Distributed Adaptive Droop Control for DC Distribution Systems Nasirian, Vahidreza ; Davoudi, Ali; Lewis, Frank; Guerrero, Josep M.

Transcription

1 Aalborg Unerstet Dstrbuted Adapte Droop Control for DC Dstrbuton Systems asran, Vahdreza ; Daoud, Al; Lews, Frank; Guerrero, Josep M. Publshed n: I E E E ransatons on Energy Conerson DOI (lnk to blaton from Publsher):.9/EC..558 Publaton date: Doument Verson Publsher's PDF, also known as Verson of reord Lnk to blaton from Aalborg Unersty Ctaton for blshed erson (APA): asran, V., Daoud, A., Lews, F., & Guerrero, J. M. (). Dstrbuted Adapte Droop Control for DC Dstrbuton Systems. DOI:.9/EC..558 General rghts Copyrght and moral rghts for the blatons made aeble n the bl portal are retaned by the authors and/or other opyrght owners and t s a ondton of aeng blatons that users reognse and abde by the legal reurements aoated wth these rghts.? Users may download and prnt one opy of any blaton from the bl portal for the rpose of prate study or researh.? You may not further dstrbute the materal or use t for any proft-makng atty or ommeral gan? You may freely dstrbute the URL dentfyng the blaton n the bl portal? ake down poly If you belee that ths doument breahes opyrght please ontat us at bn@aub.aau.dk prodng detals, and we wll remoe ae to the work mmedately and nestgate your lam. Downloaded from bn.aau.dk on: ul, 8

2 Dstrbuted Adapte Droop Control for DC Dstrbuton Systems Vahdreza asran, Student Member, IEEE, Al Daoud, Member, IEEE, Frank L. Lews, Fellow, IEEE, and Josep M. Guerrero, Senor Member, IEEE Abstrat A dstrbuted-adapte droop mehansm s proposed for seondary/prmary ontrol of d Mrogrds. he onentonal seondary ontrol, that adusts the oltage set pont for the loal droop mehansm, s replaed by a oltage regulator. A urrent regulator s also added to fne-tune the droop oeffent for dfferent loadng ondtons. he oltage regulator uses an obserer that proees neghbors data to estmate the aerage oltage aro the Mrogrd. hs estmaton s further used to generate a oltage orreton term to adust the loal oltage set pont. he urrent regulator ompares the loal perunt urrent of eah onerter wth the neghbors on a ommunaton graph and, aordngly, prodes an mpedane orreton term. hs term s then used to update the droop oeffent and synhronze per-unt urrents or, eualently, prode proportonal load sharng. he proposed ontroller presely aounts for the transmon/dstrbuton lne mpedanes. he ontroller on eah onerter exhanges data wth only ts neghbor onerters on a sparse ommunaton graph spanned aro the Mrogrd. Global dynam model of the Mrogrd s dered, wth the proposed ontroller engaged. A low-oltage d Mrogrd prototype s used to erfy the ontroller performane, lnk-falure resleny, and the plug-andplay apablty. Index erms Cooperate ontrol, d-d onerter, d Mrogrd, dstrbuted ontrol, droop ontrol. I. IRODUCIO Mrogrds, as small-sale power systems, are beomng polar n dstrbuton systems [] []. he d nature of renewable energy soures, storage elements, or emergng eletrons loads faor a d Mrogrd paradgm to aod redundant d-a-d onersons [], [5]. Moreoer, d Mrogrds an oerome some dsadantages of a systems, e.g., transformer nrush urrent, freueny synhronzaton, reate power flow, and power ualty ues [6]. Resemblng the ontrol herarhy of the legay grd, a herarhal ontrol struture s onentonally adopted for Mrogrd operaton Manusrpt reeed May, ; aepted August,. Part of the work was presented at the IEEE Appled Power Eletrons Conferene and Exposton, Fort Worth, X, USA, Marh 6. hs work was supported n part by the atonal Sene Foundaton under grants ECCS- 75 and ECCS-85 and n part by the U.S. Offe of aal Researh under grant Authors are wth the Unersty of exas at Arlngton Researh Insttute, Fort Worth, X 768 USA (emals: ahdreza.nasran@mas.uta.edu; daoud@uta.edu; lews@uta.edu). Josep M. Guerrero s wth the Department of Energy ehnology, Alborg Unersty, Denmark (oz@et.aau.dk). [7] []. he hghest leel n the herarhy (tertary) s n harge of eonomal dspath and oordnaton wth the dstrbuton system operator. It agns the Mrogrd oltage to arry out a presheduled power exhange between the Mrogrd and the man grd [] []. o satsfy the oltage demand of the tertary ontrol, the seondary ontrol measures oltages aro the Mrogrd and, aordngly, updates the oltage set ponts for the prmary ontrollers. he prmary ontrol, typally mplemented loally on nddual onerters wth a droop mehansm, regulates the outt oltage of nddual onerters and handles load sharng among soures. he seondary and tertary ontrols are typally mplemented n a entralzed fashon [], where a entral entty ommunates wth onerters through a hghlyonneted ommunaton network. Lo of any lnk n suh topologes an lead to the falure of the orrespondng unt, oerstreng other unts, and potentally leadng to systemleel nstablty and asaded falures [5]. Sne future extensons add to the ontroller omplexty, salablty s not straghtforward. Dstrbuted ontrol has emerged as an attrate alternate as t offers mproed relablty, smpler ommunaton network, and easer salablty [6]. For example, dstrbuted tertary ontrol a d sgnalng s studed n [7], [8]. Struturally, t s desrable to extend the dstrbuted ontrol paradgm to the seondary/prmary leels. Categorally, suh a ontroller shall satsfy two man ontrol obetes of d Mrogrds, namely oltage regulaton [9] and proportonal load sharng []. Proper load sharng agns the load among partpatng onerters n proporton to ther powers (or, eualently, urrents). hs approah eualzes the perunt urrents of all soures, and preents rulatng urrents [] and oerstreng of any soure []. he droop ontrol s wdely adopted for load sharng by mposng rtual outt mpedane on eah onerter [], []. Stat/dynam performane and stablty aement of droop ontrollers are nestgated n [], [], and [5]. Constant droop s ommonly used for power erene trakng and load sharng n grd-onneted and slanded modes, respetely [6], [7]. Howeer, ts load sharng performane s suseptble to transmon lne mpedanes [8]. Generally, hgher droop oeffents result n mproed load sharng, howeer, at the ost of further degradng the oltage regulaton. hus, to ahee a desrable load sharng, the droop oeffents should ary to aount for lne mpedanes and load aratons.

