Voltage Feedforward Control with Time-Delay Compensation for Grid-Connected Converters

Transcription

1 Journal of Power Electronic, to be publihed 1 Voltage Feedforward Control with Time-Delay Compenation for Grid-Connected Converter Shude Yang and Xiangqian Tong *,* School of Automation and Information Engineering, Xi an Univerity of Technology, Xi an, China Abtract In grid-connected converter control, grid voltage feedforward i uually introduced to uppre the influence of the grid voltage ditortion on the converter grid-ide AC current. However, Owing to the time-delay in the control ytem, the uppreion effect of grid voltage ditortion i eriouly affected. In thi paper, the poitive effect of the grid voltage feedforward control are analyzed in detail, and the time-delay caued by the low-pa filter (PF) in voltage filtering circuit and digital control are ummarized. In order to reduce the time-delay effect on the performance of feedforward control, a voltage feedforward control trategy with time-delay compenation i propoed, in which, a leading correction of the feedforward voltage i ued. The optimal leading tep ued for thi trategy i derived from analyzing the phae-frequency characteritic of PF and the implementation of digital control. By uing the optimal leading tep, the delay in the feedforward path can be further counteracted o that the performance of feedforward control on uppreing the influence of grid voltage ditortion on the converter output current can be improved. The validity of the propoed method i verified by imulation and experiment reult. Key word: Voltage ditortion, Time delay, Grid-connected converter, eading correction, Feedforward control I. INTRODUCTION With the rapid development of new energy and mart grid, tringent requirement for power quality have been put forward in recent year. The tatic var generator (SVG) and active power filter (APF), baed on the voltage ource converter and PWM control technology repectively, provide reliable olution to the improvement of power quality. The quality of the grid-ide current i an important factor to meaure the performance of the converter, and Ref. [1] give the limit of the harmonic current injected into the grid by the converter. In reality, the performance of the converter current control can be affected by non-ideal factor, uch a the dead-time effect, the turn-on-off delay time and the conduction voltage drop acro power witche, etc. [2], [3]. It i alo worth noticing that the grid background harmonic can alo have ignificant effect on the grid-ide current quality [4]. In the wort cae, it may caue failure of the converter output current for atifying the relevant tandard [5], [6]. For the grid-ide current control, the grid background harmonic can be regarded a a diturbance in the current control loop. According to the control theory, improving the open-loop gain at the harmonic frequencie can uppre the effect of the ditorted grid voltage on the grid-ide current. But an increae of the open-loop gain i retricted by the ytem tability. Proportional reonance (PR) regulator provide greater gain only at the elected reonant frequency. Therefore, it can work well in uppreing the grid-voltage harmonic with the reonant frequency of the PR. Multiple paralleled PR regulator can be adopted to uppre the influence of harmonic voltage on the output current with different order [7], but thi will decreae the ytem tability margin. Thu, the correponding phae compenation method have to be utilized to overcome thi problem. But thi will increae the difficulty of the control ytem deign [8], [9]. In [1], proportional integral (PI) controller in multiple ynchronou frame were adopted to uppre the grid-voltage harmonic. However, the multiple complex coordinate tranform are involved in thi method and their time conumption will increae dramatically when more grid background harmonic are neceary to be dealt with. Another way to uppre the grid-voltage ditortion i to ue grid-voltage feedforward control [11]-[13], which can reduce the tartup current of the device and improve the ytem dynamic performance [14], [15]. Compared with the multiple PR control, the grid-voltage feedforward ha no influence on the tability margin of the ytem o that it i widely ued in the

