Interfacing Modular Multilevel Converters for Grid Integration of Renewable Energy Sources

Transcription

1 nterfang Moular Multlevel Converters for Gr ntegraton of Renewable Energy Soures Fateeh Shahnazan a, Jafar Aab a,, Ers Pouresael b,, an João P. S. Catalão b,,e, a Faulty of Eletral an Coputer Engneerng, Babol (Noshrvan) nversty of Tehnology, PO Box 484, Babol, ran b NESC-D, nsttuto Superor Téno, nversty of sbon, sbon, Portugal Departent of Eletral Engneerng an Autoaton, Aalto nversty, 0150 Espoo, Fnlan NESC TEC an Faulty of Engneerng of the nversty of Porto, Porto, Portugal e C-MAST, nversty of Bera nteror, Covlha, Portugal Abstrat: Ths paper presents a ontrol etho for oular ultlevel onverters (MMCs) as an nterfae between renewable energy soures an the gr. Wth growng penetraton of renewable energy soures n the power gr, the evelopents n onverter tehnologes an ontroller esgns beoe ore pronent. n ths regar, yna an steay state analyss of the propose oel for an MMC use n a renewable energy base power syste are prove through, 1st, an n haron oels of the onverter n referene frae. Ths etale onfguraton s then use to aoplsh onverter oulaton an ontroller esgn. The frst novel ontrbuton of ths ontrol etho s to prove an aurate pulse wth oulaton (PWM) strategy base on network an onverter paraeters, n orer to aheve a stable operaton for the nterfae MMC urng onneton of renewable energy soures nto the power gr. n aton, the propose etho s able to tgate the onverter rulatng urrent by nsertng a seon haron referene n the oulaton proess of the MMC, whh s the seon ontrbuton ths paper proves over other ontrol tehnues. A apator voltage balanng algorth s also nlue n ths ontrol etho to ajust eah sub-oule (SM) voltage wthn an aeptable range. Fnally, onverter's axu stable operaton range s eterne base on the yna euatons of the propose oel. The funtonalty of the propose ontrol etho s eonstrate by etale atheatal analyss an oprehensve sulatons wth MATAB/Sulnk. Keywors: Capator voltage balanng; rulatng urrent ontrol; oular ultlevel onverter (MMC); power syste ynas; renewable energy soures. 1. ntrouton The reent energy plan s anly fouse on substtuton of urrent energy soures wth heaper, leaner, an renewable ones. Coon envronental onerns base on the rap utlzaton of hgh-pre exhaustble soures have le to ajor alteratons n power syste esgn [1]. For several eaes, t has been typal to esgn the struture of power strbuton systes raally n orer to prove the splty of the ontrol syste []. However, toay wth rsng volatlty an unpretablty of the network behavor, reatve eves are reure to hanle suh stuatons suessfully. The neessty of esgnng power networks wth axu power transfer ablty an nu osts leas to the applaton of power eletrons n power syste [3]. Developent of strbute generaton (DG), hgh voltage ret urrent transsson systes (HVDC), flexble a transsson systes (FACTS) an varable-spee rves (VSD) are the an otvaton of essental avaneents n fferent power eletron ategores suh as onverter esgn an Corresponng authors: Jafar Aab (j.aab@nt.a.r) an João P. S. Catalão (atalao@ub.pt).

