Published in: Proceedings of the 40th Annual Conference of IEEE Industrial Electronics Society, IECON 2014.

Transcription

1 Aalborg Unverstet Team-orented Adaptve Droop Control for Autonomous AC Mcrogrds Shafee, Qobad; asran, Vahdreza ; Zapata, Josep Mara uerrero; L. Lews, Frank ; Davoud, Al Publshed n: Proceedngs of the 40th Annual Conference of IEEE Industral Electroncs Socety, IECO 204. DOI (lnk to publcaton from Publsher): 0.09/IECO Publcaton date: 204 Document Verson Early verson, also known as pre-prnt Lnk to publcaton from Aalborg Unversty Ctaton for publshed verson (APA): Shafee, Q., asran, V., uerrero, J. M., L. Lews, F., & Davoud, A. (204). Team-orented Adaptve Droop Control for Autonomous AC Mcrogrds. In Proceedngs of the 40th Annual Conference of IEEE Industral Electroncs Socety, IECO 204. IEEE Press. I E E E Industral Electroncs Socety. Annual Conference. Proceedngs eneral rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts.? Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research.? You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan? You may freely dstrbute the URL dentfyng the publcaton n the publc portal? Take down polcy If you beleve that ths document breaches copyrght please contact us at vbn@aub.aau.dk provdng detals, and we wll remove access to the work mmedately and nvestgate your clam. Downloaded from vbn.aau.dk on: december 27, 208

2 Ths document s a preprnt of the fnal paper: Q. shafee, V. asran, J. M. uerrero, F. L. Lews, and A. Davoud, Team-orented Adaptve Droop Control for Autonomous AC Mcrogrds, n Proc. 40th Annu. Conf. IEEE Ind. Electron. Soc. (IECO 4), 204. Team-orented Adaptve Droop Control for Autonomous AC Mcrogrds Qobad Shafee, Vahdreza asran, Josep M. uerrero, Frank L. Lews, and Al Davoud Abstract Ths paper proposes a dstrbuted control strategy for voltage and reactve power regulaton n ac Mcrogrds. Frst, the control module ntroduces a voltage regulator that mantans the average voltage of the system on the rated value, keepng all bus voltages wthn an acceptable range. Dynamc consensus protocol s used to estmate the average voltage across the Mcrogrd. Ths estmaton s further utlzed by the voltage regulator to elevate/lower the voltage-reactve power (Q-E) droop characterstc, compensatng the drop caused by the droop mechansm. The second module, the reactve power regulator, dynamcally fne-tunes the Q-E coeffcents to handle the proportonal reactve power sharng. Accordngly, locally suppled reactve power of any source s compared wth neghbor sources and the local droop coeffcent s adusted to mtgate and, ultmately, elmnate the load msmatch. The proposed controllers are fully dstrbuted;.e., each source requres nformaton exchange wth only a few other sources, those n drect contact through the communcaton nfrastructure. A Mcrogrd test bench s used to verfy the proposed control methodology, where dfferent test scenaros such as load change, lnk falure, and nverter outage are carred out. Index Terms AC Mcrogrd, cooperatve control, dstrbuted control, droop control, load sharng, voltage control. I. ITRODUCTIO As the ntegraton of Dstrbuted enerators (Ds) wth power electronc nterfaces contnues to ncrease, the concept of Mcrogrd s becomng more popular [] [5]. These local grds are conventonally equpped wth a herarchcal control structure to address dfferent control requrements such as frequency and voltage regulaton, load sharng, etc. [4], [5]. Prmary control s a decentralzed approach that provdes frequency and voltage regulaton. Droop control s wdely adopted for the prmary control level, whch handles (actve/reactve) power sharng among sources n recprocal to ther power ratngs [6] [8]. As sources respond to more power demand, onboard droop controllers reduce ther frequency/voltage to handle load sharng and prevent overload/overstress. Identcal voltage and Ths work was supported n part by the atonal Scence Foundaton under grants ECCS and ECCS Qobad Shafee s vstng the Unversty of Texas at Arlngton, on leave from Aalborg Unversty. Qobad Shafee and Josep M. uerrero are wth the Department of Energy Technology, Alborg Unversty, Denmark (qsh@et.aau.dk; oz@et.aau.dk). Vahdreza asran, Frank L. Lews, and Al Davoud are wth the Department of Electrcal Engneerng, Unversty of Texas at Arlngton, TX USA (emals: vahdreza.nasran@mavs.uta.edu; lews@uta.edu; frequency measurements are essental to the effectveness of the droop mechansms. Unlke frequency whch s a global varable, the voltage vares across the Mcrogrd due to the dstrbuton lne mpedances. Ths voltage msmatch ncapactates the droop mechansms and results n a poor voltage regulaton and load sharng. Centralzed secondary controls are conventonally practced n the lterature, e.g., [4] [5] and [9], to restore the system frequency and voltage. The centralzed approach requres pont-to-pont communcaton, whch adds to system complexty and compromses ts relablty. Alternatvely, dstrbuted protocols have recently drawn attenton for Mcrogrd control [0], []. Secondary control, n partcular, has been the subect of studes n [2] [4]. The lne mpedance effect, however, s not taken nto account and s stll open to research. Ths paper ntroduces a dstrbuted control framework for voltage regulaton and reactve power sharng n ac Mcrogrds. Salent features of the proposed control methodology are outlned: Each source carres an embedded secondary control whch ncludes two separate control modules; a voltage regulator and a reactve power regulator. 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 generaton wth the neghbors and, accordngly, adusts the local droop coeffcent to mtgate the msmatch. A sparse communcaton network lnks the sources (controllers) to exchange control varables. Ths network must form a connected graph. Addtonally, the network shall satsfy a mnmum redundancy; the graph remans 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. The control methodology s scalable, for that pror knowledge of the system s not requred, as a new component enters the Mcrogrd. The remnder of the paper s organzed as follows: Secton II provdes an overvew of the dstrbuted control on graphs. The proposed cooperatve control framework s ntroduced n Secton III. Secton IV dscusses the dynamc consensus protocol for average voltage estmaton. Secton V studes performance of the proposed controller for an ac Mcrogrd. Secton VI concludes the paper.

