Active and reactive power control schemes for distributed generation systems under voltage dips Wang, F.; Duarte, J.L.; Hendrix, M.A.M.

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1 Active and reactive ower control schemes for distributed generation systems under voltage dis Wang, F.; Duarte, J.L.; Hendrix, M.A.M. ublished in: roceedings IEEE Energy Conversion Congress and Exosition (ECCE 29), 2-24 Setember 29, San Jose, California DOI: 1.119/ECCE ublished: 1/1/29 Document Version ublisher s DF, also known as Version of Record (includes final age, issue and volume numbers) lease check the document version of this ublication: A submitted manuscrit is the author's version of the article uon submission and before eer-review. There can be imortant differences between the submitted version and the official ublished version of record. eole interested in the research are advised to contact the author for the final version of the ublication, or visit the DOI to the ublisher's website. The final author version and the galley roof are versions of the ublication after eer review. The final ublished version features the final layout of the aer including the volume, issue and age numbers. Link to ublication General rights Coyright and moral rights for the ublications made accessible in the ublic ortal are retained by the authors and/or other coyright owners and it is a condition of accessing ublications that users recognise and abide by the legal reuirements associated with these rights. Users may download and rint one coy of any ublication from the ublic ortal for the urose of rivate study or research. You may not further distribute the material or use it for any rofit-making activity or commercial gain You may freely distribute the URL identifying the ublication in the ublic ortal? Take down olicy If you believe that this document breaches coyright lease contact us roviding details, and we will remove access to the work immediately and investigate your claim. Download date: 19. Aug. 218

2 Active and Reactive ower Control Schemes for Distributed Generation Systems Under Voltage Dis Fei Wang, Jorge L. Duarte and Marcel A. M. Hendrix Deartment of Electrical Engineering Eindhoven University of Technology 56 MB Eindhoven, The Netherlands Abstract During voltage dis continuous ower delivery from distributed generation systems to the grid is desirable for the urose of grid suort. In order to facilitate the control of distributed generation systems adated to the exected change of grid reuirements, generalized ower control schemes based on symmetric-seuence comonents are roosed in this aer for inverter-based distributed generation, aiming at maniulating the delivered instantaneous ower under voltage dis. It is shown that active ower and reactive ower can be indeendently controlled with two individually adatable arameters. By changing these arameters, the relative amlitudes of oscillating ower can be smoothly regulated, as well as the eak values of three-hase grid currents. As a result, the ower control of grid-side inverters becomes uite flexible. Furthermore, two strategies for simultaneous active and reactive ower control are roosed that reserves adative controllability. Finally, the roosed schemes are verified exerimentally. I. INTRODUCTION Voltage dis, usually caused by remote grid faults in the ower system, are short-duration decreases in rms voltage. Most voltage dis are due to unbalanced faults, while balanced voltage dis are relatively rare in ractice [1] [2]. Conventionally, a distributed generation (DG) system would be reuired to disconnect from the grid when voltage dis and to reconnect to the grid when faults are cleared. However, this reuirement is changing. With the increasing alication of renewable energy sources, more and more DG systems actively deliver electricity into the grid. In articular, wind ower generation becomes an imortant electricity source in many countries. Conseuently, in order to maintain active ower delivery and reactive ower suort to the grid, grid codes now reuire wind energy systems to ride through voltage dis without interrution [3] [4]. For the future scenario of a grid with significant DG enetration, it is necessary to investigate the ride-through control of wind turbine systems and other DG systems as well. Disregarding various ustream distributed sources and their controls, the control of DG inverters will be focused on in this aer. Concerning the control of DG inverters under voltage dis, esecially unbalanced situations, two asects should be noticed. Firstly, fast system dynamics and good reference tracking are necessary. Controllers must be able to deal with all the symmetric-seuence comonents and to have fast feedback signals for closed-loo control. Secondly, in case of unbalanced