2 swthng tehnology for ore than last twenty years [4]. The nessant progress of hgh voltage an hgh power swthng eves has a great effet on power eletron tehnology use n power networks [5]. Beses, prove effeny as well as lower losses an osts ake olleton an transsson systes ore benefal than a ones [6]. Therefore, power eletron onverters are strongly reure n ths fel. As the ost prtve type of onverters, output voltage of a -level onverter has hgh total haron storton (THD) whh neesstates atonal assve an expensve a flters. Also, large nuber of seres-onnete swthes s reure n orer to fae the hgh aount of voltage stress [7]. On the ontrary, ultlevel onverters reate a star ase voltage wavefor onsung apators, nutors, or other kns of separate voltage or urrent soures [5]. Ths akes ultlevel onverters wely aepte for nustral applatons an hgh power systes [8] ue to reue voltage stress (v/t), lower swthng losses an sall oon-oe voltages, the splty of reunany, an lower flter expenses. Aong fferent ultlevel onverter topologes propose for gr onneton of renewable energy soures, hybr ultlevel onverter strutures nlung seres onnete three-level neutral pont lape (NPC) onverter an H- brge (HB) oules, the fve-level atve neutral pont onverter (ANPC), an seres onnete fve-level ANPC an HB are ore oon (speally n wn power systes)[9]. As the voltage an power ranges of pratal swthng eves are lte ue to seonutor tehnology, seres onneton of swthes s reure n ase of hgh voltage an hgh power operaton [10]. Ths way, the non-oular onfguraton poses extra osts an ontrol oplexty on the whole syste esgn [5] whh lts the voltage level nreent of ultlevel onverters n nustral applatons. To resolve suh shortongs, Maruart an esnar propose oular ultlevel onverter (MMC) n 003 [11]. Sne then, a varety of MMC applatons suh as HVDC [1], [13] an a otor rves [14] have been ntroue n any papers. Beses ths, the onverter struture tself an be stue fro fferent aspets. There are several oulaton ethos soe of whh are ore oplex nlung any etals [15], whle the others are easer to follow. Spae vetor [16], nearest level [17], pulse wth oulaton (PWM) [18], an open loop oulaton [19] are suh note exaples aong the. Coparson of the effets of these ethos on varous outoes [0], espeally losses [1] oul lea to the best hoe proportonate to the objetve funton. n aton, apator voltage balanng [] an rulatng urrent ontrol [3] are two essental ontrol algorths that shoul be nlue n orer to aheve stable operaton. However, there are other portant ontrol objetves suh as a or voltage lnks [4], [5] an onverter energy storage apablty [6].

3 Pror to all of the above entone features, oelng has a huge pat on any other nvestgate aspet. Referene [7] represents a sngle-phase yna oel of MMC n whh su apator voltage of oules n eah ar s onsere nstea of the sngle oule voltages to reue the oplexty of the overall syste oel. n orer to have ore aurate results, a freueny oan approah oul be use to opute nner MMC varables [8]. n ths etho, frst, the rut topology an be ve nto an a parts by eouplng the rut euatons through a lnear transforaton. Then, usng terate onvoluton, the varables of seres-onnete oules are alulate n the freueny oan. On the other han, the sulaton of MMC transents espeally n ntegraton wth large networks beoes oplate as the etale oelng of onverter poses a assve oputatonal buren on eletroagnet transent-type (EMT-type) progras. n orer to fn the ost effent an aurate representaton of MMC n suh ases, fferent types of oels shoul be evelope an opare [9], [30]. Ths paper presents an analytal yna MMC oel whh s onvenent for sall sgnal MMC stablty stues an ontroller esgn. The stue onverter s onsere as an nterfae between a stable -lnk fe fro a renewable energy soure an strbuton power gr. The oelng proeure has been aoplshe n frae, whh s hosen to suss yna state-spae euatons as t has the avantage of unfe ontrol of three-phase over averagng ab oels. Thus, generatng oulaton nes relevant to external eans, as well as nternal onverter paraeters, leas to an aurate ontrol etho, beng one of the novel ontrbutons ths paper proves. A rulatng urrent ontrol algorth s also esgne base on seon haron euatons of the propose oel. Connetng renewable energy soures nto the power gr, the etale frae base onfguraton of the oel oulaton an ontrol guarantees the stable operaton of MMC swthes n the eterne axu stable operaton range. The rest of ths paper s organze as follows. Seton nlues a bref overvew of the topology followe by yna operaton analyss of the propose oel. Seton proves the steay state behavor of MMC onnete to a balane network. Moulaton nes also have been alulate usng these euatons. Crulatng urrent ontrol s nvestgate n seton -A whle apator voltage balanng algorth an onverter's stable operaton range are susse n seton -B an seton -C, respetvely. The results of ths stuy n seton V are arre out base on teoan sulatons n the MATAB/Sulnk envronent, an then followe by soe fnal onlusons n Seton V.