3 II. COOPERATIO O RAPHS A dstrbuted network of communcaton lnks can connect sources of a Mcrogrd. Such a cyber network can be represented by a graph, as shown n Fg., where sources and communcaton lnks are represented by nodes and edges, respectvely. Ths cyber network facltates cooperaton among agents (sources), where any agent s n contact wth only a few other agents as ts neghbors, and not wth all other agents. Ths cooperatve nteracton of the neghbors on the cyber layer sets the ground for the cooperatve control, whch offers convergence of the control varables (on all nodes) to a global consensus, f the communcaton graph s properly desgned. The communcaton graph s a drected graph (dgraph) between multple agents, whch s usually represented as a set of nodes V = { v g, v g,..., v g } 2 connected wth a set of edges E Ì V V and an assocated adacency matrx A = éa ù ê ú Î, where s the number of nodes ë û (sources). The Adacency matrx A carres the g g communcaton weghts, where a > 0 f ( v, v ) Î E and a = 0 otherwse. The communcaton gans, a s, can be assumed as data transfer gans. Ths paper assumes a tmenvarant adacency matrx. { g g = ( v, v ) Î E } denotes the set of all neghbors of the ode. Equvalently, f Î, then v g receves nformaton from v g. However, the lnks are not necessarly recprocal,.e., v g may not receve g n n nformaton from v. The n-degree matrx D = dag { d } n s a dagonal matrx wth d = å a. Smlarly, the outdegree matrx s D = dag{ d Î out out out }, where d = å a. Î n The Laplacan matrx s defned as L = D - A, whose egenvalues determne global dynamcs of the system. The Laplacan matrx s balanced f the n-degree of each node n out matches ts out-degree,.e., D = D. A drect path from g g v to v 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. III. COOPERATIVE COTROL FRAMEWORK Each source n a Mcrogrd has a controller. These controllers are lnked through a cyber network. Fgure 2 shows the proposed control methodology for a sngle source, e.g., Source, whch ncludes two separate modules; voltage regulator and reactve power regulator. The voltage regulator mantans the average voltage of the Mcrogrd at the rated value, whle the reactve power regulator montors the reactve power sharng and adusts the droop coeffcents to provde proportonal load sharng. It should be noted that n a practce, where the lne mpedances are not neglgble, all bus voltages cannot be regulated at dentcal values, for that t hnders the reactve power management. Typcally, the bus voltages are regulated wthn 95% to 05% of the rated voltage. Accordngly, the proposed method ams to regulate the average voltage of the whole system, rather than ndvdual buses. Electrcal Layer D D 2 D 3 D D 4 Cyber Layer Fg.. Layout of an ac Mcrogrd augmented wth a communcaton network. The communcaton network, spanned across the Mcrogrd, facltates data exchange among controllers. Each controller, e.g., the controller at ode, relays an nformaton vector, Y, to ts neghbors on graph. The nformaton vector T s formatted as Y = ée, Q Q ù ê ë max ú, where E û, Q, and Q are the estmate of the average of the voltage max ampltudes across the Mcrogrd, suppled reactve power, and rated reactve power at ode, respectvely. The term Q Q, whch s referred to here as the loadng ndex, max represents reactve loadng percentage of the Source. Each controller receves data from ts neghbors on graph and, through processng local and neghbors nformaton, t updates ts control varables. A. Dstrbuted Voltage Control The voltage regulator provdes a voltage correcton term, d E, to boost the voltage ampltude at node. Each controller has an estmator, hghlghted n Fg. 2, that estmates the average of the voltage ampltudes across the Mcrogrd, E. Functonalty of the estmator s explaned n detals n the subsequent secton. The dfference between ths estmaton ref and the reference voltage ampltude, E, s then fed to a PI controller to calculate the voltage correcton term, d E. The ref reference voltage, E, s typcally the rated voltage of the Mcrogrd and, thus, sources share dentcal reference values. Cooperaton among all the voltage regulators guarantees to have the averaged voltage ampltude across the Mcrogrd regulated at the rated value. Ψ