2 2 Journal of Power Electronic, to be publihed grid-connected converter control. However, for the traditional feedforward control ued in the above paper, the ampled grid-voltage i directly added into the current regulator output without conideration of the nonlinear factor, uch a the ignal conditioning, PWM control and ampling. In fact, the low-pa filter (PF) in the grid-voltage filtering circuit will produce different phae lag at different frequency component, and the PWM control and ampler will caue ome delay a well [16]-[19]. Both of them will reduce the performance of feedforward control on uppreing the grid background harmonic. The feedforward control with only one tep prediction of the feedforward voltage i adopted in [2], and only the delay caued by the voltage filtering i conidered in [21], which will limit the uppreion ability on grid background harmonic. The feedforward elective harmonic compenation method baed on the band-pa filter (BPF) i propoed to compenate the delay caued only by the digital control in [22]. However, when the number of the elective harmonic increae, many BPF are needed. Furthermore, the deign method of the parameter of each BPF i complex. Compared with the traditional feedforward control, the full-feedforward cheme [23]-[25] can dramatically improve the uppreion ability on grid background harmonic, but the algorithm i complex and contain the firt- and econd-order derivative function, that will amplify the high-frequency noie. Thi may affect the ytem performance and even endanger the afe of the device operation. In thi paper, the delay in the feedforward path caued by the PF in voltage filtering circuit and digital control i carefully analyzed and a new feedforward control trategy with the leading correction of feedforward voltage i propoed, which dramatically improve the uppreion ability of the converter on the grid-voltage ditortion by compenating the delay in the feedforward path. Thi paper i organized a follow. Section II introduce the principle and the poitive effect of the grid-voltage feedforward control. The main factor cauing the delay in the control ytem are analyzed in Section III, including the PF in grid-voltage filtering circuit and the digital control. The propoed control cheme i preented in Section IV, and the deign method of the optimal leading tep ued in the propoed cheme i alo given. The effectivene of the propoed cheme i verified by the imulation and experiment reult in Section V. Finally, Section VI conclude thi paper. II. GRID-VOTAGE FEEDFORWARD CONTRO A. Principle of Grid-Voltage Feedforward Control The grid-ide current control of a voltage ource converter i realized by the control of the amplitude and phae of the converter output voltage at the AC ide. The current i generated by thi voltage and the grid voltage upon the two terminal of the filter reactor. Therefore, the active and reactive component of the grid-ide current can be controlled by regulating the converter output voltage, and the DC voltage control can be realized by adjuting the active current. Fig.1 how the chematic diagram of the -filtered tatic var generator ytem ued in the following tudy. The active component reference of the grid-ide current i the output of the DC voltage regulator in the form of PI and the reactive component reference i obtained from the load current calculation or manual etting. Then the reference current in the natural coordinate can be determined by the coordinate tranformation from the active and reactive component, and the converter output voltage i given by the current regulator output according to the error between the reference and output current. Owing to the ability to track a inuoidal reference with zero teady-tate error, the PR regulator i ued in the inner current loop for the fundamental output current control of the converter. For convenient analyi, the converter output voltage at the AC ide can be divided into two component. One i the ynchronou voltage, which ha the ame amplitude and phae a the grid voltage and generate zero grid-ide current, but the other i the voltage difference between the grid voltage and converter output voltage, which generate the grid-ide current through the -filter. If the grid voltage feedforward i unued, i.e., the path denoted by f ω in Fig.1 i removed, both of the two component are generated by the current regulator. But if the grid voltage feedforward path exit, the current regulator only output the econd component generating the grid-ide current, and hence the dynamic performance of ytem can be remarkably improved a illutrated in the following. * u dc U DC C * I p * I q pq / * i Fig. 1. Grid-connected converter ytem. u o R B. Improvement of the Startup Performance Owing to Grid-Voltage Feedforward Control From the above analyi, the current regulator mut generate a ynchronou voltage component to counteract the influence of the grid voltage on the converter output current when grid voltage feedforward i not adopted. In the tartup tage of the converter, it will take ome time for the current regulator to generate thi component. Therefore, the current hock and DC voltage overhoot uually occur a hown in Fig.2 (a), where i g, i u g u u f * u o

