General Unified Integral Controller with Zero Steady-State Error for Single-Phase Grid- Connected Inverters Guo, Xiaoqiang; Guerrero, Josep M.

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1 Aalborg Univeritet General Unified Integral Controller with Zero Steady-State Error for Single-Phae Grid- Connected Inverter Guo, Xiaoqiang; Guerrero, Joep M. Publihed in: I E E E Tranaction on Smart Grid DOI (link to publication from Publiher):.9/TSG Publication date: 6 Document Verion Early verion, alo known a pre-print Link to publication from Aalborg Univerity Citation for publihed verion (APA): Guo, X., & Guerrero, J. M. (6). General Unified Integral Controller with Zero Steady-State Error for Single- Phae Grid-Connected Inverter. I E E E Tranaction on Smart Grid, 7(), 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-mang 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.droviding detail, and we will remove acce to the work immediately and invetigate your claim. Downloaded from vbn.aau.dk on: oktober 9, 8

2 Thi paper downloaded from i a preprint verion of the final paper: X. Guo and J. M. Guerrero, General Unified Integral Controller with Zero Steady-State Error for Single-Phae Grid-Connected Inverter, IEEE Tran. Smart Grid,. General Unified Integral Controller with Zero Steady-State Error for Single-Phae Grid-Connected Inverter Xiaoqiang Guo, Senior Member, IEEE, and Joep M. Guerrero, Fellow, IEEE Abtract Current regulation i crucial for operating inglephae grid-connected inverter. The challenge of the current controller i how to fat and preciely track the current with zero teady-tate error. Thi paper propoe a novel feedback mechanim for the conventional PI controller. It allow the teady-tate error uppreion with no need of additional complex control algorithm uch a the ynchronou reference frame tranformation. Five alternative implementation method are comparatively evaluated from the viewpoint of the teadytate and dynamic repone. Further, the theoretical analyi done indicate that the widely ued PR (PReonant) control i jut a pecial cae of the propoed control olution. The timedomain imulation in Matlab/Simulink and experimental reult from a TMS3F8 DSP baed laboratory prototype are in good agreement, which verify the effectivene of the propoed generalized method. Keyword- Grid-connected inverter, general unified integral controller, zero teady-tate error control I. INTRODUCTION The environmental concern and electric utility deregulation promote the development of ditributed generation and microgrid in a rapid pace [-7]. Thee ytem uing renewable energy ource (RES) have many advantage uch a the on-ite power production for the local load. Conequently, the loe of long power tranmiion line can be ignificantly reduced. Typically, a voltageource current-regulated inverter i ued for the power flow control of RES ytem [8-]. One of the mot important iue i how to fat and preciely track the current of the grid-connected inverter, trying to avoid the teady-tate error. Many current control technique have been preented in the pat decade, uch a hyterei control [], [3], one cycle control [4], predictive control [], [6], Lyapunovbaed control [7]. Among them, the proportional integral (PI) control i a imple and widely-ued olution. However, it ha the diadvantage of having teady-tate amplitude and Manucript received 4. Thi work wa upported by the National Natural Science Foundation of China (3749) and Hebei Province Education Department Excellent Young Scholar Foundation (YQ4). X. Guo are with the Key Lab of Power Electronic for Energy Conervation and Motor Drive of Hebei Province, Department of Electrical Engineering, Yanhan Univerity, Qinhuangdao 664, China ( gxq@yu.edu.cn). J. M. Guerrero i with the Department of Energy Technology, Aalborg Univerity, Aalborg DK-9, Denmark ( joz@et.aau.dk). phae error. By uing the ynchronou rotating frame, the PI regulator can eliminate the teady-tate error aociated with tationary frame PI regulator. Neverthele, it cannot be applied to ingle-phae ytem in a traightforward way. In order to overcome thi limitation, ome alternative olution have been preented in [8-], which ue a 9 degree delayed ignal, the Hilbert tranformation, or an all pa filter in order to recontruct a virtual three-phae ytem. In thi way, it i feaible to obtain a two-phae quadrature ignal, imilar a a ynchronou rotating frame, thu can be poible to apply a conventional PI for each direct and quadrature (d-q) component to achieve the zero teady-tate error. The reaon of thi fact i that d-q component are contant value in teady tate. So that PI control can track well thoe value. Another intereting approach ha been reported in [], which recontruct the 9-degree phaehift component from the capacitor voltage and current, intead of the ignal delay. However, the abovementioned PI-baed olution require many rotating frame tranformation, thu increaing the implementation complexity. The objective of thi paper i to develop an enhanced PI control, which integrate PI control with a imple feedback term to eliminate the teady-tate error with no need of additional complex algorithm uch a the ynchronou reference frame tranformation. It ha a very imple tructure and can be eaily implemented in practical application. In addition, the reonant frequency of the controller i eay to adjut. Thi i epecially attractive for application like frequency droop controlled MicroGrid, in which the frequency i changed according to the active power participation of each inverter. That mean that the output frequency reference of the inverter can change the fundamental and harmonic reonant frequencie of their repective controller []. Other application can be active power filter, uninterruptible power upplie, and o on. The paper i organized a follow. Section II preent a brief review of the conventional three- and ingle-phae ynchronou reference frame control trategy. Section III preent the propoed control trategy. Section IV evaluate the performance of the propoed general unified integral controller. Finally, concluion are provided in Section IV. II. SYNCHRONOUS REFERENCE FRAME CONTROL Thi ection will provide a brief review of the three-phae and ingle-phae ynchronou reference frame (SRF) control trategy.

