Extension of the Nearest-Three Virtual-Space-Vector PWM to the Four-Level Diode-Clamped dc-ac Converter

Transcription

1 Etension of the Nearest-Three irtual-space-ector PWM to the Four-Level Dioe-Clampe c-ac Converter S. Busquets-Monge, J. Boronau, an J. Rocabert Dept. of Electronic Engineering Technical University of Catalonia Av. Diagonal 88 Barcelona, Spain Abstract- Several pulsewith moulation strategies have been propose for the three-level three-phase ioe-clampe c-ac converter. Among them, the nearest-three virtual-space-vector (NT ) pulsewith moulation (PWM) guarantees the c-link capacitor voltage balance uner any operating conition, provie that the aition of the three phase currents equals zero. This paper etens this moulation concept to the four level converter. The new virtual vectors are presente an practical moulation solutions are efine. Conventional nearest-three space vector (NT) PWM cannot comprehensively achieve balance an stable c-link voltages. The propose moulation solutions enable the practical use of the four-level converter since they guarantee the c-link capacitor voltage balance for any operating conition an loa, provie that the aition of threephase currents equals zero. Simulation an eperimental results prove the gooness of the presente approach. I. INTRODUCTION Multilevel converter topologies []-[] have receive special attention uring the last two ecaes ue to their significant avantages compare to the conventional two level case. These topologies allow reucing the voltage across the semiconuctors without the problems associate to the series interconnection of evices, reuce the harmonic istortion of the output voltage an improve the efficiency of the converter. However, a larger number of semiconuctors is neee an the moulation strategy to control them becomes more comple. Among the possible multilevel topologies, the three-level three-phase ioe-clampe c-ac converter [] is probably the most popular. Several moulation strategies have been propose for this converter. Conventional pulsewith moulations (PWM) are base on the selection of the nearestthree space vectors (NT). However, as emonstrate in [], this PWM are not capable of balancing the voltage of the clink capacitors uner certain operating conitions. On the other han, the nearest-three virtual-space-vector (NT ) PWM [] is capable of controlling the c-link capacitor voltage balance for any loa (linear or non-linear, balance or unbalance) an moulation ine, provie that the aition of the output three-phase currents equals zero. Reference [] shows how to interface this moulation with conventional close-loop control schemes, an evelops a specific control to mitigate possible c-link voltage balance perturbations. Several stuies have focuse on ioe-clampe topologies with higher levels, in particular the four-level three-phase ioe-clampe c-ac converter in Fig. [][]. They conclue that the use of NT PWM with the four-level converter cannot achieve c-link capacitor voltage balance uner a substantial portion of the converter operating conitions. Eventually, these operating conitions lea to instabilities in the balance, causing the voltage of the mile capacitor to collapse. The limits for balance an stable operation are specifie in []. In this paper, the NT PWM presente in [] is etene to the four-level converter. The resulting PWM scheme guarantees the c-link voltage balance for any moulation ine an loa, provie that the aition of the three phase currents equals zero. Hence, this moulation enables the practical use of the four-level converter with passive front ens an only requires small c-link capacitors. The paper is organize as follows. In Section II the propose moulation scheme is efine. Section III presents the most interesting particular moulation strategies. In Sections I an, the performance of these moulations is analyze an compare to a reference NT moulation through both simulations an eperiments, an Section I outlines the conclusions. c v C v C v C C i C i C a Fig.. Four-level three-phase ioe-clampe c-ac converter. b i b c i c This work was supporte by the Ministerio e Eucación y Ciencia, Mari, Spain, uner Grant TEC-8-C. ---//$. IEEE 89 Authorize license use limite to: UNIERSITAT POLIT?CNICA DE CATALUNYA. Downloae on November, 9 at 8:9 from IEEE Xplore. Restrictions apply.

2 v bc [, ] [ i c, ] [, -i c] [, i b] [, ] [, ] [, ] [, ] [, i c] [ i c, -i c] [-i c, ] ref [, -] [-, ] [, ] [ i c, i b] [ i b, ] [i b, ] [-, ] [, ] [, ] v ca v ab II. Fig.. Normalize space vector iagram for the four-level three-phase ioe-clampe c-ac converter. NEAREST-THREE IRTUAL-SPACE-ECTOR PWM A. irtual Space ector Definition Fig. shows the space vector iagram (SD) for the fourlevel ioe-clampe c-ac converter. The converter has sityfour switching states corresponing to all the combinations of connections of each phase to the c-link points,, an ; e.g.,, corresponing to the connection of phase a to point, phase b to, an phase c to. These switching states efine thirty-seven space vectors. In the conventional NT PWM, the reference vector ( ref ) = me i ) (m [, ] for linear moulation) is synthesize in each switching cycle (with perio T s = /f s ) by a sequence of the nearest three vectors. Whenever a vector can be generate by more than one switching state, an aitional selection of one switching state or a combination of several has to be mae. In the first setant of the SD of Fig., the mipoint (MP) currents i an i corresponing to each switching state are specifie in brackets: [i, i ]. Analogous to the three-level case, the average i an average i in every switching cycle must be zero to guarantee the c-link capacitor voltage balance. In the NT PWM, whenever reunant switching states are available for a given space vector, the appropriate combination of these switching states must be selecte to guarantee that the average MP currents equal zero in every switching cycle. However, this is not possible for high moulation inees, especially when the loa angle is small (m ma =. for a zero loa angle []). To achieve full control of the c-link capacitor voltage balance, a set of new virtual vectors () is efine as a linear combination of the vectors corresponing to certain switching states. The new virtual vectors, shown in Fig. for the first setant of the SD, are efine in (). v bc 8 9 ref Fig.. irtual space vectors for the first setant of the SD Authorize license use limite to: UNIERSITAT POLIT?CNICA DE CATALUNYA. Downloae on November, 9 at 8:9 from IEEE Xplore. Restrictions apply.

3 ,,,,,, 8 9,,,,,.,,,,,,,,,,,,,,,,, These vectors have associate average MP currents in every switching cycle equal to zero, ue to analogous reasons as those iscusse for the three-level converter []. Note that virtual vectors, an present reunancy. There are two possible elementary combinations of switching states to efine each (, an, for ;, an, for ;, an, for ). In fact, any combination of both elementary options can be use to implement virtual vectors, an :,,, where,, [, ].,,,,, A particularly interesting combination is obtaine when =., since it represents an equitable combination of all switching states involve., () () B. irtual Space ector Selection The synthesis of the reference vector in each switching cycle is performe using the nearest three virtual space vectors. This efines nine small triangular regions in the iagram of Fig.. Table I specifies the selecte virtual space vectors in the cases where the tip of ref is in regions 9. The uty ratio of each selecte vector in each switching perio is calculate as ref j () where j correspons to the jth selecte virtual space vector (j =,, ). Then, the corresponing uty ratio of the ifferent switching states can be calculate. For the first setant,,, (),,,,, 8, 9. C. Switching States Sequence Finally, the sequence over time within a switching cycle of the application of the ifferent switching states has to be ecie. The chosen switching states orer is such that the sequence of connection of each phase to the c-link points is the symmetrical , as shown in Fig.. This can be achieve by simply orering the switching-states three-igit number in escening-ascening orer. TABLE I SELECTION OF FOR EACH TRIANGULAR REGION Selecte Region General NT NT _A NT _B,,,,,,,,,,,,,,,, (.),, (.),,,, (.),, (.),,, (), () (), (), (),,, (), () (), (), (),, 8 (), (), 8 (), (), 8 8,, 9 (), (), 9 (), (), 9 9, 8, 9 (.), 8, 9 (.), 8, 9 89 Authorize license use limite to: UNIERSITAT POLIT?CNICA DE CATALUNYA. Downloae on November, 9 at 8:9 from IEEE Xplore. Restrictions apply.

