Aalborg Universitet. Published in: Proceedings of the 2013 IEEE ECCE Asia DownUnder

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1 Aalborg Univeritet Modelling, Analyi, and Deign of a Frequency-Droop-Baed Virtual Synchronou Generator for Microgrid Application Du, Yan; Guerrero, Joep M.; Chang, Liuchen; Su, Jianhui; Mao, Meiqin ublihed in: roceeding of the 3 IEEE ECCE Aia DownUnder DOI (link to publication from ubliher):.9/ecce-aia ublication date: 3 Document Verion Early verion, alo known a pre-print Link to publication from Aalborg Univerity Citation for publihed verion (AA): Du, Y., Guerrero, J. M., Chang, L., Su, J., & Mao, M. (3). Modelling, Analyi, and Deign of a Frequency- Droop-Baed Virtual Synchronou Generator for Microgrid Application. In roceeding of the 3 IEEE ECCE Aia DownUnder (pp ). IEEE re. DOI:.9/ECCE-Aia General right Copyright and moral right for the publication made acceible in the public portal are retained by the author and/or other copyright owner and it i a condition of acceing publication that uer recognie and abide by the legal requirement aociated with thee right.? Uer may download and print one copy of any publication from the public portal for the purpoe of private tudy or reearch.? You may not further ditribute the material or ue it for any profit-making activity or commercial gain? You may freely ditribute the URL identifying the publication in the public portal? Take down policy If you believe that thi document breache copyright pleae contact u at vbn@aub.aau.dk providing detail, and we will remove acce to the work immediately and invetigate your claim. Downloaded from vbn.aau.dk on: juli 7, 8

2 reprint of the final paper publihed in IEEE ECCE ASIA-DOWN UNDER 3 Modeling, Analyi, and Deign of a Frequency- Droop-Baed Virtual Synchronou Generator for Microgrid Application Yan Du J. M. Guerrero, Liuchen Chang,3, Jianhui Su, Meiqin Mao School of Electrical Engineering and Automation, Hefei Univerity of Technology, Hefei, China Intitute of Energy Technology Alborg Univerity, Denmark joz@et.aau.dk 3 Dept. of Electrical & Computer Engineering Univerity of New Brunwick Abtract In thi paper, a power-frequency ( ω) controller i preented for voltage ource converter (VSC). The approach i intended for multiple parallel VSC forming a microgrid operating in both grid-connected and ilanded mode. The propoed controller allow a VSC to mimic the operation of a ynchronou generator (SG) by implementing the wing equation of SG with a primary frequency controller. In addition, a generalized model of the active power generation dynamic i developed in order to analyze the tability and to deign the main control parameter. In contrat with the conventional droop control method, the propoed controller improve the cloe-loop ytem dynamic repone without changing the frequency accuracy. The obtained reult how the good performance of the propoed controller. Index Term parallel converter, primary frequency controller, frequency regulation, inertia, microgrid, droop control. I. INTRODUCTION Microgrid i emerging a one of the promiing concept to integrate large-cale ditributed reource [], []. A microgrid, alo named minigrid, conit of a number of ditributed generation ytem, energy torage unit, and dipered load that can operate both autonomouly, i.e. in ilanded mode, or connected to the grid. Due to thi operation flexibility, microgrid can be regarded a important building block of next mart grid. The power electronic interface between the ditributed generator, energy torage ytem and even load are normally DC-AC inverter. Thoe inverter can operate a voltage ource converter (VSC), epecially in ilanded microgrid, ince they may fix the frequency or at leat to play a role in the frequency regulation [3]. Due to the limited power capacity of an inverter, a number of VSC operating in parallel may form a microgrid. Nowaday, droop control i the mot widely ued controller for VSC in microgrid application, ince it ha been uccefully ued for controlling parallel uninterruptible power upply ytem[4]. In [5], the active and reactive power reference are added into the droop method in order to integrate it in a hierarchical control ytem. Further, with the aim of improving the dynamic performance, a power angle droop control with tranient droop characteritic can be ued a well [6]. In order to retore the load-dependant frequency, a econd frequency control i added for the droop-controlled VSC formed microgrid in [3]. An alternative way to control a VSC i to mimic the dynamic characteritic of a ynchronou generator (SG), alo called virtual ynchronou generator (VSG). For intance, in [8] energy torage play a imilar role a the kinetic energy in the rotor of the SG, o that the dynamic tability of the electrical power ytem can be improved. In [9], a VSG controller wa propoed by uing the wing equation of a SG with the purpoe of generating the inverter frequency reference. On the other hand, in order to decouple the time-varying mutual fluxe in the ABC reference frame, a controller baed on a directquadrature-zero (dq) model of a SG for VSC wa preented []. However, to the bet knowledge of the author there ha not been any comparion between the above two