Conditions for Capacitor Voltage Regulation in a Five-Level Cascade Multilevel Inverter: Application to Voltage-Boost in a PM Drive

Transcription

1 Conditions for Capacitor oltage Regulation in a FieLeel Cascade Multileel Inerter: Application to oltageboost in a PM Drie John Chiasson, Burak Özpineci, Zhong Du 3 and Leon M. Tolbert 4 Abstract A cascade multileel inerter is a power electronic deice built to synthesize a desired AC oltage from seeral leels of DC oltages. uch inerters hae been the subject of research in the last seeral years, where the DC leels were considered to be identical in that all of them were either batteries, solar cells, etc. imilar to preious results in the literature, the work here shows how a cascade multileel inerter can be used to obtain a oltage boost at higher speeds for a threephase PM drie using only a single DC oltage source. The input of a standard threeleg inerter is connected to the DC source and the output of each leg is fed through an Hbridge (which is supplied by a capacitor) to form a cascade multileel inerter. A fundamental switching scheme is used, which achiees the fundamental in the output oltage while eliminating the fifth harmonic. A new contribution in this paper is the deelopment of explicit conditions in terms of the power factor and modulation index for which the capacitor oltage of the Hbridges can be regulated while simultaneously maintaining the aforementioned output oltage. This is then usedforapmmotordrieshowingthemachinecanattain higher speeds due to the higher output oltage of the multileel inerter compared to using just a threeleg inerter. I. INTRODUCTION The work here shows how a cascade multileel inerter (CMLI) using only a single DC oltage source can be used to obtain a oltage boost at higher speeds for a threephase PM drie compared to a standard threeleg inerter with the same DC source. Figure shows one leg of a standard threeleg inerter connected to a DC source with output of the leg fed through an Hbridge supplied by a capacitor, to form the CMLI. A fundamental switching scheme is used and it is chosen so that the output oltage waeform achiees the desired fundamental while eliminating the fifth harmonic. Explicit conditions are gien in terms of the power factor and modulation index to characterize when the capacitor oltage of the Hbridges can be regulated to a desired constant alue, while simultaneously haing the CMLI maintain the desired output oltage. This work was supported by Oak Ridge National Laboratory. J. Chiasson is with the ECE Department, Boise tate Uniersity, Boise ID johnchiasson@boisestate.edu Burak Özpineci is with Oak Ridge National Laboratory, 36 Cherahala Bouleard, Knoxille TN ozpinecib@ornl.go 3 Zhong Du is with Oak Ridge National Laboratory, 36 Cherahala Bouleard, Knoxille TN zhongdu@gmail.com 4 L. M. Tolbert is with the ECE Department, Uniersity of Tennessee, Knoxille, TN 37996, tolbert@utk.edu. He is also with Oak Ridge National Laboratory, 36 Cherahala Bouleard, Knoxille TN tolbertlm@ornl.go II. MULTILEEL INERTER ARCHITECTURE AND OPERATION A cascade multileel inerter is a power electronic deice built to synthesize a desired AC oltage from seeral leels of DC oltages. uch inerters hae been the subject of research in the last seeral years [][][3][4], where the DC leels were considered to be identical in that all of them were either batteries, solar cells, etc. In [5], a multileel conerter was presented in which the two separate DC sources were the secondaries of two transformers coupled to the utility AC power. Corzine et al [6] hae proposed using a single DC power source and capacitors for the other DC sources. A method was gien to transfer power from the DC power source to the capacitor in order to regulate the capacitor oltage. A similar approach was later (but independently) proposed by Du et al [7]. These approaches required a DC power source for each phase. imilar methods hae also been proposed by eenstra and Rufer [8][9]. The approach here is similar to that of Corzine et al [6] and Du et al [7] with the important exception that only a single standard 3leg inerter is required as the power source (one leg for each phase) for the three phase multileel inerter []. A significant contribution of this paper is the deelopment of explicit conditions in terms of the modulation index and power factor for when such a topology can be used to boost the output oltage compared to a standard threeleg inerter. i c DC ource C i Fig.. One leg of a 3leg inerter connected to a full Hbridge with a capacitor DC source /7/$. 7 IEEE 73

