Multilevel single phase isolated inverter with reduced number of switches

UPCommons Portal del coneixement obert de la UPC http://upcommons.upc.edu/e-prints Cristian Verdugo, Jose I. Candela, Mohamed A. Elsaharty, Pedro Rodríguez. (2018) Multilevel single phase isolated inverter with reduced number of switches. 7th International Conference on Renewable Energy Research and Applications : Paris, F rance , Oct. 14 - 17, 2018, 2018: IEEE, 2018. Pp. 1202-1208 Doi: 10.1109/ICRERA.2018.8566932. © 2018 IEEE. Es permet l'ús personal d'aquest material. S’ha de demanar permís a l’IEEE per a qualsevol altre ús, incloent la reimpressió/reedició amb fins publicitaris o promocionals, la creació de noves obres col·lectives per a la revenda o redistribució en servidors o llistes o la reutilització de parts d’aquest treball amb drets d'autor en altres treballs. Cristian Verdugo, Jose I. Candela, Mohamed A. Elsaharty, Pedro Rodríguez. (2018) Multilevel single phase isolated inverter with reduced number of switches. 7th International Conference on Renewable Energy Research and Applications : Paris, F rance , Oct. 14 - 17, 2018, 2018: IEEE, 2018. Pp. 1202-1208 Doi: 10.1109/ICRERA.2018.8566932. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Multilevel Single Phase Isolated Inverter with Reduced Number of Switches Cristian Verdugo, Jose I. Candela, Mohamed A. Elsaharty Department of Electrical Engineering Polytechnic University of Catalonia Terrassa, Spain Email: [email protected] Pedro Rodriguez Department of Electrical Engineering Loyola Andalucia University Seville, Spain Email: [email protected] Abstract—This paper proposes a cascaded single phase multilevel inverter using an off-the-shelf three-phase inverter and transformer. The concept is based on a cascaded connection of two inverter legs using a typical three phase inverter in such a way that the third leg is shared between the other two phases. The cascaded connection is achieved through an integrated series transformer with a typical three-phase transformer core. Utilization of a special transformer design has been previously proposed in the Custom Power Active Transformer. However, cascaded connection of inverter legs has not been previously investigated with such a concept. In this way, a three-leg inverter and a three-phase transformer are converted into an isolated multilevel single-phase inverter based on an unique configuration and modulation technique. Index Terms—Cascaded Transformer Multilevel Inverter, Custom Power Active Transformer, Multilevel Inverters. I. INTRODUCTION During the last years, multilevel inverters have become the most popular power electronics configurations, overtaking the classical two level inverter. Several applications have presented interest in utilizing such configurations in order to achieve high-power quality waveforms, lower switching losses and high-voltage capability [1]. The most remarkable multilevel topologies discussed in literature include: neutral point clamped, flying capacitors and cascaded H-bridge cells. The competitiveness between each of these approaches resides mainly in component count versus number of voltage levels. Moreover, other factors that affect the selection criteria involves utilization of separate dc sources, isolation and switching stress [2]. The insulation concern in application such as photovoltaic (PV) energy and battery storage systems has lead to the requirement of topologies with low or high frequency transformers. Converters with two conversion stages provide high frequency isolation through dc-dc converters [3]-[5], which are also able to decouple the dc from the ac side and control their variables independently. On the other hand, low frequency transformers are used in topologies with one conversion stage to provide galvanic isolation and step up the ac voltage. Other configurations such as cascaded connection of multiple inverters through multiple isolated transformers to create multilevel output voltage levels have been presented in [6]- [10]. However, in such a configurations, the output voltage levels as well as the number of bulky isolation transformers increase with the number of levels. Although the number of switches can be reduced as claimed in [9] by utilizing different topologies, the number of isolated transformers is always greater than one. Recently, there has been an interest in combining power electronics converters with coupled magnetic elements. Such topologies mainly benefit the