3 Moreoer, sne some soures (e.g., PV-dren modules or storage dees) lak a onstant power, dynam adustment of droop oeffents s reured as ther power hanges [9]. A pee-wse lnear droop mehansm n [8] and [] uses two dfferent droop gans for low and hgh powers. he dea s further deeloped n [] and [] where droop oeffents ontnuously ary n response to hange n power. hs approah mproes oltage regulaton; howeer, oltage drop aro the Mrogrd s stll noteable. hs method s deeloped for two-agent systems and extenson to a multonerter system s not straghtforward. Moreoer, mproed oltage regulaton has ompromsed aurate proportonal load sharng. Adapte-droop ontrol for power flow ontrol n grd-onneted mode s studed n [], []. Droop gans are adusted n reproal to power demand n [5] where ommunaton of a synhronzaton sgnal s needed among all onerters. hs reurement, n turn, ompromses the plug-and-play apablty. Deentralzed [] and supersory [6] adapte-droop approahes formulate droop gans n terms of batteres state of harges [7]. Exstng droop mehansms generally suffer from poor oltage regulaton and load sharng, partularly when the dstrbuton lne mpedanes are not neglgble [8] []. Poble solutons to the aforementoned ues hae been reewed n [6]. hese solutons are ether strutured entrally [7] or reure deelopment of a fully onneted data exhange network aro the Mrogrd, where any two nodes are n dret ontat [], [] []. Aumng eual oltages for all onerters aro the Mrogrd n [7] s not pratal, partularly, n d dstrbuton systems. Pont-to-pont ommunaton lnks are reured for all soures n [], where any lnk falure renders the whole Mrogrd noperable. he lne mpedane s taken nto aount n [5], where the data exhange reures a fully onneted ommunaton graph. Proper operaton of the ontroller demands nformaton of all nodes and, thus, any lnk falure mpars the whole ontrol funtonalty. Salablty s another hallenge; after any strutural/eletral upgrade, some ontrol settngs, e.g., the number of soures, need to be updated and embedded n all onerters. he oltage regulaton reurement s redefned n [6] to norporate the lne mpedane effet. he aerage oltage aro the Mrogrd (and only not a spef oltage) should be regulated at the global oltage set pont determned by the tertary ontrol. hs s alled the global oltage regulaton, and s onsdered here. ertary ontrol leels would nole dstrbuted optmzaton tehnues to mplement eonomal dspath and/or lo optmzaton, and s the subet of future work. hs paper fouses on the seondary/prmary ontrol of the d Mrogrds and offers the followng ontrbutons: Eah onerter s augmented wth a urrent regulator that ompares the atual per-unt urrent of that onerter wth a weghted aerage of ts neghbors and, aordngly, generates an mpedane orreton term to adust droop oeffent and, thus, prode proportonal load sharng. A oltage regulator s also added. hs regulator uses the estmaton made by a oltage obserer to adust the loal oltage set pont and prode global oltage regulaton. he oltage obserer proees neghbors data and loal oltage measurement through a so-alled dynam onsensus protool to estmate the global aerage oltage. Cooperaton of the oltage and urrent regulators s shown to effetely arry out both global oltage regulaton and proportonal load sharng, partularly, when the lne mpedanes are not neglgble. A sparse ommunaton network s spanned aro the Mrogrd to enable lmted meage pang among onerters; eah onerter only exhanges data wth ts neghbors. hs s n dret ontrast to the entralzed ontrol approahes that reure ommunaton networks wth hgh-bandwdth ommunaton lnks and a hgh leel of onnetty. hs adapte droop approah expands the work of authors n [6] and ahees a faster load sharng dynams. Compared to the exstng tehnues (e.g., [5]) the ontrol sheme employs a truly dstrbuted approah that does not reure a pror knowledge of the global parameters suh as the number of soures. hus, t s salable and sutable for the plug-and-play operaton. Unlke exstng methods that reure fully onneted graphs and may fal n ase of any ommunaton lnk falure, the proposed method s not suseptble to any sngle lnk falure, whh leads to a more relable ontrol framework. he rest of ths paper s outlned as follows: Seton II ntrodues the dstrbuted ontrol paradgm. he ooperate adapte-droop ontrol s dsued n Seton III. Seton IV, explans funtonalty of the oltage obserer. Global dynam and stat models are studed n Seton V. he ontroller performane s erfed usng a low-oltage d Mrogrd prototype n Seton VI. Seton VII onludes the paper. II. DISRIBUED COOPERAIVE COROL FRAMEWORK Mrogrd soures are mapped to a yber network as shown n Fg., where eah node represents an ate soure (or, onerter) and eah edge represents a ommunaton lnk for data exhange. he ommunaton graph mght hae a dfferent topology than the underlyng physal Mrogrd. hs yber onneton sets the groundwork for the ooperate ontrol paradgm, where neghbors nteratons an lead to a global onsensus. Aordngly, not all agents (onerters) n a large-sale dynam system need to be n dret ontat. Instead, eah agent only ommunates ts ontrol arables wth ts neghbors. hen, usng the neghbors data and ts loal measurements, the agent updates ts ontrol arables. he ooperate ontrol offers global onsensus of the desred arables, shall the ommunaton graph be desgned properly. A dreted graph (dgraph), aoated wth the yber layer n Mrogrd, s hghlghted n Fg..

4 Conerter ode Communaton etwork (Cyber Layer) Conerter Energy Soure Energy Soure Conerter Edge Conerter Energy Soure Physal Layer Energy Soure Bus Loal Load rans. Lne - Bus Bus 5 Bus rans. Lne - Bus Loal Load rans. Lne -5 rans. Lne -5 Loal Load Loal Load Remote Load 5 Fg.. General layout of a d Mrogrd nludng energy soures supplyng the grd and the yber network faltatng data exhange among soures. Suh a graph s usually represented as a set of nodes g g g V = {,,..., } G onneted a a set of edges E Ì V V, and an aoated adaeny matrx G G G A G = [ a ] Î. he Adaeny matrx A G ontans g g ommunaton weghts, where a > f (, ) Î E and a =, otherwse. a G s the ommunaton weght for data transfer from node to node. Here, a tme-narant g g adaeny matrx s aumed. = { (, ) Î E } G denotes the set of all neghbors of node,.e., f Î, then g g reees nformaton from. Howeer, n a dgraph, the lnk s not neearly reproal,.e., g mght not reee g n n nformaton from. he n-degree matrx D = dag{ d } G n s a dagonal matrx wth d = å a Î. Smlarly, the outdegree matrx s D = dag{ d out out out }, where d = G å a. Î n he Laplaan matrx s then defned as L = D - A, whose G G egenalues determne the global dynams [7]. he Laplaan matrx s balaned f the n-degree of eah node n out mathes ts out-degree,.e., D = D. Partularly, f the G G graph s undreted,.e., all lnks are bdretonal, then the g g Laplaan matrx s balaned. A dret path from to s a k seuene of edges that onnets the two nodes. A dgraph s sad to hae a spannng tree f t ontans a root node, from whh there exsts at least a dret path to eery other node. he physal layer of the Mrogrd, shown n Fg., nludes dspathable soures (nludng the power onerters), transmon lnes, and loads. he yber layer, omprsed of all ommunaton lnks, s spanned among the soures to faltate data exhange. hs s a sparse ommunaton network wth at least one spannng tree. In addton, the graph s hosen suh that n ase of any lnk falure the remanng network stll ontans at least one spannng tree. hs redundany s reured to ensure lnkfalure resleny. Eah onerter broadasts a data set, Y, to ts neghbors. he data pakage transmtted by node, Y = [, ], onts of two elements; ts estmate of the aerage oltage aro the Mrogrd,, and the measured per-unt urrent,. he term per-unt here ers to the urrent proded by the onerter dded by ts urrent,.e., I, where and I are the suppled and urrents of the th onerter, respetely. hs termnology of the per-unt s used here to represent loadng perentage of eah onerter. At the reeng ends of the ommunaton lnks, eah onerter k reees data from all ts neghbors, Y, Î, wth aoated ommunaton k weghts, a. hese weghts are desgn parameters and an be k onsdered as data transfer gans. III. ADAPIVE DROOP COROL he global oltage regulaton and proportonal load sharng are the two obetes of the seondary ontrol, whh reure proper oltage set pont agnment for nddual onerters. he proposed seondary ontroller s elabo n Fg. (a), where loal and neghbors nformaton are proeed to adust the loal oltage set pont, *. Cooperaton among onerters, at the seondary ontrol leel, helps to fnetune the oltage set ponts, *, and mtgate the urrent and oltage resdues. he oltage set pont for eah onerter s augmented wth two terms proded through ooperaton among onerters. hey are resulted from oltage and urrent regulators. Based on Fg. (a), the loal oltage set pont for an nddual onerter an be expreed as * d = - + d = - r + d, ()

