Consensus-based Synchronization of Microgrids at Multiple Points of Interconnection

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1 MITSUBISHI EECTRIC RESEARCH ABORATORIES Cosesus-based Sychroizatio of Microgrids at Multiple Poits of Itercoectio Shah, S.; Su, H.; Nikovski, D.N.; Zhag, J. TR208-2 August 7, 208 Abstract This paper presets a cosesus-based distributed sychroizatio cotrol method for microgrids with multiple poits of itercoectio. The proposed method ca sychroize a microgrid at differet poits of itercoectio usig a commo sparse commuicatio etwork amog its distributed geerators. This fuctioality is critical for the etworked operatio of multiple microgrids i the future power systems. The proposed approach uses averagig ad leader-follower modes of a commoly used cosesus algorithm for multi-aget systems to achieve microgrid sychroizatio ad smooth trasitio betwee the isladed ad grid-coected modes at differet itercoectio poits. The operatio of the proposed distributed sychroizatio method is demostrated o a microgrid with four iverters, each with a idepedet itercoectio poit to aother microgrid or a bulk power system. IEEE Power & Eergy Society Geeral Meetig This work may ot be copied or reproduced i whole or i part for ay commercial purpose. Permissio to copy i whole or i part without paymet of fee is grated for oprofit educatioal ad research purposes provided that all such whole or partial copies iclude the followig: a otice that such copyig is by permissio of Mitsubishi Electric Research aboratories, Ic.; a ackowledgmet of the authors ad idividual cotributios to the work; ad all applicable portios of the copyright otice. Copyig, reproductio, or republishig for ay other purpose shall require a licese with paymet of fee to Mitsubishi Electric Research aboratories, Ic. All rights reserved. Copyright c Mitsubishi Electric Research aboratories, Ic., Broadway, Cambridge, Massachusetts 0239

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3 Cosesus-based Sychroizatio of Microgrids at Multiple Poits of Itercoectio Shahil Shah, Hogbo Su 2, Daiel Nikovski 2, ad Jiyu Zhag 2 Resselaer Polytechic Istitute Troy, NY 280, USA shahs2@rpi.edu AbstractThis paper presets a cosesus-based distributed sychroizatio cotrol method for microgrids with multiple poits of itercoectio. The proposed method ca sychroize a microgrid at differet poits of itercoectio usig a commo sparse commuicatio etwork amog its distributed geerators. This fuctioality is critical for the etworked operatio of multiple microgrids i the future power systems. The proposed approach uses averagig ad leader-follower modes of a commoly used cosesus algorithm for multi-aget systems to achieve microgrid sychroizatio ad smooth trasitio betwee the isladed ad grid-coected modes at differet itercoectio poits. The operatio of the proposed distributed sychroizatio method is demostrated o a microgrid with four iverters, each with a idepedet itercoectio poit to aother microgrid or a bulk power system. Idex TermsSychroizatio, microgrid cotrol, distributed geerators, secodary cotrol, distributed cosesus cotrol. I. INTRODUCTION Microgrids are emergig as preferable solutio for icreasig the peetratio of distributed eergy resources i bulk power systems []. With the icreasig umber of microgrids, it will be importat to be able to quickly ad reliably coect them with each other or to a bulk power system wheever demaded by the trasmissio system operator. Because of wide geographical spread, it may be desired to coect multiple microgrids for improvig reliability [2], which may result i multiple poits of itercoectio i a microgrid. Sychroizatio parameters of a microgrid icludig voltage magitude ad frequecy at a poit of commo couplig (PCC) deped o several distributed geerators. Hece, the sychroizatio fuctio is implemeted at the cetralized secodary level cotrol, which achieves coordiatio amog grid-formig geerators i the microgrid [3]. Whe a microgrid is to be sychroized at a PCC, the differece betwee the frequecy ad voltage magitudes