3 A. Three-phae SRF Control Scheme It i well known that zero teady-tate error control of a dc value can be eaily achieved by a PI regulator. However, for an ac value, the teady-tate error can not be eliminated with PI regulator, and the error will depend, among other, on the frequency of the ac value. In practical application, there are many ac quantitie uch a the inuoidal voltage and current ignal. By tranforming the time-varying ac ignal with the ynchronou reference frame tranformation, the ac quantity will become dc ignal. In that cae, the teady-tate error can be eliminated by a PI regulator in pite of the frequency of ac inuoidal ignal to be tracked. Fig. illutrate the block diagram of the conventional three-phae SRF control trategy. Firt of all, the error (x abc ) of three-phae ac quantitie i tranformed into dc quantitie with the ynchronou reference frame tranformation, and then the teady-tate error can be eaily eliminated by uing the integral-baed regulator. Finally, the reult are tranformed back to the tationary frame. Note that, the proportional regulator can be ued in either ynchronou reference frame or tationary frame in order to enhance the ytem dynamic repone. xabc C 3 Fig.. Three-phae SRF control cheme / C 3 / yabc B. Single-phae SRF Control Scheme withvirtual Three- Phae Signal Recontruction Three-phae SRF control trategy ha been widely ued in many indutrial application due to it high control accuracy. Thi approach can alo be ued in ingle-phae application. Indeed, the ingle-phae ac quantity can be conidered a a pecial cae of three-phae unbalanced ac quantitie. More pecifically, only one phae i conidered, while the other two are neglected, a hown in Fig.. Single-phae ignal (pu) Fig.. Virtual three-phae unbalanced ac ignal Therefore, from the theoretical point of view, it eem that three-phae SRF control trategy can be alo applied to ingle-phae application. However, a pecial modification of the SRF control trategy hould be made to cope with the negative equence component, which i reulted from the unbalance of the virtual three-phae ac ignal. A poible olution i to ue the dual SRF control trategy reported in []. However, it need many ynchronou reference frame tranformation, mang it implementation more complex. In order to avoid many SRF tranformation and to implify the control trategy, many other intereting olution have been reported. The baic idea i to recontruct the virtual three-phae (or the two-phae quadrature) ac ignal from the ingle-phae ac ignal, named Signal Recontruction (SR) block. An intuitive olution to contruct a virtual three-phae ignal i to delay and 4 degree the ingle-phae ac ignal, a hown in Fig. 4. In thi way, the conventional three-phae SRF control trategy of Fig. can be applied, a hown in Fig. 3. x a SR x abc C 3 / C 3 / Fig. 3. Single-phae SRF control cheme with virtual abc frame Recontruction (pu) Recontruction (pu) Fig. 4. Signal recontruction with virtual abc frame It hould be noted that thi contruction proce need a delay of /3 fundamental period. Much delay might endanger the ytem tability. One poible olution i to delay the ingle-phae ac quantity by and 6 electrical degree, and then revere the 6-degree-delayed ignal, a hown in Fig. 4. In thi way, the maximum delay can be reduced from /3 cycle (4 degree) to /3 cycle ( degree). C. Single-phae SRF Control Scheme in Virtual Two-Phae Signal Recontruction In order to further reduce the delay and implify the control trategy, another intereting olution ha been reported in [8]. The baic idea i to recontruct virtual twophae quadrature ac ignal by delaying the delay the inglephae ac ignal by 9 electrical degree, a hown in Fig.. Recontruction (pu) Fig.. Signal recontruction with virtual αβ frame In thi way, the maximum delay can be reduced from /3 cycle (4 degree) to /4 cycle (9 degree). Then, the conventional three-phae SRF control trategy of Fig. can be applied, a hown in Fig. 6. y a

