh# srvlwlyh#g1f1# whuplqdo# ri# wkh# frqyhuwhu/# dv# vkrzq# rq# Iljxuh# D16/# wkh#frqyhuwhu#lv#lpsruwlqj#srzhu#wr#wkh#d1f1# qhwzrun#iurp# wkh#g1f1# qhwzrun# dqg#lv# wkhuhiruh# rshudwlqj#dv#dq#lqyhuwhu1# Lq#uhfwlilhu# rshudwlrq/# g1f1#fxuuhqw#iorzv#rxw# ri# wkh#srvlwlyh# g1f1#whuplqdo#dqg#lqwr#wkh#qhjdwlyh#g1f1#whuplqdo1## Lq# wkh# uhpdlqghu# ri# wklv# Dqqh{/# wkh# vljq# frqyhqwlrq# dgrswhg# lv# wkdw# wkh# ydoyh# fxuuhqw# lv# srvlwlyh#zkhq#lw#lv#iorzlqj#wrzdugv#wkh#qhjdwlyh#g1f1#whuplqdo#ri#wkh#frqyhuwhu1#Wklv#phdqv#wkdw# wkh#ydoyh#fxuuhqw#lv#pdlqo|#qhjdwlyh#dw#d#uhfwlilhu#dqg#pdlqo|#srvlwlyh#dw# dq#lqyhuwhu1#

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Generalised analysis with voltage and current out of phase

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# Figure A.5 - Phasor diagram showing a.c. system voltage, converter a.c. voltage and converter a.c. current A.2.3 Effects of third harmonic injection

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# Figure A.6 - Effect of 3rd harmonic injection on converter voltage and current

A.3
A.3.1

Conduction losses in MMC building blocks
Description of conduction paths

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Figure A.7 - Two functionally equivalent variants of a “half-bridge”, two-level MMC building block
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Negative Valve Current

Positive Valve Current

T1 D1

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0V
Bypassed
T2 D2

D2

T1 D1

T1

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T2

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Active
T2 D2

D2

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ωv

3

# Figure A.9 - Typical patterns of conduction for inverter operation (left) and rectifier operation (right) Dq# h{dpsoh# ri# d# frqyhuwhu# zlwk/# iru# looxvwudwlyh# sxusrvhv/# rqo|# rqh# PPF# exloglqj# eorfn# shu# ydoyh/#lv#vkrzq#lq#Iljxuh#D143#ehorz1#

# Figure A.10 – Example of converter with only one MMC building block per valve to illustrate switching behaviour Lqyhuwhu# rshudwlrq# ri# wklv# frqyhuwhu# lq# d# w|slfdo# fdvh# lv# vkrzq# lq# dq# h{dpsoh# lq# Iljxuh# D144# dqg#lq#uhfwlilhu#rshudwlrq#lq#Iljxuh#D1451# #

## #
W5#

?#65#?#
G5#

95:84052Hg42FG#? #LHF#

W4#

G4#

# Figure A.11 - Inverter operation example of switching events#
W5# G5#

W4#

G4#

# Figure A.12 - Rectifier operation example of switching events# Dv#wkh#wzr#vzlwfkhv#lq#hdfk#ydoyh#+V4#dqg#V5#zlwk#lwv#uhvshfwlyh#ghylfhv#khuh#ghqrwhg#W4/#G4# dqg# W5/# G5,# duh# vwuhvvhg# zlwk# gliihuhqw# fxuuhqw# dqg# vzlwfklqj# hyhqwv/# wkh|# qhhg# wr# eh# fdofxodwhg#vhsdudwho|1# Wkh# wlph# ri# wkh# vzlwfklqj# hyhqwv# dqg# wkh# dpsolwxgh# ri# wkh# fxuuhqw# duh# ghshqghqw# rq# wkh# rshudwlrqdo#frqglwlrq#ri#wkh#frqyhuwhu># ?# d1f1#yrowdjh# ?# g1f1#yrowdjh# ?# Dfwlyh#srzhu# ?# Uhdfwlyh#srzhu# ?# Prgxodwlrq#vwudwhj|# Doo#vhulhv#frqqhfwhg#PPF#exloglqj#eorfnv#zloo#eh#vwuhvvhg#zlwk#wkh#vdph#vzlwfklqj#hyhqwv/#exw# dw#gliihuhqw#rffdvlrqv1#Wkxv#wkh#vdph#dyhudjh#dqg#upv#fxuuhqwv#duh#ydolg#iru#doo#PPF#exloglqj# eorfnv1# Wkh#xsshu#ydoyh#dup#dqg#orzhu#ydoyh#dupv#duh#dovr#vwuhvvhg#lq#d#vlplodu#zd|1#

95:84052Hg42FG#? #LHF#

?#66#?#

##

Lq#uhfwlilhu#prgh/#lw#fdq#eh#vhhq#wkdw#wkh#kljkhvw#fxuuhqwv#iorz#lq#hlwkhu#W4#ru#G51#Krzhyhu/#dw# wkh# wlph# zkhq# wkh# fxuuhqw# lv# kljkhvw/# wkh# ydoyh# yrowdjh# lv# qhdu# }hur/# vr# prvw# PPF# exloglqj# eorfnv# duh# e|sdvvhg# dqg# fxuuhqw# iorzv# suhgrplqdqwo|# lq# G51# G5# wkhuhiruh# kdv# wkh# kljkhvw# frqgxfwlrq#orvv#lq#uhfwlilhu#prgh/#zlwk#rqo|#prghvw#frqgxfwlrq#orvvhv#lq#W4#dqg#G4/#dqg#yhu|# orz#frqgxfwlrq#orvvhv#lq#W51# Frqyhuvho|/#lq#lqyhuwhu#prgh/#W5#h{shulhqfhv#wkh#kljkhvw#frqgxfwlrq#orvvhv#zlwk#rqo|#prghvw# frqgxfwlrq#orvvhv#lq#W4#dqg#G4/#dqg#yhu|#orz#frqgxfwlrq#orvvhv#lq#G51# Lq# Iljxuh# D1<# lw# fdq# eh# vhhq# wkdw# wkh# shdn# ydoyh# fxuuhqw# lv# dssur{lpdwho|# htxdo# wr# wkh# g1f1# fxuuhqw># krzhyhu# wklv# lv# lq# jhqhudo# qrw# h{dfwo|# wkh# fdvh/# dv# wkh# shdn# ydoyh# fxuuhqw# pd|# eh# kljkhu# ru# orzhu# wkdq# wkh# g1f1# fxuuhqw/# ghshqglqj# rq# wkh# prgxodwlrq# vwudwhj|/# dprxqw# ri# uhdfwlyh#srzhu#dqg#wudqviruphu#wdsfkdqjhu#srvlwlrq#+li#dssursuldwh,1# A.3.2 A.3.2.1 Conduction losses in semiconductors Approximate analytical solution

Lw# zloo# eh# qrwhg# iurp# Iljxuh# D1;# wkdw# dw# dq|# wlph# wkhuh# lv# dozd|v# rqh/# dqg# rqo|# rqh/# fxuuhqw# sdwk#frqgxfwlqj#lq#hdfk#PPF#exloglqj#eorfn1# Li# wkh# rq0vwdwh# yrowdjh# fkdudfwhulvwlfv# ri# wkh# irxu# vzlwfk# srvlwlrqv# lq# wkh# PPF# exloglqj# eorfn# zhuh# lghqwlfdo/# fdofxodwlrq# ri# wkh# vhplfrqgxfwru# ghylfh# frqgxfwlrq# orvvhv# zrxog# eh# vwudljkwiruzdug/# vlqfh# wkhuh# zrxog# eh# qr# qhhg# wr# nqrz# wkh# rshudwlqj# vwdwh# ri# wkh# PPF# exloglqj# eorfn# dw# dq|# wlph1# Wkh# wrwdo# vhplfrqgxfwru# frqgxfwlrq# orvv# shu# PPF# exloglqj# eorfn# zrxog#wkhq#vlpso|#eh#jlyhq#e|=#

Rcond = P e b0 .K vav + T0 .K vrms #
zkhuh=#

(

2

)

+D15,#

Pf ## b3 /# T3## K ydy #

qxpehu#ri#vhulhv0frqqhfwhg#vhplfrqgxfwru#ghylfhv#shu#vzlwfk#srvlwlrq, duh#wkh#wkuhvkrog#yrowdjh#dqg#vorsh#uhvlvwdqfh#ri#wkh#ghylfh## lv# wkh# phdq# ydoxh# ri# wkh# uhfwlilhg# fxuuhqw# lq# wkh# ydoyh/# dyhudjhg# ryhu# rqh# srzhu0iuhtxhqf|#f|foh#+Iljxuh#D146,1##

K vav

1 = × uv (wv ) × f (wv ) # 2p 0

2p

ò

+D16,#

QRWH # # K ydy # lv# qrw# wkh# v dph# dv# wkh# phdq# ydoyh# fxuuhqw/# zklfk# lv# vlpso|# K g 261# Iru# wkhv h# sxusrv hv/# wkh# uhfwlilhg# fxuuhqw#lv#qhhghg#ehf dxvh#fxuu hqw#zloo#rqo|#iorz#lq#wkrv h#v hplfrqgxfwru#ghylf h+v,#zklfk#duh#iruzdug#eldv hg1#

K yupv #

lv#wkh#upv#fxuuhqw#lq#wkh#ydoyh/#dyhudjhg#ryhu#rqh#srzhu0iuhtxhqf|#f|foh#

K vrms

1 = × uv (wv ) 2 × f (wv ) # 2p 0

2p

ò

+D17,#

#

## #

?#67#?#

95:84052Hg42FG#? #LHF#

# Figure A.13 - Valve current and mean rectified valve current Nqrzlqj#wkdw#wkh#ydoyh#fxuuhqw#fdq#eh#h{suhvvhg#dv=#

u v (wv ) =

Kd K L × 2 + × sin(wv ) # 3 2

+D18,#

Dq#dqdo|wlfdo#vroxwlrq#fdq#hdvlo|#eh#irxqg=#

K vav =
###############

1 p

éK ù × ê d × ( 2 × q - p ) + K L × 2 × sin q ú +D19,# ?3 ? ################

K vrms =
zkhuh=#

Kd K + L # 9 4

2

2

+D1:,#

é- K × 2 ù q = cos-1 ê d ú# ê ? ? 3× KL ú
Wkh#dqjoh# θ#fruuhvsrqgv#wr#wkh#srlqw#zkhuh#ydoyh#fxuuhqw#furvvhv#}hur1#

