Aalborg Unverstet Mult-Agent-Based Dstrbuted State o Charge Balancng Control or Dstrbuted Energy Storage Unts n AC Mcrogrds L, Chendan; Dragcevc, Tomslav; Quntero, Juan Carlos Vasquez; Guerrero, Josep M.; Coelho, Ernane A. A. Publshed n: Proceedngs o the 015 IEEE Appled Power Electroncs Conerence and Exposton (APEC) DOI (lnk to publcaton rom Publsher): 10.1109/APEC.015.7104773 Publcaton date: 015 Document Verson Early verson, also known as pre-prnt Lnk to publcaton rom Aalborg Unversty Ctaton or publshed verson (APA): L, C., Dragcevc, T., Vasquez, J. C., Guerrero, J. M., & Coelho, E. A. A. (015). Mult-Agent-Based Dstrbuted State o Charge Balancng Control or Dstrbuted Energy Storage Unts n AC Mcrogrds. In Proceedngs o the 015 IEEE Appled Power Electroncs Conerence and Exposton (APEC) (pp. 967-973 ). IEEE Press. I E E E Appled Power Electroncs Conerence and Exposton. Conerence Proceedngs, DOI: 10.1109/APEC.015.7104773 General rghts Copyrght and moral rghts or the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton o accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts.? Users may download and prnt one copy o any publcaton rom the publc portal or the purpose o prvate study or research.? You may not urther dstrbute the materal or use t or any prot-makng actvty or commercal gan? You may reely dstrbute the URL dentyng the publcaton n the publc portal? Take down polcy I 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 rom vbn.aau.dk on: maj 01, 018
Ths document downloaded rom www.mcrogrds.et.aau.dk s the preprnt verson o the nal paper: C. L, T. Dragcevc, J. C. Vasquez, J. M. Guerrero, and E. A. A. Coelho, "Mult-Agent-Based Dstrbuted State o Charge Balancng Control or Dstrbuted Energy Storage Unts n AC Mcrogrds," n Proc. IEEE APEC 015 Mult-Agent-Based Dstrbuted State o Charge Balancng Control or Dstrbuted Energy Storage Unts n AC Mcrogrds Chendan L, Tomslav Dragcevc, Juan C. Vasquez, and Josep M. Guerrero Department o Energy Technology, Aalborg Unversty Aalborg, Denmark {che, tdr, juq, joz}@et.aau.dk (http://www.et.aau.dk/research-programmes/mcrogrds) Abstract In ths paper, a multagent based dstrbuted control algorthm has been proposed to acheve state o charge (SoC) balance o dstrbuted energy storage (DES) unts n an AC mcrogrd. The proposal uses requency schedulng nstead o adaptve droop gan. Each DES unt s taken as an agent and they schedule ther own requency reerence gven o the real power droop controller accordng to the SoC values o the other DES unts. Further, to obtan the average SoC value o DES, dynamc average consensus algorthm s adapted by each agent. A smallsgnal model o the system s developed n order to very the stablty o the control system and control parameters desgn. Smulaton results demonstrate the eectveness o the control strategy and also show the robustness aganst communcaton topology changes. Keywords multagent; dstrbuted control; State-o-charge balance; dstrbuted energy storage; AC mcrogrds; requency schedulng; dynamc average consensus I. INTRODUCTION Mcrogrd s ganng more and more attenton as one o the most potental technologes to ncrease ecency and relablty o power systems. A mcrogrd can be dened as a small-scale dstrbuton electrcal grd conssted o dstrbuted energy resources (DER) and dspersed loads, whch can operate n both grd connected and sland mode as an ntegrated controllable entty [1]. Due to the ntermttent nature o renewable energy resource (RES) and the lack o nerta o power electronc converters, dstrbuted energy storage (DES) unts are essental to provde ancllary