A Modulated Model Predictive Control Scheme for the Brushless Doubly-Fed Induction Machine

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1 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS A Modulated Model Pedictive Contol Scheme fo the Bushless Doubly-Fed Induction Machine Xuan Li, Tao Peng, Hanbing Dan, Guanguan Zhang, Weiyi Tang, Weiyu Jin, Patick Wheele, Senio Membe, IEEE, Maco Rivea, Senio Membe, IEEE Abstact Bushless doubly-fed induction machines featue some impotant advantages, such as high eliability and low maintenance cost, ove altenative solutions fo bushless machine applications. This pape poposes a modulated model pedictive contol algoithm fo bushless doubly-fed induction machines, which achieves a fixed switching fequency and supeio system pefomance. An impovement of powe quality is shown in this pape when compaed to the conventional finite contol set-model pedictive contol. The pape examines the design and implementation of the modulation technique as well as pesenting simulation and expeimental esults to veify the technique s opeation. Index Tems Bushless doubly-fed induction machine, modulated model pedictive contol. W I. INTRODUCTION ith the cuent concen about climate change, the wold is paying moe attention to the powe secto. To educe the emissions of cabon dioxide and minimize eliance on fossil fuels, wind powe has tuned into one of the best options fo electical gid powe geneation. In the epot of the 06 edition of the Global Wind Enegy Outlook, it was shown that wind powe could each,0 GW and supply up to 0% of global electicity by 030 [-]. The geneatos used in these wind powe applications, theefoe, need to supply high-quality and efficient electical powe to the gid [3-7]. The pemanent magnet synchonous machine (PMSM) [3-5] and the doubly-fed induction machine (DFIM) [6-7] ae the most common machines used in these applications. In a PMSM, Manuscipt eceived Febuay, 08; evised May 0, 08 and July 9, 08; accepted August, 08. This wok was suppoted by National Key R&D Pogam of China unde Gant 07YFB00900, the Key Technology R&D Pogam of Hunan Povince of China unde Gant 08SK40, the National Natual Science Foundation of China unde Gant No , the National Natual Science Foundation of China unde Gant No and FONDECYT Regula Poject. This pape was ecommended fo publication by Edito Joseph Ojo. (Coesponding autho: Hanbing Dan.) X. Li, T. Peng, H. Dan, G. Zhang, W. Tang and W. Jin ae with the School of Infomation Science and Engineeing, Cental South Univesity, Changsha, Hunan 400 China ( s: haietli@foxmail.com; pandtao@csu.edu.cn; daniel698@sina.cn; d_zgg@63.com; @csu.edu.cn; kingweiyu@63.com); P. Wheele is with the Depatment of Electical and Electonic Engineeing, Univesity of Nottingham, Nottingham NG7 RD, UK. (Pat.Wheele@nottingham.ac.uk); M. Rivea is with the Faculty of Engineeing at Univesidad de Talca, Cuico, Chile. (macoesteban@gmail.com). the geabox is not needed, which leads to high eliability and longevity, but the pice is inceased as the powe convete must pocess all the electical enegy geneated. The DFIM often has a high pefomance-pice atio when adopted in wind geneation applications, patly due to the fact that the powe convete only pocesses a faction of the electical enegy geneated. Othe advantages of the DFIM include wide opeational speed ange, vaiable speed opeation, and full powe contol capability. Howeve, the geabox and bushes of DFIM can lead to low eliability and highe maintenance costs [6]. To obtain impoved pefomance, the dual stato winding induction machine (DSWIM) and bushless doubly-fed induction machine (BDFIM) have been used as altenatives to the DFIM. The DSWIM is suitable fo electic aicaft applications [8-]. In this pape, due to the absence of bushes, the maintenance costs of a BDFIM ae lowe than a taditional doubly-fed machine. The BDFIM is, theefoe, suitable fo dive systems in applications equiing minimal maintenance, such as Wind Enegy Convesion Systems (WECS) [-3]. The BDFIM, which is shown in Fig., consists of two stato windings and one oto winding [4-6]. The pai of stato windings includes a powe winding (PW) and a contol winding (CW). These windings have a diffeent numbe of pole pais so that they can poduce the magnetic field and tansfe enegy though indiect inteaction using the oto winding. To obtain high dynamic pefomance, vecto contol (VC) [7-3] and diect toque contol (DTC) [4-7] have been poposed fo this machine configuation. VC is a popula contol method which uses a dynamic model within a unified efeence fame. A VC usually includes two contol loops, one fast inne cuent contol loop, and one oute flux/speed contol loop. In geneal, its linea natue does not conside the discete opeation of voltage souce convete, and a vecto convesion needed in the implementation, which may be complex and time-consuming. Futhemoe, VC is sensitive to paamete detuning, so the machine paametes should be chosen and monitoed caefully to satisfy the system stability and pefomance []. In applications whee a DTC is applied, coodinate tansfomation and pulse-width modulation (PWM) ae not equied, the vaiables ae contolled though toque and flux contol in both steady and tansient opeating conditions. Howeve, low-fequency cuent fluctuation, which is a featue of this technique, is often a seious disadvantage. With the apid development of digital signal pocessos and

