A Multilevel Converter-Based Universal Power Conditioner

Transcription

1 A Multileel Conerter-Based Uniersal Power Conditioner eon M. Tolbert, Fang Z. Peng Thomas G. Habetler Oak Ridge National aboratory Georgia Institute of Technology P.O. Box 9, Bldg. 9- School of Electrical and Comuter Engineering Oak Ridge, TN Atlanta, GA -5 Tel: (865) Tel: () Fax: (865) -6 Fax: () Abstract This aer resents the deeloment of a control scheme for a multileel diode-clamed conerter connected in a series-arallel fashion to the electrical system such that it can comensate for deiations in utility oltage and act as a harmonic and/or reactie current source for a load. Simulation results are gien for the real-time control scheme when alied to a 5-leel conerter for different combinations of the following ower conditioning objecties: sag comensation, oltage balancing, current harmonic comensation, and reactie ower comensation. eel usage in the series inerter and arallel inerter is analyzed for the different comensation objecties, and a method to maximize leel usage at low modulation indices is highlighted. I. INTRODUCTION Deregulation of the ower industry will undoubtedly hae a large imact on utilities cometition for customers. Many industrial and commercial customers that cannot tolerate ariations in their electrical suly will reuest remium ower with secifications restricting certain tolerances in a utility s oltage magnitude, distortion, and limits on the number of outages er year. Utilities, in turn, will ut limitations on the ower factor, current harmonic distortion, and eak ower that the customer can imose on the utility. To meet the objecties detailed in these new remium ower agreements, the imlementation of adanced ower electronic technologies that can simultaneously imroe the ower uality for both utilities and their customers will be in demand. By connecting two actie inerter-based filters with a common dc link, the combined back-to-back conerter can be interfaced with the utility system in both a series and arallel manner. By haing these two inerters connected to the electrical system, simultaneous control of the current Preared by the Oak Ridge National aboratory, Oak Ridge, Tennessee 78-88, managed by ockheed Martin Energy Research, Cor. for the U.S. Deartment of Energy under contract DE-AC5-96OR6. A contractor of the U.S. Goernment has authored the submitted manuscrit. Accordingly, the U.S. Goernment retains a nonexclusie, royalty-free license to ublish or reroduce the ublished form of this contribution, or allow others to do so, for U.S. Goernment uroses. demanded from the utility and the oltage deliered to the load can be accomlished. This series-arallel actie ower filter has been referred to as a uniersal ower conditioner [-] when alied to electrical distribution systems, and as a uniersal ower flow controller when alied at the transmission leel [-6]. Multileel oltage source inerters uniue structure allows them to san high oltages and to reduce indiidual deice switching freuency without the use of transformers. The diode-clamed inerter can synthesize a desired waeform from seeral leels of dc oltages, and all six hases of a back-to-back conerter can share the same common dc link [7]. Conseuently, the integration of a multileel diodeclamed inerter into a uniersal ower conditioner is an enticing rosect. A multileel uniersal ower conditioner (MUPC) offers many otions when deciding what tye of control should be used in the comensation of source oltages and load currents. The objecties of the comensation (oltage sag, unbalanced oltages, oltage harmonics, current harmonics, or reactie ower) also lay an imortant role in the control of the two back-to-back inerters. For a multileel ower conditioner that will erform sag comensation, the majority of its oerating mode will likely be in low modulation index oerating regions because sags are uite infreuent and for a minimal duration. Because of this, how to maximize leel usage in a diode-clamed inerter for low modulation indices has been reiously exlored []. A rocedure has been deeloed that enables the inerter to switch at higher freuencies during low modulation indices. This increases the freuency sectrum and hastens the dynamic resonse of the inerter, yet does not exceed the allowable switching loss of the actie deices. Because of the different comensation objecties of the series inerter and the arallel inerter, two distinct control techniues are adated for their use. Simulation results erify that the algorithms deeloed will enable the back-to-back diode-clamed conerter to function as a uniersal ower conditioner. PESC 99, Charleston, South Carolina, June 7 July,

