Consensus-Based Distributed Control with Communication Time Delays for Virtual. Synchronous Generators in Isolate Microgrid.

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1 Eergy ad Power Egieerig, 2017, 9, ISSN Olie: ISSN Prit: X Cosesus-Based Distributed Cotrol with Commuicatio Time Delays for Virtual Sychroous Geerators i Isolate Microgrid Laiju Che 1,2, Yuyag Wag 1, Tiawe Zheg 1,2, Zhequa Su 3 1 State Key Laboratory of Power System, Departmet of Electrical Egieerig, Tsighua Uiversity, Beijig, Chia 2 Key Laboratory of Photovoltaic Power Geeratio ad Grid-coected Techology (Qighai Electrical Power Research Istitute, Qighai Electric Power Corporatio, Xiig, Chia) 3 Shaaxi Regioal Electric Power Desig ad Research Istitute, Xi a, Chia How to cite this paper: Che, L.J., Wag, Y.Y., Zheg, T.W. ad Su, Z.Q. (2017) Cosesus-Based Distributed Cotrol with Commuicatio Time Delays for Virtual Sychroous Geerators i Isolate Microgrid. Eergy ad Power Egieerig, 9, Received: Jauary 21, 2017 Accepted: March 30, 2017 Published: April 6, 2017 Abstract A cosesus-based distributed cotrol method of coordiated VSGs with commuicatio time delays i isolate microgrid is proposed. Whe time delays are cosidered i commuicatio, there are some effects o frequecy restoratio ad active power output allocatio. I the cotrol structure, oly local iformatio exchage is eeded, while the fial frequecy ca be cotrolled to the omial value ad the VSGs ca automatically share loads accordig to their rated values. A AC microgrid with three VSGs ad some loads is implemeted. The proposed cotrol strategy is verified by MATLAB/ Simulik simulatio results. Keywords Virtual Sychroous Geerator, Time Delays, Distributed Cotrol, Cosesus Algorithm 1. Itroductio Microgrids are active clusters of distributed geerators (DG), eergy storages ad loads [1] [2]. More ad more power electroic iterfaced DGs are curretly beig istalled i microgrid. However, these DGs caot provide requisite iertia ad dampig support. Owig to the isufficiet of iertia ad dampig, serious problems may arise, such as frequecy fluctuatio [3] [4]. Therefore, virtual sychroous geerator (VSG) is proposed to solve those problems metioed before. Geerally, VSG is based o sychroous geerator trasiet model to imitate its operatig characteristics [5] [6]. VSGs ca provide DOI: /epe B013 April 6, 2017

2 sufficiet iertia ad dampig, so they are gradually applied i microgrids. I practice, it is ecessary for VSGs to cooperate to meet high power requiremet of the power supply system [7]. I [8], the mathematic model of VSG is proposed ad droop cotrol strategy is desiged to share power betwee VSGs. Sice VSGs essetially have droop characteristics, the cotrol of existig microgrid with VSGs actually belogs to the decetralized cotrol [9]. However, as the capacity of VSGs icrease, it becomes difficult to coordiate all the VSGs to achieve a commo purpose by decetralized cotrol [10]. Compared with the decetralized cotrol, the distributed cotrol ca achieve global maagemet through exchagig iformatio betwee eighbor VSGs [11]. Recetly, the cosesus-based distributed cotrol scheme for microgrids has bee itroduced to address complex distributed commuicatio problems [12] [13]. This scheme ca help system frequecy restorig ad active power sharig accordig to each VSG s omial ratigs. Nevertheless, whe iformatio is exchaged betwee coected VSGs through commuicatio, time delays from both message trasmissio ad processig should be cosidered [14]. I [15], average cosesus problem for udirected etworks of dyamic agets havig commuicatio delays is studied. I [16], a ovel agreemet framework for multiple agets evolvig o a directed iformatio graph with o-uiform delays is proposed. However, up to ow, few works cocetrate o the distributed cotrol with time delays of coordiated VSGs. Therefore, i this paper, a cosesus-based distributed cotrol method cosiderig commuicatio time delays of coordiated VSGs i isolate is desiged. With ode-to-ode distributed commuicatio, the proposed cotrol method oly eeds several iformatio exchaged betwee eighbors ad the compute is ot complex. I additio, the model with time delays has more practical value for egieerig applicatio. The rest of this paper is orgaized as follows. I Sectio II, the model of VSG is implemeted ad the coordiated cotrol structure of VSGs is formed. Furthermore, cosesus algorithm with time delays will be preseted. I Sectio III, the cosesus-based cotrol with time delays of coordiated VSGs is proposed. I Sectio IV, some simulatios are realized to show the results of coordiated VSGs with differet time delays. Fially, coclusio is summarized i sectio V. 2. Prelimiaries 2.1. Cotrol of VSGs I geeral, VSG cosists of a three phase legs ad a three-phase LCL filter. The typical topology of VSG is show i Figure 1. I Figure 1, U d, L, C ad R are DC voltage, the filter iductace, capacitor ad resistace, respectively. u 0 = (u a, u b, u c ) T ad 0 i = (i a, i b, i c ) T are output three-phase voltage ad curret, which ca be used to compute active ad reactive power. The traditioal droop cotrol strategy is geerally employed i VSGs. 103