2 / / / / Fig.. = i Output waeform Fig. 3. One way to make the output oltage zero for is to set = and =. / / / / Fig. 4. Another way to make the output oltage zero for is to set = and =. To proceed, consider the leftside of Figure, which shows a DC source connected to a single leg of a standard 3leg inerter. The output oltage of this leg (with respect to the ground) is either ( 5 closed) or ( 6 closed). This leg is connected in series with a full Hbridge, which in turn is supplied by a capacitor oltage. If the capacitor is kept charged to, then the output oltage of the Hbridge can take on the alues ( & 4 closed) ( & closed or 3 & 4 closed) or ( & 3 closed). An example output waeform that this topology can achiee is shown in Figure. When the output oltage = is required to be zero, one can either set = and = as in Figure 3 or = and = as in Figure 4. It is this flexibility in choosing how to make the output oltage zero that is exploited to regulate the capacitor oltage. As an example, in Figure, in the interal, the output oltage is zero and the current. If & 4 are closed (so that = ) along with 6 closed (so that = ), then the capacitor is discharging ( = ) and = =. On the other hand, if & 3 are closed (so that = ) and 5 is also closed (so that = ), then the capacitor is charging ( = ) and = =. The case is accomplished by simply reersing the switch positions of the case for charge and discharge of the capacitor. Consequently, the method consists of monitoring the output current and the capacitor oltage so that during periods of zero oltage output, either the switches 4 and 6 are closed or the switches 3 and 5 are closed depending on whether it is necessary to charge or discharge the capacitor. III. CONDITION FOR CAPACITOR OLTAGE REGULATION As Figure illustrates, the ability to regulate the capacitor oltage depends on the power factor. Let () = sin() () = sin( ) where () is the fundamental component of the output oltage, () is the current, and is the power factor angle (phase angle of the current with respect to the oltage). The objectie here is to compute the conditions on switching angles and and the power factor angle to ensure the capacitor can be regulated to a desired alue. A. Case Consider the case where as illustrated in Figure 5. ϕ () Fig. 5. i() 73

3 During the interal, the capacitor loses the amount of charge R sin( ) while during the interals and the capacitor can be recharged (by choosing the switch positions appropriately) by the amounts R sin( ) R sin() and R sin( ), respectiely. In this case, keeping the capacitor charged requires Z sin( ) Z sin( ) Z sin( ) Z sin( ) which reduces to cos () cos( )cos( ) () B. Case Consider the case asshowninfigure6. ϕ () i() output oltage while eliminating the fifthharmonic (Only one harmonic can be eliminated using this switching scheme and the fifth is typically significant in a threephase system), the switching angles must satisfy cos( )cos( )= cos(5 )cos(5 )= (4) Figure 7 is a plot of and (in degrees) that sole (4) ersus (the modulation index is ). witching Angles in Degrees m= cos( ) cos( ) Fig. 6. Fig. 7. and ersus During the interal, the capacitor loses the amount of charge R sin( ) while during the interals and the capacitor can be recharged (by choosing the switch positions appropriately) by the amount R sin( ) R sin( ) Thus keeping the capacitor oltage regulated requires Z sin( ) Z Z sin( ) sin( ) which reduces to cos ( ) tan() () sin ( ) In summary, the conditions for capacitor oltage regulation in terms of the µ switching angles and,andthepower µ 4 factor are, cos( )cos( )= for cos () µ cos for tan ( ) (3) sin ( ) Notice the two conditions are identical at the boundary where =. In order to achiee the fundamental in the desired Thus, for any gien alue of and, the alues of and are found ia Figure 7 and thus whether or not the capacitor oltage can be regulated is straightforwardly checked using the conditions (3). What these conditions say is, for any gien alue of in the interal 6 99 (i.e., where conditions (4) hae a solution), the capacitor oltage can be regulated proided the power factor angle is large enough. Note that both and increase as the motor speed goes up. I. FUNDAMENTAL FREQUENCY WITCHING In the simulations presented here, the DC link oltage was set to (so that the 3leg inerter produces ± ), the capacitors were regulated to, the motor s inertia is =kgm,themotorhas =4polepairs, the stator resistance is = 65 Ohms, the stator inductance is =3mH, the torque/backemf constant = =37 Nm/A (/rad/sec), and the load torque =9Nm at peak speed. The capacitor alue for the Hbridges is = F. 733