2 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS powe devices, the finite contol set-model pedictive contol (FCS-MPC) is now being consideed as an altenative contol method of powe convetes due to its advantages such as fast dynamic esponse, easy inclusion of nonlineaities and constaints of the system, and the flexibility to include othe system equiements in the contolle [8-30]. Howeve, the switching fequency is vaiable, which deceases the system pefomance. To achieve a fixed switching fequency, modulated model pedictive contol (MMPC) has been poposed [3-35]. This pape pesents the application of an MMPC stategy fo the BDFIM. MMPC incopoates a modulation technique inside the FCS-MPC algoithm. The modulation uses a cost function to minimize the pedictive algoithm by choosing two active vectos and one zeo vecto. Compaed with FCS-MPC, MMPC achieves a fixed switching fequency, highe eactive powe contol accuacy, and lowe toque ipple. Simulation and expeimental esults ae pesented to show the feasibility and effectiveness of the poposed appoach as well as to allow an analysis of the pefomance. The pesented MMPC stategy in this pape has been descibed in [36], moe pinciple details, simulation and expeimental esults ae added in this pape. This pape is oganized as follows. In Section II, the MMPC scheme fo BDFIM is descibed, which includes the model of BDFIM and the theoetical compaison of MMPC and FCS-MPC. Then in section III and IV, simulation esults of FCS-MPC and MMPC ae pesented to demonstate the feasibility of the poposed methods, and expeimental esults veify the coectness of the simulation. Fig.. The basic stuctue of a BDFIM. A. Model of the BDFIM II. MMPC SCHEME FOR THE BDFIM The BDFIM is composed of two thee-phase stato windings and a special thee-phase oto winding. One of the stato winding is denoted as powe winding (PW) and the othe one is called contol winding (CW). Assume that the PW is diectly connected to the gid in positive phase sequence, and the CW is connected to the gid via a voltage souce invete in evese phase sequence connection. To simplify the model of BDFIM, the hamonic magnetic fields and thei coupling effects ae ignoed. PW, CW, and oto ae descibed in dq efeence fames which based on PW flux oientation with p -type pole-pai. The voltages and cuents vectos of PW, CW, and oto, which ae epesented as,, and, should be tansfomed fom thei efeence fames to the dq efeence fame. dq j t αβ x = x () x e + = αβ (-x ) e () dq j( -( p p ) ) t dq j( - p ) t αβ x x (3) = e whee, ae the angula fequencies of PW and CW; and ae pole pais of PW and CW; is the angula speed of the oto. To simplify the expessions, the vecto supescipts dq ae emoved. The model of the BDFIM with the voltage and flux equations in dq efeence fame can be shown as follows. dφ u = Ri + + jφ dt (4) dφ u = Ri + + j( ( p + p ) ) φ dt (5) dφ 0 = Ri + + j ( p) φ dt (6) φ = Li + M i (7) φ = L i + M i (8) φ = L i + M i + M i (9) 3 * 3 * Te = pim[ ( φ) i ] + p Im[ φ ( i) ] (0) 3 * Q = Im [ v ( i ) ] () = p + p () ( ) d J = Te TL (3) dt whee,,,,,, and ae the PW stato voltage vecto, CW stato voltage vecto, PW stato cuent vecto, CW stato cuent vecto, oto cuent vecto, PW stato flux vecto, CW stato flux vecto and oto flux vecto;,,,, and ae the PW stato esistance, CW stato esistance, oto esistance, PW stato inductance, CW stato inductance and oto inductance; is the coupling inductance between the PW stato and oto winding; is the coupling inductance between the CW stato and oto winding;, and Q ae the electomagnetic toque, load toque and eactive powe; J and μ ae the moments of inetia and fiction coefficient; * is the conjugate symbol; Im is a symbol to obtain the imaginay pat of vecto. Since the oto esistance is much lowe than its eactance, efeence [37] ignoes the oto esistance and veifies the feasibility of the simplified model. When the BDFIM is unning at steady state,, equation (6) can be simplified as: ( ) 0 = R + j p i φ (4) Since the oto esistance has been ignoed in this simplified model, the oto flux The simplified model is deived as follows: *

3 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 3 whee di dt i u = A + B d i i u dt ( M i ) (5) v q d d Q = (6) L ( ) 3M N M L L T = (7) e diq LL L M A = * M L R j L jm j[ ( p p ) ] M R j[ ( p p ) ] L + + L M B = M L M M M M =, =, LL LL = L L L L, M M M N = p + p =, L, A discete BDFIM model can be deived fom (5) by using a fowad Eule appoximation and the elation between the discete-time vaiables can be descibed as: k+ G k = + H k i i u k+ k k i i u (8) whee,, I is a * unit matix, is the sample peiod. B. Cuent contol of the BDFIM a) Model of the convete Fig. shows the topology of a back-to-back bidiectional powe convete and its valid switching states. This convete pohibits the state that two switches in each leg ae tuned on at the same time, theefoe the shot-cicuit switch states should be pecluded. Six active vectos ae epesented by switching states -6 and the zeo vectos ae epesented by switching states 7-8. S j (j {,, 3, 4, 5, 6}) equals to when switch S j is tuned on and equals to 0 when switch S j is tuned off, espectively. Assume the value of dc-link voltage is. A constant dc-link voltage is achieved fom the thee-phase voltage souce ectifie which adopts a