+D1;,#

Vlqfh# wkh# fxuuhqw# iorzv# pdlqo|# lq# glrghv# lq# uhfwlilhu# prgh/# dqg# pdlqo|# lq# LJEWv# lq# lqyhuwhu# prgh/# d# uhdvrqdeoh# dssur{lpdwlrq#wr# wkh# frqgxfwlrq# orvvhv# shu# PPF# exloglqj# eorfn# pd|# eh# rewdlqhg#iurp#htxdwlrqv#D15/#D19#dqg#D1:#dv#iroorzv=#

95:84052Hg42FG#? #LHF# Uhfwlilhu#Prgh=##

?#68#?#

##

Rcond_rec = b0_Diode .K vav + T0_Diode .K vrms #
#Lqyhuwhu#Prgh=##

2

+D1<,#

Rcond_inv = b0_IGBT .K vav + T0_IGBT .K vrms #
A.3.2.2 Exact analytical solution

2

+D143,#

Wkh# dssur{lpdwh# dqdo|wlfdo# vroxwlrq# suhvhqwhg# lq# wkh# suhylrxv# vxe0fodxvh# dvvxphv# wkdw# Y 3 # dqg#U 3 #duh#wkh#vdph#iru#doo#wkh#LJEWv#dqg#glrghv#lq#wkh#PPF#exloglqj#eorfn1#Jhqhudoo|#wklv#lv# qrw# wuxh=# wkh# LJEWv# qrupdoo|# kdyh# gliihuhqw# ydoxhv# ri# b3 # dqg# T 3# wr# wkh# glrghv# +jhqhudoo|/# b3 # dqg# T 3 # duh# kljkhu# iru# wkh# LJEW# wkdq# wkh# glrgh,# dqg# lw# lv# srvvleoh# iru# gliihuhqw# w|shv# ri# LJEW# dqg# glrgh# wr# eh# xvhg# lq# wkh# xsshu# dqg# orzhu# vzlwfk# srvlwlrqv# lq# wkh# PPF# exloglqj# eorfn1# Lq# dgglwlrq/# wklv# dssurdfk# qhjohfwv# wkh# flufxodwlqj# fxuuhqwv# zklfk# pd|# rffxu# ehwzhhq# skdvhv/# ghshqglqj#rq#wkh#ghvljq#ri#frqwuroohu1# Lq# pdq|# fdvhv# wkhvh# dvvxpswlrqv# frxog# lqwurgxfh# dq# xqdffhswdeo|# odujh# huuru# lqwr# wkh# fdofxodwlrq#surfhvv1# D#pruh#h{dfw#surfhvv#lqyroyhv#vhsdudwho|#fdofxodwlqj#wkh#ydoxhv#ri# K dy #dqg# K upv #iru#hdfk#ri#wkh# irxu# vzlwfk# srvlwlrqv# lq# wkh# PPF# exloglqj# eorfn# dqg# wkxv# fdofxodwlqj# wkh# frqgxfwlrq# orvv# vhsdudwho|#iru#hdfk#ghylfh1## Dv# qrwhg# lq# wkh# suhylrxv# vxe0fodxvh/# wkh# orfdwlrq# ri# wkh# rqh# vzlwfk# srvlwlrq# wkdw# lv# fduu|lqj# fxuuhqw# dw# d#jlyhq#wlph# ghshqgv#rq#wkh#gluhfwlrq#ri#wkh#fxuuhqw# dqg#wkh#vzlwfklqj#vwdwh# ri#wkh# PPF#exloglqj#eorfn#+e|sdvvhg#ru#dfwlyh#vwdwh,1#Vlqfh#wkh#vzlwfklqj#vwdwh#pd|#fkdqjh#vhyhudo# wlphv# shu# ixqgdphqwdo0iuhtxhqf|# f|foh/# lw# lv# qrw# sudfwlfdo# wr# fdofxodwh# wkh# lqvwdqwdqhrxv# frqgxfwlrq# orvv# lq# hdfk# vzlwfk# srvlwlrq/# exw# qhlwkhu# lv# lw# qhfhvvdu|1# Zkdw# lv# qhhghg# lv# wr# fdofxodwh# wkh# frqgxfwlrq# orvv# lq# hdfk# vzlwfk# srvlwlrq# dyhudjhg# ryhu# d# shulrg# ri# vrph# ihz# f|fohv#ru#vhfrqgv1#Krzhyhu/#wklv#lv#dovr#qrw#vwudljkwiruzdug#wr#fdofxodwh/#vlqfh#lw#ghshqgv#lq#d# frpsoh{#zd|#rq#wkh#frqwuro#vwudwhj|#iru#wkh#frqyhuwhu1## Iru# vrph#rshudwlqj#srlqwv/# iru# h{dpsoh# zkhq#wkh#ydoyh#fxuuhqw# dqg#ydoyh#yrowdjh# duh# h{dfwo|# 4;3?# rxw# ri# skdvh/# dq# h{dfw# +wkrxjk# frpsoh{,# dqdo|wlfdo# vroxwlrq# lv# srvvleoh1# Vxfk# vroxwlrqv# uho|#rq#d#vwdwlvwlfdo# dssurdfk#wr#wkh#rshudwlqj#vwdwh#+dfwlyh#ru#e|sdvvhg,#ri#wkh#PPF#exloglqj# eorfn1#Dowkrxjk#lw#lv#qrw#srvvleoh#wr#nqrz#wkh#h{dfw#rshudwlqj#vwdwh#ri# dq#PPF#exloglqj#eorfn# dw#dq|#jlyhq#wlph/#lw#lv#srvvleoh#wr#fdofxodwh#wkh#suredelolw|#wkdw#wkh#PPF#exloglqj#eorfn#zloo#eh# lq#d#jlyhq#vwdwh#dw#wkdw#wlph/#vlqfh#wkh#suredelolw|#wkdw#wkh#PPF#exloglqj#eorfn#lv#lq#wkh#dfwlyh# vwdwh# lv# gluhfwo|# sursruwlrqdo# wr# wkh# ydoyh# yrowdjh1# Lw# lv# wkhuhiruh# srvvleoh# wr# frqvwuxfw# d# pdwkhpdwlfdo# htxdwlrq# olqnlqj# wkh# ydoyh# fxuuhqw# wr# wkh# ydoyh# yrowdjh/# erwk# ri# zklfk# fdq# eh# ghvfulehg#pdwkhpdwlfdoo|1## Wkh# vwdwlvwlfdo# suredelolw|# wkdw# d# jlyhq# PPF# exloglqj# eorfn# zloo# eh# lq# wkh# dfwlyh# vwdwh# fdq# eh# h{suhvvhg#e|#wkh#whup# rf +ω v ,=#

rc (wv ) =
zkhuh=##

w v (wv ) # P tc × wc_av (wv )

+D144,#

w y #+ωv ,# w fbdy #+ω v,#

lv#wkh#ydoyh#yrowdjh#dv#d#ixqfwlrq#ri#wlph# lv#wkh#phdq#PPF#exloglqj#eorfn#g1f1#fdsdflwru#yrowdjh#dv#d#ixqfwlrq#ri#wlph#

Wkh# suredelolw|# wkdw# d# jlyhq# PPF# exloglqj# eorfn# lv# lq# wkh# e|sdvvhg# vwdwh# lv# wkhq# vlpso|# +40# s f +ω v ,,1# #

## #

?#69#?#

95:84052Hg42FG#? #LHF#

W4#dqg#G4#rqo|#frqgxfw#zkhq#wkh#olqn#lv#lq#wkh#dfwlyh#vwdwh1#Vr#wkh#dyhudjh#dqg#upv#fxuuhqwv# duh# irxqg# e|# lqwhjudwlqj# wkh# surgxfw# ri# ydoyh# fxuuhqw# dqg# s f +ω v,# ryhu# wkh# frqgxfwlrq# shulrg# dssursuldwh#wr#hdfk#vhplfrqgxfwru1#
w v2

1 K av = × uv (wv ) × rc (wv ) × f (wv ) # 2 ×p w v

ò

+D145,#

1

K rms =

1 2 × uv (wv ) × rc (wv ) × f (wv ) # 2×p w v

w v2

ò

+D146,#

1

# zkhuh=# ω v4#dqg#ω v5 # # duh#wkh#srlqwv#dw#zklfk#wkh#ydoyh#fxuuhqw#fkdqjhv#vljq1#

W4# rqo|# frqgxfwv# zkhq# fxuuhqw# lv# qhjdwlyh1# Khqfh# iru# hydoxdwlrq# ri# wkh# fxuuhqw# lq# W4/# ω v 4 # lv# wdnhq# wr# eh# zkhuh# fxuuhqw# fkdqjhv# iurp# srvlwlyh# wr# qhjdwlyh# dqg# ω v 5# lv# wdnhq# wr# eh# zkhuh# fxuuhqw#fkdqjhv#iurp#qhjdwlyh#wr#srvlwlyh1# G4# rqo|# frqgxfwv# zkhq# fxuuhqw# lv# srvlwlyh1# Khqfh# iru# hydoxdwlrq# ri# wkh# fxuuhqw# lq# G4/# ω v 4 # lv# wdnhq# wr# eh# zkhuh# fxuuhqw# fkdqjhv# iurp# qhjdwlyh# wr# srvlwlyh# dqg# ω v5 # lv# wdnhq# wr# eh# zkhuh# fxuuhqw#fkdqjhv#iurp#srvlwlyh#wr#qhjdwlyh1# W5# dqg# G5# rqo|# frqgxfw# zkhq# wkh# olqn# lv# lq# wkh# e|sdvvhg# vwdwh1# Vr# wkh# dyhudjh# dqg# upv# fxuuhqwv# duh# irxqg# e|# lqwhjudwlqj# wkh# surgxfw# ri# ydoyh# fxuuhqw# dqg# +40 rf + ωv,,# ryhu# wkh# frqgxfwlrq#shulrg#dssursuldwh#wr#hdfk#vhplfrqgxfwru=#
2 1 K av = × uv (wv ) × (1 - rc (wv )) × f (wv ) # 2 ×p w v