4 Radians/econd Rotor peed (Max = 75 rad/sec) = F. An enlarged iew of the capacitor oltage for is shown in Figure. olts Capacitor oltage econds 97 Fig. 8. Rotor speed in rad/sec ersus time in seconds econds tator oltage Phase Fig.. Capacitor oltage ersus time. olts olts Capacitor oltage Englarged Fig econds Enlarged iew of the phase oltage in olts s time in sec. The motor was run openloop with the magnitude of the fundamental of the stator oltage ramped from 9 to 8 during the time interal from to 3 seconds (Note that the threeleg inerter produces ± so the capacitor sourced Hbridges proide the boost up to ±9 ). The stator electrical frequency was brought up smoothly from to 75 Hz in 5 seconds resulting in a peak speed of = 75 rad/sec. The resulting speed response is shown in Figure 8, which is somewhat oscillatory due to the openloop control. A iscous friction load torque was used with the iscous friction coefficient chosen to be =7 (quite large) so that at maximum speed the load torque was max = ( )=(7) (75) = 9 Nm. An enlarged section of the inerter output oltage of phase is gien in Figure 9 illustrating the fundamental switching scheme for a stator frequency of = 75 Hz. The capacitor oltage for one of the Hbridges is shown in Figure showing that the scheme regulates the oltage within 3 olts of the nominal alue. The alue of the capacitance is econds Fig.. An enlarged iew of the capacitor oltage ersus time. The stator current, the stator oltage, and a scaled ersion of the capacitor oltage are shown in Figure. caled caled capacitor oltage tator oltage tator current Time (sec) Fig.. caled capacitor oltage (), stator current (A), and stator oltage () s time. 734

5 Note that the capacitor discharges when the inerter is supplying ±, stays constant when the inerter is supplying ±, and recharges when the inerter is supplying. For example, at about =5575 seconds, the stator current becomes positie, the CMLI inerter is supplying, and the capacitor oltage is decreasing. Following this, the CMLI inerter is supplying and the capacitor oltage is constant. Next, the CMLI inerter is supplying and the capacitor is charging so that its oltage increases. For comparison purposes, the simulation was rerun using just a standard threeleg inerter supplying ± (In this case, closedloop ector control of the PM machine was used so that there is no oscillatory behaior in the response). The maximum speed possible was only rad/sec, which is shown in Figure 3 and is due to the oltage limitation. Figure 4 shows one of the stator phase oltages goes into saturation just to obtain this speed. This should be contrasted with the maximum speed of 75 rads/sec obtained using the same DC source and a multileel inerter (see Figure 8). Radians/econd Rotor peed (Max = rad/sec) econds Fig. 3. Rotor speed using a standard 3leg inerter supplying ± tator oltage Phase. CONCLUION A cascade multileel inerter topology has been proposed that requires only a single standard 3leg inerter and capacitors as the power sources. The capacitors obtain their power from the 3leg inerter allowing the cascade multileel inerter to supply significantly more oltage from a gien DC power source than just a three leg inerter alone. imulation results were presented using a fundamental frequency switching scheme. Finally, subject to conditions in terms of the power factor and modulation index [= see (4)], it was shown that the capacitor oltages could be regulated. REFERENCE [] M. Klabunde, Y. Zhao, and T. A. Lipo, Current control of a 3 leel rectifier/inerter drie system, in Conference Record 994 IEEE IA Annual Meeting, pp , 994. [] W. Menzies, P. teimer, and J. K. teinke, Fieleel GTO inerters for large induction motor dries, IEEE Transactions on Industry Applications, ol. 3, pp , July 994. [3] J. K. teinke, Control strategy for a three phase AC traction drie with three leel GTO PWM inerter, in IEEE Power Electronic pecialist Conference (PEC), pp , 988. [4] J. Zhang, High performance control of a three leel IGBT inerter fed AC drie, in Conf. Rec. IEEE IA Annual Meeting, pp. 8, 995. [5] M. Manjrekar, P. K. teimer, and T. Lipo, Hybrid multileel power conersion system: A competitie solution for highpower applications, IEEE Transactions on Industry Applications, ol. 36, pp , May/June. [6] K. A. Corzine, F. A. Hardrick, and Y. L. Familiant, A cascaded multileel Hbridge inerter utilizing capacitor oltages sources, in Proceedings of the IATED International Conference, pp. 9 95, Palm prings CA, 3. [7] Z. Du, L. M. Tolbert, J. N. Chiasson, and B. Özpineci, Cascade multileel inerter using a single source, in Proceedings of the Applied Power Electronics Conference (APEC), pp , 6. Dallas TX. [8] M. eenstra and A. Rufer, Nonequilibrium state capacitor oltage stabilization in a hybrid asymmetric nineleel inerter: Nonlinear modelpredictie control, in Proceedings of the European Control Conference, 3. Toulouse FR. [9] M. eenstra and A. Rufer, Control of a hybrid asymmetric multileel inerter for a competitie mediumoltage industrial dries, IEEE Transactions on Industry Applications, ol. IA4, pp , March/April 5. [] J.Chiasson,B.Özpineci,andL.M.Tolbert, Fieleelthreephase hybrid cascade multileel inerter using a single source, in Proceedings of the Applied Power Electronics Conference, February 5 March 7. Anaheim CA. olts 4 6 econds Fig. 4. tator oltage using a standard 3leg inerter supplying ± 735