Model-based direct control of PWM converters with an LCL filter

Transcription

1 st Power Electronic & Drie Systems & Technologies onference Moel-base irect control of PWM conerters with an LL filter M. Monfare*, Stuent member, IEEE, F. Aabi*, H. Rastegar*, H. Maai Kojabai** * Dept. of Electrical Eng., Amirkabir Uniersity of Technology, Tehran, Iran. ** Dept. of Electrical Eng., Sahan Uniersity of Technology, Tabriz, Iran. s: m.monfare@ieee.org, fari_aabi@aut.ac.ir, rastegar@aut.ac.ir, maai@sut.ac.ir Abstract This paper presents a noel moel-base strategy for irect power control of three-phase pulsewih-moulate conerters. In another paper, the authors hae reporte this moel-base metho for irect power control of three-phase PWM conerters which are connecte to the gri through an L filter. In this research work by an analogous approach the propose DP is aapte for three-phase conerters with an output LL filter. The performance of the propose technique is erifie with simulation results. Keywors: Direct power control, LL filter I. Introuction Research interest in gri connecte three-phase PWM conerters has grown rapily oer the past few years ue to some of their important aantages, such as power regeneration capabilities, control of D link oltage, low harmonic istortion of mains currents, biirectional control of actie an reactie powers, small D link capacitor, an high power factor. Various control strategies hae been propose in recent works on this type of rectifiers. Voltage oriente control (VO) is wiely employe which proies a goo ynamic an steay-state reonse by its internal current control loops. One main rawback of such a system is that the performance is highly epenent on the applie current control strategy an the connecte A network conitions []. A new control strategy calle irect power control (DP) which is base on the instantaneous actie an reactie power control has become more wiely use oer the last few years ue to the aantages of fast ynamic performance an simple control implementation. In DP, there are no internal current control loops an no PWM moulator block, because the conerter switching states are appropriately selecte by a switching table base on the instantaneous errors between the commane an measure alues of the actie an reactie powers. Howeer, among the well-known isaantages of the DP scheme are: ariable switching frequency (ifficulties of conerter an filter esign) an some problems ue to the high gain of the hysteresis controllers []-[6]. Howeer the conentional switching table base DP is popular an extensiely employe, but only simple A inuctors are use as the filter between the conerter an the gri. To achiee an acceptable harmonics performance a high alue for the A inuctance shoul be selecte; howeer this makes it expensie an bulky an leas to poor ynamic. On the contrary, the thir-orer LL filter offers reuce leel of harmonics istortion at lower switching frequencies which is a significant aantage in high power applications with smaller total inuctance alues [7]-[9]. On the other han, the LL filter may cause the steay-state an transient istortion of the mains current ue to resonances an bring control system stability problems. This problem can be reuce but not sole in VO controlle PWM conerters if the main resonance frequency is selecte in a frequency range where no harmonics of the output current exist [7]-[9]. Unfortunately, this approach oes not work for DP case where the switching harmonic ectrum is broa an not clearly efine ue to the ariable switching frequency. Another solution for the VO case is actie amping methos which hae alreay receie a lot of attentions [0], [] oerrie the moulation inex. These techniques are not possible with DP; since switching states are selecte by a switching table an not through a current control PWM loop. In this research work a noel moel-base strategy for irect power control of three-phase pulse-wihmoulate conerters is presente. In this metho, hysteresis comparators an switching table are replace by a fixe switching frequency PWM oltage moulator. The require conerter oltage in each sampling perio is irectly calculate base on only reference an measure alues of actie an reactie powers, system parameters, an the measure /0/$ IEEE 63 Authorize license use limite to: Ferowsi Uniersity of Mashha. Downloae on June 03,00 at 06:07:43 UT from IEEE Xplore. Restrictions apply.

