IN many important applications for power electronics such

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1 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 3, MARCH Power Controllability of a Three-Phase Converter With an Unbalance AC Source Ke Ma, Member, IEEE, Wenjie Chen, Stuent Member, IEEE, Marco Liserre, Fellow, IEEE, an Free Blaabjerg, Fellow, IEEE Abstract Three-phase c ac power converters suffer from power oscillation an overcurrent problems in case of the unbalance ac source voltage that can be cause by gri/generator faults. Existing solutions to hanle these problems are properly selecting an controlling the positive- an negative-sequence currents. In this paper, a new series of control strategies which utilize the zerosequence components are propose to enhance the power control ability uner this averse conition. It is conclue that by introucing proper zero-sequence current controls an corresponing circuit configurations, the power converter can enable more flexible control targets, achieving better performances in the elivere power an the loa current when suffering from the unbalance ac voltage. Inex Terms Control strategy, c ac converter, fault tolerance, unbalance ac source. Fig. 1. Typical c ac power converter application. I. INTRODUCTION IN many important applications for power electronics such as renewable energy generation, motor rives, power quality, an microgri, etc., the three-phase c ac converters are critical components as the power flow interface of c an ac electrical systems [1], [2]. As shown in Fig. 1, a c ac voltage source converter with a corresponing filter is typically use to convert the energy between the c bus an the three-phase ac sources, which coul be the power gri, generation units, or the electric machines epening on the applications an controls [3] [5]. Since the power electronics are getting so wiely use an becoming essential in the energy conversion technology, the failures or shutting own of these backbone c ac converters may result in serious problems an cost. It is becoming a nee in many applications that the power converters shoul be reliable to withstan some faults or isturbances in orer to ensure certain availability of the energy supply [6] [13]. A goo example can be seen in the win power application, where both the total installe capacity an iniviual capacity of the power conversion system are relatively high. The suen isconnection Manuscript receive October 1, 2013; revise December 11, 2013 an February 16, 2014; accepte March 20, Date of publication March 31, 2014; ate of current version October 15, Recommene for publication by Associate Eitor P.-T. Cheng. K. Ma an F. Blaabjerg are with the Department of Energy Technology, Aalborg University, Aalborg 9220, Denmark ( kema@et.aau.k; fbl@et.aau.k). W. Chen is with Zhejiang University, Hangzhou , China ( WenjieChen86@gmail.com). M. Liserre is with the Christian-Albrechts-University of Kiel, Kiel 24118, Germany ( ml@tf.uni-kiel.e). Color versions of one or more of the figures in this paper are available online at Digital Object Ientifier /TPEL Fig. 2. Gri coes of win turbines uner the gri voltage ip by ifferent countries. of the power converter may cause significant impacts on the gri stability an also on the high cost for maintenance/repair [1]. As a result, transmission system operators (TSOs) in ifferent countries have been issuing strict requirements for the win turbine behavior uner gri faults. As shown in Fig. 2, the win power converter shoul be connecte (or even keep generating power) uner various gri voltage ips for certain time accoring to the ip severity, an in some uncritical conitions (e.g., 90% voltage ip), the power converter may nee long-time operation [1], [2], [12], [13]. When the ac source shown in Fig. 1 becomes istorte uner faults or isturbances, the unbalance ac voltages have been proven to be one of the greatest challenges for the control of the c ac converter in orer to keep them normally operating an connecte to the ac source [2], [14], [15]. Special control methos which can regulate both the positive- an negativesequence currents have been introuce to hanle these problems [2], [16] [21]. However, the resulting performances by these control methos seem to be still not satisfactory: either istorte loa currents or power oscillations will be presente, an thereby not only the ac source but also the power converter will be further stresse accompanying with the costly esign consierations IEEE. Translations an content mining are permitte for acaemic research only. Personal use is also permitte, but republication/reistribution requires IEEE permission. See stanars/publications/rights/inex.html for more information.