system by providing isolation through injection transformers, reducing component count and achieving cascaded isolated connection. This has been presented in [11] by utilizing a cascade combining transformer. Such a configuration is promising in the sense of providing multilevel output voltages in an integrated structure. However, expansion to more output levels still requires several transformers. The concept presented in the Custom Power Active Transformer (CPAT) [12] shows the possibility of combining multiple series power converters in a single transformer core by utilizing multiple shunt magnetic paths. Based on this concept, cascaded connection of multiple inverters can be achieved in a single integrated transformer. Furthermore, in [13], this concept has been validated experimentally for three-phase applications. Thus, this concept can be utilized to achieve isolated cascaded connection of inverter legs that would provide a multilevel output voltage configuration. In this paper, a typical three-phase inverter is employed with a three-phase transformer to generate a five levels single-phase multilevel isolated inverter. This is achieved by employing two inverter legs for generating three output voltage levels and the third leg is used as a common return point between them. The inverter legs are connected to the three-phase transformer windings through two shunt magnetic paths. A modulation technique is proposed to generate a multilevel output voltage over the third shunt magnetic path. This magnetic path is connected to the grid where the injected current is controlled through a suitable controller. Finally, a high-quality output current is supplied to the grid due to the multilevel output voltage and the inherent filtering capability of the isolated transformer provided by the leakage inductances. Based on simulation results such concept is proven viable and promising for transformer integrated multilevel inverters. This paper is organized as follows: Section II describes the topology, its operation model and the modulation technique. Section III describes the integrated series transformer that would facilitate the cascaded connection of inverter legs. Section IV explains the control strategy to control the grid current. Section V presents the simulation results of the proposed configuration. Finally, Section VI discusses the conclusions and practical considerations of the proposed configuration. II. TOPOLOGY DESCRIPTION The multilevel single phase inverter proposed is based upon a two-level three phase inverter and a low frequency three phase transformer. The magnetic circuits theory states that each winding over a shunt core limb is equivalent to a series electrical circuit. This principle is presented in [12] where it has proved the capability of providing a cascaded connection with galvanic isolation through the magnetic circuit generated by the transformer core. Considering that all windings over the core limbs are isolated, it is possible to generate a single phase multilevel inverter with a typical three leg inverter, where the third leg operates as a common leg. In such a case, by using unipolar modulation [14], the output voltage vc1between aand nis able to provide three voltage levels, likewise vc2measured between band n. The proposed configuration shown in Fig.1, presents the three phase inverter connected to the first and second limb winding of the transformer, while the grid is connected to the third limb winding. Even though, an integrated series transformer has been used, for a sake of simplicity, a classical three phase transformer can be implemented as well. However, the connection between the three phase inverter and the classical transformer has to be performed through each winding limb of the primary or secondary side. All other winding not required are left in open circuit. This configuration provides several advantages over other topologies presented in literature such as reduced number of switches and transformer windings. Since the series connection is performed through the magnetic circuit, an inherent galvanic isolation between the ac and dc side is provided. This assists in overcoming the insulation limitation problem in dc sources such as photovoltaic panels and battery energy storage systems. In addition to this, the magnetic series connection between the voltages vc1and vc2increases the output voltage vcdespite using one dc source. This feature allows an ac voltage higher than the dc