group of VSC controller. In thi paper, a VSG-baed power-frequency ( ω) controller i propoed by adding a ditributed frequency controller (DFC) to the emulated wing equation. Thi propoed DFC ue the line frequency a a feedback ignal that produce an embedded tranient active power droop with improved cloe-loop dynamic performance. In addition, a generalized model for power generation i built in order to illutrate the imilaritie and difference between the conventional droop control (here abbreviated a droop control) and the propoed VSG approach. Reult validate the propoed control technique. II. ω DROO CONTROLLER Fig. how an example of microgrid including a cluter of VSC conited of a converter, a LC filter, and a local controller, connected through line impedance to the common bu and ditributed load. The tatic tranfer witch (STS) between the main grid and the microgrid i diconnected from the grid when working in iland mode. The VSC DC link are connected to ditributed reource like fuel cell, DC energy torage ytem, photovoltaic, and o on. Fuelcell DC torage Load LC filter Controller... LC filter Controller Line Impedance Line Impedance Line Impedance Common Bu STS Fig. configuration of microgrid ytem grid

3 reprint of the final paper publihed in IEEE ECCE ASIA-DOWN UNDER 3 Conidering inductance dominated line impedance, the active power i predominately dependent on the power angle, while the reactive power Q motly depend on the output voltage magnitude E. Therefore, droop control include ω and Q E function. To facilitate hierarchical control of microgrid, the reference of active power and reactive power ( *, Q * ) are added with it control diagram hown in Fig.. Active ower-frequency Droop * Q ω* Reactive ower-voltage Droop U* Q * ΔU KV ω ref Өref S Uref Fig. Control diagram of conventional droop control In Fig., the ω droop i ued to generate the output voltage frequency reference ( ref ) and it rotating angle ( ref ), while the Q E droop i ued to generate output voltage magnitude (U ref ). The ω droop control can be rewritten a: * * ( ) () with ω * and * being the reference of frequency and power, ω and the output frequency and power of the VSC, and K d the droop coefficient of the ω droop. Taking into account the low-pa filter of the power meaurement, a mall ignal model of the ω droop controller yield to: ˆ ˆ () where ^ denote a perturbed value, i the Laplace operator, and τ i the time contant of the low-pa filter. It how that the - droop controller can low-pa filter the perturbation of the output power. III. ROOSED VSG ω CONTROLLER The wing equation repreent the imbalance between the power and the rotating peed in a SG. In [9], the ω controller for a VSG i enhanced by adding the wing equation. Since the VSG work around the frequency reference ω *, the wing equation can be rewritten a * * * D( ) J( ) (3) where * and are the mechanical power and the electromagnetic power of a ynchronou generator, J i the inertia momentum, and D i the damping coefficient. In a VSG, * and repreent the power reference and the output power. In order to better undertand the purpoe of the wing equation (3), a mall ignal analyi can be done a following ˆ( ) (4) ˆ( ) J D which how the low-pa filter characteritic relationhip between power and frequency variation, according to the wing equation. The time contant can be defined a J/D and the gain i /D. By comparing (4) and (3), the VSG without DFC and the droop-control can have the ame dynamic in mall perturbation if the following relationhip are atified J and K d D (5) D In thi paper, the propoed VSG mimic the dynamic performance of a SG by implementing the SG model and a ditributed frequency controller, a hown in Fig.3. ω* Ditributed Frequency Controller(DFC) Q ref Q ω grid Kω Δ KV * Virtual Exciter Control I * J+D Swing Equation of SG ω* Flux Equation of SG ω* Ke ω ref Өref S Uref Fig.3. Control diagram of the VSG-baed controller. In Fig.3, the DFC uing the line frequency a feedback ignal i added to generate the extra incremental power Δ in order to decreae the frequency perturbation. Therefore, the dynamic power reference i obtained by combining the reference power * and Δ. Coefficient K ω i the main control parameter of the DFC. Then, the propoed ω controller can be expreed a * K * * ( ) ( grid ) (6) J D J D which can be een a two low pa filter applied over power and frequency error. The tatic and dynamic performance analyi of thi controller i preented in the following ubection. A. Analyi of Steady-State erformance In teady tate, frequency ω i equal to ω grid, o that (6) can be rewritten a * * ( ) ( ) D K (7) The propoed ω controller for VSG preented in (7) ha imilar form of the droop ω controller (). Furthermore, the added DFC increae the value of damping coefficient D in comparion to (5). B. Analyi of Dynamic erformance In the propoed VSG, the input ignal of the ω controller can be divided into two part commanded by ω ω grid and ω* ω, repectively. Thu the cloe-loop diagram of the active power repone in the VSG can be realized a hown in Fig.4. Kω Kω * J+D ω* - ω grid Fig.4. Control tructure of VSG-baed -ω controller In Fig.4, U i the inverter output voltage, E the CC voltage, and i the coupling inductance.