5 Data Format: Ψ =, eghbors Data Control Sheme at ode Voltage Regulator Voltage Obserer () Current Regulator δ = ba ( ) ertary Control H () s G () s δ δr d Prmary Voltage Control r Adapte Droop ε Voltage Controller d Ψ =, o eghbors δr δ r (a) Proposed Seondary Control (b) Fg.. Proposed dstrbuted ontrol poly: (a) ooperate adapte droop ontrol for a sngle agent (onerter), (b) effet of adustable oltage orreton and rtual mpedane on the droop haraterzaton. d where,, d, and r are the global erene oltage, droop oltage, oltage orreton term, and the rtual mpedane of the th onerter, respetely. hs set pont s further adusted by a oltage lmter (see Fg. (a)) to mantan the oltages wthn an aeptable range. Fgure (b) elaborates how adustable oltage orreton term, d, and rtual mpedane, r, an nagate operatng pont of the onerter. he droop mehansm, whh generates the term r n (), haraterzes outt mpedane of the onerters and helps to share load, whh leads to the oltage drop aro the Mrogrd. he oltage orreton terms, d s, are augmented to the loal erene oltages to boost the oltage aro the Mrogrd. Aordngly, the ontroller ontans two modules; a oltage regulator and a urrent regulator. he oltage regulator at node onts of a oltage obserer and a PI ontroller, H () s. he oltage obserer at eah node estmates the aeraged oltage aro the Mrogrd, where s the estmaton at node. hs estmaton s then ompared wth the global erene oltage,, to generate the oltage orreton term, d. In ase of any msmath between and, the ontroller adusts d to elmnate the dsrepany. In the slanded mode of operaton, the global erene oltages, s, are typally dental and eual to the oltage of the Mrogrd. Howeer, n the grd-ted mode, the tertary ontrol sets a new oltage leel for the Mrogrd and relays the new erene alues to nddual onerters. A ooperate obserer wll proe the loal oltage measurement and the neghbors estmates to ealuate the aerage oltage aro the Mrogrd. Funtonalty of the obserer s dsued n detal n Seton IV. he urrent regulator at node prodes the nt to the droop mehansm. he droop mehansm haraterzes the onerter outt mpedane usng the rtual mpedane r. Vrtual mpedanes are onentonally ntalzed n reproal to the onerters urrent,.e., r = m I, where m s a desgn parameter and s dental for all onerters. Howeer, the dstrbuton lne mpedanes ompromse performane of the droop ontroller. hus, the droop gans are suggested to adapt aordng to the Mrogrd loadng ondton. o ths end, a ooperate urrent regulator s nluded n the seondary ontrol of any onerter, e.g., onerter, whh ompares loal per-unt urrent,, wth the weghted aerage of the neghbors per-unt urrents and fnds the urrent msmath, d, d = ( ). å ba - () Î where b s the ouplng gan between the oltage and urrent regulators. hs msmath s then fed to a PI ontroller, G () s, to generate an mpedane orreton term, d r, whh updates the rtual mpedane, rt () = r - drt (). () If the per-unt urrents of any two neghbors dffer, the urrent regulators of the orrespondng onerters respond and adust ther mpedane orreton terms to ahee balane. IV. VOLAGE OBSERVER he obserer s the prmary stage of the oltage regulator module, as shown n Fg.. It uses a dynam ooperate framework to proe loal and neghbors nformaton and estmate the aerage oltage aro the Mrogrd. Fgure explans the dstrbuted ooperate poly for global aeragng. he obserer at node reees ts neghbors estmates, s ( Î ). hen, the obserer updates ts own estmate,, by proeng the neghbors estmates and the loal oltage measurement,, t ò å ( ) ( t) = ( t) + a ( t) - ( t) d t. () Î hs updatng protool s erred to as dynam onsensus n the lterature [8]. As seen n (), the loal measurement,.e.,, s dretly fed nto the estmatng protool. hus, n ase of any oltage araton at node, the loal estmate,, mmedately responds. hen, the hange n propagates through the ommunaton network and affets all other estmatons.

6 5 a ( ) Voltage Obserer Communaton wth neghbors Communaton wth neghbors Fg.. Dynam onsensus protool for aeragng oltage aro a Mrogrd; estmatng poly at eah node. By dfferentatng (), = + a - = + a -d. å Voltage Obserer n ( ) å Î Î he global obserer dynam an be formulate aordngly, n = -( D - A ) = - L, G G (6) where the oltage measurement etor, = [,,..., ],, arres measured oltage of all nodes. Smlarly, the oltage estmaton etor, = [,,..., ], ontans the global, aerage oltage estmated by all nodes. Eualently, n the freueny doman, sv- () = s V-() -LV, (7) where V and V are the Laplae transforms of and, respetely. Euaton () mples that () = (). heore, (5) V I L V H V (8) - = ( + ) =, obs I Î and obs Communaton Graph ( ) a where H are the dentty matrx and the obserer transfer funton, respetely. Euaton (8) represents the global dynams of the oltage obserers. It s shown n [6] that f L s balaned, then all entres of the oltage estmaton etor,, onerge to a onsensus alue, whh s the true aerage oltage,.e., the aerage of all entres n. In other words, = Q =, (9) where Q Î s the aeragng matrx, whose elements are all eual to. Î s a etor whose elements are all eual to one. x and x represent the steady-state alue of the etor x Î and the aerage of all etor elements, respetely. V. GLOBAL MODEL DEVELOPME Global model deelopment s eental to study how the proposed ontroller affets the transent response and steadystate operaton of the Mrogrd. hs model an be used to tune the desgn parameters and ahee any desred dynam. A. Global Dynam Model Swthng nature of power eletron onerters an potentally result n a nonlnear system. Aordngly, smallsgnal methods are ommonplae for dynam haraterzaton rposes (e.g., a aeragng) [9]. Suh tools are sutable for relately small dsturbanes, e.g., as shown n [5], [5]. hus, small-sgnal modelng s onsdered here, where, eah arable x s wrtten as x = x + xˆ, where x and ˆx are the uesent and small-sgnal perturbaton parts, respetely. hs representaton helps to lnearly expre the droop oltage for the th onerter,, as d d d, d ˆ ( )( ) = + ˆ = r + rˆ +. () By negletng the seond-order term,.e., r ˆˆ», () an be redued to d ˆ ˆ = r + rˆ. () Let ˆ = [ ˆ, ˆ,..., ˆ ] and ˆ = [ ˆˆ,,..., ˆ ] be the small-sgnal etors of the oltages and atual suppled d urrents, respetely. Smlarly, ˆ, ˆ, D ˆ, ˆr, and ˆ * are olumn etors ontanng small-sgnal portons of the outt oltages, droop oltages, oltage orreton terms, rtual mpedanes, and loal oltage set ponts, respetely. r and are etors of uesent rtual mpedanes and urrents, respetely. I = dag{ I } s a dagonal matrx ontanng urrents of nddual soures. ˆV, Î, ˆV, d ˆV, DV, ˆ ˆR, and V ˆ * are the Laplae transforms of ˆ, î, d ˆ, ˆ, D ˆ, ˆr, and ˆ *, respetely. Based on Fg., ˆ ( ) H V ˆ - V = DV ˆ, () where H = dag{ H ( s)} s the oltage ontroller matrx. By usng (), rˆ =- drˆ, thus, - bgli - ˆ I =-R ˆ, () where G = dag{ G ( s)} s the urrent ontroller matrx. Substtutng the obserer transfer funton, H, from (8) n obs () yelds, D V ˆ = H V ˆ -H V ˆ. () ( ) In addton, () an be wrtten n the global form, ˆd ˆ V = r I+ R ˆ, (5) obs ( ) ( ) where (): s a transformaton that maps a etor to a dagonal matrx, ([ x, x,, x] ) dag{ x, x,, x}. (6) he small-sgnal erene oltage etor, V ˆ *, an be dered usng () and ()-(5),