voltage dis, the generation of reference currents is imortant. Because this aer focuses on the second asect, the control structure of such inverters will be resented in the art of exerimental verification. Under unbalanced voltage dis, current reference generation is constrained by trade-offs. Considering the owerelectronics converter constraints, a constant dc-link voltage is desirable [5] and [6]. However, a constant dc bus is achieved at the cost of unbalanced grid currents, and this results in a decrease of maximum deliverable ower. In [7], a ower reducing scheme is used to confine the current during a grid fault. On the other hand, the effects of the grid currents on the ower system side should also be taken into account when assigning reference currents for DG inverters. As resented in [8][9], several secific strategies are ossible in order to get different ower uality levels at the grid connection oint in terms of instantaneous ower oscillation and current distortion. One of the methods in [8], which is based on instantaneous ower theory [1], obtains zero instantaneous ower oscillation but generates distorted grid currents due to asymmetry of grid voltages. Other methods in [8] lead to sinusoidal outut currents. These strategies show flexible control ossibilities of DG systems under grid faults. However, they only coe with secific cases. Therefore, starting from the ideas in [8], a generalized strategy on reference current generation is carried out in the following. This aer rooses generalized and indeendent active and reactive ower control strategies based on symmetricseuence comonents and shows exlicitly the contributions of symmetrical seuences to instantaneous ower under unbalanced voltage dis. The roosed strategy enables DG inverters to be otimally designed. Furthermore, two strategies for simultaneous active and reactive ower control are roosed that reserves the adative controllability. II. INSTANTANEOUS OWER CALCULATION To investigate ower control strategy, the instantaneous ower theory [1] [11] is revisited in this section. Then instantaneous ower calculation based on symmetric seuences /9/$ IEEE 3564 Authorized licensed use limited to: Eindhoven University of Technology. Downloaded on Aril 23,21 at 12:8:18 UTC from IEEE Xlore. Restrictions aly.

3 is develoed, and the notation for the reference current design in the next sections is defined. A. Instantaneous ower Theory For a three-hase DG system, instantaneous active ower and reactive ower at the grid connection oint are given by, resectively, = v i = v a i a + v b i b + v c i c, (1) = v i = 1 3 [(v a v b )i c +(v b v c )i a +(v c v a )i b ], with v = v, 1 1 (2) where v = [ ] T [ ] T v a v b v c, i = ia i b i c, bold symbols reresent vectors, and the oerator denotes the dot roduct of vectors. Note that the subscrit isused to reresent a vector derived from the matrix transformation in (2), although vectors v and v are orthogonal only when the three-hase comonents in vector v are balanced. B. Symmetric-seuence Based Instantaneous ower Symmetric-seuence transformation is a roven way to decomose unbalanced multi-hase uantities [12]. Conseuently, instantaneous uantities for unbalanced a-b-c voltages are reresented by v = v + + v + v, (3) where v +,, = [ v a +,, v +,, ] b v c +,, T, and subscrits +, -, and denote ositive, negative, and zero seuences, resectively. Similarly, current uantities can also be reresented in terms of symmetric seuences, i.e. i = i + + i + i, (4) where i +,, = [ i a +,, i +,, ] b i c +,, T. As a result, the calculation of instantaneous ower in (1) and (2) can be rewritten as = v i =(v + + v + v ) (i + + i + i ), (5) = v i =(v + + v + v ) (i+ + i + i ). (6) With resect to the definitions of the symmetric-seuence vector in (3), corresonding orthogonal vectors in (6) can be derived by using the matrix transformation in (2). Note that v + lags v+ by 9, v leads v by 9,andv is always eual to zero. Because the dot roducts between i and ositive-seuence or negative-seuence voltage vectors are also always zero (due to symmetry of the comonents in v + and v ), euation (5) and (6) can be simlified by = v i =(v + + v ) (i + + i )+v i, (7) = v i =(v + + v ) (i+ + i ). (8) i Fig. 1. v i i v v i i i v Decomosition of currents for indeendent Q control. Because the calculation of instantaneous ower and current references is carried out in terms of vectors, it can also be used in other reference frames, simly by substituting the vectors in the a-b-c frames with vectors derived in other frames, for examle, the stationary α-β-γ reference frame. In next sections, current control based only on ositiveseuence and negative-seuence comonents is investigated. Because zero-seuence voltages of unbalanced voltage dis do not exist in three-wire systems, nor can