wv

ò

+D147,#

1

K rms

2 1 2 = × uv (wv ) × (1 - rc (wv )) × f (wv ) # 2 ×p w v

wv

ò

+D148,#

1

W5# rqo|# frqgxfwv# zkhq# fxuuhqw# lv# srvlwlyh1# Khqfh# iru# hydoxdwlrq# ri# wkh# fxuuhqw# lq# W5/# ω v 4 # lv# wdnhq# wr# eh# zkhuh# fxuuhqw# fkdqjhv# iurp# qhjdwlyh# wr# srvlwlyh# dqg# ω v5 # lv# wdnhq# wr# eh# zkhuh# fxuuhqw#fkdqjhv#iurp#srvlwlyh#wr#qhjdwlyh1# G5# rqo|# frqgxfwv# zkhq# fxuuhqw#lv# qhjdwlyh1# Khqfh# iru# hydoxdwlrq# ri# wkh# fxuuhqw# lq# G5/# ω v 4# lv# wdnhq# wr# eh# zkhuh# fxuuhqw# fkdqjhv# iurp# srvlwlyh# wr# qhjdwlyh# dqg# ωv 5# lv# wdnhq# wr# eh# zkhuh# fxuuhqw#fkdqjhv#iurp#qhjdwlyh#wr#srvlwlyh1# Hyhq# zkhq# lw# lv# srvvleoh# wr# uhsuhvhqw# u y # dqg# r f # pdwkhpdwlfdoo|/# dqg# hyhq# iru# wkh# vlpsolilhg# fdvh# zkhuh# wkh# ydoyh# fxuuhqw# dqg#ydoyh#yrowdjh# duh# h{dfwo|# 4;3?# rxw# ri# skdvh/# wkh# dqdo|wlfdo# vroxwlrq#wr#wkhvh#htxdwlrqv#lv#frpsoh{1#Dw#wkh#wlph#ri# sxeolfdwlrq/#qr#h{dfw#dqdo|wlfdo#vroxwlrq# kdv# ehhq# irxqg# iru# wkh# jhqhudo# fdvh# zkhuh# ydoyh# fxuuhqw# dqg# ydoyh# yrowdjh# duh# qrw# h{dfwo|# 4;3?#rxw#ri#skdvh1#

95:84052Hg42FG#? #LHF# A.3.3

?#6:#?#

##

MMC building block d.c. capacitor losses

Wr# fdofxodwh# wkh# PPF# exloglqj# eorfn# g1f1# fdsdflwru# orvvhv/# lw# lv# qhfhvvdu|# rqo|# wr# nqrz# wkh# upv#fxuuhqw#lq#wkh#fdsdflwru/# K fupv 1#Wkh#phdq#fxuuhqw#lq#wkh#fdsdflwru#pxvw#eh#}hur#lq# vwhdg|0 vwdwh##

K D1_av + K T1_av = 0 1#

+D149,#

Rqfh# wkh# upv# fxuuhqw# kdv# ehhq# ghwhuplqhg# iru# hdfk# ri# wkh# irxu# vhplfrqgxfwru# ghylfhv/# dffruglqj#wr#wkh#suhfhglqj#vxe0fodxvh/#wkh#upv#fdsdflwru#fxuuhqw#fdq#eh#irxqg#hdvlo|#iurp#wkh# yhfwruldo#vxp#ri#wkh#upv#fxuuhqwv#lq#W4#dqg#G4=#

K crms = K D1_rms 2 + K T1_rms 2 #
# A.3.4 Other conduction losses

+D14:,#

Rwkhu# frqgxfwlrq# orvvhv# lq# wkh# ydoyh# duh# grplqdwhg# e|# wkh# uhvlvwlyh# + K> U,# orvvhv# lq# exveduv# iurp# hdfk# PPF# exloglqj# eorfn# wr# lwv# qhljkerxuv1# Khuh/# rqo|# wkh# upv# ydoyh# fxuuhqw# K yupv /# dv# jlyhq#lq#htxdwlrq#D1:/#lv#uhtxluhg1##

A.4
A.4.1

Switching Losses
Description of state changes General

A.4.1.1

Hyhu|#wlph#dq#PPF#exloglqj#eorfn#fkdqjhv#vwdwh#iurp#e|sdvvhg#wr#dfwlyh#vwdwh#ru#ylfh#yhuvd/# ru# wkh# gluhfwlrq# ri# fxuuhqw# uhyhuvhv/# rqh# vzlwfk# srvlwlrq# lq# wkh# PPF# exloglqj# eorfn# wxuqv# rii# dqg# dqrwkhu# wxuqv# rq1# Wkh# wxuq0rq# ri# dq# LJEW# lv# dozd|v# dffrpsdqlhg# e|# wkh# wxuq0rii# ri# d# glrgh/#dqg#ylfh0yhuvd1# Vzlwfklqj#hyhqwv#pd|#eh#fdwhjrulvhg#dv#?vriw?#ru#?kdug?1#Wudqvlwlrqv#zklfk#rffxu#dv#d#uhvxow#ri# wkh# uhyhuvdo#ri#ydoyh#fxuuhqw#wkdw# rffxuv#wzlfh# shu#f|foh# duh#uhihuuhg#wr# dv#?vriw?/# zkloh# wkrvh# wkdw# rffxu# dv# d# uhvxow# ri# vwdwh# fkdqjhv# iurp# e|sdvvhg# wr# dfwlyh# vwdwh# ru# ylfh# yhuvd/# duh# uhihuuhg# wr# dv# ?kdug?1# Rqo|# wkh# kdug# vzlwfklqj# hyhqwv# duh# ri# vljqlilfdqfh# lq# wkh# fdofxodwlrq# ri# orvvhv/# ehfdxvh# wkh# udwh# ri# fkdqjh# ri# fxuuhqw# +gu 2g v,# lv# vhyhudo# rughuv# ri# pdjqlwxgh# kljkhu# wkdq#iru#vriw0vzlwfklqj#hyhqwv1## A.4.1.2 Hard switching events

Wdeoh# D14# vxppdulvhv# wkh# hiihfwv# ri# wkh# irxu# srvvleoh# kdug# vzlwfklqj# hyhqwv# lq# wkh# PPF# exloglqj#eorfn1# Table A.1 – Hard switching events
Current direction Qhjdwlyh# Qhjdwlyh# Srvlwlyh# Srvlwlyh# MMC building block state change E|sdvvhg#wr#Dfwlyh# Dfwlyh#wr#E|sdvvhg# E|sdvvhg#wr#Dfwlyh# Dfwlyh#wr#E|sdvvhg# Effects W4#wxuqv#rq>#G5#wxuqv#rii# W4#wxuqv#rii>#G5#wxuqv#rq# W5#wxuqv#rii>#G4#wxuqv#rq# W5#wxuqv#rq>#G4#wxuqv#rii# Total switching energy

Q r qb W4 #.# Quhf bG5 # Q ri ib W4 # Q ri ib W5 # Q r qb W5 #.# Quhf bG4 #

#

## #

?#6;#?#

95:84052Hg42FG#? #LHF#

Vlqfh#glrghv#duh#qrw#frqwuroodeoh/# kdug#vzlwfklqj#hyhqwv#duh#dozd|v#lqlwldwhg#e|#wkh#vzlwfklqj# ri#dq#LJEW1#Wkh#wudqvlwlrq#iurp#LJEW#wr#glrgh#lv#lqlwldwhg#e|#wxuqlqj#rii#wkh#LJEW#zkloh#fxuuhqw# lv#iorzlqj# lq# lw1# Wkh# fxuuhqw/# zklfk# lv#iorzlqj# wkurxjk# d# vxevwdqwldo# h{whuqdo# lqgxfwdqfh/# wkhq# kdv# qrzkhuh# hovh# wr# iorz# h{fhsw# lqwr# wkh# glrgh# lq# wkh# rwkhu# vzlwfk# srvlwlrq# ri# wkh# PPF# exloglqj# eorfn1# Fxuuhqw# wkhq# frppxwdwhv#iurp# wkh# LJEW# wr# wkh# glrgh# dw# d# udwh# ghwhuplqhg# e|# wkh#lqgxfwdqfh#ri#wkh#orrs#iruphg#e|#wkh#LJEW/#glrgh#dqg#fdsdflwru1#Wkh#LJEW#h{shulhqfhv#d# yrowdjh#ryhuvkrrw#dv#d#uhvxow#ri#wklv#hyhqw1# Wkh# wudqvlwlrq# iurp# glrgh# wr# LJEW# lv# lqlwldwhg# e|# wxuqlqj# rq# wkh# LJEW# zkloh# wkh# glrgh# lq# wkh# rwkhu#vzlwfk#srvlwlrq#ri#wkh#PPF#exloglqj#eorfn#lv#frqgxfwlqj1#Wklv#whpsrudulo|#fuhdwhv#d#vkruw# flufxlw# zlwk# wkh# g1f1# fdsdflwru# frqqhfwhg# lq# vhulhv# zlwk# wkh# glrgh# dqg# wkh# LJEW# wkdw# kdv# mxvw# wxuqhg#rq1#Wkh#fxuuhqw# lq#wkh#glrgh#idoov#yhu|# udslgo|# dw# d#udwh#jlyhq#e|# wkh#fdsdflwru#yrowdjh# glylghg# e|# wkh# lqgxfwdqfh# ri# wkh# orrs# iruphg# e|# wkh# LJEW/# glrgh# dqg# fdsdflwru1# # Diwhu# wkh# fxuuhqw# lq# wkh# glrgh# sdvvhv# wkurxjk# }hur/# wkh# glrgh# h{shulhqfhv# d# vkruw# shulrg# ri# uhyhuvh# fxuuhqw#dqg#wkhq#ilqdoo|#wxuqv#rii/#lqfxuulqj#d#?uhfryhu|#hqhuj|?1## Hdfk# kdug# vzlwfklqj# hyhqw# uhvxowv# lq# d# vzlwfklqj# hqhuj|# glvvlsdwlrq# lq# wkh# LJEW# + Qrq# ru# Qrii ,# dqg# wkrvh# hyhqwv# wkdw# lqyroyh# wkh# wxuq0rii# ri# d# glrgh# dovr# uhvxow# lq# d# uhfryhu|# hqhuj|# Q uhf # +glrghv# kdyh# qhjoljleoh# wxuq0rq# orvv,1# Q rq /# Qrii # dqg# Q uhf # ghshqg# rq# wkh# lqvwdqwdqhrxv# ghylfh# fxuuhqw# dw#wkh#wlph# ri# vzlwfklqj/# wkh#g1f1# fdsdflwru#yrowdjh#dqg# wkh#mxqfwlrq#whpshudwxuh1#Wkh# ghshqghqfh# rq# fxuuhqw# lv# looxvwudwhg# rq# Iljxuh# D1471# Vzlwfklqj# dqg# uhfryhu|# hqhujlhv# dovr# lqfuhdvh#zlwk#yrowdjh#+doprvw#olqhduo|,#dqg#zlwk#whpshudwxuh1# LJEW#vzlwfklqj#hqhuj|# Glrgh#uhfryhu|#hqhuj|#