3 Journal of Power Electronic, to be publihed 3 u g and U dc are the grid current, grid voltage in one cycle and the DC voltage repectively. The grid voltage i poitive in the time interval T 1, and the DC voltage i lower than it reference value at the beginning of the tartup tage. A a reult, the poitive i g i generated from DC regulator to charge the capacitor, and the obviou voltage overhoot occur near the end of T 1. Owing to thi overhoot and the negative grid voltage during T 2, the DC voltage regulator will till generate poitive i g to dicharge the capacitor to regulate the voltage toward it reference value. When the feedforward control i adopted, the ynchronou component i directly added into the output of the current regulator without requirement of regulating proce. Accordingly, the hock in the tartup tage can be greatly reduced and the DC voltage overhoot will be eliminated a well. With the ame control parameter ued in Fig.2 (a), the tartup performance of the converter with the grid voltage feedforward control i hown in Fig.2 (b), which how a prominent improvement. u g U dc i g (a) (b) Fig.2. Experiment reult of the tartup performance. (a) Without grid-voltage feedforward control. (b) With grid-voltage feedforward control. C. The Suppreion Ability of Feedforward Control on the Influence of Grid-Voltage Ditortion Uing Kirchoff law in the main circuit hown in Fig.1, the differential equation of the phyical quantitie can be given by: di u u R i dt U dc o g (1) Uing aplace tranformation, the converter output current can be expreed in -domain a: Uo() Ug() I () R Baed on (2), the control diagram of the grid-connected converter with voltage feedforward control i hown in Fig.3, where, G F (), G PWM (), G c () and G () are the tranfer function of the PF in the grid-voltage filtering circuit, PWM control, current regulator, and the -filter. The path f in the figure i the grid-voltage feedforward path. i g (2) G () F U () g I * () U() Uo () I () G () c G () () PWM G Fig.3. Control diagram of the converter with grid-voltage feedforward. From (2), the tranfer function of the -filter can be written a: G () R 1 If a PR controller i ued in the inner current loop, it tranfer function can be expreed a [26]: G () K c p 2K r c 2 2 2c where, K p i the proportional gain mainly affecting the repone peed of the ytem, ω the reonant frequency, ω c the reonance bandwidth, and K r the reonance gain at the reonant frequency. In thi tudy, K p =2, K r =8, ω =1 and ω c =4 are ued. From Fig.3, the relation between the grid voltage and grid-ide current can be given by: I () G () G () 1 U G G G (3) (4) F PWM G () (5) g() 1 c() PWM () () In the ideal condition of G PWM () =1 and G F () =1, the right-hand ide term of the above equation i zero. That i, the influence of grid background voltage harmonic on the converter output current can be completely eliminated by the grid voltage feedforward control. III. TIME DEAY CAUSED BY PF AND DIGITA CONTRO The principle of the uppreion of grid-voltage ditortion for feedforward control i that the converter quickly output the voltage which i exactly equal to the ditorted grid voltage. Therefore, the ditorted grid voltage will be completely counteracted by thi voltage, and the influence of grid voltage ditortion on grid-ide current can be avoided. However, if delay exit between the feedforward voltage and the real grid voltage, the compenation preciion of the grid-voltage diturbance will be decreaed, and the

4 4 Journal of Power Electronic, to be publihed uppreion ability of feedforward control on harmonic voltage will be weakened. The delay between the feedforward voltage and the real grid voltage may be caued by quite amount of factor in practice. Among them, the PF in voltage filtering circuit and digital control are two major factor. A. Time Delay Caued by Analog Filter In the control ytem for grid-connected converter, the PF i uually deigned to filter the noie and enure the accuracy of the ampling ignal. Fig.4 how the control board ued in the following experimental tudy, which contain the current detection, temperature detection, PF, fault detection, fault diplay and protection, CPU and PWM ignal. The widely-ued econd-order PF can be expreed a: G () F Q 2 cf cf 1 where, ω cf and Q are the cut-off frequency and quality factor of the PF. The phae lag caued by the PF at frequency ω f can be given by: df arctan( ) Q f cf 2 2 ( cf f ) Due to the approximately linear phae-hift characteritic below the cut-off frequency, the