2 Utility Vsa Vsb i sa i Sb C C Vb Va i a i b oad Sab, Sca Synchronizing Voltage (-) θ sync nom oad Voltage Reference Generator () * * * a, b, c - () Sab, Sbc, Sca SI SI Vsc SI SIc SIb SIa series multileel diode-clamed inerter common dc link i Sc i PIc Vc PIc arallel multileel PIb diode-clamed inerter PIa i PIb C i PIa i c PI m f [n] A m V dc f m a m [ ()] [(m-)v dc ] - f c [n] [ ()] Amlitude Calculation Reference Rotation or SFO-PWM V offset [ (-)] Multilier for ow Modulation Indices [(Table III) (j, j, j) Redundant State Addition θ sync * SIa, * SIb, * SIc [(8)] Variable Multiband Carrier Generation [ (9)] V * SIa j, V * SIb j, V * SIc j Series Inerter Gate Drier Signal Generator [ (5)] s a, Fig.. Series-arallel connection to electrical system of back-to-back multileel diode clamed inerters for uniersal ower conditioner. Fig.. Serial inerter control block diagram. II. SERIES INVERTER CONTRO Fig. shows a block diagram of the two inerters (series and arallel) and the interconnection with the electrical system. For the analysis in this aer, the turns ratio for each of the series transformers was chosen to be. The algorithm used to regulate the load oltage is the short time window samling techniue roosed by Joos and Moran [8]. The load reference oltage, which must be synchronized with the source hase oltages, is generated directly from the samle of two line-line source oltages oer a short time frame. This techniue reuires that the source oltage be close to sinusoidal, which is the case for the majority of electrical installations at the interface between a large industrial customer and a utility. To determine the hase angle for a sinusoidal synchronizing oltage, sync, one can make use of the following euations: sin( ωts ) ( ) ωts synck synck θ sync = arctan, () sync cos k where sync Sab Sca =, () and where Sab and Sca are source line-line instantaneous samles and T s is the samling eriod. For a system with samles er cycle, ωt s = π/ radians. By samling these two line-line oltages, a synchronization signal can be obtained een if one of the hase oltages collases to zero, as in the case of a single hase to ground solid fault. The three instantaneous load reference oltages can then be gien by the following euations: V ( θ ) * nom a = sin sync, * Vnom = sin π b θ sync, () * Vnom π c = sin θ sync, where V nom is the nominal or desired line-line oltage for the load electrical system. The instantaneous reference signals for the series inerter to comensate for deiations in the source oltage are then eual to the difference between the instantaneous load reference oltages gien in () and the actual source hase oltages deried from the line-line instantaneous samles: * * Sab Sca SIa = a, * * Sbc Sab SIb = b, () * * Sca Sbc SIc = c. These three series inerter reference signals () are the modulation waeforms that are comared against a set of triangular carrier waes to determine the switching of the series inerter actie deices. A control structure is shown in block diagram form in Fig.. From the serial inerter reference oltages (), the amlitude modulation index (m a ) is determined. For low modulation indices (m a <.5 for all three hases), the PESC 99, Charleston, South Carolina, June 7 July,

3 (a) source hase oltages, Sa, Sb, Sc (a) source hase oltages, Sa, Sb, Sc (b) load line-line oltages, ab, bc, ca (b) load line-line oltages, ab, bc, ca (c) series inerter hase oltage, SIa (c) series inerter hase oltage, SIa (d) series inerter hase oltage, SIb (d) series inerter hase oltage, SIb (e) series inerter hase oltage, SIc Fig.. System oltage waeforms for single-hase sag ( Sa) to. V nom. (e) series inerter hase oltage, SIc Fig.. System oltage waeforms for two-hase sag ( Sa, Sb) to.5 V nom. carrier freuency can be increased, and the reference oltages are rotated among carrier bands as detailed in []. For high modulation indices (m a >.), SFO-PWM is imlemented as discussed in []. The modified reference signals, which may differ from the original reference signals by a trilen addition (SFO-PWM) or redundant state addition (reference rotation), are then comared against the multiband triangular carriers to calculate the switching signals that are the control signals for the actie deices. Comuter simulations were used to ealuate the erformance of the synchronizing and balancing algorithm under different sag or surge conditions. The amlitude magnitude of the load reference oltage V nom was chosen to be eual to a 5-leel diode-clamed inerter s dc link oltage. In order to reduce the rile in the load oltage because of injection of oltage by the series inerter, the low ass filter formed by SI and C in Fig. is necessary. For a 6 Hz electrical system, the otimum cutoff freuency