Aalborg Univeritet A Synchronization Method for Grid Converter with Enhanced Small-Signal and Tranient Dynamic Steinkohl, Joachim; Taul, Mad Graungaard; Wang, Xiongfei; Blåbjerg, Frede; Haler, Jean- Philippe Publihed in: Proceeding of 2018 IEEE 19th Workhop on Control and Modeling for Power Electronic (COMPEL) DOI (link to publication from Publiher): 10.1109/COMPEL.2018.8460113 Publication date: 2018 Document Verion Accepted author manucript, peer reviewed verion Link to publication from Aalborg Univerity Citation for publihed verion (APA): Steinkohl, J., Taul, M. G., Wang, X., Blåbjerg, F., & Haler, J-P. (2018). A Synchronization Method for Grid Converter with Enhanced Small-Signal and Tranient Dynamic. In Proceeding of 2018 IEEE 19th Workhop on Control and Modeling for Power Electronic (COMPEL) (pp. 1-7). Italy: IEEE Pre. http://doi.org/10.1109/compel.2018.8460113 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: december 16, 2018
A Synchronization Method for Grid Converter with Enhanced Small-Signal and Tranient Dynamic J. Steinkohl, M. G. Taul, X. Wang and F. Blaabjerg Department of Energy Technology Aalborg Univerity Aalborg, Denmark joa@et.aau.dk, mkg@et.aau.dk, xwa@et.aau.dk, fbl@et.aau.dk J. -P. Haler ABB FACTS Väterå, Sweden jean-philippe.haler@e.abb.com Abtract An increaing integration of voltage ource baed renewable energy ytem into the power ytem i a global trend, that ha led to requirement for converter control during low voltage and fault ituation. To guarantee table operation, grid ynchronization i a key factor, which greatly influence the tability and ride-through performance of the converter. Thi paper propoe an improved grid ynchronization technique, which enhance the tranient performance of the converter under evere grid condition, uch a three phae fault and voltage phae jump. Thi i achieved by combining a low bandwidth Synchronou Reference Frame Phae-Locked Loop (SRF-PLL) together with a feed-forward term. Thi combination effectively reult in a ynchronization unit including high noie immunity, e.g. enhanced mall-ignal performance and a fat dynamic repone with a phae tracking capability below 5 m. The propoed ynchronization unit i teted during phae jump and ymmetrical three-phae fault to analyze it performance, which i validated through imulation and experimental reult. Index Term Grid Connected Converter, Fault Ride Through, Grid Synchronization, Phae-Locked-Loop I. INTRODUCTION Due to an increaing penetration of renewable into the power ytem, Tranmiion Sytem Operator (TSO) have iued grid code requiring e.g. wind farm to tay connected during fault event and perform voltage upport through reactive current injection [1], [2]. For proper fault performance, the grid-ide converter of e.g. a wind turbine or Photo-Voltaic power converion ytem mut be able to control it injected current in a fat and accurate manner. However, a fat inner current loop in a vector controlled converter will not alone be reponible for uch behavior, ince it reference generation i determined by the ynchronization unit of the converter, often a Synchronou Reference Frame Phae-Locked Loop (SRF-PLL) [3] [5]. Extenive tudie have been conducted for the SRF-PLL to invetigate it influence on controller performance and converter tability [6]. To avoid coupling between the current controller and the outer ynchronization loop, which decreae the mall-ignal tability, een a frequency ocillation, the SRF-PLL i often tuned with a low bandwidth to achieve a high noie immunity. Furthermore, the SRF-PLL i reported to be detabilized during weak grid condition and fault event [7] [9]. Several approache have been propoed to keep a table and low SRF- PLL, while being able to inject deired current during lowvoltage ride-through condition. Thee include freezing the SRF-PLL or etting the bandwidth low enough uch that the SRF-PLL eentially i not aware of the fault event. In uch a way, the frequency and angle etimation remain contant and the current controller can quickly inject reactive current into the grid to upport the voltage. However, in cae of any phae jump during a fault, thee two method will completely change the performance of the ytem and will make it difficult to comply with grid code requirement. Firtly, when entering a fault, full reactive current hould be injected within 20 