4 reprint of the final paper publihed in IEEE ECCE ASIA-DOWN UNDER 3 Conidering the inductance dominated line impedance due to the tranformer or the ue of LCL filter, the active power can be conidered in mall-ignal ene a proportional to the power angle: grid in (8) Conequently, the ω controller of the VSG can be rewritten a follow: * K *. (9) J D K J D K Notice that the firt part on the right ide of (9) repreent a low pa filter over the power deviation, imilarly a the droop controller. However, the econd term take the form of a high-pa filter, which i a derivative term with limited bandwidth applied over the output power, which only work during the frequency tranient. In cae of an ilanded microgrid formed by a number of paralleled VSC, frequency ω grid i determined by all VSC. Frequency ω differ from ω grid according to the power delivered. A a reult, the frequency deviation term, ω ω grid, in (9) automatically reult in a tranient frequency droop that enhance the dynamic better than the droop control doe. From the above analyi, although both controller may have the ame teady frequency performance, the dynamic of the two controller may be different due to the diimilaritie between the controller tructure. IV. ACTIVE OWER FLOW ANALYSIS AND MODELING In thi ection, a general model of power generation for the droop control and the VSG i developed in order to compare their dynamic. In thi model, grid frequency ω grid i added a a diturbance due to the diturbance in the grid-frequency of the ilanded microgrid. Moreover, meaurement filter are added in thi model conidering their impact over the ytem dynamic and tability. The cloe-loop control diagram of both controller are hown in Fig.5 * Kω τpll+ τ+ = ω* - ω grid a) ω controller of the droop control * J+D τ+ = ω* - ω grid b) VSG-baed controller Fig.5. Block diagram of cloe-loop ytem. Fig. 5 how that the active power repone i generated by two reference: i) the power reference * and ii) the grid-frequency deviation. Therefore, the generated output power take the form: G ( ) G ( ) () * where * i the power reference, G () i the tranfer function between power reference and output power, i the frequency deviation, and G () i the tranfer function between the frequency deviation and the output power. G () can be defined a the power tracking which indicate the power repone for a power reference change, while G () can be defined a the virtual inertia, which indicate the extra power generated during ytem frequency change. Therefore, the VSC can be modeled a a two-terminal Thévenin equivalent circuit, a hown in Fig.6. G(). * G() Fig.6 Generalized mode of power generation in VSC. Thi electrical model decribe the active power generation, which indicate the active power dynamic i determined by G () and G (). Note that in thi equivalent circuit, the voltage repreent the power, and the current repreent the frequency. In grid-connected mode, ω grid equal ω*, the active power dynamic i determined by G (). In ilanded mode, ω grid fluctuate, and the active power dynamic i determined by both G () and G (). Finally, the dynamic analyi i completed by the invetigation of G () and G () eparately. Notice that the power (circuit voltage) droop down when the frequency (circuit current) increae. Conequently, if we want to aociate more parallel inverter, the overall equivalent circuit will conit of individual inverter Thévenin equivalent connected in erie. Thi way the frequency (circuit current) will be common and the power (circuit voltage) will increae when adding more inverter in parallel (circuit erie). V. DYNAMIC ERFORMANCE ANALYSIS According to the previou analyi, the dynamic power repone of the droop control cannot be adjuted without changing D and τ parameter. Therefore, it can be ued a the baeline to analyze the power dynamic of the propoed VSG. Further, the following aumption are conidered in the dynamic analyi: ) The ame teady-tate droop coefficient (D) By comparing () and (7), it can be concluded that the VSG may have the ame teady-tate frequency a the droop control if the following equation i atified: K * d () D K ) The ame power change time-contant (τ) The time contant of the power change in the VSG i determined by the both J and D. By comparing () and (6), the following relationhip i atified to meet the teady-tate requirement () J D + - 3