of the microgrid ad the power system are added to the cetralized secodary cotrol to elimiate the voltage ad frequecy errors. The phase sychroizatio is achieved either passively usig a frequecy offset or actively usig a dedicated sychroizer [4]. The cetralized ature of secodary cotrol defies the fudametal objective of microgrids of providig a electrical ad cotrol ifrastructure for the itegratio of distributed eergy resources while keepig the cetral coordiatio at miimum. Two major disadvatages of cetralized secodary cotrol are 2 Mitsubishi Electric Research aboratories Cambridge, MA 0239, USA {hogbosu, ikovski, jzhag}@merl.com existece of a sigle poit-of-failure ad requiremet of commuicatio from the secodary cotroller to each of the grid-formig geerators i the microgrid. Additioally, cetralized secodary cotrol supports sychroizatio oly at oe poit of itercoectio. If there is a additioal poit of itercoectio i the microgrid, additioal secodary cotroller with remote sesig circuit is required at the ew PCC if sychroizatio with a power system at the ew PCC is desired. This will also require commuicatio liks from the ew PCC to all the geerators, leadig to a dese commuicatio etwork ad low reliability. Several distributed secodary cotrol methods are proposed as alterative to cetralized secodary cotrol for voltage ad frequecy restoratio after trasiets [-7]. I these methods, each grid-formig geerator has its ow local secodary cotroller to elimiate the local frequecy ad voltage errors by vertically shiftig its droop characteristics. A commuicatio framework is also provided for coordiatig the secodary cotrollers of geerators to avoid disruptio of power sharig amog them. A simple ad versatile distributed secodary cotrol method is preseted i [6, 7]. It requires each geerator to commuicate oly with a few eighbor geerators. It achieves the voltage ad frequecy restoratio without disturbig power sharig through cosesus amog geerators o the shifts of their droop characteristics. The cosesus-based distributed secodary cotrol method requires oly a sparse commuicatio etwork ad it does ot itroduce a sigle-poit-of-failure. However, the frequecy ad voltage refereces remai fixed i this method [7]. Hece, it is ot applicable for sychroizig a microgrid with aother power system, which requires the microgrid to track the frequecy ad voltage levels of the power system. This paper builds upo the work i [7] ad presets a distributed cotrol method for sychroizig a microgrid with power systems located at differet itercoectio poits usig a commo ad sparse commuicatio etwork amog its gridformig geerators. The steady-state power sharig remais uaffected by the itroductio of the distributed frequecy ad voltage sychroizatio cotrol laws. II. CONSENSUS-BASED DISTRIBUTED CONTRO For a microgrid with grid-formig geerators, its commuicatio etwork ca be represeted as a directed graph G(V, E, A) with ode set V = {,...,}, edge set E V V, ad adjacecy matrix A [8]. If ij E, the there is a lik directed from i th to

4 j th ode, ad the j th ode ca receive iformatio from the i th ode. Each lik is associated with a positive weight a ij A. A particular weight a ij is zero, if there is o direct lik betwee the i th ad j th odes. For a udirected graph a ij = a ji. Two cocepts of coectivity of graphs are importat for this paper. First, a udirected graph is coected if there is a udirected path betwee ay two distict odes. Secod, i a directed graph G(V, E, A), a graph G (V, E, A ) is a rooted directed spaig tree if G is a subgraph of the directed graph G(V, E, A), it cotais all the odes of the paret directed graph G(V, E, A), ad it is a rooted directed tree. A rooted directed tree is a directed graph i which every ode has exactly oe paret except for the oe, which has o paret ad it is called root. I a rooted directed tree, a directed path exist from the root to all the other odes i the tree. Assume x i (t) represets a iformatio state associated with i th ode. The most commoly applied algorithm for achievig cosesus amog the iformatio states of odes i a graph is [8]: x i = a ij x i x j where i V. () j = Two modes of the cosesus algorithm are used i this paper: ) Averagig Mode For a udirected coected graph, the cosesus algorithm results i the iformatio states of all odes to coverge to a weighted average of their iitial values [8]. If all o-zero weights a ij are equal, the iformatio states will coverge to the average of their iitial values. Oe trivial sceario is if the iformatio states are at a commo value whe the cosesus algorithm is activated, all the states will cotiue to stay at the same commo value. 