m [10], which implie that a fat ynchronization method mut be utilized to achieve thi. Secondly, during fault recovery, wind turbine or PV plant mut quickly witch back to upply the load of the ytem. Conidering a low SRF-PLL and phae jump in the grid voltage during fault recovery, the converter ytem will inject reactive power into a healthy network leading to overvoltage, which i highly undeired. Thu, during evere grid condition, a fat SRF-PLL cheme i needed [11]. In [4], a comprehenive review of a large number of tudie regarding different SRF-PLL-enhancement are preented. Since the difference mainly lie in the way the phae detection i performed, i.e. advanced pre-filtering technique, mot available SRF-PLL tructure are not able to achieve a dynamic repone fater than 20 m. One exception could be a type-1 PLL, which only utilize one integrator by eliminating the internal PI controller. Thi controller poe fat dynamic behaviour but i unable to track the grid during any frequency drift due to the elimination of the PI controller [12]. Intead of attenuating unwanted effect from the input uing filter, which decreae the dynamic performance, a delayed ignal cancellation method can be ued, which block certain ignal rather than attenuating them [13]. Thi unfortunately hare the diadvantage a for type-1 PLL, which i a deteriorated repone if the grid frequency drift from the nominal value. In [11], a hybrid SRF-PLL i propoed which in cae of a tranient event witche to a fuzzy logic controller, which i able to ynchronize to the grid within 5 m. Thi method, however, require logic to decide when to ue the
fuzzy controller due to it ocillating repone under normal operation and it i a rather complex controller to implement, which i not likely to be adopted by indutry. To mitigate the aforementioned limitation, thi paper preent a fat and imple converter ynchronization method, poeing robut teady-tate performance while being able to track tranient event with a high bandwidth and preciion. Thi i achieved by utilizing a tructure baed on a SRF-PLL together with a ideal angle etimation, which can be deigned to achieve a deired dynamic performance. The paper i organized a follow. A decription of the exiting SRF-PLL ynchronization method i preented in Section II and a decription of the propoed controller i Section III. Analyi of the method together with imulation reult are preented in Section IV-A, which i experimentally validated in Section IV-B. Finally, Section V ummarize the concluion of the paper. II. SRF-PLL The SRF-PLL i a control algorithm ued to extract the angle θ G of the grid voltage vector in order to contruct a deired current reference value in a grid connected power converter. Thi i done, by uing the Park-Tranformation with the etimated angle of the grid from the SRF-PLL [14]. The mathematical repreentation for V d and V q are given by (1) and (2). and V d = V G co ( θ G θ PLL ) (1) V q = V G in ( θ G θ PLL ) (2) The ynchronization i done, by controlling the q-axi voltage component to zero, a hown in Fig. 1. Any deviation in V q from zero i corrected by the PI controller by adjuting the internal frequency etimation, which i then integrated in order to obtain the ynchronou angle θ PLL. the inu of the mall angle ignal (θ G θ PLL ) i the angle difference itelf. But thi i till a implification, that i only valid for mall angle diturbance. Due to the fact, that the SRF-PLL i normally tuned with a low bandwidth to avoid intability iue and coupling effect with the current controller, the dynamic performance and tracking capability of the ynchronization unit i inherently low. Thi i not allowed under tranient condition, in the cae of grid fault, where the phae can change rapidly. III. PROPOSED CONTROLLER The controller will combine the advantage of the SRF-PLL with the dynamic feed-forward of the error angle information, that can be calculated from V q and V d a decribed in [16]. Thi allow, to control not the value V q, that i dependent on the voltage magnitude and the phae, but directly the phae. The control diagram can be een in Fig. 2. The controller feed the error ignal of the angle deviation forward to the output angle ignal. Thi feed-forward doe not have a direct impact on the inner control loop to the SRF-PLL dynamic a it i propoed in [17]. The impact of the current output