Space Vecto Pulse Width Modulation (SVPWM) stategy [38]. The output voltage in dq efeence fame is expessed as: ( ) ( ) 4 * j -( p + p ) t j j 3 3 u = e S S3e S5e u (9) dc 3 (a) (b) Fig.. The topology of a bidiectional powe convete (a) and its valid switching states (b). b) Contol stategies of FCS-MPC and MMPC A supeio contol stategy could make the contolled vaiables catch up with the coesponding efeence value espectively at the end of the sampling peiod. The opeation of the BDFIM is equied to satisfy two tagets: (i), the desied eactive powe Q * in PW should be obtained; (ii), the speed of the BDFIM should tack the efeence speed. Accoding to equation (6), the taget (i) can be obtained by setting: * * d LQ id = (0) M M v q To achieve the taget (ii), a popotional-integal (PI) egulato shown in Fig. 3 is adopted. The output of this PI egulato is a efeence electomagnetic toque, which can be satisfied with an appopiate accoding to equation (7). The efeence value is: L L T * * e q = 3MN d M L L i ( ) () The pedictive CW cuent in the next sampling peiod can be deived fom the discete BDFIM model. To obtain these two tagets, the cost function g is defined as the deviation between the efeence CW cuent and the pedictive CW cuent. And it is expessed as: * * ( d d ) ( q q ) g = i i + i i ()

4 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 4 Fig. 3. PI-MMPC contol scheme of a MMPC stategy fo the BDFIM. ) FCS-MPC The FCS-MPC is a well-known technique which uses the finite numbe of all possible switching states geneated by the powe convete to ealize the optimal contol. In this pape, the possible switching states ae geneated by the bidiectional powe convete shown in Fig.. Eight pedictive values ae evaluated with the efeence in the cost function g. Then, the fist optimum vecto switching state with the least value of the evaluation is chosen in the next sampling time. Fig. 4 shows the diagam of an FCS-MPC fo the BDFIM. gg 0 k d j = g0g j + g j gk + g0gk gg 0 j dk = (4) g0g j + g j gk + g0gk gg j k d0 = g0g j + g j gk + g0gk Then the new cost function Cost can be defined as: Cost = d g + d g + d g (5) j j k k 0 0 At last, the two active vectos of the minimum cost function value ae the optimal solutions and ae used to the bidiectional powe convete at the next sampling time. Theeafte, the appopiate atio which is detemined by the duty cycles (,, ) is shown in Fig. 5 within each sampling peiod. Fig. 4. Diagam of an FCS-MPC fo the BDFIM. ) MMPC The poposed MMPC stategy shown in Fig. 3 evaluates an exta cost function based on the FCS-MPC. To obtain a fixed switching fequency, two adjacent active vectos and, and a zeo vecto will be chosen in each sampling peiod. It is assumed that the cost functions g of these vectos ae g j, g k and g 0 espectively., and ae the duty cycles of these vectos. is the sampling peiod. K is a positive constant. The duty cycles fo the two active vectos ae calculated by solving: d j = K / g j dk = K / gk (3) d0 = K / g0 d j + dk + d0 = Thus, the duty cycles fo each vecto ae given as: Fig. 5. Switching patten. C. Poposed PI-MMPC contol scheme Fig. 3 shows the diagam of the poposed hybid PI-MMPC scheme, which can be divided into two pats: oute speed loop and inne cuent loop. The oute speed loop consists of a oto speed egulato and a toque tansfe function. The oto speed egulato is used to adjust the oto speed to the set value. PI-based contolles will be used fo the oute loop. The inne cuent loop consists of a eactive powe tansfe function, an MMPC contolle of CW cuent and a phase-locked loop (PLL). The efeence cuent value is obtained accoding to the toque tansfe function. The efeence cuent value is obtained accoding to the

5 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 5 eactive powe tansfe function. The MMPC contolle geneates two active vectos and a zeo vecto accoding to the cost function, which ae used to the convete at the next sampling time. Fig. 6 shows the calculation of and the PLL is used to tack the phase angle of the thee-phase gid voltage accuately. Fig. 6. Calculation of. III. SIMULATION RESULTS The opeation and implementation of an MMPC fo the BDFIM ae veified using a simulation in MATLAB/Simulink. Table I shows simulation paametes of the system. Accoding to equation (), when PW and CW ated fequency ae espectively 50 Hz and 0 Hz, the natual oto speed is 750 /min. The PW stato is diectly connected to the gid. And the CW stato is fed by the back-to-back bidiectional powe convete. Test : at t = 3 s, the load toque changes fom 50 N m to 5 N m, and the efeence of oto speed is 600 /min. Fig. 7 shows simulation esults of the conventional FCS-MPC and Fig. 8 shows the esults of the poposed MMPC. Both esults show the wavefoms of the oto speed, the dq-axis CW stato cuent and the eactive powe. It is obvious that the dq-axis CW stato cuent ipple of the MMPC scheme is lowe than the conventional FCS-MPC scheme. And the MMPC scheme featues highe contol accuacy. Since the eactive powe is indiectly contolled by the dq-axis CW stato cuent, esults with a highe accuacy will be poduced in powe tacking due to lowe CW stato cuent ipple. In both cases, satisfying dynamic esponses ae obseved in the dq-axis CW stato cuents. The conventional FCS-MPC pedicts the behavio of all possible switching states accoding to its mathematical