Floquet-Theory-Based Small-Signal Stability Analysis of Single-Phase Asymmetric Multilevel Inverters With SRF Voltage Control

This paper proposes a small-signal model and Floquet-theory-based method for analyzing small-signal stability of a single-phase asymmetric cascaded H-bridge multilevel inverter (ACHMI) operating in the stand-alone mode. The studied ACHMI system consists of the power stage and cascaded control loops, which includes the voltage loop in the synchronous reference frame (SRF), capacitor current feedback control, and hybrid modulation scheme. Due to the SRF voltage control, the derived small-signal model under linear and nonlinear load conditions are inherently periodically time-variant. Therefore, the Floquet theory is employed to analyze the stability regions of the dual-loop control parameters of the ACHMI. Furthermore, the loci and moduli of Floquet multipliers are calculated to accurately evaluate the respective effects of control parameters on the stability of the system. With the stability analysis based on the small-signal model and Floquet-theory-based method, an effective selection range of control parameters of the multilevel inverter can be obtained. Finally, the experimental results from a reduced-scale laboratory prototype ACHMI are presented to validate the theoretical analysis, and the effectiveness of proposed analysis method in high-power applications is verified by the simulation results from a 10-kV medium-voltage ACHMI.

[1]  Cassiano Rech,et al.  Hybrid Multilevel Converters: Unified Analysis and Design Considerations , 2007, IEEE Transactions on Industrial Electronics.

[2]  Josep M. Guerrero,et al.  Analysis, Design, and Experimental Verification of a Synchronous Reference Frame Voltage Control for Single-Phase Inverters , 2014, IEEE Transactions on Industrial Electronics.

[3]  C. E. Hammond,et al.  Efficient numerical treatment of periodic systems with application to stability problems. [in linear systems and structural dynamics] , 1977 .

[4]  Juan Dixon,et al.  Asymmetrical Multilevel Inverter for Traction Drives Using Only One DC Supply , 2010, IEEE Transactions on Vehicular Technology.

[5]  S. Mariethoz,et al.  Systematic Design of High-Performance Hybrid Cascaded Multilevel Inverters With Active Voltage Balance and Minimum Switching Losses , 2013, IEEE Transactions on Power Electronics.

[6]  L.G. Franquelo,et al.  The age of multilevel converters arrives , 2008, IEEE Industrial Electronics Magazine.

[7]  J. Pontt,et al.  Power Distribution in Hybrid Multi-cell Converter with Nearest Level Modulation , 2007, 2007 IEEE International Symposium on Industrial Electronics.

[8]  Bruno Putzeys,et al.  Small-Signal Analysis of Naturally-Sampled Single-Edge PWM Control Loops , 2018, IEEE Transactions on Power Electronics.

[9]  Leopoldo G. Franquelo,et al.  Multilevel Converters: Control and Modulation Techniques for Their Operation and Industrial Applications , 2017, Proceedings of the IEEE.

[10]  K. Y. Sze,et al.  Bifurcation and route-to-chaos analyses for Mathieu–Duffing oscillator by the incremental harmonic balance method , 2008 .

[11]  Krishna Shenai,et al.  Efficiency Evaluation of the Modular Multilevel Converter Based on Si and SiC Switching Devices for Medium/High-Voltage Applications , 2015, IEEE Transactions on Electron Devices.

[12]  D. Xu,et al.  An Extremely High Efficient Three-Level Active Neutral-Point-Clamped Converter Comprising SiC and Si Hybrid Power Stages , 2018, IEEE Transactions on Power Electronics.

[13]  Francesc Guinjoan,et al.  Energy-Balance Control of PV Cascaded Multilevel Grid-Connected Inverters Under Level-Shifted and Phase-Shifted PWMs , 2013, IEEE Transactions on Industrial Electronics.

[14]  Xiaotian Zhang,et al.  Study of Multisampled Multilevel Inverters to Improve Control Performance , 2012, IEEE Transactions on Power Electronics.

[15]  C. Rech,et al.  Impact of Hybrid Multilevel Modulation Strategies on Input and Output Harmonic Performances , 2007, IEEE Transactions on Power Electronics.

[16]  Hirofumi Akagi,et al.  Multilevel Converters: Fundamental Circuits and Systems , 2017, Proceedings of the IEEE.

[17]  Alessandro Costabeber,et al.  Stability Boundary Analysis in Single-Phase Grid-Connected Inverters With PLL by LTP Theory , 2018, IEEE Transactions on Power Electronics.

[18]  M. Takasaki,et al.  A Transformerless D-STATCOM Based on a Multivoltage Cascade Converter Requiring No DC Sources , 2012, IEEE Transactions on Power Electronics.

[19]  Ahmed Al-Durra,et al.  Simplified Small-Signal Model for Output Voltage Control of Asymmetric Cascaded H-Bridge Multilevel Inverter , 2018, IEEE Transactions on Power Electronics.