voltage level. Moreover, adjusting the number of turns in each limb and implementing a specific modulation technique, it is possible to increase the number of voltage levels at the grid side, thus reducing the current ripple injected to the grid. Since the voltage vc1and vc2rely on the switching states and the dc source, the output voltage vccan be mathematically modeled by: vc=vdc ·(s1−s3)   vc1 +vdc ·(s2−s3)   vc2 (1) In addition, the dynamic model on the grid side is given by: c v g L g i g v 1c v 2c v 1c i 2c i 1 s 2 s 3 s 1 s 2 s 3 s 1 F 1 F 2 F 3 F 1 ) 2 ) 3 ) dc v n a b Fig. 1: Proposed configuration vc=(LT+Lg)·dig dt +RT·ig+vg(2) Where LTrepresents the equivalent inductance of the transformer, which provides an inherent filter effect on the grid current, Lgis the line filter, RTis the resistive losses of the transformer, igis the grid current and vgis the grid voltage. A. Modulation Strategy The modulation technique used is based on the classical multilevel carrier modulation strategy presented in [15]. This strategy requires N−1carrier signals to generate Noutput voltage levels in the grid side. Since vc1and vc2are able to generate three voltage levels, the output voltage vcis able to generate until five voltage levels, unless different turn ratios are used in the limb windings. In such a case, higher voltage levels could be generated. Assuming that each limb winding has the same turn ratio, as mentioned, five voltage levels can be generated. Therefore, four carrier signal (two positive and two negative) displaced in vertical shift are required. Fig.2 shows the modulation technique proposed, where the carrier signals {tr1,tr2,tr3and tr4}are compared with the modulation index min order to provide the switching states of the inverter legs. S1controls the first leg, S2controls the second leg and S3 controls the third leg (common leg). The combination of these three signals provide nine possible combinations to generate the corresponding output voltage levels. Table.I presents the nine possible states, where the output voltage levels can be simplified to 2vdc,vdc,0,−vdc and −2vdc. It can be observed that 2vdc and −2vdc are generated through one state, while the others voltage levels are achieved through two states. This redundancy allows to decrease the switching stress in the semiconductor devices, since the conduction time can be reduced by alternating those states. The equivalent circuit for the corresponding switching states are shown in Fig.3. m 3r t 4r t 2r t 1r t 0 1 S 2 S 3 S c v dc v 2 dc v dc v 2 dc v Fig. 2: Modulation technique Following with the modulation analysis shown in Fig.2, the carrier signal tr1is responsible of providing the 2vdc level, while tr2and tr3determine vdc,0and−vdc. Finally, tr4 defines the −2vdc level. TABLE I: Switching states and voltages levels S1S2S3v1v2v3 110vdc vdc 2vdc 100vdc 0vdc 010 0 vdc vdc 000 0 0 0 111 0 0 0 011−vdc 0−vdc 101 0 −vdc −vdc 001−vdc −vdc −2vdc It is worth mentioning that the configuration proposed generates symmetrical voltage levels, despite using equal or different turns ratio between each limb. This characteristic is due to the fact that one dc source is connected to all legs, therefore, vc1and vc2change according to the same dc voltage level. In this way, voltage changes will not create asymmetrical levels. This is an advantage over other cascaded configurations, in which modules use independent dc sources. Therefore, slight voltage differences will affect the grid current and the power quality unless voltage balancing control strategies are used. III. INTEGRATED SERIES TRANSFORMER The electrical circuit of the integrated series transformer can be analyzed from the magnetic circuit’s law [16]. As mentioned, windings wound on a common core are equivalent to a parallel connection of voltage sources, while windings wound over parallel shunt cores are equivalent to a series connection of voltage sources. This concept can be studied by considering an ideal transformer, where the coupling factor is 1 and the leakage inductance is zero. From the Faraday’s law, a voltage vkis induced in Nturns of wires by changing the total magnetic flux Φipassing through the coils according to: vk=−Ni dΦi dt (3) Where the sub-index krepresents the inverter leg and ithe number of limb. In the Ampere’s law, the magneto-motive force (mmf) represented by Fiin Fig.1 across the reluctance in a close path can be represented by: dΦi dt =1  dFi dt (4) Moreover, the winding Fidepends on