Desgn, Control and pplcaton of Modular Multlevel Converters for HVDC Transmsson Systems by Kamran Sharfabad, Lennart Harnefors, HansPeter ee, Staffan orrga, Remus Teodorescu IS0: 885560 Copyrght Wley 206 Chapter 6 Modellng and Smulatons
bstractzaton level Leg Level veraged (LL) rm Level veraged (L) SubModule Level veraged (SL) SubModule Level Swtched (SLS) Two types of programs: Crcut smulators (PLECS, PSCD, PSIM, Smulnk/SmPowerSys, etc) Equaton solvers (Matlab, MthCad, Mathematca, Maple, etc)
Leg Level veraged (LL)model v d n u n l s 2 sl R c u C v cu 2R v cu l C v cl v cl c R nu nl vd L 2L 2L L c c d nu nu v s cu 0 0 v cu dt C 2 C v cl n v cl l nls 0 0 C C v v T 3 states c cu cl Reflects the dynamc nteractons between the upper and lower arm sumcapactor voltages, crculatng current, dc bus voltage, output phase current, and nserton ndces hmed,.; ngqust, L.; orrga, S.; ntonopoulos,.; Harnefors, L.; ee, H.-P., " Computatonally Effcent Contnuous Model for the Modular Multlevel Converter," n Emergng and Selected Topcs n Power Electroncs, IEEE Journal of, vol.2, no.4, pp.39-48, Dec. 204
Complete leg model v d s controller rm balancng control. Drect Modulaton v d v a s * s plant s f ks k p s 2 2 s 2 sl R f st a ST n u n l LL v cu v cl s c controller P v d c * c 2 2Ra Ra s 2 2 2 R v c * v d /2 c Easy to mplement n smulaton programs based on equaton solvers Useful for HIL smulaton
Submodule Level veraged (SL) v d based leg model n u, n l, s sl R 2 c n v u, cu, u l C u, C l, n l v, cl, 2R v cu, v cl, c nul, n R l, vd L 2L 2L c L c d n u, nu, v s cu, 0 0 v cu, dt Cu, 2 Cu, vcl, vcl, n l, nl, s 0 0 C C l, l, v 2 states c cu, cl, n u, are (nserted) or 0 (bypassed) llow tolerance n capactor values C Vectorzed model, s parameter Good for HIL smulaton (e. In FPG) v T, C u, l,
rm Level veraged (L) n u,l v u,l V v cu, l C/ cu,l u,l v n v ul, ul, cul, n cu, l u, l u, l sgnal wre What s neglected? PWM dynamcs Dscontnuous nserton number functon Capactor voltage (mean value) unbalance wthn the arm Good for control desgn of output and crculatng current controllers Second harmonc n sum-capactor voltage s vsble!
L wth blockng capablty (LLK) LK S blk Dbp2 D bp n ul, ul, What s added? LK wre C swtch S blk controlled by the blockng sgnal (LK) produced by the protecton crcut. ypass dode D bp representng the antparallel dode of the hgher swtch n the HSM and s used to represent the reverse current capablty n both normal and blocked state bypass dode D bp2 s ntroduced n parallel wth S blk n order to represent the antparallel dode of the lower swtch n the HSM and to allow postve current flowng durng blockng state. V Cu, l sgnal Good for MTDC system-level DC fault studes! v cu, l C Leterme, W.; hmed,.; eerten, J.; ngqust, L.; Van Hertem, D.; orrga, S., " new HVDC grd test system for HVDC grd dynamcs and protecton studes n EMT-type software," n C and DC Power Transmsson, th IET Internatonal Conference on, vol., no., pp.-7, 0-2 Feb. 205
Submodule Level veraged (SL) n ul, v ul, V v cu, l C ul, Cu, l ul, sgnal wre v n v ul, ul, cul, n cu, l u, l u, l What s neglected? PWM dynamcs Dscontnuous nserton number functon The dfferences are due to tolerance n capactor values and dfferent nternal consumpton of submodules!
Vectorzed SL model (PLECS) C C 2 2 () 2 () SM - C 2 2 C [ C, C.. C ] () MULTIPLEXED MODEL SERIES COECTIO () Vectoral (multpleed) smulaton- for e. PLECS becomes a parameter!
Submodule Level Swtched (SLS) G uh S uh V v c u C ul, R ul, G ul S ul sgnal wre Can be realzed vectorzed lke SL ypassed perods are vsble as flat lnes Swtchng and conducton losses can be estmated on SM level Good for effcency studes wth advanced modulaton Good for the study of PWM or LC as well as for losses estmaton!
Multple carrers PSC n u,l > n u,l c G u,l for : : IntPhase() end f sw Vectorzed carrer generaton (automatcally scale wth ) Can be mplemented n both PLECS and Smulnk Same method can be appled for LSC
n eample n PLECS Ths PLECS model s avalable on the book companon webste!
L and SL SL s vectorzed L ()
SLS PWM SLS-PSC SLS- LSCS&S Ideal IGT and dodes models wth off-lne loss estmaton (PLECS) PSC can acheve balancng usng non nteger frequency rato LSC needs Sort&Select to balance
SLS LCS&S element nt echange; Do { //bubble sortng algorthm echange = 0; //suppose, there were no modfcaton n the sortng for (nt nde = 0; nde < (num_module); nde){ //search on the lst for unsorted f (module_array[nde].v_cap < module_array[nde].v_cap) { //check f the consecutve elements are n order module module_temp;//defne a tempoary storage place //echange the two SM parameters module_temp.nde_cap = module_array[nde].nde_cap; module_temp.v_cap = module_array[nde].v_cap; module_array[nde].nde_cap = module_array[nde].nde_cap; module_array[nde].v_cap = module_array[nde].v_cap; module_array[nde].nde_cap = module_temp.nde_cap; module_array[nde].v_cap = module_temp.v_cap; } } whle(echange); echange = ;//there was modfcaton stay n the loop } LC results n starcase type reference and need Sort&Select for balancng Sortng can be a typcal algorthm lke for eample bubble sortng Select s typcal changng the order of sortng accordng to the drecton of arm current To reduce the swtchng frequency, the S&S s only eecuted when the starcase reference has been changed (n steps) The equvalent swtchng frequency s not constant
Conclusons MMC complety requres dfferent modellng and smulaton technques dependng on the type of study. veraged models can be leglevel (LL), armlevel (L) or SMlevel (SL). They can be used for control desgn as can easly smulate systems wth large. For representng the dc fault behavor (MTDC) the armlevel averaged model can be enhanced wth blockng capablty (LLK). Some crcutsmulator programs (e.g. PLECS) allow vectorzed model whch s an effcent feature when dealng wth dfferent number of SMs. The feature can be used for smulatng capactors, carrers. For modulaton, balancng or losses studes, swtched models (SLS) are needed. Sort & Select (e. ubble sortng) are needed to balance SLSLSC and SLSLC. PLECS smulaton model s demonstrated and can be freely downloaded from the book companon webste and can be eecuted wth demo verson of PLECS (free download at www.plem.com).