7 6 d Vˆ * = Vˆ - Vˆ +DVˆ Vˆ ( r ) ˆI ( ) Rˆ H( Vˆ H Vˆ obs ) - ( I H) Vˆ ( r ) b( ) GLI ˆI = = HH Vˆ. obs ( ) (7) On the other hand, dynam behaor of any onerter wth losed-loop oltage regulator an be expreed as ˆ V = G () sv ˆ *, (8) where V ˆ and V ˆ * are the Laplae transforms of and ˆ ˆ *, respetely. G s the losed-loop transfer funton of the th onerter. he losed-loop transfer funtons are dered n [9] for a wde arety of onerters. Global small-sgnal dynam of the onerters an be found aordng to (8), ˆ ˆ * V = G V, (9) where G = dag{ G } s the onerters transfer funton matrx. By substtutng (9) n (7), ( G - + HH obs) Vˆ = () ˆ - I + H V - r + b GLI ˆI. ( ) ( ( ) ( ) ) For a d Mrogrd, t s a ommon prate to aume that the transmon/dstrbuton lne and load mpedanes are predomnantly rete [5]. Aordngly, one an use the Mrogrd ondutane matrx, g, to relate suppled urrents to the oltages, =g. () Small-sgnal perturbaton expands (), ˆ + = g + gˆ + ˆ. () ( ) ( )( ) he small-sgnal porton of the ondutane matrx, ĝ, models any small-sgnal hanges n the ondutane matrx, g, aused by load hange or transmon network reonfguraton. egletng the seond-order term,.e., gˆ ˆ», smplfes (), ˆ = g ˆ+ gˆ. () Or, eualently, n the freueny doman, ˆ ˆ ˆ I=g V+ G. () where Ĝ s the Laplae transform of ĝ. Substtutng () n () prodes the global dynam model of the Mrogrd wth the proposed ontroller n effet, - ( ( ( ) b( ) ) ) obs ( ) ( + ˆ - ( ) + b ( ) ) G - + HH + r + GLI g Vˆ = I H V r GLI Gˆ. - (5) Euaton (5) mples that the Mrogrd s systematally a mult-nt-mult-outt plant where ˆV and Ĝ are the nts and ˆV and Î are the outts. he global dynam model n (5) formulates the transfer funtons from eah nt to the prmary outt, ˆV. B. Desgn Approah For a gen Mrogrd, the matrx of onerters losedloop transfer funtons, G, and the urrent ratng matrx, I are known. he ommunaton graph needs to be a onneted graph wth the mnmal redundany defned n Seton III, where no sngle lnk falure an ompromse ommunaton onnetty. Weghts of the ommunaton lnks, a, and, thus, the Laplaan matrx, L, may, then, be hosen to prode any desred dynam response for the oltage obserers by ealuatng (8). It should be noted that the seleton of the ommunaton weghts must satsfy a balaned Laplaan matrx. For the gen Mrogrd wth known transmon/ dstrbuton network, one an ealuate g aumng base loads at all onsumpton termnals. Aordngly, uesent oltage and urrent etors ( and, respetely) an be found by terately solng (6)-(7), =g, (6) = I (7) - = n, where n s a poste real number. he desgner may ntalze the rtual mpedanes as r = m é I, I,, I ù, ê ë ú û (8) where m s a poste salar desgn parameter [7]. he adapte-droop mehansm adusts the rtual mpedanes to prode proportonal load sharng. Due to the lne mpedanes, ths adustment results n dfferent alues than the ntal alues,.e., r ¹ r. Howeer, empral studes n Seton VI wll show that the uesent rtual mpedane etor remans almost ntat for arous operatng ondtons. hus, one an run a steady-state numeral analy to fnd r for the base load ondton and further use t n the desgn proedure. Gen the Laplaan matrx, L, the obserer transfer funton, H, the onerters transfer funton matrx, G, obs and all other onstant etors n (5), one an use ths euaton to desgn the oltage and urrent ontroller matres ( H and G, respetely) and the ouplng gan, b, to prode any desred asymptotally stable dynam response for the entre Mrogrd, where all poles of the transfer funtons extrated from (5) le on the Open Left Hand Plane (OLHP). C. Steady-State Analy Steady-state analy of the Mrogrd operaton s eental to ensure that the ooperate ontrollers satsfy both operatonal reurements; the global oltage regulaton and the proportonal load sharng. Sne the onerters oltages math the Mrogrd oltage, wth no lo of generalty, one an aume = (9), where s the Mrogrd oltage. It s also aumed that the ontrol parameters are properly tuned, based on the desgn approah n Seton V-B, to stablze oltage and urrent throughout the Mrogrd.

8 7 Let s aume that the Mrogrd oltages and urrents are n the steady state for t ³ t. he oltage and urrent ontroller of the th onerter an be expreed as P I P I H = H + H s and G = G + G s, respetely, P P I I where H and G are the proportonal and H and G are the ntegral gans. One an show that, wth stable oltages, all oltage obserers onerge to the true aerage oltage,.e., æ ö = ç å =, () çè = ø where x represents the steady-state alue of the arable x. Aordng to Fg., for t ³ t one an wrte, D = W ( t ) + H ( - ) P () + H ( - )( t -t ), I where W ( t ) s a etor that arres ntegrator outts of the oltage regulators at t = t. Smlarly, D r = W( t ) + G (-bl ) r P () + G (-bl )( t-t ), I where W ( t ) s a etor that arres ntegrator outts of the r * urrent regulators at t = t. In the steady state, =, thus, aordng to (), ( ) ( ) = - r +D r r. () = - -D +D By substtutng ()-() n (), = ( b( ( t t ) P I ) ( t ) r ) ( )( H H ( t t ) P I ) W ( t ). - r + G + G - L - W () Euaton () holds for all t ³ t. hus, the tme aryng term n () s zero. Aordngly, ( - ) = ( b ) H GL (5). I I One an see that f G s a dagonal matrx and b a real number then, for any etor x, ( b ) b ( ). Gx = G x (6) he transformaton property n (6) helps to rewrte (5), ( ) ( ) L I = - G H (7) b - -. I I Both ( L ) and I are dagonal matres and, thus, Aordngly, ( ) ( ) L I = I L (8). ( ) ( ) L = - b I G H I I = ( - ) éu u u ù êë úû I I /( ) =, then, (9) mples,,,. (9) u = H bg I >. If any of the urrents s =. where zero, e.g., Fg.. DC Mrogrd prototype: (a) Int a soures, (b) Buk onerters drng eah soure, () Loal and remote loads, (d) dstrbuton lne, (e) dsapce ontrol board (DS), (f) Programmng/montorng PC. Otherwse, one an safely aume that all urrents are poste (.e., > ); soures only deler power. Usng (9), é u u u ù L = ( - ),,,. () êë úû wth the balaned Laplaan matrx, L, Aordngly, L ( ) = u = - å, = >. () = () whh, eualently, satsfes the global oltage regulaton,.e., the ontroller suefully regulates the aerage oltage of the Mrogrd,, at the alue,. For any etor x one an nestgate that ( x) = x. () Multplyng both sdes of (9) from left by ( ) ( ) =, one an wrte L = - u =, () whh s a uadrat euaton. It s shown n Appendx I that = k, (5) s the only soluton to the uadrat euaton n (), where k s a poste real number. Euaton (5) ensures onsensus of the per-unt urrents or, eualently, aheement of proportonal load sharng. å VI. EXPERIMEAL VERIFICAIO A low-oltage d Mrogrd, wth the struture shown n Fg., s prototyped. Fgure shows the test benh where four adustable solated a soures are used as energy soures. Eah soure s dren by a buk onerter wth an nt retfer.

