Model predictive control of inverters for both islanded and grid-connected operations in renewable power generations
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- Pearl Heath
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1 Publshed n IET Renewable Power Generaton Receved on 10th March 2013 Revsed on 6th June 2013 Accepted on 2nd July 2013 ISSN Model predctve control of nverters for both slanded and grd-connected operatons n renewable power generatons Jefeng Hu, Janguo Zhu, Davd G. Dorrell Faculty of Engneerng and Informaton Technology, Unversty of Technology, Sydney, Australa E-mal: Jefeng.Hu@uts.edu.au Abstract: As the penetraton of renewable power generaton unts connected to the grd ncreases, hgh power qualty and flexble power regulaton have rased much concern. Ths study proposes a compettve model predctve control strategy for nverters n renewable power generaton applcatons. The controller uses the system model to predct the system behavour n each samplng nterval for each voltage vector, and the most approprate vector s then chosen accordng to an optmsaton crteron. In slanded mode, the control objectves of the cost functon are the α and β components of the voltage so that stable voltage for the local loads can be establshed. In addton, a fast re-synchronsaton scheme s ntroduced to acheve smooth grd connecton. After connected to the grd, a new predcton scheme s developed to fulfll flexble actve and reactve power regulaton. Furthermore, a swtchng frequency reducton scheme s presented to reduce swtchng losses, whch are especally sgnfcant when consderng effcency for renewable power generatons. The effectveness of the proposed control strategy was tested by smulaton usng MATLAB/ Smulnk and expermentally valdated on a laboratory prototype. 1 Introducton Owng to the rapd depleton of fossl fuels and the government polcy of reducng carbon doxde emssons, more and more dstrbuted generaton (DG) plants are beng developed, especally plants that explot renewable energy such as wnd turbnes and photovoltac (PV) plants. These are usually connected to low-voltage dstrbuton lnes. As the penetraton and capactes of DG unts ncrease, the power converters assocated wth these plants are requred to operate more effcently and effectvely n order to mantan hgh power qualty and dynamc stablty [1 3]. To fulfll these requrements, advanced control technques are essental. In a DG system, there are generally two operaton modes: the slanded mode and the grd-connected mode. In the slanded mode, the DG sources and the local loads form an solated small power system, where the loads are totally powered by the DG unts. In ths case, the nverters should be able to provde a stable and hgh qualty voltage for the local loads. In addton, these DG unts should be able to acheve grd synchronsaton and re-connecton. A basc requrement here s that the transfer process should be as fast as possble, and not have any negatve effect on the utlty grd or the DG tself [4, 5]. After grd connecton, the DGs should flexbly regulate actve and reactve powers njected nto the grd. They could also be used to provde voltage support and power qualty mprovement at the low voltage dstrbuton level [6, 7]. Although many control methods have been developed to control the nverters connected to a dstrbuted generaton system, these methods manly focus on one specfc operaton mode; ether slanded operaton or grd-connected operaton. In the last decade, some studes have nvestgated the control of nverters n slanded operaton wth a partcular focus on unnterruptble power supply (UPS) applcatons. These nclude deadbeat control [8, 9], adaptve control [10], multloop feedback control [11, 12] and others. However, these schemes use the output voltage and current wth outer and nner control loops, thus proportonal-ntegral (PI) regulators and pulse-wh modulaton (PWM) modulators are requred, and tunng effort s needed n practcal mplementaton. Recently a control approach based on model predctve control (MPC) was proposed, there s no need for nternal current-control loops or modulators, and the scheme s easy to mplement [13]. Attenton has also been pad to the control of grd-connected nverters. Drect power control (DPC), derved from drect torque control of an AC machne, has become one of the most popular control strateges for grd-connected nverters because of ts smplcty and excellent dynamc response. However, hgh power rpple s the man drawback of the conventonal swtchng-table-based DPC (STDPC), leadng to dstorted lne currents [14]. Recently some mproved DPC methods have been developed for better performance [15 17]. Even more recently predctve control technques have become an attractve alternatve for the control of power converters