2 1592 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 3, MARCH 2015 Fig. 3. Phasor iagram efinitions for the voltage ips in the ac source of Fig. 1. V A,V B,anV C means the voltage of three phases in the ac source. This paper targets to unerstan an improve the power control limits of a typical three-phase c ac converter system uner the unbalance ac source. A new series of control strategies which utilizes the zero-sequence components are then propose to enhance the power control ability uner this averse conition. Besies the gri integration, the propose control methos have the potential to be applie uner other applications like the motor/generator connections or microgris, where the unbalance ac voltage is likely to be presente; therefore, the basic principle an feasibility are mainly focuse. Fig. 4. Typical three-phase three-wire 2L-voltage source converter. TABLE I CONVERTER PARAMETERS FOR THE CASE STUDY II. LIMITS OF A TYPICAL THREE-WIRE CONVERTER SYSTEM In orer to analyze the controllability an the performance of the power electronics converter uner an averse ac source, a severe unbalance ac voltage is first efine as a case stuy in this paper. As shown in Fig. 3, the phasor iagram of the threephase istorte ac voltage are inicate, it is assume that the type B fault happens with the significant voltage ip on phase A of the ac source. Also, there are many other types of voltage faults which have been efine as type A F in [22]. Accoring to [2] an [19], any istorte three-phase voltage can be expresse by the sum of components in the positive sequence, negative sequence, an zero sequence. For simplicity of analysis, only the components with the funamental frequency are consiere in this paper, however, it is also possible to exten the analysis to higher orer harmonics. The istorte three-phase ac source voltage in Fig. 3 can be represente by V S = V + + V + V 0 v a sin(ωt + ϕ + ) = v b = V + sin(ωt ϕ + ) sin(ωt ϕ + ) v c sin(ωt + ϕ ) sin(ωt + ϕ 0 ) + V sin(ωt ϕ ) + V 0 sin(ωt + ϕ 0 ) (1) sin(ωt ϕ ) sin(ωt + ϕ 0 ) where V +,V, an V 0 are the voltage amplitue in the positive, negative, an zero sequence, respectively. An ϕ +, ϕ, an ϕ 0 represent the initial phase angles in the positive sequence, negative sequence, an zero sequence, respectively. The preefine voltage ip as inicate in Fig. 3 shoul contain voltage components in all the three sequences [2], [11]. A typically use three-phase three-wire two-level voltage source c ac converter is chosen an basically esigne, as shown in Fig. 4 an Table I, where the converter configuration an the parameters are inicate, respectively. It is note that the three-phase ac source is represente here by three winings with a common neutral point, which can be the winings of an electric machine or a transformer. Because there are only three wires an a common neutral point in the winings of the ac source, the currents flowing in the three phases o not contain zero-sequence components. As a result, the three-phase loa current controlle by the converter can be written as I C = I + + I. (2) With the voltage of the ac source in (1) an the current controlle by the converter in (2), the instantaneous real power p an the imaginary power q in αβ coorinate, as well as the real power p 0 in the zero coorinate can be calculate as p q p 0 = v α i α + v β i β v α i β v α i β v 0 0 P + P c2 cos(2ωt)+p s2 sin(2ωt) = Q + Q c2 cos(2ωt)+q s2 sin(2ωt). (3) 0 Then, the instantaneous three-phase real power p 3Φ an the imaginary power q 3Φ of the ac source/converter can be written

3 MA et al.: POWER CONTROLLABILITY OF A THREE-PHASE CONVERTER WITH AN UNBALANCED AC SOURCE 1593 as [ p3φ q 3φ ] [ ] p + p0 = q [ ] P = Q + [ Pc2 Q c2 ] cos(2ωt)+ [ Ps2 Q s2 ] sin(2ωt) (4) where P an Q are the average parts of the real an imaginary power, P c2,p s2 an Q c2,q s2 are the oscillation parts, which can be calculate as P = 3 2 (v+ i+ + v+ q i + q + v i + v q i q ) P c2 = 3 2 (v i+ + v q i + q + v + i + v+ q i q ) P s2 = 3 2 (v q i + v i+ q v + q i + v+ i q ) (5) Q = 3 2 (v+ q i + v+ i+ q + v q i v i q ) Q c2 = 3 2 (v q i + v i+ q + v + q i v+ i q ) Q s2 = 3 2 ( v i+ v q i + q + v + i + v+ q i q ) (6) where a positive q synchronous reference frame an a negative q synchronous reference frame are applie, respectively, to the positive- an negative-sequence voltage/current. Each of the components on the corresponing positive- an negative-q axis can be written as v + = V + cos(ϕ + ) v q + = V + sin(ϕ + ) v = V cos(ϕ ) vq = V sin(ϕ ) (7) i + = I+ cos(δ + ) i + q = I + sin(δ + ) i = I cos(δ ) i q = I sin(δ ). (8) Then, (5) an (6) can be formulate as a matrix relation as P v + v q + v v q i + Q = 3 v q + v + vq v i + q P s2 2 vq v v q + v + i. (9) P c2 v vq v + v q + i q It can be seen from (9) that if the ac source voltage is ecie, then the converter has four controllable freeoms (i +, i+ q, i, an i q ) to regulate the current flowing in the ac source. That also means: four control targets/functions can be establishe. Normally, the three-phase average active an reactive powers elivere by the converter are two basic requirements for a given application, then, two control targets have to be first settle as P 3φ = P = P ref Q 3φ = Q = Q ref. (10) It is note that ifferent applications may have ifferent requirements for the control of the average power, e.g., in the power prouction application, the active power reference P ref injecte to the gri is normally set as positive, meanwhile the large amount of the reactive power Q ref may be neee in orer to help to support the gri voltage [12], [13]. As for the electric machine application, the P ref is set as negative for the generator moe an positive for the motor moe, there may be no or just a few reactive power Q ref requirements for magnetizing of the electric machine. While in most power quality applications, e.g., STACOM, P ref is normally set to be very small to provie the converter loss, an a large amount of Q ref is normally require. Consequently, for the three-phase three-wire converter system, there are only two more current control freeoms left to achieve another two control targets besies (10). These two aing control targets may be utilize to further improve the performances of the converter uner the unbalance ac source, which have been generally investigate in [2] an [16] [18]. However, this paper focuses more on the evaluation of control limits an the control possibilities uner the whole voltage ipping range. In the following, two of the most mentione control methos achieve by three-wire converter structure are investigate uner the unbalance ac source. A. Elimination of the Negative-Sequence Current In most of the gri integration applications, there are strict gri coes to regulate the behavior of the gri connecte converters. The negative-sequence current which always results in the unbalance loa current may be unacceptable from the point view of a TSO [13]. Therefore, extra two control targets which aim to eliminate the negative-sequence current can be ae as i =0 i q =0. (11) Translating the control targets in (10) an (11), all the controllable current components can be calculate as i + = 2 3 v+ P ref + v + q Q ref (v + )2 (v )2 i + q = 2 3 Pref v + i =0 v+ v + q i + (12) i q =0. (13) When applying the current references in (12) an (13), the ac source voltage, loa current, sequence current amplitue, an the instantaneous power elivere by the converter are shown in Fig. 5. The simulation is base on the parameters preefine in Fig. 4 an Table I. The ac source voltage is set with V A