3 Figure 1. Topology of VSG. The active power-frequecy cotroller is show i Figure 2 ad the active power-frequecy droop cotrol characteristics of VSG are show graphically i Figure 3. It is show i Figure 2 that P* ad P are rated active power ad actual value. J is the imagiary momet of iertia, which ca provide VSG with iertia i dyamic process. D is dampig coefficiet, which is used as feedback gai. ω 0, ω ad θ are rated agular frequecy, actual agular frequecy ad agle. I Figure 3, f a is omial frequecy, P a is omial active power output. Firstly the operatio ode is A. Whe load power icreases to P b, the operatio ode moves from A to B, ad correspodig frequecy is f b. As we ca see from Figure 3, there exist frequecy deviatios for the chage of active power output, which should be compesated. I order to solve this problem, the coordiated cotrol structure of VSGs is proposed, as show i Figure 4. It ca be see from Figure 4 that the coordiated cotrol structure of VSGs is performed at two levels. Active power-frequecy droop cotrol is implemeted for primary level. At the secod level, the distributed cotrol is utilized to exchage iformatio betwee eighbor VSGs, thus achievig frequecy restoratio ad reasoably active power sharig Cosesus Algorithm Based o Graphs Theory The cosesus algorithm is beefit for distributed cooperative cotrol of VSGs. Cosider a udirected graph, the adjacecy matrix A represets the coectio coditio of commuicatio topology. Because the odes are mutually coected, A is a symmetric matrix. Meawhile, the degree matrix D, is a diagoal matrix, where the degree of vertex stads for the umber of coected VSGs. The Laplacia matrix L of a udirected graph is the defied as L= D A (1) Whe the commuicatio topology is satisfied with the demad of a spaig tree, which meas each ode ca reach every ode by acertai way, the L is positive semi-defiite with oe zero eigevalue [17]. The cosesus algorithm ca be described as x = γ l ( x x ) (2) i ij i j j= 1 where x i, x j are cotrol variables of VSG i ad VSG j, is the umber of VSGs, γ is 104

4 Figure 2. Active power-frequecy droop cotroller. Figure 3. Active power-frequecy droop cotrol characteristic. Figure 4. Coordiated cotrol structure of VSGs. called the diffusio costat ad l ij is the elemet of L. If time delays are take ito cosideratio, formula (2) is modified as ( ) ( ) x = γ l x t τ x t τ (3) i ij i i j j j= 1 I the simplest case of τ i = τ j = τ, it meas that trasmissio ad processig time delays of all VSGs are equal. Whe the system meets the demad of a spaig tree ad time delays are i a certai rage, all VSGs may globally reach a average-cosesus as described below 1 lim x ( t) = lim x ( t) = x (0) (4) t + i j k t + k = 1 105

5 I a word, cosesus algorithm ca be used to reach active power output agreemet amog VSGs. 3. Cosesus-Based Distributed Cotrol Performace 3.1. Cosesus-Based Distributed Cotrol Accordig to the coordiated cotrol structure of VSGs ad the cosesus algorithm, the cotrol method is depicted as follows Jωω + D ( ω ω) = P P p (5) set reg i 0 i pi, i 0 i i i p k p P P p l ( ) (6) reg reg reg = set reg + pi j p, i i i i i ij j 1 D = pi, Dp, j set reg where P i ad P i are rated active power ad actual value of VSG i ad p i is the regulated value of active power, the subscript i is the serial umber of VSGs. D p,i, D p,j are the dampig coefficiet of VSG i ad VSG. j k p,i is the frequecy restoratio coefficiet of VSGi. J i is the imagiary momet of iertia, ω 0 is rated agular frequecy. Neighbor VSGs will exchage the iformatio to achieve cosesus. Fially, accordig to the cosesus algorithm, whe the Dp,1 Dp,2 Dp, = =... = (7) P P P set set set 1 2 P P P = = = (8) P P P set set set 1 2 Accordig to (8), the active power output of each VSGs are determied by their rated active power [10] Cosesus-Based Distributed Cotrol with Time Delays I practice, trasmissio ad processig time delays should be cosidered. Whe time delays are itroduced, the cotrol method ca be described as reg ( t τ ) pj ( t τ j) reg p reg set reg i i kp, i p i = Pi Pi pi + l ij (9) j= 1 Dpi, D p, j I accordace with (5) ad (9), the cotrol block diagram for each VSG is show i Figure 5. As is show i Figure 5, there are three mai sectios, icludig droop uit, restoratio uit ad cosesus uit. Droop uit ad restoratio uit ca coduct primary frequecy regulatio ad secod frequecy regulatio. Cosesus uit exchages active power regulatio iformatio betwee eighbor VSGs. Time delays, which geerally exist i commuicatio, are maily cosidered. Thus the cosesus-based distributed cotrol with time delays for VSGs is comprehesively built. 106