they roagate to the secondary side of star-ungrounded or delta connected transformers in four-wire systems, most case-studies only consider ositive and negative seuences. Even for unbalanced systems with zero-seuence voltage, four-leg inverter toologies can eliminate zero-seuence current with aroriate control. Simlifying assumtions we will use: - Only ositive-seuence and negative-seuence currents are resent; - Only fundamental voltages exist, in ractice they can be extracted out; - The amlitude of the ositive-seuence voltage is higher than the negative seuence. III. STRATEGIES FOR INDEENDENT &Q CONTROL In order to searately analyze the contribution of currents to indeendent active and reactive ower control, seuence currents i +, can be decouled into two orthogonal uantities, i.e. i +, and i +,, as deicted in Fig. 1. The subscrit reresents active ower related uantities, and reactive ower related uantities. A. Reactive ower Control For reactive ower control, only i + and i are resent, which are defined in hase with v + and v, resectively, in order to generate reactive ower only. Rewriting (7) and (8) in terms of i + and i, we obtain = v + i + v i + }{{} 2ω, (9) = v + i+ + v }{{} Q + i }{{} Q + v i+ + v + i, (1) }{{} 2ω where Q + and Q denote the constant reactive ower introduced by ositive and negative seuences, resectively, 3565 Authorized licensed use limited to: Eindhoven University of Technology. Downloaded on Aril 23,21 at 12:8:18 UTC from IEEE Xlore. Restrictions aly.

4 2ω is oscillating active ower, and 2ω oscillating reactive ower. It can be found that the two terms of 2ω are in-hase uantities oscillating at twice the fundamental freuency. A similar roerty can be found for the two terms of 2ω. Because oscillating active ower can reflect a variation on the DC-link voltage, and high DC voltage variation may cause over-voltage roblems, outut distortion, or even control instability, it is desirable to eliminate 2ω. On the other hand, the oscillating reactive ower 2ω also causes ower losses and oerating current rise, and therefore it is advantageous to mitigate 2ω as well. A trade-off between 2ω and 2ω is not straightforward and deends on ractical reuirements. In the following, strategies to achieve controllable oscillating active and reactive ower are derived from two considerations. 1) Controllable oscillating reactive ower: For given reactive ower Q, the first two terms of (1) are deigned to meet Q = v + i+ + v i. (11) Since the two terms of 2ω in (1) are in-hase uantities that add to each other, it is exected that these two terms can comensate each other. By setting intentionally v + i = k v i+, k 1, (12) after some maniulations the negative-seuence current i is derived from (12) as i = k v + i+ v + 2 v. (13) where v + 2 = v + 2 = v + v +, oerator means the norm of a vector. Substituting (13) into (11), and using v +, 2 = v +, 2, we obtain Q v + 2 =( v + 2 k v 2 ) ( v + ) i+. (14) Then, based on (13) and (14), currents i + and i can be calculated as i + = Q v + 2 k v 2 v+, (15) i = k Q v + 2 k v 2 v. (16) Finally, the total current reference is the sum of i + and i, that is i = Q v + 2 k v 2 (v+ k v ), k 1. (17) 2) Controllable oscillating active ower: Instead of comensating the oscillating reactive ower in (1), we can similarly control the oscillating active ower in (9). For this urose negative-seuence currents are imosed to meet v + i = k v i +, k 1. (18) By considering euation v + i = v + i (because v + lags v + by 9 and i leads i by 9 ), the left side of (18) can be rewritten as v + i = v + i = k v i +, (19) where i denotes the orthogonal vector of i (2). Then, it follows that according to i = k v + i+ v + 2 v. (2) Hence the negative-seuence current i from (2) as i follows directly = k v + i+ v + 2 v. (21) Solving (21) and (11), the ositive-seuence current and negative-seuence current are derived as i + = i = Q v k v 2 v+, (22) k Q v k v 2 v. (23) Again, the total current reference is the sum of i + and i, that is, i = Q v k v 2 (v+ + k v ), k 1. (24) 3) Merging strategies 1) and 2): Simle analysis reveals that (17) and (24) can be ut together as i Q = v k v 2 (v+ + k v ), 1 k 1. (25) Further, by substituting (25) into (9) and (1), it follows that = Q(1 k ) ( v + v ) v k v 2, (26) = Q + Q(1 + k ) ( v + v v k v 2. (27) It can be seen that the variant terms of (26) and (27), i.e. oscillating active ower and reactive ower, are controlled by the coefficient k. These two arts of oscillating ower are orthogonal and eual in maximum amlitude. Simulation results are obtained in Fig. 2 by sweeing arameter k. It is illustrated that either oscillating active ower or ) 3566 Authorized licensed use limited to: Eindhoven University of Technology. Downloaded on Aril 23,21 at 12:8:18 UTC from IEEE Xlore. Restrictions aly.