4 1594 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 3, MARCH 2015 Fig. 5. Simulation of the converter with no negative-sequence current control (three-phase three-wire converter, P ref = 1 p.u., Q ref = 0 p.u., I = 0 p.u., I q = 0 p.u., V A = 0 p.u., I+, I, ani 0 means the amplitue of the current in the positive, negative, an zero sequences, respectively). ipping to zero. The average active power reference P ref for the converter is set as 1 p.u. an the reactive power reference Q ref is set as 0. It can be seen from Fig. 5 that with the extra control targets in (11), there is no zero-sequence nor negative-sequence components in the loa current, i.e., the currents among the three phases of converter are symmetrical uner the given unbalance ac source conition. The current amplitue in ifferent sequences an the elivere active/reactive power with relation to the voltage amplitue of the ipping phase V A are shown in Fig. 6(a) an (b), respectively. It is note that only the positive-sequence current is generate by the converter, an there is up to ±0.5 p.u. oscillations both in the active an reactive power when V A ips to zero. The significant fluctuation of the active power woul result in the voltage fluctuation of the c bus [16] [19], compromising not only the THD but also the reliability performances of the converter accoring to [23]. B. Elimination of the Active Power Oscillation In orer to overcome the isavantage of the active power oscillation uner the unbalance ac source, another two extra control targets which aim to cancel the oscillation items in the instantaneous active power can be use to replace (11) as Fig. 6. Profile of converter control with no negative-sequence current (threephase three-wire converter, P ref = 1 p.u., Q ref = 0 p.u., I = 0 p.u., I q = 0 p.u.). (a) Sequence current amplitue versus V A (I+, I, ani 0 means the amplitue of the current in the positive, negative, an zero sequences, respectively). (b) P an Q oscillation range versus V A. Then, accoring to (9), each of the current components can be calculate as i + v + v q + v v 1 q P ref i + q i = 2 v q + v + vq v 0 3 vq v v q + v + 0 i q v vq v + v q + 0 v + = 2P v ref + q 3M v (15) where v q M =(v + )2 +(v + q ) 2 (v )2 (v q ) 2. (16) P 3φc2 = P c2 =0 P 3φs2 = P s2 =0. (14) When applying the current references in (15), the corresponing source voltage, loa current, sequence current, an the instantaneous power elivere by the converter are shown in Fig. 7.

5 MA et al.: POWER CONTROLLABILITY OF A THREE-PHASE CONVERTER WITH AN UNBALANCED AC SOURCE 1595 Fig. 7. Simulation of the converter control with no active power oscillation (three-phase three-wire converter, P ref = 1 p.u., Q ref = 0 p.u., P s2 = 0 p.u., P c 2 = 0 p.u., V A = 0p.u.I+, I, ani 0 means the amplitue of the current in the positive, negative, an zero sequences, respectively. It can be seen that the active power oscillation at twice of the funamental frequency can be eliminate. However, the isavantage of this control strategy is also significant: first, the converter has to eliver up to 3 p.u. loa current in the faulty phase which is much larger than the currents in other two normal phases this large current may cause over loaing of the system an result in failures. Moreover, significant fluctuation of the reactive power will be presente compare to the control strategy in Fig. 5. In case of the gri-connecte application, this significant reactive power oscillation may cause gri voltage fluctuation, which is unpreferre especially with weak gri an gri faults. The current amplitue in the ifferent sequences, as well as the elivere active/reactive power with relation to the voltage amplitue on the ipping phase is shown in Fig. 8(a) an (b), respectively. It is note that the converter has to eliver both the positive- an negative-sequence current to achieve this control strategy, an up to ±1.3 p.u. oscillation in the reactive power is generate when V A ips to zero. Another three possible control strategies which can eliminate the oscillation of the reactive power as shown in (17) or reuce the oscillations of both active an reactive power as shown in (18) an (19), are also possible for the three-phase three-wire converter uner the unbalance ac source Q c2 =0 Q s2 =0 (17) P c2 =0 Q s2 =0 (18) P s2 =0 Q c2 =0. (19) Fig. 8. Profile of converter control with no active power oscillation (threephase three-wire converter, P ref = 1 p.u., Q ref = 0 p.u., P s2 = 0 p.u., P c 2 = 0 p.u.). (a) Sequence current amplitue versus V A.(I+, I-,anI 0 means the amplitue of the current in the positive, negative, an zero sequences, respectively). (b) P an Q range versus V A. III. CONVERTER SYSTEM WITH THE ZERO-SEQUENCE CURRENT PATH As can be conclue, in the typical three-phase three-wire converter structure, four control freeoms for the loa current seem to be not enough to achieve satisfactory performances uner the unbalance ac source. (No matter what combinations of control targets are use, either significant power oscillation or overloae/istorte current will be presente.) Therefore, more current control freeoms are neee in orer to improve the control performance uner the unbalance ac source conitions. Another series of the converter structure are shown as inicate as the four-wire system in Fig. 9(a) an the six-wire system in Fig. 9(b). Compare to the three-wire converter structure, these types of converters introuce the zero-sequence current path [24] [26], which may enable extra current control freeoms to achieve better power control performances. It is note that in the gri-connecte application, the zero-sequence current is not injecte into the gri but trappe in the typically use -Y transformer.