2 Among these, MPC has attracted much attenton, predomnantly because t has a flexble control scheme that allows the easy ncluson of system constrants and non-lneartes. In ths control, a model s used to predct the system behavour, and a cost functon s employed as a crteron to select the optmal swtchng states. The control objectves of MPC can vary consderably accordng to the applcaton. For example, the control objectve s the nverter output voltage for a UPS system n [13]. In other applcatons, the objectves are the actve and reactve powers n [18, 19] for a rectfer; and the currents n [20 22] for an nverter connected to an electrcal machne or other electrc load. Nevertheless, the MPC strategy for a grd-connected nverter s seldom mentoned n the lterature. Ths paper proposes a MPC strategy for an nverter utlsed n a renewable power generaton system whch s suffcently flexble to acheve slanded operaton, grd synchronsaton, and grd-connected operaton. By changng the cost functon correctly ths control strategy can be employed to acheve stable voltage, fast and smooth grd synchronsaton, and flexble actve and reactve power regulaton. Ths control strategy s smple and easy to mplement. No PI regulators and PWM modulators are requred; synchronous coordnate transformaton s also elmnated, presentng excellent steady state and dynamc performance. 2 System modellng A three-phase two-level nverter-based renewable power generaton system s consdered n ths paper, as shown n Fg. 1. The nverter output voltage V can be controlled to eght vectors and determned by the swtchng states, whch can be expressed n complex space vectors as 2 V = 3 V dce j( 1)p 3 ( = 1 6) 0 ( = 0, 7) (1) current vector ( o = L ). The voltage equaton of the nductor n the LC flter can be descrbed by V = V c + f R + L d f where R and L are the flter resstance and nductance, respectvely. 2.2 Model of grd-connected operaton In grd-connected operaton, the statc transfer swtch S 1 s ON whle the bypass swtch S 2 s OFF. The nverter s connected to the grd through the lne nductor, and the renewable power generaton system supples the power to the local load together wth the grd. The excess power generated wll be njected to the grd. In ths case, the mathematcal model of the system can be expressed as (3) f = o (4) o = L + g (5) V = V g + o R + L d o where V g s the grd voltage vector, g s the current vector njected nto the grd and o s the nverter output current vector (after the LC flter), as depcted n Fg. 1. The nverter nstantaneous output actve and reactve powers are P = 3 { } 2 Re V g o { } Q = 3 2 Im V g o = 3 2 V ga oa + V gb ob = 3 2 V gb oa V ga ob (6) (7) (8) 2.1 Model of slanded pperaton In slanded operaton, the statc transfer swtch S 1 s OFF whle the bypass swtch S 2 s ON. The renewable power generaton system supples the power to the local load. In ths scenaro, the dynamc behavour of the capactor n the LC flter can be expressed as C dv c = f L (2) where C s the flter capactance, V c s the capactor voltage vector, f s the nductor current vector, and L s the load where * donates the complex conjugate, V gα and V gβ are the real and magnary components of V g, whle oα and oβ are the real and magnary components of o.inotherwords,v g = V gα + jv gβ, o = oα + j oβ. 3 Voltage control n slanded mode In the slanded mode, the am of the MPC controller s to manage the nverter to establsh a stable voltage for the local loads wthout power supply from the grd. Wth ths goal, the MPC voltage controller predcts the future behavour of the capactor voltage V c. Combnng (2) and (3), the system model can be rewrtten as a state-space system dx = Ax + BV + D L (9) Fg. 1 One-phase model of nverter-based renewable power generaton system where [ x = ] [ ] [ f R/L 1/L, A =, B = 1/L ], V c 1/C 0 0 [ ] 0 D = 1/C 241