5 Vabc (v) (kw), (Var) k (d) Fig. 2. Simulation results of the roosed reactive ower control with Q =1kVar, =, where voltages of hase A and B di to 7% at t=.255s, hase voltages, injected currents, instantaneous,, and (d) adjustable coefficient k sweeingfrom-1to1. oscillating reactive ower can be controlled and even can be eliminated at the two extremes of the k curve. This controllable characteristic allows to enhance system control flexibility and facilitates system otimization. It is ointed out that the strategies roosed in [9] namely ositive-negativeseuence comensation (NSC), average active-reactive control (AARC), and balanced ositive-seuence (BS) are euivalent to the results of the roosed strategy when k euals -1, 1, and, resectively. B. Active ower Control For given ower, the current reference for active ower control can be derived similarly, as calculated by i = v k v 2 (v+ +k v ), 1 k 1, (28) where k is the adjustable coefficient for active ower control. Detailed derivation of (28) is resented in [13], as well as the alicability for otimization based on this strategy. IV. STRATEGIES FOR COMBINED &Q CONTROL As already mentioned, some grid codes also reuire DG systems to contribute with reactive ower [3]. For examle, with resect to the amlitude dro of voltages, DG systems having agreements with grid oerators are exected to deliver both active ower and reactive ower during grid faults. Hence the reference currents for this case, named i, can be derived by adding (25) and (28), as exressed by i = i + i = v k v 2 (v+ + k v ) Q + v k v 2 (v+ + k v ), (29) with 1 k 1, 1 k 1. It can be seen that there are infinite combinations for (29) with indeendent coefficients k and k. This also imlicates that the linear controllability benefiting from revious indeendent control strategies does not really exist. In order to reserve the controllability, two joint strategies are roosed to simlify (29) by linking the two coefficients. A. Joint Strategy with Same-Sign Coefficients By setting k = k = k in (29), reference current calculations are simlified and rewritten as i = S v k v 2 R(ϕ)(v+ + k v ), (3) where S is the aarent ower with = S cos ϕ, Q = S sin ϕ,andϕtheower factor angle. Since the α-β reference frame is used in the exeriments, it can be derived that [ ] cos ϕ sin ϕ R(ϕ) =. (31) sin ϕ cos ϕ Note that R(ϕ) will be different in the a-b-c reference frame. On the basis of (3), the resulting currents and oscillating owers can now be redicted and adatively adjusted. To hel understanding, a vector diagram reresenting voltage and current trajectories and the relationshi between oscillating ower are lotted with k as an adjustable arameter under an unbalanced voltage di, where ϕ =3. AsshowninFig.3,whenk changes from 1 to -1, the length of current vectors changes and reaches a minimum value at k =. In Fig. 3, the amlitudes of the oscillating owers also vary with the change of k, which can be redicted by substituting (3) into (7) and (8). Note that when ϕ is not or 9, i.e. active ower and reactive ower are 3567 Authorized licensed use limited to: Eindhoven University of Technology. Downloaded on Aril 23,21 at 12:8:18 UTC from IEEE Xlore. Restrictions aly.