4 3 x T / T / y U d S3 S L I g U g SR coωt inωt inωt coωt coωt inωt inωt coωt Fig. 6. Single-phae SRF control cheme with virtual αβ frame III. PROPOSED CONTROLLER A dicued in the previou Section, the SRF control trategy can be extended to ingle-phae application with zero-teady-teady error, thank to the ignal recontruction (SR) block. It might be a good olution from a theoretical point of view. However, it till need many ynchronou reference frame tranformation, which inevitably increae the computational burden. In order to olve the abovementioned problem, a general unified integral controller i propoed. It i imilar to the PI controller, except for a imple feedbacath. The baic diagram of propoed control i illutrated in Fig. 7. x ω / / j Fig. 7. Baic diagram of propoed control method y imple feedbacath The tranfer function in Fig. 7 i given in (). It can achieve the zero teady-tate error control of both dc and ac component. That i the reaon we call it the general unified integral controller. M() jω C () = = () jω jω For example, when the control variable i a Hz dc component, the coefficient ω in () i et to. That i, equation () become the claical proportional integral controller. And it i well known that PI controller can achieve the zero teady-tate error control of dc component. On the other hand, if the control variable i a Hz ac component, the coefficient ω in () i et to π to achieve the zero teady-tate error control of the fundamental frequency component. In the ame way, the coefficient ω can be et to other value to accurately control the harmonic fundamental a well. A. Cae tudy Fig. 8 how the chematic diagram of a typical inglephae grid-connected inverter, which i an illutrative example to tet the control propoal. Note that, following will focu on the current control, while other iue uch a the maximum power point tracng, anti-ilanding protection, grid ynchronization and leakage current uppreion [3-6] are out of cope of thi paper. S4 S Fig. 8. Diagram of ingle-phae grid-connected inverter Auming that the witching frequency i high enough to neglect the inverter dynamic, the equivalent repreentation of the ingle-phae current regulated grid-connected inverter i obtained a hown in Fig. 9, where C() i the current regulator tranfer function, K i the PWM gain, T d i the control delay, and L and R are the filter inductor and it equivalent erie reitor. * I g C () K T d I g U g L R Fig.9. Linear control model of ingle-phae grid-connected inverter The ytem cloed-loop tranfer function can be derived from Fig. 9 a follow: KC() * Ig() = I () g LTd ( RTd L) R KC() () T d U () g LTd ( RTd L) R KC() Equation () indicate that the grid current Ig () i dependent on the current reference I * g () and the grid voltage U g (), which can be een a a diturbance here. By ubtituting () into (), the ytem cloed-loop tranfer function can be expreed a follow: A ( ) *)))))))))))))))) KM () * Ig = I () g [ LTd ( RTd L) R]( jω ) KM ( ) B () *)))))))))))))))) ( jω )( T d ) U g () [ LTd ( RTd L) R]( jω ) KM ( ) (3) From (3), we can obtain that the term A()= and B()= when the angular frequency of the reference I * () and the diturbance () g U are equal to ω. That i to ay, the regulated grid current I g (jω ) perfectly track it reference. So that, zero teady-tate error current regulation i achieved. B. Parameter Tuning Thi ection will provide a practical tuning method for the controller parameter. Traditionally, in a PI control the higher i the control bandwidth, the better are the teadytate and dynamic repone. Neverthele, in practice the high bandwidth uually lead to intability due to the control delay, epecially in digital control application [7]. A practical way to avoid intability i to keep the control bandwidth below one fifth of the ample frequency. For example, the control bandwidth i elected below khz with the ample frequency of khz. g

5 4 For implicity, the ESR and control delay T d are neglected due to their mall value. The ytem magnitude-frequency function can be derived from () and () a follow: T () = i p( ωω ) K k k i p ( Lωω Lω Kk ) ( Kk )( ω ω ) The following tep are propoed in order to elect properly the main control parameter. Step. Auming that only proportional control i activated, i.e. k i =, the equation (4) can be implified a K T () = () ( Lω) ( Kk ) It i well known that the bandwidth i defined a the frequency where the magnitude attenuation i -3 db. If the expected initial bandwidth ω ib p (4) i fixed, the proportional parameter can be calculated from () a Lωib = (6) K Step. Auming that the integral control with the imple feedback term i integrated into the proportional control, the magnitude-frequency characteritic can be expreed by (4). If the expected final bandwidth ω fb i decided, the integral parameter k i can be calculated from (4) a ( ωfb ω) ( (( ) = ωfbl K kp ωfbl ) (7) K Step 3. Evaluate the ytem tability by confirming that the cloed-loop ytem ha no right-half-plane pole. In thi paper, the expected initial and