3 Snce the samplng tme T s s very small, one can assume e AT s = 1 + AT s + (AT s) (AT s) n 2! n! (10) 1 + AT s Therefore the dscrete-tme model of the LC flter for a samplng tme T s can be expressed by Cortés et al. [13] where x(k + 1) = A a x(k) + B b V (k) + D d L (k) (11) A a = e AT s, B b = Ts 0 e At, D d = Ts 0 e At D Consequently, the capactor voltage at (k + 1)th nstant can be predcted: V c (k + 1) = V c (k) + e T s /C f (k) + C ( et s /C ) 1 V L (k) T s C L(k) (12) To control the capactor voltage, the cost functon J V can be defned so that ( J V = V ref ca V k+1 ) 2+ 2 ca V ref cb V k+1 cb (13) where V k+1 ca and V k+1 cb are the real and magnary components of the predcted capactor voltage vector, respectvely. In other words, V c (k + 1) = V k+1 ca + jv k+1 cb. Accordng to ths cost functon, the voltage vector that generates the least value of J V wll be appled durng the next samplng perod. The block dagram of the voltage control s llustrated n Fg. 2. Accordng to (13), the V c can track ts reference because the α and β components are tghtly controlled. Based on ths analyss, t s expected that grd synchronsaton can be acheved by replacng the referenced voltage V ref c wth the grd voltage V g, as llustrated n Fg. 2. Therefore the cost functon can be revsed: 2+ 2 J V = V ga V k+1 ca Vgb V k+1 cb (14) Usng (14), the capactor voltage can closely track the grd voltage n terms of phase angle, ampltude and frequency. When the grd synchronsaton process s completed, the renewable power generaton system s ready for grd connecton. 4 Flexble power regulaton n grd-connected mode Once a DG unt s connected to the man grd, flexble actve and reactve power regulaton must be acheved to help mprove system stablty and power qualty [23, 24]. Therefore the control the objectves of MPC become the actve and reactve powers. Once the statc transfer swtch S 1 s closed, the bypass swtch S 2 s swtched OFF. The nverter s then supplyng actve and reactve power to the local load and the grd through the L flter. Accordng to (7) and (8), the nverter actve and reactve power dervatves can be calculated from dp = 3 ( dv ga d 2 oa + V oa ga + dv ) gb d ob ob + V gb (15) dq = 3 ( dv gb d 2 oa + V oa gb dv ) ga d ob ob V ga (16) If we consder snusodal and balanced lne voltage, one can obtan V g = V ga + jv gb = V g e jvt = V g cos vt + j V g sn vt (17) dv ga d V g cos vt = = v V g sn vt = vv gb (18) dv gb d V g sn vt = = v V g cos vt = vv ga (19) where ω s the grd voltage frequency n rad/s. The nverter output actve and reactve power dervatons can then be obtaned by substtutng (6), (18) and (19) nto (15) and (16) so that dp = 3 [ 2 vv gb oa + V ga V L a V ga oa R ] + vv ga ob + V gb V b V gb ob R (20) dq = 3 [ 2 vv ga oa + V gb V L a V ga oa R ] + vv gb ob V ga V b V gb ob R (21) By consderng (7), (8), V g V = V ga V a + V gb V b + j V gb V a V ga V b, and V g 2 = V 2 ga + V 2 gb, (20) and (21) can be rewrtten as dp = R L P vq + 3 ( ) 2L Re V gv V g 2 (22) dq = vp R L Q + 3 2L Im V gv (23) Fg. 2 Block dagram of voltage control where once agan * donates the complex conjugate. Therefore the actve and reactve power at the end of the samplng 242
4 Fg. 3 Block dagram of flexble power regulaton perod T s can be predcted from [ P k+1 = T s R L P vq + 3 ( )] 2L Re V gv V g 2 + P k (24) [ Q k+1 = T s vp R L Q + 3 ] 2L Im V gv + Q k (25) However, t can be seen that the power predcton usng (24) and (25) would be very complcated, makng mplementaton dffcult. In ths paper, a new and smple predcton scheme s developed. The dscrete-tme model of (6) can be expressed as o (k + 1) = T s V (k) V g (k) o (k)r /L + o (k) (26) Assumng the grd voltage s constant durng the samplng perod, P(k + 1) and Q(k + 1) can be calculated by substtutng (26) nto (7) and (8). Ths predcton scheme s more straghtforward than (24) and (25) where power dervatves are used, thus reducng the computatonal burden. Ths s qute useful for MPC because calculatng the cost functon can be very tme consumng for a hardware processor, especally f several constrants are ncluded n the cost functon whle hgh samplng frequency s requred. After the power s predcted, the next step s to evaluate the effects of each voltage vector on the actve and reactve powers and to select the one whch produces the least power rpple accordng to a specfc cost functon. In ths paper, the cost functon s defned by ( J P = P ref P k+1 ) 2+ ( Q ref Q k+1 ) 2 (27) The block dagram of grd-connected operaton s as shown n Fg Swtchng frequency reducton When the renewable power generaton system njects power nto the grd, power converson effcency s a sgnfcant