the winding effective current according to: Fi=Niik(5) The total mmf around a close path add up to zero. Therefore, assuming an ideal transformer with no leakage inductance, the relationship between the mmf in any limb of Fig.1 is equal to any of other two limbs. This can be expressed by: F1=F2=F3(6a) N1ic1=N2ic2=−N3ig(6b) In addition, according to the Ampere’s law, the sum of all magnetic fluxes in the three limbs of the transformer should be equal to zero. Φ1+Φ 2+Φ 3=0 (7) Replacing the magnetic flux equation presented above by the mmf expression of (6), the relationship between the induced voltage across each winding is mathematically expressed by: vc1 N1 +vc2 N2 −vc N3 =0 (8) Where N1,N2and N3represents the number of winding turns. The electric circuit of the integrated series transformer can be represented as a multiple series circuits as is shown in [12] and [13]. Each winding on a magnetic limb in Fig.4 can be considered as a voltage source vkwith a series leakage inductance Lk. Moreover, shunt non-linear inductances LL represent the limb magnetizing inductance. Such inductance can be considered significantly large and it has a minor impact on the cascaded circuit since transformer core limb reluctances are designed to be minimal to achieve maximum coupling between windings. Furthermore, the non-linear effect of magnetizing inductance can be observed in a transformer c v g i n 2c v 1c v 1c i 2c i a b c v g i n 2c v 1c v 1c i 2c i a b c v g i n 2c v 1c v 1c i 2c i a b c v g i n 2c v 1c v 1c i 2c i a b c v g i 2c v 1c v 1c i2c i c v g i n 2c v 1c v 1c i 2c i a b c v g i n 2c v 1c v 1c i 2c i a b c v g i n 2c v 1c v 1c i 2c i a b 0 c v 2 cdc vv cdc vv cdc vv 0 c v cdc vv  cdc vv  2 cdc vv  n a b Fig. 3: Switching states mangetizing current which is typically minimal. Another nonlinear element in the equivalent circuit is the yoke inductance LYwhich has similar characteristics to LL. As shown in [13], the magnetizing non-linear current required by such inductances to magnetize the core can be provided through the connected converters. Core leakage inductance L0represents the homopolar inductance of a typical three-phase transformer 1 L Y L L L Y L Y L Y L Y L Y L L L k L L L 2 L 0 L 1 Limb 2 Limb k Limb 1 v 2 v k v 1 Limb 2 Limb k Limb 0 L k L 2 L 1 L 1 v 2 v k v (a) (b) Fig. 4: Integrated series transformer. (a) Equivalent electric circuit, (b) Simplified electric circuit and it can be realized as the leakage flux from the core through the air. Such inductance can play a role in future design of the integrated series transformer since it is in series with the circuit and can affect the filtering capability of the transformer. Based on these assumptions and the mathematical analysis provided before, core magnetizing inductances can be considered negligible and the transformer circuit can be represented as in Fig.4(b) as cascaded series voltage sources with winding leakage inductances and a core leakage inductance. IV. CONTROL STRATEGY The grid current is regulated using the single-phase voltage oriented control (VOC), which has an inner control loop to regulate the grid current and an external control loop to regulate the dc voltage. In addition, a synchronization control strategy such as Phase Locked Loop (PLL) is required to provide the synchronous grid angle and ensure unitary power factor. This control strategy is presented in Fig.5, where the voltage difference between the reference and the measured voltage vdc is regulated using a PI controller which returns the power reference delivered to the grid. This reference is transformed into the grid current reference amplitude and then multiplied by a sinusoidal signal synchronized with the grid. In this way, the total power delivered by the inverter is mainly active, however different angles can be set to provide reactive power if necessary. The dc-link voltage measurement is filtered with a notch filter to eliminate the second harmonic ripple presented in the dc voltage which is caused by the grid rectification. This Modulation PR PLL PI g v g i Grid dc v * 2L-VSC f H * c v v' ref i sin g T dcF v dc v i s g L Fig. 5: Single-phase voltage oriented control scheme filter avoids the third harmonic component introduced in the grid current reference when the current reference amplitude is multiplied by the synchronization signal. The grid current reference is compared to the measured current igand its error is regulated through a PR controller since no rotating reference