2 If one chose ω as the angular ee of the A source oltage, the equations ()-(3) in the q frame become: oltage of the A source. Then, the PWM generator synthesizes the reference oltage an generates the switching pulses for the oltage source conerter. The authors hae alreay reporte this moel-base control strategy for irect power control of threephase PWM conerters which are connecte by an A inuctance filter to the mains which shows superior performance than the VO an the conentional DP techniques []. In this research work, by an analogous approach, the propose DP is aapte for three-phase conerters with an output LL filter. SVM Pref Qref Eqs. (6) an (7) P Q L L s PLL L ωi (k ) + i q (k ) c (k + ) = 3 Fig. Three-phase LL filter base PWM conerter. i R L R cq (k + ) = i i (k + ) = Rf f s (9) Fig. Equialent circuit of PWM conerter with LL filter. [i (k ) i (k )] + ω q (k ) + (k ) () () i q (k ) i q (k ) ω (k ) + q (k ) L (3) [ R i (k ) + (k ) (k )] (4) R i q (k ) + q (k ) q (k ) L ωi (k ) + i q (k ) Neglecting the small olt-rop on Rf, this configuration can be moele by the following ifferential equations in the stationary reference frame: (0) + ωi q (k ) + i (k ) i q (k + ) = i abc = R i abc + sabc abc L abc = i abc i abc R i abc + abc abc i abc = L (8) Ri q (k ) + sq (k ) q (k ) L q abc L (7) i q (k + ) = sabc (6) [ Ri (k ) + s (k ) (k )] + ωi q (k ) + i (k ) iabc sα sβ i (k + ) = Rf f Power calculation θ (5) These equations show how the an q components of the currents an the capacitor oltage are epenent by the cross-coupling terms. Assuming a small sampling perio (T), equations (4)-(9) can be written in iscrete form: ri 3φ PWM onerter i q + ωi = Ri q + sq q L R i q + q q i q + ω i = L The block iagram of the propose DP system with an LL filter is epicte in Fig.. To eelop the control metho, the equialent circuit of the griconnecte conerter through an LL filter is emphasize in Fig.. Switching Pulses (4) ω q = [i i ] q + ω = i q i q i ωi q = [ R i + ] L II. Propose DP for LL filter base conerter i ωi q = [ Ri + s ] L (5) The actie an reactie powers in the rotating reference frame are: P (k + ) = s (k + )i (k + ) + sq ( k + )i q (k + ) (6) Q (k + ) = sq (k + )i (k + ) s (k + )i q (k + ) (7) () We will assume that R = R = 0, L = L an L = al. Also the source oltage can be assume constant uring a small sampling perio an thanks to the PLL, the control system will be synchronize with the A source oltage (s(k+) = s(k), sq(k+) = sq(k) = 0). () (3) 64 Authorize license use limite to: Ferowsi Uniersity of Mashha. Downloae on June 03,00 at 06:07:43 UT from IEEE Xplore. Restrictions apply.

3 Also, the target of the control is to make the loa actie an reactie powers at the sampling point (k+), equal to the reference actie an reactie power alues currently aailable at the sampling point (k). So, using these assumptions an replacing equations (0) an () in (6) an (7) we will obtain: T Pref = P( k + ) = s s L + Pk ( ) TωQk ( ) (8) T Qref = Q( k + ) = s q L + Q + T ωp (9) We can assume that the filter is well esigne an works perfectly, therefore the changes in the i an uring a small sampling perio can be neglecte ( (k+) = (k), q (k+) = q (k), i (k+) = i (k), i q (k+) = i q (k)). Applying these simplifying assumptions, the equations ()-(5) become: q = [ i i ] ω (0) i q iq ω () = alωiq + () = alωi + (3) q q usually calle switching table base DP, the hysteresis controllers are eliminate, so the problems of their high gain hae been aoie. For example, the control sensitiity to A current ripples is minimize an consequently the switching an sampling frequencies can be smaller. Furthermore, in the propose DP, the gate signals are generate by a PWM moulator instea of the hysteresis regulators, so the switching frequency is constant an much lower than the classical DP case, an also aance moulation techniques can be use to achiee higher efficiencies an better harmonics performance. Last but not least, the propose DP control strategy is eelope for three-phase conerters with an output LL filter. A high orer LL filter compare to a simple L filter allows reuce leel of harmonics istortion at lower switching frequencies with smaller total inuctance alue. III. Performance ealuation In orer to confirm the effectieness of the propose system, simulations hae been one in MATLAB/SIMULINK. One can sole the equations (0)-(3) for capacitor oltage an replace the results in equations (8) an (9) an rearrange them for an q : L( alω ) = ref + T s L( alω ) s alωq ( k ) P P T ωq + (6) T L( alω ) q = Qref Q TωP T s alωp ( k ) (7) s The aboe equations are the an q components in the rotating q reference frame that satisfy the control conition of P ref (k) = P (k+), an Q ref (k) = Q (k+). Equations (6) an (7) show that the q components of the conerter oltage can be irectly controlle accoring to only the reference an measure alues of actie an reactie powers, system parameters, an the measure oltage of the A source. The gating signals of the PWM conerter will then be prouce accoring to these references. In the propose strategy, the oltage moulator has the ominant ynamics an the controller can almost reach the maximum system ynamic reonse. Since in the propose DP, in ite of the classical one which is s Fig. 3 Simulation results for switching table base DP (L =.5 mh) []. 65 Authorize license use limite to: Ferowsi Uniersity of Mashha. Downloae on June 03,00 at 06:07:43 UT from IEEE Xplore. Restrictions apply.