final bandwidth are et to khz and. khz repectively and, thu, the controller parameter can be calculated by the three-tep method, yielding k p =. and k i = 8. Then, the cloe-loop pole ( jand j ) are located on the left half plane, which indicate the ytem i table. C. Practical implementation of the term j In a ingle-phae grid-connected inverter ytem, it i very difficult to implement the term j in Fig. 7. However, the total harmonic ditortion of the grid current hould be le than %, a pecified in IEEE Std.99- and IEEE Std.47. Therefore, in mot cae, the fundamental component i dominant, and current harmonic are mall enough to neglect. In thi cae, the term j can be phyically implemented by conidering the unity amplitude and 9 degree phae hift at the fundamental frequency. Phyical implementation of the complex number j can be claified into two main method: the time-domain and frequency-domain baed method. The implet time-domain method i hown in Fig., where the delay, that i m, i equivalent to the complex number j from the viewpoint of the unity gain and 9 degree phae hift feature. with characteritic of the unity gain and 9 degree phae hift at the fundamental frequency by low pa filter or all pa filter, a lited in Table I. It i our worth to note that the propoed controller will be equivalent to the well-known PR controller [8-3], if the firt-order low pa filter i ued, a hown in Fig.. Therefore PR controller i jut a pecial cae of the propoed general unified controller. TABLE I. PRACTICAL FILTERS FOR J Low Pa Filter Firt order Second order x kω k All Pa Filter ω ω ω ω ω ω / / ω / k k p i ω ω ω ω ω ω ω k k k k Fig.. Propoed controller when j i implemented with ω / We emphaize that the controller in SubSection C i not mathematically equivalent to the controller in Fig. 7 in the entire frequency range, o the tranient repone are different, a hown in the following SubSection. However, the characteritic are the ame at the fundamental frequency to achieve the zero teady-tate error for the ingle-phae grid-connected inverter. D. Performance Evaluation A dicued in the previou ection, there are five alternative implementation method of the propoed control. The performance comparion of the five alternative method will be hown in thi SubSection. The comparion criteria ued will be the dynamic repone, tability and the total harmonic ditortion (THD) of the grid current. It i well know that the ytem cloed-loop pole are ueful to tudy the ytem tability and tranient repone. In general, the ytem i table if all the pole are located in the left half plane. When the left-half-plane pole are far away from the imaginary axi the dynamic repone became fater. Fig. how the dominant pole of the cloed-loop ytem with different olution. All the method can enure the ytem tability due to the dominant pole located in the left half pane. In addition, it can be oberved that three olution (A, D and E) how lower dynamic repone, while the other two olution (B and C) have fater dynamic repone due to their dominant pole further away from the imaginary axi. y x ω / / SR Delay m Fig.. Single-phae natural frame control with SR On the other hand, from the fundamental frequency point of view, j can be implemented in the frequency domain y

6 Imaginary Axi Real Axi Fig.. Dominant pole of different olution On the other hand, the ytem diturbance rejection characteritic how the effect of the grid voltage harmonic on the grid current, a following: Ig () ( jω )( T d ) D () = = U () [ LT ( RT L) R]( jω ) KM ( ) g d d (8) Note that the harmonic component of the grid voltage mainly conit of a low-order harmonic, and their magnitude may tend to be lower a their frequency increae. Therefore, only the third (Hz) harmonic of the grid voltage i conidered a an example in the following theoretical performance evaluation. Te ytem diturbance rejection characteritic for different olution (k=) i depicted in Fig. 3. It can be oberved that olution C i enitive to low-order harmonic of the grid voltage, while the other three olution (A, B, D and E) have better grid diturbance rejection capability due to their maller gain of I ()/ U (). Magnitude (ab) B B g C C g Bode Diagram Frequency (Hz) Fig. 3. Diturbance rejection characteritic Ig()/ Ug() Table II ummarize the ytem diturbance rejection characteritic for the low-order harmonic frequencie and the dominant pole a well. It can be concluded that Solution B and C are better from the dynamic repone viewpoint. On the