4 . General Syste Overvew an Dyna Operaton Analyss of the Propose Moel The eletrty proue by renewable energy soures an be transtte n fferent fors. Meanwhle, transsson systes are ore avantageous than a ones, espeally n long stane transssons where the hgh expenses for power eletron onverters beoe ore ost effetve. nrease penetraton of suh systes ue to lower epenene on fossl fuels as well as onserable use of renewable energy soures an lea to the greater portane of fault anageent an the evelopent of ult-ternal networks. Ths way, the superor features of MMC wll nrease the portane of the struture evelopent an ontroller esgn. The general struture of a three phase MMC /a onverter uner gr-onnete operatng oe s shown n Fg. 1(a). Eah leg s opose of upper an lower ars whh onsst of N seresonnete sub-oules (SM). The ost oon struture of SMs, as llustrate n Fg. 1(b), are half-brges wheren GBT swthes are use along wth apators.beses that, the fault urrents as well as haron oponents of ar-urrents are lte by two ar nutors, represente by nutane ar. Parast resstanes (Rar) vary base on the operatonal ontons as they nate nutor resstanes an onverter losses. Desre output voltage an be aheve by varyng the upper an lower ar voltages whh epen on the nuber of nserte SMs n eah ar. nserte voltages of eah upper an lower ar (enote by u an l respetvely) an be efne as ux nux ux an lx nlx lx, x a,b, where ( n ux, n lx ) are ontrol oulaton nes an ( ux, lx ) represent su apator voltages of eah ar. n aton to that, aorng to Fg. 1(a), the orresponng ar urrents ux an lx an be expresse as: ux x rx (1) lx x rx () where, x s the funaental sne wave urrent of phase x an rx s the rulatng urrent of leg x (whh s flowng through lnk an upper an lower ars of eah leg). Crulatng urrent onssts of an seon haron oponents an an be gven as: rx ux lx (3) Followng that, applyng KV to both upper an lower ars of the MMC struture represente n Fg. 1(a) leas to:

5 SM 1 SM 1 SM 1 v pper ar r a ua la SM N ar R ar ub lb SM N ar R ar u l SM N ar R ar R a b R R v ga v gb v g v lower ar SM 1 ar R ar SM 1 ar R ar SM 1 ar R ar SM N SM N SM N (a) C (b) Fg.1.General struture of MMC n gr-onnete operatng oe, (a) Crut agra, (b) SM onfguraton. v n ux ux ux v R x ar t ar ux (4) v n v lx lx lx R x ar t ar lx (5) where, v x represents the output voltage of phase x. As the frst step of esgnng a ontrol etho n orer to proue an approprate oulaton nex, we nee to estate the haron oponents of the oulaton nes. n ths regar, su apator voltages of eah ar ( ux, ) n euatons (4) an (5) an be estate by v lx. Beses that, v x (as the snusoal output voltage of the onverter) an be wrtten as a snusoal oeffent of v. Also, the reanng parts n euatons (4) an (5) nlung upper an lower ar urrents, a extra seon haron oeffents of v to the aboveentone esrptons (base on the expressons prove n euatons (1) an (), ar urrents onsst of, funaental, an seon haron oponents). Therefore, euatons (4) an (5) an be rewrtten as follows:

6 1x os t 1 x os t (6) v n ux v v v v 1x os t 1 x os t n lx v v v (7) Therefore, oulaton nes ( n ux, n lx ) are onsere havng, funaental, an seon haron oponents. Aorngly, oulaton nes an be expresse as: 1 1x os t 1 x os t n ux (8) 1 1x os ωt 1 x os ωt n lx (9) Note that oulaton nes n ux an n lx are alulate aorng to the rato between the su apator voltage an the esre voltage of eah ar an thus vary fro 0 to 1. Applyng ab to 0 transfor, (8) an (9) an be alulate as: 1 n os ωt sn ωt os ωt u sn ωt (10) 1 n os ωt sn ωt os ωt l sn ωt where subsrpts an represent the two funaental freueny rotatng oponents at ω=πf, whle subsrpts, represent the seon haron rotatng oponents at ω, an subsrpt 0 represents zero seuene oponent [31]. On the other han, ue to the presene of fferent haron oponents n both upper an lower ar urrents, SM apator voltages wll sure be affete. Ths way the su apator voltages nlue, funaental, an seon haron oponents as well. Therefore: u t u 0 u 1 os t u u os t u u 0 u u u u (11) (1) l t l 0 l 1 os t l l os t l l 0 l l l l (13) As the a s to present a stanar MMC average oel, stuyng yna euatons of the onverter beoes useful. The store energy n SM apators of eah ar an be expresse as follows: N 1 u,l u,l 1 W C u Where, u represents eah SM apator voltage. Beses, the ebee apator n eah SM s (14) onsere large enough so that the voltage evatons fro the ean value Therefore (14) an be rewrtten as: u,l N an be neglete.