concern. Snce large capacty dstrbuted power generaton wth hgh voltage levels s lkely to ncrease n popularty, swtchng frequency reducton has attracted attenton. Ths s because the swtchng loss can be reduced by use of lower swtchng frequency n the converter. Wth lower the swtchng frequency, there can be less power loss wth no system performance deteroraton; that s, hgher effcency can be obtaned. Here, n order to reduce the swtchng Fg. 4 Actve power trajectores and swtchng poston wth N-step predcton frequency, the expresson of cost functon (27) s revsed to (( J P = P ref P k+1 ) 2+ ( Q ref Q k+1 ) 2 ) + l 2 D k+1 D k =a,b,c (28) where D k+1 and D k represent the swtchng state of the rectfer leg ( = a, b, c) at the current control perod and the next control perod, respectvely. D = 0 or 1, 0 means the upper transstor s OFF and the lower one s ON, 1 ndcates the nverse swtchng state, λ 2 s the weghtng factor. The frst term n (28) reduces the power rpple and helps track the reference whle the second term contrbutes to the objectve of swtchng frequency reducton. A large value of the weghtng factor λ 2 mples greater prorty to the latter objectve. Therefore by defnng the cost functon as (28), the swtchng frequency can be taken nto account. Bear n mnd that eght possble vectors should be evaluated n (28) for swtchng frequency reducton, although only seven vectors are needed for (27) because the effects of V 0 and V 7 are the same when the reducton of the swtchng frequency s not consdered. Note that f λ 2 s too large; that s, swtchng frequency reducton s more aggressve than necessary, the system stablty wll deterorate, resultng n excessvely large currents and power rpple. In order to reduce the swtchng frequency wthout system performance deteroraton, an N-step horzontal predcton for system stablty mprovement has been developed. The nverter output power at the (k + N)th nstant s predcted from the value at the (k + 1)th and (k + 2)th nstants usng lnear extrapolatons. To vsualse ths predcton theory, Fg. 4 depcts an example of the actve power trajectory and the swtchng poston wth N-step predcton. The actve and Table 1 System parameters Lne resstance R 0.51 Ω flter nductance L 4.8 mh flter capactor C 36 uf lne-lne voltage V g 120 V (rms) voltage frequency f 50 Hz DC source voltage V dc 250 V samplng perod T s 50 μs local load R L 50 Ω weghtng factor λ 2 75 weghtng factor λ
5 Fg. 5 Block dagram of the proposed MPC strategy for renewable power generatons reactve powers at the (k + N)th nstant can be predcted from P k+n = P k+1 ( + (N 1) P k+2 P k+1 ) (29) Q k+n = Q k+1 ( + (N 1) Q k+2 Q k+1 ) (30) where P k +1, Q k+1, P k +2 and Q k+2 can be obtaned usng the method presented n Secton 4. In ths paper, N =5. Consequently, the cost functon (28) can be further revsed to (see (31)) where λ 3 s the weghtng factor of the component n charge of system stablty. Usng lnear extrapolaton for the approxmate predcton, where the concdence pont N s larger than 2, ths s feasble, especally when the samplng perod s short. Ths wll be valdated n the smulaton and expermental results n the next sectons. 6 Smulaton results Fg. 6 Smulaton results of capactor voltage and load current The proposed control strategy was tested n smulaton usng MATLAB/Smulnk. The system parameters are lsted n Table 1. A constant 250 V DC source s used to smulate the renewable energy source output. The control system starts to operate at 0.02 s, the grd synchronsaton begns at 0.1 s and the DG system s connected to the grd at 0.15 s wth P ref = 0 W and Q ref = 0 VAr ntally. A block dagram of the whole proposed control strategy s shown Fg. 5. The basc operaton of the proposed renewable power system s as follows. When a utlty grd fault occurs, the renewable power system should be solated from the grd. In ths case, the grd s unavalable and a stable and hgh qualty voltage must be establshed for the local load wthn the renewable power system. Therefore the voltage control cost functon (13) should be used. After clearance of the grd fault, the renewable power system should be re-connected to the grd, whch can be acheved smply by usng the grd voltage as the reference; that s, the grd synchronsaton cost functon (14) should be utlsed. After grd connecton, the utlty grd voltage s avalable to the local load. In ths case, obvously the renewable power system should be able to supply actve and reactve powers to the utlty grd flexbly and effcently. Consequently, the cost functon (31) for flexble power regulaton wth swtchng frequency reducton should be employed. 