of the filter was found to be 6 Hz. Higher cutoff freuencies of the filter resulted in high rile content of the load oltage, and lower cutoff freuencies resulted in large hase shifts between the source oltage and load oltage and a reduction in the magnitude of the load oltage. Fig. shows series comensation for a single-hase fault on hase a that decreased its oltage to. V nom. The inerter comensates immediately and almost instantaneously for this fault such that the load oltage is well regulated and balanced. Een with this seere fault, the reference waeforms for the three hases of the inerter hae an amlitude modulation index less than.5 (for a transformer turns ratio of ), and hence only three of the fie aailable leels in the diode-clamed inerter are needed. As shown in Fig. (c), (d), and (e), the synchronization and oltage regulation algorithm makes use of all three inerter hases to comensate for a sag in just one of the three source oltage hases. This illustrates that this algorithm is alicable to only three-hase, three-wire systems and not to three-hase, four-wire systems. For the examle reresented in Fig., rotation of the reference waeform among different carrier band sets is ossible as discussed in []. A singlehase fault that reduces the source oltage to less than PESC 99, Charleston, South Carolina, June 7 July,

4 (a) source hase oltages, Sa, Sb, Sc (a) source hase oltages, Sa, Sb, Sc (b) load line-line oltages, ab, bc, ca (b) load line-line oltages, ab, bc, ca (c) series inerter hase oltage, SIa (c) series inerter hase oltage, SIa (d) series inerter hase oltage, SIb (d) series inerter hase oltage, SIb (e) series inerter hase oltage, SIc Fig. 5. System oltage waeforms for two-hase sag ( Sb, Sc) to. V nom. (e) series inerter hase oltage, SIc Fig. 6. System oltage waeforms for three-hase unbalanced sag when source oltage has 5% 5 th harmonic distortion..5 V nom is necessary before use of all fie leels in one hase of the diode-clamed inerter is reuired. For the algorithm defined by () and (), a significant double hase fault that inoles hase a results in a hase shift between the load oltage and source oltage at the initiation and conclusion of comensation by the series inerter. Fig. reresents the case where hases a and b hae a double-hase fault to ground that causes the source oltage to di by 65% to.5 V nom. The hase shift in the load oltages can be seen at the beginning and end of the fault. For this articular examle, the hase shift introduced was.5. The worst case would be when two hases are comletely grounded, and the resultant hase shift is 6.8 in the hase oltage at the beginning and ending of oltage comensation. Because hase a is the reference for the other two hases in the synchronization algorithm, simulations hae shown that if hase a is not inoled in the fault, howeer, no substantial hase shift is introduced in the load oltages. Fig. 5 shows the case where hases b and c of the source oltage hae been reduced to. V nom by a seere sag. As shown in Fig. 5, the load oltages are well regulated, een for this extreme case. A double-line to ground fault that reduces the source oltage to less than.5 V nom is necessary before all fie leels of the diode-clamed inerter are needed. A less seere fault will result in only three leels being used and reference rotation being ossible []. The drawback of the synchronizing and balancing algorithm is that it cannot comensate for oltage harmonics because it was deried for sinusoidal source oltages. The algorithm does function for small distortions in the source oltage (generally less than 5% total harmonic distortion), but the load oltage will hae about the same harmonic content as the source oltage. Fig. 6 reresents three source oltages that hae a 5% 5 th harmonic seuence and exerience a threehase unbalanced sag for a three-cycle duration. The load oltage is balanced and well regulated, but it has about the same distortion as the source oltage. Another drawback of the algorithm is that hardware imlementation is difficult because of the recision needed PESC 99, Charleston, South Carolina, June 7 July,