2) eader-follower Mode For a directed graph cotaiig exactly oe rooted directed spaig tree, the cosesus algorithm i () results i iformatio states of all the follower odes to coverge to the iformatio state of the root ode. The iformatio state of the root ode is idepedet of other odes. For example, if k th ode is made the leader, its iformatio state ca follow a idepedet referece: x k = x ref III. DISTRIBUTED SYNCHRONIZATION OF MICROGRIDS A. Distributed Frequecy Sychroizatio The proposed method implemets sychroizatio cotrol based by addig a cosesus-based sychroizatio layer to the distributed secodary cotrol preseted i [7]. The frequecy droop cotrol law icludig distributed sychroizatio ad secodary cotrol fuctios is: i = i m i P i i where i, m i, ad P i are respectively the frequecy, P- droop (2) (3) costat, ad active power output of the i th geerator. is fixed omial frequecy referece. Offset i ad i are outputs of respectively the distributed secodary cotrol ad the distributed sychroizatio cotrol. i mitigates the error betwee the geerator frequecy i ad the frequecy referece ( i ). O the other had, i modifies the frequecy referece of the i th geerator so that the geerator frequecy ca track the frequecy of the power system to which the microgrid is to be sychroized. The update laws for i ad i are discussed i the followig. The distributed secodary cotroller output i is updated based o the followig cosesus law: d i k i = dt i i a ij i j j = The first part o the right-had side of (4) esures that the error betwee the geerator frequecy i ad modified frequecy referece ( i ) coverges to zero i steady-state. The secod part is similar to the cosesus algorithm i () ad it esures that offsets i s of all the grid-formig geerators are equal i steady-state. This preserves the active power sharig amog geerators depedig o their droop slopes m i s while achievig frequecy regulatio. The cosesus amog correctios i s oly requires that the udirected graph formed by bidirectioal commuicatio liks amog grid-formig geerators is coected. Hece, each geerator does ot require to commuicate with all the remaiig geerators. Frequecy referece correctio i i (4) eables geerator to track a time-varyig frequecy referece. i at each geerator is obtaied accordig to the microgrid operatio mode: ) eader-follower Mode If the microgrid is to be sychroized at a poit of itercoectio ear say k th geerator, the frequecy referece correctio at the k th geerator k is obtaied as differece betwee the measured frequecy of the power system with which the microgrid is to be sychroized ad the omial referece : k = PCCk The frequecy referece correctios at remaiig geerators are obtaied usig the followig cosesus law: It ca be iferred from () ad (6) that the frequecy referece correctio states follow leader-follower mode described i Sectio II with geerator k as the leader. Hece, the frequecy refereces of all geerators ( i ) coverge to the frequecy of the power system at the k th geerator. Fig. a) ad c) respectively demostrate sychroizatio at PCC- ad usig the proposed cosesus-based method. d k s i = a where. (6) dt ij i j i V i k j = (4) ()