servces to the grd and to balance electrcty generaton and consumpton n slanded mode. Moreover, to ncrease the system relablty, more than one set o dstrbuted energy system unts tend to be needed []. Furthermore, SoC balance s oten desrable among DES unts, whch present hgher ecency and State-o-Health (SoH) when ther SoC s wthn n a certan range whch depends also on the technology, e.g. between 0% and 80%. I SoC o the all the DES unts s consstent by makng t balance, no sngle unt tends to go outsde ths range. Thus, the power capacty o the DES s maxmzed all the tme,.e., t s less lkely that one o the unts s orced olne due to very hgh or very low SoC, so that the nstantaneous chargng/dschargng Ernane A. A. Coelho Núcleo de Pesqusa em Eletrônca de Potênca (NUPEP) Unversdade Federal de Uberlânda (UFU) - Faculdade de Engenhara Elétrca (FEELT) Uberlânda, Mnas Geras, Brasl 38400-90 ernane@uu.br power can be maxmzed. Several prevous works have been done to acheve SoC balancng []-[10]. However, most o them are ocused on DC mcrogrd systems, whle lttle work has been done n ths area or AC mcrogrds [4], [10]. For nstance, n [10], a SoC-dependent adaptve droop uncton s proposed to balance DES unts; however the system stablty s very senstve to the droop coecent, so that large values may lead to system nstablty [11].Moreover, centralzed control can be used to manage DES [7], but they are prone to a sngle pont o alure o the supervsory devce. In ths paper, a MAS based dstrbuted control algorthm has been proposed to acheve state o charge (SoC) balance o dstrbuted energy storage (DES) unts n an AC mcrogrd. Takng each DES unt as an agent, requency schedulng nstead o adaptve droop gan s adopted to control ts chargng and dschargng autonomously. The communcaton among the agents to obtan the global normaton necessary to make the local decson,.e, the average SoC value o DES, s mplemented through dynamc average consensus algorthm. The rest o the paper s organzed as ollows. Secton II brely ntroduces the conguraton o the example AC mcrogrd wth MAS controlled DES. Secton III descrbes the requency schedulng method or balancng the DES unts. Secton IV presents multagent based dynamc average consensus algorthm and complete control method o each agent s provded. In the last secton, Hardware n the loop result s presented to show the eectveness o the proposed control method. Fnally, Secton IV concludes the paper and possble uture work. II. SYSTEM CONFIGURATION Fg. 1 shows an example o AC mcrogrd conguraton, whch conssts o RES (wnd and solar), AC load, and three DES unts controlled by a mult-agent system (MAS). As the only grd ormng component n the mcrogrd, DES s responsble to balance the msmatch between the power produced by RES and that needed by the load. Normally, the load s ed by RES when there s enough amount o power avalable, and DES s workng n chargng mode. When the output power rom the RES s not enough and the mcrogrd s operatng n slanded mode, DES swtches to dschargng mode. It s desred that durng dschargng mode, the DES unt wth hgher SoC wll provde more power than the others, and