# Figure A.14 - IGBT and diode switching energy as a function of collector current

#

Lq#rughu#wr#eh#deoh#wr#fdofxodwh#wkh#vzlwfklqj#orvvhv#iru#dq|#rshudwlqj#frqglwlrq/#wkh#LJEW#dqg# glrgh# xvhg# vkrxog# eh# fkdudfwhulvhg# wkrurxjko|# wr# ghilqh# H rq/ #H rii# dqg# H uhf # dv# ixqfwlrqv# ri# yrowdjh/# fxuuhqw# dqg# whpshudwxuh1# Wkh# fkdudfwhulvdwlrq# uhvxowv# pd|# eh# suhvhqwhg# judsklfdoo|# ru# lq# d# orrn0xs# wdeoh# exw# d# pdwkhpdwlfdo# prgho# lv# suhihuuhg/# vlqfh# lw# shuplwv#wkh# vxevhtxhqw# fdofxodwlrq#surfhvv#wr#eh#pruh#hdvlo|#dxwrpdwhg1# A.4.1.3 Soft switching events

Wdeoh# D15# vxppdulvhv# wkh# hiihfwv# ri# wkh# irxu# srvvleoh# vriw# vzlwfklqj# hyhqwv# lq# wkh# PPF# exloglqj#eorfn1# Table A.2 – Soft switching events
Change of current direction Qhjdwlyh#wr#srvlwlyh# Qhjdwlyh#wr#srvlwlyh# Srvlwlyh#wr#qhjdwlyh# Srvlwlyh#wr#qhjdwlyh# MMC building block state E|sdvvhg# Dfwlyh# E|sdvvhg# Dfwlyh# Effects G5#wxuqv#rii>#W5#wxuqv#rq# W4#wxuqv#rii>#G4#wxuqv#rq# W5#wxuqv#rii>#G5#wxuqv#rq# G4#wxuqv#rii>#W4#wxuqv#rq##

95:84052Hg42FG#? #LHF#

?#6<#?#

##

Wkh#vriw#vzlwfklqj#hyhqwv#duh#phqwlrqhg#rqo|#iru#wkh#vdnh#ri#frpsohwhqhvv/#vlqfh#wkh|#gr#qrw# gluhfwo|#uhvxow#lq#vzlwfklqj#hqhuj|#glvvlsdwlrq#lq#wkh#vhplfrqgxfwruv1#Krzhyhu/#wkh#fkdqjhv#ri# fxuuhqw#gluhfwlrq#pd|#lqgluhfwo|#suryrnh#vrph#kdug#vzlwfklqj#hyhqwv/#dv#wkh#fdsdflwru#yrowdjh# edodqflqj#dojrulwkp#pd|#fdxvh#vrph#PPF#exloglqj#eorfnv#wr#fkdqjh#iurp#dfwlyh#wr#e|sdvvhg# dqg#vrph#rwkhuv#wr#fkdqjh#iurp#e|sdvvhg#wr#dfwlyh1# A.4.2 Analysis of state changes during cycle

Lq# sulqflsoh/# fdofxodwlrq# ri# wkh# wrwdo# vzlwfklqj# orvvhv# lq# wkh# PPF# exloglqj# eorfn# uhtxluhv# rqo|# wkdw# wkh#lqvwdqwdqhrxv#yrowdjh#dqg# fxuuhqw#lv#nqrzq#iru# hdfk# ri# wkh#ydulrxv#vzlwfklqj#hyhqwv# gxulqj#d#f|foh1#Wkh#vzlwfklqj#hqhuj|#shu#hyhqw#fdq#wkhq#eh#fdofxodwhg#iurp#nqrzohgjh#ri#krz# Q rq/#Q rii #dqg#Q uhf #ydu|#zlwk#yrowdjh#dqg#fxuuhqw#iru#wkh#dssolfdeoh#mxqfwlrq#whpshudwxuh/#dqg#wkh# vzlwfklqj#orvvhv#lq#wkh#frpsohwh#f|foh#duh#rewdlqhg#e|#vxpplqj#hdfk#lqglylgxdo#hyhqw1# Krzhyhu/# xqolnh# d# 50ohyho# frqyhuwhu/# zkhuh# wkh# g1f1# fdsdflwru# yrowdjh# lv# il{hg# dqg# wkh# vzlwfklqj#sdwwhuq#lv#ghwhuplqlvwlf#dqg#hdvlo|#dqdo|vhg/#fdofxodwlqj#wkh#vzlwfklqj#frqglwlrqv#iru# hyhu|# vzlwfklqj# hyhqw# lq# d# Prgxodu# Pxowl0Ohyho# Frqyhuwhu# lv# yhu|# frpsoh{1# Wkhuh# duh# wzr# sulqflsdo#uhdvrqv#ohdglqj#wr#wklv#frpsoh{lw|=# ?# Wkh# wlplqjv# ri# wkh# vzlwfklqj# hyhqwv# zlwk# uhvshfw# wr# wkh# ydoyh# fxuuhqw# zdyhirup# duh# vrphzkdw# xqsuhglfwdeoh/# vlqfh# wkh|# duh# jryhuqhg# e|# wkh# dojrulwkpv# xvhg# iru# prqlwrulqj# dqg#edodqflqj#wkh#PPF#exloglqj#eorfn#g1f1#fdsdflwru#yrowdjhv1# ?# Ehfdxvh# wkh#ydoyh#fxuuhqw#iorzv#wkurxjk#wkh#PPF#exloglqj#eorfn# g1f1#fdsdflwru#iru#sduw#ri# hdfk# f|foh/# wkh# fdsdflwru# h{shulhqfhv# d# y hu|# odujh# ulssoh# yrowdjh# +w|slfdoo|# ?53(# ri# qrplqdo,1# Pruhryhu/# hyhu|# PPF# exloglqj# eorfn# g1f1# fdsdflwru# lq# wkh# ydoyh# zloo# kdyh# d# gliihuhqw#fdsdflwru#yrowdjh#dw#dq|#lqvwdqw1# Iru# wkhvh# uhdvrqv# wkh# rqo|# sudfwlfdo# zd|# ri# ghwhuplqlqj# wkh# dyhudjh# vzlwfklqj# orvvhv# lq# wkh# LJEWv# dqg# glrghv#lv# e|#phdqv# ri# d#yhu|# ghwdlohg#qxphulfdo# vlpxodwlrq1#Wkh# vlpxodwlrq#prgho# vkrxog# uhsuhvhqw# wkh# ydoyh# lq# dv# pxfk# ghwdlo# dv# srvvleoh/# lqfoxglqj# d# pdwkhpdwlfdo# prgho# uhsuhvhqwlqj#wkh#vzlwfklqj#hqhujlhv#ri#wkh#vhplfrqgxfwru#ghylfhv/#dorqj#zlwk#d#uhsuhvhqwdwlrq# ri# dw# ohdvw# wkrvh# sduwv# ri# wkh# frqwuro# v|vwhp# wkdw# duh# uhvsrqvleoh# iru# surgxflqj# wkh# ydoyh# yrowdjh#rughu#dqg#iru#edodqflqj#wkh#PPF#exloglqj#eorfn#g1f1#fdsdflwruv1# A.4.3 Worked example of switching losses

Wr# looxvwudwh# wkh# w|slfdo# vzlwfklqj# ehkdylrxu# ri# dq# PPF# ydoyh/# wklv# vxe0fodxvh# ghvfulehv# d# vlpsoh# vlpxodwlrq# shuiruphg# rq# d# k|srwkhwlfdo# PPF# ydoyh# frqvlvwlqj# ri# 8# vxeprgxohv# lq# vhulhv/#hdfk#zlwk#d#qrplqdo#vxeprgxoh#g1f1#fdsdflwru#yrowdjh#ri#5#nY1#Wkh#ydoyh#lv#dvvljqhg#d# vlqxvrlgdo#yrowdjh#rughu#htxdo#wr#8#nY#0#8#nY?frv#+ω v,#dqg#fduulhv#d#vlqxvrlgdo#fxuuhqw#htxdo#wr# +666#D#.#99:D?frv#+ω v,,1# Vxeprgxohv#duh#vzlwfkhg#rqo|#dw#4#pv#lqwhuydov/#dffruglqj#wr#d#vlpsoh#vhw#ri#uxohv=# ?# Li# wkh# fxuuhqw# wkurxjk# wkh# ydoyh# lv# positive # +lh/# lq# wkh# gluhfwlrq# zklfk# charges xs# wkh# vxeprgxohv# wkdw# duh# lq# dfwlyh# prgh,/# wkhq# wkh# vxeprgxoh# zlwk# wkh# lowest yrowdjh# lv# vzlwfkhg#lqwr#flufxlw#iluvw/#wkhq#wkh#rqh#zlwk#wkh#vhfrqg#orzhvw#yrowdjh/#dqg#vr#rq#xqwlo#wkh# wdujhw#yrowdjh#lv#phw#dv#forvho|#dv#srvvleoh1# ?# Li# wkh# fxuuhqw# wkurxjk# wkh# ydoyh# lv# negative # +lh/# lq# wkh# gluhfwlrq# zklfk# discharges wkh# vxeprgxohv# wkdw# duh# lq# dfwlyh# prgh,/# wkhq# wkh# vxeprgxoh# zlwk# wkh# highest yrowdjh# lv# vzlwfkhg#lqwr#flufxlw#iluvw/#wkhq#wkh#rqh#zlwk#wkh#vhfrqg#kljkhvw#yrowdjh/#dqg#vr#rq#xqwlo#wkh# wdujhw#yrowdjh#lv#phw#dv#forvho|#dv#srvvleoh1# Wkh# uhvxowv# ri# d# vlpxodwlrq# lq# zklfk# wkh# ilyh# vxeprgxohv# lqlwldoo|# kdyh# yrowdjhv# ri# 4;33#Y/# 4<33#Y/#5333#Y/#5433#Y#dqg#5533#Y#duh#vkrzq#judsklfdoo|#rq#Iljxuh#D1481#