5 a) b) c) PCC2 E PCC Fig.. Proposed distributed sychroizatio method. a) leader-follower mode for sychroizatio at PCC-, b) averagig mode for isladed operatio, ad c) leader-follower mode for sychroizatio at. 2) Averagig Mode Oce the microgrid is sychroized or if it has to retur to the isladed mode, there is o eed to keep oe geerator as the leader. Hece, the update law for the frequecy referece correctio states is switched to the averagig mode: Fig. b) depicts the averagig mode of the distributed sychroizatio cotrol. It is to be oted from Fig. that the graph formed by commuicatio liks i the averagig mode is udirected ad coected. Whereas, it becomes directed i the leader-follower mode as the liks coected to the leader geerator are modified from udirected bidirectioal commuicatio liks to uidirectioal liks directed away from the leader. B. Decouplig Cosesus Algorithm ad Frequecy Cotrol I the leader-follower mode, all the frequecy referece correctio states i s coverge to the leader state k. They will cotiue to stay at the same value whe the cotrol is switched to the averagig mode. Hece, trasitio from the leader-follower mode to the averagig mode is smooth. However, trasitio from the averagig mode to the leader-follower mode is ot smooth 3 i 3 i 3 i PCC E PCC PCC- PCC- PCC- Commuicatio iks Trasmissio ies d k s i = a where. (7) dt ij i j i V j = sice the leader ode will be the first to have iformatio o the correctio required i its frequecy referece. The frequecy referece correctio states of the follower odes will coverge to that of the leader ode with covergece rate depedig o the speed of commuicatio ad the commuicatio etwork topology [8]. It may happe that the leader geerator starts chagig its frequecy toward that of the power system with which the microgrid is to be sychroized faster tha the remaiig geerators ca follow. This may trasietly disturb active power sharig amog geerators ad overload certai geerators. To avoid trasiet overloadig, the frequecy referece correctio state at each geerator, obtaied usig either (6) or (7), is passed through a low-pass filter before usig it i (3) ad (4). The output of the filter is idicated by a asterisk as : i i = (8) i T s Filter time-costat T is kept few tes of times higher tha the covergece rate of the cosesus algorithm. This esures that the frequecy referece at each geerator evolves at a rate much slower tha the cosesus algorithm used for distributed sychroizatio. This avoids large mismatch i the frequecy refereces of geerators ad miimizes the trasiet overloadig effect. C. Distributed Voltage Sychroizatio Distributed voltage sychroizatio is similarly achieved as frequecy sychroizatio by itroducig a iformatio state i the Q V droop cotrol law represetig correctio to the omial voltage referece E: E i = E E i i Q i e i where i V (9) where E i, i, ad Q i are respectively the voltage magitude, Q-V droop costat, ad reactive power output of the i th geerator. E is fixed omial voltage referece. Distributed sychroizatio cotrol output E i modifies the voltage referece to track the voltage of the power system to which the microgrid is to be sychroized. Same as the distributed frequecy sychroizatio, the voltage referece correctio state E i is determied usig either leader-follower mode or averagig mode. The cosesus laws are similar to (6) ad (7); they are ot preseted here because of space costrait. Same as frequecy sychroizatio, the cosesus algorithms for voltage sychroizatio ad the voltage cotrol of geerators are decoupled usig a low-pass filter with time costat T E. D. Iteractio with Distributed Secodary Cotrol Distributed secodary cotrol output e i i (9) ca be used to mitigate the error betwee the geerator voltage E i ad referece ( E E i ) while achievig reactive power sharig [6, 7]. However, because of the fiite voltage drops across trasmissio lies, exact reactive power sharig caot be achieved while regulatig the voltages at geerators at the same level [7]. This coflict ca create potetial stability problem i the distributed