7 1 C W u,l N u,l (15) On the other han, the nstantaneous power njete to eah ar euals the energy ervatve at any te nstant. Therefore: W u,l C u,l t N t u,l u,l u,l (16) Substtutng u,l nu,l u,l followng ynas of the su apator voltages are obtane as: C ux nux N t ux C lx nlx N t lx Conserng haron oponents of su apator voltage, oulaton nex, an ar urrent, the aboveentone euaton an be rewrtten n 0 frae as follows: C u 0 u os t u sn t u os t u sn t N t 1 os t sn t os t sn t os t sn t os t sn t uo u u u u whh leas to: C u 0 u os t u sn t u sn t u ost u os t u snt N t t t t u sn t u os t t 1 os t sn t os t sn t uo u os t u sn t u os t u sn t Multplyng the two expressons n rght han se of the euaton (19), fferent haron oponents of the prout sgnal an be represente n fferent atrx rows. Meanwhle, the ultplaton an haron separaton proess s learly expresse n the appenx. Therefore: 1 uo u 4 u 4 u 4 u 4 u u u u u uo u 4 u 4 u 4 u 4 u C C u 1 N t N u 4 u 4 u u0 u u u 1 0 u0 4 u 4 u u u u0 1 u0 4 u 4 u 4 u 4 u (17) (18) (19) (0)

8 On the other han, applyng KV to Fg. 1(a) leas to: v x ux R x v gx n R t ux ux ar t ar ux (1) Sne x ux lx, prevous euaton an be rewrtten as: v ( ux lx ar ) ( R R ar ) ux R lx v gx n t t ux ux () Fnally, aorng to (10)-(13) an appenx notes, the MMC yna state-spae euaton oul be erve n frae as: u l ( R R ar ) ( ) ω 0 ar u R ω 0 v l g 0 ( ar ) u l ( ar ) ω ( R R ar ) 0 u ω R 0 t t l v g ( R R ar ) 0 0 R uo lo uo lo 0 v 1 u 0 u 4 u 4 u 4 u 4 u 1 u 0 u 4 u 4 u 4 u 4 u 1 u 0 4 u 4 u 4 u 4 u (3) 3. Steay-State Operaton Analyss of the Propose Moel n orer to alulate oulaton nes n steay-state operaton oe of the onverter, all uanttes shoul be replae wth ther referene values n stable oe. n ths regar, all ervatve values n (0) are euate to zero as well as seon haron oponents of urrents. Also, an oul be neglete base on esgne ontrollers. Zero oponent of su apator voltages ( u 0 ) s eual to -lnk voltage referene (Vr). Aorngly, fro the last row of atrx (0), (4) an be expresse as: s s u 0 u u (4) n the sae way, other uanttes an be alulate as: u u s N 4Cω N s 4Cω u u (6) N s Ns u u u 8Cω 8Cω (7) N Ns s u u u 8Cω 8Cω (8) (5)

9 On the other han, the nstantaneous varatons n referene values of ar urrents shoul be onsere n ontrol algorth to obtan the best perforane urng hanges fro transent to steay-state operatng oes of the nterfae onverter. Conseuently: u u av l av av,, l av, t avu t avu t avl t avl (9) Substtutng nstantaneous urrents wth ther referene values gves: u u, u u,,, l l l l u0 l 0 0 (30) Therefore, by substtutng (4)-(30) n (3), steay-state euatons of the propose oel an be expresse as: R 3 8 ar N s s ar s ar R Cω V av g N 3 s s 8 ar 0 ar 0 V R s ar R av g 64Cω Vr 0 s s V 8 8 r 0 scωr ar Ns s CωR ar Ns 4 ar 4 ar 0 3Cω 3Cω ast row of (31) leas to: ar R ar N ar R ar N s 4 av 4 16 s C 4 av 4 16C A B t s obvous that A an B are onstant values, so there woul be a lnear relaton between s an s. Thus, frst row of (31) an lea to a uarat euaton n ters of s as: 3NA B V r ar R ar 1 ar 64 s V ( ) R ( ) s g av 8C C B By solvng the uarat euaton above, s an ' s an be alulate as: (31) (3) (33) 3 NA B V R r 1 V ( ar ) R ar ( ar ) 4 16 g av 8C CB 16C B V r s 3NA B 3NA B 3C B 3 NA B V r R V ( ar ) R ar ( ar ) g av 8C CB 16C B ' V r s 3NA B 3NA B 3C B Then, substtutng the n (3), s an ' s an be alulate. (34)