phae lag caued by the PF can be treated a a pure time delay. Taking the power frequency for intance, the delayed time can be expreed a: T PF arctan( ) / 1 Q( ) 1 cf 2 2 cf 1 where, ω 1 i the power frequency. Therefore, below the cut-off frequency, the PF can be expreed imply a: G e F TPF () (6) (7) (8) (9) Fig.4. Prototype of the control board for grid-connected converter. Both of the frequency repone of the PF decribed by (6) and correponding pure time delay function obtained from (9) are hown in Fig.5 for comparion. Obviouly, the PF can be well equivalent to a pure time delay function below the cut-off frequency. Magnitude (db) Phae (deg) Sytem: PF Frequency (Hz): 2e+3 Magnitude (db): -3 Cut-off frequency -9 Pure time delay -135 PF Frequency (Hz) Fig.5. Frequency repone of the PF and correponding pure time delay function. B. Time Delay Caued by Digital Control With the rapid development of digital ignal proceing technology, the digital control ha become the maintream technology for grid-connected converter. Compared with the analog control, the digital control i of higher reliability, being maller in volume, le in energy conumption and higher in flexibility. argely owing to uch advantage, it i convenient to realize complex and intelligent algorithm for higher performance of the converter. However, it alo bring ome drawback. Jut to take the PWM technology widely ued in the converter control for example, one of the drawback i the maximal duty-cycle limitation becaue of the ampling and computation, o that the one-tep-delay control method i uually ued for the converter control. Thi will produce ome delay between the calculation of the output-voltage reference of the converter and the updating of the PWM comparion value [16]. The updating frequency i related to the loading mode of PWM module in the digital ignal proceor (DSP). The PWM comparion value uually update only at the peak or the trough of the carrier wave. That i to ay, it update once in a witching cycle. If it update at the peak and the trough of the carrier wave, thi will be twice in a witching cycle. Whether it update once or twice in a witching cycle, the delay alway exit. The mechanim of the delay caued by PWM updating i illutrated in Fig.6 when the comparion value update once in a witching cycle (only updated at the trough of the carrier wave).

5 Journal of Power Electronic, to be publihed 5 IV. TIME-DEAY COMPENSATION FOR GRID-VOTAGE FEEDFORWARD CONTRO Fig.6. The delay caued by PWM loading. In order to analyze the time delay in the feedforward path, the control diagram of Fig.3 i equivalently converted into Fig.7 (a). Obviouly, the total delay between the feedforward voltage and the real grid voltage i the um of the delay caued by PF and digital control, which can be expreed a (13). Provided that the DSP i interrupted at n moment, the PWM comparion value correponding with u f (n-1)+u(n-1) obtained in the previou period will be updated immediately (the meaning of ymbol u f and u i hown in Fig.1). In the preent period, the grid voltage u f (n) will be ampled, and from Fig.1, the output-voltage reference of the converter can be determined by the um of u f (n) and u(n), but the correponding PWM comparion value make no contribution in the current witching cycle. It will not be loaded until the DSP i interrupted again in the next witching cycle. From the above, it i obviou that thi loading mode of PWM comparion value will produce one witching cycle delay. Therefore, the delay caued by the PWM loading can be modeled a: G () e d T (1) where, T i the witching cycle. In addition, when the PWM comparion value i updated, thi value will be maintained contantly until the next witching cycle, and the duty cycle of the PWM wave i generated by the comparion between thi value and the triangular carrier wave. Thi behavior can be modeled a a zero order holder (ZOH) [17], which can be expreed a (1 e T ) /. In view of the ampler repreented by 1/T, the delay caued by ZOH and ampler can be modeled a: 1 1 e G () e h T.5T (11) T The PWM comparion value update only at the trough of the carrier wave in the following tudy, that i, it update once in a witching cycle. Therefore, the total time delay caued by digital control i about 1.5T, which can be expreed a: 1.5 T G e (12) PWM () From the above analyi, if the PWM comparion value update twice in a witching cycle, the total time delay caued by digital control will be about one witching cycle. G () PWM G () F U () g I * () U() Uo () I () G () c G () () PWM G (a) G () P G () PWM G () F U () g I * () U() Uo () I () G () c G () () PWM G (b) I * () U() Uo () I () G () c G () () PWM G (c) Fig.7. Control