Controle robusto H∞ por meio de LMIS aplicado a conversores conectados

Abstract

This work presents a robust current control for grid-connected converters subject to uncertain parameters in the grid impedance. Specifically, a voltage source inverter is connected by means of an LCL filter to a predominantly inductive electrical grid, belonging to a bounded interval. The grid injected current is controlled by means of a state feedback strategy capable to ensure, for all the set of grid uncertainties: i) a bound for the H1 norm of the closed-loop system; ii) the assignment of the closed-loop poles inside the unit circle; iii) the tracking of sinusoidal references and the rejection of disturbances with harmonics. Properties i) and ii) are ensured by means of an H1 control design condition based on linear matrix inqualities. Property iii) is ensured by the use of resonant controllers. The main contributions of this work are: a) to make an H1 state feedback control viable for this application by means of a limitation on the control gains and using slack variables in the design; b) to apply a genetic algorithm to tune the parameters of linear matrix inequalities of design. An important extension, which is also a contribution of this work, is to provide a design procedure for a robust state observer also based on linear matrix inequalities, which allows the implementation of the state feedback H1 control with a reduced number of sensors. Simulation results, in the time and frequency domains, indicate the capacity of the closed-loop system to track sinusoidal references and to reject harmonic disturbances from the grid, besides exhibiting good transient and steady state performances. Experimental results present good correspondence with the simulation results, confirming that the proposed design procedures are capable of providing grid currents in compliance with international standards, allowing the implementation of the control with a reduced number of sensors, being an alternative for the design of robust controllers and observers for grid-connected converters.