model at each sampling peiod. The output voltage vecto which is epesented by the chosen switching states is diffeent, which means the switching fequency is vaiable. Fo this eason, it may cause a high cuent ipple in some cases. TABLE I PARAMETERS OF BDFIM To confim the effectiveness and supeioity of the MMPC, the esults of the MMPC ae compaed with the esults obtained by the conventional FCS-MPC at sub-synchonous and supe-synchonous speeds. Two tests have been caied out to veify the esponses both in FCS-MPC and MMPC. Test : the expected eactive powe is 0 Va, the efeence oto speed inceases fom 600 /min to 800 /min duing the peiod 3-5 seconds when the load toque is 50 N m. Fig. 7. Simulation esults of FCS-MPC: Test : the efeence oto speed is changed fom 600 /min to 800 /min within 3-5 s. (a) the oto speed (b) d-axis CW stato cuent (c) q-axis CW stato cuent (d) the eactive powe. Test : the load toque is changed fom 50 N m to 5 N m at t = 3 s. (e) the oto speed (f) d-axis CW stato cuent (g) q-axis CW stato cuent (h) the eactive powe.

6 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 6 (a) Fig. 8. Simulation esults of MMPC: Test : the efeence oto speed is changed fom 600 /min to 800 /min within 3-5 s. (a) the oto speed (b) d-axis CW stato cuent (c) q-axis CW stato cuent (d) the eactive powe. Test : the load toque is changed fom 50 N m to 5 N m at t = 3 s. (e) the oto speed (f) d-axis CW stato cuent (g) q-axis CW stato cuent (h) the eactive powe. In the poposed MMPC, a modulation technique which is simila to the space vecto modulation (SVM) is added in the conventional FCS-MPC. Two active vectos and one zeo vecto ae selected fo the next sampling peiod, and the duty cycles fo the chosen vectos ae calculated by the cost function duing the sampling peiod. Then, a switching patten pocedue is adopted to choose two active vectos and one zeo vecto. A highe and fixed switching fequency is obtained by using this modulation. The cuent ipple does not have much impact on the mechanical obustness of the system, and speed dynamics ae smooth fo both FCS-MPC and MMPC. Howeve, the eactive powe unde the MMPC scheme is close to zeo than the eactive powe unde FCS-MPC scheme, which will impove the powe quality. To obtain a good compaison and show the effectiveness of the poposed contol stategy, the hamonic specta fo the CW cuent based on CW static αβ efeence fame ae shown in Fig. 9 and 0. The hamonic components fo MMPC in Fig. 0 ae shown to be lowe thoughout the fequency ange compaed to FCS-MPC in Fig. 9. These esults show that supeio system pefomance in tems of cuent hamonics can be obtained when using the poposed MMPC scheme in compaison to the FCS-MPC scheme. (b) Fig. 9. Spectum gaphics of (a) and (b) fo FCS-MPC when the efeence oto speed is 600 /min and the load is 50 N m / 3 kw. (a) (b) Fig. 0 Spectum gaphics of (a) and (b) fo MMPC when the efeence oto speed is 600 /min and the load is 50 N m / 3 kw.

7 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 7 IV. EXPERIMENTAL RESULTS In ode to futhe investigate the poposed MMPC stategy, a pototype of the BDFIM shown in Fig. is implemented, and the expeimental paametes ae same with the simulation paametes shown in Table. The expeimental system aangement is shown in Fig.. To test the pefomance of the poposed contol method with diffeent loads, a 30 kw induction moto which is coupled with the BDFIM is woked as a load machine. The PW stato of BDFIM is diectly connected to the powe gid (380 V/50 Hz), the CW stato is fed by a back-to-back voltage souce convete. The constant dc-link voltage which is achieved fom the thee-phase voltage souce ectifie is 650V. The poposed contol stuctue is implemented in a combination of a digital signal pocesso (DSP) TM30F8335 and a field-pogammable gate aay (FPGA) EPC8T44C8N. The maximum cuent limit is selected as 40A to sufficiently supply the CW cuent of 0 A. This is chosen within the actual maximum limits fo contol design veification. And a sampling fequency of 4 khz (50 μs sampling peiod) is chosen fo the MMPC scheme. espectively. It can be seen that the oto speed tacks its efeence value well, the eo between them is contolled at about /min. The eactive powe fluctuates ound ±400 Va at 600 /min and 800 /min. If the BDFIM is opeating at a ated powe of 30 kw, the input powe facto is still nealy unity even if the eactive powe fluctuation is ±400 Va. The CW stato cuents ae also stable with small fluctuates. Decoupled fom the model calculation in (0) and (), coesponds to the eactive powe of PW stato and coesponds to the electomagnetic toque. Although thee ae some oscillations in these fou vaiables, the esults ae acceptable in pactical applications. Fig.. Expeimental esults of MMPC: the steady-state of BDFIM when the efeence oto speed is set to 600 /min. (a) the oto speed (b) d-axis CW stato cuent (c) q-axis CW stato cuent (d) the eactive powe. Fig.. The expeimental platfom. Case : In Fig. and Fig. 3, the expected eactive powe is 0 Va, and the efeence oto speed is set to 600 /min and 800 /min which means that the BDFIM woks in the sub-synchonous mode and supe-synchonous mode, Fig. 3. Expeimental esults of MMPC: the steady-state of BDFIM when the efeence oto speed is set to 800 /min. (a) the oto speed (b) d-axis CW stato cuent (c) q-axis CW stato cuent (d) the eactive powe..