6 1596 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 3, MARCH 2015 A potential control structure is propose in Fig. 10, in which an extra control loop is introuce to enable the controllability of the zero-sequence current. After introucing the regulate zero-sequence current, the three-phase current generate by the converter can be written as [27] [29] I C = I + + I + I 0. (20) By operating the voltage of the ac source (1) an the current controlle by the power converter (20), the instantaneous generate real power p, the imaginary power q in the αβ coorinate, an the real power p 0 in the zero coorinate can be calculate as p q p 0 = v α i α + v β i β v α i β v α i β v 0 i 0 P + P c2 cos(2ωt)+p s2 sin(2ωt) = Q + Q c2 cos(2ωt)+q s2 sin(2ωt). (21) P 0 + P 0c2 cos(2ωt)+p 0s2 sin(2ωt) Fig. 9. Converter structure with the zero-sequence current path. (a) Four-wire system. (b) Six-wire system. Then, the instantaneous three-phase real power p 3Φ an the imaginary power q 3Φ of the converter can be written as [ p3φ q 3φ ] [ ] [ ] p + p0 P + P0 = = q Q [ ] [ ] Pc2 + P 0c2 Ps2 + P 0s2 + cos(2ωt)+ sin(2ωt). (22) Q c2 Q s2 It is note that the voltage an the current in zero sequence only contribute to the real power p 3Φ of the converter. Each part of (22) can be calculate as P = 3 2 (v+ i+ + v+ q i + q + v i + v q i q ) P c2 = 3 2 (v i+ + v q i + q + v + i + v+ q i q ) P s2 = 3 2 (v q i + v i+ q v + q i + v+ i q ) (23) Q = 3 2 (v+ q i + v+ i+ q + v q i v i q ) Q c2 = 3 2 (v q i + v i+ q + v + q i v+ i q ) Q s2 = 3 2 ( v i+ v q i + q + v + i + v+ q i q ) (24) Fig. 10. current. Control structure for the converter system with the zero-sequence P 0 = 3 2 (v0 Re i 0 Re + v 0 Im i 0 Im) P 0c2 = 3 2 (v0 Re i 0 Re v 0 Im i 0 Im) P 0s2 = 3 2 ( v0 Im i 0 Re v 0 Re i 0 Im). (25)

7 MA et al.: POWER CONTROLLABILITY OF A THREE-PHASE CONVERTER WITH AN UNBALANCED AC SOURCE 1597 Then, the relationship of (23) (25) can be formulate to a matrix equation as P + P 0 P c2 + P 0c2 P s2 + P 0s2 Q Q c2 Q s2 v + v q + v vq vre 0 v 0 Im v vq v + v q + vre 0 v 0 Im = 3 vq v v q + v + vim 0 v0 Re 2 v q + v + vq v 0 0 vq v v q + v v vq v + v q i + i + q i i q i 0 Re i 0 Im. (26) It is note that unlike the traitional approach in which the zero sequence components are normally minimize, the zerosequence voltage an the current here look like single-phase AC components running at the same funamental frequency. As a result, the zero-sequence voltage/current can be represente by vectors in a synchronous reference frame in the zero sequence as V 0 = vre 0 + vimj 0 I 0 = i 0 Re + i 0 Imj (27) where the real part an imaginary part can be represente as follows: vre 0 = V 0 cos(ϕ 0 ) vim 0 = V 0 sin(ϕ 0 ) i 0 Re = I 0 cos(δ 0 ) i 0 Im = I 0 sin(δ 0 ). (28) It can be seen from (26) that if the three-phase ac source voltage is ecie, then the converter has six controllable freeoms (i +, i+ q, i, i q,i 0 Re, an i0 Im ) to regulate the current flowing in the ac source. That means: six control targets/functions can be establishe by the converter having the zero-sequence current path. Similarly, the three-phase average active an reactive power elivere by the converter are two basic requirements for a given application, then, two control functions nee to be first settle as P 3φ = P + P 0 = P ref Q 3φ = Q = Q ref. (29) So, for the converter system with the zero-sequence current path, there are four control freeoms left to achieve two more control targets than the traitional three-wire system, this also means extene controllability an better performance uner the unbalance ac source. A. Elimination of Both the Active an Reactive Power Oscillation. Because of more current control freeoms, the power converter with the zero-sequence current path can not only eliminate the oscillation in the active power, but also cancel the oscillation in the reactive power at the same time. This control targets can be written as P 3φc2 = P c2 + P 0c2 =0 P 3φs2 = P s2 + P 0s2 =0 (30) Q c2 =0 Q s2 =0. (31) The power oscillation cause by the zero-sequence current P 0c2 an P 0s2 are use to compensate the power oscillation cause by the positive- an negative-sequence currents P c2 an P s2. When combing (26), (30), an (31), each of the current components controlle by converter can be calculate as i + i + q i i q i 0 Re i 0 Im v + v q + v vq vre 0 v 0 1 Im P ref v vq v + v q + vre 0 v 0 Im 0 = 2 vq v v q + v + vim 0 v0 Re 0 3 v q + v + vq v. 0 0 Q ref vq v v q + v v vq v + v q (32) In orer to facilitate the analytical solution, assuming that the -axis or the real axis in the synchronous reference frame is allie with the voltage vectors in each of the sequence (positive, negative, an zero), then all of the controllable current components with the zero-sequence current path can be solve by i i + q 2 3 i v v + i q v v + P ref (v + v ) (1 v /v+ ) v + i + Q ref +(v )2 /v + (33) i + q (34)