frame is used. This PR controller ensures perfect tracking with zero steady state error at the grid frequency. According to the dynamic model presented in (2), the output current control defines the dynamic response of the voltage difference between vcand vg. Therefore, the output voltage reference v∗ ccan be represented according to: v∗ c=Δv∗+vg(9) Where Δv∗is the voltage difference provided by the current control loop. Finally, the output voltage reference is used by the modulation technique to provide the switching stages required by the inverter to generate the proper voltage level at the ac side. V. SIMULATIONS RESULTS The effectiveness of the proposed configuration and its modulation technique are validated using Matlab-Simulink. In the case of study, a two level three-phase inverter is connected to a integrated series transformer such as presented in Fig.1. The inverter has a rated power of 3 kW and a grid voltage of 230/50 V/Hz. Due to the series connection provided by the magnetic circuit, the maximum output voltage level at the grid side is twice the dc voltage. The dc voltage and other parameters are listed in Table.II. In the following analysis all results are in per unit, where the base power SBis 3 kVA and the base voltage VBis 230 V. The converter voltage waveforms and switching states are studied in steady state operation, meanwhile grid waveforms such as the current, grid voltage and active power are studied in dynamic state operation. In Fig.6 the induced voltage in all limb winding terminals are shown. The middle point of the first and second leg are TABLE II: Simulation Parameters Parameters Symbol Value Nominal power Po3kW DC voltage vdc 300 V Grid voltage amplitude ˆvg320 V Grid frequency fs50 Hz DC-link capacitance Cdc 4700 μF Switching frequency fc2500 Hz Line inductance Lg1mH Transformer voltage VT400 V Inductance primary winding Lp0.9113 mH Inductance secondary winding Ls0.9113 mH Resistance primary winding Rp0.2518 Ω Resistance secondary winding Rs0.2518 Ω Magnetizing inductance Lm2H Base voltage VB220 V Base power SB3kW Base current IB18.77 A connected to two independent limb windings, meanwhile the third phase is used as a common leg between them. As a single-phase H-bridge inverter, the first and second winding limb generate three voltage levels. However, asymmetrical levels are observed due to the fact that the common leg does not allow another voltage pattern to generate the expected five voltage levels in the third limb winding. Fig.6(c) shows the five voltage levels of the output voltage vc. Due to the droop voltage introduced by the leakage inductances of the transformer, the maximum amplitude achieved is 1.8vdc. The previous results are obtained through the switching states shown in Fig.7. As presented in the modulation technique, a multilevel PWM modulation is implemented to gener- -1 0 1  -1 0 1  0.49 0.5 0.51 0.52 0.53 0.54 Time ( s ) -2 0 2  (a) (b) (c) Fig. 6: Voltage waveforms. (a) Converter voltage vc1, (b) Converter voltage vc2, (c) Output voltage vc 0 0.5 1  0 0.5 1  0.49 0.5 0.51 0.52 0.53 0.54 Time(s) 0 0.5 1  (a) (b) (c) Fig. 7: Switching states. (a) S1, (b) S2, (c) S3 ate the switching state in each inverter leg. Since S1depends on the carrier signals tr1and tr2, its state changes when the modulation index has positive values. On the other hand, negative values of the modulation index compared with tr3 and tr4affect the switching state S2. In case of S3, the carrier signals tr2and tr3set its pattern. To demonstrate the performance of the proposed topology connected to the grid, Fig.8 shows the dynamic response under an active power step. The step takes place at t=0.27 s, at that time, the grid current shown in Fig.8(b) increase up to its rated value. The small current ripple is due to the multilevel voltage generated in the grid side and the inherent filtering capability of the transformer leakage inductance. Furthermore, since a stiff grid is connected, the voltage shown in Fig.8(a) does not present any disturbance under the power step. VI. CONCLUSION This paper proposes a novel configuration for utilizing an off-the-shelf three-phase inverter and transformer to form an isolated multilevel single-phase inverter for grid connected applications. Based on the operation mode of an integrated series transformer, the proposed topology shows how the shunt magnetic limbs can be utilized to create a cascaded configuration by connecting two inverter legs to each terminal of two limb