diagram of the grid-connected converter. (a) Equivalent control diagram of Fig.3. (b) Delay compenation in the feedforward path. (c) Equivalent control diagram when the time delay i fully compenated. mt G () G () G () e (13) D PWM where, m i defined a the leading correction factor in the bae of witching cycle T. In view of the analyi in III.A and III.B and the PWM loading mode ued in the following tudy, the value of m can be given by: F TPF m 1.5 (14) T In order to compenate the delay in the feedforward path, a leading correction function G p () for feedforward voltage i propoed to be embedded in the feedforward path a hown in Fig.7 (b). If we elect the tranfer function a: () 1/ () mt GP G e (15) D the delay in the feedforward path will be fully compenated

6 6 Journal of Power Electronic, to be publihed and the correponding control diagram can be implified a Fig.7(c). When the leading correction algorithm decribed by (15) can be realized with the leading correction factor obtained from (14), the delay in the feedforward path will be fully compenated, and the grid-ide current will not be affected by the grid voltage ditortion. However, it hould be noticed that the leading correction factor m hould be an integer in practice due to the dicretene of the digital control period, while it i uually decimal according to (14). The integer m i called the leading tep in the following tudy. Since the AD converion and PWM reveral can t be completed immediately, the optimal leading tep hould be the mallet integer which i greater than or equal to the number calculated from (14) in practice. Therefore, the optimal leading tep hould be elected a: m T T 1.5 PF (16) If m ha been elected a an integer according to (16), in z domain, the leading correction algorithm with the optimal leading tep decribed by (15) can be expreed a: G ( ) P z z m (17) For a poitive integer, the (17) cannot be realized in general control ytem. However, the ditorted grid voltage i uually periodic. Owing to the periodic recurrence characteritic of the integer harmonic in the grid voltage, the leading correction algorithm can be realized in erie with a one-cycle delay module, which can be expreed a: ( ) N m Nm GP z z z z (18) where, N i the ampling point in a power cycle, which i et a 192 in the following tudy. With the conideration of the leading correction in the feedforward path in Fig.7 (b), the effect of the grid voltage on grid-ide current can be expreed in z-domain a: I ( z) G ( z) G ( z) G ( z) 1 U z G z G z G z P F PWM G ( z) (19) g( ) 1 c( ) PWM ( ) ( ) The cut-off frequency and quality factor ued for the PF i 2 khz and.77 repectively in the following tudy, which can be expreed a (6). In order to analyze the effect of grid voltage harmonic on grid-ide current in z-domain, the Firt-Order Holder (FOH) [27] method i ued here to obtain G c (z), G (z), G PWM (z) and G F (z) from the correponding -domain tranfer function, where, G PWM () i approximately equivalent to a firt-order proce. For the PF and PWM loading mode ued in thi tudy, the optimal leading tep m =3 can be obtained according to (8) and (16). Magnitude (db) Sytem: Feedforward_control Frequency (HZ): 55 Magnitude (db): With leading correction Without leading correction Frequency (HZ) Fig.8. Frequency repone of grid-ide current veru grid voltage with feedforward control. When the leading correction of feedforward voltage i not ued, G p (z) =1 hould be elected. Subtituting the dicrete tranfer function into (19), the frequency repone of grid-ide current veru grid voltage can be obtained. Both of the amplitude-frequency characteritic at the integer harmonic frequencie with and without the leading correction algorithm are hown in Fig.8. Fig.8 how that without the leading correction of the feedforward voltage, the amplitude at the lower integer frequencie uch a 3 rd, 5 th harmonic are relatively lower, but the amplitude at the frequency of 11 th harmonic i only about -4.5dB, which reflect low uppreion ability on the grid-voltage harmonic. Thu, it can be concluded that owing to the delay caued by PF and digital control, the performance of feedforward control on reducing the effect of grid voltage harmonic on grid-ide current i poor, epecially at the relatively higher harmonic frequencie, and even the harmonic near 1 Hz will be enlarged. It alo how that the amplitude-frequency characteritic at the integer harmonic hift down when the leading correction i adopted, which illutrate the improved uppreion ability of the control ytem on grid voltage harmonic with leading correction. V. SIMUATION AND EXPERIMENT RESUTS In order to verify the effectivene of the propoed control