other hand, all of them have imilar teady-tate performance, while olution A, B, D and E are lightly uperior in term of grid diturbance rejection capability. Notice that the ytem performance of olution D and E are dependent on the cutoff frequency of filter, more pecifically, the coefficient k. From Table II, it can be oberved that the ytem performance tend to be better for Solution D and Solution E. Therefore, k hould be carefully deigned for better performance in practical application. A D C A A D D B E E E Delay m (Solution A) TABLE II PERFORMANCE EVALUATON Dominant pole D ()@Hz i i ω -34i (Solution B) -3-4i ω (Solution C) -44i ω --44i (k=) i kω i kω ω (k=) (Solution D) -973i -9-73i (k=) i kω ω kω i kω ω kω (k=) (Solution E) -843i -8-43i.3.76 (k=).43 (k=).39 (k=).3 (k=).78 Another conideration that hould be noted i that the zero teady-tate error i achieved on condition that the grid frequency i time-invarying. However, in practical ituation the grid frequency may uffer fluctuation, uch a in cae of weak grid or ilanded MicroGrid []. In thi cae, it i recommended that the propoed controller hould be adaptively adjuted. For example, the buffer length will be adaptively changed with the frequency when uing olution A. Furthermore, ome other poible olution have been reported in [3], which are beyond the cope of thi paper. IV. PERFORMANCE EVALUATION AND DISCUSSION In order to verify the effectivene of the propoed control trategy, the imulation and experimental tet are carried out baed on a ingle-phae grid-connected inverter. The ytem conit of an H-bridge with four IGBT and two plit inductor (L =L =3mH). The dc-link voltage of the inverter i fed with a DC power upply (rated V). The ytem output i connected to the grid through a /-V 3-kVA ingle-phae tranformer. The grid current reference i A. The inverter i controlled by a 3-bit fixed-point MHz TMS3F8 DSP platform, and the witching frequency and ampling frequency i et to khz. In thi ection, we will provide the performance evaluation reult of the propoed control with the five aforementioned alternative implementation, in contrat with the conventional PI controller

7 6 Fig. 4. Tet reult with PI control. Simulation reult. Experimental reult. Fig. 4 how the time-domain imulation reult. It can be clearly oberved that the grid current ha teady-tate error in both amplitude and phae when uing the conventional PI control. On the other hand, the correponding experimental reult are hown in Fig. 4, which are in good agreement with the imulation reult. However, the grid current preent a light ditortion, mainly reulting from the ditorted grid voltage. Error: A/div current track it reference with zero teady-tate error after the tartup tranient within one and a half cycle. In good agreement with the theoretical analyi in the previou ection, there i a 7. Hz decaying, ocillating repone, which i mainly dependent on the imaginary part of the dominant, poorly damped low-frequency pole (ee Table II). On the other hand, the experimental reult are imilar of thoe from the imulation one, except for the mall current ditortion, which i due to the background harmonic of the grid voltage. Fig. 6 how the imulation and experimental reult when uing olution B. The zero teady-tate error tracng of the current reference can be oberved. Note that the tranient repone of Solution B i about m, being fater than the olution A. The reaon of thi i that the dominant pole of olution B are more far from the imaginary axi than thoe of olution A (ee Table II). Therefore, it can be concluded that the teady-tate performance i almot the ame for both olution. However, the dynamic performance of olution B i better than the olution A, which i in agreement with the theoretical analyi preented in Table II Error: A/div Error: A/div Fig.. Tet reult with Solution A. Simulation reult. Experimental reult. The time-domain imulation reult in olution A (ee Table II) i hown in Fig.. It can be oberved that the grid Fig. 6. Tet reult with Solution B. Simulation reult. Experimental reult. Fig. 7 how the imulation and experimental reult of olution C. A can be derived from Table II, the tranient repone time of olution C i almot the ame a olution B. The reaon for thi i that the ditance of their dominant pole are imilarly far from the imaginary axi. On the other hand, there i a 7.8 Hz decaying, ocillating repone, which i mainly dependent on the imaginary part of the dominant, but poorly damped low-frequency pole.