8 1598 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 3, MARCH 2015 Fig. 11. Simulation of converter control with no active an reactive power oscillation (three-phase converter with the zero-sequence path, P ref = 1 p.u., Q ref = 0 p.u., P s2 = 0 p.u., P c 2 = 0 p.u., Q s2 = 0 p.u., Q c 2 = 0 p.u., V A = 0 p.u.). i 0 Re 2 3 Pref P v 0 Re i 0 Im v+ i q v i+ q vre 0. (35) When applying the current references in (33) (35), the corresponing ac source voltage, loa current, sequence current, an the instantaneous power elivere by the converter are shown in Fig. 11. It can be seen that by this control strategy, the oscillation of both the active an reactive power at twice of the funamental frequency can be eliminate. Moreover, compare to the control strategies for the three-wire system, the amplitue of the loa current in each phase is not further increase, an the current in the faulty phase is smaller than the other two normal phases this is a significant improvement. The current amplitue in ifferent sequences, as well as the elivere active/reactive power with relation to the voltage amplitue on the ipping phase is shown in Fig. 12(a) an (b), respectively. It is note that the converter has to eliver positive-, negative-, an zero-sequence currents to achieve this control strategy. An the zero sequence current is controlle as zero when the voltage ip is at 1.0 p.u. B. Elimination of the Active Power Oscillation an the Negative-Sequence Current. Another promising control strategy for the converter using the zero-sequence current path is to eliminate the active power oscillation, an meanwhile cancel the negative-sequence current. The extra two control targets besies (26) can be written Fig. 12. Profile of converter control with no active an reactive power oscillation (three-phase converter with the zero sequence path, P ref = 1 p.u., Q ref = 0 p.u., P s2 = 0 p.u., P c 2 = 0 p.u., Q s2 = 0 p.u., Q c 2 = 0 p.u.). (a) Sequence current amplitue versus V A.(I+, I,anI 0 means the amplitue of the current in the positive, negative, an zero sequences, respectively). (b) P anq ranges versus V A. as P 3φc2 = P c2 + P 0c2 =0 P 3φs2 = P s2 + P 0s2 =0 (36) i =0 i q =0. (37) Combing (26), (36), an (37), the matrix equation of (26) can be egrae as P + P 0 v + v q + vre 0 v 0 Im P c2 + P 0c2 P s2 + P 0s2 = 3 v vq vre 0 v 0 Im 2 vq v vim 0 v0 Re Q v + q v i + i + q i 0 Re i 0 Im. (38)

9 MA et al.: POWER CONTROLLABILITY OF A THREE-PHASE CONVERTER WITH AN UNBALANCED AC SOURCE 1599 Fig. 13. Simulation of converter control with no active power oscillation an no negative sequence (three-phase converter with the zero-sequence current path, P ref = 1 p.u., Q ref = 0 p.u., P s2 = 0 p.u., P c 2 = 0 p.u., i = 0 p.u., i q = 0 p.u., V A = 0p.u.I+, I-,anI 0 means the amplitue of the current in the positive, negative, an zero sequences, respectively). An each of the current components can be calculate as i + v + v q + vre 0 v 0 1 Im P ref i + q i 0 = 2 v vq vre 0 v 0 Im 0 Re 3 v i 0 q v vim 0 v0 Re 0. Im v q + v Q ref (39) In orer to facilitate the analytical solution, assuming that the -axis or the real axis in the synchronous reference frame is allie with the voltage vectors in each of the sequence, then all of the controllable current components with the zero-sequence current path can be solve as i P ref (v + v ) i + q 2 3 Qref v + (40) i =0 i q =0 (41) i 0 Re v i+ v 0 Re i 0 Im 0. (42) When applying the current references in (40) (42), the corresponing source voltage, loa current, sequence current, an the instantaneous power elivere by converter are shown in Fig. 13. It can be seen that by this control strategy, the oscillation of the active power at twice of the funamental frequency can be eliminate, an the loa current in the faulty phase is reuce to zero. The current amplitue in the ifferent sequences, as well as the elivere active/reactive power with relation to the volt- Fig. 14. Profile of converter control with no active power oscillation an no negative sequence (three-phase converter with the zero-sequence current path, P ref = 1 p.u., Q ref = 0 p.u., P s2 = 0 p.u., P c 2 = 0 p.u., i = 0 p.u., i q = 0 p.u.). (a) Sequence current amplitue versus V A.(b)P an Q ranges versus V A. age on the ipping phase are shown in Fig. 14(a) an (b), respectively. It is note that the converter has to eliver constant positive- an zero-sequence currents in orer to achieve this control strategy uner ifferent ips of the source voltage. The oscillation of the reactive power is maintaine in a much smaller range (up to ±0.3 p.u.) compare to that in the three-wire system (up to ±1.3 p.u.) in Fig. 8(b). The zero-sequence current is controlle as zero when the voltage ip is at 1.0 p.u. Finally, the converter stresses for the active/reactive power oscillations an the current amplitue in the faulty/normal phases are compare in Table II, where ifferent control strategies an converter structures are inicate, respectively. It can be seen that by introucing the converter structures with the zerosequence current path an corresponing controls, the power oscillations uner the unbalance ac source are significantly reuce; meanwhile, the current amplitue in the normal phases is not further stresse, an the current stress in the faulty phases is significantly relieve. It is worth to mention that when enabling the propose control methos, the zero-sequence current is flowing in/out of the mipoint of the c bus at the funamental frequency, thereby

