Unversty of Kurdstan Dept. of Electrcal and Computer Engneerng Smart/Mcro Grd Research Center smgrc.uok.ac.r Droop-free Team-orented Control for AC Dstrbuton Systems V. Nasran,. Shafee, J. M. Guerrero, F. L. Lews, A. Davoud ublshed (to be publshed) n: proceedngs of the Appled ower Electroncs Conference and Exposton (AEC) (Expected) publcaton date: 05 Ctaton format for publshed verson: V. Nasran,. Shafee, J. M. Guerrero, F. L. Lews, A. Davoud. (05). Droop-free Team-orented Control for AC Dstrbuton Systems. In proceedngs of the Appled ower Electroncs Conference and Exposton (AEC), Charlotte, US, pp. 9-98. Copyrght polces: Download and prnt one copy of ths materal for the purpose of prvate study or research s permtted. ermsson to further dstrbutng the materal for advertsng or promotonal purposes or use t for any proftmakng actvty or commercal gan, must be obtaned from the man publsher. If you beleve that ths document breaches copyrght please contact us at smgrc@uok.ac.r provdng detals, and we wll remove access to the work mmedately and nvestgate your clam. Copyrght Smart/Mcro Grd Research Center, 06
Droop-free Team-orented Control for AC Dstrbuton Systems Vahdreza Nasran, obad Shafee, Josep M. Guerrero, Frank L. Lews, and Al Davoud Abstract Droop control s conventonally used for load sharng n AC dstrbuton systems. Despte decentralzed nature of the droop technque, t requres centralzed secondary control to provde voltage and frequency regulaton across the system. Dstrbuted control, as an alternatve to the centralzed controller, offers mproved relablty and scalablty. Accordngly, a droopfree dstrbuted framework s proposed that fne-tunes the voltage and frequency at each source to handle ) Voltage regulaton, ) Reactve power sharng, 3) Frequency synchronzaton, and 4) Actve power sharng. The controller ncludes three modules, namely, voltage regulator, reactve power regulator, and actve power regulator. The voltage regulator boosts the voltage across the dstrbuton system to satsfy the global voltage regulaton. roportonal load sharng s adopted, where the total load s shared among sources n proporton to ther rated powers. The actve power regulator addresses frequency synchronzaton wthout usng any frequency feedback/measurement, whch mproves the system dynamc. Smulaton results are provded to verfy the performance of the proposed control methodology. Index Terms AC mcrogrds, Cooperatve control, Dstrbuted control, Droop control, Inverter. I. INTRODUCTION Mcrogrds are small-scale power systems that have ganed popularty n dstrbuton systems for ther mproved effcency, relablty, and expandablty [], []. Inverters are commonly used to ntegrate energy resources, e.g., photovoltac arrays, storage elements, and fuel cells, to the AC mcrogrd dstrbuton network [3]. A three-ter herarchcal control structure s conventonally adopted for the mcrogrd operaton [4]. The prmary control, usually mplemented by a droop mechansm, operates on a fast tmescale and regulates nverters output voltage and handles load sharng among nverters [5]. Ths work was supported n part by the Natonal Scence Foundaton under grants ECCS-37354 and ECCS-40573 and n part by the U.S. Offce of Naval Research under grant N0004-4--078. Vahdreza Nasran, Frank L. Lews, and Al Davoud are wth the Department of Electrcal Engneerng, Unversty of Texas, Arlngton, TX 7609 USA and are also wth the Unversty of Texas at Arlngton Research Insttute (UTARI), Fort Worth, TX 768 USA (emals: vahdreza.nasran@mavs.uta.edu; lews@uta.edu; davoud@uta.edu). obad Shafee and Josep M. Guerrero are wth the Department of Energy Technology, Aalborg Unversty, Denmark. obad Shafee was also on leave wth the Unversty of Texas, Arlngton, TX. (Emals: qsh@et.aau.dk; oz@et.aau.dk). The secondary control compensates for the voltage and frequency devatons caused by the prmary control by updatng the voltage and frequency set ponts [6], [7]. Ultmately, the tertary control carres out the scheduled power exchange between the mcrogrd and the man grd [8]. Droop mechansm