4 Phase c-link connection T s / T s/ T s/ T s/ T s / T s T s / T s/ T s/ T s / Fig.. Selecte sequence of connection of phase (a, b or c) to each of the c-link points (,,, an ). Therefore, a practical implementation of the propose moulation strategy only requires the computation of uty ratios a, b, c, a, b, c, a, b, c, a, b, c (where y is the uty ratio of the phase connection to the c-link point y), as the aition of the appropriate switching state uty ratios calculate in Section II.B. For eample, in the first setant, to obtain a. () a D. Phase Duty-Ratio Epressions Fig. shows the simulate uty ratios a an a, for any NT PWM, m =.8 an a line perio. The simple pattern observe for a can be mathematically epresse as : m cos a : a () : a m cos. The epression for uty ratio a is the same as () but phase-shifte 8. The epressions for the b an c phase uty ratios are the same as for phase a, but phase shifte an, respectively. These epressions allow obtaining irectly a, b, c, a, b, c as a function of the reference vector length m an angle, without the nee of ientifying the triangle in which the reference vector is locate an then performing calculations ()(). This significantly simplifies the computations. Note that these epressions are the same as for an, bn, cn, ap, bp, cp in the three-level converter []. The epressions for a, b, c, a, b, c epen upon the selection of,,an. III. PARTICULAR MODULATION STRATEGIES In the preceing Section, we have presente the general NT PWM for the four-level three-phase c-ac converter. In orer to etermine a particular moulation strategy, we still nee to select the proper value of,, ; i.e., which combination of the reunant we will use to implement, an. A choice of,, =. seems to be goo a priori, since all possible reunant are then equally employe in approimating the reference vector. t a a -. 8 (eg) Fig.. a an a as a function of (m =.8). The resulting epressions for a an a are very simple: a a a a. () However, in triangles 8 this solution leas to employ a set of switching states that cannot follow the sequence efine in Fig., an the number of switching transitions in these four triangles woul be much higher than in others. An alternative coul be to set,, = (or = ) in regions 8, efining what we esignate as the NT _A moulation solution (see Table I). Still, this solution presents a pattern for the phase uty-ratios a an a in regions an that can be simplifie if we select virtual vectors,, an in both regions, efining what we esignate as the NT _B moulation solution (see Table I). Since we are not selecting the true nearest three in triangles an, the output voltage istortion will increase slightly, but not significantly. As a result, solution NT _B presents a fairly simple uty-ratio pattern. For the first setant: Regions an 9: a a a a (8) Regions 8: a a a. a Solution NT _A presents pairs of switching transitions (one switch turns off an another turns on) in regions an 9 per half switching cycle. In regions an 8 presents only pairs of switching transitions. Solution NT _B presents pairs of switching transitions in regions an 9. In regions 8, it only presents. Therefore, solution NT _B is also superior from the point of view of switching transitions. I. SIMULATION RESULTS The performance of the propose moulation has been verifie through simulation. The converter has been moele in Matlab-Simulink an simulations have been carrie out in open loop. The performance of the propose moulation is compare to a particular NT PWM. In this moulation use as a reference for comparison, the uty ratio assigne to each space vector is equally share in every switching cycle by all associate switching states. Fig. presents the results of the 89 Authorize license use limite to: UNIERSITAT POLIT?CNICA DE CATALUNYA. Downloae on November, 9 at 8:9 from IEEE Xplore. Restrictions apply.

5 comparison at m =. for the phase a uty ratios an the clink capacitor voltages. As epecte, the propose moulation guarantees the c-link balance while the NT PWM not only can not guarantee the balance but also leas to the collapse of v C. In Fig., we observe that the c-link voltage balance is achieve at the epense of a higher output voltage istortion compare to what one woul obtain from a NT PWM if the c-link capacitors where replace by c voltage sources.. EXPERIMENTAL RESULTS Eperimental tests have been conucte to verify the performance observe in simulations. A kw prototype has been use for this purpose. The converter is operate in open loop, with a c power supply connecte between c-link points an an a three-phase series R-L loa connecte to the ac sie. The computation of the nine inepenent phase uty-ratios is performe by the embee PowerPC of Space a. a a.. a a. a a.. a vc,vc, vc () 8 v C v C v C vc,vc, vc () v C v C v C (a) 9 (b) Fig.. Simulation results for a, a, a, a, v C, v C an v C in the following conitions: c =, m =., C =. mf, f s = khz, an a linear an balance loa with per-phase impeance Z L =..º (series R-L loa). (a) Reference NT PWM. (b) Propose NT _A an NT _B PWM. 89 Authorize license use limite to: UNIERSITAT POLIT?CNICA DE CATALUNYA. Downloae on November, 9 at 8:9 from IEEE Xplore. Restrictions apply.