8 7 Gri current (A) Error: A/div Error: A/div Fig. 7. Tet reult with Solution C. Simulation reult. Experimental reult Fig. 9. Tet reult with Solution D (k=). Simulation reult. Experimental reult. Fig. 8 and Fig. 9 how the imulation and experimental reult of olution D for different coefficient (k= and k=). It can be oberved that the teady-tate performance i imilar in both cae. However, the tranient repone of olution D would be better for higher gain of k, a expected from Table II. The imulation and experimental reult of olution E for different coefficient (k= and k=) are hown in Fig. and Fig.. It can be oberved that the teady-tate performance i imilar for both cae. However, the tranient repone of olution E for k= i the lowet one among all aforementioned olution, which i in agreement with the theoretical analyi preented in Table II. On the other hand, the tranient repone i better for higher gain of k=. The reaon i that the dominant pole for k= are far away from the imaginary axi than thoe for k= (ee Table II). Error: A/div Fig. 8. Tet reult with Solution D (k=). Simulation reult. Experimental reult

9 8 TABLE III PERFORMANCE COMPARISON Repone time Current THD Delay m (Solution A) 3m 3.8% Error: A/div ω (Solution B) m 3.8% ω (Solution C) m 4.4% ω kω k ω ω (Solution D) kω ω kω k k ω ω ω (Solution E) 3m(k=) m(k=) 3m(k=) m(k=) 3.8%(k=) 3.7% (k=) 3.6% (k=) 4.% (k=) Fig.. Tet reult with Solution E (k=). Simulation reult. Experimental reult Error: A/div Fig.. Tet reult with Solution E (k=). Simulation reult. Experimental reult. Table III ummarize the performance comparion between all the cae. In good agreement with the theoretical analyi in Table II, olution A, D (k=), and E (k=) preent lower dynamic repone, while olution B, C, D (k=), and E (k=) how fater dynamic repone. On the other hand, all of thee olution have imilar teady-tate error performance, while olution C and E (k=) are not preferred from the viewpoint of grid diturbance rejection capability. V. CONCLUSION Thi paper ha preented how a imple feedback term i integrated into the conventional PI controller to eliminate the teady-tate error of the grid current at the fundamental frequency without any other complex control algorithm. Five alternative implementation method of the propoed control are comparatively evaluated from the viewpoint of the teady-tate and dynamic repone. Theoretical analyi, imulation and experimental reult are in good agreement, which indicate five alternative method can achieve the zero teady-tate error control for the ingle-phae PV inverter. But their dynamic repone and grid diturbance rejection performance are lightly different. Therefore, a careful election among five alternative method hould be needed for the high performance control of the ingle-phae gridconnected inverter. It i recommended that Solution B and D would be good choice in term of the teady-tate and dynamic performance. It hould be note that, the total harmonic ditortion of the grid current i generally le than %, a pecified in IEEE Std. 99- and IEEE Std.47. Therefore, in mot cae, the fundamental component i dominant, and current harmonic are relatively mall. But when the reference i very mall, the harmonic in the current might be comparable to the fundamental. In thi cae, the propoed control hould be modified to control the harmonic component. It need a comprehenive and ytematic invetigation, which will be the ubject of our future reearch. REFERENCES [] 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. 8, no., pp. 8 7, Jan.. [] Y. A.-R. I.Mohamed and A. Radwan, Hierarchical control ytem for robut micro-grid operation and eamle mode-tranfer in active ditribution ytem, IEEE Tran. Smart Grid, vol., no., pp. 3 36, Jun.. [3] T. L. Vandoorn, B. Render, L. Degroote, B. Meerman, and L. Vandevelde, Active load control in ilanded microgrid baed on the grid voltage, IEEE Tran. Smart Grid, vol., no., pp. 39, Mar.. [4] Y. Li and Y. W. Li, Power management of inverter interfaced autonomou microgrid baed on virtual frequency-voltage frame, IEEE Tran. Smart Grid, vol., no., pp. 3 4,. [] K. T. Tan, X. Y. Peng, P. L. So, Y. C. Chu, and M. Z. Q. Chen, Centralized control for parallel operation of ditributed generation inverter in microgrid, IEEE Tran. Smart Grid, vol. 3, no. 4, pp , Dec..