6 set P i P i + - Cosesus Uit Restoratio Uit 1 k pi, + s + reg - i p D pi, p 1 reg ( t τ ) pj ( t τ j) reg i i lij j= 1 Dpi, Dp, j ( J i ω ω 0 ) i 1 s + s + Droop Uit ω 0 θ i Figure 5. Cofiguratio of VSGs cosesus-based distributed cotrol with time delays. 4. Simulatio Aalysis A AC microgrid with three VSGs ad oe aggregate load was implemeted to test the effectiveess of the cosesus-based distributed cotrol formulatio (5) ad (9) preseted i Sectio III. set set set The mai parameters of simulatio are that P 1 = 10 kw, P 2 = 20 kw, P 3 = 30 kw, D p1 = 1000 kw/rad s 1, D p2 = 2000 kw/rad s 1, D p3 = 3000 kw/rad s 1, k p1 = k p2 = k p3 = 4 s ad J 1 = J 2 = J 3 = kg m 2. Figure 6 shows the commuicatio topology. It ca be see from Figure 6 that VSG 1 ca commuicate with VSG 2, while VSG 2 ad VSG 3 have commuicatio liks. At 0 s, three VSGs will provide eergy to the commo load, whose power cosumptio is 60 kw. Differet value of time delays are cosidered, icludig τ = 0, it represets o time delay, τ = 0.1 s, τ = 0.2 s, τ = 0.3 s ad τ = 0.5 s. Simulatio results of system frequecy are show i Figure 7 with differet time delays. As is show i Figures 7(a)-(c), for the icrease of load, the system frequecy declies ad it takes about 1s for frequecy to restore to 50 Hz. However, whe time delays are chose to be 0.3 s ad 0.5 s, show i Figure 7(d), Figure 7(e), the frequecy oscillates ad the system is ustable. Simulatio results of active power output are also show i Figure 8 with differet time delays. It ca be observed from Figure 8(a), it takes about 1s to achieve stability. Furthermore, P 1, P 2 ad P 3 are about 10 kw, 20 kw ad 30 kw, respectively. So the active power output allocatio ratio is 1:2:3, which is equal to the scale of the rated value of three VSGs. I Figure 8(b), the time delay is 0.1 s ad the active power output will quickly reach stability, too. Moreover, i Figure 8(c), whe the time delay is set to be 0.2 s, the active power output will have slight fluctuatios. With time delay beig 0.1 s or 0.2 s, the fial ratio of active power output ca maitai the settig proportio. However, if the time delay is 0.3 s or 0.5 s, as is show i Figure 8(d) ad 107

7 VSG1 VSG2 VSG3 Distributed commuicatio lik Figure 6. Commuicatio topology. 50 Frequecy/Hz (a) 50 Frequecy/Hz (b) 50 Frequecy/Hz (c) Frequecy/Hz (d) Frequecy/Hz (e) Figure 7. Waveform of frequecy, (a) τ = 0, (b) τ = 0.1 s, (c) τ = 0.2 s, (d) τ = 0.3 s, (e) τ = 0.5 s. 108

8 35 Active Power/kW P 1 P 2 P (a) Active Power/kW P 1 P 2 P 3 5 (b) Active Power/kW P 1 P 2 P 3 Active Power/kW P 1 P 2 (c) P (d) Active Power/kW P 1 P 2 (e) P 3 Figure 8. Waveform of active power, (a) τ = 0, (b) τ = 0.1 s, (c) τ = 0.2 s, (d) τ = 0.3 s, (e) τ = 0.5 s. 109