9 8 (a) (b) () (d) Fg. 5. Alternate ommunaton topologes formng a onneted graph wth: (a) o redundant lnk, (b) Suboptmal lnk redundany, () Optmal lnk redundany, and (d) full onneton. he onerters hae smlar topologes but dfferent ratngs,.e., the urrents of the frst and the fourth onerters are twe those for the other two onerters. Eah dstrbuton lne s bult usng a p rut model. he Mrogrd has fe onsumpton termnals; four to supply loal loads and one to supply a remote load, as seen n Fg.. Although dfferent oltage leels are poble [5], [5], a 8 V system s onsdered here. he typal aeptable oltage deaton s about 5% of the oltage [] and, thus, the oltage lmters are set wth e =.5 V. Eletral and ontrol parameters of the Mrogrd are proded n Appendx II. Alternate ommunaton topologes for a group of four agents are represented n Fg. 5, where all lnks are aumed bdretonal to feature a balaned Laplaan matrx. Despte arryng spannng tree, not all alternates satsfy the ommunaton redundany reured for the safe operaton (lnk falure resleny) of the proposed method. In other words, some topologes are suseptble to lose onnetty n the ase of a sngle lnk falure. For example, f any of the lnks hghlghted n red n Fgs. 5(a) or 5(b) s lost, the orrespondng graph loes ts onnetty, whh renders the whole ontrol mehansm noperable. Howeer, the rular ommunaton struture n Fg. 5() s the sparsest network where no sngle lnk falure an ompromse the graphal onnetty. Fgure 5(d) shows a fully onneted graph, whh prodes a smlar redundany feature yet laks sparsty. heore, the ommunaton struture n Fg. 5() s onsdered for ths study. he ommunaton hannels are aumed deal and are modeled n the dsapce. Wrele or fber opt networks may be used for physal mplementaton of the data network. he effet of non-dealtes suh as nose, lmted bandwdth, hannel delay, paket drop, et. s studed n [5]. Moreoer, onsensus protools are talored for non-deal data networks n [55] [57], whose applaton n the power dstrbuton systems wll be the subet of future studes. he ontrol approah s bult n Smulnk on a programmng/montorng PC whh s lnked to a dspace ontrol board (DS). he PC omples the Smulnk model and, aordngly, programs the DS. It also generates a arable desrpton fle further used by the dspace montorng software, ControlDesk 5., to prode a le ew of any arable. When the proposed ontrol methodology s n effet, the ControlDesk enables the desgner to tune any ontrol parameter onlne and montor the system performane. A. Constant Droop ersus Adapte Droop Fgure 6 omparately studes the performane of the proposed methodology. he Mrogrd s ntally ontrolled usng the onentonal droop ontroller, where a fxed droop mpedane s used,.e., r() t = r. As seen n Fg. 6(a), t leads to oltages le than the desred alue,.e., = 8 V. In addton, although the ntal alues of the droop gans are desgned reproal to the onerters urrents, the transmon lne effet has learly napatated the droop mehansm, resultng n a poor load sharng where onerters wth dental ratngs supply dfferent urrents (see Fg. 6(b)). he proposed ontroller s engaged at t =. s. Conseuently, the oltages are boosted aro the Mrogrd and the aerage oltage s fnely regulated at the set pont,.e., = 8 V. Fgure 6(b) shows that the proportonal load sharng s also arred out, where the frst and the fourth onerters arry twe the urrent as the other two onerters. Dynam performane of the ontroller an be tuned by adustng the ommunaton weghts (or, eualently, entres of the Adaeny matrx). In omparson wth alternate soluton n [6], t an be seen that the dstrbuted adapte droop has proded a faster load sharng; almost twe as fast as the method n [6]. he oltage obserers s studed n Fg. 6(), where a good agreement s reported between the true aerage oltage,, and the nddual estmated alues, s. Fgure 6(d) exprees how the proposed ontroller sets oltage orreton terms, d s, to boost the oltage aro the Mrogrd and oerome the natural oltage drop aused by the droop mehansms. Fgure 6(e) shows how the urrent ontroller adusts the rtual mpedanes, r s, to prode proportonal load sharng. B. Load Varaton he ontroller performane n ase of load hange s studed n Fg. 7, where the remote load at fe, R 5, s hanged n step between W and W. ght oltage regulaton and load sharng an be obsered n Fgs. 7(a) and 7(b). Exellent transent load sharng s also noteable n Fg. 7(b). Estmatons of the aerage oltage aro the Mrogrd are plotted n Fg 7() where a good agreement between the true and estmated alues ( and s, respetely) an be seen. Comparng Fgs. 7(d) and 7(e), one an obsere that load hange mostly affets oltage orreton terms, d s, and has a neglgble mpat on the rtual mpedanes. C. Plug-and-Play Capablty Fgure 8 studes plug-and-play apablty of the proposed method and ts performane n the ase of a onerter falure. As seen, when the seond onerter fals at t = 7. s, the ontroller adusts the oltages to regan the global oltage regulaton. When the Conerter fals, the oltage at the seond,, s no longer aalable.

10 9 Voltage (V) Proposed Controller Voltage (V) Droop Controller.9 s Step load hange n the remote termnal (a) 9 me (s) (a) me (s) Current (A) 5 Droop Controller Proposed Controller Current (A) 5 R = Ω Ω R = Ω Ω 5 5,, (b) 9 me (s) (b) me (s) Estmated Voltage (V) Estmated Voltage (V) () 9 me (s) () me (s) Voltage Correton (V) δ δ δ δ Droop Controller Proposed Controller Voltage Correton (V) Step load hange n the remote termnal δ δ δ δ (d) 9 me (s) (d) me (s) Vrtual Impedane (Ohm) r r r r Droop Controller Proposed Controller Vrtual Impedane (Ohm) Step load hange n the remote termnal r r r r (e) 9 me (s) (e) me (s) Fg. 6. Comparate studes of the onentonal droop ontrol and the dstrbuted adapte-droop ontrol: (a) ermnal oltages, (b) Suppled urrents, () Estmatons of the aerage oltage, (d) Voltage orreton terms, (e) Vrtual mpedanes. Fg. 7. Performane of the dstrbuted adapte-droop ontroller n a ase of load hange: (a) ermnal oltages, (b) Suppled urrents, () Estmatons of the aerage oltage, (d) Voltage orreton terms, (e) Vrtual mpedanes.

11 Voltage (V) 55 5 Voltage (V) Lnk - Fals 5 (a) Current (A) me (s) Conerter Fals Conerter Plugs n (a) Current (A) me (s) R = Ω Ω 5 R = Ω Ω 5 (b) 6 8 me (s) Fg. 8. Conerter falure and plug-and-play studes: (a) ermnal oltages, (b) Suppled urrents. hus, the ontroller aerages the three remanng measurements,.e.,,, and, and regulates ths new aerage at the erene alue. he ontroller also readusts the load sharng among the remanng onerters. It should be noted that a onerter falure also mples lo of all ommunaton lnks attahed to that partular onerter. Aordngly, falure of the seond onerter automatally renders the lnk - (between nodes and ) and lnk - noperable. Howeer, the remanng lnks stll form a onneted graph wth balaned Laplaan matrx (see Fg., yber layer) and, thus, the whole ontrol system s stll funtonal. hen, the Conerter s plugged bak at t =.6 s. As seen, the ontroller has properly updated the load sharng and global oltage regulaton, afterwards. D. Lnk-falure Resleny Resleny to a sngle lnk falure s studed next n Fg. 9. he orgnal ommunaton graph n Fg. s desgned to arry a mnmal redundany, so no sngle lnk falure an ause lo of onnetty n the graph. hus, the ontrol system shall reman operatonal. As seen n Fg. 9, the lnk - has faled at t =. s, but t does not hae any mpat on oltage regulaton or load sharng. Controller response to the step load hange n the remote load s also studed wth the faled lnk, where a satsfatory performane an be seen. It should be noted that the reonfguraton aused by the lnk falure affets the Laplaan matrx and, thus, the whole system dynam but not the steady-state performane. Generally, any lnk falure lmts nformaton flow and an slghtly slow down the transent response. Smlar to Fg. 7(e), Fg. 9(d) demonstrates neglgble mpat of load hange on the rtual mpedanes. Howeer, by omparson, Fg. 7(e) shows more stable mpedanes than those of Fg. 9(d). (b) Voltage Correton (V) () Vrtual Impedane (Ohm) (d) me (s) 6 8 me (s) 6 8 me (s) Fg. 9. Lnk-falure resleny: (a) ermnal oltages, (b) Suppled urrents, () Voltage orreton terms, (d) Vrtual mpedanes. hs obseraton onludes that hgher graphal onnetty results n more stable droop mpedanes. In addton, small aratons of the rtual mpedane terms n Fgs. 7(e) and 9(d) mples that the deeloped small-sgnal model n Seton V-A s approprate for modelng and stablty analy of the proposed adapte droop mehansm. VII. COCLUSIO δ δ δ δ An adapte droop-based dstrbuted seondary ontroller s proposed for d Mrogrds. he ontroller on eah onerter omprses two modules; the oltage regulator and the urrent regulator. he oltage regulator uses a ooperate oltage obserer to estmate the global aerage oltage. hs estmaton s then further used to boost the loal oltage set pont to prode global oltage regulaton. he urrent r r r r