10 Beses that, ontrollng soe other features suh as rulatng urrent an apator voltage are of portane n MMC operaton. A. Crulatng urrent ontrol The rulatng urrents, ause by the nternal voltage fferenes between eah phase an the lnk, onsst of a an a seon haron oponent. The ter s n harge of to a power transfer whle the a ter oes not affet the a-se output voltages an urrents. However, t nreases the rs values of urrents n eah ar resultng n hgher power losses an thus, shoul be elnate. Assung t, the phase seuene use n the transforaton to the rotatonal referene frae s a--b. Applyng the transforaton, the KV n onverter phase loops beoes as follows: u R ar ar u u u u u ar t u R ar ar u 1 4 u 4 u u 0 u n orer to aheve a stable operaton of MMC, seon haron urrents are esre to be zero. n suh ase, seon haron oponents of oulaton nes an be evaluate an then spose to zero. (35) s s 1 s ar u R ar u ar u t 4 u 4 u u u 0 s s 1 s ar u R ar u ar t u 4 u 4 u u u 0 (36) (37) B. Capator voltage balanng algorth The ost popular apator voltage-balanng etho apple to MMCs, s base on a sortng algorth, n whh, the voltages of SM apators n eah ar are easure an sorte urng every ontrol pero. Then, base on the reton of ar urrent, the reure nuber of SMs havng the lowest (or hghest) voltage values wll be swthe on. The only weakness s that the aoplshent of the sortng algorth urng every ontrol pero leas to unneessary swthng transtons wthn SMs. Sne the algorth s apple to all sorte SMs, regarless of ther prevous states, swthng ay our even at a onstant nuber of nserte SMs. To prove ths hgh swthng freueny, a new voltage-balanng etho base on a reue swthng freueny (RSF) has been ofe [3]. n ths etho, N (whh s the nuber of SMs that shoul be ae n the next ontrol pero) s expresse as N new N ol (where N ol s the urrent nuber of swthes n on state an Fg.. N new s the newly expete nuber), as shown n

11 N new N ol N N N new ol N 0 N 0 N 0 N ol N new Fg..RSF apator voltage balanng algorth apple to eah ar. Aorng to the reton of ar urrents ar : ux or lx, swthng transtons of eah ar wll be perfore as follows: f N s postve an atonal SMs are neee to be swthe on, the seleton proess wll only take plae between SMs n the off-state. Ths way, hargng urrent ar 0 leas to the seleton of SMs wth lowest voltage values whle ar 0 turns on SMs wth hghest apator voltages. f N s negatve an the nuber of the on-state SMs nees to be reue, the seleton proess wll only take plae between SMs n the on-state an no ore SMs wll be swthe on. Therefore, hargng urrent ar 0 leas to the seleton of SMs wth hghest voltage values whle ar 0 turns off SMs wth lowest apator voltages. t shoul be note that n oparson wth the onventonal algorths, RSF voltage balanng etho an onserably reue the overall swthng losses by lowerng the average swthng freueny. The general sheat agra an prnple of the propose ontrol etho s shown n Fg. 3.