windings while the third leg is the common return point. A modulation technique has been proposed for this configuration to control the common leg as well as providing the five voltage levels without the requirement of auxiliary devices. Simulation analysis has shown the capability of the transformer connection to provide such voltage levels with the requirement of small passive filters, thanks to the inherent filtering capability of the transformer leakage inductances. The proposed cascaded configuration can be further expanded -1 0 1  -1 0 1  0.2 0.3 0.4 0.5 0.6 Time(s) 0 0.5 1  (a) (b) (c) Fig. 8: Grid waveforms. (a) Voltage, (b) Current, (c) Active power using multiple inverter legs and multiple shunt magnetic paths for several voltage steps and a higher quality output voltage. ACKNOWLEDGMENTS This work has been supported by European Commission under project FLEXITRANSTORE H2020-LCE-2016-2017SGS-774407 and by the Spanish Ministry of Science under project ENE2017-88889-C2-1-R. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the host institutions or funders. REFERENCES [1] Rodriguez, J., Lai, J.S., Peng, F.Z.: Multilevel inverters: survey of topologies, controls, and applications, IEEE Trans. Ind. Appl., 2002, 49, (4), pp. 724738 [2] S. Kouro et al., ”Recent Advances and Industrial Applications of Multilevel Converters,” in IEEE Transactions on Industrial Electronics, vol. 57, no. 8, pp. 2553-2580, Aug. 2010. [3] H. Krishnaswami and N. Mohan, ”Three-Port Series-Resonant DCDC Converter to Interface Renewable Energy Sources With Bidirectional Load and Energy Storage Ports,” in IEEE Transactions on Power Electronics, vol. 24, no. 10, pp. 2289-2297, Oct. 2009. [4] J. Echeverra, S. Kouro, M. Prez and H. Abu-rub, ”Multi-modular cascaded DC-DC converter for HVDC grid connection of large-scale photovoltaic power systems,” IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Vienna, 2013, pp. 6999-7005. [5] B. Zhao, Q. Song, W. Liu and Y. Sun, ”Overview of Dual-Active-Bridge Isolated Bidirectional DCDC Converter for High-Frequency-Link PowerConversion System,” in IEEE Transactions on Power Electronics, vol. 29, no. 8, pp. 4091-4106, Aug. 2014. [6] C. Verdugo, J. I. Candela, F. Blaabjerg and P. Rodriguez, ”Model and control of the isolated multi-modular converter,” IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society, Beijing, 2017, pp. 1286-1292. [7] S. G. Song, F. S. Kang and S. J. Park, ”Cascaded Multilevel Inverter Employing Three-Phase Transformers and Single DC Input,” in IEEE Transactions on Industrial Electronics, vol. 56, no. 6, pp. 2005-2014, June 2009. [8] A. K. Panda and Y. Suresh, ”Performance of cascaded multilevel inverter by employing single and three-phase transformers,” in IET Power Electronics, vol. 5, no. 9, pp. 1694-1705, November 2012. [9] M. R. Banaei, H. Khounjahan and E. Salary, ”Single-source cascaded transformers multilevel inverter with reduced number of switches,” in IET Power Electronics, vol. 5, no. 9, pp. 1748-1753, November 2012. [10] H. Khoun jahan, K. Zare and M. Abapour, ”Verification of a Low Component Nine-Level Cascaded-Transformer Multilevel Inverter in GridTied Mode,” in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 6, no. 1, pp. 429-440, March 2018. [11] A. A. Gandomi, S. Saeidabadi, S. H. Hosseini, E. Babaei and M. Sabahi, ”Transformer-based inverter with reduced number of switches for renewable energy applications,” in IET Power Electronics, vol. 8, no. 10, pp. 1875-1884, 10 2015. [12] M. A. Elsaharty, J. I. Candela and P. Rodriguez, ”Custom Power Active Transformer for Flexible Operation of Power Systems,” in IEEE Transactions on Power Electronics, vol. 33, no. 7, pp. 5773-5783, July 2018. [13] M. A. Elsaharty, J. Rocabert, I. Candela and P. Rodriguez GAE, ”Three-Phase Custom Power Active Transformer for Power Flow Control Applications,” in IEEE Transactions on Power Electronics [14] D. Grahame Holmes; Thomas A. Lipo, ”Appendix 3: ThreePhase and HalfCycle Symmetry Relationships,” in Pulse Width Modulation for Power Converters:Principles and Practice , 1, Wiley-IEEE Press, 2003, pp.744- [15] B. P. McGrath and D. G. Holmes, ”Multicarrier PWM strategies for multilevel inverters,” in IEEE Transactions on Industrial Electronics, vol. 49, no. 4, pp. 858-867, Aug. 2002. [16] Yim-Shu Lee, Leung-Pong Wong and D. K. -. Cheng, ”Simulation and design of integrated magnetics for power converters,” in IEEE Transactions on Magnetics, vol. 39, no. 2, pp. 1008-1018, March 2003.