12 regulator at eah soure ompares loal per-unt urrent wth ts neghbors and, aordngly, adusts the loal rtual mpedane to arry out proportonal load sharng. hs ontrol paradgm uses a sparse ommunaton network for data exhange among onerters. Studes show that the proposed ooperate ontrol prodes prese global oltage regulaton and proportonal load sharng. Plug-and-play apablty and lnk-falure resleny of the ontrol struture are also erfed through experments. It s also dsued that the droop oeffents show slght aratons n response to load aratons, whh makes the small-sgnal modelng a able approah for stablty analy of the proposed ontroller. Future works fous on two man areas: ) Study of alternate ommunaton nfrastrutures, effets of hannel non-dealtes (e.g., delay or paket drop), and, onseuently, to talor onsensus protools to aount for non-deal data network; ) Deelopment of dstrbuted optmzaton tehnues for ost optmzaton n the tertary ontrol leel. APPEDIX I: SOLUIO O HE QUADRAIC EQUAIO heorem A.: Aume L s the Laplaan matrx of a ommunaton graph wth at least one spannng tree. If L s balaned then, the only soluton to the uadrat euaton xlx = s x= k, where k s a real number. Proof: he uadrat form, xlx, s a real number. hus, æ ö L+ L x Lx = ( x Lx) = x L x = x ç x. (A.) çè ø Let s defne the o-laplaan matrx as L ( L + L ), whh s a symmetr matrx. Aume L = [ l ] Î and L = [ l ] Î. hen, ìï ï l = l ³, í (A.) ï l = l + l = l, ¹ ïî Sne the Laplaan matrx, L, s balaned, l =- ål =- å l =- å l. (A.) Î = ( ¹ ) = ( ¹ ) =- ( + ) =- =- = ( ¹ ) = ( ¹ ) = ( ¹ ) Aordngly, one an formulate dagonal elements of the o- Laplaan matrx, L, l å l l å l å l. (A.) he uadrat euaton an be expanded usng (A.) x Lx = x L x =, = åxl + åxlx = ¹ æ ö =- å l x xl x ç å + å = = ( ¹ ) ¹ çè ø = =- - = å( xl x x l x l xl x ) < ål ( x x ) < å xl x (A.5) where x = [ x, x,, x ]. All off-dagonal entres of the o- Laplaan matrx, L, are non-poste. hus, (A.5) holds f and only f for eery two onneted nodes,.e., a >, x = x. he ommunaton graph has a spannng tree and, thus, has a root node, from whh there exsts a path to eery other node. Aume that g s the root node then, for any other g g node,, one an fnd a seuene of nodes onnetng to, g g g g g. k l (A.6) Gen that for eery two onneted nodes aoated entres of the etor x are eual, one an onlude x = x = = x = x. k l hus, the etor x has eual entres,.e., a real number. APPEDIX II (A.7) x= k, where k s Eah of the underlyng buk onerters has L = 6 mh and C =. mf and operates wth F = 6 khz swthng s freueny. Impedanes of the transmon lnes are Z = Z = Z and Z = Z = Z, where the base b mpedane s Z = (5 mh) 5 s. Impedanes b of the loal b loads are R = W and R = R = R = W. Voltages of the (retfed) nt soures are V s = V s = V and V = V = 8 V. he ontrol parameters are as follow, s s I = dag{6,,,6}, b =.5, P I (A.8) (A.9) H =. I, H =.5 I, (A.) G =. I, G = 5 I, (A.) P I é ù é.5 ù A =,. r = G (A.) ê ú ê.5 ë û ë ú û REFERECES [] D. Chen and L. Xu, Autonomous d oltage ontrol of a d Mrogrd wth multple slak termnals, IEEE rans. Power Syst., ol. 7, no., pp , o.. [] M. Datta,. Senyu, A. Yona,. Funabash, and C. H. Km, A freueny-ontrol approah by photoolta generator n a PV-desel hybrd power system, IEEE rans. Energy Coners., ol. 6, no., pp , Jun.. [] S. eleke, M. E. Baran, A. Q. Huang, S. Bhattaharya, and L. Anderson, Control strateges for battery energy storage for wnd farm dspathng, IEEE rans. Energy Coners., ol., no., pp. 75 7, Sept. 9. [] Y. K. Chen, Y. C. Wu, C. C. Song, and Y. S. Chen, Desgn and mplementaton of energy management system wth fuzzy ontrol for d Mrogrd systems, IEEE rans. Power Eletron., ol. 8, no., pp , Apr..