#

## #
45333 43333
Valve Voltage (V)

?#73#?#

95:84052Hg42FG#? #LHF#

4533 <33 933 633 3 0633 0933 3135
Valve Current (A)

;333 9333 7333 5333 3 3 31338 3134 Time (s) 31348

Yy+w, ly+w,

Submodule 1

Submodule 2

Submodule 3

Submodule 4

Submodule 5
3 31338 3134 Time (s) 31348 3135

# Figure A.15 - Valve voltage, current and switching behaviour for a hypothetical MMC valve consisting of 5 submodules Lw# zloo# eh# revhuyhg# wkdw# wzr# ri# wkh# vxeprgxohv# xqghujr# wkuhh# frpsohwh# rq2rii# f|fohv# gxulqj# wkh# ixqgdphqwdo# iuhtxhqf|# f|foh/# zkloh# wkh# rwkhu# wkuhh# xqghujr# rqo|# wzr1# Wdeoh# D16# vxppdulvhv#wkh#57#vzlwfklqj#hyhqwv#gxulqj#wkh#f|foh1# Li# wkh# vzlwfklqj# hqhujlhv# Q rq/# Qrii # dqg# Q uhf # fdq# eh# uhsuhvhqwhg# dv# ixqfwlrqv# ri# yrowdjh# dqg# fxuuhqw/# hlwkhu# pdwkhpdwlfdoo|# ru# yld# orrn0xs# wdeohv/# wkh# vzlwfklqj# hqhuj|# fdq# eh# fdofxodwhg# iru#hdfk#hyhqw#dqg#wkhq#vxpphg#iru#wkh#frpsohwh#ydoyh1# Table A.3 – Summary of switching events from Figure A.15
Time (ms) 5# 7# 7# 7# 8# Current (A) ;:6# 86<# 86<# 86<# 666# Submodule no. 4# 4# 5# 6# 7# Submodule voltage 4;33# 53;:# 4<33# 5333# 5433# State change E|sdvvhg#0#Dfwlyh# Dfwlyh#0#E|sdvvhg# E|sdvvhg#0#Dfwlyh# E|sdvvhg#0#Dfwlyh# E|sdvvhg#0#Dfwlyh# Switching energy

Q ri ib W5# Q r qb W5 #.# Quhf bG4# Q ri ib W5 # Q ri ib W5 # Q ri ib W5 #

95:84052Hg42FG#? #LHF#
Time (ms) :# :# :# <# 46# 47# 47# 47# 48# 48# 48# 49# 49# 49# 49# 4:# 4:# 4:# 4;# Current (A) 08<## 08<## 08<## 0635# 08<## 45:# 45:## 45:## 666## 666## 666## 86<## 86<## 86<## 86<## :58## :58## :58## ;:6## Submodule no. 4# 5# 8# 5# 7# 6# 7# 8# 4# 5# 6# 4# 5# 6# 7# 4# 5# 8# 8#

?#74#?#
Submodule voltage 53;:# 536<# 5533# 536<# 4;98# 4;8;# 4;98# 4<4<# 4;85# 4;;6# 4;8;# 4;85# 4;;6# 4<79# 4<<;# 4<:<# 5343# 4<4<# 53:<# State change E|sdvvhg#0#Dfwlyh# Dfwlyh#0#E|sdvvhg# E|sdvvhg#0#Dfwlyh# E|sdvvhg#0#Dfwlyh# Dfwlyh#0#E|sdvvhg# Dfwlyh#0#E|sdvvhg# E|sdvvhg#?#Dfwlyh# Dfwlyh#0#E|sdvvhg# Dfwlyh#0#E|sdvvhg# Dfwlyh#0#E|sdvvhg# E|sdvvhg#?#Dfwlyh# E|sdvvhg#?#Dfwlyh# E|sdvvhg#?#Dfwlyh# Dfwlyh#0#E|sdvvhg# Dfwlyh#0#E|sdvvhg# Dfwlyh#0#E|sdvvhg# Dfwlyh#0#E|sdvvhg# E|sdvvhg#?#Dfwlyh# Dfwlyh#0#E|sdvvhg# Switching energy

##

Q r qb W4 #.# Quhf bG5 # Q ri ib W4 # Q r qb W4 #.# Quhf bG5 # Q r qb W4 #.# Quhf bG5 # Q ri ib W4 # Q r qb W5 #.# Quhf bG4 # Q ri ib W5 # Q r qb W5 #.# Quhf bG4 # Q r qb W5 #.# Quhf bG4 # Q r qb W5 #.# Quhf bG4 # Q ri ib W5 # Q ri ib W5 # Q ri ib W5 # Q r qb W5 #.# Quhf bG4 # Q r qb W5 #.# Quhf bG4 # Q r qb W5 #.# Quhf bG4 # Q r qb W5 #.# Quhf bG4 # Q ri ib W5 # Q r qb W5 #.# Quhf bG4 #

Dowkrxjk# wklv# lv# rqo|# d# sxuho|# k|srwkhwlfdo# h{dpsoh/# lw# looxvwudwhv# wkh# frpsoh{# dqg# xqsuhglfwdeoh# qdwxuh# ri# wkh# vzlwfklqj# ehkdylrxu# ri# wkh# PPF# ydoyh/# dqg# wkh# idfw# wkdw# wklv# ehkdylrxu# lv# yhu|# pxfk# lqioxhqfhg# e|# wkh# dojrulwkpv# xvhg# iru# edodqflqj# wkh# fdsdflwru# yrowdjhv1# Wkh#h{dpsoh#dovr#vkrzv#krz#hiihfwlyh#wkh#vlpsoh#fdsdflwru#edodqflqj#vwudwhj|#rxwolqhg#deryh# fdq#eh/#hyhq#zlwk#vzlwfklqj#wlphv#olplwhg#wr#yhu|#frduvh#vwhsv#ri#4#pv1#Dq#lqlwldo#yrowdjh#udqjh# ri# 733#Y# +4;3305533#Y,# kdv#frqyhujhg#wr#d# 466#Y# udqjh# +4<79053:<#Y,# diwhu# rqo|# rqh#f|foh1# Lq#sudfwlfh#d#pxfk#idvwhu#xsgdwh#udwh#zrxog#eh#xvhg/#jlylqj#hyhq#idvwhu#frqyhujhqfh1# Dowkrxjk#wkh# h{dpsoh# vkrzv# rqo|# d# vlqjoh# ixqgdphqwdo# f|foh/# dq# dqdo|vlv# ri# wklv#w|sh# zrxog# qhhg#wr#h{whqg#ryhu#vhyhudo#f|fohv#lq#rughu#wr#rewdlq#uhsuhvhqwdwlyh#dyhudjh#uhvxowv1#

A.5
A.5.1

Other losses
Snubber losses

Dowkrxjk#pdq|#PPF0w|sh#ydoyhv#duh#deoh#wr#rshudwh# zlwkrxw# vqxeehu#flufxlwv/#lq#vrph#fdvhv# vqxeehu# flufxlwv# pljkw# qhyhuwkhohvv# eh# ilwwhg# wr# doohyldwh# wkh# vzlwfklqj# vwuhvvhv# rq# wkh# vhplfrqgxfwru# ghylfhv# ru# +lq# wkh# fdvh# ri# wkh# Fdvfdghg# Wzr0Ohyho# frqyhuwhu,# wr# dvvlvw# zlwk# yrowdjh#vkdulqj#dprqjvw#wkh#vhulhv0frqqhfwhg#vhplfrqgxfwruv1# Vqxeehu#flufxlwv#idoo#lqwr#wzr#pdlq#w|shv=## ?# ?wxuq0rq?# vqxeehuv/# zklfk# lqyroyh# dq# lqgxfwdqfh# lq# vhulhv# zlwk# wkh# vhplfrqgxfwru# ghylfh# dqg# duh# lqwhqghg# wr# olplw# wkh# udwh# ri# fkdqjh# ri# fxuuhqw# dqg# wkhuhiruh# uhgxfh# wkh# wxuq0rq# vwuhvv#lq#wkh#LJEW#dqg#wkh#uhfryhu|#vwuhvv#rq#wkh#rssrvlqj#glrgh# ?# ?wxuq0rii?#vqxeehuv/# zklfk#lqyroyh#d#fdsdflwdqfh#lq# sdudooho# zlwk#wkh# vhplfrqgxfwru# ghylfh# dqg# duh#lqwhqghg#wr#olplw#wkh#udwh# ri#ulvh# ri#yrowdjh# diwhu# wxuq0rii#dqg#wkhuhiruh#uhgxfh#wkh# wxuq0rii#vwuhvv#rq#wkh#LJEW1## #