6 k = 1 k =.5 k = β Currents trajectories k = 1 k = ω k = k =.4 k = k =.4 k = 1 1 k ω ω α 2 ω -1 1 k -1 re-fault voltage Unbalanced Voltage dis re-fault Current Fig. 3. Grahic reresentation of grid voltage and current trajectories before and after unbalanced voltage dis in the stationary frame, and relationshi between oscillating active ower 2ω and reactive ower 2ω with k as an adjustable arameter under the joint strategy of, where k = k = k. k =.5 k = β k = 1 k =.5 k = 1 k = 1 % 2 ω k =.4 k = k =.4 k = 1 1 k ω ω α % 2 ω -1 1 k -1 Fig. 4. Grahic reresentation of grid voltage and current trajectories before and after unbalanced voltage dis in the stationary frame, and relationshi between oscillating active ower 2ω and reactive ower 2ω with k as an adjustable arameter under the joint strategy of, where k = k = k. not zero, 2ω or 2ω cannot be eliminated since either active ower or reactive ower delivery will introduce oscillating ower at the two extremes of k. B. Joint Strategy with Oosing-Sign Coefficients By setting k = k = k in (29), the reference current is reresented by i = S cos ϕ v k v 2 (v+ + k v ) S sin ϕ + v + 2 k v 2 (v+ k v ). (32) Illustrative lots are drawn in Fig. 4. It can be seen from (32) that this joint strategy actually reuiring twice the comutation time of joint strategy A. Fortunately, zero 2ω or 2ω can be achieved at the two extremes of k,asshown in Fig. 4. Similar to joint strategy A, when shifting k towards zero the length of current vectors decreases and the current trajectory tends to be a circle. Therefore it can be summarized that the simle adative controllability of indeendent ower control is reserved in the two joint strategies above. This enables DG systems to be otimized under unbalanced voltage dis, e.g. the outut ower maximization, and the limitation of oscillating active ower / reactive ower. V. EXERIMENTAL RESULTS To verify the roosed strategy, exeriments are carried out on a laboratory exerimental system constructed from a four-leg inverter that is connected to the grid through LCL filters, as shown in Fig. 5. The system arameters are listed in Table I. By using a four-leg inverter, zero-seuence currents can be eliminated when the grid has zero-seuence voltages. For the cases where the zero-seuence voltage of unbalanced grid dis is isolated by transformers, a three-leg inverter can be alied. A 15kVA three-hase rogrammable AC ower source (SITZENBERGER+ SIES DM 15/AS) is used to emulate the unbalanced utility grid, and the distributed source is imlemented by a dc ower suly. The controller is designed on a dsace DS114 setu by using Matlab / Simulink. A. Control Realization The roosed controller is realized with a double-loo current controller, which consists of an outer control loo 3568 Authorized licensed use limited to: Eindhoven University of Technology. Downloaded on Aril 23,21 at 12:8:18 UTC from IEEE Xlore. Restrictions aly.

7 v ga Z ga oc i a i La V dc v gb Z gb v gc Z gc Z gn g v a v b v c i b i c L sa L sb L sc C a Cb Cc L a L b L c L n i Lb ilc a b c n C dc Distributed sources v abc abc v Seuence Detection Filter i abc v 1 v 1 i abc i i i* i * ower control strategies +R +R +R i Labc abc vabc abc abc SWM Fig. 5. Circuit diagram and control structure of exerimental four-leg inverter system. TABLE I SYSTEM ARAMETERS Descrition Symbol Value Outut filtering inductor L sa,b,c 2mH Outut filtering caacitor C a,b,c 5μF Outut filtering inductor L a,b,c 2mH Neutral filtering inductor L n.67mh DC-link voltage V dc 75V DC-link caacitors C dc 44uF / 9V dc Switching freuency f sw 16kHz System rated ower S rat 15kVA Tested aarent ower S 25VA with roortional-resonant (R) controllers for eliminating the steady-state error of the delivered currents, and an inner inductor current control loo with simle roortional gain to imrove stability. In addition, a feed-forward loo from the grid voltages is used to imrove system resonse to voltage disturbances. The control for both ositive-seuence and negativeseuence comonents would be much too comlicated and comutation-time consuming when conventional I control with coordinate transformation is used. Furthermore, the seuence detection of feedback currents can be left out. Therefore, it is referred to choose a R controller in the stationary frame. A uasi-roortional-resonant controller with high gain at the fundamental freuency is used 2K r ω br s G i (s) =K + s 2 +2ω br s + ω1 2, (33) where K is the roortional gain, K r is the resonant gain, ω 1 denotes the fundamental radian freuency, and ω br the euivalent