s a common decentralzed approach to realze the prmary control. It emulates vrtual nerta for AC systems and mmcs the role of governors n tradtonal synchronous generators [9]. Despte smplcty, the droop mechansms suffers from ) load-dependent frequency/voltage devaton, ) poor transent performance for nonlnear loads [0], and 3) poor reactve power sharng n presence of unequal bus voltages. Unequal bus voltages are essental to perform the scheduled reactve power flow. Droop technques cause voltage and frequency devatons. Thus, the supervsory secondary control updates the set ponts of the local prmary control [] [3]. Such central controllers requre two-way hgh-bandwdth communcaton lnks between the controller and each nverter. Ths desgn compromses the system relablty as falure of any communcaton lnk hnders the overall controller functonalty. The central controller s also a sngle-pont of falure that ntroduces another relablty rsk. Scalablty s another ssue because t adds to the complexty of the communcaton network. Spatally dspersed nverter-based mcrogrds naturally lend themselves to dstrbuted control technques to address the synchronzaton and coordnaton requrements. Dstrbuted control archtectures can dscharge dutes of a central controller whle beng reslent to faults or system uncertantes. Dstrbuted control processes necesstate that each agent (.e., the nverter) exchange nformaton wth other agents accordng to some restrcted communcaton protocol [4], [5]. These controllers use a sparse communcaton network and have less computatonal complexty at each nverter controller [6]. Networked control of parallel nverters n [7] embeds the functonalty of the secondary control n all nverters and requres a fully connected communcaton network. The master node n the networked master-slave methods [8] [0] s stll a sngle pont-offalure. Dstrbuted cooperatve control s recently ntroduced for DC and AC mcrogrds [] [7]. Dstrbuted control of AC mcrogrds are dscussed n [8], [9]. The maorty of such approaches are stll based on the droop control (and, thus, nhert ts shortcomng), requre system nformaton (e.g., 978--4799-6735-3/5/$3.00 05 IEEE 9
number of nverters, nverter parameters, total load demand), and manly handle actve power sharng and frequency regulaton (or only reactve power sharng/voltage regulaton). Ths paper provdes a droop-free dstrbuted cooperatve soluton that satsfes the secondary/prmary control obectves for an autonomous AC mcrogrd. The method treats each nverter as an agent of a mult-agent system (.e., the mcrogrd); each nverter exchanges data wth a few other neghbor nverters and processes the nformaton to update ts local voltage set ponts and synchronze ther normalzed power and frequences. The proposed controller ncludes three modules: voltage regulator, reactve power regulator, and actve power regulator. Salent features of the proposed control methodology are as lsted: ) The voltage regulator mantans the average voltage ampltude of the mcrogrd at the rated value. Dynamc consensus protocol s used n the voltage regulator to estmate the average voltage across the mcrogrd. ) The reactve power regulator compares local reactve loadng rato wth the neghbors and, accordngly, adusts the voltage ampltude set pont to mtgate the msmatch. 3) The actve power regulator compares local actve loadng rato wth the neghbors and, accordngly, adusts the frequency set pont to mtgate the msmatch. Ths sngle module handles both actve power sharng and frequency synchronzaton. 4) Unlke exstng methods, the proposed technque does not requre any frequency feedback or frequency measurement, whch can help to mprove dynamc response of the system. 5) A sparse communcaton network lnks the sources (controllers) to exchange control varables. Ths network must form a connected graph. Addtonally, the network shall carry some redundant lnks; the graph must reman connected n case of any sngle lnk falure. As long as the communcaton network remans connected, mparments such as delay or packet loss, may not compromse the system performance. 