13 [5] A. Kwasnsk and C,. Onwuhekwa, Dynam behaor and stablzaton of d Mrogrds wth nstantaneous onstant-power loads, IEEE rans. Power Eletrons, ol. 6, pp. 8-8, Marh. [6] R. S. Balog, W. Weaer, and P.. Kren, he load as an energy aet n a dstrbuted d Smartgrd arhteture, IEEE rans. Smart Grd, ol., pp. 5-6, Marh. [7] J. M. Guerrero, J. C. Vasuez, J. Matas, L. G. de Vnuña, and M. Castlla, Herarhal ontrol of droop-ontrolled a and d Mrogrds a general approah toward standardzaton, IEEE rans. Ind. Eletron., ol. 58, pp. 58 7, Jan.. [8] M. Saagheb, A. Jallan, J. C. Vasuez, and J. M. Guerrero, Seondary ontrol sheme for oltage unbalane ompensaton n an slanded droop-ontrolled Mrogrd, IEEE rans. Smart Grd, ol., no., pp , Jun.. [9] X. Lu, J. M. Guerrero, K. Sun, J. C. Vasuez, R. eodoresu, and L. Huang, Herarhal ontrol of parallel a-d onerter nterfaes for hybrd Mrogrds, IEEE rans. Smart Grd, ol. 5, pp , Mar.. [] C. Ln, P. Wang, J. Xao, Y. ang, and F. H. Choo, Implementaton of herarhal ontrol n d Mrogrds, IEEE rans. Ind. Eletron., ol. 6, pp., Aug.. [] L. Xu and D. Chen, Control and operaton of a d Mrogrd wth arable generaton and energy storage, IEEE rans. Power Del., ol. 6, no., pp. 5 5, Ot.. [] H. Kanhe, D. Lu, F. Colas, V. Lazaro, and B. Franos, Energy management and operatonal plannng of a Mrogrd wth a PV-based ate generator for smart grd applatons, IEEE rans. Ind. Eletron., ol. 58, no., pp , Ot.. [] C. Chen, S. Duan,. Ca, B. Lu, and G. Hu, Optmal alloaton and eonom analy of energy storage system n Mrogrds, IEEE rans. Power Eletron., ol. 6, no., pp , Ot.. []. Zhou and B. Franos, Energy management and power ontrol of a hybrd ate wnd generator for dstrbuted power generaton and grd ntegraton, IEEE rans. Ind. Eletron., ol. 58, no., pp. 95, Jan.. [5] P. C. Loh, D. L, Y. K. Cha, and F. Blaaberg, Autonomous ontrol of nterlnkng onerter wth energy storage n hybrd a d Mrogrd, IEEE rans. Ind. Appl., ol. 9, no., pp. 7 8, May/Jun.. [6] S. Anand, B. G. Fernandes, and J. M. Guerrero, Dstrbuted ontrol to ensure proportonal load sharng and mproe oltage regulaton n lowoltage d Mrogrds, IEEE rans. Power Eletron., ol. 8, no., pp. 9 9, Apr.. [7] J. Shönberger, R. Duke, and S. D. Round, DC- sgnalng: a dstrbuted ontrol strategy for a hybrd renewable anogrd, IEEE rans. Ind. Eletron., ol. 5, no. 5, pp. 5 6, Ot. 6. [8] D. Chen, L. Xu, L. Yao, DC oltage araton based autonomous ontrol of d Mrogrds, IEEE rans. Power Del., ol. 8, no., pp , Apr.. [9] P. Karlon and J. Senon, DC oltage ontrol for a dstrbuted power system, IEEE rans. Power Eletron., ol. 8, no. 6, pp. 5, o.. [] Y. Ito, Y. Zhongng, and H. Akag, DC Mrogrd based dstrbuton power generaton system, n Pro. th Int. Power Eletron. Moton Control Conf. (IPEMC),, pp [] X. Lu, K. Sun, J. M. Guerrero, J. C. Vasuez, and L. Huang, State-ofharge balane usng adapte-droop ontrol for dstrbuted energy storage systems n d Mrogrd applatons, IEEE rans. Ind. Eletron., ol. 6, no. 6, pp. 8 85, June. [] R. A. F. Ferrera, H. A. C. Braga, A. A. Ferrera, and P. G. Barbosa, Analy of oltage droop ontrol method for d Mrogrds wth Smulnk: modelng and smulaton, n Pro. th IEEE/IAS Int. Conf. Ind. Appl. (IDUSCO),, pp. 6. [] J. A. P. Lopes, C. L. Morera, and A. G. Madurera, Defnng ontrol strateges for Mrogrds slanded operaton, IEEE rans. Power Syst., ol., no., pp. 96 9, May 6. [] A. uladhar, H. Jn,. Unger, and K. Mauh, Control of parallel nerters n dstrbuted a power systems wth onsderaton of lne mpedane effet, IEEE rans. Ind. Appl., ol. 6, no., pp. 8, Jan./Feb.. [5] Y. Mohamed and E. F. El-Saadany, Adapte deentralzed droop ontroller to presere power sharng stablty of paralleled nerters n dstrbuted generaton Mrogrds, IEEE rans. Power Eletron., ol., no. 6, pp , o. 8. [6] J. Km, J. M. Guerrero, P. Rodrguez, R. eodoresu, and K. am, Mode adapte droop ontrol wth rtual outt mpedanes for an nerter-based flexble a Mrogrd, IEEE rans. Power Eletron., ol. 6, no., pp , Mar.. [7]. R. Chaudhur and B. Chaudhur, Adapte droop ontrol for effete power sharng n mult-termnal d (MDC) grds, IEEE rans. Power Syst., ol. 8, no., pp. 9, Feb.. [8] S. Y. Yang, C. W. Zhang, X. Zhang, R. X. Cao, and W. X. Shen, Study on the ontrol strategy for parallel operaton of nerters based on adapte droop method, n Pro. IEEE Conf. Ind. Eletron.s Appl., 9, pp. 5. [9] J. Yuan, F. Gao, H. Gao, H. Zhang, and J. Wu, An adapte ontrol strategy for parallel ope photoolta nerters, n Pro. 7th Int. Power Eletron. Moton. Control Conf. (IPEMC),, pp [] R. Maumder, A. Ghosh, G. Ledwh, F. Zare, Power system stablty and load sharng n dstrbuted generaton, n Pro. IEEE Jont Int. Conf. Power Syst. ehnol., 8, pp. 6. [] W. Yao, M. Chen, M. Gao, and Z. Qan, A wrele load sharng ontroller to mproe the performane of parallel-onneted nerters, n Pro. IEEE rd Annu Appled Power Eletron. Conf. Expo. (APEC), 8, pp [] W. Yao, M. Chen, M. Gao, and Z. Qan, Deelopment of ommunatonle hot-swap parallelng for sngle-phase UPS nerters based on adapte droop method, n Pro. IEEE rd Annu Appled Power Eletron. Conf. Expo. (APEC), 9, pp [] J. C. Vasuez, J. M. Guerrero, E. Gregoro, P. Rodrguez, R. eodoresu, F. Blaaberg, Adapte-droop ontrol appled to dstrbuted generaton nerters onneted to the grd, n Pro. IEEE Int. Symp. Ind. Eletron. (ISIE), 8, pp. 5. [] J. C. Vasuez, J. M. Guerrero, A. Luna, P. Rodrguez, and R. eodoresu, Adapte-droop ontrol appled to oltage-soure nerters operatng n grd-onneted and slanded modes, IEEE rans. Ind. Eletron., ol. 56, no., pp , Ot. 9. [5] A. D. Erdogan and M.. Aydemr, Applaton of adapte-droop method to boost onerters operatng at the outt of fuel ells, n Pro. Int. Ele. Eletron. Eng. Conf. (ELECO), 9, pp.i- I-5. [6]. Drage, J. M. Guerrero, J. C. Vasuez, and D. Skrle, Supersory ontrol of an adapte-droop regulated d Mrogrd wth battery management apablty, IEEE rans. Power Eletron., ol. 9, no., pp , Feb.. [7] H. Lu, Z. Hu, Y. Song, and J. Ln, Deentralzed ehle-to-grd ontrol for prmary freueny regulaton onsderng hargng demands, IEEE rans. Power Syst., ol. 8, no., pp. 8 89, Aug.. [8] S. Anand and B. G. Fernandes, Steady state performane analy for load sharng n d dstrbuted generaton system, n Pro. th Int. Conf. Enronment Elet. Eng. (EEEIC),, pp.. [9] Y. W. L and C.. Kao, An aurate power ontrol strategy for powereletrons-nterfaed dstrbuted generaton unts operaton n a low oltage mult- Mrogrd, IEEE rans. Power Eletron., ol., no., pp , De. 9. [] J. He and Y. W. L, Analy, desgn and mplementaton of rtual mpedane for power eletrons nterfaed dstrbuted generaton, IEEE rans. Ind. Appl., ol. 7, no. 6, pp , o./de.. [] W. Qu and Z. Lang, Pratal desgn onsderatons of urrent sharng ontrol for parallel VRM applatons, n Pro. th Annu. Appl. Power Eletron. Conf. Expo., 5, pp [] H. Laaksonen, P. Saar, and R. Komulanen, Voltage and freueny ontrol of nerter based weak LV network Mrogrd, n Pro. Int. Conf. Future Power Syst., 5, pp. 6. []. L. Vandoorn, B. Meersman, L. Degroote, B. Renders, and L. Vandeelde, A ontrol strategy for slanded Mrogrds wth d-lnk oltage ontrol, IEEE rans. Power Del., ol. 6, no., pp. 7 7, Apr.. [] Q. Shafee, J. M. Guerrero, and J. C. Vasuez, Dstrbuted seondary ontrol for slanded Mrogrds A noel approah, IEEE rans. Power Eletron., ol. 9, no., pp. 8, Feb.. [5] X. Lu, J. M. Guerrero, K. Sun, and J. C. Vasuez, An mproed droop ontrol method for d Mrogrds based on low bandwdth ommunaton wth d oltage restoraton and enhaned urrent sharng auray, IEEE rans. Power Eletron., ol. 9, no., pp. 8 8, Apr.. [6] V. asran, S. Moayed, A. Daoud, and F. L. Lews, Dstrbuted ooperate ontrol of d Mrogrds, IEEE rans. Power Eletron., to be blshed, DOI:.9/PEL..579.