4 ref E E E () s E Q E E Q Q max q H() s n n P L C L o Q P L v Fg. 2. Cooperatve adaptve droop control for the -th source of an ac Mcrogrd. B. Dstrbuted Adaptve Droop Control The reactve power regulator at ode, receves the loadng ndces of all ts neghbors,.e., the terms Q Q max from all nodes, Î. Then, t compares ts loadng ndex, Q, wth a weghted average of ts neghbors to calculate the loadng msmatch, d q, Q Q dq = ( ) å ba - Î Q max Q max æ Q ö æ ö Q = ba å b a. - Î Q å () ç è max ø èç Î Q ø max The loadng msmatch ndcates how far s the reactve power sharng from an deal sharng scenaro, where the whole reactve power s shared among the sources n proporton to ther rated power. Accordngly, ths term s further used to fne adust dstrbuton of the reactve powers. As seen n Fg. 2, the loadng msmatch, d q, s fed to a PI controller to generate the droop correcton term, d n. Ths correcton term s used to update the droop coeffcent, n () t = n - dn (). t (2) 0 where n s the ntal droop assgnment. Ths adustment 0 helps to lower the loadng msmatch among neghbors sources and, ultmately, n the whole Mcrogrd. Equvalently, the loadng ndces converge to a global consensus, shall the communcaton graph carry a spannng tree wth a balanced Laplacan matrx. Consensus n loadng ndces satsfes proportonal reactve power sharng among sources. It should be noted that the droop correcton term, d n, must be lmted, as large values mght affect system stablty. IV. DYAMIC COSESUS PROTOCOL The estmator module at ode (see Fg. 2) provdes the average voltage ampltude across the Mcrogrd. Fgure 3 elaborates the so-called dynamc consensus protocol whch s a dstrbuted decson makng approach for estmatng the average voltage. Accordngly, the estmator at ode, updates ts estmate based on E -th Voltage Estmator Fg. 3. Dynamc consensus protocol at ode to averagng the voltage ampltude. t Communcaton wth neghbors å ( ) a E E 2 ( ) E ( t) = ò a E ( t) - E ( t) d t + E ( t), (3) 0 Î where E s the voltage ampltude at ode and E s the estmate of the average voltage ampltude provded by the estmator at ode. As seen n (3), the updatng protocol uses the local voltage, E, whle no other neghbors measurement s drectly fed nto the estmaton process. Indeed, any voltage varaton at any node, e.g., ode, would mmedately affect the estmaton at that node, E. ven 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 features 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 grd. In other words, for each node, the estmated averaged voltage s lm E ( t) = E ( t). t å (4) = Communcaton raph V. CASE STUDY An ac Mcrogrd test bench, shown n Fg. 4, s consdered to study performance of the control methodology. s E E