[20]  Jeffrey H. Lang,et al.  Analysis of Instability in Electrical Machines , 1986, IEEE Transactions on Industry Applications.

[21]  Yu. A. Kuznetsov,et al.  Applied nonlinear dynamics: Analytical, computational, and experimental methods , 1996 .

[22]  Fernando L. M. Antunes,et al.  Multilevel Inverter Topologies for Stand-Alone PV Systems , 2013, IEEE Transactions on Industrial Electronics.

[23]  Kenichiro Sano,et al.  A Transformerless 6.6-kV STATCOM Based on a Hybrid Cascade Multilevel Converter Using SiC Devices , 2018, IEEE Transactions on Power Electronics.

[24]  Josep M. Guerrero,et al.  Small-Signal Modeling of Digitally Controlled Grid-Connected Inverters With $LCL$ Filters , 2013, IEEE Transactions on Industrial Electronics.

[25]  Josep M. Guerrero,et al.  Stability Analysis for the Grid-Connected Single-Phase Asymmetrical Cascaded Multilevel Inverter With SRF-PI Current Control Under Weak Grid Conditions , 2019, IEEE Transactions on Power Electronics.

[26]  Subhashish Bhattacharya,et al.  Power Loss Analysis of Medium-Voltage Three-Phase Converters Using 15-kV/40-A SiC N-IGBT , 2016, IEEE Journal of Emerging and Selected Topics in Power Electronics.

[27]  C. Klumpner,et al.  Repetitive and Resonant Control for a Single-Phase Grid-Connected Hybrid Cascaded Multilevel Converter , 2013, IEEE Transactions on Power Electronics.

[28]  Ahmed Al-Durra,et al.  Multifunctional control strategy for asymmetrical cascaded H-Bridge Inverter in microgrid applications , 2015, 2015 IEEE Industry Applications Society Annual Meeting.

[29]  Baoming Ge,et al.  Medium-Voltage Multilevel Converters—State of the Art, Challenges, and Requirements in Industrial Applications , 2010, IEEE Transactions on Industrial Electronics.

[30]  Eisuke Masada,et al.  Harmonic analysis of a capacitor‐filtered rectifier with line impedance , 1989 .

[31]  E. Babaei,et al.  A Generalized Cascaded Multilevel Inverter Using Series Connection of Submultilevel Inverters , 2013, IEEE Transactions on Power Electronics.

[32]  Bin Wu,et al.  Model-Predictive Control of Grid-Tied Four-Level Diode-Clamped Inverters for High-Power Wind Energy Conversion Systems , 2014, IEEE Transactions on Power Electronics.

[33]  Josep M. Guerrero,et al.  Stability Analysis of Digital-Controlled Single-Phase Inverter With Synchronous Reference Frame Voltage Control , 2018, IEEE Transactions on Power Electronics.

[34]  Haitham Abu-Rub,et al.  Model Predictive Control of Multilevel Cascaded H-Bridge Inverters , 2010, IEEE Transactions on Industrial Electronics.

[35]  Jian Sun,et al.  Small-Signal Methods for AC Distributed Power Systems–A Review , 2009, IEEE Transactions on Power Electronics.

[36]  M. J. Samotyi,et al.  An investigation of harmonics attenuation and diversity among distributed single-phase power electronic loads , 1994, Proceedings of IEEE/PES Transmission and Distribution Conference.

[37]  Bin Wu,et al.  Control of a cascaded H-bridge multilevel converter for grid connection of photovoltaic systems , 2009, 2009 35th Annual Conference of IEEE Industrial Electronics.

[38]  Hebertt Sira-Ramírez,et al.  Generalized Proportional Integral Tracking Controller for a Single-Phase Multilevel Cascade Inverter: An FPGA Implementation , 2014, IEEE Transactions on Industrial Informatics.

[39]  A. Ajami,et al.  Symmetric and Asymmetric Design and Implementation of New Cascaded Multilevel Inverter Topology , 2014, IEEE Transactions on Power Electronics.

[40]  Jessika Eichel.  Practical Bifurcation And Stability Analysis From Equilibrium To Chaos , 2016 .

[41]  Jean-Claude Vannier,et al.  Flying capacitor multilevel inverters and DTC motor drive applications , 2002, IEEE Trans. Ind. Electron..

[42]  Samir Kouro,et al.  Circuit Topologies, Modeling, Control Schemes, and Applications of Modular Multilevel Converters , 2015, IEEE Transactions on Power Electronics.

[43]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[44]  Subhashish Bhattacharya,et al.  Solid-State Transformer and MV Grid Tie Applications Enabled by 15 kV SiC IGBTs and 10 kV SiC MOSFETs Based Multilevel Converters , 2015, IEEE Transactions on Industry Applications.