14 Vahdreza asran (S ) reeed the B.S. and M.S. degrees n eletral engneerng from Sharf Unersty of ehnology, ehran, Iran, n 7 and, respetely. He s urrently workng toward the Ph.D. degree at he Unersty of exas at Arlngton, Arlngton, X, USA. Hs researh nterests nlude the modelng and ontrol of power eletrons and eletr dres, mrogrd ontrol, transportaton eletrfaton, and renewable and sustanable energy systems. Mr. asran was the repent of the gold medal at the th atonal Mathemats Olympad n n ehran, Iran, and the bronze medal at the nd Slk Road Mathemats Competton n n urkey. He was also the repent of the Iranan atonal Eltes Foundaton Fellowshp for 8 and the Carrzo Ol & Gas In. Graduate Researh Fellowshp for. Al Daoud (S M ) s urrently an Astant Profeor at the Eletral Engneerng department of the Unersty of exas-arlngton. He reeed hs Ph.D. n Eletral and Comter Engneerng from the Unersty of Illnos, Urbana-Champagn, USA, n. He worked for Solar Brdge ehnologes, exas Instruments In., and Royal Phlps Eletrons. He s an Aoate Edtor for IEEE RASACIOS O IDUSRY APPLICAIOS and IEEE RASACIOS O RASPORAIO ELECRIFICAIO. He was a guest edtor for IEEEE RASACIOS O SMARGRID, speal ue on Smart DC dstrbuton Systems; IEEE RASACIOS O VEHICULAR ECHOLOGY, speal ue on Adaned modelng, smulaton, ontrol and optmzaton paradgms for ehular power systems; and IEEE RASACIOS O EERGY COVERSIO, speal ue on Adaned dstrbutedd ontrol of energy onerson dees and systems. Hs researh nterests are arous aspets of modelng and ontrol of power eletrons and fnte-nerta power systems. [7] R. Olfat-Saber and R. M. Murray, Consensus problems n networks of agents wth swthng topology and tme-delays, IEEE rans. Autom. Control, ol. 9, no. 9, pp. 5 5, Sept.. [8] D. P. Spanos, R. Olfat-Saber, and R. M. Murray, Dynam onsensus for moble networks, n Pro. 6th Int. Fed. Aut. Control (IFAC), 5, pp. 6. [9] R. W. Erkson and D. Maksmo, Fundamental of Power Eletrons, nd Ed. orwell, MA: Kluwer,. [5] V. asran, Y. Karm, A. Daoud, M. R. Zolghadr, M. Ahmadan, and S. Moayed, Dynam model deelopment and arable swthng- IEEE rans. Ind. Appl., ol. 9, no. 6, pp , o./de.. [5] S. Moayed, V. asran, F. L. Lews, and A. Daoud, eam-orented load sharng n parallel d-d onerters IEEE rans. Ind. Eletron., to freueny ontrol for DCVM Cúk onerters n PFC applatons, be blshed, DOI:.9/IA [5] J. M. Guerrero, M. Chandorkar,. Lee, and P. C. Loh, Adaned ontrol arhtetures for ntellgent Mrogrds part I: deentralzed and herarhal ontrol, IEEE rans. Ind. Eletron., ol. 6, no., pp. 5 6, Apr.. [5] D. lon and A. Sannno, Effeny analy of low- and medum oltage d dstrbuton systems, n Pro. IEEE Power Eng. So. Gen. Meetng,, pp. 5. [5] S. Anand and B. G. Fernandes, Optmal oltage leel for d Mrogrds, n Pro. 6th Annu. Conf. IEEE Ind. Eletron. So. (IECO),, pp. 9. [55]. Amelna and A. Fradko, Consensus problem n stohast network systems wth swthed topology, nose, and delay, n Pro. th Int. Conf. etwork,, pp. 8. [56] R. Olfat-Saber and R. M. Murray, Consensus problems n networks of agents wth swthng topology and tme-delays, IEEE rans. Automat. Control, ol. 9, no. 9, pp. 5 5, Sept.. [57] S. Kar and J. M. F. Moura, Dstrbuted onsensu algorthms n sensor networks wth mperfet ommunaton: lnk falures and hannel nose, IEEE rans. Sgnal Proe., ol. 57, no., pp , Jan. 9. Frank L. Lews (F 9) s urrently wth he Unersty of exas at Arlngton (UA), Arlngton, X, USA. He works n feedbak ontrol, renforement learnng, ntellgent systems, and dstrbuted ontrol systems. He s the author of 7 ournal papers, 75 onferene papers, 5 books, hapters, and ournal speal ues and s the holder of 6 U.S. patents. Dr. Lews s a member of the atonal Aademy of Inentors, a Fellow of IFAC and the U.K. Insttute of Measurement and Control, a Profeonal Engneer n the State of exas, and a U.K. Chartered Engneer. He s also a UA Dstngushed Sholar Profeor, a UA Dstngushed eahng Profeor, and the Mon-O Donnell Char at he Unersty of exas at Arlngton Researh Insttute. He s also an IEEE Control Systems Soety Dstngushed Leturer. He reeed the Fulbrght Researh Award, SF Researh Intaton Grant, ASEE erman Award, Internatonal eural etwork Soety Gabor Award n 9, and U.K. Insttute of Measurement and Control Honeywell Feld Engneerng Medal n 9. He reeed the IEEE Comtatonal Intellgene Soety eural etworks Poneer Award n. He was a Dstngushed Foregn Sholar of the anng Unersty of Sene and ehnology. He was also a Proet Profeor at ortheastern Unersty, Chna. He reeed the Outstandng Sere Award from the Dallas IEEE seton and was seleted as Engneer of the Year by the Fort Worth IEEE Seton. He was lsted n the Fort Worth Busne Pre op Leaders n Manufaturng. He reeed the IEEE Regon 5 Outstandng Engneerng Eduator Award and the UA Graduate Dean s Exellene n Dotoral Mentorng Award. He was eleted to the UA Aademy of Dstngushed eahers n. He sered on the AE Commttee on Spae Staton n 995. He s the Foundng Member of the Board of Goernors of the Medterranean Control Aoaton. He helped wn the IEEE Control Systems Soety Best Chapter Award (as Foundng Charman of the DFW Chapter), the atonal Sgma X Award for Outstandng Chapter (as Presdent of the UA Chapter), and the U.S. SBA bbetts Award n 996 (as Dretor of ARRI s SBIR Program). Josep M. Guerrero (S -M -SM 8) reeed the B.S. degree n teleommunatons engneerng, the M.S. degree n eletrons engneerng, and the Ph.D. degree n power eletrons from the ehnal Unersty of Catalona, Barelona, n 997, and, respetely. Sne, he has been a Full Profeor wth the Department of Energy ehnology, Aalborg Unersty, Denmark, where he s responsble for the Mrogrd Researh Program. From he s a guest Profeor at the Chnese Aademy of Sene and the anng Unersty of Aeronauts and Astronauts; and from he s har Profeorr n Shandong Unersty. Hs researh nterest s orented to dfferent mrogrd aspets, nludng power eletrons, dstrbuted energy-storage systems, herarhal and ooperate ontrol, energy management systems, and optmzaton of mrogrds and slanded mngrds. Prof. Guerrero s an Aoate Edtor for the IEEE RASACIOS O POWER ELECROICS, the IEEE RASACIOS O IDUSRIAL ELECROICS, and the IEEE Industral Eletrons Magazne, and an Edtor for the IEEE RASACIOS O SMARGRID. He has been a Guest Edtor for the IEEEE RASACIOS O POWER ELECROICS Speal Iues: Power Eletrons for Wnd Energy Conerson and Power Eletrons for Mrogrds; the IEEE RASACIOS O IDUSRIAL ELECROICS Speal Setons: Unnterruptble Power Supples systems, Renewable Energy Systems, Dstrbuted Generaton and Mrogrds, and Industral Applatons and Implementaton Iues of the Kalman Flter; and the IEEE RASACIOS O SMARGRID Speal Iue on Smart DC Dstrbuton Systems. He was the har of the Renewable Energy Systems ehnal Commttee of the IEEE Industral Eletrons Soety. In he was awarded as ISI Hghly Cted Researher.