7 Journal of Power Electronic, to be publihed 7 trategy, imulation and experiment reult of the propoed control trategy are preented and compared. The main circuit and control block diagram of the grid-connected converter ued in the imulation and experiment are hown in Fig.1, and the main parameter for the ytem are hown in Table I. TABE I SYSTEM PARAMETERS Symbol Decription Value U g Grid voltage (rm) 38 V I o Rated current 1 A f Switching frequency 9.6 khz Filter inductance.25 mh R -filter reitor 1 m C DC capacitor 282F Fig.1 (a) how the ditorted grid voltage ued for the imulation. The output current of the converter with or without the leading correction of the feedforward voltage i hown in Fig.1(c) and (b) repectively and their harmonic pectrum are alo given in Fig.1 (d) for detailed comparion. Obviouly, becaue of the delay in the feedforward path, the grid-ide current i eriouly affected by the grid voltage harmonic when the leading correction i not adopted. But thi affection can be well uppreed by uing the propoed leading correction cheme. With the abovementioned control parameter, the bode plot of the open-loop tranfer function are given in Fig.9. The cro-over frequency i et a 1 khz, which i about one-tenth of the witching frequency [28], and the phae margin i about 47. The gain at 5Hz i about 6dB, which guarantee the trong ability to track the power frequency ignal. (a) 8 Magnitude (db) Phae (deg) Sytem: SVG_Control Phae Margin (deg): 47.3 Delay Margin (ec):.124 At frequency (HZ): 1.6e+3 Cloed oop Stable? Ye Frequency (HZ) Fig.9. Bode plot of the open-loop tranfer function. A. Simulation Reult The imulation model i built in Matlab/PECS environment, and the control algorithm i realized in the S-Function. The PWM comparion value update once in a witching cycle for imulation and experiment. The optimal leading tep ued in the following tudy i 3. Output current/a (b) (c) Without leading correction With leading correction Harmonic order (d) Fig.1. Simulation reult. (a) Ditorted grid voltage. (b) Grid-ide current for feedforward control without leading

8 8 Journal of Power Electronic, to be publihed correction. (c) Grid-ide current for feedforward control with leading correction. (d) Harmonic pectrum of the grid-ide current. B. Experiment Reult The propoed cheme i alo verified in a tatic var generator prototype with a TMS32F28335 controller. Fig.11 (a) how the grid voltage with a certain ditortion ued in the experiment, and the grid-ide current for the feedforward control without leading correction i hown in Fig.11 (b). It can be een that the grid-ide current contain ome harmonic caued by the grid voltage ditortion, and the total harmonic ditortion (THD) of the grid-ide current i about 8.8%. With the ame control parameter and experimental condition, the grid-ide current for the propoed cheme i hown in Fig.11(c). In addition, Fig.11 (d) how the harmonic pectrum of the output current of the converter with or without the propoed cheme. Obviouly, owing to the leading correction of the feedforward voltage, the effect of the grid voltage harmonic can be uppreed well, and the THD of the grid-ide current i reduced from 8.8% to 2.23%. There are ome difference between the experiment and imulation reult a hown in Fig.1 and Fig.11. Thee difference can be caued by the following factor. Normally variation do exit between the nominal and the real value of the -filter and the PF ued in experiment and the inductance varie with it current level, o that it value are not contant during operation [29], [3]. All of them will affect the uppreion ability of the converter on the grid-voltage ditortion. In addition, ome other factor will caue harmonic in the grid-ide current except the grid voltage ditortion, uch a the dead-time that i injected into the PWM ignal to avoid the hoot-through of the power witche in the converter leg. (a) Output current/a (b) (c) Without leading correction With leading correction Harmonic order (d) Fig.11. Experiment reult. (a) Ditorted grid voltage. (b) Grid-ide current for feedforward control without leading correction. (c) Grid-ide current for feedforward control with leading correction. (d) Harmonic pectrum of the grid-ide current. In order to quantify the uppreion ability of the converter on h th grid voltage harmonic, an equivalent admittance for h th harmonic i defined a: A I h h (2) U h where, A h i the converter equivalent admittance at h th harmonic frequency, I h and U h are the h th harmonic component in the grid-ide current and voltage repectively. A h reflect the repone of converter to the grid voltage harmonic under different control trategie or parameter.