4 The power tracking, current shaping an harmonics performance of the propose DP with LL filter is compare to the conentional switching table base DP [] an the propose DP with the output L filter []. The system parameters are the same for all cases of stuy an the total alue of the filter s inuctance is chosen to be.5 mh. The switching an sampling frequencies are 0 khz. The LL filter is esigne accoring to a well-known step by step esign proceure which minimizes the current ripple an the reactie power of the capacitor an at the same time proies aequate stability margin an passie amping [7]-[9]. The parameters of the filter foun to be L = 0.9 mh, L =.6 mh, f = 60 μf an R f = 4Ω. Simulation results for three systems uner stuy are shown in Figs Fig. 3 clearly shows that the conentional DP with these alues of sampling frequency (0 khz) an filter s inuctance (.5 mh) cannot proie an acceptable performance. In fact, the switching table base DP can guarantee the performance only uner high alues of sampling frequency an filter s inuctance, which is not usually feasible in high power applications. Fig 5. for propose DP with LL filter confirm the superiority of the propose metho in proiing more precise current control with minimum istortion an less harmonic noises (THD) an at the same time, more accurate regulation an less istortion in the output actie an reactie powers. The harmonic ectrums of the mains current are also shown in Figs One can recognize that the classical DP in Fig. 3 has a broaban harmonic ectrum that reas oer a wie low frequency range. Because of these low frequency harmonics, the esign of LL filters will be practically impossible in orer to aoi resonances. On the other han, comparing the total harmonic istortion (THDi) alues of Figs. 4 an 5 approes better harmonics performance with a thir orer LL filter instea of a simple L filter while the total inuctance alues are equal for both filters. Fig. 4 Simulation results for propose DP with L filter (L =.5 mh) []. Fig. 5 Simulation results for propose DP with LL filter (L +L =.5 mh). 66 Authorize license use limite to: Ferowsi Uniersity of Mashha. Downloae on June 03,00 at 06:07:43 UT from IEEE Xplore. Restrictions apply.

5 IV. onclusions A noel moel-base strategy for irect power control of three-phase pulse-wih-moulate conerters which are connecte to the gri through an LL filter is propose. Besies using an LL filter instea of an L one an the simplicity, simulations show the better performance of the propose metho compare to the classical switching table base DP. References [] S. Buso, an P. Mattaelli, Digital ontrol in Power Electronics, Morgan & laypool, USA, 006. [] T. Noguchi, H. Tomiki, S. Kono, an I. Takahashi, Direct power control of PWM conerter without power-source oltage sensors, IEEE Trans. Inustry Applications, ol. 34, no. 4, pp , 998. [3] M. Malinowski, M. Jasinski, an M. P. Kazmierkowski, Simple irect power control of three-phase PWM rectifier using ace-ector moulation (DP-SVM), IEEE Trans. Inustrial Electronics, ol. 5, no., pp , 004. [4] P. ortes, J. Roriguez, P. Antoniewicz, an M. Kazmierkowski, Direct power control of an AFE using preictie control, IEEE Trans. Power Electronics, ol. 3, no. 5, pp , 008. [5] J. Restrepo, J.. Viola, J. M. Aller, an A. Bueno, Algorithm ealuation for the optimal selection of the ace ector oltage using DP in power systems, in Proc. European onf. Power Electronics an Applications, pp. -9, 007. [6] A. Bouafia, F. Krim, an J. P. aubert, Design an implementation of high performance irect power control of three-phase PWM rectifier, ia fuzzy an PI controller for output oltage regulation, Energy onersion an Management, ol. 50, no., pp. 6-3, 009. [7] T.. Wang, Z. Ye,. Sinha, an X. Yuan, Output filter esign for a gri-interconnecte three-phase inerter, in Proc. 34th Annu. IEEE onf. Power Electronics Specialists, pp , 003. [8] S. V. Araujo, A. Engler, an F. L. M. Antunes, LL filter esign for gri-connecte NP inerters in offshore win turbines, in Proc. 7th Int. onf. Power Electronics, Daegu, pp , 007. [9] B.. Parikshith, an J. Vino, Higher orer output filter esign for gri connecte power conerters, in Proc. 5th National onf. Power Systems, Bombay, pp , 008. [0] E. Wu, an P. W. Lehn, Digital current control of a oltage source conerter with actie amping of LL resonance, IEEE Trans. Power Electronics, ol., no. 5, pp , Sep [] S. Y. Yang, X. Zhang,. W. Zhang, an Z. Xie, Stuy on actie amping methos for oltage source conerter with LL input filter, in Proc. 6th IEEE Int. onf. Power Electronics an Motion ontrol, pp , 009. [] M. Monfare, H. Rastegar, an H. M. Kojabai, High performance DP for PWM conerters, in Proc. 6th Int. onf. Electrical an Electronics Engineering, Bursa, Authorize license use limite to: Ferowsi Uniersity of Mashha. Downloae on June 03,00 at 06:07:43 UT from IEEE Xplore. Restrictions apply.