10 1600 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 3, MARCH 2015 TABLE II CONVERTER STRESS COMPARISON BY DIFFERENT CONTROL STRATEGIES (VALUES ARE REPRESENTED IN p.u., P ref = 1 p.u., Q ref = 0 p.u., AND V A = 0 p.u.) a larger c capacitance or a rectifier with controllability of the mipoint potential is preferre for the four-wire converter structure shown in Fig. 9(a). However, there is no such problem in the six-wire converter structure shown in Fig. 9(b). Moreover, accoring to (35) an (42), the reference current for the zero sequence is inverse proportional with the zero sequence voltage v 0. The effectiveness of the propose control methos shoul rely on the amount of v 0 in the unbalance ac source. In some cases of two-phase or three-phase faults with no or very small v 0, the performance of the propose control strategies will be ifferent, an new control methos which o not utilize the power from the zero sequence are neee. It is also note that the ynamical performance an the sequence-extracting algorithm are also critical consierations for the control methos uner the unbalance ac source, either for the transient conition (e.g., LVRT) or the stability uring the steay-state operation, however, they are out of the scope of this paper. Fig. 15. Configurations of the experimental setup. (a) Circuit topology (b) Setup photo. TABLE III DETAIL PARAMETERS OF THE EXPERIMENTAL SETUP IV. EXPERIMENTAL RESULTS The control results by ifferent converter structures an control strategies are valiate on a ownscale c ac converter. As shown in Fig. 15, the circuit configurations an setup photo are both illustrate. A three-phase two-level converter with corresponing LCL filter is use to interconnect two c voltage sources an a programmable three-phase ac voltage source. The etail parameters of the experimental setup are shown in Table III. It is note that the converter is controlle to operate at the inverter moe, where the active power is flowing from the c source to the ac source. By opening an closing a switch shown in Fig. 15(a), the converter can be shifte between the typical three-wire system an four-wire system with the zero-sequence current path. The amplitue of the phase A voltage in the programmable ac source is ajuste to 0.1 p.u. (22 V rms ) in orer to establish an averse unbalance conition. The control performance of the converter with the three-wire structure are shown in Fig. 16, where the given conitions an the two control strategies mentione in Figs. 5 an 7 are applie, respectively. It can be seen that the experimental results agree well with the analysis an simulation results, where either the significant power oscillations or the overloae current in the faulty phase are presente. After enabling the zero current path an propose controls, the performances of the given converter are shown again in Fig. 17, where the same conitions an two control strategies mentione in Figs. 11 an 13 are applie, respectively. It can be seen that the experimental results also agree well with the simulation results, where the power oscillations are much more reuce or even totally cancelle; meanwhile, the current stress in the faulty phase is significantly relieve. These critical performances are har to be achieve by a single three-wire converter structure using existing control strategies. The capability to control the reactive power is also a critical performance for the converter uner the unbalance ac source, the propose two control methos are also teste uner the

11 MA et al.: POWER CONTROLLABILITY OF A THREE-PHASE CONVERTER WITH AN UNBALANCED AC SOURCE 1601 Fig. 16. Experimental control performance of the converter in Fig. 15(a) with only three wires (units are nominalize by parameters in Table III, reference given: P ref = 0.5 p.u., Q ref = 0 p.u., ac source conition: amplitue of the phase voltage V A = 0.1 p.u., V B =V C = 1 p.u.). (a) No negative-sequence current control (b) No P oscillation control. Fig. 17. Experimental control performance of the converter in Fig. 15(a) after enabling the zero-sequence current path (units are nominalize by parameters in Table III, reference given: P ref = 0.5 p.u., Q ref = 0 p.u., amplitue of the phase voltage V A = 0.1 p.u., V B =V C = 1 p.u.). (a) No P an no Q oscillation control (b) No negative-sequence current an no P oscillation control. conitions to eliver the inuctive/capacitive reactive power. As shown in Figs. 18 an 19, the No P & No Q oscillation control an No negative-sequence current & No P oscillation control are applie, respectively, to eliver the inuctive an capacitive reactive power with phase A voltage ipping to 0.5 p.u. It can be seen that the avantages of the smaller/eliminate power oscillation an the relieve current loaing in the faulty phase are still maintaine. It is note that the power elivering uner the unbalance AC source shoul give priority to the current limits of the power evices. This topic has been well iscusse in the existing control methos base on the three-wire structure [30], an it is also an important consieration in the propose control methos which utilize the zero-sequence components. In the experiment, the maximum reactive power is limite by the

