Robust Stability Analysis of Grid-Connected Converters Based on Parameter-Dependent Lyapunov Functions

• Published in: Journal of control, automation & electrical systems Vol. 28; no. 2; pp. 159 - 170
• Main Authors: Braga, Márcio F., Morais, Cecília F., Maccari, Luiz A., Tognetti, Eduardo S., Montagner, Vinicius F., Oliveira, Ricardo C. L. F., Peres, Pedro L. D.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2017; Springer Nature B.V
• Subjects: Closed loops; Continuous time systems; Control; Control and Systems Theory; Digital signal processors; Discrete time systems; Discretization; Electrical Engineering; Engineering; Feedback control; Inductance; Liapunov functions; Linear matrix inequalities; Mechatronics; Microprocessors; Numerical models; Parameters; Polynomials; Robotics; Robotics and Automation; Robustness; Series expansion; Stability analysis; Taylor series; Linear matrix inequalities; Grid-connected converters; Sampled-data systems; Parameter-dependent Lyapunov function; Robust stability analysis
• ISSN: 2195-3880; 2195-3899
• DOI: 10.1007/s40313-017-0301-7

This paper deals with the problem of robust stability analysis of grid-connected converters with LCL filters controlled through a digital signal processor and subject to uncertain grid inductance. To model the uncertain continuous-time plant and the digital control gain, a discretization procedure, described in terms of a Taylor series expansion, is employed to determine an accurate discrete-time model. Then, a linear matrix inequality-based condition is proposed to assess the robust stability of the polynomial discrete-time augmented system that includes the filter state variables, the states of resonant controllers and the delay from the digital control implementation. By means of a parameter-dependent Lyapunov function, the proposed strategy has as main advantage to provide theoretical certification of stability of the uncertain continuous-time closed-loop system, circumventing the main disadvantages of previous approaches that employ approximate discretized models, neglecting the errors. Numerical simulations illustrate the benefits of the discretization technique and experimental results validate the proposed approach.