bandwidth of the resonant controller. A detailed design for the R controller has been resented in [14], it is not dulicated here. Through otimizing, the arameters used in the exeriment are K =2, K r =1, and ω br =1 rad/s. Since the whole controller is designed in the stationary frame, the seuence detection of grid voltages is also realized Vabc (V) Fig. 6. Emulated grid voltages to be faulty at t=.3s, where hases A and B di to 7%. based on a stationary frame filter cell in the α β frame [15]. The basic filter cell can be easily imlemented using a multistate-variable structure. Besides, a high erformance outut can still be achieved under distorted grid voltages. Concerning the ower factor angle ϕ, two values are tested in the exeriment. Firstly, a slightly modified aroach is used here to calculate the angle ϕ according to the grid code in [3]. Secifically, the DG system should inject at least 2% of the rated current for each ercent of the fundamentalseuence voltage di. Therefore the desired angle ϕ is calculated by ( ϕ =sin 1 2 V + ) V N, (34) V N where V N is nominal voltage amlitude, and V + the ositiveseuence voltage amlitude. Furthermore, it is also reuired in [3] that a reactive ower outut of at least 1% of the rated current is ossible when necessary. Hence also ϕ =9 is assigned directly to test a comlete ower change from active ower to reactive ower. Note that dc-link voltage control is not added here. Usually, 3569 Authorized licensed use limited to: Eindhoven University of Technology. Downloaded on Aril 23,21 at 12:8:18 UTC from IEEE Xlore. Restrictions aly.

8 (W), (Var) (W), (Var) (W), (Var) Fig. 7. Exerimental results of the joint strategy A with k set to 1,, and -1, where the waveforms from the to down are injected currents and instantaneous ower when ϕ = (W), (Var) (W), (Var) (W), (Var) Fig. 8. Exerimental results of the joint strategy A with k set to 1,, and -1, where the waveforms from the to down are injected currents and instantaneous ower when ϕ = 9. a dc-link voltage control loo is included in the control structure, for instance, in a rectifier system [6] or for a wind turbine inverter [7]. The dc bus in the exerimental system is only controlled by the dc ower suly with a uite low bandwidth to maintain a stable dc bus in an average sense. Since the exeriment intends to investigate the effects of the roosed strategy when choosing different k,itis convenient to leave out the dc voltage control in order to only observe the erformance of the roosed strategy. B. Exerimental Results By shifting the controllable arameter k, the system is tested under unbalanced voltage dis with the joint strategies. In order to cature the transient reaction of the system, three situations are intentionally tested for comarison at the start moment voltage dis. As shown in Fig. 6, grid voltages are emulated to be faulty at t =.3s where hases A and B di to 7%. Conseuently, the ower factor angle ϕ derived in the control is 23 and the corresonding results of joint strategy A are obtained in Fig. 7. It can be seen that the reactive ower suort starts within half a cycle after voltage dis. As analyzed in Section IV, the instantaneous active ower and reactive ower always have oscillating ower riles, and the injected grid currents get balanced only when k gets near to zero. In case of ϕ euals 9, the joint strategy A turns out to be a reactive ower control strategy as exressed by (25). Therefore, comaring with the simulation results in Fig. 2 at the oint of k =-1, and 1, it can be seen that the results in Fig. 8 show the same effects on the regulation of oscillating ower rile and reference current. Under the same test conditions, exerimental results are also measured for joint strategy B. As shown in Fig. 9, zero oscillating reactive ower and active ower are achieved at k = 1 and -1, resectively. When k =, the results of joint strategy B are same as the results of joint strategy A, since both joint strategies only deend on ositive-seuence comonents in this case. The results with ϕ = 9 are given in Fig. 1. Comaring with the results in Fig. 8 of joint strategies A, it is easily found that both joint strategies turn out to be the same but needing an oosing sign of k. VI. CONCLUSION This aer rooses generalized strategies for indeendent active and reactive ower control of distributed generation inverters oerating under unbalanced voltage dis. Using 357 Authorized licensed use limited to: Eindhoven University of Technology. Downloaded on Aril 23,21 at 12:8:18 UTC from IEEE Xlore. Restrictions aly.