12 + v pper & ower Gate Sgnals 3-phase MMC ux1 ux. uxn ω 0 t ux T ab/ T ab/ u u u0 u u ω 0 t s ' s s ' s u 0 P + ux + Controller rx ar ω T u ab/ s ' s s ' s u ar ω lx ω 0 t + P Controller u 0.5 R R R v gb Crulatng urrent ontrol ' s / s ' s / s ω 0 t v ga v g T ab/ v g v g E.34 & E.3 T /ab ω 0 t R ar ar R V g V r 4 N C s & s + T /ab ref /1.5 g P v ref /1.5 g Q v ' s & ' s P ref Q ref ω ω 0 t Capator Voltage Balanng Algorth Nn ux Nn lx pw n ux n lx 0 n 1 ab ' 1ab ' 1ab ab n ux & n lx E.8 & E.9 n' ux & n' lx Fg. 3. General sheat agra of the propose ontrol etho for ontrol of MMCs n gr-onnete oe. C. Maxu stable operaton range The onverter an elver a ertan aount of power whh epens on fferent strutural oponents an therefore, the argn shoul be elnate n orer to guarantee the stablty of operaton. Negletng losses, power transfer fro to a an be expresse as: v v v (38) Applyng KV to the output of MMC shown n Fg. 1(a) results n euatons esrbng onverter voltages whh then, an be transferre to frae as: v v R g t (39) v v g R t (40) Therefore, replang (39) an (40) n (38) leas to: v v g R v g R t t (41) Replang te ervatves of urrents wth average values an then vng both ses of (41) by R leas to: v v g g v R av R R av R R (4)

13 Then the ters av v g R an av v g R are ae to the both ses of the euaton. Therefore: av v g av v g v v v av g av g v av g R R R R R R av v g R Fnally, onverter s urrent urve an be obtane as (44): av v g av v g v v R v / R R R av g av g 4 4 (43) (44) Conserng 3 P v g an Q 3 v, atve an reatve power urve of MMC an be obtane as: 3v g av 3v 3v g g av P Q v v v R v / R 4R 4R 3 g av 3v g 3 g av 36 g 8 On the other han, onserng frst row of (35) as n steay-state operaton oe, followng euaton an be aheve u 4 u u (46) Then, usng (5)-(8), t an be rewrtten as follows: N N s ( s ) s s N s N s 0 16C ω 16C 16C 16C Applyng splfatons to the above euaton leas to: N N N s s s N s C ω C 16C 16C Therefore, (48) (45) (47) 3N 3 s N s 0. Ths way (50) an be erve as: s s Replang (3) n (50) gves: ar R ar N 4 av 4 16 C ar R ar N 4 av 4 16C (49) (50) (51)

14 Multplyng two ses of (51) leas to: N ar R R N ar ar ar 4 av 4 16C 4 av 4 16C (5) Applyng splfatons to the above euaton leas to: ar ar av av 0 (53) R ar R ar Then the two oponents of ar av an ar av are ae to both ses of the above R ar R ar euaton as: ar ar ar ar ar ar R av R av R av R av R av R av ar ar ar ar ar ar Ths an be rewrtten n the for of: (54) ar ar ar R av R av 4 av av ar ar R ar (55) Conserng 3 P v g an Q 3 v, (56) an be obtane as: ar ar ar Q ref v P v v 4 g av R ref 4R g av 16 g av av ar ar R ar (56) Euaton (44) esrbes a rle wth the enter of av v g av v g 4R v / 4R av v g av v g, R R an raus of, whle (55) s the euaton for a hyperbol. By rawng the together, we an estate the urrent urve for the stable operaton of MMC n the propose oel (Fg. 4(a)). The power flow urve of MMC shown n Fg. 4(b) an also be erve n the sae way. P Q B O α β A R R ar ar ar ar av av ar AB av 9 ' ' av ar A B v 4R g av av ar 16R a r (a) (b) Fg. 4.Regon for stable operaton of MMCs n gr-onnete operatng oe, (a) urrent urve, (b) P-Q urve. B O α β A 3 ' ar v 4R g av ar 3 ' ar v 4R g av ar

15 4. Results an Dsusson The etale oel s sulate n MATAB/Sulnk n orer to verfy operaton of the propose ontrol an swthng etho n ontrol an operaton of MMCs n power syste. The values of fferent rut oponents an operatonal ontons apple to sulatons are lste n Table. Fg. 5(a) shows the oulaton nex of the upper ar of phase-a (nua), generate by the propose oulaton etho. plyng that, a arrer-base oulaton wth phase opposton sposton (POD) arrers s use n whh nvual trangular arrers are apple for eah ell. Applyng ths fxe PWM pattern to swthng funtons of eah phase, the nner efs of eah phase leg rvng output urrents of MMC are obtane base on total ar voltages as: lx e ux x As shown n Fg. 5(b), these voltage levels are fxe at esre values whh ean that the balanng algorth s workng properly. n orer to verfy the effeny of RSF voltage balanng algorth, a oparson s also prove. Fg. 6(a) llustrates the gate sgnal apple to the frst SM n the upper ar of phase-a (Gua1) whle onventonal voltage balanng algorth s apple. Applyng RSF algorth, Gua1 s then agan eonstrate n Fg. 6(b). The oparson results learly show an effetve reuton n swthng freueny as the RSF algorth avos unneessary swthng transtons. (55) Table 1. MMC Paraeters an Operatonal Contons Apple to Sulatons tes a syste voltage V g (-,rs) Values 10 kv a syste nutane a syste resstane R bus voltage V r Nuber of SMs per ar N SM apatane C Ar nutane ar Ar euvalent resstane R ar SM apator voltage V s Carrer freueny f sw atve power P ref reatve power Q ref 30 H 0.5 Ω 0 kv μf 9 H 0.7 Ω 1 kv 5 khz 14 MW 6 Mvar