6) The control methodology s scalable, for that no pror knowledge of the system s requred by any new source to enter and servce the system. The rest of the paper s outlned as follows: Secton II revews a prelmnary of the dstrbuted cooperatve control and proposes the control methodology. Secton III revews the consensus protocol used n voltage observers. erformance of the controller s studed on a low-voltage AC mcrogrd, where the results are reported n Secton IV. Secton V concludes the paper. II. ROOSED CONTROL METHODOLOGY An AC dstrbuton system, augmented wth a sparse communcaton network, s adopted here (see Fgs. (a) and (b)). For each source, attached communcaton lnks facltate data exchange wth few other sources on the other end of the lnk. (a) (b) (c) Source Source Source N Node (Converter) Edge (Communcaton) Source Source N Source N Dstrbuton Network Node Source Electrcal System Source Communcaton System Graphcal Model Fg.. General layout of an AC mcrogrd: (a) Sources supplyng the mcrogrd, (b) Communcaton nfrastructure spanned across the mcrogrd, (c) Graphcal representaton of the cyber-physcal system (.e., the mcrogrd). Thus, not all sources are n contact wth each other or wth a centralzed supervsory control. Instead, each agent exchanges control nformaton wth ts neghbors; to whom the agent s drectly lnked on the communcaton graph. Ths cyberphyscal system can be represented as a graphcal nteracton of dynamc agents, as shown n Fg. (c), where each node nherts ts assocated source dynamc and each edge models correspondng communcaton channel. Fgure (c) shows a typcal drected communcaton graph (dgraph) between multple agents. Such a graph s usually represented by an assocated adacency matrx N N A G = éa ù ê ú Î. The Adacency matrx A ë û G carres the communcaton weghts, where a > 0 f Node receves data from Node and a = 0 otherwse. N denotes the set of all neghbors of Node. The n-degree and out-degree n n matrces D = dag{ d } and out { out D = dag d } are n out dagonal matrces wth d = å a and d = ÎN å a, ÎN respectvely. The Laplacan matrx s defned as n L = D -A G, whose egenvalues determne the global dynamcs of the system. 9
E ref E E G () s de,max å ba ( - ) ÎN,max,max H () s de E * L L o,max å ca ( - ) ÎN,max,max dw wref w * L v C,max,max Fg.. roposed secondary control for AC dstrbuton systems; the controller at Source. The Laplacan matrx s balanced f the n-degree and outdegree matrces are equal, n partcular, an undrected (bdrectonal) data network satsfes ths requrement. A drect path from Node to Node s a sequence of edges that connects the two nodes. A dgraph s sad to have a spannng tree f t contans a root node, from whch, there exsts at least a drect path to every other node. Here, the communcaton graph assumes to be balanced. Moreover, the graph shall carry mnmal redundancy,.e., n case of any lnk falure, the remanng lnks form a connected graph. Each source, e.g., Source, exchanges an nformaton vector Y = ée,, ù ê ë,max,max ú to ts neghbors on the û communcaton graph, where E,,,, and,max,max are the estmated average voltage of the mcrogrd, measured actve and reactve powers, and rated actve and reactve powers for Source, respectvely. Heren, the second and the thrd elements of the nformaton vector, Y, are called reactve and actve loadng ratos, respectvely. Fgure demonstrates schematc of the proposed cooperatve control polcy. Voltage regulaton, frequency synchronzaton, and actve/reactve load sharng are the man control obectve n any ac system. Fne adustment of frequency and voltage would satsfy all these obectves. artcularly, actve and reactve powers respond to any change n the frequency and voltage magntude, respectvely. As hghlghted n Fg., the proposed controller at each source carres three modules, voltage regulator, reactve power regulator, and actve power regulator. Two voltage correcton terms adust the voltage set pont for each source,.e., E * = E + d E + d E, where E s ref the reference voltage (rated voltage of the system). d E ref and