12 1602 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 3, MARCH 2015 Fig. 18. Experimental results of the converter s reactive power capability when using no P & no Q oscillation control in Fig. 17(a). (units are nominalize by parameters in Table III, reference given: P ref = 0 p.u., Q ref ±0.25 p.u. when the maximum loa current achieves 1 p.u., the amplitue of the phase voltage V A = 0.5 p.u., V B =V C = 1 p.u.). (a) Deliver inuctive reactive power (Q+). (b) Deliver capacitive reactive power (Q ). Fig. 19. Experimental results of the converter s reactive power capability when using no negative-sequence current an no P oscillation control shown in Fig. 17(b). (units are nominalize by parameters in Table III, reference given: P ref = 0 p.u., Q ref ±0.5 p.u. when the maximum loa current achieves 1 p.u., the amplitue of the phase voltage V A = 0.5 p.u., V B =V C = 1 p.u.). (a) Deliver inuctive reactive power (Q+). (b) Deliver capacitive reactive power (Q ). maximum current loaing, which all achieve 1 p.u. in Figs. 18 an 19. V. CONCLUSION In a typical three-phase three-wire converter structure, there are four current control freeoms, an it may be not enough to achieve satisfactory performances uner the unbalance ac source, because either significantly the oscillate power or the overloae current will be presente. In the three-phase converter structure with the zero sequence current path, there are six current control freeoms. The extra two control freeoms coming from the zero sequence current can

13 MA et al.: POWER CONTROLLABILITY OF A THREE-PHASE CONVERTER WITH AN UNBALANCED AC SOURCE 1603 be utilize to exten the controllability of the converter an improve the control performance uner the unbalance ac source. By the propose control strategies, it is possible to totally cancel the oscillation in both the active an the reactive power, or reuce the oscillation amplitue in the reactive power. Meanwhile, the current amplitue of the faulty phase is significantly relieve without further increasing the current amplitue in the normal phases. The avantage an features of the propose controls can be still maintaine uner various conitions when elivering the reactive power. The analysis an propose control methos are well agree by experimental valiations. REFERENCES [1] F. Blaabjerg, M. Liserre, an K. Ma, Power electronics converters for win turbine systems, IEEE Trans. In. Appl., vol. 48, no. 2, pp , Mar./Apr [2] R. Teoorescu, M. Liserre, an P. Roriguez, Gri Converters for Photovoltaic an Win Power Systems. New York, NY, USA: Wiley-IEEE, [3] J. Rocabert, G. M. S. Azeveo, A. Luna, J. M. Guerrero, J. I. Canela, an P. Roriguez, Intelligent connection agent for three-phase gri-connecte microgris, IEEE Trans. Power Electron, vol. 26, no.10, pp , Oct [4] J. W. Kolar an T. Frieli, The essence of three-phase PFC rectifier systems Part I, IEEE Trans. Power Electron., vol. 28, no. 1, pp , Jan [5] J. Hu, L. Shang, Y. He, an Z. Z. Zhu, Direct active an reactive power regulation of gri-connecte c/ac converters using sliing moe control approach, IEEE Trans. Power Electron., vol. 26,no.1,pp ,Jan [6] C. Wessels, F. Gebhart, an F. W. Fuchs, Fault rie-through of a DFIG win turbine using a ynamic voltage restorer uring symmetrical an asymmetrical gri faults, IEEE Trans. Power Electron., vol. 26, no. 3, pp , Mar [7] F. Aghili, Fault-tolerant torque control of BLDC motors, IEEE Trans. Power Electron., vol. 26, no. 2, pp , Feb [8] Y. Xiangwu, G. Venkataramanan, W. Yang, D. Qing, an Z. Bo, Grifault tolerant operation of a DFIG win turbine generator using a passive resistance network, IEEE Trans. Power Electron., vol. 26, no. 10, pp , Oct [9] B. A. Welchko, T. A. Lipo, T. M. Jahns, an S. E. Schulz, Fault tolerant three-phase AC motor rive topologies: A comparison of features, cost, an limitations, IEEE Trans. Power Electron., vol. 19, no. 4, pp , Jul [10] F. Blaabjerg, K. Ma, an D. Zhou, Power electronics an reliability in renewable energy systems, in Proc. IEEE Int. Symp. In. Electron.,May 2012, pp [11] Y. Song an B. Wang, Survey on reliability of power electronic systems, IEEE Trans. Power Electron., vol. 28, no. 1, pp , Jan [12] M. Altin, O. Goksu, R. Teoorescu, P. Roriguez, B. Bak-Jensen, an L. Helle, Overview of recent gri coes for win power integration, in Proc. 12th Int. Conf. Optim. Elect. Electron. Equip., 2010, pp [13] Gri Coe. High an Extra High Voltage, E.ON-netz, Bayreuth, Germany, Apr [14] P. Roríguez, A. Luna, R. Muñoz-Aguilar, I. Etxeberria-Otaui, R. Teoorescu, an F. Blaabjerg, A stationary reference frame gri synchronization system for three-phase gri-connecte power converters uner averse gri conitions, IEEE Trans. Power Electron., vol. 27, no.1, pp , Jan [15] A. J. Roscoe, S. J. Finney, an G. M. Burt, Traeoffs between AC power quality an DC bus ripple for 3-phase 3-wire inverter-connecte evices within microgris, IEEE Trans. Power Electron., vol.26,no.3,pp , Mar [16] C. H. Ng, Li Ran, an J. Bumby, Unbalance-gri-fault rie-through control for a win turbine inverter, IEEE Trans. In. Appl.,vol.44,no.3, pp , May/Jun [17] P. Roriguez, A. V. Timbus, R. Teoorescu, M. Liserre, an F. Blaabjerg, Flexible active power control of istribute power generation systems uring gri faults, IEEE Trans. In. Electron., vol. 54, no. 5, pp , Oct [18] H. Song an K. Nam, Dual current control scheme for PWM converter uner unbalance input voltage conitions, IEEE Trans. In. Electron., vol. 46, no. 5, pp , Oct [19] H. 