5 4 D Load Z Z 2 4 Cyber etwork 2 3 D2 D3 Fg. 4. A 4-bus Mcrogrd test bench facltated wth cyber network. Z 23 The underlyng Mcrogrd ncludes four Ds wth varous rated powers supplyng local and dstant loads. Rated power of the frst two Ds are twce those for the last two. Rated voltage of the system s 230 V wth the frequency of 50 Hz. Dstrbuton lne mpedances are modeled wth seres RL branches. A communcaton network, hghlghted n green n Fg. 4, facltates cooperaton of the Ds. The lnks are all bdrectonal to feature a balanced Laplacan matrx. 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 2) mantan graphcal connectvty n case of a lnk/ nverter falure. The proposed control strategy s smulated n Matlab Smulnk. Assocated adacency matrx of the cyber network, A, and the couplng gan between voltage and power regulators, b, are é ù A =, b = (5) ê ë ú û Other electrcal and control parameters of the underlyng system are tabulated n detals n Table I. Performance of the cooperatve controller s evaluated through subsequent studes: A. Fxed Droop versus Cooperatve Adaptve Droop Mcrogrd performance wth the proposed control algorthm s compared wth the conventonal droop control, whch uses fxed droop coeffcents. The coeffcents are chosen n nverse proporton to the nverters rated power. Fgure 5 shows the results, where for t < 5 s the fxed droop controller s effectve. Voltage devaton from the rated value can be observed n all voltage ampltudes (see Fg. 5(a)). Z 34 Load 4 Z 4 Load 2 Load 3 Z2 Z3 D 4 Electrcal Test System Control Parameters TABLE I MICRORID TEST BECH ELECTRICAL AD COTROL PARAMETERS Parameters Symbol Quantty Value V dc DC voltage 650 V E ref M voltage ampltude V f M frequency 50 Hz C LCL flter capactance 25 μf L LCL flter nductance.8 mh Lo LCL flter mpedance.8 mh Z, Z 2 Load, Load Ω Z 3, Z 4 Load 3, Load Ω Z 2 Lne mpedance, 2 R2.2 Ω, L2 5.4 mh Z 23 Lne mpedance 2, 3 R Ω, L23.8 mh Z 34 Lne mpedance 3, 4 R Ω, L mh Symbol Quantty Ds & 2 Ds 3 & 4 P max Rated actve power 2200 W 00 W Q max Rated actve power 2200 VAr 00 VAr m P droop coeffcent n Q E droop coeffcent k pq Q sharng P term k Q Q sharng I term k pv Voltage control P term k v Voltage control I term.8.8 Moreover, the bus voltages dffer because of the lne mpedance effect, whch has clearly affected the effcacy of the reactve power sharng, as seen n Fg. 5(b). Actvaton of the proposed controller (see Fg. 5(a)) at t = 5 s, boosts all voltages across the Mcrogrd such that to regulate the average voltage at the rated value,.e., ref ( E ) = E = å. The voltage correcton terms, de s, are presented n Fg. 5(e). 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. As t can be seen n Fg. 5(b), fne adustment of the droop coeffcent, usng the adaptve droop mechansm, results n accurate reactve power sharng, where the frst two sources provde twce as reactve power as the other two do. Droop coeffcent adustment s demonstrated n Fg. 5(c) Voltage estmator performance s studed n Fg. 5(d). Estmatons of the average voltages are plotted n ths fgure for all controllers. Estmatons are compared wth the true average voltage ampltude whch s the average of the four voltages. An excellent agreement s reported n Fg. 5(d) between the estmatons, E s, and the true average, E. B. Transent Response to Load Change Fgure 6 depcts the Mcrogrd varables durng step load changes. The local load at the second bus s unplugged at t = 5 s and plugged back n att = 20 s. As seen n Fgs. 6(a) and 6(b), global voltage regulaton and proportonal reactve power sharng are perfectly carred out. Excellent voltage estmaton s reported n Fg. 6(d), where the estmatons tghtly follow true the average voltage, even durng transents. Controller response to load change s elaborated n Fgs. 6(c) and 6(e), where the droop coeffcents, n s, and voltage correcton terms, de s, are shown to vary to mantan voltage regulaton and proportonal load sharng.