d E are the frst and the second voltage correcton terms generated by the voltage regulator and the reactve power regulator, respectvely. The voltage regulator features a voltage estmator that uses dynamc consensus protocol to estmate the global average voltage across the mcrogrd, E. Dynamc consensus protocol s explaned the subsequent secton. The estmated average voltage, E, s then compared wth the reference voltage, E ref, to update the frst voltage correcton term, d, E E G s E E ref d = ()( - ), () that helps to boost the voltage across the mcrogrd. The voltage regulator addresses the global voltage regulaton defned n [5], where no ndvdual bus voltage shall be regulated at the rated value, nstead, the average of all voltages should match the rated value. The global voltage regulaton allows slght voltage devaton (however, less than 5%) to provde accurate load sharng. The reactve power regulator at ny source, e.g., Source, compares the local reactve loadng rato,, wth,max those of ts neghbors and, accordngly, calculates the second voltage correcton term, d E, æ ö de = H () s ba ( ), - ç å ÎN,max () çè,max ø where b s the couplng gan between the voltage and reactve power regulators. Upon successful operaton of the voltage and reactve power regulator, the average voltage across the mcrogrd would satsfy the rated value and all reactve loadng ratos wll synchronze; whch satsfes global voltage regulaton and proportonal reactve load sharng. Actve power regulator compares the local actve loadng rato,, wth those of ts neghbors to fnd the actve,max loadng msmatch and, accordngly, adusts the frequency set pont as, * w = w + ( ), ref å ca - (3) ÎN,max,max where w s the desred system frequency and c s a ref couplng gan. 93
Voltage Estmator at Source E DG DG 4 E N N ( ) a E E s E Z Z 4 Communcaton wth neghbors Node N Z Z 34 Node Node Node Cyber Layer (Communcaton Graph) Fg. 3. Dynamc consensus protocol used at Node to provde the average voltage of the mcrogrd. DG DG3 Z 3 In steady-state operaton, the actve loadng ratos wll converge to the same value, whch provdes actve proportonal load sharng. In addton, accordng to (3) all frequences successfully synchronze to the desred value. III. DYNAMIC CONSENSUS ROTOCOL The estmator module at Node (see Fg. ) provdes the average voltage ampltude across the mcrogrd. Fgure 3 elaborates functonalty of the so-called dynamc consensus protocol. Ths protocol s used as a dstrbuted decson makng approach for estmatng the average voltage. Accordng to Fg. 3, the estmator at Node, updates ts estmaton based on t å ( ) E () t = E () t + ò a E ( t) -E ( t)d t, (4) 0 ÎN where E s the voltage ampltude of the Source and E s the estmaton of the average voltage ampltude provded by the estmator at Node. As seen n (4), the updatng protocol uses the local voltage, E, however, no other neghbors measurement s drectly fed nto the estmaton process. Indeed, any voltage varaton at any Source, e.g., at Source, would mmedately affect the estmaton at that node, E. Gven a connected communcaton graph, the varaton n E would propagate across the network and affect all other estmatons. It s shown n [5] that f the communcaton graph carres a spannng tree and wth a balanced Laplacan matrx, all estmatons,.e., E s, converge to a global consensus, whch s the true average of the voltage ampltudes across the mcrogrd. In other words, N lm E ( t) = E ( t). t å (5) N = IV. CASE STUDY A three-phase AC mcrogrd test bench, shown n Fg. 4, s adopted to study performance of the control methodology. Z Z3 Fg. 4. Schematc of the studed AC mcrogrd wth the hghlghted communcaton graph. The electrc network forms a radal connecton whle the communcaton network shapes a rng. The underlyng mcrogrd ncludes four Dstrbuted Generators (DGs), wth dfferent rated powers, supplyng local loads assstng remote loads. Rated powers of the DGs and are twce those of the DGs 3 and 4. Rated rms voltage (Lne-to-Neutral) of the system s 30 V ( E = 30 = 35 V ) wth the ref frequency of 50 Hz. LCL flters are used n the