Stability Boundary Analysis in Single-Phase Grid-Connected Inverters With PLL by LTP Theory

Stability analysis of power converters in ac networks is complex due to the nonlinear nature of the conversion systems. Whereas interactions of converters in dc networks can be studied by linearizing about the operating point, the extension of the same approach to ac systems poses serious challenges, especially for single-phase or unbalanced three-phase systems. A general method for stability analysis of power converters suitable for single-phase or unbalanced ac networks is presented in this paper, based on linear time periodic theory. A single-phase grid-connected inverter with phase-locked loop (PLL) is considered as case study. It is demonstrated that the stability boundaries can be precisely evaluated by the proposed method, despite the nonlinearity introduced by the PLL. Simulation and experimental results from a 10-kW laboratory prototype are provided to confirm the effectiveness of the proposed analysis.

[1]  Alessandro Costabeber,et al.  A generalised harmonic linearisation method for power converters input/output impedance calculation , 2016, 2016 18th European Conference on Power Electronics and Applications (EPE'16 ECCE Europe).

[2]  J.A. Melkebeek,et al.  Small-signal Laplace-domain analysis of uniformly-sampled pulse-width modulators , 2004, 2004 IEEE 35th Annual Power Electronics Specialists Conference (IEEE Cat. No.04CH37551).

[3]  L. Michels,et al.  Stability analysis of half-bridge rectifier employing LTP approach , 2012, IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society.

[4]  Math Bollen,et al.  Future work on harmonics - some expert opinions Part II - supraharmonics, standards and measurements , 2014, 2014 16th International Conference on Harmonics and Quality of Power (ICHQP).

[5]  Frede Blaabjerg,et al.  Harmonic instability analysis of single-phase grid connected converter using Harmonic State Space (HSS) modeling method , 2015, 2015 IEEE Energy Conversion Congress and Exposition (ECCE).

[6]  Rui Li,et al.  Influence of Delay on System Stability and Delay Optimization of Grid-Connected Inverters With LCL Filter , 2014, IEEE Transactions on Industrial Informatics.

[7]  Frede Blaabjerg,et al.  Harmonic interaction analysis in grid connected converter using Harmonic State Space (HSS) modeling , 2015, 2015 IEEE Applied Power Electronics Conference and Exposition (APEC).

[8]  A. R. Wood,et al.  Harmonic State-Space Model of a Controlled TCR , 2013, IEEE Transactions on Power Delivery.

[9]  Frede Blaabjerg,et al.  Analysis of phase-locked loop influence on the stability of single-phase grid-connected inverter , 2015, 2015 IEEE 6th International Symposium on Power Electronics for Distributed Generation Systems (PEDG).

[10]  Alessandro Costabeber,et al.  Stability analysis of single-phase grid-feeding inverters with PLL using Harmonic Linearisation and Linear Time Periodic (LTP) theory , 2016, 2016 IEEE 17th Workshop on Control and Modeling for Power Electronics (COMPEL).

[11]  Norman M. Wereley,et al.  Generalized Nyquist Stability Criterion for Linear Time Periodic Systems , 1990, 1990 American Control Conference.

[12]  Paolo Mattavelli,et al.  Digital Control in Power Electronics, 2nd Edition , 2015, Digital Control in Power Electronics, 2nd Edition.

[13]  Jian Sun.  Input impedance analysis of single-phase PFC converters , 2005, IEEE Transactions on Power Electronics.

[14]  E. Mollerstedt,et al.  Out of control because of harmonics-an analysis of the harmonic response of an inverter locomotive , 2000, IEEE Control Systems.

[15]  Patrizio Colaneri,et al.  Invariant representations of discrete-time periodic systems , 2000, Autom..

[16]  Bo Wen,et al.  Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters , 2016, IEEE Transactions on Power Electronics.

[17]  E. Mollerstedt,et al.  A harmonic transfer function model for a diode converter train , 2000, 2000 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.00CH37077).

[18]  Jian Sun,et al.  Modeling and analysis of DC-link harmonic instability in LCC HVDC systems , 2013, 2013 IEEE 14th Workshop on Control and Modeling for Power Electronics (COMPEL).

[19]  Leandro Michels,et al.  Modeling and analysis of single phase full-bridge PFC boost rectifier using the LTP approach , 2011, XI Brazilian Power Electronics Conference.

[20]  Math Bollen,et al.  Future work on harmonics - some expert opinions Part I - wind and solar power , 2014, 2014 16th International Conference on Harmonics and Quality of Power (ICHQP).

[21]  Leila Parsa,et al.  On impedance modeling of single-phase voltage source converters , 2016, 2016 IEEE Energy Conversion Congress and Exposition (ECCE).

[22]  Jian Sun,et al.  Impedance-Based Stability Criterion for Grid-Connected Inverters , 2011, IEEE Transactions on Power Electronics.

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

[24]  I. Postlethwaite,et al.  The generalized Nyquist stability criterion and multivariable root loci , 1977 .

[25]  Michael Sheng-Pu Hwang,et al.  A new modelling framework for power supply networks with converter based loads and generators - the Harmonic State-Space , 2012, 2012 IEEE International Conference on Power System Technology (POWERCON).

[26]  Bo Wen,et al.  Experimental Validation for Impedance-Based Small-Signal Stability Analysis of Single-Phase Interconnected Power Systems With Grid-Feeding Inverters , 2016, IEEE Journal of Emerging and Selected Topics in Power Electronics.

[27]  K.J. Karimi,et al.  Small-signal input impedance modeling of line-frequency rectifiers , 2008, IEEE Transactions on Aerospace and Electronic Systems.

[28]  Norman M. Wereley,et al.  Frequency response of linear time periodic systems , 1990, 29th IEEE Conference on Decision and Control.

[29]  C. Sidney Burrus,et al.  A unified analysis of multirate and periodically time-varying digital filters , 1975 .