6.1 Islanded operaton Fg. 6 shows the capactor voltage (V c ) and load current ( L )n slanded operaton. It can be seen that a stable voltage s establshed very quckly, and ths s snusodal wth low dstorton (total harmonc dstorton (THD) = 2.54%). A zoom-n of the phase A voltage V ca and ts spectrum are shown n Fg Grd Synchronsaton The grd synchronsaton process and grd connecton are presented n Fg. 8. From top to bottom, the waveforms are: capactor phase A voltage (V ca ), grd phase A voltage (V ga ), and nverter output currents ( o ). It can be seen that the nverter output voltage can match the grd voltage n less than 1 ms once the grd synchronsaton algorthm starts to (( J P = P ref P k+1 ) 2+ ( Q ref Q k+1 ) 2 )+ l 2 D k+1 D k ( + l 3 P ref P k+n + Q ref Q k+n ) =a,b,c (31) 244
6 Fg. 7 Spectra of capactor voltage, THD = 2.54% Fg. 9 Smulaton results of flexble power regulaton operate. After the voltage s synchronsed wth the grd voltage, n terms of ampltude, frequency and phase angle, the renewable power generaton system s connected to the grd through the statc transfer swtch. The capactor of the LC flter s bypassed at 0.15 s. It can be observed that the grd connecton s very smooth wthout obvous over-shoot current. It can also be noted that the P and Q references are set to zero durng the grd connecton process. After successful grd connecton at 0.15 s, the nverter system can be controlled n order to output any actve or reactve power wthn ts capacty. Here, the nverter starts to output actve power at 0.22 s, as llustrated n Fg. 9. Therefore the nverter output current o s zero between 0.15 s and 0.22 s because P and Q are controlled to be zero. 6.3 Flexble power regulaton n grd-connected mode Fg. 9 presents the power regulaton performance. Intally the reactve power s set to 0 VAr whle the actve power s stepped from 0 to 2 kw at 0.22 s and backed to 0 W at 0.24 s. After that, the actve power s kept at 0 W whle the reactve s stepped to 1 kvar and then to 1 kvar. It can be seen that the proposed MPC strategy presents excellent dynamc response, trackng the references n less than 0.5 ms. 7 Expermental results The proposed control strategy was further valdated by experment usng a laboratory PV system setup, as shown n Fg. 10. It conssts of the followng devces: a three-phase Semkron ntellgent nsulated gate bpolar transstor power module as the nverter, an ABB DC power source, a three-phase LC flter, an over-current protecton devce and a three-phase solated transformer to ncrease the nverter output voltage from 120 to 415 V from the man grd. A dspace DS1104 power PC (PPC)/dgtal sgnal processor (DSP) control board was employed n order to mplement the real-tme algorthm codng usng C language for the control. The voltages and currents are sampled usng ControlDesk, whch s nterfaced wth the DS1104 and a PC at a rate of 20 khz. The system parameters are the same as the smulaton. 7.1 Islanded operaton In slanded operaton, the statc transfer swtch S1 s OFF whle the bypass swtch S2 s ON, and the slanded mode s selected, as llustrated n Fg. 5. The expermental results of the slanded operaton are shown n Fg. 11. From top to bottom, the curves shown n Fg. 11a are the capactor voltage, load current and nductor current of the LC flter. It Fg. 8 Smulaton results of grd synchronsaton and connecton Fg. 10 Laboratory setup for renewable power generatons 245
7 Fg. 11 Expermental results of slanded operaton a capactor voltage, load current, and lne nductor current b spectra of capactor voltage, THD = 3.70% Fg. 12 Expermental results of grd synchronsaton a capactor lne-to-lne voltage and grd lne-to-lne voltage durng grd synchronsaton b capactor voltage, grd voltage and nverter output current at grd connecton moment can be seen that the expermental results are n good agreement wth the smulaton. The capactor voltage was establshed quckly and t s very stable. Owng to the resstve load, the load current s proportonal to the capactor voltage. The nductor current presents hgh-frequency harmoncs whch are attenuated by the flter. A zoom of the capactor phase A voltage, V ca, and ts spectrum are shown n Fg. 11b. 7.2 Grd synchronsaton Fg. 12a shows the waveforms of the capactor