5 Image Axi reprint of the final paper publihed in IEEE ECCE ASIA-DOWN UNDER 3 A. ower tracking tranient performance ) Droop control: The cloe-loop power tracking control diagram i hown a Fig.7. Then, the tranfer function G () take the form droop G K (3) d K d which dynamic i determined by parameter K d and τ. Their effect have been dicued in []. Since K d i determined by the teady-tate control objective, the dynamic of the power tracking cannot be independently controlled. * S τ + Fig.7. ower tracking cloe-loop block diagram of the droop control ) VSG: The cloe-loop power tracking control diagram of the droop control i hown a Fig.8. * J +D τ + Fig.8 cloe-loop diagram of power tracking of VSG. In thi figure, a low pa filter i added to meaure the active power, and τ in the VSG i the time contant of thi filter. The tranfer function of the VSG can be expreed a following: ( ) VSG G () (4) 3 J ( D J ) D Thi model how that the VSG become a third order ytem. The reaon of the increae of order i due to the ue the power meaurement filter. The DFC ha no effect on the power tracking performance, while parameter D, J, and τ impact the dynamic of the VSG. According to (), D decreae when increaing K ω auming that the teady-teady maximum frequency deviation requirement i fixed. Therefore, the VSG dynamic can be adjuted without compromiing the teady-tate performance. Since the intantaneou power i ued to calculate the virtual mechanical power according to the SG model, reduced time contant for power meaurement filter i ued. Fig. 9 how the effect of the time contant (τ) over the dynamic of the VSG. The arrow how the evolution of the correponding pole when τ increae. With a maller τ, 3 i far away from origin, and and become dominant, reulting in an approximated econd order ytem Real Axi root locu with variou time cont of meaurement filter S3 Fig. 9 Family root of VSG for τ variation S S S S Fig. compare the root locu plot of VSG and the droop control by uing the parameter lited in Table І. Table І arameter of Dynamic Analyi arameter Value (Unit) Nominal Amplitude (V) Voltage Amplitude (V) Droop Coefficient () x -4 Time contant of LF(τ).- () Common load 4(Ω) Connecting inductor (mh) araitic Reitor.5(Ω) In Fig., the droop control conider a variation of τ from -4 to, while the VSG ha the correponding value of J, by uing () for different K ω value. Notice that both ytem can be regarded a a econd order ytem for which the dynamic are mainly determined by the conjugated pole and. Thee pole tend to move far away from the real axi, thu becoming complex conjugate pole when τ or J increae, reulting in a more ocillated dynamic family root locu with.<to<. (Kw=,5,,) kw= kw=5 kw= kw= Fig.. Root locu of the power tracking performance for the droop control and the VSG, with <K ω< A Fig. how, the VSG without uing K ω ha the ame root locu plot a the droop control (blue and black line). By conidering the poition of the cloe-loop zero in both controller, the droop control ha fater dynamic than the VSG due to the larger value of τ in the power meaurement. However, the dynamic of the VSG can be improved by increaing K ω, due to the fact that the eparating point of the VSG i moving away from the origin (ee Fig. ). B. Tranient performance of the virtual inertia Virtual inertia i another mechanim that enable the VSG to inject extra power if the frequency of the grid (ω grid ) deviate from the frequency reference. ) Droop control:the tranfer function of the virtual inertia in cae of the droop control i given by the following tranfer function (ee Fig. ): ( ) droop G (5) Compared to the power tracking tranfer function (G droop ), the tranfer function of the virtual inertia (G droop ) preent the ame tranient repone, except by a maller gain. Notice that ytem dynamic cannot be changed in cae of the droop control if D and τ are elected due to the teady-tate requirement. 4