## #

?#75#?#

95:84052Hg42FG#? #LHF#

Hdfk# kdug# vzlwfklqj# hyhqw# lq# dq# PPF# exloglqj# eorfn# zloo# uhvxow# lq# hqhuj|# ehlqj# glvvlsdwhg# lq# wkh# vqxeehu# flufxlwv/# wkh# dprxqw# ri# hqhuj|# ghshqglqj# rq# wkh# lqvwdqwdqhrxv# yrowdjh# dqg# fxuuhqw#lq#wkh#diihfwhg#vhplfrqgxfwru#ghylfh1## Zkhuh#d#wxuq0rq#vqxeehu#lv#ilwwhg/#hdfk#PPF#exloglqj#eorfn#vwdwh#fkdqjh#lqyroylqj#wxuq0rq#ri# dq# LJEW# zloo# uhvxow# lq# dq# hqhuj|# glvvlsdwlrq# Q vqbrq # ehlqj# glvvlsdwhg# lq# wkh# vqxeehu# frpsrqhqwv1# Zkhuh#d#wxuq0rii#vqxeehu#lv#ilwwhg/#hdfk#PPF#exloglqj#eorfn#vwdwh#fkdqjh#lqyroylqj#wxuq0rii#ri# dq# LJEW# zloo# uhvxow# lq# dq# hqhuj|# glvvlsdwlrq# Q vqbrii # ehlqj# glvvlsdwhg# lq# wkh# vqxeehu# frpsrqhqwv1# Wkh# vhqvlwlylw|# ri# Qvqbrq # dqg# Qvqbrii # wr# wkh# yrowdjh# dqg# fxuuhqw# dw# wkh# wlph# ri# vzlwfklqj# zloo# ghshqg# rq# wkh# ghvljq# ri# wkh# vqxeehu# dqg# vkrxog# eh# ghprqvwudwhg# e|# vxlwdeoh# whvwv# ru# vlpxodwlrqv1#Wkhq/# wkh#ghwhuplqdwlrq#ri# wkh#vqxeehu# orvvhv#lq#wkh#PPF#exloglqj#eorfn# ryhu# d# frpsohwh#f|foh#uhtxluhv#dq#xqghuvwdqglqj#ri#wkh#yrowdjh#dqg#fxuuhqw#dw#hdfk#vzlwfklqj#hyhqw1# Wkh# fdofxodwlrq# pd|# eh# shuiruphg# lq# d# yhu|# vlplodu# zd|# wr# wkdw# glvfxvvhg# deryh# iru# wkh# vhplfrqgxfwru#vzlwfklqj#orvvhv1# A.5.2 d.c. voltage-dependent losses

Wkh# g1f1# yrowdjh0ghshqghqw# orvvhv# ri# wkh# ydoyh# duh# vlpso|# wkh# a 52 T # orvvhv# lq# uhvlvwlyh# frpsrqhqwv#frqqhfwhg#lq#sdudooho#zlwk#wkh#ydoyh#ru#zlwk#sduwv#ri#wkh#ydoyh1# Lq# dq# PPF# ydoyh# wkhvh# uhvlvwlyh# frpsrqhqwv# idoo# lqwr# wzr# pdlq# fdwhjrulhv=# wkrvh# wkdw# duh# frqqhfwhg#lq#sdudooho# zlwk#wkh#PPF#exloglqj#eorfn#g1f1# fdsdflwru# ri# hdfk# PPF# exloglqj#eorfn# +vxfk# dv# fdsdflwru# glvfkdujh# uhvlvwruv,# dqg# wkrvh# wkdw# duh# frqqhfwhg# lq# sdudooho# zlwk# wkh# frpsohwh#ydoyh#ru#odujh#sduwv#ri#wkh#ydoyh#+iru#h{dpsoh#zdwhu#frrolqj#slshv,1# A.5.2.1 D.C. voltage-dependent losses with MMC building block – analytical method

Uhvlvwlyh# frpsrqhqwv# frqqhfwhg# lq# sdudooho# zlwk# wkh# g1f1# fdsdflwru# ri# hdfk# PPF# exloglqj# eorfn#h{shulhqfh#d#yrowdjh#wkdw#lv#suhgrplqdqwo|#g1f1#exw#zlwk#d#odujh#ulssoh#frpsrqhqw1# Pdnlqj#dq#dvvxpswlrq#wkdw#wkh#uhvlvwdqfh#sdudooho#zlwk#hdfk#PPF#exloglqj#eorfn#lv#lghqwlfdo#wr# hdfk#rwkhu#+d#k|srwkhvlv#dfwxdoo|#qrw#wuxh#gxh#wr#ohdndjh#fxuuhqwv#lq#LJEWv#dqg#glrghv#hwf1,/# wkh#srzhu#glvvlsdwlrq#fdq#eh#vlpsolilhg#dv=#

RV4 =
wk

1 × T

?a
u

2 rms _ u

#

+D14;,#

Wkh#upv#yrowdjh#ri#wkh# u #PPF#exloglqj#eorfn=#

a rms _ u =
zkhuh#

1 × wi (v ) 2 × fv ` v =0

`

ò

+D14<,# #

w l +v ,#

lv#wkh#lqvwdqwdqhrxv#ydoxh#+lqfoxglqj#g1f1#frpsrqhqw,#ri#wkh#yrowdjh#dfurvv#wkh# u wk #uhvlvwlyh#frpsrqhqw/#ghwhuplqhg#hlwkhu#e|#qxphulfdo#vlpxodwlrq#ru#dqdo|wlfdo# fdofxodwlrq1#

Iru#doo#wkh#fdsdflwruv#lq#wkh#ydoyh/#w|slfdoo|/#wkh#yrowdjh#frpsulvhv#d#frqvwdqw#g1f1#frpsrqhqw/# orz#rughu#kduprqlfv#+d#odujh#sduw,#dqg#kljk#rughu#kduprqlfv#+uhodwlyho|#vpdoo,1#Li#wkh#fdsdflwru# yrowdjh# edodqflqj# dojrulwkp# fdq# hiihfwlyho|# vxssuhvv# wkh# gliihuhqfh# dprqj# wkh# fdsdflwru# yrowdjhv/# dq# dssur{lpdwlrq# xvlqj# phdq# yrowdjh# ri# wkh# fdsdflwruv# fdq# eh# dssolhg1#

95:84052Hg42FG#? #LHF# Iru#doo#fdsdflwruv#lq#wkh#ydoyh=#

?#76#?#

##

R = P tc × O × a cav ×
zkhuh#

fa cav fv #

+D153,#

R# Pwf # a fdy#

lv#wkh#fkdujlqj#srzhu#rq#wkh#ydoyh#dv#h{suhvvhg#e|#v|vwhp#sdudphwhuv# qxpehu#ri#PPF#exloglqj#eorfnv#shu#ydoyh# lv#wkh#phdq#yrowdjh#ri#wkh#fdsdflwruv1##

Wklv#lv#qrw#hdv|#wr#jlyh#rxw#dq#dqdo|wlfdo#uhvxow#iru# a fdy/#exw#qrwlqj#wkdw=#

òR = 2×P
zkhuh# Δ a#

1

tc

× O × (a 0 + Da ) 2 -

1 2 +D154, × P tc × O × a 0 ? P tc × O × a 0 × Da 2 ######

lv#wkh#upv#ulssoh#ri#wkh#phdq#yrowdjh#ri#fdsdflwruv#

Lq#wkh#deryh#htxdwlrq/#wkh#whup# Δa 5 #kdv#ehhq#qhjohfwhg1#Frqvhtxhqwo|/#wkh#srzhu#glvvlsdwlrq# fdq#eh#h{suhvvhg#e|#lqsxw#sdudphwhuv1# Qrwh# wkdw# wkh# srzhu# glvvlsdwlrq# lv# uhodwlyho|# odujh# zkhq# wkh# frqyhuwhu# lv# devruelqj# uhdfwlyh# srzhu#iurp#wkh#df#qhwzrun/#gxh#wr#wkh#lqfuhdvlqj#ulssoh#yrowdjh1# Iru#uhgxqgdqw#ohyhov/#wzr#srvvleoh#vfhqdulrv#vkrxog#eh#frqvlghuhg=# d,# Wkh# fdsdflwru# yrowdjhv# duh# frqvwdqw# hyhq# zkhq# wkh# uhgxqgdqw# ohyhov# duh# vkruwhg/# zklfk# phdqv# wkh# uhgxqgdqw# ohyhov# mxvw# sduwlflsdwh# lq# wkh# edodqflqj# dfwlrq/# exw# qrw# wr# exlog# wkh# g1f1# yrowdjh1# Dv# wkh# uhgxqgdqw# ohyhov# duh# vkruwhg/# wkh# wrwdo# orvvhv# zloo# ghfuhdvh/# exw# wkh# vlqjoh#PPF#exloglqj#eorfn#orvv#zloo#lqfuhdvh#gxh#wr#wkh#lqfuhdvlqj#ulssoh># e,# Wkh#fdsdflwru#yrowdjhv#duh#qrw#frqvwdqw/#zklfk#phdqv#doo#PPF#exloglqj#eorfnv#duh#lqsxw#wr# exlog#wkh#g1f1#yrowdjh1#Dv#wkh#uhgxqgdqw#ohyhov#duh#vkruwhg/#wkh#wrwdo#orvvhv#dqg#wkh#vlqjoh# PPF# exloglqj# eorfn# orvv# zloo# erwk# lqfuhdvh# gxh# wr# wkh# lqfuhdvlqj# gf# frpsrqhqw# ri# hdfk# fdsdflwru># A.5.2.2 D.C. voltage-dependent losses with valve– analytical method

Iru# uhvlvwlyh# frpsrqhqwv# frqqhfwhg# lq# sdudooho# zlwk# wkh# frpsohwh#ydoyh# ru# odujh# sduwv# ri# wkh# ydoyh# vxfk# dv# zdwhu# frrolqj# slshv/# wkh# yrowdjh# h{shulhqfhg# fdq# dovr# eh# dfklhyhg# e|# d# vwdwlvwlfdo#dssurdfk1# Iru# dq|# PPF# exloglqj# eorfn/# wkh# suredelolw|# ri# ehlqj# lq# wkh# dfwlyh# vwdwh# lv# lghqwlfdo# wr# wkh# rwkhuv/#zklfk#lv#sursruwlrqdo#wr#wkh#ydoyh#yrowdjh=#

rc (wv ) =
zkhuh#

w v (wv ) P tc × wcav (wv )

+D155,# #

Pwf # w y #+ ωv ,# w fbdy #+ ω v,#

qxpehu#ri#PPF#exloglqj#eorfnv#shu#ydoyh# lv#wkh#ydoyh#yrowdjh#dv#d#ixqfwlrq#ri#wlph# lv#wkh#phdq#PPF#exloglqj#eorfn#g1f1#fdsdflwru#yrowdjh#dv#d#ixqfwlrq#ri#wlph#