6 vab () vab () ab (rms) THD =. % ab (rms) THD =. % f (khz) (a) f (khz) (b) Fig.. Simulation results for output voltage v ab, an FFT(v ab ) in the following conitions: pn =, m =., C =, f s = khz, an a linear an balance loa with per-phase impeance Z L =..º (series R-L loa). (a) Reference NT PWM. (b) Propose NT _A an NT _B PWM. DS. This information is sent to an Altera EPFK programmable logic evice in charge of generating the eighteen switch control signals. In Fig. 8, we can observe that the NT PWM use as a reference for comparison leas to the collapse of the mile capacitor voltage. The same woul occur with any other NT PWM. On the other han, in the propose NT PWM all three capacitor voltages are fairly balance in the absence of a close-loop control. I. CONCLUSIONS A new moulation approach for the comprehensive control of the c-link capacitor voltage balance in the four-level threephase ioe-clampe c-ac converter has been presente (patent pening). The c-link voltage balancing is achieve for any loa (linear or nonlinear, balance or unbalance) over the full range of converter output voltage an for all loa power factors provie that i b i c =. Thus, the propose moulation not only enables the use of the four-level ioeclampe converter with passive front ens, but also allows operating with small c-link capacitors. The c-link capacitance require to limit the voltage ripple across these capacitors iminishes as the switching frequency increases, eventually allowing the use of non-electrolytic capacitors. Practical moulation strategies have been efine. The phase uty-ratio of these strategies can be escribe with simple mathematical epressions, leaing to a very compact computation implementation. These epressions are only epenent on the moulation ine an reference vector angle. In particular, they o not epen on the loa. Therefore, no knowlege of the loa is require to implement the propose moulation. The benefits of the propose solution over conventional NT PWM have been verifie through simulation an eperiments. These benefits are obtaine at an epense of a higher output-voltage high-frequency istortion, compare to a NT PWM applie to a converter with c voltage sources replacing the c-link capacitors. This istortion, however, can be easily attenuate using an aequate filter. 89 Authorize license use limite to: UNIERSITAT POLIT?CNICA DE CATALUNYA. Downloae on November, 9 at 8:9 from IEEE Xplore. Restrictions apply.

7 REFERENCES [] J. Roríguez, J. Lai, an F. Peng, Multilevel inverters: a survey of topologies, controls an applications, IEEE Trans. In. Electron., vol. 9, pp. 8, Aug.. [] L. Demas, T.A. Meynar, H. Foch, an G. Gateau, Comparative stuy of multilevel topologies: NPC, multicell inverter an SMC with IGBT, in Proc. IEEE Inustrial Electronics Soc. Conf., vol.,, pp [] A. Nabae, I. Takahashi, an H. Akagi, A new neutral-point clampe PWM inverter, IEEE Trans. In. Applicat., vol. IA-, pp. 8, Sept./Oct. 98. [] N. Celanovic an D. Boroyevich, A comprehensive stuy of neutralpoint voltage balancing problem in three-level neutral-point-clampe voltage source PWM inverters, IEEE Trans. Power Electron., vol., pp. -9, Mar.. [] S. Busquets-Monge, J. Boronau, D. Boroyevich, an S. Somavilla, The nearest three virtual space vector PWM a moulation for the comprehensive neutral-point balancing in the three-level NPC inverter, IEEE Power Electron. Lett., vol., pp. -, Mar.. [] S. Busquets-Monge, J. D. Ortega, J. Boronau, J. A. Beristain, an J. Rocabert, Close-loop control esign for a three-level three-phase neutral-point-clampe inverter using the optimize nearest-three virtualspace-vector moulation, in Proc. IEEE Power Electronics Specialists Conf.,. [] M. Marchesoni, M. Mazzucchelli, F.. P. Robinson, an P. Tenca, A minimum-energy-base capacitor voltage balancing control strategy for MPC conversion systems, in Proc. IEEE International Symposium on Inustrial Electronics, 999, pp. -. [8] G. Sinha an T. A. Lipo, A four-level inverter base rive with a passive front en, IEEE Trans. Power Electron., vol., pp. 8-9, Mar.. [9] M. Marchesoni, M. Mazzucchelli, an P. Tenca, An optimal controller for voltage balance an power losses reuction in MPC AC/DC/AC converters, in Proc. IEEE Power Electronics Specialists Conf.,, pp. -. [] M. Marchesonn P. Tenca, Theoretical an practical limits in multilevel MPC inverters with passive front ens, in Proc. European Conference on Power Electronics an Applications,. [] J. Pou, R. Pinao, an D. Boroyevich, oltage-balance limits in fourlevel ioe-clampe converters with passive front ens, IEEE Trans. In. Electron., vol., pp. 9-9, Feb.. v C v C v C v C v C v C v ab v ab (a) Fig. 8. Eperimental results for v C, v C, v C, an v ab in the following conitions: c =, m =., C = F, f s = khz, an a linear an balance loa with per-phase impeance Z L =. 8.º (series R-L loa). (a) Reference NT PWM. (b) Propose NT _A an NT _B PWM. (b) 898 Authorize license use limite to: UNIERSITAT POLIT?CNICA DE CATALUNYA. Downloae on November, 9 at 8:9 from IEEE Xplore. Restrictions apply.