and grd voltages. Once the grd synchronsaton process begns, the two curves are n close agreement n terms of phase, frequency and magntude and ths s realsed very quckly. The grd-connecton s then done n a safe and smooth manner by closng S1 and swtchng off S2, as shown n Fg. 12b. 7.3 Grd-connected mode Once connected to the grd, the bypass swtch S 1 s off and the power control algorthm s actvated, so the DG system supples power to the local load and the grd. If the power generated s less than the local load demand, more power would be mported from the grd. On the other hand, f the power generated s larger than the local load demand, the excess wll be exported to the grd. Snce the conventonal STDPC [14, 15] s commonly used t s used here as a benchmark. Fg. 13 shows the dynamc responses of STDPC and the proposed MPC strategy. It can be observed that both the methods present excellent transent performance. However, the power rpples of the proposed strategy are much smaller than that of STDPC, leadng to much more snusodal lne currents. It can be noted that the actve and reactve powers shown n Fg. 13 are from the nverter output, not those exchanged between the man grd and the mcrogrd. For example, the DG system generates 2kW ( 2 kw means power s flowng out from the DG ( system), ) the local load consumes 2= 3 120/RL 288 W, so there are about kw of power fed nto the grd by the DG system. In order to valdate the effectveness of the swtchng frequency reducton of the proposed MPC strategy, a comprehensve set of tests were carred out. These used 246
8 Fg. 13 Expermental results of flexble power regulaton a STDPC, left: actve power steps, rght: reactve power steps b proposed MPC strategy, left: actve power steps, rght: reactve power steps STDPC, the proposed MPC strategy usng (27), the proposed MPC strategy usng (28) and the proposed MPC strategy usng (31). The average swtchng frequency s calculated by countng the total commutaton nstances of the PWM gate drve sgnals of a phase leg were durng a fxed perod. To obtan a better understandng of the proposed MPC strategy, the quanttatve results of the dfferent strateges are summarsed n Table 2. It can be seen that the performance of the proposed MPC strategy usng (27) s much better than that of STDPC n terms of the power rpple and current THD. Ths s as expected because the MPC controller selects the most approprate voltage Table 2 Quanttatve comparson of steady-state performance Strategy f s, Hz f sw, Hz THD, % P rp,w Q rp, Var STDPC 20 k MPC (27) 20 k MPC (28), λ 2 = k MPC (31), λ 2 = 75, λ 3 = k ( f s : samplng frequency; f sw : average swtchng frequency) (P rp, Q rp : actve and reactve power rpples, calculated usng standard devaton) vector-based on a cost functon rather than choosng the vector accordng to a look-up table. Furthermore, f the swtchng frequency reducton s also ntroduced to the cost functon, that s usng (28), the average swtchng frequency s reduced consderably to only 968 Hz. However, the system performance deterorates sgnfcantly at ths low frequency, wth large power rpple and severely dstorted nverter output currents wth THD = 15.59%. If one further step s made to add a component to (28), that s usng (31), the system s stablsed, and the swtchng frequency s reduced sgnfcantly wth only slght deteroraton n terms of current THD and power rpple compared to the system usng (27). Fnally, t s worth mentonng that the optmsaton of the weghtng factor λ 2 and λ 3 s out of scope of ths paper, ths specfc research topc combned wth the knowledge of mathematcs and optmsaton desgn s nvestgated n other research studes such as [22]. 8 Conclusons Ths paper proposes a model predctve control strategy for renewable power generaton. The proposed control strategy can be used as a general control approach for dstrbuted generaton unts to acheve slanded operaton, grd 247