8 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 8 Case : To synchonize the output fequency of the BDFIM with the gid, it is appaent that the oto speed must tack the oto s speed efeence value. In this case, the efeence oto speed is inceased fom 600 /min to 800 /min duing the 3-5 seconds. And the load toque and its powe value ae set to 50 N m and 3 kw. The conditions of the expeiment in Case ae the same as those of Test in the simulation. In Fig. 4(a), speed tacking pefomance is pesented when the oto speed vaies, it can be seen that the oto speed tacks the efeence value fast afte the oto speed is changed. has a maximum change of about 0 A and the maximum eactive powe vaiation is about 500 Va when the oto speed is changed. Although the CW cuent and the eactive powe have some oscillations in Fig. 4(b)-(c), the esults ae acceptable in pactical applications. Fig. 5 shows the wavefoms of the PW line voltage, the PW phase cuent, and the CW phase cuent in an oscilloscope. Within 5 seconds, Fig. 5(a) shows fou states of and in Case and Fig. 5(b) shows the expeimental wavefom of. These thee vaiables change apidly and stabilize quickly afte the oto speed has stabilized. Fig. 4. Expeimental esults of MMPC: the efeence oto speed is changed fom 600 /min to 800 /min at t = 3 s. (a) the oto speed (b) d-axis CW stato cuent (c) q-axis CW stato cuent (d) the eactive powe. Fig. 5. The wavefoms of PW line voltage, PW phase cuent and CW phase cuent in oscilloscope. The efeence oto speed is changed fom 600 /min to 800 /min when the load is 50 N m/ 3 kw.

9 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 9 Case 3: Load change may be equied duing the opeation of the BDFIM. To evaluate the load impact on the poposed contol method, in this case, the load is educed fom 50 N m/ 3 kw to 5 N m/.5kw. The oto speed is set at 600 /min and emains constant. The conditions of the expeiment in Case 3 ae the same as those of Test in the simulation. In Fig. 6, as the load changes, a few adjustments take place in the oto speed, CW cuent, and the eactive powe. Moeove, the oto speed inceases because the electomagnetic toque is lage than the load toque at the change moment, then the oto speed ecoves to its oiginal state when the electomagnetic toque deceases due to the decease of. Afte about 0. seconds, these fou vaiables tend to each a steady state and deceases to a lowe value in the steady state. Like case, we ecoded wavefoms of,, and in the oscilloscope in Fig. 7. This expeiment confims the designed MMPC-based contolle is capable of maintaining stable opeation of the dive system when the load changes and it can also achieve an excellent dynamic contol pefomance. Fig. 6. Expeimental esults of MMPC: the load is changed fom 50 N m / 3 kw to 5 N m/.5kw when the oto speed is 600 /min. (a) the oto speed (b) d-axis CW stato cuent (c) q-axis CW stato cuent (d) the eactive powe. Fig. 7. The wavefoms of PW line voltage, PW phase cuent and CW phase cuent in oscilloscope. The load is changed fom 50 N m/ 3 kw to 5 N m/.5 kw when the efeence oto speed is 600 /min.