outputs of the DGs to elmnate swtchng harmoncs. Seres RL mpedances are used to model dstrbuton lne mpedances. Detaled parameters of the mcrogrd are lsted n Table I. The bdrectonal communcaton network, hghlghted n Fg. 4, facltates cooperaton among the DGs. It should be noted that alternatve cyber structures wth less lnks could also meet the operatonal requrements. However, a sngle spare lnk s consdered to ) mprove the system dynamcs and ) mantan graphcal connectvty n case of any sngle lnk/nverter falure. The proposed control strategy s smulated n MATLAB Smulnk. Adacency matrx of the cyber network, A, and G the couplng gans b and c are, é 0.8 0.8ù.8 0.8 0 A =, b =, c = G 0.05. 0.8 0.8 (6) ê.8 0.8 0 ë û ú erformance of the cooperatve controller s evaluated through subsequent studes: A. Transent Response to Load Change All sources of the mcrogrd are ntally commanded wth * dentcal voltage set ponts; E = 35 V and * w = p 50 rad/s. The nner control loops of the drvng nverters produce the gatng sgnals accordng to the desred voltage ampltudes and frequences. 94
Electrcal Test System Control arameters TABLE I MICROGRID TEST BENCH ELECTRICAL AND CONTROL ARAMETERS arameters Symbol uantty Value V dc DC voltage 650 V E ref MG voltage ampltude 35 V f MG frequency 50 Hz C LCL flter capactance 5 μf L LCL flter nductance.8 mh L o LCL flter mpedance.8 mh Z, Z Load, Load 300 + 34 Ω Z 3, Z 4 Load 3, Load 4 50 + 57 Ω Z Lne mpedance, R =. Ω, L = 5.4 mh Z 3 Lne mpedance, 3 R 3 = 0.4 Ω, L 3 =.8 mh Z 34 Lne mpedance 3, 4 R 34 = 0.4 Ω, L 34 = 3. mh Symbol uantty DGs & DGs 3 & 4 max Rated actve power 00 W 00 W max Rated actve power 00 VAr 00 VAr k p sharng term 0.0 0.0 k sharng I term 7 7 k pv Voltage control term 0.008 0.008 k v Voltage control I term 4 4 Fgures 5 and 6 show the voltage regulaton and load sharng performance for t < 5 s, where the proposed controller s stll nactve. It can be seen that all the voltages are less than the desred value due to the voltage drop across the LCL flters. In addton, the load sharng s compromsed. Indeed, sources wth less ratng delver more power. The proposed controller s then actvated at t = 5 s. The outer voltage feedback loops are actvated to compensate for the voltage drop of the LCL flters. In addton, the voltage and reactve power regulators cooperate to generate voltage correcton terms, de = de + de, (see Fg. 5(c)) to ensure global voltage regulaton and proportonal reactve load sharng. As seen n Fg. 5(a), the average voltage across the mcrogrd s successfully regulated on the desred value of 35 V,.e., ( N N ) å E = E. It s noteworthy that = B ref although the bus voltages are dfferent than the rated voltage, voltage devatons are kept wthn an acceptable range. Ths voltage dfference s essental to manage the reactve power flow. Reactve load sharng performance s studed n Fg. 5(b) where the reactve power s shown to be perfectly shared among DGs n proporton to ther ratngs. Frequency and suppled actve powers of the DGs are presented n Fg. 6. ror to the controller actvaton,.e., for t < 5 s, the DG frequences are all synchronzed, however, poor actve power sharng s reported. Smlar to Fg. 5(b), the DGs wth less power ratng provde the maorty of the load demand. By controller actvaton at t = 5 s, the power regulators have collectvely vared the frequences to gan the desred actve power sharng. It should be noted that the power regulator do not devate the frequency set ponts n the steady state; however, transent varaton of the frequences tunes the phase angles to navgate the actve powers and provde proportonal load sharng. Bus voltage (V) Reactve power (VAr) Voltage correcton term (V) 330 35 30 35 0 5 0 5 30 35 40 00 000 800 600 400 00 0 5 0-5 -0 E B E B E B3 E B4 3 4 0 5 0 5 30 35 40 δe δe δe 3 δe 4 0 5 0 5 30 35 40 Tme (s) Fg. 5. erformance of the proposed controller n case of a : (a) Voltage regulaton, (b) roportonal reactve power sharng, (c) Voltage correcton terms. Frequency (Hz) (a) Actve power (W) (b) 50.005 50 49.995 00 000 800 600 400 00 roposed controller actvated 0 5 0 5 30 35 40 3 4 0 5 0 5 30 35 40 Tme (s) Fg. 6. erformance of the proposed controller n case of a : (a) Frequency synchronzaton, (b) roportonal actve power sharng. f f f 3 f 4 95