Zkhwkhu# iru# frpsohwh# ydoyh# ru# sduwv# ri# wkh# ydoyh/# wkh# yrowdjh# ehwzhhq# wkh# uhvlvwlyh# frpsrqhqwv#fdq#eh#h{suhvvhg#dv=#

#

## #

?#77#?#

95:84052Hg42FG#? #LHF#

w (wv ) =

p × w v (wv ) # P tc

+D156,#

zkhuh=#

p#

lv# wkh# wrwdo# qxpehu# ri# PPF# exloglqj# eorfnv# lq# sdudooho# zlwk# wkh# uhvlvwlyh# frpsrqhqwv#+iru#frpsohwh#ydoyh/# p@ P wf ,#

Iru#d#w|slfdo#vlqxvrlgdo#prgxodwlrq/#wkh#dqdo|wlfdo#uhvxow#fdq#eh#h{suhvvhg#dv=#

? p × w v (wv ) ? ? ÷ 2×p ? 2×p P tc ÷ 1 1 p2 è ? × × f (wv ) = × Rav = 2 × p 0 P tc 2 2 ×p 0 T

2

ò

ò

? ad ? ±aO ÷ ? 2 ? × f (wv ) ×è T

2

Rav =
zkhuh#

p2 ×a d
2

2

4 × P tc × T

+

o2 × p2 ×a d 8 × P tc × T
2

2

+D157, #

o#

lv#wkh#prgxodwlrq#lqgh{#

QRWH# 4# 0# Iru# qxphulfdo# vroxwlrq/# wkh# ydoyh# vkrxog# eh# vlpxodwhg# lq# vrph# ghwdlo# zlwk# vxiilflhqwo|# ghwdlohg# uhsuhv hqwdwlrq# ri# wkh# frqwuro# v |vwhp/# ru# ghwdlohg# uhvlvwdqfh# sdudooho# zlwk# PPF# exloglqj# eorfn# fdsdflwruv# dqg# wkh# ydoyh# ru# ydoyh# vhfwlrqv# vxfk# dv=# Uhvlvwlyh# yrowdjh#judglqj# flufxlwv# +g1f1# judglqj# flufxlwv,/# uhvlvwlyh# yrowdjh#glylghuv# iru# yrowdjh# phdvxuhphqw/# zdwhu# frrolqj# slshzrun/# vkxqw# uhvlvwlyh# orvvhv# dfurvv# fdsdflwru# glhohfwulf# pdwhuldo/# glvfkdujh#uhvlvwruv#dfurvv#g1f1#fdsdflwruv1#

A.5.3 A.5.3.1

Valve Electronics Power Consumption General

Wkh# edvlf# sulqflsoh# ri# wkh# ydoyh# hohfwurqlfv# srzhu# frqvxpswlrq# lv# doprvw# wkh# vdph# dv# wkdw# ghvfulehg# lq# LHF# 95:84041# Zlwk# wkh# PPF# wrsrorj|/# wkh# gliihuhqfh# lv# wkdw# wkh# srzhu# frqvxpswlrq#ri# wkh#ydoyh# hohfwurqlfv#iru# hdfk# PPF# exloglqj# eorfn#ydulhv#iurp# f|foh#wr#f|foh/# vlqfh# wkh# LJEW# rq0rii# rshudwlrq# vwdwxv# lv# qrw# lqvwdqwdqhrxvo|# wkh# vdph# lq# doo# PPF# exloglqj# eorfnv1#Khqfh/#lw#lv#qhfhvvdu|#wr#wdnh#dq#dyhudjh#ydoxh#wr#hydoxdwh#wkh#srzhu#frqvxpswlrq1## A.5.3.2 A.5.3.2.1 Topology of power supply circuit General

Wzr#w|shv#ri# srzhu# vxsso|#flufxlw# kdyh#ehhq#dvvxphg/# wkh#iluvw#lq#zklfk#wkh# srzhu# vxsso|#lv# frqqhfwhg#dfurvv#hdfk#LJEW#dqg#wkh#vhfrqg#lq#zklfk#wkh#srzhu#vxsso|#lv#frqqhfwhg#ehwzhhq# wkh#whuplqdov#ri#wkh#vxeprgxoh#g1f1#fdsdflwru1## A.5.3.2.2 Type A

Wkh# srzhu# flufxlw# lv# frqqhfwhg# wr# wkh# froohfwru# dqg# wr# wkh# hplwwhu# ri# hdfk# YVF# ohyho1# Wkh# flufxlw# ghulyhv# wkh# srzhu# iurp# wkh# yrowdjh# dfurvv# YVF# ohyho# dqg# vxsso|# wr# wkh# ydoyh# hohfwurqlfv1#Iru#hdv|#xqghuvwdqglqj/#wkh#frqfhsw#lv#vkrzq#lq#Iljxuh#D149# 1#

95:84052Hg42FG#? #LHF#

?#78#?#

##

lJX+w, ydoyh hohfwurqlfv xJX+w, Srzhu# vxsso| Jdwh dqg# Prqlwrulqj LJEW

rSa (v ) = wSa (v ) · uSa (v )
Jdwh#vljqdo Prqlwrulqj#vljqdo

Ydoyh#edvh# hohfwurqlfv

#

Figure A.16 - Power supply from IGBT terminals Lq# wklv# fdvh/# wkh# lqvwdqwdqhrxv# srzhu# frqvxphg# lq# wkh# srzhu# vxsso|# lv# jlyhq# e|# pxowlso|lqj# wkh#yrowdjh#dqg#fxuuhqw#dv#vkrzq#lq#wkh#iljxuh1#Wkhq/#lq#rughu#wr#rewdlq#wkh#dyhudjh#ydoxh/#wkh# lqvwdqwdqhrxv#srzhu#lv#lqwhjudwhg#iru#rqh#vhfrqg1# Diwhu#wdnlqj#dyhudjh/#wkh#dyhudjh#srzhu#ri# hyhu|#YVF#ohyho#lv#vxpphg#xs#wr#rewdlq#wkh#wrwdo# srzhu#frqvxpswlrq#ri#wkh#ydoyh1# Zkhq#wkh#srzhu#flufxlw#lv#lqwhjudwhg#lqwr#wkh# vqxeehu# flufxlw/# wkh#srzhu#frqvxpswlrq#pd|# eh# lqfoxghg#lq#wkh#vqxeehu#flufxlw#orvv1# Wklv#W|sh#D#fdq#eh#dssolhg#wr#wkh#YVF#ohyho#ri#wkh#FWO#fhoo#dv#vkrzq#Iljxuh#D14:1#

YVF#ydoyh#ohyho lJX+w, ydoyh#hohfwurqlfv xJX +w, Srzhu# vxsso| Jdwh dqg# Prqlwrulqj LJEW

rSa (v ) = wSa (v ) · uSa (v )
Jdwh#vljqdo Prqlwrulqj#vljqdo

Ydoyh#edvh# hohfwurqlfv FWO fhoo

#

Figure A.17 - Power supply from IGBT terminals in cell #

#

## # A.5.3.2.3 Type B

?#79#?#

95:84052Hg42FG#? #LHF#

Wkh#srzhu#flufxlw#lv#frqqhfwhg#wr#wkh#whuplqdov#ri#g1f1#fdsdflwru#lq#wkh#vxeprgxoh1#Wkh#flufxlw# ghulyhv#wkh# srzhu# iurp# wkh#yrowdjh# ri# wkh# g1f1# fdsdflwru# dqg# vxsso|# wr# wkh#ydoyh# hohfwurqlfv1# Wkh#frqfhsw#lv#vkrzq#lq#Iljxuh#D14;1# Lq#wklv#fdvh/#wkh#srzhu#flufxlw#ihhgv#wkh#srzhu#wr#wzr#LJEWv#lq#wkh#vxeprgxoh1#Wkh#qxpehu#ri# srzhu# flufxlwv#lv#htxdo# wr#wkh# qxpehu# ri# vxeprgxohv1# Wkhq/#wkh# qxpehu#iru# vxppdwlrq#lv#wkh# qxpehu#ri#vxeprgxohv#wr#rewdlq#wkh#wrwdo#srzhu#frqvxpswlrq#ri#wkh#ydoyh1#

Vxeprgxoh

lJX+w, ydoyh#hohfwurqlfv Jdwh dqg# Prqlwrulqj

LJEW

xJX+w,

Srzhu# vxsso| ydoyh#hohfwurqlfv

PPF#vxeprgxoh

Jdwh dqg# Prqlwrulqj LJEW

r Sa (v ) = w Sa (v ) · uSa (v )

#

Figure A.18 - Power supply from d.c. capacitor in submodule Wklv# w|sh# E# pdlqo|# dssolhv# wr# wkh# vxeprgxoh0w|sh# ydoyh1# Lw# lv# qrw# frqvlghuhg# wr# eh# hdv|# wr# dsso|# wr# FWO# vlqfh# lqvxodwlrq# ehwzhhq# wkh# srzhu# vxsso|# dqg# LJEW# uhtxluhv# pxfk# kljkhu# yrowdjh#zlwkvwdqg#fdsdelolw|1#

A.6
A.6.1

Application to other variants of valve
Other variants of MMC valve without series-connection of IGBT-diode pairs General

A.6.1.1

Wkh# suhylrxv# dqdo|vlv# kdv# frqvlghuhg# rqo|# wkh# wzr0ohyho/# ?kdoi0eulgjh?# PPF# exloglqj# eorfn1# Dowkrxjk# wklv# lv# d# zhoo0nqrzq# yduldqw# ri# wkh# ydoyh/# lw# lv# qrw# wkh# rqo|# yduldqw# wkdw# lv# srvvleoh1# ?Ixoo0eulgjh?#yduldqwv#ri# PPF#exloglqj#eorfnv#duh#dovr#srvvleoh/# dv#duh#PPF#exloglqj#eorfn# v# edvhg#rq#wkuhh0ohyho#ru#rwkhu#pxowl0ohyho#frqyhuwhu#duudqjhphqwv1# A.6.1.2 Two-level full-bridge MMC building block