to the voltage of the grid i till remaining, epecially under low voltage condition. Thi control tructure lead to two ignificant improvement. Firt, the SRF-PLL i now not only linearized around mall angle, but the input of the PI controller i inherently the angle difference, that ha to be controlled to zero. Second, thi angle difference i not a inuoidal ignal, but a DC ignal. Thi allow further control that are not recommended for periodic ignal. By making a feed-forward ignal a hown in Fig. 2 allow to get a fater repone to tranient event, without changing the internal dynamic of the SRF-PLL. In the feedforward, there can be low-pa filter (LPF) or other additional logic. The angle information for the current control loop i hown in (4). The propoed ynchronization allow to decouple the teady tate frequency-dependent change rate of the angle and the tranient event angle deviation. By controlling the feedforward, i it now poible to control directly the dynamic under tranient event. θ OUT = θ PLL + F F (θ G θ PLL ) (4) Fig. 1. Conventional tructure of SRF-PLL. A hown in (2), V q i dependent on the voltage magnitude a well. To compenate thi, it can be normalized with the voltage magnitude to get a value, that i only relying on the phae difference, a in [15]. Thi normalization lead then to V q norm = V q V G = in ( θ G θ PLL ) (3) In (3), the angle difference i mall under teady-tatecondition. So the mall angle implification can be ued, where The feed-forward block can include a wide range of control functionality, e.g. a low-pa filter which can be optimized to entail a deired performance. A. Analyi The tranfer function of the PI controller in the SRF-PLL can be written a G P I () = K p + K i 1 The open-loop and cloed-loop tranfer function of the linear SRF-PLL without the propoed feed-forward technique are (5)
Fig. 2. Propoed tructure of SRF-PLL with feed-forward. and G ol () = G P I () 1 G cl () = G P I() 1 1 + G P I () 1 To analyze the ytem with feed-forward, the teady tate model ha been developed. It i hown in Fig. 3. (6) (7) G ol,f F () = F F () + G P I() 1 1 F F () (11) Realizing the feed-forward path a a firt order low-pa filter, F F () = α F (12) α F + the expanded open-loop and cloed-loop tranfer function for the propoed ynchronization unit become G ol,f F () = (K p + α F ) 2 + (K p α F + K i ) + K i α F 3 (13) and Fig. 3. Small ignal model of the linear SRF-PLL with feed-forward control. Conidering the effect of the feed-forward path, the output etimated phae angle i ( θ OUT () = (θ G () θ P LL ()) G P I () 1 ) + F F () (8) where G P I () i the tranfer function of the internal PI controller of the SRF-PLL and F F () i a linear block that repreent the feed-forward tranfer function. θ OUT can be expreed a ( θ OUT () = θ P LL () 1 + F F () ) G P I () 1 (9) Thi allow the elimination of θ P LL in (8) and the cloedloop relationhip between the phae angle of the grid voltage and the etimated output phae angle i G cl,f F () = θ OUT () θ G () = G P I() 1 + F F () 1 + G P I () 1 which ha the open-loop tranfer function (10) G cl,f F () = (K p + α F ) 2 + (K p α F + K i ) + K i α F 3 + (K p + α F ) 2 + (K p α F + K i ) + K i α F (14) A it can be een if α F = 0, the original cloed-loop tranfer function hown in (7) i obtained a expected from (14). By neglecting the inner current loop and the coupling between the injected current and the PCC voltage, the open-loop tranfer function and, hence, the dynamic of the linear SRF-PLL and linear SRF-PLL including feed-forward are different. By only looking at the characteritic equation, the SRF-PLL will alway have complex conjugated pole in the left-half plane if K p > 0 and K i > Kp/4. 2 Likewie by including a lowpa filter in the feed-forward path, the ytem will be table with a complex conjugated pole pair and a real pole in the left-half plane if the ame condition are meet and provided that the bandwidth of the low-pa filter i poitive, which i alway true. Therefore, een from the analyi of characteritic equation and Routh-Hurwitz tability criterion, the propoed feed-forward control doe not change the tability. Actually, the pole of the characteritic equation of (14) i p 1 = α F (15) K p ± Kp 2 4K i p 2,3 = (16) 2 Thi mean that the two pole p 2,3 are not dependent on the low-pa filter but only on the gain of the PI controller.