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Singh, Performance of voltage an frequency controller in isolate win power generation for a three-phase four-wire system, IEEE Trans. Power Electron., vol. 26, no. 12, pp , Dec [25] K. Ma, F. Blaabjerg, an M. Liserre, Thermal analysis of multilevel gri sie converters for 10 mw win turbines uner low voltage rie through, IEEE Trans. In. Appl., vol. 49, no. 2, pp , Mar./Apr [26] J. Holtz an N. Oikonomou, Optimal control of a ual three-level inverter system for meium-voltage rives, IEEE Trans. In. Appl., vol. 46, no. 3, pp , May/Jun [27] E. H. Watanabe, R. M. Stephan, an M. Arees, New concepts of instantaneous active an reactive powers in electrical systems with generic loas, IEEE Trans. Power Del., vol. 8, no. 2, pp , Apr [28] M. Arees an E. H. Watanabe, New control algorithms for series an shunt three-phase four-wire active power filters, IEEE Trans. Power Del., vol. 10, no. 3, pp , Jul [29] M. Arees, J. Hafner, an K. Heumann, Three-phase four-wire shunt active filter control strategies, IEEE Trans. Power Electron., vol. 12, no. 2, pp , Mar [30] C.-T. Lee, C.-W. Hsu, an P.-T. Cheng, A low-voltage rie-through technique for gri-connecte converters of istribute energy resources, IEEE Trans. In. Appl., vol. 47, no. 4, pp , Jul./Aug Ke Ma (S 09 M 11) receive the B.Sc. an M.Sc. egrees in electrical engineering from Zhejiang University, Hangzhou, China, in 2007 an 2010, respectively, an the Ph.D. egree from Aalborg University, Aalborg, Denmark, in He is currently working as a Postoctoral Researcher in the Department of Energy Technology, Aalborg University. His research interests inclue the power electronics an reliability in the application of renewable energy generations. Dr. Ma receive the IEEE Inustry Applications Society Inustrial Power Converter Committee Thir Prize Paper Awar in 2012, an outstaning presentation awar in Applie Power Electronics Conference an Exposition U.S. in 2013, an a prize paper awar at the International Symposium on Inustrial Electronics, Polan, in 2011.

14 1604 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 3, MARCH 2015 Wenjie Chen (S 13) receive the B.Sc. egree in electrical an information engineering from Zhejiang University, Hangzhou, China, in 2009, where he is currently working towar the Ph.D. egree in power electronics in the College of Electrical Engineering. His current research interests inclue control of the win power converter uner noniea gri voltage. Marco Liserre (S 00 M 02 SM 07 F 13) receive the M.Sc. an Ph.D. egrees in electrical engineering from the Bari Polytechnic, Bari, Italy, in 1998 an 2002, respectively. He was an Associate Professor at Bari Polytechnic an Professor in reliable power electronics at Aalborg University, Aalborg, Denmark. He is currently a Full Professor an the Chair of Power Electronics at Christian-Albrechts-University of Kiel, Kiel, Germany. He has publishe 168 technical papers (44 of them in international peer-reviewe journals), three chapters of a book an a book (Gri Converters for Photovoltaic an Win Power Systems. New York, NY, USA: IEEE-Wiley, also translate in Chinese). These works have receive more than 6000 citations. He was a Visiting Professor at Alcala e Henares University, Mari, Spain. He has been recently aware with an ERC Consoliator Grant for an overall buget of 2 million euros for the project The highly efficient an reliable smart transformer (HEART), a new Heart for the Electric Distribution System. Dr. Liserre is a Member of the Inustry Applications Society, Power Electronics Society, Power an Energy Society, an Inustrial Electronics Society. He is Associate Eitor of the IEEE TRANSACTIONS ON INDUSTRIAL ELEC- TRONICS, theieee Inustrial Electronics Magazine, the IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, where he is currently Co-Eitor-in-Chief, IEEE TRANSACTIONS ON POWER ELECTRONICS, an the IEEE JOURNAL OF EMERG- ING AND SELECTED TOPICS IN POWER ELECTRONICS. He has been the Founer an Eitor-in-Chief of the IEEE Inustrial Electronics Magazine, the Founer an the Chairman of the Technical Committee on Renewable Energy Systems, Cochairman of the International Symposium on Inustrial Electronics (ISIE 2010), IES Vice-Presient responsible of the publications. He has receive the IES 2009 Early Career Awar, the IES 2011 Anthony J. Hornfeck Service Awar, the 2011 Inustrial Electronics Magazine best paper awar, an the Thir Prize paper awar by the Inustrial Power Converter Committee at Energy Conversion Congress an Exposition He is Senior Member of IES ACom. Free Blaabjerg (S 86 M 88 SM 97 F 03) receive the Ph.D. egree from Aalborg University, Aalborg, Denmark, in He was with ABB-Scania, Raners, Denmark, from 1987 to He became an Assistant Professor in 1992, an Associate Professor in 1996, an a Full Professor of power electronics an rives in 1998, at Aalborg University. His current research interests inclue power electronics an its applications such as in win turbines, PV systems, reliability, harmonics, an ajustable spee rives. Dr. Blaabjerg receive 15 IEEE Prize Paper Awars, the IEEE PELS Distinguishe Service Awar in 2009, the EPE-PEMC Council Awar in 2010, an the IEEE William E. Newell Power Electronics Awar He was Eitor-in- Chief of the IEEE TRANSACTIONS ON POWER ELECTRONICS from 2006 to He has been a Distinguishe Lecturer for the IEEE Power Electronics Society from 2005 to 2007 an for the IEEE Inustry Applications Society from 2010 to 2011.