(a) (b) Reactve power (VAr) (c) Frequency (Hz) (d) Actve power (W) (e) Bus voltage (V) 330 35 30 35 00 000 800 600 400 00 50.005 50 49.995 00 000 800 600 400 00 Lnk 3-4 fals E B E B E B3 E B4 5 0 5 30 Lnk 3-4 fals 5 0 5 30 Lnk 3-4 fals 4 49.99 5 0 5 30 Lnk 3-4 fals 3 Lnk 3-4 fals 5 0 5 30 Tme (s) Fg. 7. Reslency to communcaton lnk falure: (a) Communcaton graph, (b) Bus voltages, (c) Suppled reactve powers (d) Frequences, (e) Suppled actve powers. Controller response to step s studed next. The local load at Bus 3 s unplugged at t = 3 s and plugged back n at t = 3 s. As seen n Fgs. 5 and 6, global voltage regulaton, frequency synchronzaton and proportonal load sharng are perfectly carred out durng the load transents. 4 3 3 4 f f f 3 f 4 3 4 Fgures 5(c) and 6(a) show how the voltage, reactve power, and actve power regulators respond to and readust the voltage set ponts and phase angles to mantan voltage regulaton and proportonal load sharng. B. Communcaton-Lnk Falure Reslency Effcacy of the controller s practced durng a step load change wth a faled lnk. The communcaton Lnk 3-4 (between DGs 3 and 4) s ntentonally dsabled at t = 7 s. As seen n Fg. 7, the lnk falure does not mpact voltage regulaton or load sharng n the mcrogrd, for that the lnk falure does not compromse connectvty of the communcaton graph. Fgure 7(a) demonstrates how the graph reconfgures n respond to Lnk 3-4 falure. It can be seen n Fg. 7(a) that the new graph s stll connected, thus, the controller shall reman operatve. However, any loss of connecton affects the Laplacan matrx and, thus, the system dynamc. Generally, less communcaton lnks lmts the nformaton flow and slows down the transent response of the system. Load changes are then ntroduced wth the faled lnk at moments t = 9 s and t = 5 s. It can be observed from Fg. 7 that the voltage regulaton and actve/reactve load sharng are successfully handled. However, comparng Fgs. 5(b) and 7(c) mples that the system dynamc has slowed down n Fg. 7(c) due to the loss of a communcaton lnk. Smlarly, Fg. 6(b) shows a faster response n comparson to Fg. 7(e). C. Loss of a Source Controller response to a DG falure s an mportant study snce t s a common contngency n mcrogrds. Accordngly, the nverter drvng DG 3 s ntentonally turned off at t = 7 s to practce loss of the Source 3. ractcally, loss of a source follows by the loss of all communcaton lnks attached to that partcular source. Fgure 8(a) llustrates how the communcaton network reconfgures after the loss of Source 3. It can be seen that the network remans connected and, thus, the controller s expected to reman operatonal. Fgure 8 shows the voltage, frequency, and the suppled powers for all DGs before and after the loss of DG 3. After the loss of ths source, the global voltage regulaton and frequency synchronzaton are preserved and the excessve load s proportonally shared among the remanng sources. It may be observed that the actve/reactve powers suppled to Bus 3 do not promptly drop to zero. Ths s due to the low-bandwdth flters appled to the power measurements to smoothen the readngs and elmnated undesred noses. V. CONCLUSION A cooperatve control framework s ntroduced that handles voltage regulaton, frequency synchronzaton and proportonal load sharng n AC mcrogrds. The mcrogrd s augmented wth a cyber network for data exchange. Each controller broadcasts an nformaton vector to neghbor controllers, to whom t s drectly lnked n the cyber doman. 96