Therefore, a it can be een by increaing the bandwidth of the low-pa filter, the real pole i moved way out in the left-half plane giving a fat repone of the ytem. By introducing the feed-forward term to the linear SRF- PLL, the open-loop tranfer function where the SRF-PLL i tuned with a bandwidth of 10 Hz and a firt and a econd order low-pa filter in the feed-forward path with a bandwidth of 100 Hz i preented in Fig. 4. Fig. 5. Cloed-loop tranfer function of the linear SRF-PLL with and without feed-forward control. Fig. 4. Open-loop tranfer function of the linear SRF-PLL with and without feed-forward control. Here it i evident that a high gain i introduced at in a higher frequency range uing the feed-forward control which improve it high-frequency dynamic repone. The phae margin of the two are identical and i φ m = 85.5 which i introduced by the low inner SRF-PLL. Since the phae increae a the frequency increae the gain margin of the ytem with and without feed-forward control i -34.5 db and - db, repectively. Since the frequency i increaing, a negative gain margin imply mean that the gain can be lowered by the mentioned amount without looing tability. A it can be een in Fig. 5, by uing phae angle error feed-forward a table repone with a ignificantly increaed bandwidth can be achieved with a firt order low-pa filter. In Fig. 5 the bandwidth of the firt order low-pa filter matche exactly the bandwidth of the cloed-loop ytem, i.e. 100 Hz for thi deign. The ame dynamic repone can be achieved with a SRF-PLL and the a bandwidth of 100 Hz, o there i no further increae neither in dynamic nor tability by only uing a firt order LPF. Additional control can till be included to enhance the performance. Thi i further hown in Section III-B. Neverthele, with a econd order low-pa filter i it poible to achieve a higher bandwidth, but higher frequencie are controlled a with a low tuned SRF-PLL. A trade-off between bandwidth and tability can be achieved with optimized tuning of the econd order filter. Deign Guideline: The SRF-PLL can be tuned to give a deired damping ratio and natural frequency baed on the general econd order ytem hown in (7). When thi i done, the bandwidth of the low-pa filter can be increaed to improve the dynamic repone of the overall ytem. However, it hould be noticed that ignoring the effect of the inner current controller and digital delay will only be valid for α F α c where α c i the bandwidth of the inner current regulator. Therefore, α F hould be tuned dependent on ytem and network parameter and it i recommended to elect α F < f /50 where f i the ampling frequency of the control ytem. Thi i to make ure the ynchronization loop i kept ufficiently lower than the inner current loop. In thi way, a fat ynchronization unit can be achieved a fat dynamic repone but the inner SRF-PLL can be deigned with a low bandwidth (<10 Hz) to limit the teady-tate frequency ocillation. B. Feed-Forward Thi Section will further decribe ome of the poibilitie to deign the feed-forward block hown in Fig. 2. In Fig. 6 a phae jump of 60 i performed to viualize the input/output of the propoed controller preented in Fig. 2. The proceing in the feed-forward i a low-pa filter with a cutoff frequency of 100 Hz. A it can be een, a filtered ignal of the angle deviation i ued to eamlely track the phae jump within 5 m. A it can be een in Fig. 6 the feed-forward term i following the error ignal with ome delay, that i inherent in the lowpa filter. The delay will caue a over-compenation of the error ignal in the feed-forward. Thi can be compenated by a reduction of the gain of the LPF. The gain reduction and the effect on the feed-forward value can be een in Fig. 7. Beide filtering, the error ignal can alo be limited in value or in rate of change. Furthermore, the controller tructure make it alo poible to ue a dead-band to decide, baed on the angle error ignal, whether the propoed
Fig. 6. Feed-forward Function with a low-pa filter during a 60 phae jump. Fig. 8. Feed-forward Function with a low-pa filter and a dead-band during a 60 phae jump. reult to be preented, the feed-forward block i realized a a firt order LPF with a cut-off frequency of 100 Hz, which wa found to give a mooth but till fat repone. Fig. 7. Feed-forward Function with a low-pa filter with reduced gain during a 60 phae jump. feed-forward hould be activated, or not. A. Simulation Reult The propoed controller i ubjected to two imulation tet, performed with the imulation oftware EMTDC / PSCAD. At firt, the ynchronization i teted during a 60 phae jump to reveal the performance of the controller dynamic. Secondly, the ynchronization i teted during a ymmetrical three-phae fault including a 60 phae jump and a drop of the voltage to 0.2 pu. One way to moothly enable and diable the feed-forward ignal i e.g. to ue deadband and then a LPF. Thi allow the decoupling of the feed-forward during the teady tate. There will be no influence to the