PCC IBS Dstrbuted Energy Storage System Agent Agent 1 Agent 3 AC mcrogrd B. Estmaton o the SoC Beore ntroducng requency schedulng or SoC balance, the SoC estmaton method s descrbed rst. Although many technques have been proposed to measure or montor the SoC o a cell or the battery, charge countng or current ntegraton s the most commonly used technque [3] and thus s chosen n ths paper. The basc o smpled SoC calculaton can be wrtten as * 1 SoC = SoC b_ dt C () e_ Man Utlty Grd Wnd Power AC Load Fg.1 AC mcrogrd wth multagent controlled DES durng the chargng mode, the ones wth lower SoC wll absorb more power, so that the SoC balance among DES can be mantaned. III. FREQUENCY SCHEDULING FOR SOC BALANCING IN AN AC MICROGRID A. Real power control based on droop To make SoC o DES balance, real power o each unt should be regulated accordng to the SoC o the DES. Droop control s one o the most popular methods or real and reactve power regulaton [1]. Not lke reactve power, real power sharng s not senstve to derent lne mpedance and thus can be regulated well by the requency droop controller as = K P (1) 0 P There are two possbltes to change the way how real power shared, whch s llustrated n Fg.. It can be seen that ether changng the requency droop gan Fg. (b) or changng requency gven can change the real power sharng. Prevous work [4] and [10] has employed adaptve requency droop gan to acheve SoC balance. Instead o adjustng the droop gan, the possblty o adaptve requency gven s nvestgated n the paper. PV where b_, SoC *, and C e_ are the output current, ntal value o SoC, and battery capacty or unt respectvely. I the power loss n the converter can be omtted and assume the output voltages o the batteres are the same, there exsts ollowng approxmaton or each DES unt. P = P = V (3) n_ n b_ where V n, P and P n_ are the nput voltage o the converter, output power o the converter, and nput power o the converter, or unt, respectvely. Here we assume that values o the nput voltage o all the converters are the same. So combnng the () and (3), the SoC calculaton can be wrtten as 1 where µ = C V, e_ n SoC = SoC μ p dt (4) * C. Frequency schedulng or SoC Balance In order to take SoC o all DES unts nto consderaton, the requency gven 0 o real power droop n (1) s moded by addng an tem respect to the values o SoC o all the unts n the DES. The control dagram s shown n Fg.3, and the equaton o the ths method can be wrtten as: 0 = + K (SoC SoC ) (5) * 0 SoC mean beng SoC mean the average value o SoCs o all DES unts, K SoC * a proportonal coecent, and 0 the nomnal ndvdual requency or agent. 01 0 01 > 0 K = K p1 p = 01 0 01 = 0 K > K p1 p P1 P (a) K p s xed P Fg. Real power droop prncple (b) P 1 P 0 s xed Fg. 3 Control dagram o requency schedulng or SoC Balance
Δ = Δ K Δp 1 01 p 1 + s Δ = Δ K Δp 0 p + s (13) (14) Fg.4 System topology or small sgnal analyss D. Small sgnal model o requency schedulng method or SoC Balance In order to analyze the eects o the parameter K SoC towards system stablty, small sgnal model based on [13] s set up consderng ths newly added requency schedulng controller. For smplcty, the model consders system wth two DES unts supplyng a common load, and the topology s shown n Fg. 4. In addton to (1), the characterstcs o reactve droop s dened as E = E K Q (6) 0 Q The local droop controller ncludes a low pass lter, expressed as P = p + s Q = q + s where p, q and are measured real power and reactve power o DES unt and cut-o requency o the low pass lter, respectvely. Accordng to (3), the controller o the requency schedulng can be wrtten as: * K 01 SoC 01 SoC1 SoC (7) (8) = + ( ) (9) * K 0 SoC 0 SoC SoC1 = + ( ) (10) Consderng (4), (9) and (10) can be small-sgnal perturbed as μk SoC 01 p1 p Δ = ( Δ Δ ) (11) μk SoC 0 p p1 Δ = ( Δ Δ ) (1) Assumng that droop gans are the same or the two unts, by perturbng (1), t yelds Takng a common d-q reerence rame or all the converters, the vector E can be represented as E = ed + jeq (15) The angle and magntude o the vector can be wrtten as eq δ = arctan( ) (16) ed E = E = ed + eq (17) Consderng Δ (s) = s Δ δ(s), and combnng (11), (1), (13), (14), (6) and (8), the state equaton or each converter can be obtaned as Δ Δ Δ Δ ΔP = + (18) 0 0 M C Δe d Δe d ΔQ Δe q Δeq where the detaled expressons or matrx obtaned rom above mentoned equatons. M and C can be Consderng the expressons o actve and reactve power suppled by each converter, P = e dd+ e qq (19) Q = edq eqd (0) Lnearzng the equatons above at the equlbrum pont, we get the ollowng expresson n a symbolc orm, Δ S = I Δ e+ E Δ (1) s where I s and Es are constant matrces wth respect to the state at equlbrum pont, and Δ e = [ Δe 1, 1,, ] T d Δeq Δed Δ eq, Δ = [ Δ, Δ, Δ, Δ ] T. d1 q1 d q Perturbng the nodal admttance matrx equaton o the network, we get Δ = YsΔ e () where Y s s the nodal admttance matrx o the network. Substtutng () n (1), we can get Δ S = ( I + EY ) Δ e (3) s s s The state equaton o the whole system can now be obtaned as s
TABLE I. CONTROL PARAMETER FOR EACH DES UNIT Item Symbol Value Lne resstor (real(zlne)) R lne 0.1Ω Lne nductor(mag(zlne)) L lne 6.8 mh Cut-o requency o LPF 0.7 rad/s Nomnal requency 0 314 rad/s Frequency droop gan K P 0.00 rd/ws Voltage droop gan K Q 0.00 V/Var Constant n SoC estmaton µ 6000(Ah V) -1 Load Z load 50 Ω 50 40 30 0 10 0-10 -0-30 -40 λ 7, λ 8 X = MX+ C( I + EY) KX= AX (4) s s s s s s where X 1 01 ed1 eq 1 0 ed eq = [ Δ, Δ, Δ, Δ, Δ, Δ, Δ, Δ ] T, C1 M 1 Cs = C, M = M, K s 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 =, 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 A= M + C ( I + EY ) K. s s s s s s The root locus plot o the system or K SoC rom 0 to 1 s shown n Fg. 5, wth the control parameters shown n Table I. Two egenvalues appear n the orgn because the system matrx s sngular due to the redundant state n the model, and thus not nluence the dynamcs. As can be seen, when K SoC s λ 6 λ 3 λ 1, λ -50-4.5-4 -3.5-3 -.5 - -1.5-1 -0.5 0 0.5 λ 4 λ 5 Fg. 5 Egenvalue trace wth derent K soc zero, λ 3 s redundant, and t s just lke the conventonal droop control, and when K SoC ncreases, λ 4 and λ 5 move away rom the real axs whch wll make the system more oscllatng, so that K SoC can be bounded. IV. SOC INFORMATION DISCOVERY BASED ON DYNAMIC AVERAGE CONSENSUS In order to get the value o SoC mean, two alternatves are avalable. One possblty s to choose a supervsory note and make all the unts communcate wth ths master and the average value s then passed down to each unt agan ater ths supervsory node processes all the normaton t gets. However, ths s method wll cause heavy communcaton burden and t s prone to the alure o the supervsory note. Another alternatve s to solve ths problem n a dstrbuted ashon through a amly o algorthms known as average consensus, where each agent only exchanges normaton wth a subset peers (e.g. ther drect neghborhood n the communcaton network). Here we model the mult-agent network as an undrected and connected graph wth a set o agent N and a set o edges E, where each edge {, j} E represents a bdrectonal communcaton lnk between two dstnct agents. Each agent stores a state wth an ntal value, whch wll be updated n each teraton wth the teraton counter value k, and nally reach an agreement on the average o the state. Essentally, the consensus algorthm can be descrbed n two steps: 1) each agent communcate wth ts mmedate neghbors to exchange the value o the state; ) all the agents update ther state normaton through a protocol whch s a lnear combnaton o ther own state normaton and the state normaton o ther neghbors obtaned rom last step. In