9 synchronsaton and grd-connected operaton. By changng the cost functon approprately, dfferent control objectves can be fulflled. In slanded mode, the control objectves are the α and β components of the voltage. In order to acheve grd connecton, the voltage reference n the cost functon can be replaced by the grd voltage wthout changng the control structure. After connecton to the grd, a new predcton scheme s developed for grd-connected operaton, whch s a smple and effectve way to fulfll flexble actve and reactve power regulaton. Last but not least, an effectve swtchng frequency reducton algorthm s proposed, whch s very attractve n terms of ncreasng the effcency of renewable power generaton systems. 9 References 1 Maza-Ortega, J.M., Gomez-Exposto, A., Barragan-Vllarejo, M., Romero-Ramos, E., Marano-Marcoln, A.: Voltage source converter-based topologes to further ntegrate renewable energy sources n dstrbuton systems, IET Renew. Power Gener., 2012, 6, (6), pp Foster, S., Xu, L., Fox, B.: Coordnated reactve power control for facltatng fault rde through of doubly fed nducton generator- and fxed speed nducton generator-based wnd farms, IET Renew. Power Gener., 2010, 4, (2), pp Blaabjerg, F., Lserre, M., Ma, K.: Power electroncs converters for wnd turbne systems, IEEE Trans. Ind. Appl., 2012, 48, (2), pp Blaabjerg, F., Teodorescu, R., Chen, Z., Lserre, M.: Overvew of control and grd synchronzaton for dstrbuted power generaton, IEEE Trans. Ind. Electron., 2006, 53, (5), pp Qunonez-Varela, G., Cruden, A.: Modellng and valdaton of a squrrel cage nducton generator wnd turbne durng connecton to the local grd, IET Gener. Transm. Dstrb., 2008, 2, (2), pp Wang, F., Duarte, J.L., Hendrx, M.A.M.: Grd-nterfacng converter systems wth enhanced voltage qualty for mcrogrd applcaton concept and mplementaton, IEEE Trans. Power Electron., 2011, 26, (12), pp Majumder, R., Ghosh, A., Ledwch, G., Zare, F.: Load sharng and power qualty enhanced operaton of a dstrbuted mcrogrd, IET Renew. Power Gener., 2009, 3, (2), pp Kukrer, O.: Deadbeat control of a three-phase nverter wth an output LC flter, IEEE Trans. Power Electron., 1996, 11, (1), pp Mattavell, P.: An mproved deadbeat control for UPS usng dsturbance observers, IEEE Trans. Ind. Electron., 2005, 52, (1), pp Marwal, M.N., Keyhan, A.: Control of dstrbuted generaton systems Part I: voltage and currents control, IEEE Trans. Power Electron., 2004, 19, (6), pp Abdel-Rahm, M., Quacoe, J.E.: Analyss and desgn of a multple feedback loop control strategy for sngle-phase voltage-source UPS nverters, IEEE Trans. Power Electron., 1996, 11, (4), pp Loh, P.C., Newman, M.J., Zmood, D.N., Holmes, D.G.: A comparatve analyss of multloop voltage regulaton strateges for sngle and three-phase UPS systems, IEEE Trans. Ind. Electron., 2003, 18, (5), pp Cortés, P., Ortz, G., Yuz, J.I., Rodríguez, J., Vazquez, S., Franquelo, L.G.: Model predctve control of an nverter wth output LC flter for UPS applcatons, IEEE Trans. Ind. Electron., 2009, 56, (6), pp Noguch, Tomk, H., Kondo, S., Takahash, I.: Drect power control of PWM converter wthout power-source voltage sensors, IEEE Trans. Ind. Appl., 1998, 34, (3), pp Monfared, M., Sanatkar, M., Golestan, S.: Drect actve and reactve power control of sngle-phase grd-te converters, IET Power Electron., 2012, 5, (8), pp Alonso-Martnez, J., Eloy-Garca, J., Arnaltes, S.: Table-based drect power control: a crtcal revew for mcrogrd applcatons, IEEE Trans. Power Electron., 2010, 25, (12), pp Eloy-Garca, J., Arnaltes, S.: Drect power control of voltage source nverters wth unbalanced grd voltage, IET Power Electron., 2008, 1, (3), pp Pavlou, K.G., Vasladots, M., Manas, S.N.: Constraned model predctve control strategy for sngle-phase swtch-mode rectfers, IET Power Electron., 2012, (5), pp Cortes, P., Rodrguez, J., Antonewcz, P., Kazmerkowsk, M.: Drect power control of an AFE usng predctve control, IEEE Power Electron., 2008, 23, (5), pp Prendl, M., Schaltz, E., Thogersen, P.: Swtchng frequency reducton usng model predctve drect current control for hgh-power voltage sources nverters, IEEE Trans. Ind. Electron., 2011, 58, (7), pp Geyer, T., Papafotou, G., Morar, M.: Model predctve drect torque control Part I: concept, algorthm, and analyss, IEEE Trans. Ind. Electron., 2009, 56, (6), pp Thelemans, S., Vyncke, T.J., Melkebeek, J.: Weght factor selecton for model-based predctve control of a four-level flyng-capactor nverter, IET. Power Electron., 2012, 5, (3), pp Shahab, M., Haghfam, M.R., Mohamadan, M., Nabav-Nak, S.A.: Mcrogrd dynamc performance mprovement usng a doubly fed nducton wnd generator, IEEE Trans. Energy Convers., 2009, 24, (1), pp Bojo, R.I., Lmong, L.R., Rou, D., Tencon, A.: Enhanced power qualty control strategy for sngle phase nverters n dstrbuted generaton systems, IEEE Trans. Power Electron., 2011, 26, (3), pp
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