9 (W), (Var) (W), (Var) (W), (Var) Fig. 9. Exerimental results of the joint strategy B with k set to 1,, and -1, where the waveforms from the to down are injected currents and instantaneous ower when ϕ = (W), (Var) (W), (Var) (W), (Var) Fig. 1. Exerimental results of the joint strategy B with k set to 1,, and -1, where the waveforms from the to down are injected currents and instantaneous ower when ϕ = 9. derived formulas and grahic reresentations, the contributions of symmetric-seuence comonents to the instantaneous ower and the interactions between symmetric seuences were exlained in detail. Furthermore, for simultaneously controlling active and reactive ower, two joint strategies are roosed that reserves the adative controllability. The flexible adativity of the roosed strategy allows it to coe with multile constraints and to be otimized in ractical alications. The erformance of the roosed control strategies is verified by exeriments. REFERENCES [1] M. F. McGranaghan, D. R. Mueller, M. J. Samotyj, Voltage sags in industrial systems, IEEE Trans. Ind. Al., vol. 29, no. 2, , Mar./Ar [2] L. Zhang, and M. H. J. Bollen, Characteristic of voltage dis (sags) in ower systems, IEEE Trans. ower Del., vol. 15, no. 2, , Ar. 2. [3] Grid Code for high and extra high voltage, E.ON Netz Gmbh, Ar. 26. [4] The Grid Code, National Grid Electricity Transmission lc, U.K., May. 29. [5] Y. Suh and T. A. Lio, A control scheme in hybrid synchronousstationary frame for WM AC/DC converter under generalized unbalanced oerating conditions, IEEE Trans. Ind. Al., vol. 42, no. 3, , May/Jun. 26. [6] B. Yin, R. Oruganti, S. anda, and A. Bhat, An outut-ower-control strategy for a three-hase WM rectifier under unbalanced suly conditions, IEEE Trans. Ind. Electron., vol. 55, no. 5, May 28. [7] H. Chong, R. Li, and J. Bumby, Unbalanced-grid-fault ride-through control for a wind turbine inverter, IEEE Trans. Ind. Al., vol.44, no. 3, , May/Jun. 28. [8]. Rodriguez, A. V. Timbus, R. Teodorescu, M. Liserre, and F. Blaabjerg, Flexible active ower control of distributed ower generation systems during grid faults, IEEE Trans. Ind. Electron., vol. 54, no. 5, , Oct. 27. [9]. Rodriguez, A. V. Timbus, R. Teodorescu, M. Liserre, and F. Blaabjerg, Indeendent Q control for distributed ower generation systems under grid faults, in roc, IECON, 26, [1] H. Akagi, E. H. Watanabe, and M. Aredes, Instantaneous ower theory and alications to ower conditioning, IEEE ress, 27. [11] F. Z. eng, and J. -S. Lai, Generalized instantaneous reactive ower theory for three-hase ower systems, IEEE Trans. Instrum. Meas., vol. 45, no.1, , Feb [12]. M. Andersson, Analysis of faulted ower systems, New York: IEEE ress, [13] F. Wang, J. Duarte, M. Hendrix, Active ower control strategies for inverter-based distributed ower generation adated to grid-fault ridethrough reuirements, in roc. EE, 29, to be ublished. [14] D. Zmood and D. Holmes, Stationary frame current regulation of WM inverters with zero steady-state error, IEEE Trans. ower Electron., vol. 18, no. 3, , May 23. [15] F. Wang, J. Duarte, M. Hendrix, High erformance stationary frame filters for symmetrical seuences or harmonics searation under a variety of grid conditions, in roc. IEEE AEC, 29, Authorized licensed use limited to: Eindhoven University of Technology. Downloaded on Aril 23,21 at 12:8:18 UTC from IEEE Xlore. Restrictions aly.