6 Imag Axi reprint of the final paper publihed in IEEE ECCE ASIA-DOWN UNDER 3 equivalent K ω and J value. Family Root Locu with.<t<.(kw=,5,,) 8 τ + Fig.. Cloe-loop block diagram of virtual inertia of Droop ) VSG: Due to the ue of DFC, which ue a phae locked loop (LL), the VSG ha different virtual inertia characteritic. A low pa filter with time contant value of τ pll which model the LL by approximating it a a firt order ytem, i alo added in the frequency meaurement in order to invetigate it effect on the dynamic behavior. The VSG control diagram i hown in Fig.. (τpll+)-kω(τ+) ((J+D)(τpll+)+Kω)(τ+) Fig.. Cloe-loop diagram of the virtual inertia of the VSG From Fig., the tranfer function of the virtual inertia in cae of the VSG can be derived a follow: G VSG () ( )[ ( )( )] o K K J D pll () ( ) ( )( J D)( ) K ( ) (6) In thi cae, D change with K ω, o that the power repone to frequency variation i alo dependent on K ω and τ pll. Fig. 3 how the family of root loci conidering variation of coefficient K ω and τ pll from to.5. In (6) there are 4 pole aociated with virtual inertia. A Fig. 3 how, and are two complex conjugated fixed pole, and i a real pole moving toward the origin, according to the arrow direction when increaing τ pll. Therefore, and are dominant pole with mall τ pll, while 3 become dominant for large τ pll value. Beide, the poition of and i effected by K ω, i.e. when increaing K ω, the imagery part of and i moving toward the real axi, reulting in a le damped ytem. Therefore, the larger K ω and τ pll, the le ocillating the repone become Kw= S3 pll Kw= Kw= Kw= Fig. 3. Family of root loci for VSG with τ pll change and K ω=,, and With the aim to compare the dynamic of the virtual inertia for both controller, a family of the root locu plot by uing the parameter lited in Table І i hown in Fig. 4. Similarly a in the imulation of the power tracking cae, the droop control conider a variation of τ from -4 to and the VSG ha it correponding S S pll kw=5 kw= kw= Real Axi Fig. 4. Family of root loci of the virtual inertia for the droop control and the VSG for <K ω< In contrat to the droop control, in the VSG cae when increaing K ω, pole and move away from the origin, thu letting 3 dominant. Therefore, a bigger K ω lead to a more damped dynamic of the virtual inertia repone. In a practical deign, for intant a number of parallel inverter forming an iolated microgrid, it i important to obtain an over-damped power repone. However, ytem dynamic cannot be independently adjuted by the droop method, unle K d i different o that the teady-tate performance will be degraded. Therefore, the droop control cannot get better dynamic without compromiing it tability. In a harp contrat, the VSG tability i determined by both D and K ω parameter, while the tranient droop i determined by K ω. The above analyi how the dynamic of both the power tracking and the virtual inertia can be adjuted by changing K ω and τ pll value. The unique control tructure of the VSG give the poibility of optimizing it dynamic without compromiing the tability. VI. SIMULATION RESULTS The droop control and VSG are imulated with the parameter lited in Table I and cheme hown in Fig. for two paralleled inverter. In the cae of VSG, K ω and τ pll are elected to enure a good tranient repone, while D and J are adjuted to fulfill the imulation aumption a hown in () and (). Fig. 5 how the repone of power tracking for variou K ω for the VSG and compare thoe with the droop control. It clearly how that the VSG ha lower dynamic repone than the droop control for low value of K ω. The reaon i that the zero determined by the value of τ in the droop control i cloer to the imaginary axi. Thu, the VSG tranient repone become fater and le damped when increaing K ω becaue the eparating point of the complex-conjugated pole i moving away from the origin. kw= 3 5

7 active power(w) active power(w) active power(w) active power(w) reprint of the final paper publihed in IEEE ECCE ASIA-DOWN UNDER Compariion of tranient repone of active power. Droop.8.6 Kw=5(VSG) Kw=5(VSG) Kw=3(VSG) Kw=5(VSG) 5 VSG VSG Droop.4 Droop time() Fig. 5. Dynamic repone of power tracking for the droop control and the VSG with K ω variation Fig. 6 and Fig. 7 how the tranient repone of the virtual inertia ( o / ) in cae of the droop control and the VSG for different value of K ω and τ pll eparately. Fig. 6 illutrate how the tranient repone turn more damped and fater when increaing K ω, ince it attract the two complex-conjugated pole toward the real axi, a hown in Fig. 4. From Fig. 3, thi fact alo can be explained ince the eparating point i moving away from