9 Journal of Power Electronic, to be publihed 9 A h / eading tep = eading tep = 1 eading tep = 2 eading tep = 3 eading tep = 4 eading tep = 5 eading tep = 6 ACKNOWEDGMENT Thi work wa upported by the National Nature Science Foundation of China under grant , the Major Scientific and Technological Innovation Project of Shaanxi Province under grant 215ZKC2-1 and the Key Dicipline Special Foundation of Shaanxi Province under Grant 5X Harmonic order Fig. 12. Experiment admittance of the converter at different voltage harmonic with different leading tep. Fig.12 give the experiment reult of converter equivalent admittance at different harmonic frequencie with different leading tep. It how that the leading tep of 3 i the optimum value, and the more deviation of the leading tep from it i, the larger the admittance of the converter at harmonic frequencie become, or the larger the influence of grid voltage ditortion on the grid-ide current will be. VI. CONCUSIONS Grid voltage feedforward control i an effective method for uppreing the influence of the grid voltage ditortion on the converter output current and attenuating the tarting current. However, the delay in the feedforward path uch a the PF and digital control will weaken it uppreion ability on grid-voltage harmonic. By the above theoretical analyi, imulation and experiment reult, it can be concluded that: 1) Both of the PF in the conditioning circuit for the grid voltage detection and digital control will introduce ome delay in the grid voltage feedforward path. 2) The delay in the feedforward path will caue an aynchrony between the feedeforward voltage and the real grid voltage. Thi aynchrony will reduce the performance of feedforward control on uppreing the influence of grid voltage ditortion on the converter output current. 3) The delay in the feedforward path can be compenated by introducing a leading correction function of the feedforward voltage, and owing to thi trategy, the performance of feedforward control can be improved markedly. 4) In digital control, an optimal leading tep exit for a given PF and PWM operation mode, and the more deviation from thi tep i, the poorer the feedforward performance on uppreing the influence of grid voltage ditortion on the converter output current become. REFERENCES [1] IEEE Standard for Interconnecting Ditributed Reource With Electric Power Sytem, IEEE Std , Jul. 28, 23. [2] I. Dolgunteva, R. Krihna, D. E. Soman, and M. eijon, Contour-baed dead-time harmonic analyi in a three-level neutral-point-clamped inverter, IEEE Tran. Ind. Electron., Vol. 62, No. 1, pp , Jun [3] D.-H. ee and J.-W. Ahn, A imple and direct dead-time effect compenation cheme in PWM-VSI, IEEE Tran. Ind. Appl., Vol. 5, No. 5, pp , Sep [4] H. Zhou, Y. W. i, N. R. Zargari, Z. Cheng, R. Ni, and Y. Zhang, Selective harmonic compenation (SHC) PWM for grid-interfacing high-power converter, IEEE Tran. Power Electron., Vol. 29, No. 3, pp , Mar [5] IEEE Recommended Practice and Requirement for Harmonic Control in Electrical Power Sytem, IEEE Std , May 1, [6] IEEE Recommended Practice for Utility Interface of Photovoltaic (PV) Sytem, IEEE Std , Jan. 2. [7] Z. i, Y. i, P. Wang, H. Zhu, C. iu, and F. Gao, Single-loop digital control of high-power 4-Hz ground power unit for airplane, IEEE Tran. Ind. Electron., Vol. 57, No. 2, pp , Feb. 21. [8]. F. A. Pereira, J. V. Flore, G. Bonan, D. F. Coutinho, and J. M. G. D. S. Jr, Multiple reonant controller for uninterruptible power upplie A ytematic robut control deign approach, IEEE Tran. Ind. Electron., Vol. 61, No. 3, pp , Mar [9] Y. Yang, K. Zhou, and M. Cheng, Phae compenation reonant controller for PWM converter, IEEE Tran. Ind. Informat., Vol. 9, No. 2, pp , May [1] P. Xiao, K. A. Corzine, and G. K. Venayagamoorthy, Multiple reference frame-baed control of three-phae PWM boot rectifier under unbalanced and ditorted input condition, IEEE Tran. Power Electron., Vol. 23, No. 4, pp , Jul [11] A. uo, Y. Chen, Z. Shuai, and C. Tu, An improved reactive current detection and power control method for ingle-phae photovoltaic grid-connected DG ytem, IEEE Tran. Energy. Conver., Vol. 28, No. 4, pp , Dec.213. [12] J. Kan, S. Xie, Y. Wu, Y. Tang, Z. Yao, and R. Chen, Single-tage and boot-voltage grid-connected inverter for fuel-cell generation ytem, IEEE Tran. Ind. Electron., Vol. 62, No. 9, pp , Sep [13] Y. Han, P. Shen, and J. M.Guerrero, Stationary frame current control evaluation for three-phae grid-connected inverter with PVR-baed active damped C filter,

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