16 Fg. 5. Apple oulaton etho, (a) oulaton nex of the upper ar n phase-a generate by the propose oulaton etho, (b) nner efs of phase legs. G ua1 G ua1 Fg. 6. Gate sgnals apple to the frst SM of upper ar n phase-a, (a) onventonal voltage balanng algorth, (b) RSF voltage balanng algorth.

17 n orer to valate the propose rulatng urrent ontrol, as t an be seen n Fg. 7(a), the algorth s ntally sable but then re-enable at 0.4 s. As an be seen, the haron part of the rulatng urrent s reue effetvely whle approprate oponents generate by the ontroller are ae to oulaton nes. sng ths proeure leas to a ore snusoal ar urrent wavefor as the storton s tgate. Fg. 7(b) llustrates the upper ar urrent of phase-a. t shoul be note that the oponent n the ar urrent s neessary as t represents the transsson of atve power between the a an ses. Fg. 7() represents SM apator voltages of upper ar for phase-a. The voltages are n the reasonable rtera an well balane as well as the sgnfant reuton of the voltage flutuaton s aheve. t shoul be note that slar to any other ontrollng proess, there s a transent pero whh happens nevtably before oplete aoplshent of steay state operaton. n ths regar, t an be seen that the ar urrent as well as SM apator voltages are ealng wth soe osllatons urng ths transent pero whh by the way ens perfetly at 0.55 s when the esre steay state operaton an be aheve as well. Output voltages an urrents of the onverter are shown n Fg. 7() an Fg. 7(e), respetvely. Sne rulatng urrents are onsere as nteror uanttes, averse effets of the ontroller on the outer yna perforanes of the onverter are not esrable. Consstent wth ths onept, the a-se uanttes see to rean the sae an wthout any sgnfant hanges. However, a slght reuton n output voltage THD s obtane, whh oul be onsere as a result of the reutons ourre n the SMs' voltage flutuatons. Hene, the ontroller proves output voltage ualty as well as the nner yna perforanes. n orer to valate the propose ontroller, all ar,, an C uanttes use n sulatons have been hange by an aount of ±%0 an the results are eonstrate. As t an be seen n Fg.8 (a), nreasng ar,, an C values results n lower rulatng urrent aount whh then leas to a ore snusoal ar urrent an less flutuatons n apator voltages (shown n Fg. 8(b) an Fg. 8() respetvely). Applyng the propose rulatng urrent ontrol at 0.4s, the seon haron oponent of urrent has been elnate effetvely an the overall perforane of the onverter s prove as t an be seen n the sulaton results. Applyng 0% erease to ar,, an C values, rulatng urrent has been sgnfantly nrease as t s eonstrate n Fg. 9(a). Ths way the ar urrent s ontanng ore haron oponents an the apator voltage flutuatons are nrease as well. As t an be seen n Fg. 9(a), applyng the propose rulatng urrent at 0.4s leas to a sgnfant reuton n seon haron oponent of rulatng urrent. Also the ore snusoal ar urrent wavefor an reue apator voltage flutuatons have been eonstrate n Fg. 9(b) an Fg. 9()

18 respetvely. Therefore, the esre MMC operaton base on the propose oulaton an ontrol etho has been valate. Fg. 7. Sulate wavefors of the MMC usng rulatng urrent ontrol: (a) seon haron oponent of the rulatng urrent, (b)upper ar urrent of phase-a, () upper ar SM apator voltages of phase-a, () output voltages of MMC, an (e) output urrents of MMC.