5 m f [n] ab, bc, ca f m [()] [()] i a, i b, i c Extraction Circuit to Find Reactie and/or Harmonic Current Comonents (5-9) [(m-)v dc ] - f c [n] I * PIa, I * PIb, I * PIc A m m a Amlitude Calculation Reference Rotation or SFO-PWM V offset [ (-)] Multilier for ow Modulation Indices [ (Table III)] PI (j, j, j) Redundant State Addition V ab, V bc, V ca V * PIa, V * PIb, V * PIc [ (8)] Fig. 7. Parallel inerter control block diagram. - I PIa, I PIb, I PIc () () () Variable Multiband Carrier Generation [ (9)] V * PIa j, V * PIb j, V * PIc j Parallel Inerter Gate Drier Signal Generator [ (5)] s PIa, s PIb, s PIc or and b a =, c b a c a c c b =, c =. a For the comensation objectie of making the source current unity ower factor (and sinusoidal for a source oltage with little distortion), c * is set eual to and c * is set eual to the load rile actie ower, where ~ = b b a, (8) and where is the dc comonent of the load actie ower. A low ass filter is necessary for extraction of the dc comonent from the load actie ower. A digital low ass filter was imlemented as follows: for the calculation of the denominator of (). The analog to digital conersion for most digital signal rocessors will not hae the reuired recision for a samling rate of samles/cycle. Execution time of the rocessor is also a concern when calculating () because of the arctan term. III. PARAE INVERTER CONTRO The arallel inerter is resonsible for sulying the reactie and/or harmonic current demanded by the load. Generalized instantaneous ower theory, as outlined by Peng in [9], is used for the control of the arallel inerter. This theory works well for balanced oltages, which should be the case for the load oltages because of the series comensation of the source oltage. For the case where unbalanced oltages were resent, the instantaneous ower theory where the currents are chosen to follow the oltage waeform is more aroriate []. A control structure is shown in block diagram form in Fig. 7. Using instantaneous ower theory (generalized -theory), the instantaneous reference current for the arallel comensation control is gien by the following ector euation: k Tc = Ts T c k Ts k Ts T, (9) c where T c is the inerse of the filter s cutoff freuency f c. For a samling freuency of times er cycle and a 6 Hz electrical system, the otimum cutoff freuency of the low ass filter was found to be 5 Hz. Simulation results showed that with a lower cutoff freuency of the low ass filter, more of the actie ower rile is filtered but at the exense of an extended resonse time to ste changes in the load current. Higher cutoff freuencies resulted in better resonse times but at the exense of filtering less of the actie ower rile. With the 5 Hz cutoff freuency, the resonse time to a ste change was aroximately.5 cycles and generally better than 9% of the actie ower rile was filtered. The arallel inerter of the MUPC injects currents by imressing a oltage across the arallel inductors, PI, that is the difference between the load oltage V and outut oltage V PI. The arallel inerter has to roide a oltage V PI * such that the inerter sulies a current that tracks the current reference comuted in (5). This oltage was comuted from the following ector euation: i * PI * c = * c (5) * * PI = PI ( i i ) PI ωt s. () where c * and c * are extracted from the actie and reactie ower of the load, and, which are gien as follows: = = a a b b c c ; (6) = i, (7) Again from simulation, an imedance of the arallel inductance of ωt s ohms yielded a current that tracked the reference current well. Smaller alues resulted in comensation currents with a high rile content, and for larger alues, the tracking of the reference current was too slow to eliminate the distortion resent in the load current. Simulation results showed that the amlitude of the desired load oltage V nom should not be more than 7% of the oerall PESC 99, Charleston, South Carolina, June 7 July,

6 dc link oltage for the MUPC to be able to imress enough oltage across the arallel inductance to comensate for reactie currents when the load oltage is at its maximum or minimum amlitude. Without this margin, comlete comensation of reactie currents may not be ossible. Fig. 8 shows waeforms for an electrical system with current comensation where the load current had a % 7 th harmonic comonent and a.7 dislacement ower factor. The source current immediately becomes sinusoidal and in hase with the source hase oltages once comensation by the MUPC has begun. The arallel inerter sulies a substantial reactie current to comensate for the large reactie ower drawn by the load. The filter described by (9) does not comletely filter the rile in the load ower for seerely unbalanced conditions. Fig. 9 shows what the source oltage, load current, and source current look like for comensation of the load current under unbalanced current conditions (i b = -i a, i c = ). Fig. shows some waeforms from an MUPC system with an ideal low-ass filter with the same load current examle as used in Fig. 9. The currents are now almost comletely distortion-free as shown in Fig. (b), and the rile in the real ower transmitted to the load has been eliminated as shown in Fig. (f) (a) load currents, i a, i b, i c (b) source currents, i Sa, i Sb, i Sc (c) source hase oltages, Sa, Sb, Sc (d) arallel inerter current for hase a, i PIa IV. CONCUSIONS In this aer, a real-time control scheme was deeloed for a comlete multileel uniersal ower conditioner system. Because of the different comensation objecties of the series inerter and arallel inerter, two distinct techniues were adated for use by the two conerters. The short time window samling techniue emloyed for use with the series inerter enabled regulation of the load oltage under unbalanced fault conditions with the assumtion that the source oltage is fairly sinusoidal. Simulation results showed that only for a seere fault would all of the leels in a MUPC be reuired for comensation. For the majority of the sags exerienced on an electrical system, only art of the oltage leels in a MUPC are used. Under these conditions, the rotation of leel usage as described in [] is an effectie means of balancing leel usage and in some cases increasing ossible switching freuency. The generalized -method was used for load current comensation by the arallel inerter. This method minimized the currents drawn from the utility by eliminating all of the reactie ower and the rile in the real ower transferred to the load. Because the arallel inerter of the MUPC injects currents by imressing a oltage across an inductance with resect to the load oltage, in most cases all of the oltage leels in the arallel inerter are used. In addition, the desired load oltage V nom should not be more than 7% of the dc link (e) arallel inerter hase oltage, PIa (f) load real ower, Fig. 8. System waeforms for current comensation with load current that has % 7th h armonic comonent and a dislacement ower factor of.7. oltage, so that the MUPC can still imress the roer oltage across the arallel inductance when the load oltage is at its maximum or minimum amlitude. REFERENCES [] H. Fujita, H. Akagi, The Unified Power Quality Conditioner: The Integration of Series- and Shunt-Actie Filters, IEEE Transactions on Power Electronics, ol., no., March 998,. 5-. [] S.-J. Jeon, G.-H. Cho, A Series-Parallel Comensated Uninterrutible Power Suly with Sinusoidal Inut Current and Sinusoidal Outut Voltage, IEEE Power Electronics Secialists Conference, 997, [] F. Kamran, T. G. Habetler, Combined Deadbeat Control of a Series- Parallel Conerter Combination Used as a Uniersal Power Filter, IEEE Transactions on Power Electronics, ol., no., Jan. 998, PESC 99, Charleston, South Carolina, June 7 July,

7 (a) load currents, i a, i b, i c (a) load currents, i a, i b, i c (b) source currents, i Sa, i Sb, i Sc (b) source currents, i Sa, i Sb, i Sc (c) source hase oltages, Sa, Sb, Sc (c) source hase oltages, Sa, Sb, Sc (d) arallel inerter current for hase a, i PIa (d) arallel inerter current for hase a, i Pia (e) arallel inerter hase oltage, PIa (e) arallel inerter hase oltage, PIa (f) load real ower, Fig. 9. System waeforms for current comensation under unbalanced current conditions (i b = - i a, i c = ) using the filter described by (9). (f) load real ower, Fig.. System waeforms for current comensation for unbalanced current conditions (i b = - i a, i c = ) using an ideal low-ass actie filter. [] B. Mwinyiwiwa, B.-T. Ooi, Z. Wolanski, Multimodular UPFC Oerated by Phase-Shifted Triangle Carrier SPWM Strategy, Conference Record IEEE Industry Alications Society Annual Meeting, 997, [5] Y. Chen, B. Mwinyiwiwa, Z. Wolanski, B.-T. Ooi, Unified Power Flow Controller (UPFC) Based on Choer Stabilized Multileel Conerter, IEEE Power Electronics Secialists Conference, 997,. -7. [6]. Gyugi, et. al., The Unified Power Flow Controller: A New Aroach to Power Transmission Control, IEEE Transactions on Power Deliery, ol., no., Aril 995, [7] J. S. ai, F. Z. Peng, Multileel Conerters A New Breed of Power Conerters, IEEE Transactions on Industry Alications, ol., no., May 996, [8] G. Joos,. Moran, Princiles of Actie Power Filters, IEEE IAS 98 Tutorial Course Notes, St. ouis, Missouri, October 998. [9] F. Z. Peng, G. W. Ott, Jr., D. J. Adams, Harmonic and Reactie Power Comensation Based on the Generalized Instantaneous Reactie Power Theory for Three-Phase Four-Wire Systems, IEEE Transactions on Power Electronics, ol., no. 6, No. 998, []. M. Tolbert, T. G. Habetler, Noel Multileel Inerter Carried-Based PWM Methods, Conference Record - IEEE Industry Alications Society Annual Meeting, 998,. -. []. M. Tolbert, F. Z. Peng, T. G. Habetler, Multileel Carrier-Based PWM Methods at ow Modulation Indices, IEEE Alied Power Electronics Conference, 999,. -9. []. Rossetto, P. Tenti, Ealuation of Instantaneous Power Terms in Multi-Phase Systems: Techniues and Alications to Power- Conditioning Euiment, ETEP, ol., No. 99, PESC 99, Charleston, South Carolina, June 7 July,