6 5 Voltage Ampltude (V) Reactve power (VAr) Q Q 2 Q 3 Q Voltage Ampltude (V) Reactve power (VAr) Q Q 2 Q 3 Q 4 Droop Coeffcent n n 2 n 3 n 4 Droop Coeffcent n n 2 n 3 n 4 Averaged Voltage (V) Voltage Correcton Term (V) E Tme (s) Fg. 5. Performance of proposed controller versus conventonal droop control: (a) Bus voltages, (b) Reactve powers, (c) Droop coeffcents, (d) Average voltage estmates, (e) Voltage correcton terms. Averaged Voltage (V) Voltage Correcton Term (V) Tme (s) Fg. 6. Performance of the proposed controller n case of a load change: (a) Bus voltages, (b) Reactve powers, (c) Droop coeffcents, (d) Averaged voltage estmates, (e) Voltage correcton terms. E

7 6 Communcaton graph (a) Voltage Ampltude (V) (b) Lnk 3-4 fals Lnk 3-4 fals Voltage Ampltude (V) Reactve power (VAr) load change Q Q 2 Q 3 Q 4 Reactve power (VAr) Q Q 2 Q 3 Q 4 (c) Tme (s) Tme (s) Fg. 7. Communcaton lnk falure: (a) Bus voltages, (b) Suppled reactve powers. Fg. 8. Inverter falure: (a) Bus voltages, (b) Suppled reactve powers. C. Lnk-Falure Reslency Effcacy of the controller s practced durng a load change wth a faled lnk. The communcaton lnk 3-4 (between nverters 3 and 4) s ntentonally dsabled at t = 5 s. As seen n ths fgure, the lnk falure does not mpact voltage regulaton or load sharng n the Mcrogrd, for that no sngle lnk falure does not hnder the graphcal connectvty. Ths concept s llustrated n Fg. 7(a), where t s shown that the graph remans connected when the lnk 3-4 s dsabled. However, any loss of connecton affects the Laplacan matrx and, thus, the system dynamc. enerally, less communcaton lnks slows down the transent response of the system. Load change s then practced wth the faled lnk at moments t = 8 s and t = 25 s. It can be observed n Fgs. 7(b) and 7(c) that the voltage regulaton and load sharng are successfully handled. However, comparng Fg. 6(b) and 7(c) mples that the system dynamc has slowed down n Fg. 7(c) due to the loss of a communcaton lnk. D. Loss of a D Loss of a source (D) s a common contngency n the Mcrogrds and, thus, controller performance for such a scenaro s subected to study. Accordngly, the thrd nverter s ntentonally turned off to mmc loss of the thrd source. It should be noted that, n practce, loss of a source also means the loss of all communcaton lnks attached to that partcular source. Fgure 8(a) llustrates the reconfguraton of the communcaton network after loss of the thrd source. It can be see that the network remans connected and, thus, the controller s expected to reman operatonal. Mcrogrd voltages and suppled reactve powers are shown n Fgs. 8(b) and 8(c) for after the loss of the thrd nverter, where the global voltage regulaton s preserved and the excess reactve power s shared among the remanng sources. It also can be seen that the reactve power suppled to the thrd bus does not suddenly drop to zero. The slow drop of the reactve power s because of the LCL flter placed between the nverter and the bus. VI. COCLUSIO A cooperatve control framework s ntroduced that handles voltage regulaton and reactve power sharng n an ac Mcrogrd. 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. Each controller processes local and neghbors nformaton through two separate modules; the voltage regulator and the reactve power regulator. The voltage regulator features an estmator that estmates the average voltage across the Mcrogrd. The power regulator

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