Singular perturbation stability analysis of three phase two-level power converters

In this paper, the stability of a three phase two-level rectifier is studied. This type of power converter has two operation modes, as rectifier or as inverter. The dynamics of the rectifier consist of a set of equations highly nonlinear. Through the definitions of the instantaneous active and reactive powers, the model of the system is sometimes expressed in terms of power instead of current. Since this new model takes the form of a standard singular perturbation model, the system can be studied in separate time scales. This work propose an analysis of the system in two-time-scale based on the decomposition of the model into reduced (slow) and boundary-layer (fast) models where both should satisfy some conditions to prove the stability of the equilibrium point of the whole system. This analysis will show the stability of the equilibrium of the system via Lyapunov's method and, consequently, will eliminate stiffness difficulties for the implementation of a future controller.

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

[2]  Hirofumi Akagi,et al.  Instantaneous Reactive Power Compensators Comprising Switching Devices without Energy Storage Components , 1984, IEEE Transactions on Industry Applications.

[3]  Tokuo Ohnishi,et al.  Three phase PWM converter/inverter by means of instantaneous active and reactive power control , 1991, Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation.

[4]  Sergio Vazquez,et al.  A Model-Based Direct Power Control for Three-Phase Power Converters , 2008, IEEE Transactions on Industrial Electronics.

[5]  G. Papanicolaou,et al.  Stability and Control of Stochastic Systems with Wide-band Noise Disturbances. I , 1978 .

[6]  Hassan K. Khalil,et al.  Multirate and composite control of two-time-scale discrete-time systems , 1985 .

[7]  Dragoslav D. Siljak,et al.  Multiparameter singular perturbations of linear systems with multiple time scales , 1983, Autom..

[8]  F. Gordillo,et al.  Observer-based Direct Power Control for three-level NPC rectifiers , 2009, 2009 35th Annual Conference of IEEE Industrial Electronics.

[9]  Ali Saberi,et al.  Quadratic-type Lyapunov functions for singularly perturbed systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[10]  P. Kokotovic,et al.  Singular perturbation method for reducing the model order in optimal control design , 1968 .

[11]  Leopoldo García Franquelo,et al.  Modeling Strategy for Back-to-Back Three-Level Converters Applied to High-Power Wind Turbines , 2006, IEEE Transactions on Industrial Electronics.

[12]  G. Blankenship,et al.  Singularly Perturbed Linear Stochastic Ordinary Differential Equations , 1979 .

[13]  K. W. Chang.  Singular Perturbations of a General Boundary Value Problem , 1972 .

[14]  J.W. Kolar,et al.  Virtual-Flux Direct Power Control for Mains Connected Three-Level NPC Inverter Systems , 2007, 2007 Power Conversion Conference - Nagoya.

[15]  Farhat Fnaiech,et al.  Linear and Nonlinear Control Techniques for a Three-Phase Three-Level NPC Boost Rectifier , 2006, IEEE Transactions on Industrial Electronics.

[16]  J. Fernando Silva,et al.  Optimal Predictive Control of Three-Phase NPC Multilevel Converter for Power Quality Applications , 2008, IEEE transactions on industrial electronics (1982. Print).

[17]  J. L. Rodriguez-Amenedo,et al.  Extended direct power control for multilevel inverters including DC link middle point voltage control , 2007 .

[18]  Sergio Busquets-Monge,et al.  Interfacing Renewable Energy Sources to the Utility Grid Using a Three-Level Inverter , 2006, IEEE Transactions on Industrial Electronics.

[19]  Jan T. Bialasiewicz,et al.  Power-Electronic Systems for the Grid Integration of Renewable Energy Sources: A Survey , 2006, IEEE Transactions on Industrial Electronics.

[20]  S. Aurtenechea,et al.  Predictive Direct Power Control of MV Grid-connected Three-level NPC Converters , 2007, 2007 IEEE International Symposium on Industrial Electronics.

[21]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[22]  J. Leyva-Ramos,et al.  Control of a three level converter used as a synchronous rectifier , 2004, 2004 IEEE 35th Annual Power Electronics Specialists Conference (IEEE Cat. No.04CH37551).