19 Te[s] (a) Te[s] (b) Te[s] () Va Vb V Te[s] () Fg. 8. Sulate wavefors of the MMC wth 0% nrease n all ar,, an C oponent values: (a) seon haron oponent of the rulatng urrent, (b)upper ar urrent of phase-a, () upper ar SM apator voltages of phase-a, an () output voltages of MMC.

20 Fg. 9. Sulate wavefors of the MMC wth 0% erease n all ar,, an C oponent values: (a) seon haron oponent of the rulatng urrent, (b)upper ar urrent of phase-a, () upper ar SM apator voltages of phase-a, an () output voltages of MMC.

21 On the other han, rulatng urrent ontrol has also been evaluate base on the seon haron ynas of MMC (presente n euaton (35) of the anusrpt). As t an be seen, rulatng urrent an be affete by ether ar or u varatons whle the latter epens on SM apator values. n ths regar, the operaton of the propose ontroller has been evaluate, applyng ±%0 hanges n ar values an the results are eonstrate n Fg. 10(b) an Fg. 10() respetvely. t an be seen that the propose ontroller s apable of elnatng the seon haron oponents of urrent n both senaros. Moreover, the ontroller has also been evaluate, applyng ±%0 hanges n C SM values an the results are eonstrate n Fg. 10() an Fg. 10(e) respetvely. Sulaton results show that the ontroller s apable of provng an effetve reuton n seon haron oponents of rulatng urrents n ether ase. Also, the propose ontroller s apable of provng spefe values of atve an reatve power wthn the axu stable operaton range. As t an be seen n Fg. 11, the output atve an reatve power sgnals of the onverter are perfetly followng the spefe referene values. 5. Conluson n ths paper, an nnovatve ontrol etho has been presente for MMC as an nterfae between renewable energy soures an the gr. Dyna an steay state analyss of the propose oel were prove through, 1st an n haron oels of the onverter n frae. Converter oulaton was perfore base on the propose ntegrate yna oel. Provng aurate oulaton nes relevant to network paraeters an onverter paraeters was the frst novel ontrbuton of the propose ontrol etho over other ontrol tehnues. Followng the aton of apator voltage balanng algorth, the funtonalty of the propose ontroller was verfe by rgorous sulatons n MATAB/Sulnk. On the other han, onverter's stable operaton range has been evelope base on the euatons of transferre power. n orer to aheve a stable perforane, rulatng urrent ontrol has been esgne base on seon haron ynas of the propose oel, whh was onsere as the seon novel ontrbuton of the propose ontrol etho. t has been shown that by ang spef oponents to the pror oulaton nes, the seon haron oponent of the rulatng urrents an be effetvely reue. Therefore, the haron losses were elne whle ar urrents of eah phase beae ore snusoal. As learly verfe n ths paper, ths operaton strategy base on the propose ontrol etho erease apator voltage flutuatons, resultng n an enhane output ualty.

22 Fg. 10. Sulaton results for seon haron oponent of ra, (a) ar=9h an C SM=10F, (b) ar=1. 9H an C SM=10F, () ar=0.8 9H an C SM=10F, () ar=9h an C SM=1. 10F, (e) ar=9h an C SM=0.8 10F.

23 Fg. 11. Sulaton results for power oponents exhange wth the gr, (a) atve power of the onverter, (b) reatve power of the onverter. 6. Appenx Two nonspef sgnals X(t) an Y(t), are onsere nlung zero seuene, funaental an seon haron oponents as: X t X 0 X D os t X Q sn t X D os t X Q sn t Y t Y 0 Y D os t Y Q sn t Y D os t Y Q sn t By expanng the ab frae for an negletng 3r an 4th haron oponents, the prout sgnal Z(t)=X(t).Y(t) wll be obtane for zero seuene, funaental freueny an seon haron as follows: X Y X Q Y Q X Y X Q Y Q Z t X 0 Y 0 D D D D Z 0 X Y X Q Y Q X Y X Y Q Q X D Y Q X Q Y D X QY D X DY D D D D Q X DY 0 X 0Y D os t X Y Q 0 X 0Y Q sn t Z Z X D Y D X QYQ X QY D X DYQ 0 0 os 0 0 sn X Y Y X t D D X Q Y Y Q X t Z Z

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