6 E, E 4, 4 TABE I PARAMETERS OF SIMUATED MICROGRID v dc PCC- PCC-4 Z 4 R R 2 v dc4 Parameter Nomial grid voltage peak, E Nomial frequecy, Phase reactor, P- droop slopes: m ad m 4 Value 32.3 V 260 rad/s.8 mh v dc4 E 2, 2 Z 2 Z 34 PCC-3 E 3, 3 v dc3 P- droop slopes: m 2 ad m 3 Trasmissio lie impedace, Z 2 Trasmissio lie impedace, Z 4 2.x0 3.0x j3.6x j.8x0 3 Trasmissio lie impedace, Z j.9x0 3 Distributed secodary cotrol gai, k i 2.0 Commuicatio etwork weights, a ij a 2, a 2, a 23, a 32, a 34, a 43 are uity; Other weights are zero Fig. 2. Simulated microgrid. Dashed lies show commuicatio liks. secodary voltage cotrol [7]. Possible iteractio betwee the proposed distributed voltage sychroizatio ad distributed secodary voltage cotrol may further deteriorate the microgrid stability ad must be properly ivestigated. Such aalysis is beyod the scope of this paper; the reactive power sharig is ot cosidered i the followig by droppig the terms o the righthad side of (9) that are outside of the parethesis. IV. SIMUATION CASE STUDY The operatio of the proposed distributed sychroizatio method is demostrated by a simulatio case study of sigle-phase microgrid show i Fig. 2 [7]. It has four voltage-cotrolled voltage source iverters actig as grid-formig geerators ad two loads R ad R 2, coected respectively at the iverter- ad iverter-4. The microgrid has four differet PCCs that ca be used to coect it with adjacet power grids. Parameters of the simulated microgrid are show i Table I. Each iverter i the microgrid implemets the P droop cotrol law i (3) to develop its frequecy referece i. Sice the reactive power sharig is ot cosidered, the voltage referece of each iverter is set to ( E E i ). Fig. 3 ad 4 show simulated resposes of the isladed microgrid i Fig. 2. Fig. 3 shows frequecies, voltage magitudes, ad calculated active power outputs of all the four iverters. Fig. 4 shows iformatio states icludig i (distributed secodary cotrol), i (distributed frequecy sychroizatio), ad E i (distributed voltage sychroizatio) at all the four iverters. Evets durig the simulatio period are described below: t 0 : Simulatio is started with the distributed sychroizatio cotrol i the averagig mode, t : Distributed sychroizatio cotrol is chaged to the leader-follower mode with iverter- as the leader. Its iformatio states is reduced from 0 to 2 rad/s to reduce the microgrid frequecy from 60 to 9 Hz, ad E is icreased to 0.0E to icrease the microgrid Distributed sychroizatio gai, k s 0.2 ow-pass filter time-costat, T, T E 0 voltage by % above the omial voltage E. t 2 : Iverter-3 is made the leader. Its frequecy correctio state 3 is kept equal 2 ad the voltage correctio state E 3 is reduced to 0.0E to reduce the microgrid voltage by % below the omial voltage E. t 3 : Iverter-4 is made the leader. Its frequecy correctio state 4 is icreased to 2 to icrease the microgrid frequecy to 6 Hz ad the voltage correctio state E 4 is made equal to 0.02E to icrease the microgrid voltage to 2% below the omial voltage E. t 4 : oad R 2 is doubled from 2 kw to 4 kw. After the simulatio is started at t 0, the distributed secodary cotrol iformatio states i s start icreasig to restore the microgrid frequecy to 60 Hz. The total load o the microgrid is 4 kw, which is shared by the four iverters depedig o the P droop slopes m i s. Active power supplied by iverters ad 4 is double tha that supplied by iverters 2 ad 3 because the droop slopes m ad m 4 are half tha the droop slopes m 2 ad m 3. The distributed sychroizatio states i Fig. 4b) ad c) cotiue to stay at a commo value because of the averagig mode. Iverter- is assiged the leader at t ad the distributed sychroizatio cotrol is chaged from the averagig mode to the leader-follower mode. The distributed sychroizatio iformatio states of the remaiig iverters start approachig that of the iverter-, as see i Fig. 4b) ad c). Sice, the follower iverters take sometime before covergig their sychroizatio iformatio states to that of the iverter-, there is a trasiet power mismatch amog the iverters, as see i Fig. 3c). The trasiet power mismatch is miimized by usig a low-pass filter as discussed i Sectio III B. Depedig o the sychroizatio iformatio states set by the leader iverter-, the microgrid frequecy ad voltage settle respectively to 9 Hz ad.0e. Distributed sychroizatio is switched back to the averagig mode at aroud 30s without resultig i ay trasiets.