the origin. Fig. 7 how the tendency toward a le ocillatory repone when increaing τ pll, ince the real pole become more dominant, a hown in Fig Droop Kw=5(VSG) Kw=(VSG) Kw=5(VSG) Kw=(VSG) time() Fig. 6. Dynamic repone of the virtual inertia for the droop control and the VSG for K ω variation time() Fig.8 ower tranient repone of the paralled inverter equipped with droop control and VSG After the initial active power peak due to the initial phae error between inverter, a fater tranient repone and better dynamic performance are achieved by the VSG, a hown in Error! Reference ource not found.. Thee reult confirm that the VSG can achieve better power tranient repone than the droop control. VII. CONCLUSION A virtual ynchronou generator (VSG) baed ω controller ha been preented in thi paper. Thi -ω controller conit of implementing the wing equation of a ynchronou generator (SG) model connected to a ditributed frequency controller which can produce a tranient frequency droop during tranient. The comparion baed on a generalized model how that the propoed controller i able to modify the dynamic repone without compromiing the teady-tate performance by properly tuning the main control parameter. The reult how that the dynamic performance i improved in comparion to the conventional droop control Tpll=.(VSG) Tpll=.(VSG) Tpll=.(VSG) Tpll=.(VSG) Droop time() Fig. 7. Dynamic repone of the virtual inertia for the droop control and the VSG for τ pll variation In ummary, Fig. 5, Fig. 6, and Fig. 7 how that the tranient repone of the power tracking and the virtual inertia of a VSG can be modified with thoe parameter, while the tranient repone of the droop control cannot be adjuted without changing K d and τ. According to the above reult, the VSG can obtain a better dynamic performance than the conventional droop control by adjut K ω and τ pll to get an over-damped fat repone for both power tracking and virtual inertia. In order to verify the dynamic performance of both controller, an initial phae difference of.5rad i intentionally ettled between both two paralleled inverter. Error! Reference ource not found. how the tranient active power with the initial phae difference, uing droop control and VSG repectively. REFERENCES [] B. Kropoki, R. Laeter, T. Ie, S. Morozumi, S. apathanaiou, and N. Hatziargyriou, Making microgrid work, IEEE ower & Energy Magazine, 8, 6(3), pp [] M. Barne, J. Kondoh, H. Aano, J. Oyarzabal, G. Ventakaramanan, and R. Laeter, N. Hatziargyriou, T. Green, Real-world MicroGrid An overview, 7 IEEE International Conference on Sytem of Sytem Engineering, SOSE, 7, April. [3] J. M. Guerrero, J. C. Vaquez, J. Mata, L.G. de Vicuna, and M. Catilla, Hierarchical control of droop-controlled AC and DC microgrid - A general approach toward tandardization, IEEE Tran. Ind. Electron., vol. 55, no., pp. 58-7, Jan.. [4] T. Kawabata and S. Higahino, arallel operation of voltage ource inverter, IEEE Tran. Ind. Appl.,vol IA-4, pp.8-87, Mar./Apr [5] Y. Li, D. M. Vilathgamuwa, and.-c. Loh, Deign, analyi and real-time tet of a controller for multibu microgrid ytem, IEEE Tran. ower Electron., 4,9(5). [6] J. M. Guerrero, J. Mata, L. G. devicuna, M. Catilla, and J. Miret, Wirele-Control Strategy for arallel Operation of Ditributed-Generation Inverter, IEEE Tran. Ind. Electron., vol. 53, no. 5, Oct. 6, pp [7] J. M. Guerrero, J. C. Vaquez, J. Mata, L.G. de Vicuna, and M. Catilla, Hierarchical control of droop-controlled AC and DC microgrid - A general approach toward tandardization, IEEE Tran. Ind. Electron., vol. 55, no., pp. 58-7, Jan. [8] H.-. Beck and R. Hee, Virtual ynchronou machine, Electrical ower Quality and Utiliation, 7, EQU 7, 9th International Conference on. 6

8 reprint of the final paper publihed in IEEE ECCE ASIA-DOWN UNDER 3 [9] Q.-C. Zhong and G. Wei, Synchronverter: Inverter That Mimic Synchronou Generator, IEEE Tran. Ind. Electron.,,58(4), pp [] Y. Du, J. Su, and M. Mao, Autonomou controller baed on ynchronou generator dq model for micro grid inverter, 8th International Conference on ower Electronic,, May 3- June 3, Shilla Jeju, Korea. [] E. A. A. Coelho,. C. Cortizo, and. F. D. Garcia, A Smallignal tability for parallel-connected inverter in tand-alone AC upply ytem, IEEE Tran. Ind. Applicat., vol. 38, no., pp , Mar/Apr.. 7