10 9 [6] P. C. Loh, D. Li, Y. K. Chai, and F. Blaabjerg, "Autonomou operation of hybrid microgrid with AC and DC ubgrid," IEEE Tran. on Power Electron., vol. 8, no., pp. 4-3, May 3. [7] R. Majumder, A hybrid microgrid with dc connection at back to back converter, IEEE Tran. Smart Grid., vol., no., pp. 9, Jan. 4. [8] J. He, Y. W. Li, D. Bonjak, and B. Harri, Invetigation and active damping of multiple reonance in a parallel-inverter-baed microgrid, IEEE Tran. Power Electron., vol. 8, no., pp , Jan. 3. [9] J. Sun, Impedance-baed tability criterion for grid-connected inverter, IEEE Tran. Power Electron., vol. 6, no., pp , Nov.. [] W. Li, X. Ruan, D. Pan, and X. Wang, Full-feedforward cheme of grid voltage for a three-phae LCL-type grid-connected inverter, IEEE Tran. Ind. Electron., vol. 6, no. 6, pp. 37, Jun. 3 [] M. A. Herran, J. R. Ficher, S. A. Gonzalez, M. G. Judewicz, and D. O. Carrica, Adaptive dead-time compenation for grid-connected PWM inverter of ingle-tage PV ytem, IEEE Tran. Power Electron., vol. 8, no. 6, pp. 86 8, Jun. 3. [] Z. Yao and L. Xiao, Two-witch dual-buck grid-connected inverter with hyterei current control, IEEE Tran. Power Electron., vol. 7, no. 7, pp , Jul.. [3] W. Fengjiang, S. Bo, Z. Ke, and S. Li, Analyi and olution of current zero-croing ditortion with unipolar hyterei current control in grid-connected inverter, IEEE Tran. Ind. Electron., vol. 6, no., pp , Oct. 3. [4] Y. Chen and K. M. Smedley, One cycle controlled three-phae gridconnected inverter and their parallel operation, IEEE Tran. Ind. Appl., vol. 44, no., pp , Mar./Apr. 8. [] Q. Zeng and L. Chang, An advanced SVPWM-baed predictive current controller for three-phae inverter in ditributed generation ytem, IEEE Tran. Ind. Electron., vol., no. 3, pp. 3 46, Mar. 8. [6] V. Yaramau and B. Wu, A model predictive decoupled active and reactive power control for high power grid-connected four-level diode clamped inverter, IEEE Tran. Ind. Electron., vol. 6, no. 7, pp , [7] C. Meza, D. Biel, D. Jeltema, and J. Scherpen, Lyapunov-baed control cheme for ingle-phae grid-connected PVcentral inverter, IEEE Tran. Control Syt. Technol., vol., no., pp. 8, Mar.. [8] R. Zhang, M. Cardinal, P. Szczeny, and M. Dame, A Grid imulator with control of ingle-phae power converter in D-Q rotating frame, in Proc. IEEE Power Electron. Spec. Conf.,, pp [9] R. Y. Kim, S. Y. Choi, and I. Y. Suh, Intantaneou control of average power for grid tie inverter uing ingle phae D-Q rotating frame with all pa filter, in Proc. IEEE Ind. Electron. Conf., Buan, Korea, Nov. 4, pp [] M. Milané-Montero, E. Romero-Cadaval, A. Rico de Marco, V. Minambre-Marco,and F. Barrero-Gonzalez, Novel method for ynchronization to diturbed three-phae and ingle-phae ytem, in Proc. IEEE Ind. Electron. Conf., Vigo, Spain, 7, pp [] S. Chung, Steady-tate error minimization technique for ingle-phae PWM inverter, Electronic Letter, vol. 38, no., pp , Oct.. [] Z. R. Ivanovic, E. M.Adžić, M. S. Već, S. U. Grabić, N. L. Čelanović, and V. A. Katić, HIL evaluation of power flow control trategie for energy torage connected to mart grid under unbalanced condition, IEEE Tran. Power Electron., vol. 7, no., pp , Nov.. [3] S. Adhikari, F. Li, Coordinated V-f and P-Q control of olar photovoltaic generator with MPPT and battery torage in microgrid, IEEE Tran. Smart Grid, vol., no. 3, pp. 7 8, May. 4. [4] X. Wang, W. Freita, and W. Xu, Dynamic non-detection zone of poitive feedback anti-ilanding method for inverter-baed ditributed generator, IEEE Tran. Power Del., vol. 6, no., pp. 4, Apr.. [] D. Yazdani, A. Bakhhai, G. Joo, and M. Mojiri, A nonlinear adaptive ynchronization technique for grid-connected ditributed energy ource, IEEE Tran. Power Electron., vol. 3, no. 4, pp. 8 86, Jul. 8. [6] H. F. Xiao, X. P. Liu, and K. Lan, An Optimized Full Bridge Tranformerle PV Grid-Connected