7 (kw) (V) (Hz) a) b) c) i 2 E i P i t 0 t t 2 t 3 t 4 t (s) Fig. 3. Performace of distributed sychroizatio cotrol: a) Iverter output voltage frequecies i /(2), b) iverter output voltage magitudes E i, ad c) iverter active power outputs P i. Solid red lies: iverter-, dashed blue lies: iverter-2, dotted gree lies: iverter-3, ad dashed-dotted pik lies: iverter-4. At t 2, the iverter-3 is made the leader. Sice the iverter-3 does ot demad chage i the microgrid frequecy, there is o disturbace i the active power sharig amog the iverters at t 2. The microgrid voltage settles to a ew value 0.9E depedig o E 3 set by the iverter-3. At t3, the iverter-4 is made the leader ad it is evidet from Fig. 3 ad 4 that the microgrid frequecy ad voltage coverge to values demaded by the leader iverter-4. At t 4, load R 2 is icreased from 2 to 4 kw, makig the total load o the microgrid to be 6 kw. It is to be oted that the sychroizatio states i Fig. 4b) ad c) remai uaffected as the load trasiets are urelated to the distributed sychroizatio dyamics. O the other had, the distributed secodary cotrol iformatio states i s start icreasig to compesate for the icremet i the total microgrid load ad restore the frequecy back to the value demaded by the leader iverter. V. CONCUSION This paper proposed a cosesus-based distributed sychroizatio method for microgrids with multiple poits of itercoectio. Ulike cetralized secodary cotrol based sychroizatio approach, the proposed method does ot require separate commuicatio system for each itercoectio poit ad it eables microgrid sychroizatio at multiple itercoectio poits usig a commo sparse commuicatio etwork. (V) (rad/s) (rad/s) a) b) c) E i t 0 i i t t 2 t 3 t 4 t (s) Fig. 4. Iformatio states of distributed secodary ad distributed sychroizatio cotrol. a) Secodary frequecy cotrol output i, b) distributed frequecy sychroizatio cotrol output i, ad c) distributed voltage sychroizatio cotrol output E i. Solid red lies: iverter-, dashed blue lies: iverter-2, dotted gree lies: iverter-3, ad dashed-dotted pik lies: iverter-4. Future work will ivestigate the effects of the proposed distributed sychroizatio method o the reactive power sharig performace ad the stability of the microgrid. REFERENCES [] Microgrid Cotrollers The Heart ad Soul of Microgrid Automatio, IEEE Power Eergy Mag., vol., o. 4, July/Aug [2] M. Shahidehpour, Z. i, S. Bahramirad, Z. i, ad W. Tia, Networked microgrids IEEE Power Eergy Mag., vol., o. 4, pp.63-7, July/ Aug [3] J. M. Guerrero, J. C. Vasquez, J. Matas,. G. de Vicua, ad M. Castilla, Hierarchical cotrol of droop-cotrolled ac ad dc microgrids a geeral approach toward stadardizatio, IEEE Tras. Id. Electro., vol. 8, o., pp. 8-72, Ja. 20. [4] S. Shah, H. Su, D. Nikovski, ad J. Zhag, VSC-based active sychroizer for geerators, IEEE Tras. Eergy Cov., Early Access, 207. [] Q. Shafiee, J. M. Guerrero, ad J. C. Vasquez, Distributed secodary cotrol for isladed microgrids a ovel approach, IEEE Tras. Power Electro., vol. 29, o. 2, pp , Feb [6] J. W. Simpso-Porco, F. Dorfler, ad F. Bullo, Sychroizatio ad power sharig for droop-cotrolled iverters i isladed microgrids, Automatica, vol. 49, o. 9, pp , Sep [7] J. W. Simpso-Porco, Q. Shafiee, F. Dorfler, J. C. Vasquez, J. M. Guerrero, ad F. Bullo, Secodary frequecy ad voltage cotrol of isladed microgrids via distributed averagig, IEEE Tras. Id. Electro., vol. 62, o., pp , Nov. 20. [8] W. I. Re, R. W. Beard, E. M. Atkis, Iformatio cosesus i multivehicle cooperative cotrol, IEEE Cotrol Syst. Mag., vol. 27, o. 2, pp. 7-82, April 2007.