ths applcaton, the state o nterest s the SoC o DES unt. The consensus approach used here s based on dynamc average consensus algorthm [14], whch s the dscrete tme algorthm o [15]. The normaton dscovery process or agent s represented as ollows. SoCmean _ (k+ 1) = SoC n_ + σ δj(k+ 1) (5) j N δ (k+ 1) = δ (k) + SoC (k) SoC (k) (6) j j mean _ j mean _ Where SoC mean_ s the average SoC o DES calculated by agent, SoC nt_ s the ntal SoC o DES unt, and σ s a scalng actor, whch s desgned accordng to the stablty; here σ s chosen as 1/3. Ater a lmted number o teratons, the average SoC o DES calculated by each agent can converge by only communcatng wth ther closest neghbor. At that pont, each agent can make smultaneously ther own decson n the same way. The control dagram o the proposed approach or each DES agent s shown n Fg. 6. As can be seen n the bottom o the control dagram, each converter s controlled by droop controller whch s mposed outsde the current loop and voltage loop, as dscussed n (1) and (6). The detaled desgn o nter loop can be ound n [16]. To make the SoC balanced, requency gven s moded accordng to SoC mean,.e., the average value o SoC, based the method proposed n secton III
TABLE II. PARAMETER OF THE SYSTEM Parameters Symbol Value Unts Power stage Nomnal voltage E0 30 V * Nomnal requency 0 314 rad/s Lne 1 resstor R lne_1 0.1 Ω Lne 1 nductor L lne_1 5.4 mh Lne resstor R lne_ 0.1 Ω Lne nductor L lne_ 6.8 mh Lne 3 resstor R lne_3 0.09 Ω Lne 3 nductor L lne_3 7.8 H LC lter nductor or each DES unt L 1.8 mh LC lter capactor or each DES unt C 7 µf Control parameters Cut-o requency o low pass lter or each DES unt 0.7 rad/s Proportonal requency droop or each DES unt K P 0.00 rad/ws Proportonal ampltude droop or each DES unt K Q 0.0 V/Var Proportonal coecent o requency schedulng or each DES unt K SoC 0.15 - DES unt parameters Intal SoC or DES unt 1 SoC nt_1 80 % Intal SoC or DES unt SoC nt_ 70 % Intal SoC or DES unt 3 SoC nt_3 60 % Constant or SoC estmaton μ 6000 (Ah V)-1 part C. The normaton dscovery o SoC mean s based on dynamc average consensus algorthm as just dscussed. Each agent nteracts wth another only n terms o exchangng the updated SoC normaton. V. HARDWARE-IN-THE-LOOP RESULTS In order to very the eectveness o the proposed dstrbuted control strategy, hardware n the loop smulaton based on dspace s carred out. The tested system s a mcrogrd wth three DES unts connected n parallel to the common AC bus through transmsson lne, controlled by the MAS n a rng communcaton topology, as shown n Fg. 1. Neghborng Agent j SoC (k) mean _ SoC (k) mean _ j SoC (k+ 1) = SoC + λ δ (k+ 1) mean _ n_ j j N δ (k+ 1) = δ (k) + SoC (k) SoC (k) _ j j mean j mean _ Frequency schedulng Inormaton Dscovery Agent The power stage and control parameters are presented n Table II. In order to test the eectveness o the control system under derent operaton modes o the DES, the DES was at begnnng supplyng a load at 100 Ω n the dschargng mode. At the tme 0s, an extra1700w real power was startng to be produced by RES n the mcrogrd, whch wll render the power to be surplus besdes meetng the demand o the load and trgger the DES to change rom dschargng mode to chargng mode. As can be seen n the Fg. 7, the values o SoC n derent DES unt are convergng n both the chargng and dschargng modes n (a) as the result o the real power s unevenly shared by each unt as shown n (b). In order to test the robustness o the control system under certan communcaton topology changes, n addton to the power changes, n the meanwhle, communcaton lnk between unt 