through comparson of the local and neghbors suppled reactve powers. Smlarly, the actve power regulator adusts the local frequency set pont through comparson of the local and neghbors suppled actve powers. Smulaton studes show that the proposed controller successfully carres out the global voltage regulaton, frequency synchronzaton, and proportonal load power sharng. Frequency (Hz) Voltage ampltude (V) Reactve power (VAr) Actve power (W) 330 35 30 35 500 000 500 50.004 50.00 500 000 500 E B E B E B3 E B4 5 6 7 8 9 0 3 0 5 6 7 8 9 0 3 50 49.998 49.996 49.994 5 6 7 8 9 0 3 0 5 6 7 8 9 0 3 Tme (s) Fg. 8. Falure of a source: (a) Communcaton graph, (b) Bus voltages, (c) Suppled reactve powers (d) Frequences, (e) Suppled actve powers. Each controller processes local and neghbors nformaton through three separate modules; the voltage regulator, the reactve power regulator, and the actve power regulator. The voltage regulator uses dynamc consensus protocol to estmate the average voltage across the mcrogrd, whch s further used to mplement global voltage regulaton. The reactve power regulator dynamcally adusts the local voltage set pont 3 4 f f f 3 f 4 3 4 REFERENCES [] R. Maumder, B. Chaudhur, A. Ghosh, R. Maumder, G. Ledwch, and F. Zare, Improvement of stablty and load sharng n an autonomous mcrogrd usng supplementary droop control loop, IEEE Trans. ower Syst., vol. 5, no., pp. 796 808, May 00. [] M. Datta, T. Senyu, A. Yona, T. Funabash, and C. H. Km, A frequency-control approach by photovoltac generator n a V-desel hybrd power system, IEEE Trans. Energy Convers., vol. 6, no., pp. 559 57, Jun. 0. [3] C. K. Sao and W. Lehn, Control and power management of converterfed mcrogrds, IEEE Trans. ower Syst., vol. 3, pp. 088 098, Aug. 008. [4] J. C. Vasquez, J. M. Guerrero, J. Mret, M. Castlla, and L.G. de Vcuña, Herarchcal control of ntellgent mcrogrds, IEEE Ind. Electron. Mag., vol. 4, pp. 3 9, Dec. 00. [5] A. Bdram and A. Davoud, Herarchcal structure of mcrogrds control system, IEEE Trans. Smart Grd, vol. 3, pp. 963 976, Dec 0. [6] J. A.. Lopes, C. L. Morera, and A. G. Madurera, Defnng control strateges for mcrogrds slanded operaton, IEEE Trans. ower Syst., vol., pp. 96 94, May 006. [7] F. Katrae, M. R. Iravan, and. W. Lehn, Mcrogrd autonomous operaton durng and subsequent to slandng process, IEEE Trans. ower Del., vol. 0, pp. 48 57, Jan. 005. [8] C. Chen, S. Duan, T. Ca, B. Lu, and G. Hu, Optmal allocaton and economc analyss of energy storage system n mcrogrds, IEEE Trans. ower Electron., vol. 6, no. 0, pp. 76 773, Oct. 0. [9] T. L. Vandon, B. Meersman, J. D. M. De Koong, and L. Vandevelde, Analogy between conventonal grd control and slanded mcrogrd control based on a global DC-lnk voltage droop, IEEE Trans. ower Del., vol. 7, pp. 405 44, July 0. [0] A. H. Etemad, E. J. Davson, R. Iravan, A decentralzed robust strategy for mult-der mcrogrds art I: Fundamental concepts, IEEE Trans. ower Del., vol. 7, pp. 843 853, Oct. 0. [] A. Mcallef, M. Apap, C. Spter-Stanes, J. M. Guerrero, and J. C. Vasquez, Reactve power sharng and voltage harmonc dstorton compensaton of droop controlled sngle phase slanded mcrogrds, IEEE Trans. Smart Grd, vol. 5, pp. 49 58, May 04. [] A. Mehrz-San and R. Iravan, otental-functon based control of a mcrogrd n slanded and grd-connected modes, IEEE Trans. ower Syst., vol. 5, pp. 883 89, Nov. 00. [3] A. Kahrobaean and Y. A. R. I. Mohamed, Networked-based hybrd dstrbuted power sharng and control of slanded mcro-grd systems, IEEE Trans. ower Electron., vol. 30, no., pp. 603 67, Feb. 05. [4]. Hu and W. Haddad, Dstrbuted nonlnear control algorthms for network consensus, Automatca, vol. 4, pp. 375 38, Sept. 008. [5] J. Fax and R. Murray, Informaton flow and cooperatve control of vehcle formatons, IEEE Trans. Automat. Control, vol. 49, pp. 465 476, Sept. 004. [6] Z. u, Cooperatve control of dynamcal systems: Applcatons to autonomous vehcles. New York: Sprnger-Verlag, 009. [7]. Shafee, C. Stefanovc, T. Dragcevc,. opovsk, J. C. Vasquez, and J. M. Guerrero, Robust networked control scheme for dstrbuted secondary control of slanded mcrogrds, IEEE Trans. Ind. Electron., vol. 6, pp. 5363 5374, Oct. 04. [8] Y. Zhang and H. Ma, Theoretcal and expermental nvestgaton of networked control for parallel operaton of nverters, IEEE Trans. Ind. Electron., vol. 59, pp. 96 970, Apr. 0. 97
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