9 Figure 8(e), the system will become ustable. I a word, whe the commuicatio time delays are i a certai rage, the system ca keep stable, while the commuicatio time delays is out of this rage, the system will get ustable. Therefore it is very importat to fid a maximum boudary of time delays. Through the improvemet of commuicatio techology, time delays should be limited less tha the maximum boudary. 5. Coclusio I this paper, a cosesus-based distributed cotrol with time delays for coordiated VSGs is desiged. With ode-to-ode distributed cotrol, the commuicatio cost decreases ad the commuicatio stability icreases. Uder ideal coditio, there is o commuicatio time delays ad the system performsvery well. However, i practical egieerig, time delays caot be avoided. If the time delays are large eough, the system will ot be stable. This research ca provide useful referece for the applicatio of VSG i microgrid ad active power distributio etwork. I the future, we will research the maximum boudary of time delays, which ca maitai system stability Ackowledgemets This work was fuded by the Natioal Natural Sciece Foudatio of Chia (Grat Nos , ) ad Chia Postdoctoral Sciece Foudatio (2016M601025). Refereces [1] Wag,Z. Y., Che, B. K., Wag, J. H., et al. (2015) Coordiated Eergy Maagemet of Networked Microgridsi Distributio Systems.IEEE Trasactios o Smart Grid, 2015, 6, [2] Che, L. J., Wag,Y. Y., Yag, L. B., et al. (2016) Cosesus Cotrol Strategy with State Predictor for Virtual Sychroous Geerators i Isolated Microgrid. Power System Techology (POWERCON), 2016 IEEE Iteratioal Coferece o. IEEE, 1-5. [3] Xi, H.H.,Liu,Y., Qu, Z. H., et al. (2014) Distributed Cotrol ad Geeratio Estimatio Method for Itegratig High-Desity Photovoltaic Systems.IEEE Trasactios o Eergy Coversio, 29, [4] Xu,Y. L. ad Li,Z. C.(2015) Distributed Optimal Resource Maagemet Based o the Cosesus Algorithm i a Microgrid.IEEE Trasactios o Idustrial Electroics,62, [5] Zhog,Q. C., Weiss, G. (2011) Sychroverters: Iverters That Mimic Sychroous Geerators.IEEE Trasactios o Idustrial Electroics, 58, [6] Zheg,T. W., Che, L. J., Che, T. Y. ad Mei, S. W.(2015) Review ad Prospect of Virtual Sychroous Geerator Techologies. Automatio of Electric Power Systems, 39, [7] Dua,S. X. adli, X. C.(2013) Parallel Operatio Cotrol Techology for Distributed Modular Iverters. Publishig House of Electroics Idustry, Beijig, [8] Dig,M., Ya,X. Z. ad Su, J. Z.(2009) Cotrol Strategies of Iverters Based o Vir- 110

10 tual Sychroous Geerator i a Microgrid.Automatio of Electric Power Systems, 33, [9] Xi,H. H., Lu,Z. Liu, Y., et al. (2014) A Ceter-Free Cotrol Strategy for the Coordiatio of Multiple Photovoltaic Geerators. IEEE Trasactios o Smart Grid, 5, [10] Lu,L. Y.ad Chu, C. C.(2015) Cosesus-Based Secodary Frequecy ad Voltage Droop Cotrol of Virtual Sychroous Geerators for Isolated AC Micro-Grids. IEEE Joural o Emergig ad Selected Topics i Circuits ad Systems, 5, [11] Xi,H. H., Zhag,M., Seuss,J.,et al. (2013) A Real-Time Power Allocatio Algorithm ad Its Commuicatio Optimizatio for Geographically Dispersed Eergy Storage Systems.IEEE Trasactios o Power Systems, 28, [12] Olfati-Saber, R. ad Murray, R.M. (2004) Cosesus Problems i Networks of Agets with Switchig Topology ad Time-Delays.IEEE Trasactios o automatic cotrol, 49, [13] Cai, H. ad Hu, G. Q.(2016) Cosesus-based Distributed Noliear Hierarchical Cotrol of Ac Microgriduder Switchig Commuicatio Network.Cotrol ad Automatio (ICCA), th IEEE Iteratioal Coferece o. IEEE, [14] Re,W. adbeard, R. W.(2008) Distributed Cosesus i Multi-Vehicle Cooperative Cotrol. Spriger-Verlag, Lodo. [15] Blima,P.A. ad Ferrari-Trecate, G. (2008) Average Cosesus Problems o Networks of Agets with Delayed Commuicatios. Automatica, 44, [16] Lee, D., Spog, M. W. (2006) Agreemet with No-Uiform Iformatio Delays America Cotrol Coferece. IEEE, 6. [17] Bidram, A., Davoudi, A. ad Lewis, F.L. (2014) A Multiobjective Distributed Cotrol Framework for Isladed AC Microgrids.IEEE Trasactios o idustrial iformatics, 10, Submit or recommed ext mauscript to SCIRP ad we will provide best service for you: Acceptig pre-submissio iquiries through , Facebook, LikedI, Twitter, etc. A wide selectio of jourals (iclusive of 9 subjects, more tha 200 jourals) Providig 24-hour high-quality service User-friedly olie submissio system Fair ad swift peer-review system Efficiet typesettig ad proofreadig procedure Display of the result of dowloads ad visits, as well as the umber of cited articles Maximum dissemiatio of your research work Submit your mauscript at: Or cotact epe@scirp.org 111