1 and unt 3 s dsconnected at tme 60.5s. As s shown n the Fg.7(c) and (d), the communcaton topology changes wll cause a tny dsturbance o the consensus result o SoC mean, and thus the trval transent n the requency gven or the droop controller. However, ths tny dsturbance brngs no eects on the SoC o the DES unt and the real power t produces. Accordng to average consensus theory, as long as the graph o the communcaton topology remans connected, consensus wll be reached. P/Q Droop control Droop control Reerence generator v re Voltage loop Inner loops Current loop Fg.6 Control dagram or each agent PWM generator o PWM I. CONCLUSIONS Ths paper proposed a dstrbuted control method to acheve SoC balance or DES usng requency schedulng based on MAS. Instead o usng adaptve droop gan, the possblty o modyng the requency gven s explored. A smple method based on the normaton o average SoC o the DES to adjust the requency gven s proposed. Frequency schedulng method s analyzed through small sgnal model to gve the
[Hz] [W] Fg. 7 Results o hardware n the Loop smulaton gude o choosng the control parameters o t. Average SoC o the DES s successully dscovered by dynamc consensus algorthm whch oers robustness to the system aganst certan communcaton connecton loss. Promsng drectons or uture work nclude testng the scalablty, lexblty and plug and play eatures o ths control strategy, consderng power network topology and other objectves such as letme maxmzaton, along wth the mplementaton o ths method to hybrd DES wth dstnctve chargng/ dschargng characterstcs o derent DES unts. REFERENCES [1] Hatzargyrou, N.; Asano, H.; Iravan, R.; Marnay, C., "Mcrogrds," Power and Energy Magazne, IEEE, vol.5, no.4, pp.78,94, July-Aug. 007 [] Kakgano, H.; Mura, Y.; Ise, T., "Dstrbuton Voltage Control or DC Mcrogrds Usng Fuzzy Control and Gan-Schedulng Technque," Power Electroncs, IEEE Transactons on, vol.8, no.5, pp.46,58, May 013; do: 10.1109/TPEL.01.17353 [3] Wangxn Huang; Qahouq, J.AA, "Dstrbuted battery energy storage system archtecture wth energy sharng control or charge balancng," Appled Power Electroncs Conerence and Exposton (APEC), 014 Twenty-Nnth Annual IEEE, vol., no., pp.116,1130, 16-0 March 014 [4] Guerrero, J.M.; Vasquez, J.C.; Matas, J.; de Vcuña, L.G.; Castlla, M., "Herarchcal Control o Droop-Controlled AC and DC Mcrogrds A General Approach Toward Standardzaton," Industral Electroncs, IEEE Transactons on, vol.58, no.1, pp.158,17, Jan. 011 [5] Xaonan Lu; Ka Sun; Guerrero, J.M.; Vasquez, J.C.; Lpe Huang, "State-o-Charge Balance Usng Adaptve Droop Control or Dstrbuted Energy Storage Systems n DC Mcrogrd Applcatons," Industral Electroncs, IEEE Transactons on, vol.61, no.6, pp.804,815, June 014;do: 10.1109/TIE.013.79374; [6] N. L. Daz, Dragcevc, T.; Vasquez, J. C.; Guerrero, J. M., "Fuzzylogc-based gan-schedulng control or state-o-charge balance o dstrbuted energy storage systems or DC mcrogrds," Appled Power Electroncs Conerence and Exposton (APEC), 014 Twenty-Nnth Annual IEEE, vol., no., pp.171,176 [7] Dragcevc, T.; Guerrero, J.M.; Vasquez, J.C.; Skrlec, D., "Supervsory Control o an Adaptve-Droop Regulated DC Mcrogrd Wth Battery Management Capablty," Power Electroncs, IEEE Transactons on, vol.9, no., pp.695,706, Feb. 014 [8] Chendan L; Dragcevc, T.; Daz, N.L.; Vasquez, J.C.; Guerrero, J.M., "Voltage schedulng droop control or State-o-Charge balance o dstrbuted energy storage n DC mcrogrds," Energy Conerence (ENERGYCON), 014 IEEE Internatonal, vol., no., pp.1310,1314, 13-16 May 014
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