10 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 0 Compaed with the simulation esults, the tacking eo of the CW cuent and the eactive powe ae lage in expeiments, which ae mainly caused by the non-ideal powe souces, inaccuate moto paametes, and the convete losses. Howeve, the esults ae acceptable in pactical applications. In sum, the coectness and meits of the MMPC used in a BDFIM ae veified. Though the poposed method, excellent dynamic esponse and low ipple cuent ae obtained. V. CONCLUSION An MMPC scheme with a fixed switching fequency fo the BDFIM has been poposed in this pape. The modulation technique incopoates the SVM to the FCS-MPC. With a simple implementation stuctue, a satisfying tacking pefomance of the eactive powe and oto speed ae achieved by a cost function. Compaed with the esults of the FCS-MPC, low cuent ipple and highe contol accuacy ae obtained. An outstanding system pefomance has been achieved and simulation esults show the feasibility and effectiveness of the poposed method. The steady-state pefomance and fast dynamic pefomance of MMPC ae veified by expeimental esults. The MMPC etains the desiable advantage ove the FCS-MPC, such as fast dynamic pefomance. Moeove, a fixed switching fequency is obtained by using a PWM scheme in this technique. The MMPC stategy is also dependent on the machine paametes, the evaluation on paamete sensitivity of the MMPC stategy is wothy of study in the futue wok. REFERENCES [] F. Blaabjeg and K. Ma, "Wind Enegy Systems," in Poceedings of the IEEE, vol. 05, no., pp. 6-3, Nov. 07. [] Global wind enegy council. (Oct. 06). Global wind enegy outlook 06. [Online]. Available: global-wind-enegy-outlook-06/ [3] S. Ekanayake, R. Dutta, M. F. Rahman and D. Xiao, "Diect toque and flux contol of inteio pemanent magnet synchonous machine in deep flux-weakening egion," IET Electic Powe Applications, vol., no., pp , 08. [4] Y. Miao, H. Ge, M. Peindl, J. Ye, B. Cheng and A. Emadi, "MTPA fitting and toque estimation technique based on a new flux-linkage model fo inteio-pemanent-magnet synchonous machines," IEEE Tansactions on Industy Applications, vol. 53, no. 6, pp , Nov.-Dec. 07. [5] A. H. Abosh, Z. Q. Zhu and Y. Ren, "Reduction of toque and flux ipples in space vecto modulation-based diect toque contol of asymmetic pemanent magnet synchonous machine," IEEE Tansactions on Powe Electonics, vol. 3, no. 4, pp , Apil 07. [6] L. J. Cai and I. Elich, "Doubly fed induction geneato contolle design fo the stable opeation in weak gids," IEEE Tansactions on Sustainable Enegy, vol. 6, no. 3, pp , July 05. [7] R. Cadenas, R. Pena, S. Alepuz and G. Ashe, "Oveview of contol systems fo the opeation of DFIGs in wind enegy applications," IEEE Tansactions on Industial Electonics, vol. 60, no. 7, pp , July 03. [8] H. Xu, F. Bu, W. Huang, Y. Hu, H. Liu and Y. Zhao, "Analysis, compaison, and discussion of contol stategies fo dual stato-winding induction geneato DC geneating system," IEEE Jounal of Emeging and Selected Topics in Powe Electonics, vol. 4, no. 3, pp , Sept. 06. [9] F. Bu, S. Zhuang, W. Huang, N. Su and Y. Hu, "Asymmetical opeation analysis fo dual stato-winding induction geneato vaiable fequency AC geneating system with unbalanced loads," IEEE Tansactions on Industial Electonics, vol. 64, no., pp. 5-59, Jan. 07. [0] H. Xu, F. Bu, W. Huang, Y. Hu and H. Liu, "Contol and pefomance of five-phase dual stato-winding induction geneato DC geneating system," IEEE Tansactions on Industial Electonics, vol. 64, no. 7, pp , July 07. [] S. Basak and C. Chakaboty, "A new optimal cuent contol technique fo dual stato winding induction geneato," IEEE Jounal of Emeging and Selected Topics in Powe Electonics, vol. 5, no., pp , June 07. [] V. Yaamasu, A. Dekka, M. J. Duán, S. Kouo and B. Wu, "PMSG-based wind enegy convesion systems: suvey on powe convetes and contols," IET Electic Powe Applications, vol., no. 6, pp , [3] N. K. Swami Naidu and B. Singh, "Doubly fed induction geneato fo wind enegy convesion systems with integated active filte capabilities," IEEE Tansactions on Industial Infomatics, vol., no. 4, pp , Aug. 05. [4] L. J. Hunt, "A new type of induction moto," Electical Enginees, Jounal of the Institution of, vol. 39, no. 86, pp , Septembe 907. [5] R. Li, A. Wallace, R. Spee and Y. Wang, "Two-axis model development of cage-oto bushless doubly-fed machines," IEEE Tansactions on Enegy Convesion, vol. 6, no. 3, pp , Sept. 99. [6] S. Williamson, A. C. Feeia and A. K. Wallace, "Genealised theoy of the bushless doubly-fed machine. I. Analysis," IEE Poceedings - Electic Powe Applications, vol. 44, no., pp. -, Ma 997. [7] L. Sun, Y. Chen, J. Su, D. Zhang, L. Peng and Y. Kang, "Decoupling netwok design fo inne cuent loops of stand-alone bushless doubly fed induction geneation powe system," IEEE Tansactions on Powe Electonics, vol. 33, no., pp , Feb. 08. [8] F. Baati, R. McMahon, S. Shao, E. Abdi and H. Oaee, "Genealized vecto contol fo bushless doubly