ynchronization, if the angle deviation doe not exceed the threhold. Only during tranient event will be a coupling and the controller interaction are limited to thee event. Thi can epecially be helpful under low voltage condition, where the fat angle ignal in highly dependent on the converter output itelf. In the imulation hown in Fig. 8 i a dead-band together with a low-pa filter ued. The dead-band i et to reduce angle deviation, that are lower than 10 in thi cae. Thi combination allow a fat angle deviation tracking when there are evere angle deviation, but alo a robutne againt low magnitude angle deviation, that are caued by harmonic or meaurement uncertaintie. Thi low deviation robutne can be een after 28 m in the imulation reult. In thi cae, the feed-forward i decoupled from the ynchronization. Hence thi control tructure can be adapted and tailored for any performance criteria of interet. If the angle difference i not proceed at all, then the controller will react a an ideal angle control with the fatet repone poible. IV. VERIFICATION OF PROPOSED CONTROLLER In thi ection, the operation of the propoed controller i preented with imulation and experimental reult. For the Fig. 9. Comparion of SRF-PLL and the propoed controller during a 60 phae jump in the abc grid voltage. In ubfigure a), b) and c), yellow i SRF-PLL and red i propoed method. Blue in ubfigure a) and b) i the reference value of the current. Blue in ubfigure c) i the angle etimation with an ideal angle calculation. Fig. 9 how the controller behavior during a phae jump occurring at 0 ec. A anticipated, the propoed method greatly enhance the dynamic performance of the ynchronization and it i able to track the phae jump within 5 m, wherea the SRF-PLL take around two fundamental cycle to track the changed grid voltage angle.
Fig. 10. Comparion of SRF-PLL and the propoed controller during a evere three-phae ymmetrical fault. In ubfigure a), b) and c), yellow i SRF-PLL and red i propoed method. Blue in ubfigure a) and b) i the reference value of the current. Blue in ubfigure c) i the angle etimation with an ideal angle calculation. Fig. 11. Comparion of SRF-PLL and the propoed controller during a 60 phae jump in the abc grid voltage. In ubfigure a), b) and c), yellow i SRF-PLL and red i propoed method. Blue in ubfigure a) and b) i the reference value of the current. Blue in ubfigure c) i the angle etimation with an ideal angle calculation. Fig. 10 how the ynchronization proce for a evere threephae fault with a 60 phae jump. Again a large improvement in the tranient repone i evident and the propoed controller i almot able to keep the revered active power flow from occurring. Looking at the repone for the SRF-PLL, revered active power flow i happening for two fundamental cycle, which i not acceptable according to grid code and alo inconvenient for the converter itelf. B. Experimental Reult The propoed ynchronization unit i teted on a laboratory etup coniting of a three-phae two-level VSC connected to a grid imulator through an inductive impedance for validation of the imulation reult. The grid-connected converter i equipped with an LCL-filter on the output and the converter regulate the converter ide current uing proportional reonant controller implemented in α β - frame. Similarly a hown for the imulation, two tet were performed, a 60 phae jump during normal operating condition and a ymmetrical three-phae fault with a 60 phae jump and 0.2 pu grid voltage. Fig. 11 how a comparion between the propoed method and SRF-PLL during a phae jump. A it can be een, the propoed controller i able to track the phae of the grid voltage within 5 m, wherea the low SRF-PLL take everal fundamental cycle to do o. Thi make it poible to quickly regulate the reactive current to return to zero. An overhoot i preent in the d-axi current, which i anticipated to be due to improper tuning of the current controller, which i not the focu of thi paper. Fig. 12 illutrate the repone for a ymmetrical three-phae fault including a 60 phae jump. A demontrated before, the propoed method quickly track the phae jump, which Fig. 12. Comparion of SRF-PLL and the propoed controller during a evere three-phae ymmetrical fault. In ubfigure a), b) and c), yellow i SRF-PLL and red i propoed method. Blue in ubfigure a) and b) i the reference value of the current. Blue in ubfigure c) i the angle etimation with an ideal angle calculation. allow the current controller to regulate the active and reactive current to their reference value within the requirement et by the grid code. A it can be een for the cae of SRF- PLL, revered active power flow i oberved for everal cycle, which i highly undeired during uch condition due to the power being accumulated on the DC-ide of the grid-connected converter. V. CONCLUSIONS Fat and accurate ynchronization capability of gridconnected converter i particularly important to enure proper
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