Inverter With Low Conduction Lo and Low Leakage Current, IET Power Electron., vol. 7, no. 4, pp. 8-, Feb. 4. [7] R. Turner, S. Walton, and R. Duke, "Stability and bandwidth implication of digitally controlled grid-connected parallel inverter, IEEE Tran. Ind. Electron., vol. 7 no., pp , Nov.. [8] R. Teodorecu, F. Blaabjerg, M. Lierre, and P. C. Loh, Proportional reonant controller and filter for grid-connected voltage-ource converter, Proc. Int. Elect. Eng. Elect. Power Appl., vol. 3, no., pp. 7 76, Sep. 6. [9] A. G. Yepe, F. D. Freijedo, J. Doval-Gandoy, O. Lopez, J. Malvar, and P. Fernandez-Comeana, Effect of dicretization method on the performance of reonant controller, IEEE Tran. Power Electron., vol., no. 7, pp. 69 7, Jul.. [3] A. G. Yepe, F. D. Freijedo, O. Lopez, and J. Doval-Gandoy, High performance digital reonant controller implemented with two integrator, IEEE Tran. Power Electron., vol. 6, no., pp , Feb.. [3] F. D. Freijedo, Contribution to grid-ynchronization technique for power electronic converter, Ph.D. diertation, Dept. Electron. Technol., Vigo Univ., Vigo, Spain, Jun. 9. X. Guo (M' -SM' 4) received the B.S. and Ph.D. degree in electrical engineering from Yanhan Univerity, Qinhuangdao, China, in 3 and 9, repectively. He ha been a Potdoctoral Fellow with the Laboratory for Electrical Drive Application and Reearch (LEDAR), Ryeron Univerity, Toronto, ON, Canada. He i currently an aociate profeor with the Department of Electrical Engineering, Yanhan Univerity, China. He ha authored/coauthored more than fifty technical paper, in addition to nine patent. Hi current reearch interet include high-power converter and ac drive, electric vehicle charging tation, and renewable energy power converion ytem. Dr. Guo i a Senior Member of the IEEE Power Electronic Society and IEEE Indutrial Electronic Society. He i an active Referee for IEEE Tranaction on Indutrial Electronic and IEEE Tranaction on Power Electronic. Joep M. Guerrero (S -M 4-SM 8-F ) received the B.S. degree in telecommunication engineering, the M.S. degree in electronic engineering, and the Ph.D. degree in power electronic from the Technical Univerity of Catalonia, Barcelona, in 997, and 3, repectively. Since, he ha been a Full Profeor with the Department of Energy Technology, Aalborg Univerity, Denmark, where he i reponible for the Microgrid Reearch Program. From he i a guet Profeor at the Chinee Academy of Science and the Nanjing Univerity of Aeronautic and Atronautic; from 4 he i chair Profeor in Shandong Univerity; and from he i a ditinguihed guet Profeor in Hunan Univerity. Hi reearch interet i oriented to different microgrid apect, including power electronic, ditributed energy-torage ytem, hierarchical and cooperative control, energy management ytem, and optimization of microgrid and ilanded minigrid. Prof. Guerrero i an Aociate Editor for the IEEE TRANSACTIONS ON POWER ELECTRONICS, the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, and the IEEE Indutrial Electronic Magazine, and an Editor for the IEEE TRANSACTIONS on SMART GRID and IEEE TRANSACTIONS on ENERGY CONVERSION. He ha been Guet Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS Special Iue: Power Electronic for Wind Energy Converion and Power Electronic for Microgrid; the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Special Section: Uninterruptible Power Supplie ytem, Renewable Energy Sytem, Ditributed Generation and Microgrid, and Indutrial Application and Implementation Iue of the Kalman Filter; and the IEEE TRANSACTIONS on SMART GRID Special Iue on Smart DC Ditribution Sytem. He wa the chair of the Renewable Energy Sytem Technical Committee of the IEEE Indutrial Electronic Society. In 4 he wa awarded by Thomon Reuter a Highly Cited Reearcher, and in he wa elevated a IEEE Fellow for hi contribution on ditributed power ytem and microgrid.