fed machines with nested-loop oto," IEEE Tansactions on Industial Electonics, vol. 60, no. 6, pp , June 03. [9] A. Zhang, X. Wang, W. Jia and Y. Ma, "Indiect stato-quantities contol fo the bushless doubly fed induction machine," IEEE Tansactions on Powe Electonics, vol. 9, no. 3, pp , Mach 04. [0] R. Zhao, A. Zhang, Y. Ma, X. Wang, J. Yan and Z. Ma, "The dynamic contol of eactive powe fo the bushless doubly fed induction machine with indiect stato-quantities contol scheme," IEEE Tansactions on Powe Electonics, vol. 30, no. 9, pp , Sept. 05. [] J. Chen, W. Zhang, B. Chen and Y. Ma, "Impoved vecto contol of bushless doubly fed induction geneato unde unbalanced gid conditions fo offshoe wind powe geneation,"ieee Tansactions on Enegy Convesion, vol. 3, no., pp , Mach 06. [] P. Han, M. Cheng, X. Wei and N. Li, "Modeling and pefomance analysis of a dual-stato bushless doubly fed induction machine based on spial vecto theoy," IEEE Tansactions on Industy Applications, vol. 5, no., pp , Mach-Apil 06. [3] G. Zhang, J. Yang, Y. Sun, M. Su, W. Tang, Q. Zhu and H. Wang,, "A obust contol scheme based on ISMC fo the bushless doubly fed induction machine," IEEE Tansactions on Powe Electonics, vol. 33, no. 4, pp , Apil 08. [4] S. J. Fattahi and A. A. Khayyat, "Diect toque contol of bushless doubly-fed induction machines using fuzzy logic," 0 IEEE Ninth Intenational Confeence on Powe Electonics and Dive Systems, Singapoe, 0, pp [5] W. R. Bassfield, R. Spee and T. G. Habetle, "Diect toque contol fo bushless doubly-fed machines," IEEE Tansactions on Industy Applications, vol. 3, no. 5, pp , Sep/Oct 996. [6] R. A. McMahon, P. C. Robets, X. Wang and P. J. Tavne, "Pefomance of BDFM as geneato and moto," IEE Poceedings - Electic Powe Applications, vol. 53, no., pp , Mach 006. [7] K. Potsenko and D. Xu, "Modeling and contol of bushless doubly-fed induction geneatos in wind enegy applications," IEEE Tansactions on Powe Electonics, vol. 3, no. 3, pp. 9-97, May 008. [8] J. Rodiguez et al., "State of the at of finite contol set model pedictive contol in powe electonics," IEEE Tansactions on Industial Infomatics, vol. 9, no., pp , May 03. [9] M. Rivea, P. Wheele and A. Olloqui, "Pedictive contol in matix convetes pat I: pinciples, topologies and applications," 06 IEEE

11 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS Intenational Confeence on Industial Technology (ICIT), Taipei, 06, pp [30] M. Rivea, P. Wheele and A. Olloqui, "Pedictive contol in matix convetes pat II: contol stategies, weaknesses and tends," 06 IEEE Intenational Confeence on Industial Technology (ICIT), Taipei, 06, pp [3] L. Taisciotti, A. Fomentini, A. Gaeta, M. Degano, P. Zanchetta, R. Rabbeni and M. Pucci, "Model pedictive contol fo shunt active filtes with fixed switching fequency," IEEE Tansactions on Industy Applications, vol. 53, no., pp , Jan.-Feb. 07. [3] M. Vijayagopal, P. Zanchetta, L. Empingham, L. de Lillo, L. Taisciotti and P. Wheele, "Contol of a diect matix convete with modulated model-pedictive contol," IEEE Tansactions on Industy Applications, vol. 53, no. 3, pp , May-June 07. [33] M. Rivea, F. Moales, C. Baie, J. Muñoz, L. Taisciotti, P. Zanchetta and P. Wheele, "A modulated model pedictive contol scheme fo a two-level voltage souce invete," 05 IEEE Intenational Confeence on Industial Technology (ICIT), Seville, 05, pp [34] S. S. Yeoh, T. Yang, L. Taisciotti, C. I. Hill, S. Bozhko and P. Zanchetta, "Pemanent-magnet machine-based state geneato system with modulated model pedictive contol," IEEE Tansactions on Tanspotation Electification, vol. 3, no. 4, pp , Dec. 07. [35] M. Vijayagopal, P. Zanchetta, L. Empingham, L. de Lillo, L. Taisciotti and P. Wheele, "Contol of a diect matix convete with modulated model-pedictive contol," IEEE Tansactions on Industy Applications, vol. 53, no. 3, pp , May-June 07. [36] X. Li, T. Peng, H. Dan, G. Zhang, W. Tang and P. Wheele, "A modulated model pedictive contol scheme fo the bushless doubly-fed induction machine," 07 IEEE Enegy Convesion Congess and Exposition (ECCE), Cincinnati, OH, 07, pp [37] S. Tohidi, "Analysis and simplified modelling of bushless doubly-fed induction machine in synchonous mode of opeation," IET Electic Powe Applications, vol. 0, no., pp. 0-6, 06. [38] P. Sinivasan, B. L. Naasimhaaju and N. V. Sikanth, "Space-vecto pulse width modulation scheme fo open-end winding induction moto dive configuation," IET Powe Electonics, vol. 8, no. 7, pp , been a Pofesso with the School of Infomation Science and Engineeing, Cental South Univesity. He eseach inteests include fault diagnosis and toleant contol fo powe electonic devices and systems, contol theoy and application. Hanbing Dan was bon in Hubei, China, in 99. He eceived the B.S. degee in Automation, and Ph.D degee in Contol Science and Engineeing fom Cental South Univesity, Changsha, China, in 0, and 07, espectively. He was a visiting eseache in Faculty of Engineeing at the Univesity of