D# ?ixoo0eulgjh?# PPF# exloglqj# eorfn# lv# vkrzq# lq# Iljxuh# D14<1# Wklv# shuirupv#wkh# vdph# ixqfwlrq# dv# wkh# kdoi0eulgjh# PPF# exloglqj# eorfn# exw# kdv# dgglwlrqdo# ioh{lelolw|/# lq# wkdw# wkh# fdsdflwru# fdq# eh#lqvhuwhg#lqwr#wkh#flufxlw#lq#hlwkhu#srodulw|1#Krzhyhu/#wklv#flufxlw#frqwdlqv#irxu#LJEWv#lqvwhdg# ri#wzr/#dqg#wkhuhiruh#vxiihuv#iurp#pxfk#kljkhu#frqgxfwlrq#orvvhv#shu#PPF#exloglqj#eorfn#+iru# d#jlyhq#fxuuhqw/#dssur{lpdwho|#wzlfh#wkdw#ri#wkh#kdoi0eulgjh#PPF#exloglqj#eorfn,1#

95:84052Hg42FG#? #LHF#

?#7:#?#

##

# Figure A.19 - One “full-bridge”, two-level MMC building block Wkh# ixoo0eulgjh# PPF# exloglqj# eorfn# kdv# irxu# srvvleoh# rshudwlqj# vwdwhv# iru# hdfk# srodulw|# ri# fxuuhqw=# dfwlyh# srvlwlyh/# dfwlyh# qhjdwlyh/# xsshu# e|sdvv# dqg# orzhu# e|sdvv1# Wkh# wzr# ?e|sdvv?# vwdwhv#duh#uhgxqgdqw1## Li# ?dfwlyh# srvlwlyh?# lv# wdnhq# wr# eh# wkh# vwdwh# lq# zklfk# wkh# ohiw# kdqg# whuplqdo# lv# srvlwlyh# zlwk# uhvshfw# wr# wkh# uljkw0kdqg# whuplqdo/# wkhq# wkh# hljkw# frpelqdwlrqv# ri# fxuuhqw# gluhfwlrq# dqg# PPF# exloglqj#eorfn#vwdwh#duh#dv#iroorzv=## ?# Fxuuhqw#→/#Xsshu#e|sdvv=# # ?# Fxuuhqw#→/#Orzhu#e|sdvv=# # ?# Fxuuhqw#→/#Dfwlyh#Srvlwlyh=# # ?# Fxuuhqw#←/#Xsshu#e|sdvv=# # ?# Fxuuhqw#←/#Orzhu#e|sdvv=# # ?# Fxuuhqw#←/#Dfwlyh#Srvlwlyh=# # #G4.W6#frqgxfwlqj# W5.G7#frqgxfwlqj# G4.G7#frqgxfwlqj# W4.G6#frqgxfwlqj# G5.W7#frqgxfwlqj# W4.W7#frqgxfwlqj#

?# Fxuuhqw#→/#Dfwlyh#Qhjdwlyh=# # W5.W6#frqgxfwlqj#

?# Fxuuhqw#←/#Dfwlyh#Qhjdwlyh=# # G5.G6#frqgxfwlqj# Lq# frqwudvw# wr# wkh# kdoi0eulgjh# PPF# exloglqj# eorfn/# zkhuh# fxuuhqw# iorzv# pdlqo|# lq# glrghv# lq# uhfwlilhu# prgh# dqg# LJEWv# lq# lqyhuwhu# prgh/# wkh# LJEWv# dqg# glrghv# lq# wkh# ixoo0eulgjh# PPF# exloglqj#eorfn#fduu|#dssur{lpdwho|#wkh#vdph#fxuuhqw1#Frqvhtxhqwo|#wkh#frqgxfwlrq#orvvhv#duh# dssur{lpdwho|#wkh#vdph#lq#erwk#uhfwlilhu#dqg#lqyhuwhu#prghv/#zklfk#lv#qrw#wkh#fdvh#iru#wkh#kdoi0 eulgjh#PPF#exloglqj#eorfn1# Dowkrxjk#wkh#frqgxfwlrq#orvvhv#ri#d#ixoo0eulgjh#PPF#exloglqj#eorfn#duh#dssur{lpdwho|#wzlfh#dv# kljk# dv# wkrvh# ri# d# kdoi0eulgjh# PPF# exloglqj# eorfn# rshudwlqj# dw# wkh# vdph# fxuuhqw/# wkh# ixoo0 eulgjh# duudqjhphqw# doorzv# wkh# frqyhuwhu# wr# eh# ?ryhu0prgxodwhg?/# dfklhylqj# d# shdn# frqyhuwhu# d1f1#yrowdjh#wkdw#h{fhhgv#wkh#g1f1#sroh0wr0sroh#yrowdjh#dqg#shuplwwlqj#d#orzhu#d1f1#fxuuhqw1#Wkh# ryhudoo# frqgxfwlrq#orvvhv#ri# wkh#ixoo0eulgjh# frqyhuwhu# duh# wkhuhiruh# vrphzkdw#ohvv#wkdq#wzlfh# wkrvh#ri#d#kdoi0eulgjh#frqyhuwhu1# Iru#d#jlyhq#yrowdjh#dqg#fxuuhqw/#wkh#vzlwfklqj#orvvhv#ri#wkh#ixoo0eulgjh#PPF#exloglqj#eorfn#duh# wkh#vdph#dv#iru#wkh#kdoi0eulgjh#PPF#exloglqj#eorfn1#Wklv#lv#ehfdxvh#hdfk#lqglylgxdo#vzlwfklqj# hyhqw#rqo|#diihfwv#rqh#vlgh#ri#wkh#eulgjh#dw#d#wlph1# A.6.1.3 Multi-level MMC building blocks

Wkh# PPF# exloglqj# eorfnv# vkrzq# lq# Iljxuh# D1:# dqg# Iljxuh# D14<# duh# edvhg# rq# wkh# wudglwlrqdo# ?wzr0ohyho?# frqyhuwhu/# zklfk# wkh|# surgxfhv# wzr# glvfuhwh# ydoxhv# ri# rxwsxw# yrowdjh# lq# hdfk# shuplwwhg#srodulw|1#Lq#sulqflsoh#lw#lv#srvvleoh#wr#frqfhlyh#ri#PPF#exloglqj#eorfn#ghvljqv#edvhg# rq# odujhu# qxpehuv# ri# rxwsxw# ohyhov1# Iru# h{dpsoh/# wkhuh# duh# irxu# srvvleoh# ghvljqv# ri# PPF# exloglqj#eorfn#edvhg#rq#?wkuhh0ohyho?#frqyhuwhu#wrsrorjlhv/#dv#vkrzq#rq#Iljxuh#D1531#

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95:84052Hg42FG#? #LHF#

# Figure A.20 - Four possible variants of three-level MMC building block Wkh# wkuhh0ohyho# kdoi0eulgjh# yduldqwv# hdfk# kdyh# wzlfh# dv# pdq|# vhplfrqgxfwru# ghylfhv# shu# PPF# exloglqj# eorfn# dv# wkh# wzr0ohyho# kdoi0eulgjh# PPF# exloglqj# eorfn/# dqg# dw# dq|# jlyhq# wlph# wzr# vhplfrqgxfwru# ghylfhv# shu# PPF# exloglqj# eorfn# duh# dozd|v# lq# frqgxfwlrq1# Rq# wkh# rwkhu# kdqg# wkh# rxwsxw# yrowdjh# ri# wkh# wkuhh0ohyho# PPF# exloglqj# eorfn# lv# wzlfh# wkdw# ri# wkh# wzr0ohyho# PPF#exloglqj#eorfn/#vr#wkh#ryhudoo#frqgxfwlrq#orvvhv#ri#wkh#ydoyh#duh#hvvhqwldoo|#wkh#vdph#dv# wkrvh#ri#d#ydoyh#edvhg#rq#wkh#wzr0ohyho#kdoi0eulgjh#PPF#exloglqj#eorfn1## Olnhzlvh/# wkh# wkuhh0ohyho# ixoo0eulgjh# yduldqwv# kdyh# dssur{lpdwho|# wzlfh# wkh# frqgxfwlrq# orvvhv# +shu# PPF# exloglqj# eorfn,# ri# wkh# wzr0ohyho# ixoo0eulgjh# PPF# exloglqj# eorfn/# exw# wkh# ryhudoo# frqgxfwlrq#orvvhv#ri#wkh#ydoyh#duh#hvvhqwldoo|#wkh#vdph#dv#wkrvh#ri#d#ydoyh#edvhg#rq#wkh#wzr0 ohyho#ixoo0eulgjh#PPF#exloglqj#eorfn1## Dqdo|vlv#ri# wkh# vzlwfklqj#orvvhv#ri# vxfk#frqyhuwhuv#lv#voljkwo|#pruh# frpsoh{# wkdq#iru# wkh#wzr# ohyho#frqyhuwhuv/#exw#wkh#sulqflsoh#vwloo#krogv#wuxh#wkdw#hdfk#vzlwfklqj#hyhqw#uhvxowv#lq#hlwkhu#wkh# wxuq0rq# ri# dq# LJEW# dqg# wkh# wxuq0rii# ri# d# glrgh/# ru# ylfh0yhuvd1# Frqvhtxhqwo|/# iru# d# jlyhq# yrowdjh#udwlqj/#wkhuh#vkrxog#eh#qr#vljqlilfdqw#gliihuhqfh#ehwzhhq#wkh#vzlwfklqj#orvv#ri#d#wkuhh0 ohyho# PPF# exloglqj# eorfn# dqg# wkh# frpelqhg# vzlwfklqj# orvvhv# ri# wkh# wzr/# wzr0ohyho# PPF# exloglqj#eorfnv#wr#zklfk#lw#lv#htxlydohqw1# Rwkhu# yduldqwv# fdq# dovr# eh# lpdjlqhg/# zlwk# erwk# kdoi0eulgjh# dqg# ixoo0eulgjh# yduldqwv# zlwk# irxu/# ilyh#ru#hyhq#pruh#ohyhov/#dqg#hyhq#zlwk#dv|pphwulfdo# rxwsxw#yrowdjhv#+iru#h{dpsoh#.5Y/#.4Y/# 3#dqg#04Y,1#

95:84052Hg42FG#? #LHF#

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