Nottingham, Unitied Kingdom duing 06 and 07. He is cuently an associate pofesso with the School of Infomation Science and Engineeing, Cental South Univesity, China. His eseach inteests include matix convete, finite contol set-model pedictive contol, moto contol, fault diagnosis and fault toleant of powe convete, wieless powe tansfe. Guanguan Zhang eceived the B.S. degee and the Ph.D. degee in automation and powe electonics and powe tansmission fom Cental South Univesity, Changsha, China, in 0 and 08, epectively. Fom Decembe 06 to Decembe 07, she was a joint Ph.D. student suppoted by the China Scholaship Council with the Depatment of Enegy Technology, Aalbog Univesity, Aalbog, Denmak, whee she focused on the eliability analysis of wind powe system. She is cuently a Postdoctoal Reseach Fellow with the School of Infomation Science and Engineeing, Shandong Univesity, Jinan, China. He eseach inteests include matix convete, moto contol and wind powe system. Xuan Li was bon in Hunan, China, in 995. She eceived the B.S. degee in Electical Engineeing and Automation fom Cental South Univesity, Changsha, China, in 06, whee she is cuently woking towad M.S. degee in electical engineeing. He eseach inteests include moto contol and model pedictive contol. Weiyi Tang was bon in Jiangsu, China, in 99. He eceived his B.S. degee in Automation fom Cental South Univesity, Changsha, China, in 03, whee he is now pusuing Ph.D. degee in Contol Science and Engineeing. His eseach inteests include moto contol and wieless powe tansfe. Tao Peng was bon in Hunan, China, in 965. She eceived the B.S. degee in industial electic automation fom the Hunan Univesity of Technology, Zhuzhou, China, in 99. She eceived the M.S. degee in detection instument and mete fom the National Univesity of Defense Technology, Changsha, China, in 99. She eceived the Ph.D. degee in contol science and engineeing fom the Cental South Univesity, Changsha, China, in 005. Fom 004 to 00, she was a Pofesso with the Hunan Univesity of Technology. Since 00, she has Weiyu Jin was bon in Hunan, China, in 969. He eceived the B.S. degee in Industial electical automation fom Cental South Univesity, Changsha, China, in 99. He eceived maste's degee in Contol Engineeing fom Hunan Univesity, Changsha, China, in 005. He began woking towad

12 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS Ph.D. degee in Contol Science and Engineeing fom Cental South Univesity, Changsha, China, in 009. His eseach aea includes powe qulity contol, bushless doubly fed induction machine s contol system and its application. Patick Wheele Pof Pat Wheele eceived his BEng [Hons] degee in 990 fom the Univesity of Bistol, UK. He eceived his PhD degee in Electical Engineeing fo his wok on Matix Convetes fom the Univesity of Bistol, UK in 994. In 993 he moved to the Univesity of Nottingham and woked as a eseach assistant in the Depatment of Electical and Electonic Engineeing. In 996 he became a Lectue in the Powe Electonics, Machines and Contol Goup at the Univesity of Nottingham, UK. Since Januay 008 he has been a Full Pofesso in the same eseach goup. He is cuently Head of the Depatment of Electical and Electonic Engineeing at the Univesity of Nottingham and the Li Dak Sum Chai Pofesso in Electical and Aeospace Engineeing at the Univesity of Nottingham, China. He is a membe of the IEEE PELs AdCom and was an IEEE PELs Distinguished Lectue fom 03 to 07. He has published 500 academic publications in leading intenational confeences and jounals. Maco Rivea eceived his B.Sc. in Electonics Engineeing and M.Sc. in Electical Engineeing fom the Univesidad de Concepcion, Chile, in 007 and 008, espectively. He eceived his PhD degee fom the Depatment of Electonics Engineeing, Univesidad Tecnica Fedeico Santa Maia, in Valpaaiso, Chile, in 0 with a scholaship fom the Chilean Reseach Fund CONICYT. Duing 0 and 0, Pof. Rivea held a Post Doctoal position and woked as pat-time pofesso of Digital Signal Pocessos and Industial Electonics at Univesidad Tecnica Fedeico Santa Maia. Cuently he is an Associate Pofesso in the Faculty of Engineeing at Univesidad de Talca, Cuico, Chile. Pof. Rivea Abaca was awaded a scholaship fom the Maie Cuie Host Fellowships fo ealy stage eseach taining in electical enegy convesion and conditioning technology at the Univesity College Cok, Cok, Ieland in 008. In 0, Pof. Rivea was awaded the Chilean Academy of Science Doctoal Thesis Awad (Pemio Tesis de Doctoado Academia Chilena de Ciencias), fo the best PhD thesis published in 0, selected fom among all national and intenational students enolled in any exact o natual sciences pogam in Chile and also he was awaded as an Outstanding Enginee in 05. His eseach inteests include matix convetes, pedictive and digital contols fo high-powe dives, fou-leg convetes, enewable enegies and development of high pefomance contol platfoms based on Field-Pogammable Gate Aays.

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